Excited States and Photochemistry of Organic Molecules

Excited States and Photochemistry of Organic Molecules Martin Klessinger WestBlische Wilhelms-Universitat Monster

Josef Michl University of Colorado

VCH

Martin Klessinaer Organisch-~hemischesInstitut WestfMische Wilhelms-UnivenitBt P48149 Monster Germany

Josef Michl Department of Chemistry and Biochemistry University of Colorado Boulder, CO 80309-02 15

Library of Congress CaWoging-in-Publiestion Data Klessinger. Martin. Excited states and photochemistry of organic molecules I Martin Klessinger, Josef Michl. p. cm. Includes index. ISBN 1-56081-588-4 1. Chemistry, Physical organic. 2. Photochemistry. 3. Excited . 11. Title. state chemistry. I. Michl, Josef, 1939QD476.K53 1994 547.1'354~20

92-46464 CIP

To our teachers WOLFGANG LUTTKE RUDOLF ZAHRADN~K

AND

8 1995 VCH Publishers, Inc. This work is subject to copyright. All rights reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Registered names, trademarks, etc., used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Printed in the United States of America ISBN 1-56081-588-4 VCH Publishers, Inc. Printing History: 10987654321 Published jointly by VCH Publishers, Inc. VCH Verlagsgesellschaft mbH 220 East 23rd Street P.O. Box 10 11 61 New York, New York 10010 D-69451 Weinheim Federal Republic of Germany

VCH Publishers (UK) Ltd. 8 Wellington Court Cambridge CBI IHZ United Kingdom

Preface

This graduate textbook is meant primarily for those interested in physical organic chemistry and in organic photochemistry. It is a significantly updated translation of Lichtabsorption und Photochemie organischer Molekule, published by VCH in 1989. It provides a qualitative description of electronic excitation in organic molecules and of the associated spectroscopy, photophysics, and photochemistry. The text is nonmathematical and only assumes the knowledge of basic organic chemistry and spectroscopy, and rudimentary knowledge of quantum chemistry, particularly molecular orbital theory. A suitable introduction to quantum chemistry for a Germanreading neophyte is Elektronenstruktur organischer Molekule, by Martin Klessinger, published by VCH in 1982 as a volume of the series, Physikalische Organische Chemie. The present textbook emphasizes the use of simple qualitative models for developing an intuitive feeling for the course of photophysical and photochemical processes in terms of potential energy hypersurfaces. Special attention is paid to recent developments, particularly to the role of conical intersections. In emphasizing the qualitative aspects of photochemical theory, the present text is complementary to the more mathematical specialized monograph by Josef Michl and Vlasta BonaCiC-Kouteckl, Electronic Aspects of Organic Photochemistry, published by Wiley in 1990.

Chapter 1 describes the basics of electronic spectroscopy at a level suitable for nonspecialists. Specialized topics such as the use of polarized light are mentioned only briefly and the reader is referred to the monograph by Josef Michl and Erik Thulstrup, Spectroscopy with Polarized Light, pub-

viii

PREFACE

lished by VCH in 1986 and reprinted as a paperback in 1995. Spectra of the most important classes of organic molecules are discussed in Chapter 2. A unified view of the electronic states of cyclic n-electron systems is based on the classic perimeter model, which is formulated in simple terms. Chapter 3 completes the discussion of spectroscopy by examining the interaction of circularly polarized light with chiral molecules (i.e., natural optical activity), and with molecules held in a magnetic field (i.e., magnetic optical activity). An understanding of the perimeter model for aromatics comes in very handy for the latter. Chapter 4 introduces the fundamental concepts needed for a discussion of photophysical and photochemical phenomena. Here, the section on biradicals and biradicaloids has been particularly expanded relative to the German original. The last three chapters deal with the physical and chemical transformations of excited states. The photophysical processes of radiative and radiationless deactivation, as well as energy and electron transfer, are treated in Chapter 5. A qualitative model for the description of photochemical reactions in condensed media is described in Chapter 6, and then used in Chapter 7 to examine numerous examples of phototransformations of organic molecules. All of these chapters incorporate the recent advances in the understanding of the role of conical intersections ("funnels") in singlet photochemical reactions. Worked examples are provided throughout the text, mostly from the recent literature, and these are meant to illustrate the practical application of theory. Although they can be skipped during a first reading of a chapter, it is strongly recommended that the reader work them through in full detail sooner or later. The textbook is meant to be self-contained, but provides numerous references to original literature at the end. Moreover, each chapter concludes with a list of additional recommended reading. We are grateful to several friends who offered helpful comments upon reading sections of the book: Professors E Bernardi, R. A. Caldwell, C. E. Doubleday, M. Olivucci, M. A. Robb, J. C. Scaiano, P. J. Wagner, M. C. Zerner, and the late G. L. Closs. The criticism of the German version provided by Professors W. Adam, G. Hohlneicher and W. Rettig was very h e l p ful and guided us in the preparation of the updated translation. We thank Dr. Edeline Wentrup-Byme for editing the translation of the German original prepared by one of us (M. K.), and to Ms. Ingrid Denker for a superb typing job and for drawing numerous chemical structures for the English version. It was a pleasure to work with Dr. Barbara Goldman of VCH and her editorial staff, and we appreciate very much their cooperation and willingness to follow our suggestions. Much of the work of one of us (J. M.) was done during the tenure of a BASF professorship at the University of Kaiserslautern; thanks are due to Professor H.-G. Kuball for his outstanding hospitality. We are much indebted to our respective families for patient support and understanding during what must have seemed to be interminable hours, days

PREFACE

and weeks spent with the manuscript. Last but not least, we wish to acknowledge the many years of generous support for our work in photochemistry that has been provided by the Deutsche Forschungsgemeinschaft and the U.S. National Science Foundation. Many fine books on organic excited states, photophysics, and photochemistry are already available. Ours attempts to offer a different perspective by placing primary emphasis on qualitative theoretical concepts in a way that we hope will be useful to students of physical organic chemistry. Miinster Boulder March 1995

Acknowledgments The authors wish to thank the following for permission to use their figures in this book. Academic Press, Orlando (USA) Figures 2.9, 2.10, 7.4, 7.5 and 7.53 Academic Press, London (UK) Figure 7.15 American Chemical Society, Washington (USA) Figures 2.11, 2.37, 3.7, 3.9, 3.10, 3.13, 3.17, 3.21, 4.8, 5.14, 5.17, 5.34, 5.39, 5.40, 6.1, 6.16, 6.17, 6.21, 6.27, 7.2, 7.18, 7.24, 7.34, 7.38, 7.39, 7.42 and 7.43 American Institut of Physics, New York (USA) Figures 2.6,2.17 and 2.18 The BenjaminlCummings Publishing Company, Menlo Park (USA) Figures 1.11, 5.4, 5.11, 7.19 and 7.57 Bunsengesellschafffur Physikalische Chemie, Darmstadt (G) Figures 1.15 and 1.17 Elsevier Science Publishers B.V., Amsterdam ( N L ) Figures 1.20, 5.32, 5.33, 7.3, 7.6, and 7.13 Gordon and Breach Science Publishers, Yverdon (CH) Figure 6.8 Hevetica Chimica Acra, Basel (CH) Figures 2.35 and 7.50 International Union of Pure and Applied Chemistry, Oxford (UK) Figures 2.30,3.15, 3.16, 5.24 and 5.25 Kluwer Academic Publishers, Dordrecht ( N L ) Figures 1.25,4.12,4.13,7.20 and 7.21 R. Oldenbourg Verlag GmbH, Msinchen (G) Figure 5.38 Pergamon Press, Oxford (UK) Figures 2.15,2.29,3.11,3.14, 3.18,3.19,4.27,4.28,5.15,5.16,5.30 and 5.36 Plenum Publishing Corp, New York (USA) Figure 5.10 Royal Society of Chemistry, Cambridge (UK) Figure 2.28

ACKNOWLEDGMENTS

The Royal Society, London ( U K ) Figure 1.14 Springer-Verlag, Heidelberg (G) Figures 1.23, 1.24, 6.3, 6.20 and 7.8 VCH Publishers, Inc., New York (USA) Figure 1.16 VCH Verlagsgesellschaft mbH, Weinheim (G) Figures 1.8, 2.7, 2.25, 2.27,2.34,2.38,2.42, 3.3, 3.6,4.21, 5.9,5.18, 5.19, 5.20,6.5,6.9, 6.13, 6.23, 6.25, 7.28,7.33 and 7.51 Weizmann Science Press of Israel, Jerusalem Figure 7.22 John Wiley & Sons, Znc., New York (USA) Figures 1.3, 2.2,2.3,2.45,4.5,4.6,4.10,4.11, 4.16,4.20,4.22,4.23,4.24, 6.19 and 6.28 John Wiley & Sons, Ltd., West Sussex ( U K ) Figures 7.12 and 7.14

Contents

Notation

xix

1. Spectroscopy in the Visible and UV Regions

1.1 Introduction and Theoretical Background 1 1.1.1 Electromagnetic Radiation 1 1.1.2 Light Absorption 5 1.2 MO Models of Electronic Excitation 9 9 1.2.1 Energy Levels and Molecular Spectra 1.2.2 MO Models for the Description of Light Absorption 13 1.2.3 One-Electron MO Models 16 1.2.4 Electronic Configurations and States 20 1.2.5 Notation Schemes for Electronic Transitions 1.3 Intensity and Band Shape 21 1.3.1 Intensity of Electronic Transitions 21 1.3.2 Selection Rules 27 34 1.3.3 The Franck-Condon Principle 36 1.3.4 Vibronically Induced Transitions 1.3.5 Polarization of Electronic Transitions 38 1.3.6 lko-Photon Absorption Spectroscopy 40 1.4 Properties of Molecules in Excited States 44 1.4.1 Excited-State Geometries 44 1.4.2 Dipole Moments of Excited-State Molecules 47 1.4.3 Acidity and Basicity of Molecules in Excited States

CONTENTS

xiv

1.5 Quantum Chemical Calculations of Electronic Excitation 1.5.1 Semiempirical Calculations of Excitation Energies 56 1.5.2 Computation of Transition Moments 1.5.3 Ab Initio Calculations of Electronic Absorption Spectra 58 60 Supplemental Reading

2. Absorption Spectra of Oqjanic Molecules

52 53

2.1 Linear Conjugated n Systems 63 2.1.1 Ethylene 64 65 2.1.2 Polyenes 71 2.2 Cyclic Conjugated n Systems 71 2.2.1 The Spectra of Aromatic Hydrocarbons 2.2.2 The Perimeter Model 76 2.2.3 The Generalization of the Perimeter Model for Systems with 81 4N + 2 n Electrons 2.2.4 Systems with Charged Perimeters 85 2.2.5 Applications of the PMO Method Within the Extended Perimeter Model 87 2.2.6 Polyacenes 92 96 2.2.7 Systems with a 4N n-Electron Perimeter 2.3 Radicals and Radical Ions of Alternant Hydrocarbons 101 2.4 Substituent Effects 104 2.4.1 Inductive Substituents and Heteroatoms 104 2.4.2 Mesomeric Substituents 109 118 2.5 Molecules with n+n* Transitions 2.5.1 Carbonyl Compounds 119 2.5.2 Nitrogen Heterocycles 122 2.6 Systems with CT Transitions 123 2.7 Steric Effects and Solvent Effects 126 2.7.1 Steric Effects 126 2.7.2 Solvent Effects 129 Supplemental Reading 135

3. Optical Activity

CONTENTS

3.3 Magnetic Circular Dichroism (MCD) 154 3.3.1 General Introduction 154 3.3.2 Theory 160 3.3.3 Cyclic n Systems with a (4N + 2)-Electron Perimeter 164 167 3.3.4 Cyclic n Systems with a 4N-Electron Perimeter 3.3.5 The Mirror-Image Theorem for Alternant jc Systems 170 3.3.6 Applications 171 Supplemental Reading 177

4. Potential Energy Surfaces: Barriers, Minima, and Funnels 179 4.1 Potential Energy Surfaces 179 4.1.1 Potential Energy Surfaces for Ground and Excited States 179 4.1.2 Funnels: True and Weakly Avoided Conical Intersections 182 4.1.3 Spectroscopic and Reactive Minima in Excited-State Surfaces 186 4.2 Correlation Diagrams 193 4.2.1 Orbital Symmetry Conservation 193 4.2.2 Intended and Natural Orbital Correlations 197 4.2.3 State Correlation Diagrams 200 4.3 Biradicals and Biradicaloids 205 4.3.1 A Simple Model for the Description of Biradicals 205 4.3.2 Perfect Biradicals 208 4.3.3 Biradicaloids 210 4.3.4 Intersystem Crossing in Biradicals and Biradicaloids 219 4.4 Pericyclic Funnels (Minima) 229 4.4.1 The Potential Energy Surfaces of Photochemical [2, + 2,] and x[2, + 2,l Processes 230 4.4.2 Spectroscopic Nature of the States Involved in Pericyclic Reactions 238 Supplemental Reading 239

139

3.1 Fundamentals 139 3.1.1 Circularly and Elliptically Polarized Light 139 3.1.2 Chiroptical Measurements 141 3.2 Natural Circular Dichroism (CD) 143 3.2.1 General Introduction 143 3.2.2 Theory 145 147 3.2.3 CD Spectra of Single Chromophore Systems 3.2.4 lko-Chromophore Systems 152

5. Photophysical Processes

243

5.1 Unimolecular Deactivation Processes 243 5.1.1 The Jablonski Diagram 243 5.1.2 The Rate of Unimolecular Processes 245 5.1.3 Quantum Yield and Efficiency 247 5.1.4 Kinetics of Unimolecular Photophysical Processes 5.1.5 State Diagrams 25 1

250

CONTENTS 5.2 Radiationless Deactivation 252 252 5.2.1 Internal Conversion 254 5.2.2 Intersystem Crossing 257 5.2.3 Theory of Radiationless Transitions 5.3 Emission 260 260 5.3.1 Fluorescence of Organic Molecules 5.3.2 Phosphorescence 266 272 5.3.3 Luminescence Polarization 276 5.4 Bimolecular Deactivation Processes 277 5.4.1 Quenching of Excited States 278 5.4.2 Excimers 281 5.4.3 Exciplexes 283 5.4.4 Electron-Transfer and Heavy-Atom Quenching 287 5.4.5 Electronic Energy Transfer 297 5.4.6 Kinetics of Bimolecular Photophysical Processes 301 5.5 Environmental Effects 5.5.1 Photophysical Processes in Gases and in Condensed Phases ' 301 302 5.5.2 Temperature Dependence of Photophysical Processes 303 5.5.3 Solvent Effects Supplemental Reading 306

6. Photochemical Reaction Models

309

6.1 A Qualitative Physical Model for Photochemical Reactions 309 in Solution 310 6.1.1 Electronic Excitation and Photophysical Processes 313 6.1.2 Reactions with and without Intermediates 6.1.3 "Hot" Reactions 320 322 6.1.4 Diabatic and Adiabatic Reactions 324 6.1.5 Photochemical Variables 332 6.2 Pericyclic Reactions 332 6.2.1 Tho Examples of Pericyclic Funnels 339 6.2.2 Minima at Tight and Loose Geometries 341 6.2.3 Exciplex Minima and Barriers 344 6.2.4 Normal and Abnormal Orbital Crossings 349 6.3 Nonconcerted Photoreactions 6.3.1 Potential Energy Surfaces for Nonconcerted Reactions 349 6.3.2 Salem Diagrams 355 356 6.3.3 Topicity Supplemental Reading 359

CONTENTS

7. Oqanic Photochemistry

361

7.1 Cis-trans Isomerization of Double Bonds 362 362 7.1.1 Mechanisms of cis-trans Isomerization 364 7.1.2 Olefins 7.1.3 Dienes and Trienes 366 369 7.1.4 Stilbene 372 7.1.5 Heteroatom, Substituent, and Solvent Effects 7.1.6 Azomethines 374 376 7.1.7 Azo Compounds 378 7.2 Photodissociations 7.2.1 cx Cleavage of Carbonyl Compounds (Norrish v p e I Reaction) 380 387 7.2.2 N, Elimination from Azo Compounds 392 7.2.3 Photofragmentation of Oligosilanes and Polysilanes 7.3 Hydrogen Abstraction Reactions 395 395 7.3.1 Photoreductions The Norrish v p e I1 Reaction 399 7.3.2 404 7.4 Cycloadditions 7.4.1 Photodimerization of Olefins 404 41 1 7.4.2 Regiochemistry of Cycloaddition Reactions 417 7.4.3 Cycloaddition Reactions of Aromatic Compounds 424 7.4.4 Photocycloadditions of the Carbonyl Group 7.4.5 Photocycloaddition Reactions of a,fiunsaturated Carbonyl 433 Compounds 434 7.5 Rearrangements 434 7.5.1 Electrocyclic Reactions 445 7.5.2 Sigmatropic Shifts 448 7.5.3 Photoisomerization of Benzene 7.5.4 Di-n-methane Rearrangement 453 7.5.5 Rearrangements of Unsaturated Carbonyl 460 Compounds 7.6 Miscellaneous Photoreactions 464 464 7.6.1 Electron-Transfer Reactions 7.6.2 Photosubstitutions 474 476 7.6.3 Photooxidations with Singlet Oxygen 7.6.4 Chemiluminescence 480 Supplemental Reading 485

Epilogue 491 References 493 Index 517

Notation

Operators One-electron Many-electron vectors Matrices Wave functions Electronic configuration Electronic state

Nuclear Vibronic Orbitals General Atomic Molecular Spin orbital Universal Constants c, = 2.9979 x loi0cm/s e = -1.6022 x 10-I9C

speed of light in vacuum electron charge

NOTATION

h = 6.626 x erg s Planck constant fc = h/21 = 1.0546 x erg s m, = 9.109 x g electron rest mass NL = 6.022 x mol-I Avogadro constant k = 1.3805 x 10-l6 erg K-I Boltzmann constant

Throughout this book, we use energy units common among U.S. chemists. Their relation to SI units is as follows: AG, AGO, A@ f;( J?

1 cal = 4.194 J 1 eV = 1.602 x 10-l9 J 1 erg = 10-l7 J Frequently Used Symbols (Section of first appearance or definition is given in parentheses) interaction matrix element between and r$ (2.2.3) perimeter MOs absorbance or optical density (1.1.2) A, B, and C term of the i-th transition of the MCD spectrum (3.3.1) vector potential (1.3.1) interaction matrix element between and #,+, (2.2.3) perimeter MOs @ dot-dot states of biradicals (4.3.1) magnetic flux density (1.3.1) magnetic field vector (I. I . I) excited states of (4N + 2)-electron perimeter (2.2.1) excited states of (4N 2)-electron perimeter (2.2.3) concentration (1.1.2) LCAO coefficient of A 0 X, in MO r$i (1.2.2) path length (I. 1.2) doubly excited state of the 3 x 3 model (4.4.1) and of 4N-electron perimeter (2.2.7) dipole strength of transition i (3.3.1) unit vector in direction U (1.3.1) energy (I. 1.2) electric field vector (I. I. I) electron affinity (1.2.3) excitation energy (1.2.3) oscillator strength (1.3.1)

,-,

fe?)(q) Avib

( j sQ)

As0 HSO AH, AH AHL, AHSL Ahom*o Z = Zoe-ad IC ISC IPi Jik

K Kik

K b ,

K;z

fluorescence (5.1.1) Fock matrix (I 3 . 1 ) reaction field (2.7.2) matrix element of the Fock operator between AOs x,, and x,, (I S.1) electron repulsion operator (1.2.3) ground state of the 3 x 3 model (4.4.1) and of 4N-electron perimeter (2.2.7) free energy (1.4.3) one-electron operator of kinetic and potential energy (1.2.3) Hamiltonian (1.2.3) matrix element of the Hamiltonian between configurational functions @, and @, (1.2.4) electronic Hamiltonian (1.2.1) nuclear Hamiltonian (1.2.1) spin-orbit coupling operator (1.3.2) spin-orbit coupling vector (4.3.4) enthalpy (I .4.3) parameters for MCD spectra of systems derived from 4N-electron perimeter (3.3.4) energy splitting of the pair of highest occupied perimeter MOs (2.2.3) intensity (1.1.2) internal conversion (5.1.1) intersystem crossing (5.1.1) ionization potential (I .2.3) Coulomb integral (I .2.3) rate constant of process j (5.1.2) wave vector (I .3.1) exchange integral (1.2.3) electron repulsion integrals in biradicals and biradicaloids (4.3.2) angular momentum quantum number (1.3.2) orbital angular momentum operator, , (1.3.2) origin of coordinates at atom u lowest excited states of (4N + 2)electron perimeter (2.2.1) lowest excited states of (4N + 2)electron perimeter (2.2.3) energy splitting of the pair of lowest unoccupied perimeter MOs (2.2.3)

xxii

NOTATION

mass of particle j (1.3.1) one-electron electric dipole operator (1-3.1) one-electron magnetic dipole operator (3.2.2) electric dipole operator (1.1.2) magnetic dipole operator (1.1.2) z component of total spin (4.2.2)

so, SI, SZ, Sbf ST t

T T Tl,T2, TS

u, v, x, vibrionic transition moment (1.3.1) electronic transition moment (1.3.1) configurational electronic transition moment (1.3.1) number of electrons (1.1.2) number of atoms in the perimeter (2.2.2) refractive index (1.1.1) circular birefringence (3.1.2) occupation number of MO (1.2.3) number of n electrons in the perimeter is 4N + 2 or 4N (2.2.1) excited states of 4N-electron perimeter (2.2.7) phosphorescence (5.1.1) degree of polarization (5.3.3) linear momentum operator of particle j (1.3.1) charge of particle j (1-3.1) electronic coordinates (1-2.1) electric quadrupole operator (1.1.2) nuclear coordinates (1-2.1) quencher (5.4.1) position vector of electron j (1.3.1) vector pointing from nucleus p to electron j (1.3.1) degree of anisotropy (5.3.3) position vector of nucleus p or A (1.3.1) rotational strength (3.2.2) interaction matrix element between MOs +, and of a 4N-electron perimeter (2.2.7) spin angular momentum operator (1.3.2) singly excited state of the 3 x 3 model (4.4.1) and of 4N-electron perimeter (2.2.7)

= E (t)

- .-

singlet states (1.4.3) two-photon transition tensor (1.3.6) singlet-triplet intersystem crossing (5.1.2) time (1.1.1) temperature (1.1.2) triplet state of the 3 x 3 model (4.4.1) triplet states (1.4.3) triplet-singlet intersystem crossing (5.1.2) real (4N + 2)-electron perimeter configurations (2.2.3) transition moment (1.1.2) one-center valence-state energy (1.5.1) gradient difference and nonadiabatic coupling vectors that define the branching space at a conical intersection (4.1.2) partition function (1.1.2) charge of nucleus A or L,A (1.3.1) hole-pair states of biradical(4.3.1) rotation angle, molar rotation (3.1.2) absorption coefficient (1.1.2) perturbation of Coulomb integral a, (2.4.1) phase factor in complex interaction matrix element a or b (2.2.3) resonance integral (1.5.1) perturbation of resonance integral (2.4.1) covalent perturbation in hom*osymmetric and nonsymmetric biradicaloids (4.3.3) Coulomb repulsion integral (1.5.1) polarization perturbation in heterosymmetric and nonsymmetric biradicaloids (4.3.3) polarization perturbation in critically heterosymmetric biradicaloids (4.3.3) two-photon absorption cross sections (1.3.6) decadic molar extinction coefficient (1.1.2) circular dichroism (3.1.2) orbital energy of MO +i(1-2.3) atomic spin-orbit coupling parameter (4.3.4) efficiency (5.1.3) ellipticity, molar ellipticity (3.1.2) triplet spin functions (4.3.4)

CHAPTER

NOTATION

reorganization energy (5.4.4) wavelength (1.1.1) dipole moment vector (2.7.2) frequency (1.1.1) wave number (1.1.1) density of states (5.2.3) phase factor in complex interaction matrix element of 4N-electron perimeter (2.2.7) singlet spin function (4.3.4) lifetime (5.1.2) molecular orbital (MO) (1.2.2) highest occupied real perimeter MOs (2.2.5) lowest unoccupied real perimeter MOs (2.2.5) paired MOs of alternant hydrocarbon (1.2.4) complex perimeter MOs (2.2.2) ground configuration (1.2.2) singly excited configuration (1.2.2) configurational wave function (1.2.2) quantum yield (5.1.3) character of irreducible representation (1.2.4) atomic orbital ( A O ) (1.2.2) vibrational wave function (1.2.1) Franck-Condon factor (1.3.3) spin orbital (1.2.2) electronic wave function (1.2.1) wave functions of ground and final state (1.2.2) CI (configuration interaction) wave function (1.2.2) Born-Oppenheimer wave function (1.2.1) polarization degree for two-photon absorption (1.3.6)

Spectroscopy in the Visible and W Regions

I. 1 Introduction and Theoretical Background 1.1.1 Electromagnetic Radiation Ultraviolet ( U V ) and visible (VIS) light constitute a small region of the electromagnetic spectrum which also comprises infrared (IR) radiation, radio waves, X-rays, etc. A diagrammatic representation of the electromagnetic spectrum is shown in Figure 1.1. Electromagnetic radiation can be envisaged in terms of an oscillating electric field and an oscillating magnetic field that are perpendicular to each other and to the direction of propagation. The case of linearly polarized light where the planes of both the electric and the magnetic field are fixed is shown in Figure 1.2. In vacuum, the electric vector of a linearly polarized electromagnetic wave at any point in space is given by E(r) = Eo sin (

+ 6~)

(1.1)

where E, is a constant vector in a plane perpendicular to x, the direction of propagation of the light; (2.rrvr + 8) is the phase at time t ; 8 is the phase at time r = 0; and v is the frequency in Hz. The direction of E is referred to as the polarization direction of the light. As a function of position along the x axis, the electric vector E(x) and the magnetic vector B(x) are given by E(x,r) = Eo sin [27~(vt- xIA) B(x,r) = Bo sin [21r(vt - xIA)

+ 61 + 61

106

lo8

101°

SPECTROSCOPY IN THE VISIBLE AND UV REGIONS 1012

10"

id"0l8

lo2'

1 0 ~ ~ ~ 2

200

1eOnm

INTRODUCTION AND THEORETICAL BACKGROUND

1.1

700 600 500

LOO

300

Figure 1.1. Frequencies v and wavelengths I for various regions of the electromagnetic spectrum. In the UVNIS region, which is of special interest in this book, nm is the commonly used unit of wavelength. Wave numbers t, which are proportional

to frequencies, are expressed in cm-I.

B, is a constant vector perpendicular to Eo (Figure 1.2).

is the wavelength, and c is the speed of light, whereas 8 is the phase for 0, t = 0. In vacuum, c = c0 = 2.9979 x 10iOcmls, and in a medium of refractive index n, c = c,ln. If light passes from one medium to another, the frequency v remains constant, whereas the wavelength A changes according to Equation (1.3) with the speed of light. If the polarization directions of two linearly polarized light waves, 1 and 2, with identical amplitudes Il#)1 = frequencies v, = v,, and directions of propagation x, are mutually orthogonal, and if the phases of the two waves are identical, 8, = 8, = 0, their superposition will produce a new linearly polarized wave

x =

)a)1,

E(x) =

(a) + Ef)) sin [21~(vt- xIA) + 01

(1.4)

The amplitude of the new wave is fl times larger than that of either of the original waves, and its direction of polarization forms an angle of 45" with the polarization directions of either of the two waves. If the phases of wave I and wave 2 differ by 1~12,which according to Equation (1.2) is equivalent to a difference in optical path lengths of x = U4, the superposition of the two waves results in a circularly polarized wave sin [2m(vt - x/A) + 81 + a'cos [2m(vt - xlA) + 81

E(x) =

(1.5)

that has a constant amplitude 1E:'l = I@'[. The direction of its electric vector at a given point xo rotates with frequency v about the x axis. The general result of a superposition of linearly polarized waves with phases that do not

Figure 1.2. The variation of the electric field (E) and the magnetic flux (B) of linearly polarized light of wavelength 1a) in space (at time t = t,) and b) in time (at point x = x,). The vectors E and B and the wave vector K, whose direction coincides with the propagation direction x, are mutually orthogonal.

differ by an integral multiple of d 2 is a wave of elliptical polarization. (Cf. Chapter 3.) In changing from the classical to the quantum mechanical description of light, one of the principal results is that light is emitted or absorbed in discrete quanta known as photons, with an energy of

hv = hc5

where h is Planck's constant, h number defined as

6.626 x

(1.6) erg s, and 5 is the wave

The common wave-number unit is cm-I. Since 5 is linearly related to the energy according to Equation (1.6), in spectroscopy "energies" are frequently expressed in wave numbers; that is, Elhc is used instead of E. Table I. 1 shows the numerical relationship between wavelengths, wave numbers, and energies for the visible and the adjacent regions of the spectrum; the values in the last columns have been converted into molar energies by multiplication with Avogadro's number. (Cf. Example l. l .)

SPECTROSCOW IN THE VISIBLE AND UV REGIONS

VIS

A (nm)

i (cm - I)

kJlmol

kcallmol

200 250 300 350 400 450 500 550 600 650 700 800 1, m 5,000

50,000 40,000 33,333 28,571 25,000 22,222 20,000 18,182 16,666 15,385 14,826 12,500 10,000 2,ooo

6.20 4.% 4.13 3.54 3.10 2.76 2.48 2.25 2.07 1.91 1.77 1.55 1.24 0.25

598 479 399 342 299 266 239 218 199 184 171 150 120 24

142.9 114.3 95.2 81.6 71.4 63.5 57.1 51.9 47.6 44.0 40.8 35.7 28.6 5.7

' Conversion factors: 1 e V

8,066 cm-I

INTRODUCTION AND THEORETICAL BACKGROUND

an electromagnetic wave the intensity is proportional to the squared amplitude of the electric field vector (or the magnetic field vector).

Table 1.1 Conversion of Wavelength A, Wave Number 5, and Energy AE? Spectral Region

1.1

1.1.2 Light Absorption Light is absorbed if the molecule accepts energy from the electromagnetic field, and spontaneous or stimulated emission occurs if it provides energy to the field. The latter is the basis of laser action but will not be treated here. A molecule in a state i of energy Eican change into a state k of energy E, by absorption of light of frequency v, if the relation is fulfilled. A photon can be absorbed only if its energy corresponds to the difference in energy between two stationary states of ihe molecule. Absorption occurs only if the light can interact with a transient molecular charge or current distribution characterized by the quantity

%.485 kJlmol = 23.045 kcallmol; 1 kcallmol = 4.1868

Wlmol.

Example 1.1:

From Equation (1.6) which yields AE in erg if 5 is given in cm-I; after multiplication with Avogadro's number N, = 6.022 x 10U mol-' and taking into account the appropriate conversion factor (1.4383 x loi3),the molar energy in kcaVmol is found to be AE = 0.0029 5

An absorption at 50 cm- I , 1,500cm-I, or 33,333 cm- therefore corresponds to an energy gain of 0.14 kcaUmol, 4.3 kcdmol, and 95 kcdmol, respectively. The average bond energy of a C--C bond is roughly 85 kcaUmo1; that is, the energies corresponding to the absorption of visible light are of the same order of magnitude as bond energies. They transfer the molecule from the ground state into an electronically excited state. On the other hand, the amount of energy corresponding to an absorption in the IR region is considerably smaller and is in the range of energy required to excite molecular vibrations. The intensity of radiation is measured in erg s-' cm-* as the energy of radiation falling on unit area of the system in unit time; this energy is related directly through Planck's constant to the number of quanta and their associated frequency. On the other hand, in the classical description of light as

referred to as the transition moment between molecular states i and k, described by the wave functions Y iand qk,respectively.* 0 is an operator that corresponds either to the electric dipole moment (&), to the magnetic dipole moment or to the electric quadrupole mo(4). Accordingly electric dipole transitions, magnetic dipole transiment tions, and electric quadrupole transitions are distinguished. (Higher-order transitions can normally be ignored.) For an allowed transition in the visible region the transition moments of the electric and the magnetic dipole operator and of the electric quadrupole operator are roughly in the ratio lo7 : 102 : 1. It is therefore quite common to confine the discussion to electric dipole transitions. However, magnetic dipole transition moments cannot be neglected in magnetic resonance spectroscopy and in the treatment of optical activity. (Cf. Chapter 3.) Since the electric dipole moment operator is a vector operator, the electric dipole transition moment will also be a vector quantity. The probability of an electric dipole transition is given by the square of the scalar product between the transition moment vector in the molecule and the electric field vector of the light, and is therefore proportional to the squared cosine of the angle between these two vectors. Thus, an orientational dependence results for the absorption and emission of linearly polarized light. The orientation of the transition moment with respect to the molecular system of axes is

(a,

* The bracket notation introduced by Dirac for the matrix element

IF (1, . . ., n)0(1. . . ., n)Y,(l, . . .. n)dr, . . . dr, of the operator 19is advantageous, particularly if the integration is not carried out explicitly.

SPEC 1 KOSCOI'L I11 I lit \. IbIULlr. AND UV KCGIOIVb

frequently called the absolute polarization direction, whereas the relative polarization direction of two distinct transitions refers to the angle between their two transition moments. Samples used in spectroscopic measurements usually consist of a very large number of molecules. According to Bolrzmann's law, in thermal equilibrium at temperature T the number Nj of molecules in a state of energy Ej is given by (1.10) Nj = (N,lZ) e -EjlkT where No is the total number of molecules, k is the Boltzmann constant, and Z is the partition function, that is, the sum over the Boltzmann factors e-4IhTfor a11 possible quantum states of the molecule. The average number Njof molecules in a state of energy Ej is thus larger than the number N , of molecules in a state of higher energy El. Since absorption and stimulated emission are intrinsically equally probable, more molecules are raised from the lower state j into the higher state 1 than the reverse. This perturbs the thermal equilibrium distribution, but due to interactions with the environment, transitions to other energy states are possible and the equilibrium distribution can be restored. For excitations in the UVIVIS region the return to equilibrium, which is referred to as relaxation, is so fast that at ordinary light intensities the thermal equilibrium in the irradiated sample is hardly perturbed at all. Saturation, which corresponds to identical populations in the ground and the excited state and inhibits further absorption of energy, a well-known phenomenon in NMR spectroscopy, is therefore hard to achieve in optical spectroscopy except temporarily in the case of laser excitation. Example 1.2: From Equation (1.10)the ratio N,IN, of the number of molecules in two states of energy E, and Ej, respectively, is given by

INTRODUCTION AND THEORETICAL BACKGROUND

I. 1

and and

In the case of molecular vibrations with excitation energies of about 50 cm-I, exemplified by restricted rotations about single bonds, nearly one-half of all molecules reside in the energetically higher state. For excitation energies of 1,500 cm-I, which are typical for a stretching vibration, there are less than 0.1% of the molecules in the upper state. Finally, for electronically excited states the population at room temperature is so small that it can be ignored, and practically all the molecules are in the ground state.

Emission in the UVIVIS region is observed at room temperature only if the equilibrium of the molecular system with its surroundings has been disturbed by external effects, for example, by radiation, heat, colli4ion with an electron, or chemical reaction. When a collimated monochromatic light beam of intensity I passes through an absorbing hom*ogeneous isotropic sample, it is attenuated. The loss of intensity d l is proportional to the incident intensity I and to the thickness dx of the absorbing material, that is, d l = - aldx where a = a(S)is an absorption coefficient characteristic of the absorbing medium and dependent on the wave number of the light. It is proportional to the difference ( N j - Nl) of the number of molecules in the ground state and the excited state. With I = I, for x = 0, integration over the thickness d of the sample yields

If wave numbers are used the energies have to be replaced by $ = Eilhc. At room temperature, given k = 1.3805 x 10-l6 erg K- and the conversion factor 1 erglhc = 5.034 x 10" cm-I, we have kT 200 cm-I. Thus, for an energy difference $ - E, = 50 cm-I .J

N,IN, = e--

0.78

With N, + N , = loo%, we obtain Nj = 56% and N,= 44%. In the same way, for El - = 1,500 cm- and for El - I?, = 33,333 cm- I,

, c is the concentration of the absorbing species, Setting a = 2.303 ~ cwhere yields the Lambert-Beer law:

The dimensionless quantity A is called the absorbance or optical density of the sample. The concentration c is traditionally given in mol1L and the

SPECTROSCOPY IN THE VISIBLE AND UV KEtiIONb

thickness of the sample din cm. E = dG)is then the decadic molar extinction coefficient; its unit is L mol-I cm-1 and is understood but not explicitly stated on spectra. In general the Lambert-Beer law is obeyed quite well. Exceptions can be attributed, for example, to interactions between the solute molecules (changes of the composition of the system with concentration), to perturbations of the thermal equilibrium by very intense radiation, or to the population of a very long-lived state.

The example of the UV spectrum of phenanthrene (1)in Figure 1.3 shows that the molar extinction coefficient E = t(A) or E = dt),expressed as a function of wavelength or wave numbers varies over several orders of magnitude. It is therefore common to sacrifice some detail and to use a logarithmic scale or to plot log E versus P, as shown in Figure 1.3~.Spectra are usually measured down to 200 nm. (Most often solutions of a concentration mol/L are used in cells of 1-cm thickness.) The region of of about shorter wavelengths, which is sometimes referred to as the far-UV region, is experimentally less accessible, because solvents and even air tend to absorb strongly. The term vacuum UV is applied to the region below 180 nm since an evacuated spectrometer is required.

1.2 MO Models of Electronic Excitation 1.2.1 Energy Levels and Molecular Spectra 6-10'

Absorption spectra of atoms consist of sharp lines, whereas absorption spectra of molecules show broad bands in the UVNIS region. These may exhibit some vibrational structure, particularly in the case of rigid molecules (Figure 1.4b). Rotational fine structure can be observed only with very high resolution in the gas phase and will not be considered here. (See, however, Section 1.3.6.) Polyatomic molecules possessing a large number of normal vibrational modes of varying frequencies have very closely spaced energy levels. As a result of line broadening due to the inhom*ogeneity of the interactions

&.lo'

2.10'

loC, 200

280 A lnml

320

360

Figure 1.3. The absorption spectrum of phenanthrene in various presentations: a) absorbance A versus A, b) E versus A, and c) log E versus B (by permission from Jaffe and Orchin, 1%2).

Figure 1.4. Atomic and molecular spectra: a) sharp-line absorption typical for isolated atoms in the gas phase, b) absorption band with vibrational structure typical for small or rigid molecules. and c) structureless broad absorption typical for large molecules in solution (adapted from Turro, 1978).

MO MODELS OF ELECTRONIC EXCITATION

1.2

between solute molecules and solvent, to hindered rotations, and to the short lifetimes of the higher excited states, the vibrational structure may be either unresolved or only partly resolved, so that in general only broad unstructured bands can be observed in condensed phase (Figure 1.4~). The vibrational structure may be explained as follows: For each state of a molecule there is a wave function that depends on time, as well as on the internal space and spin coordinates of all electrons and all nuclei, assuming that the overall translational and rotational motions of the molecule have been separated from internal motion. A set of stationary states exists whose observable properties, such as energy, charge density, etc., do not change in time. These states may be described by the time-independent part of their wave functions alone. Their wave functions are the solutions of the timeindependent Schrodinger equation and depend only on the internal coordinates q = q , , q2, . . . of all electrons and the internal coordinates Q = Q , . Q,, . . . of all nuclei. Within the Born-Oppenheimer approximation (cf. McWeeny, 1989: Section 1. I ) the total wave function qTof a stationary state is written as

where j characterizes the electronic state and u the vibrational sublevel of that state. (Cf. Figure 1.5.) The electronic wave function *Y(q) is an eigenfunction of the electronic Hamiltonian kf$(q) defined for a particular geom-

etry Q. There is a different electronic wave function qf(q) with a different energy EP for a given Cj-th) state for each value of the parameter Q. The vibrational wave functions x{,(Q) are eigenfunctions of the vibrational Hamiltonian e i b ( j , ~ ) ,which is defined for a particular electronic state j as an operator containing q,the electronic plus nuclear repulsion energy of state j, as the potential energy of the nuclear motions. For every electronic state j, there is a different potential energy and therefore a different vibrational Hamiltonian A,,,(~,Q). Due to the product form of the total wave function in Equation (1.12) the energy of a stationary state can be written as As a result, each electronic state of a molecule with energy Eel)= EP carries a manifold of vibrational sublevels, and the energy of an electronic excitation may be separated into an electronic component and a vibrational component (cf. Figure 1.5) according to Similarly, a rotational component ErO') and a translational component ,#jYtmnS) are obtained when all 3N displacement coordinates of the N nuclei are used rather than the internal coordinates, which are obtained by separating the motion of center-of-mass and the rotational motions.

1.2.2 MO Models for the Description of Light Absorption The determination of state energies and transition moments requires the knowledge of the wave functions *f(q) and of the ground state 0 and the excited (final) state f. In general, the exact wave functions are not known, but nowadays approximate semiempirical or even ab initio LCAOMO-SCF-CI wave functions are fairly easily available for most molecules. These wave functions are obtained starting with atomic orbitals (AOs) x,,, from which molecular orbitals (MOs) @i are formed as linear combinations by application of the self-consistent field (SCF) method: @i

Zwp C

Figure 1.5. Schematic representation of potential energy curves and vibrational levels of a molecule. (For reasons of clarity rotational sublevels are not shown.)

(1.13)

Multiplying each MO with one of the spin functions a and /3 yields the spin orbitals k W = @,b?a(ll = q+ and vhl = @,d~J&l = 4. Here, the space and spin coordinates of the electron are indicated by the number j of the electron and in the shorthand notation only the /3 spin is indicated by a bar. Each possible selection of occupied orbitals $,. defines an orbital configuration, from which configurational functions may be obtained. These are antisymmetric with respect to the interchange of any pair of electrons and are spin eigenfunctions. Thus the singlet ground configurational function

SPECTROSCOPY IN THE VISIBLE AND UV REGIONS

of a closed-shell molecule, with the lowest-energy nl2 orbitals all doubly &cupied, is given by an antisymmetrized spin-orbital product known as a Slater determinant: '@o =

I@141@2&

. - @n/*$n/2I

( I . 14)

The general definition of a Slater determinant is

1.2

MO M O D E b O F ELECTRONlC EXCITATION

Michl and BonaCiC-Koutecky, 1990: Appendix 111.) This procedure is referred to as configuration interaction (CI). Once wave functions of the type shown in Equation (1.18) are known, the electronic excitation energies AEe" may be calculated from Equation (1.8) as the energy difference between the ground state described by q$ and the excited state described by P ' Jrp: According to Equation (1.9), the transition moment is given by

Other configurations are referred to as excited configurations. Singly and multiply excited configurations differ from the ground configuration in that one or several electrons, respectively, are in orbitals that are not occupied in the ground configuration. Consider the following example of singly excited singlet and triplet configurations:

The configurational functions of all three components of the triplet state are listed on the three lines of Equation (1.17). From top to bottom, they correspond to the occupation of the MOs @i and $ with two electrons with an a spin, with one electron each with a and spin, and with two electrons with a spin. The z component of the total spin is equal to M s = 1,0, and - 1, respectively. The three triplet functions are degenerate (i.e., have the same energy) in the absence of external fields and ignoring relativistic effects (i.e., with a spin-free Hamiltonian). For our purposes, it is therefore sufficient to consider only one of the components, e.g., the one corresponding to M s = 0. Finally, states of given multiplicity M = 2 s + I, e.g., singlet (S = 0) and triplet (S = 1) states, may be described by a linear combination of configurational functions of appropriate multiplicity and symmetry:

can be either the ground configuration Qo or any of the singly or Here multiply excited configurational functions @,, etc. The coefficients CKjare determined from the variational principle by solving a secular problem. (Cf.

0 may be the electric dipole operator M,the magnetic dipole operator M, or the electric quadrupole operator 6. 1.2.3 One-Electron MO Models The singlet ground state of most organic molecules is reasonably described by the ground configuration Q0; that is, Coin Equation (I .l8) is nearly 1. The lowest singlet and triplet excited states are frequently characterized by singly excited configurations, but in some cases doubly excited configurations may also be of vital importance. (Cf. Section 2.1.2.) If, however, an excited state can be described by just one singly excited configuration M@i-h,as is frequently possible to a good approximation for transitions from the highest occupied MO (hom*o) into the lowest unoccupied MO (LUMO), the formulae for the excitation energies and the transition moments can be simplified considerably. This is particularly true for simple one-electron models, such as the Hiickel MO method (HMO), that do not take electron repulsion into account explicitly. The Hamiltonian of the HMO model,

is a sum of one-electron operators. The energy EK of the electron configuration is given by

where E~ is the orbital energy and ni = 0, 1, or 2 is the occupation number of MO It follows that the excitation energy is so the excitation energy is equal to the difference of orbital energies at the Huckel level. In practical applications, it can be useful to replace Equation (1.21) by

MO MODELS OF ELECTRONIC EXCITATION

1.2

which allows for the fact that electron interaction is implicitly present in the HMO operator h(j1. [Cf. Equation (1.23) and Equation (l.24).] The additive constant C has different values for different classes of compounds. (Cf. Section 2.2.1 .) If electron interaction is taken explicitly into account by writing the Hamiltonian in the form

and

Thus, due to the existence of the electron repulsion term J,, - 2K,, the singlet excitation energy is only about half the orbital energy difference, and the exchange interaction 2K,, is about one third of the Coulomb interaction J,,.

where hu) is a one-electron operator for the kinetic and potential energy of an electron j in the field of all atoms or atomic cores, whereas g(i,j) represents the Coulomb repulsion between electrons i and j, the excitation energy is calculated to be

The dipole moment operator is a one-electron operator, and within the independent particle model, with explicit treatment of electron repulsion as well as without, the transition moment becomes

(See, e.g., Michl and BonaCiC-Kouteckq, 1990: Section 1.3.) The Coulomb integral J,, which represents the Coulomb interaction between the charge distributions 1@J2 and and the exchange integral K,,, which is given by the electrostatic self-interaction of the overlap density are both positive, and the singlet as well as the triplet excitation energy is smaller than the difference in orbital energies. Within this approximation, the difference between the singlet and triplet excitation energies is just twice the exchange and the energies of the integral K,,. As a rule, Kt, is much smaller than JiA, singlet and triplet levels resulting from the same orbital occupancy are not vastly different.

where we have used the rules for matrix elements between Slater determinants (Slater rules; see, e.g., McWeeny, 1989: Section 3.3). Thus, if the excited state is described by a single configuration, the excitation energy and transition moment are completely determined by the two MOs, @, and @., This is rather an oversimplification, and configuration interaction is indispensable for a more realistic description of electronic excitations. However, in Chapter 2 it will become clear under which favorable conditions qualitative predictions and even rough quantitative estimates based on this simple model are possible.

Example 1.3: The ionization potential and electron affinity of naphthalene were determined experimentally as 1P = 8.2 eV and EA = 0.0 eV. According to Koopmans' theorem it is possible to equate minus the orbital energies of the occupied or unoccupied MOs with molecular ionization potentials and electron affinities, respectively (IP, = - E, and EA, = -el). Thus, in the simple one-electron model. the excitation energy of the H O M b L U M O transition in naphthalene may be written according to Equation ( I .22) as

AE,

+ C = IP, - EA, + C = 8.2eV + C

Experimental values for the singlet and triplet excitations corresponding to the H O M b L U M O transition are 4.3 and 2.6 eV, respectively. If the value of C in the above expression is equated to the electron repulsion terms in Equation (1.23) and Equation (1.24).

particularly illuminating is the free-electron MO model (FEMO) based on the assumption that n electrons can move freely along a one-dimensional molecular framework. Stationary states are then characterized by standing waves, and using the de Broglie relationship for the wavelength of an electron of mass m, and velocity vone obtains standing waves only if there is an integral number of half-wavelengths between the ends of the potential well of length L-that is, if Eliminating A by means of the de Broglie relationship yields

SPECTROSCOPY IN THE VISIBLE AND UV REGIONS

for the orbital energy. The energy needed to excite an electron from the hom*o, the highest-occupied MO r#Jk (k = n/2), into the LUMO, the lowestunoccupied MO #k +,, is then h2

Uk-.t+

[(k + 8mJ2

lI2 - k21

Thus, for the trimethinecyanine 2 with 6 n electrons,

erg s and insertion of the values of the physical constants h = 6.626 x g and of the plausible value L = 6 x 140 pm for the and me = 9.109 x length of the potential well yields an energy that corresponds to a wavelength of approximately 333 nm. This is in excellent agreement with the experimental value A,, = 313 nm for this cyanine in methanol solvent. R2NR !-2

? .2.4

Electronic Configurations and States

It has already been mentioned that the ground configuration (Dois in many cases quite sufficient to characterize organic molecules in their singlet ground states, whereas a single configuration constructed from ground-state SCF MOs is generally not suited for the description of an excited state; that is, an excited-state wave function can in general be improved considerably by configuration interaction. The interaction between two configurations a, and aLincreases with the increasing absolute value of the matrix element HKLand the decreasing absolute value of the difference HKK- HLLof the energies of the two configurations. If two configurations a, and a, belong to different irreducible representations of the point group of the molecule, HKL= 0, and the two configurations cannot interact. Therefore, configurations can contribute to the wave function of a given state only if they are of the appropriate symmetry, that is, if they belong to the same irreducible representation as the state under consideration. In approximate models such as the PPP method (cf. Section 1.5.1), degeneracies of orbital energy differences may carry over to the corresponding many-electron excitation energies, leading to degenerate configurations of the same symmetry. In these cases, configuration interaction is of paramount importance, since it determines the energy-level scheme. It has therefore been termed first-order configuration interaction, in contrast to configuration interaction among nondegenerate configurations, which in general affects the results only to a smaller and less fundamental degree, and which is therefore referred to as second-order configuration interaction (Mofitt, 1954b). Hence, in the case of first-order configuration interaction, two

1.2

MO MODELS OF ELECTRONIC EXCITATION

or more configurational functions are needed to construct the wave function of a state in a given MO basis. Such a state can no longer be characterized by specifying a single electron configuration. In the case of second-order configuration interaction, one of the configurational functions may predominate to such an extent that the specification of a state in terms of a single electron configuration may still be justified, at least qualitatively. The excited states of alternant hydrocarbons may serve as an example of the importance of first-order configuration interaction. Due to the pairing theorem that is valid for both the HMO and the PPP methods (cf. Koutecky, 1966), configurational functions for the excitation of an electron from @, into and from @A into @;, are degenerate, if the MO @; is paired with @;., and the MO is paired with The configurational functions ,@ ,,, and ,.@ ;,, are of the same symmetry, and their energies are split by configuration interaction. Figure 1.6 shows the splitting for the lowest excited configurations of an alternant hydrocarbon. If the interaction matrix element H,, is sufficiently large, the splitting may be sufficient to bring one of the two states that result from the splitting of the degenerate configurations below the state that corresponds primarily to the excitation of an electron from the hom*o to the LUMO. In this text orbitals that are occupied in the ground configuration will frequently be numbered 1, 2, 3 . . . starting from the hom*o, and the unoccupied MOs by l', 2', 3' . . . starting from the LUMO. The advantage of this numbering system is that the frontier orbitals responsible for light abfor the two highest sorption will be denoted in the same way (@, and occupied MOs and @,, and @., for the lowest unoccupied MOs) for all mol-

Schematic representation of first-order configuration interaction for aiternant hydrocarbons. Within the PPP approximation, configurations corresponding to electronic excitation from MO r#Ji into r#J&, and from MO.r#Jkinto r#Ji. are degenerate. The two highest occupied MOs ( i = 1, k = 2) and the two lowest unoccupied MOs (i' = 1' and k' = 2') are shown. Depending on the magnitude of the interaction, the HOM-LUMO transition @,-+@,. corresponds approximately to the lowest or to the second-lowest excited state. F i r e 1.6.

SPECTROSCOPY IN THE VISIBLE AND UV REGIONS

ecules irrespective of which electrons (n electrons, valence electrons, o r even inner shells) are taken into account. Within the PPP approximation the singlet and triplet CI matrices for a n alternant hydrocarbon each factor into two separate matrices for the "plus" states and the "minus" states corresponding t o the linear combinations

13@Lk=

[l.3@+h, 5 1 3 @ h + i , ] / a

1.2

MO MODELS OF ELECTRONIC EXCITATION

and making allowance for the classification into plus and minus states, the HOMCkLUMO transition may be denoted as a transition from an 'A; ground state into an excited state of symmetry 'B:. The degenerate configurations .,,, are of the same symmetry: and @

(1.26)

The ground state behaves like a minus state since it interacts only with minus states; excited configurations of the type Qbi., however, behave like plus states. In this approximation the transition moments between two plus states o r two minus states vanish, and such transitions are forbidden. Electric dipole transitions are allowed only between plus and minus states (Pariser, 1956).

Using typical PPP parameters it is found that is larger than the difference E(@,,,.) - E(@,-,.), which corresponds to the situation shown in Figure 1.6 on the right, with the 'A; state below the 'B: state. Thus, the lowest-energy transition is forbidden and the next one allowed. For anthracene, for the state that is characterized by the HOMCkLUMO excitation, we have

Example 1.5:

In Figure 1.7 the HMO orbital energy levels of anthracene and phenanthrene are given together with the labels of the irreducible representations of the point groups D, and Cz,. The ground configuration with fully occupied orbitals is totally symmetric and belongs to the irreducible representation A, or A,. The symmetry of a singly excited configuration @I, is given by the direct product of the characters x of the irreducible representation of the singly occupied MOs ipi and $I. For phenanthrene,

Figure 1.7. Orbital energy diagrams of anthracene and phenanthrene. For each HMO energy level the irreducible representation of the n MO is given.

LOO

300

Inml

250

200

Figure 1.8. Absorption spectra of anthracene (---) and phenanthrene (-) permission from DMS-UV-Atlas 1%6-71).

(by

SPECTROSCOPY IN THE VISIBLE AND W REGIONS

whereas the orbitals below the hom*o and above the LUMO are accidentally degenerate, so four configurations have to be considered. Only the following two have u symmetry:

For anthracene is smaller than the difference E(cP,,,.) E(@l+l.) and the allowed hom*o+LUMO transition ('A,-*'BL) is lower in energy than both the IB, and IB:, states split by configuration interaction. This is shown on the left of Figure 1.6. Now, the lowest-energy transition is allowed and the next one is forbidden. This contrast of phenanthrene and anthracene is obvious in the absorption spectra shown in Figure 1.8. The forbidden second transition in anthracene is hard to discern under the intense first one.

1.3

INTENSITY AND BAND SHAPE

spectively. Platt's nomenclature is derived from the perimeter model and denotes the same bands as 'La, 'L,, and 'B,. (Cf. Section 2.2.2.) A very simple scheme is obtained using consecutive numbering of the singlet states, denoted by S, and the triplet states, denoted by T. The longest wavelength transition in the spectrum of phenanthrene or anthracene is then referred to as the So-.Sl transition. This nomenclature does not reveal anything about the nature of the states involved except for their multiplicity and their energy order. Another disadvantage is that the detection of a new transition automatically means that all higher transitions have to be renamed. According to Mulliken (1939) the ground state is denoted by N and the valence excited states by V. The bands observed in the phenanthrene spectrum are called V+N transitions. In addition, Rydberg transitions and transitions that involve electron lone pairs (cf. Section 2.5) are denoted by R t N and Q t N , respectively. Finally, Kasha (1950) specifies only the nature of the orbitals involved in the transition, using n-n* transitions, etc.

1.2.5 Notation Schemes for Electronic Transitions Various schemes have been proposed to denote the states of a molecule and the absorption bands that correspond to transitions between these states. Some of these schemes are collected in Table 1.2. The discussion in the previous section revealed the advantages as well as the disadvantages of the group theoretical nomenclature. For cyclic n-electron hydrocarbons two more schemes, introduced by Clar (1952) and Platt (1949), are widely used. Clar's empirical scheme is based on the appearance of the absorption bands and designates the first three bands in the spectrum of phenanthrene as the a,p, and /3 bands, re-

Table 1.2 Labeling of Electronic Transitions System

State Symbol

Enumerative

SO S , , S?, S, . . . T,, T2, T, . . . A, B, E, T (with indices g, u, I . 2, '. ") o. n . n 8 .nL A B. L (with indices a. b) N Q. V. R (I. p. 1'3

Group theory Kasha Platt Mulliken Clar

t The upper left index indic;tte> the moltiplicily.

Example Singlet ground state Excited singlet states Triplet states Irreducible representations of point group of the molecule Ground state orhitals Excited state orbitals Ground state Excited states

so-s

Ground state Excited states Intensity and band shape

V t N

S"+S? T,-+T, 'A,-.'B,t 'A,tlB,. lAl~'El. n-n* wn* lA-.iB.,t I

1.3 Intensity and Band Shape 1.3.1 Intensity of Electronic Transitions A rough measure of the intensity of an electronic transition is provided by the maximum value E, of the molar extinction coefficient. A physically more meaningful quantity is the total area under the absorption band, given by the integral J ~ d c or , the oscillator strength which is proportional to the integrated intensity.f is a dimensionless quantity that represents the ratio of the observed integrated absorption coefficient to that calculated classically for a single electron in a three-dimensional harmonic potential well. The maximum value off for a fully allowed transition is of the order of unity. In order to obtain a theoretical expression for the oscillator strength, perturbation theory may be used to treat the interaction between electromagnetic radiation and the molecule. Since an oscillating field is a perturbation that varies in time, time-dependent perturbation theory has to be used. Thus, the Hamiltonian of the perturbed system is

A+lL,

QtN

where is the Hamiltonian of the unperturbed system, that is, of the molecule in the absence of any electromagnetic radiation, and fl(I)(t) describes the interaction between light and molecule. It turns out that the probability of a transition from a state 0 with total wave function Tr into a state with wave function TT is proportional to the

SPECTROSCOPY IN 'THE VISIBLE AND W REGIONS

light intensity and to the squared matrix element I i

is the matrix element of the linear momentum operator. Equation (1.30) is called the dipole velocity formula for the oscillator strength.

* Both the electric field E(r.1) and the magnetic flux density B(r.1) may be derived from the vector potential A(r.1). Using the so-called Coulomb gauge one obtains = - (llc)aA(r.l)lat

and B(r.1) =

x A(r.1)

More commonly used (cf. Example 1.6) is the related dipole length formula

y r )= (4rrm,/3he2)p- leu . k A 2 where is the transition moment, and

is the dipole moment operator. The first sum in Equation (1.34) runs over the electrons j and the second sum over the nuclei A of charge ZA.Making use of the product form of the total wave function given in Equation (1.12), one has

is the gradient operator.

When the origin of coordinates is chosen to lie within a molecule of ordinary size, the length is much smaller than A for UV light and light of longer wavelengths. Therefore, K.5 4 1, and the expansion of the exponential eS"i into an infinite series converges rapidly

E(r.1)

INTENSITY AND BAND SHAPE

1.3

where the first term vanishes for every fixed nuclear configuration Q due to the orthogonality of ground-state and excited-state wave functions. For electronically allowed transitions the geometry dependence of the electronic transition moment

may be neglected, so the overall transition dipole moment becomes Mol-n,* = Mw.f<xb,k,>

(1.36)

The electronic transition dipole moment Mh, determines the overall intensity of the transition. The overlap integrals <x:.I&,> of the vibrational wave functions of the ground and excited electronic states determine the intensity of the individual vibrational components of the absorption band. (Cf. Section 1.3.3.) If only the total intensity of the electronic transition is of interest, it is sufficient to calculate the electronic dipole transition moment from Equation (1.35). Here, and frequently in the following, the index Q for molecular geometry is omitted for clarity of notation. The transition dipole moment M,, is a vector quantity, and one has

w=iq+q+w with

SPECTROSCOPY IN THE VISIBLE AND W REGIONS

where a = x, y, z denotes the electronic coordinates. If the transition dipole moment is measured in Debye ( I D = 10-%su cm), the oscillator strength is given by

Example 1.6: From the above derivation it is seen that after the series expansion of the exponential in the space part of the vector potential, the transition moment operator involves the linear momentum operator @, or the gradient operator Equation (1.32) is obtained from Equation (1.30) in the following way: From the commutation relation [h,r,] = fir, - r,fi = bj, we have

From the Hermitean property of f i it follows that' = ,so for exact eigenfunctions of h, for which fiY, = E,*,, the following relation holds:

Thus, two different expressions are obtained for the oscillator strength:

and

If Yoand qfare exact eigenfunctions of the molecular Hamiltonian the two expressions give identical results, but this is generally not true for approximate wave functions. (Cf. Yang, 1976, 1982.) Thus, nonempirical SCF calculations based on the ZDO approximation yield for the N+V transition of ethylene (the longest-wavelength singlet-singlet transition) the following values: and which differ by a factor of 2. Refinement of the wave function by including some configuration interaction leads to and and fp' on further re(Hansen, 1967). Convergence to a common value of finement of the wave function is to be expected. (See also Example 1 .I4 and Figure 1.23, as well as Bauschlicher and Langhoff, 1991.)

1.3

INTENSITY AND BAND S W E

The second term in the series expansion of the exponential in Equation (1.29). iK-5,leads to an integral that may be separated into two parts. The square of the first part

describes the contribution of the magnetic dipole transition moment to the intensity of the transition qo--+*,, whereas the square of the second part

determines the value of the electric quadrupole transition moment. Here,

and

are the operators of the magnetic dipole moment and of the electric quadr u p l e moment, respectively. We have already mentioned that contributions from these operators may be neglected for dipole-allowed transitions, and that even higher-order terms in Equation (1.29) may be safely ignored. From Equation (1.33, the electric dipole transition moment M,, may be . transithought of as the dipole moment of the transition density *Ir;9,,The tion density is a purely quantum mechanical quantity and cannot be inferred from classical arguments. A more pictorial representation of the electric dipole transition moment equates it to the amplitude of the oscillating dipole moment of the molecule in the transient nonstationary state that results from the mixing of the initial and the final states of the transition by the timedependent perturbation due to the electromagnetic field, and which can be written as a linear combination: c,,T,, + c,V, + . . . This emphasizes the fact that the absolute direction of the transition moment vector has no physical meaning. Using the CI expansion (1.18), qoand 9,can be written in terms of the configurations a,. From Equation (1.25), the contribution C,Ci-I.,M,-A to the transition moment that is provided by the configurations a, and a,,, is proportional to where the total electric dipole moment operator M = X$ = - IelCq is given by a sum of contributions provided by each electron j. By substituting the LCAO expansion from Equation (1.13) one obtains

1.3

IN'I'ENSI'IY AND BAND SHAPE

Introduction of the ZDO approximation, appropriate for n-electron systems, gives <x#x,,> = S,,<X,,(~X,,>; the remaining integrals may be evaluated easily by writing the position vector 5 of electron j as

where R, is the position vector of the nucleus p on which the orbital x,, is centered, and is independent of the electronic coordinates. The vector pointing from nucleus p to electron j is r;."= 5 - R,. By symmetry of the A 0 x,, <xPlqP(x,,> = 0, and

Mhk = - l e ~ f l ~ c ; , ~ , j t , ~

(1.41)

Therefore, in the ZDO approximation, M,, is given by the electric dipole moment of point charges at the centers p. However, these point charges are not due to the orbital charge distributions -1el 1+,12 and - [el 1qjkI2of an electron in one of the MOs (gi o r @L,but rather from the overlap charge distribution - lel@;$i, which is positive in some regions of space and negative in others. Integration over all space yields zero, as the MOs and are mutually orthogonal.

Example 1.7:

Starting from the HMOs of butadiene

Figure 1.9. Cartesian coordinates of n centers of a) s-trans-butadiene and b)

s-cis-butadiene, assuming equal lengths lofor all bonds. HOM-LUMO transition is predicted to be more intense for s-trans-butadiene than for s-cis-butadiene. For the transitions $,+$, and $,+$,, which are degenerate due to the pairing properties of alternant hydrocybons, the same arguments lead to MI,,

= MI,,

= - (e/fl[0.37

x 0.60 (R,

+ R,

- R,

R,)]

When first-order configuration interaction is taken into account, the contributions from these two transitions add in-phase for excitation into the plus state and out-of-phase for excitation into the minus state; cf. Equation (1.26). From the coordinates x,, and y, or y, and z, depicted in Figure 1.9, it is easy to see that for s-trans-butadiene M, = M, = 0. Accordingly M? = 0, the transition probability is zero and the transitions into the plus and the minus states are both forbidden. For s-cis-butadiene. which does not possess a center of symmetry, M , = 0, but M, # 0. The transition moment differs from zero and is oriented perpendicular to the long axis of the molecule. The transition into the plus state is therefore allowed. For excitation into the minus state the two contributions cancel each other and this transition is forbidden irrespective of the molecular geometry. (Cf. also Example 1.9.)

the transition dipole for the hom*o-*LUMO transition may be calculated within the HMO approximation as follows: From Equation (1.41),

1.3.2 Selection Rules Using Equation (1.37) for the components of M in the system of axes shown in Figure 1.9, and assuming that all bond lengths are equal to I, and all 'valence angles to 1200, one obtains for s-trans-butadiene

where m = - lell,. The x as well as the y components are nonzero, and the transition moment is oriented along the long axis of the molecule. The system of axes for s-cis-butadiene is different, and the y component is the same as the x component for s-trans-butadiene. The z component vanishes, and the transition moment is oriented parallel to the y axis. Since M? = + w or M? = M + @, the absorption band due to the

Selection rules that differentiate between formally "allowed" and "forbidden" transitions can be derived from the theoretical expression for the transition moment. A transition with a vanishing transition moment is referred to as being forbidden and should have zero intensity. But it should be remembered that the transition moment of an allowed transition, although nonvanishing, can still be very small, whereas a forbidden transition may be observed in the spectrum with finite intensity if the selection rule is relaxed by an appropriate perturbation. The most important example are vibrationally induced transitions, which will be discussed later. (Cf. Section 1.3.4.) Other effects such as solvent perturbations may play a significant role also. Finally, since a series of approximations is necessary in order t o derive the selection rules, they can be obeyed only within the limits of validity of these approximations.

SPECTROSCOPY IN THE VISIBLE AND UV REGIONS

For instance, from the approximations introduced into the theoretical treatment of the radiation field it follows that only one-photon processes are allowed. However, very intense radiation fields, especially those produced by lasers, can cause simultaneous absorption of two photons, thus making it possible to reach molecular states that are not accessible from the ground state via one-photon absorption. Quite often, the only other evidence for the existence of these states is indirect, and two-photon absorption spectroscopy is complementary to conventional one-photon spectroscopy. (Cf. Section 1.3.6.) The spin selection rule is a consequence of the fact that the electric dipole and quadrupole moment operators d o not operate on spin. Integration over the spin variables then always yields zero if the spin functions of the two states qoand Yf are different, and an electronic transition is spin allowed only if the multiplicities of the two states involved are identical. As a result, singlet-triplet absorptions are practically inobservable in the absorption spectra of hydrocarbons, o r for that matter, other organic compounds without heavy atoms. Singlet-triplet excitations are readily observed in electron energy loss spectroscopy (EELS), which obeys different selection rules (Kuppermann et at., 1979). Strictly speaking, however, the spin angular momentum and its components are not constants of motion in nonlinear molecules, and the classification of states by multiplicity is therefore only approximate. Spin-orbit coupling is the most important of the terms in the Hamiltonian that cause a mixing of zero-order pure multiplicity states. The interaction between the spin angular momentum of an electron and the orbital angular momentum of the same electron causes the presence of a minor term in the Hamiltonian, which may be written as

1.3

INTENSITY AND BAND SHAPE

lets, etc. However, since such a "singlet" state contains a small triplet contribution and the "triplet" state a small singlet contribution, the transition moment for such a singlet-triplet transition

can be different from zero, depending on the values of A, and A,.

Example 1.8: Singlet-triplet transitions are of considerable importance not only for heavy atom compounds but also for carbonyl compounds. This can be visualized simply by reference to the principle of conservation of angular momentum, based on the fact that the spin-orbit coupling operator mixes states related by a simultaneous change of spin angular momentum and orbital angular momentum. Intersystem crossing between states represented by single configurations is therefore most favorable if they differ by promotion of an electron between molecular orbitals containing atomic p orbitals whose axes are mutually perpendicular in one and the other MO (Salem and Rowland, 1972; Michl, 1991). In order to examine the spin-orbit interaction between a '(n,n*) and a )(n,n*) state for a carbonyl compound, it is sufficient to consider the 2p, and the 2p,, AOs, xo and yo, on oxygen and the 2p, AO, y,, on carbon. The '(n,n*) state and the three components TI. To, and T - , of the '(n,n*) state may then be written as

and

Here, = ry x p, is the orbital angular momentum operator of the electron j, ry is the vector pointing from nucleus p t o electron j, and the sums run over all electrons j and all nuclei y . Spin-orbit coupling is particularly significant in the presence of atoms of high atomic number Z, ("heavy atom effect "). The presence of an inseparable scalar product l?j 8, of one operator that acts only on the spatial part of the total electronic wave function and another one that acts only on its spin part will cause an interaction between the various pure multiplicity wave functions. The resulting eigenfunctions of fie, will therefore be represented by mixtures of functions that differ in multiplicity. However, since f i , constitutes only a very small term in fie,, mixing is normally not very severe, and the resulting wave functions contain predominantly functions of only one multiplicity. Commonly, such "impure singlets," "impure triplets," etc., are still referred to simply as singlets, trip-

For an evaluation of the matrix element of the operator given in Equation (1.42), it is convenient to first determine the effect of the spin part of the three components /$,, f,s^,., and fzs^; of the scalar product 1 . Son the triplet function and to perform the spin integration, which reduces the number of terms considerably. In this way one obtains the following:

1.3

In this case, the x and y components of the operator i . give vanishing contributions. If the orbitals involved are centered at the same atom, as is the case for carbonyl compounds, the spin-orbit coupling is particularly large due to the factor Irf13in the denominator of Equation (1.42). The '(n,n*) c* '(n,n*) and '(n,n*) c* '(n,n*) transitions are forbidden by the angular momentum conservation rule, since only the spin angular momentum changes, causing all one-center terms of the spin-orbit coupling to vanish. The results for a '(n,n*) * '(n,n*) transition are similar to those for a '(n,n*) c* '(n,n*) transition. This result is sometimes represented pictorially using up-and-downdirected arrows to represent electron spin. It is difficult to do this correctly, since it is the To component of the triplet state that is responsible for the intersystem crossing, and not the T, or T-,, which are the ones that are easily represented pictorially.

Spatial symmetry selection rules are another very important type of selection rules. They occur because the transition dipole moment in Equation (1.35) can vanish not only due to spin integration but also as a result of integration over the space coordinates of the electrons. This is always the case if the integrand is not totally symmetric or does not contain a totally symmetric component. If the integrand is antisymmetric with respect to at least one symmetry operation of the point group of the molecule, the integral vanishes, since positive and negative contributions from different regions of space defined by one or more symmetry operations cancel. Whether or not the integrand is totally symmetric can be decided easily by determining the irreducible representation x of the point group of the molecule for the ground state qo,the excited state qf,and for the transition moment operator, and forming the direct product of all three. The components M aof the electric dipole transition moment are given by the Cartesian coordinates a = x, y, and z. The a component of the transition dipole vanishes unless the direct product forms a basis for the totally symmetric irreducible representation or a reducible representation that contains the totally symmetric irreducible representation. If all three components M a vanish by symmetry the transition is said to be symmetry forbidden. Since the ground state \Ir, of closed-shell systems is totally symmetric, a transition can be symmetry allowed only if the excited state qfand at least one of the Cartesian coordinates a form bases of the same irreducible representation of the molecular point group. In point groups with a center of symmetry, x, y, and z are of ungerade parity (u); that is, they change sign upon inversion. Therefore, one and only one of the two states qoand gIr, has to be of ungerade parity if the transition moment is to be nonzero. Thus, within the electric dipole approximation

INTENSITY AND BAND SHAPE

only transitions g o u between a gerade and a ungerade state are allowed, whereas transitions g t,g and u o u between states of the same parity are forbidden. In applications of these symmetry selection rules it has to be remembered that the symmetry of a molecule can be lowered by vibrational motions so that symmetry-forbidden transitions may nevertheless be observed-for instance, the two longest-wavelength singlet-singlet transitions in benzene, Vibronic coupling and the shape of the absorption bands will be discussed in the following sections. --

Example 1.9: In applying the symmetry selection rules it is frequently quite convenient to start from Equation (1.39) and examine whether or not the integral vanishes by symmetry. Thus, it is easy to see that for s-trans-butadiene, which belongs to the point group C,, and has been discussed already in Example 1.7, the transition dipole of the hom*o-+LUMO transition +,(b,)-++,(a,) has nonzero x and y components: both the x and y coordinates form a basis of the irreducible representation B, and B, x B, x A, = A,. The transitions c#~,(b,)++~(b,) and +,(a,,)+$~,(a,,) are parity forbidden, as B, x B, = A, x A, = A, and the symmetry of the Cartesian coordinates is ungerade. (Cf. Figure 1.10.) Since s-cis-butadiene belongs to the point group C,,, which has no center of symmetry, it has no parity-forbidden transitions. M, # 0 for the transition

Figure 1.10. Schematic representation and symmetry labels of n MOs a) of strans- and s-cis-butadiene and b) of benzene.

SPECTROSCOPY IN THE VISIBLE AND UV REGIONS

1.3

INTENSI'W AND BAND SHAPE

&(a3 + #,(b,) because A, x B, = B,, and they coordinate transforms like B?. However, M,# 0 for the transitions described by #,(a,) + #,(a,) and #,(b,) -* @,(€I,), since the z coordinate forms a basis for the totally symmetric representation A,. In benzene the hom*o and LUMO are degenerate. The MO and #, form a basis for the irreducible representation El,, whereas the MOs #,and #, form a basis for the irreducible representation E,, of the point group D,. (Cf. Figure 1.10.) From the direct product 0

El, x E,, = B," + B," + El"

it is seen that one allowed degenerate transition is to be expected, since the x and y coordinates form a basis for the irreducible representation El,. For the other two transitions one has M = 0; hence they are electronically forbidden by symmetry and can be observed only as a result of vibronic coupling. (Cf. Section 1.3.4.)

Finally, according to Equation (1.39) the transition moment also vanishes if the differential overlap &@, is zero everywhere in space. This is not strictly possible (except within the ZDO approximation), but the product +;& may reach very small values if the amplitude of MO $k only is large in those regions of space where the amplitude of is very small, and vice versa. Consequently the transition dipole moment will also be very small in such a case. This is true for n-n* transitions, where an electron is excited from a lone-pair orbital in the molecular plane into a n* orbital of an unsaturated system, for which the molecular plane is also a nodal plane. Similar reasoning applies to so-called charge transfer transitions, that is, those in which an electron is transferred from one subsystem to another, the orbitals @, and are localized in different regions of space. Such transitions are overlap forbidden. This is not, however, a very strict selection rule, since it is not based on a vanishing but only on a small value of the transition moment. The differential overlap is never exactly zero in practice. Table 1.3 Selection Rules for Electronic Transitions Rule

Criteria

Spin

Symmetry

~ ( ' 4 'x~ x(YJ ) # x(a) or ~ ( 4 x) x(&) # ~ ( a ) , with a = x , y, z Y++Y+ or Y -+Y -

Alternant pairing Local symmetry or overlap Section 1.3.4.

&I#J~

allowed

Validity Strict (however, see spin-orbit coupling) Strict (however, see vibronic coupling^ Moderately strict Weak

forbidden

\ StCL

Figure 1.11. Schematic representation of the absorption spectrum of an organic molecule with some allowed transitions and some that are forbidden by spin, symmetry, or overlap selection rules (from left to right). The log E and f values of the ordinate are only meant to provide rough orientation. In particular, according to Equation (1.27), there is no simple relation between log E and f (by permission from Turro, 1978).

Note that overlap-forbidden transitions also tend to have small singlettriplet splitting. This is given in the first approximation by 2K,, that is, by twice the self-repulsion of the overlap charge density &&. If the overlap charge density is small everywhere, its self-repulsion can hardly be large. Table 1.3 presents all the selection rules discussed so far, and Figure 1.1 1 represents schematically the relative intensity of various allowed and forbidden transitions. Example 1.10: The absorption spectrum of naphthalene is shown in Figure 1.17 (cf. also Figure 2.7): A very weak transition near 32,000 cm-' is followed by a mediumintensity transition near 35,000 cm-, and a very intense transition near 45,000 cm-I. All three are n+n* transitions; the first one is nearly exactly forbidden by the (approximate)alternant pairing symmetry, as it is a transition 'between two minus states (cf. Example 1.5); the intensity is due nearly entirely to vibronic coupling. (Cf. the first transition of benzene, Example 1.11 .) The transition, and the transition second one is predominantly the HOM-LUMO moment is determined by the transition density I$~,MO#,,MO. In the azulene transition corresponds to the spectrum (Figure 2.28) the HOM-LUMO longest-wavelength absorption near 14,500 cm-I and is much weaker (E= 200) than the H O M h L U M O transition of naphthalene (E = 6,500). This lower intensity is due to the fact that the hom*o and LUMO of azulene are localized largely on different atoms in the rr system, so the transition density &,,o#~,Mo is small, and so is its dipole moment (Section 1.3.1). This is only possible because azulene is nonalternant. The hom*o and LUMO of naphthalene are mostly localized on the same atoms, as they must be for an alternant hydro-

1.3

carbon; the transition density is much larger, as is its dipole moment. It is not transition in azulene also has a a coincidence that the weak HOM-LUMO small singlet-triplet splitting. From Equations (1.23) and (1.24), this is given by 'BE,, - 'AE,, = 2K,,, where K,i is the exchange integral that is equal to the self-repulsion of the transition density @L,,o+,oMo (Section 1.2.3). Clearly, a small transition density is more likely to have a small self-repulsion energy than a large one. In fact, from the experimental excitation energies one finds 2KH0,,,,,, = 1.70 eV for naphthalene and 0.50 eV for azulene. (Cf. Example 1.3 and Michl and Thulstrup, 1976.) Similar arguments apply to w n * transitions in carbonyl compounds. The n and the JPorbitals are largely located in different parts of space and the transition density is small. These transitions are weak: E = 35 in acrolein (see also the spectra of pol yene aldehydes shown in Figure 2.37). and the singlet-triplet splitting is small: 0.2 eV in the case of the wlic transition of acrolein (Alves et al., 1971). In the case of CT complexes, the hom*o is primarily located on the donor, the LUMO is primarily located on the acceptor, and the transition density is again small. The intensity of the CT transition is again low and the S-T splitting small.

INTENSITY AND BAND SHAPE

If the potential governing the nuclear motion is accidentally similar in the initial and final electronic states described by qoand qf,respectively, with a minimum at the same equilibrium geometry, the two operators AVib(j, Q) for these two states as well as their vibrational wave functions are identical. The vibrational wave functions X',. and f, then are orthonormal. The nonvanishing factors will be = d,.,, and only the b 0 , I+], . . ., v+v vibrational transitions will be observed in absorption or emission. The transition is then called Franck-Condon allowed. More commonly, the potentials and the equilibrium geometries of the electronic states qoand qf will differ, X',. and fir will be eigenfunctions of different operators Avib(j,~), and will be nonorthogonal. The Franck-Condon factor < x ~ . I ~ ,will > ~ then be a measure of the relative intensity of the vibrational component of the absorption band that corresponds to a transition from the vibrational level v of the initial state (frequently the lowest vibrational level) into the vibrational level v' of the excited state.

1.3.3 The Franck-Condon Principle When discussing symmetry selection rules it was mentioned that vibrational motion can influence both the shape and the intensity of electronic absorption bands. In the usual Born-Oppenheimer approximation with molecular wave functions written as products as in Equation (1.12) this can be understood as follows. Electronic motion with a typical frequency of 3 x lOI5s- ( 5 = 1 cm - I ) is much faster than vibrational motion with a typical frequency of 3 x lOI3 s-I ( 5 = I@ cm-I). As a result of this, the electric vector of light of frequencies appropriate for electronic excitation oscillates far too fast for the nuclei to follow it faithfully, so the wave function for the nuclear motion is still nearly the same immediately after the transition as before. The vibrational level of the excited state whose vibrational wave function is the most similar to this one has the largest transition moment and yields the most intense transition (is the easiest to reach). As the overlap of the vibrational wave function of a selected vibrational level of the excited state with the vibrational wave function of the initial state decreases, the transition moment into it decreases; cf. Equation (1.36). Absorption intensity is proportional to the square of the overlap of the two nuclear wave functions, and drops to zero if they are orthogonal. This statement is known as the FranckCondon principle (Franck, 1926; Condon, 1928; cf. also Schwartz, 1973): I~ol-,r*12

I ~ h f 1I<x:.,lfi.>12 2

( 1-45)

The squared overlap integrals of the vibrational wave functions are referred to as the Franck-Condonfacrors.

Figure 1.12. Illustration of the Franck-Condon principle in the case of a diatomic molecule: the absolute value of the integral 1

where, neglecting overlap, m is given by m =

- l e l d d [ 2 a sin (nln)]

Thus, in view of Section 1.3.1, we obtain the transition moment matrix elements for the unperturbed [nlannulene, = V(Z: = m(eI + ie,)

From this matrix representation it is easy to see that for Ahom*o = ALUMO Y does not mix with any of the other states, because in this case (la1 - Ibl) = 0, and that the interaction between X and V vanishes for rp = 0 and that between X and U for rp = IT. In Example 2.6 it will be shown that similar arguments apply to transition dipole moments. Thus, it follows that the 'L, and 'B, transitions are both polarized along a line that bisects two opposite bonds, whereas if for symmetry reasons rp = 0 or IT (cf. Figure 2.12) the 'La and 'B, transitions are polarized along a line that passes through two opposite atoms and is perpendicular to the former. If Ahom*o = ALUMO and rp = 0, 'L, has zero intensity, and if rp = IT, 'La has zero intensity. Even if there is no symmetry, as long as Ahom*o = ALUMO and rp = 0 or IT, the 'L, transition is polarized parallel to the 'B, transition and perpendicular to the 'La and 'B, transitions and either 'L, (rp = 0) or 'L, (rp = IT) has zero intensity. For other values of the relative phase angle, the polarization directions of the four transitions 'L,, 'I+ 'Bll and 'B, need no longer be parallel or at right angles; indeed, when Ahom*o = ALUMO, 'L, and 'L, actually may be polarized parallel to each other, for example, in z-substituted naphthalenes (Friedrich et al., 1974).

= V(Z: = m(el - ie,) whereas

Thus, in agreement with the arguments in Section 2.2.2, nonzero transition moments are obtained only for transitions in which the angular momentum quantum number changes by + I, that is, where the sense of electron circulation is preserved. Finally, the application of Equation (2.1 1) gives the transition moments between the ground configuration and the real excited perimeter configurations

+ e, sin y) = V(Z:m(- el sin y + ez sin y )

< @ o l ~ l ~= >a r n ( e , cos y

The intensities and polarization directions of the four transitions 'L,, IL,, 'B,, and 'B, can then be estimated by introducing configuration mixing a s given by Equation (2.12). Thus it is easy to see that for la[ - lbl = 0 the L states can acquire their intensity only by mixing with the X state and hence have to be polarized parallel to each other.

2.2.4 Systems with Charged Perimeters * For y = 0 the definition of X and Y is identical with that given by Moffitt (1954a). that is, X = (a,+ a Z ) / Gand Y = (a,- @,)/(iG); however. X = -(@, - a 2 ) / ( i d )and Y = -(al + @ ? ) l ffor l y = d2.

The.spectra of (4N + 2)-electron charged perimeter n systems are appreciably different from uncharged perimeter n systems, irrespective of whether the perimeter is even or odd-that is, of whether or not the ion is derived

2.2

from an alternant or a nonalternant hydrocarbon. This is illustrated in Figure 2.13, which compares the absorption spectra of the tropylium ion and the cyclooctatetraene dianion with that of benzene. At the HMO level all three systems are characterized by a fourfold degenerate transition between the degenerate hom*o and the degenerate LUMO. Of the configurations composed of the perimeter MOs according to Equation (2.4), @, and @, as well as @, and @, are pairwise degenerate. This corresponds to a splitting into the 'B,,, states on the one hand and the 'L,,L, states on the other hand. In a charged perimeter with n # 4N+2, these configurations do not interact, as has been discussed already in Section

CYCLIC CONJUGATED n SYSTEMS

2.2.2, so only two transitions are to be expected. The difference between the benzene spectrum and the spectra of the ions is therefore due to different symmetry of the excited-state configurations. This was first pointed out by Heilbronner (1%6) in the case of the tropylium ion. Symmetry also affects the spectra of derivatives of charged perimeters with 4N+ 2 electrons. (Cf. Section 2.2.5.) Similar arguments apply to perimeters with 4N n electrons, but the situation is more complicated and a different classification of excited states applies. (Cf. Section 2.2.7.)

2.2.5 Applications of the PMO Method within the ~xtended Perimeter Model The following hierarchy of perturbations has been found useful in discussing the spectra of aromatic molecules derived from a (4N + 2)-electron perimeter through the introduction of a series of perturbations. (I)

1 1

Bridging

Hydrocarbon (2)

Cross-linking

Hydrocarbon (3)

2-Electron or 0-Electron Heteroatom Replacement

Heterocycle 1-Electron Heteroatom Replacement

(4) t

Heterocycle (5)

Substitution

Target Molecule Bridging is defined as the insertion of additional n centers within the perimeter. Examples are the production of acenaphthylene (16) from the [ I l]annulenium cation and a CG fragment or the production of pyrene (17) from [14]annulene and the C=C ethylene unit:

Figure 2.13. Comparison of the absorption spectra of benzene, the tropylium ion, and the cyclooctatetraene dianion (adapted from Heilbronner, 1%6 and Dvorak and Michl, 1976).

ABSORPTION SPECTRA OF ORGANIC MOLECULES

Bridging units tend to introduce new orbitals between the hom*os and the LUMOs of the perimeter. This is especially true in cases such as in 16 where the bridge contains an odd number of n centers and possesses nonbonding orbitals. Excitations to or from these additional orbitals cannot of course be classified in terms of the unperturbed perimeter transitions. Cross-linking is defined as the introduction of n bonds between nonadjacent centers in the perimeter, producing, for example, naphthalene (14) and azulene (15) from [IOIannulene; 2-electron and 0-electron heteroatom re-NR-, -S, or a placement refers to the replacement of C@by &, similar group with two n electrons, and the replacement of C@by -BHor a similar heteroatom with no n electron in its p, AO, respectively, as illustrated in 18 and 19.

2.2

CYCLIC CONJUGATED n SYSTEMS

integral &aP of the atom Q (heteroatom replacement) modifies the energy E~ of the i-th perimeter orbital by

The change in the orbital energy is proportional to the product ccoior to the square of the LCAO coefficients, respectively. The effect of introducing a bond between different fragments R and S (bridging or substitution) on the energy E~ of the i-th perimeter orbital is approximated by the secondorder expression

l describes the interaction between the SOs, and u is a phase factor. The magnitude of the interaction and hence the nature of the ground-state wave function is determined significantly by the kind of perturbation involved. Since uncharged 4N-electron perimeters are alternant hydrocarbons, perturbations can be classified as even or odd in the same way as in Section 2.2.5. For even perturbations u = 0 [or 2n(n/2)] and the interaction matrix is already diagonal. Figure 2.20a shows the energies of the ground state G, and of the singly and doubly excited states S and D, relative to that of the triplet state as a function of the perturbation strength Is(. For odd perturbations u = nI2 [or (2n + I )(1~/2)1and a,and a,will mix. In Figure 2.20b it is

2.2

CYCLIC CONJUGATED n SYSTEMS

Figure 2.20. Energies of the biradicaloid singlet states G , S, and D relative to the triplet state T as a function of the perturbation Is1 ; a) of uncharged 4N-electron perimeters for even, and b) for odd perturbations, and c) of charged 4N-electron perimeters. The discussion of spectra applies only to the shaded region of strong perturbations (adapted from HiSweler et al., 1989).

Absorption spectra a) of I ,3-di-t-butylpentalene-4,s-dicarboxylic ester (adapted from HiSweler et al., 1989) and b) of biphenylene (adapted from Jgirgensen et al., 1978). Due to the large variation in intensity the various bands are scaled as indicated. Figure 2.21.

shown how in this case the relative energies of the lowest three singlet states depend on the perturbation strength. (See also Figure 4.20.) As all three singlet states are composed of perimeter configurations that differ only in the occupation of the orbitals @, and @,whose quantum numbers differ by more than a unity, the transition moments vanish. (See Example 2.6.) In Section 4.3.2 it will be shown that the energy ordering given in Figure 2.20a and for Is1 = 0 for the unperturbed uncharged 4N-electron perimeter is characteristic for so-called perfect pair biradicals. In discussing the spectroscopic properties of nonaromatic compounds derived from a 4N-electron perimeter it is assumed that @, is a good approximation to the ground-state wave function. From Figure 2.20 it is clear that such is the case when Is1 is sufficiently large so that the G state is energetically below the S state. The following arguments apply therefore only if this condition is fulfilled. This is virtually guaranteed for all systems of real interest even if no structural perturbations are present, due to Jahn-Teller and pseudo-Jahn-Teller distortions. From Figure 2.20a it is easily seen that the dipole-forbidden first absorption of uncharged perimeters, which corresponds to the G+S transition, is expected to occur at longer wavelengths for systems with even perturbations than for systems with odd perturbations. This is confirmed by the absorption spectra of a substituted pentalene (even perturbation) and of biphenylene (odd perturbation) depicted in Figure 2.21. The spectrum of the pentalene also exhibits the slow rise of the absorption profile of the first band starting

at 10,000 cm-I, which is known as "tailing" and is very typical for systems with even perturbations. In order to discuss higher states, the orbitals @+,,and @ +,,, or their real combinations obtained by the transformation Equation (2.17) have to be also considered. Four of the configurations that result in this way are doubly excited with respect to a,, and since in general they mix only insignificantly or not at all with singly excited configurations they give rise to states that cannot be observed by one-photon spectroscopy. These high-energy configurations are therefore disregarded in the following discussion. The remaining four configurations are singly excited and depend in a complicated manner on the configurations of the unperturbed system. If the molecule still contains a mirror plane perpendicular to the molecular plane after the perturbation, these configurations interact only in pairs and yield two low-lying minus combinations N l and N, and two higher plus combinations P, and P,, similar to the L and B states of aromatic compounds. Intensities of G+N transitions are low, due to mutual cancellation of contributions from the two configurations contributing to the excited state. Intensities of the G+P transitions are high, due to their mutual reinforcement. Since transition momen$ of the interacting configurations are parallel, the corresponding N and P

100

ABSORPTION SPECTRA OF ORGANIC MOLECULES

transitions have the same polarization direction. Both N and P transitions are polarized along lines that both pass through either opposite atoms or bonds. A distinction between a and b transitions as in the case of (4N+2)electron perimeters is therefore not possible. For charged 4N-electron perimeters the degeneracy of the ground state is lifted by perturbations. The phase angles are not multiples of 1~12;hence a classification of perturbations as even or odd is not possible. Figure 2.20~ shows how the energies of the states G, S, and D depend on the perturbation strength Isl. The energy order for unperturbed charged perimeters at Is1 = 0 is typical for perfect axial biradicals. (See Section 4.3.2.) The classification into N and Pas well as the ordering and the polarization of the excited states is analogous to that of systems derived from uncharged 4N-electron perimeters. These results are important because quinones (26), for instance, can be viewed as derivatives of doubly positively charged 4Nelectron perimeters.

The results for all cyclic nonaromatic systems are summarized again in Figure 2.22. Perturbations that affect the diagonal elements (e.g., heteroatom replacements) shift the HO, SO, and LU levels that are shown for the

2.3

W I C A L S AND KAL)ILAL IONS OF ALI CKIUAUI

;

..................

101

general case. Uncharged 4N-electron perimeters are alternant hydrocarbons, and their HO and LU levels are arranged symmetrically with respect to &(SO). Off-diagonal perturbations (e.g., bond-length alternation) split the orbital levels by AH, AS, and AL, respectively. Cross-links can affect both diagonal and off-diagonal elements. The transitions denoted by O and @ correspond essentially to the G-S transition and to the G-D transition, respectively. The latter is a two-electron transition and is therefore expected to be of relatively high energy and very low intensity. The transitions denoted by 0-0correspond to the N and P bands.

2.3 Radicals and Radical Ions of Alternant Hydrocarbons Radicals with an odd number of electrons can be either uncharged odd hydrocarbons or radical ions of even hydrocarbons or systems derived from such hydrocarbons. Of special interest are the relationships that exist for radicals and radical ions of alternant hydrocarbons. Figure 2.23a gives a schematic representation of the frontier orbital energy levels of an uncharged odd alternant hydrocarbon. It is seen that

LUMO

- - SOMO hom*o

- El,

+q,

€1

+- +++ + + $- + St+ +++ 200.1. 201*0

E (SO)

t I 1L ) I I U C ~ ~ U I U ~

,-,.2@:-,.4@,*,.

Is. I.... , , * , 6 1 b

_..........

+.! .......... ~ L U M O

6F..... . .

€hom*o

F i r e 2.22. Schematic representation of the perturbation-induced shifts and splittings of the degenerate orbitals of 4N-electron perimeters. The indicated transitions correspond to the main contributions to the observed absorption bands; the broken arrows symbolize the double excitation 0 (adapted from Haweler et al., 1989).

Figure 2.23. Odd alternant hydrocarbon radicals: a) Schematic representation of the frontier orbital energy levels and of the various configurations that are obtained by single excitations from the ground configuration cPO' (It should be remembered that spin eigenstates cannot be represented correctly in these diagrams.) b) Energies of these configurations and effect of first-order configuration interaction.

-..,

the two transitions that may be referred to as hom*o+SOMO and SOM&LUMO transitions and that produce the doublet configurations o,@2 and 2@,,., respectively, are degenerate for alternant hydrocarbons. In contrast to closed-shell systems, there are no higher multiplicity transitions that correspond to these lowest-energy excitations. The H O M b L U M O transition is the first one for which a quartet configuration is possible, in addition to two doublet configurations. One of the doublet is obtained from the ground configuration only by configurations, ,.,;@2 flipping the spin of one of the electrons during the excitation. The transition moment between the ground configuration and this configuration therefore vanishes by the spin selection rule. (Cf. Section 1.3.2.) Figure 2.23b shows the expected energy diagram, including electron repulsion effects. The configurations that correspond to the hom*o+SOMO and the S O M b L U M O excitation are split into 2qIr_ and +!4'2 states by firstorder configuration interaction, familiar from even alternant systems. The components of the transition moment from the configurations 0,@2 and 2@, either mutually cancel or reinforce, so the longer wavelength transition is forbidden whereas the other one is allowed. In agreement with these expectations the absorption spectrum of the benzyl radical shows a weak band near 450 nm and a strong band near 300 nm (Porter and Strachan, 1958). Calculations for the ally1 radical suggest that the quartet state is located between the 2qIr_ and 2q+states as indicated in Figure 2.23. At which

Figure 2.24. Orbital energy levels of alternant hydrocarbon ions: a) anions and cations of odd-alternant systems. and b) radical anions and radical cations of evenalternant systems in the HMO approximation and c) in the PPP approximation.

IWL)IL,iLb /\IVL, IG\LJICAL IONS OF ALTERNANT HYDROCARBONS

103

energies the states arising from,,,2@ and ,,,@ are to be found in larger systems is not yet entirely settled. The most characteristic feature in the spectra of ions from odd alternant hydrocarbons as well as from radical ions of even alternant hydrocarbons is the fact that the spectra of the anions and the cations should be identical as long as the pairing theorem is valid. (Cf. Koutecky, 1966.) At the level of the HMO model this is immediately evident from the orbital energy scheme in Figure 2.24. McLachlan (1959) has shown that at the PPP level of approximation the pairing theorem for positive and negative ions has to be modified. The bonding and antibonding MOs of any one radical ion are not paired; rather the bonding MOs of the radical cation are paired with the antibonding MOs of the radical anion and vice versa, as depicted in Figure 2.24~.such

700

500

LOO

300

250

Figure 2.25.

Absorption spectra of the radical anion (-)

and the radical cation (. - .) (by permission

(---I of tetracene in comparison with the spectrum of tetracene from DMS-UV-Atlas 1966-71).

' I

104 j

ABSORPTION SPECTRA OF ORGANIC MOLECULES

systems are called mutually paired. As a consequence the identity of the absorption spectra of an anion and a cation of an alternant hydrocarbon is retained when electron interaction terms are included in the model. It can be seen from the spectra of the tetracene radical anion and cation shown in Figure 2.25 that this result is in remarkably good agreement with experiment.

LUMO

hom*o

2.4I Substituent Effects ' \ I . * h

Most organic compounds that show absorption in the visible or in the nearUV region have a linear or cyclic n system as the chromophoric system. Therefore, the results of the previous sections may be used and extended to discuss light absorption of all those compounds that can be derived from linzar and cyclic hydrocarbons by including the influence of substituents in an appropriate way. (Cf. Michl, 1984.) A complete theory of substituent effects comprises all areas of organic chemistry. Here, only the fundamental concepts of the influence of inductive and mesomeric substituents will be considered. In order to simplify the discussion, substituent effects will be called inductive if in the HMO model they can be represented by a variation of the Coulomb integral a, of the substituted n center p. If they are due to an extension of the n system they will be called mesomeric.

2.4.1 Inductive Substituents , and Heteroatoms The replacement of a C atom in a conjugated system by a heteroatom such as N may be considered the simplest example of a purely inductive substituent effect. The influence on the orbital energies may then be estimated by first-order perturbation theory using the relation = ciiSa,

(2.19)

For alternant hydrocarbons ci, = c:,. for all p, and there is no first-order energy change for the H O M h L U M O transition, as is apparent from Figure 2.26. This result is remarkably well confirmed by the absorption spectra of naphthalene, quinoline, and isoquinoline shown in Figure 2.27. For nonalternant hydrocarbons, however, a bathochromic or a hypsochromic shift may result, depending on the absolute magnitude of the LCAO coefficients of the hom*o and LUMO. This is also shown in Figure 2.26 and is clearly illustrated by the absorption spectra of azulene, 4-azaazulene, and 5-azaazulene, given in Figure 2.28. =As-, etc., If a C atom is replaced by groups such as =SiH-, =P-, the relation

Figure 2.26. hom*o and LUMO of naphthalene and azulene together with the orbital energy changes 6~,,,, and SE~,,,, calculated by first-order perturbation theory for a purely inductive substituent S.

has to be used instead of Equation (2.19). The sum runs over all bonds p-v connected to the replacement center p and takes into account the reduction of the resonance integrals /?, that , is to be expected for bonds between carbon and elements of the third or lower rows of the periodic table. The effect of both terms in Equation (2.20) is illustrated in Figure 2.29 for the replaceIt is seen that the variation d/? decreases the ment of =CH- by =SiH-. = E,,,, - E,,,,. This results in an apprehom*o-LUMO separation ciable bathochromic shift of the 'L, band in going from benzene to silabenzene and 1,4-disilabenzene, as can be seen from the absorption spectra shown in Figure 2.30. While first-order effects of purely inductive substituents on excitation energies of alternant hydrocarbons vanish, higher-order perturbation theory gives nonzero contributions. Thus, Murrell (1963), using second-order perturbation theory, derived the relation

h [nml

2.4

LOO

SUBSTITUENT EFFECTS

Aa: U

Aa:0 AP: 4

Figure 2.29. First-order effects of one-electron heteroatom replacement on frontier orbital energies of a (4N+ 2)-electron annulene; a) for N as an example of an electronegative second-row element (da, < 0, a&,= 0) and b) for Si as an example of an electropositive third-row element (&, > 0, 64, > O).The effects of change in electronegativity 6a are shown as white vertical arrows (by permission from Michl, 1984).

Figure 2.27. Absorption spectra of naphthalene, quinoline, and isoquinoline (by permission from DMS-UV-Atlas 1-71). 800 1

700

600

A Inml 500

LOO

300

200

Figure 2.28. Absorption spectra of azulene. 4-azaazulene. and 5-azaazulene (by permission from Meth-Cohn et al.. 1985).

Figure 2.30. Absorption spectra of benzene (. ..), silabenzene (---), and 1.4-disilabenzene (-) (by permission from Maier. 1986).

108

ABSORPTION SPECTRA OF ORGANIC MOLECULES

for the substituent effect on the energy of the excited state. Here, Hik = is the matrix element of the perturbation between the state wave functions 'Piand 'Pkin the case of a monosubstituted benzene. The B,&) are constants depending on the number and relative positions of substituents g and are derived from group theoretical arguments. It follows that the shift of the benzene 'L, band can be written as

2.4

SUBSTITUENT EFFECTS

109

Table 2.4 Substituent Effects on the Intensity of the 'L,Band of Benzene Substitution Pattern

Intensity Enhancementa

Substitution Pattern

Intensity Enhancementa

Multiples of the value (Ahom*o)? = (1/36ax)' for monosubstitution by a group X.

where nA represents a perturbation that is proportional to the number n of substituents and the constants I, and 6 depend on the substitution pattern and on the nature of the substituents, respectively. A relation of this type derived from experimental data was first proposed by Sklar (1942). The intensity of the 'L, band arises essentially from a substituent-induced interaction with the 'B, state. This can be envisaged by means of the perimeter model as follows. Purely inductive substituents give rise to even perturbations; from Figure 2.16 it is seen that in this case the only interaction is between configurations X and V [see Equation (2.12)] and is given by (la1 + lbl) = (Ahom*o + ALUM0)/2. To first order in perturbation theory, this is equal to Ahom*o. To a first approximation, the amount of the configuration X that is mixed into the 'L, state is therefore proportional to Ahom*o. This contribution causes the intensity increase of the 'L,band due to purely inductive substituents. Since the intensity is given by the square

...... .......

Ahom*o ....... .....

of the transition moment, it should be proportional to (Ahom*o)*.Ahom*o can be determined quite easily from Equation (2.13) by means of the LCAO coefficients of the real MOs @s and @, of Equation (2.15). This is illustrated in Figure 2.31 for substitution in position 1 as well as in positions 1 and 2 of benzene. Depending on the substitution pattern, the perturbation produces the MO order @, @, @,., @, or @, @, @,. @,. The intensity enhancements obtained from these arguments for various substitution patterns are collected in Table 2.4. The polarization direction of a transition depends on the location of the nodal planes of the orbitals involved in the excitation. As the introduction of perturbations may influence the location of the nodal planes, the effect of several simultaneous perturbations may change the polarization directions accordingly. The cross-linking that produces naphthalene from the perimeter causes the 'L, and 'La bands to be polarized along the long axis and the short axis of the molecule, respectively. Heteroatom replacement in a (4N + 2)electron perimeter results in every MO having either a node or an antinode at the position of the heteroatom. (See Figure 2.29.) Since both the hom*o and LUMO of naphthalene have an antinode in position 1 (Figure 2.26) whereas the adjacent MOs below the hom*o and above the LUMO have a node in this position, there is no change in the polarization direction going from naphthalene to quinoline. The polarization directions of the 'L, and 'L, band remain mutually perpendicular. However, the situation is different for isoquinoline, where the location of the nodal planes required by cross-linking and by heteroatom replacement do not coincide. In all four naphthalene MOs of interest, the nodes and antinodes are equally far removed from position 2. In this particular case the effect of the aza group is sufficiently strong to dominate the location of the nodal plane. Hence, the polarization directions of the 'L, and 'L, transitions are nearly parallel (Friedrich et al., 1974).

2.4.2 Mesomeric Substituents Figure 2.31. The effect of purely inductive substituents in position 1 (on the left) and in positions 1 and 2 (on the right) on Ahom*o and ALUM0 of benzene (adapted from Castellan and Michl, 1978).

Mesomeric substituents possess orbitals of IC symmetry and can therefore extend the conjugated system. Benzene substituted by a donor with a doubly occupied p A 0 or substituted by an acceptor with an empty p A 0 is isoelec-

110

ABSOKI"1'ION SI'ECI'IM OF ORGANIC MOLECULES

tronic with the benzyl anion or benzyl cation. respectively, for which the nonbonding MO is either the hom*o or the LUMO, respectively. (See Figure 2.24a.) A substituent may also possess several orbitals which, depending on their occupancy, may have different donor and acceptor properties. The substituent effect on the hydrocarbon MOs may again be estimated by perturbation theory. However, it has to be remembered that first-order contributions vanish according to Slf =

a&: = cE.c;pp

(2.23)

unless the orbitals r#f of the hydrocarbon R and c#$ of the substituent S are nearly degenerate. In the general case second-order perturbation theory has to be applied and the relation

has to be used, which requires special precautions if r#f and & are nearly degenerate. 6# in Equation (2.24) depends not only on c& but also on the quantity as well as on (lf - .$). It is therefore not possible to characterize the mesomeric effect by a single substituent strength. In fact, depending on lf the same substituent can act as a donor with respect to one hydrocarbon and yet as an acceptor with respect to another one if it possesses occupied as well as unoccupied orbitals. An example is provided by the vinyl group with its nand JPorbitals, which acts as an acceptor when attached to the CsHs@ anion and as a donor when attached to the C7H7@cation. For spectroscopic applications it has proven very useful to characterize the mesomeric effect of particular substituents with respect to an alternant hydrocarbon by the way in which they affect the energy differences Ahom*o and ALUMO between those orbitals, which in the unperturbed (4N + 2)-electron perimeter are the degenerate highest occupied and lowest unoccupied MOs, respectively. A substituent is referred to as a n donor or + M substituent, if Ahom*o > ALUMO, and as a n acceptor or - M substituent, if Ahom*o < ALUMO.* If Ahom*o = ALUMO, for instance when a vinyl substituent is attached to benzene, the n electron-donating ability and the n electron-withdrawing ability exactly compensate each other in their net effect. In most instances this definition of donors and acceptors agrees with those based on the measurements of other properties, such as the amount of charge transfer between the substituent and the ring in the

2.4

111

SUBSfITUENT EFFECTS

ground state as measured by the n-electron contribution to the dipole moment or by NMR chemical shifts (Michl, 1984). If a substituent possesses only one p orbital which in most cases is doubly occupied as in -NH, or --OH, Equation (2.24) is simplified and becomes

since c2 = 1. The interaction of the substituent with the n system will then be characterized by two substituent parameters: the energy of the p, orbital E; and the resonance integral pp,. The relative importance of the two factors will depend on the choice of the hydrocarbon to which the substituent is attached; while the effect of a change in pp is simply multiplicative and is the same for all perimeter MOs, the effect of the variation in the energy difference (E;R - E:) in the denominator is different for each perimeter MO depending on its energy E;R. The distinct effect of nominator and denominator in Equation (2.25) on the frontier orbitals @u, @,, @a,, and I$,, of a (4N 2)electron perimeter is illustrated in Figure 2.32. Halving the resonance integral /3, halves both Ahom*o and ALUMO and the substituent becomes a weaker donor (Figure 2.32b). Subsequent halving of the separation AE = E;R - E; between the energies of the donor orbital & and the hom*o $f = @, of the perimeter restores the magnitude of Ahom*o but hardly affects the more distant r#f = @., and ALUMO (Figure 2.32~).Thus, in the first and the last cases [a) and c) in Figure 2.321 the difference Ahom*o - ALUMO is of comparable magnitude and according to the definition given above the sub-

-.....

:.........:... i . ALUMO

* According to Dewar (l%9) a n donor is referred to as - E substituent and a nacceptor

as + E substituent. This is the sign convention originally introduced by Lapworth and Robinson. Here, we use the opposite sign convention, which was proposed later by Ingold.

Figure 2.32. Effect of a + M substituent S with one n orbital only o n the energies of the frontier orbitals of a (4N + 2)-electron perimeter for different values of the parameters 8 and AE; a) 8, AE, b) 812, AE, and c) 812, A d 2 , (adapted from Michl, 1984).

112

ABSORPTION SPECTRA OF ORGANIC MOLECULES

stituents possess a similar + M effect. On the other hand, in the second and the third cases [b) and c) in Figure 2.321 ALUMO is comparable and the substituents have equal donor strength if measured by the amount of charge transferred into the ring. For alternant hydrocarbons c&, = c&,,and E, = a + x,B with x,. = - xm, so from Equation (2.25) the change 6AE of the HOM-LUMO excitation energy is seen to be

2.4

SUBSTITUENT EFFECTS

113

lated to be at 214 + (2 x 5) + 5 = 229 nm, as compared to the experimental value A, = 231 nm. Similarly, the values calculated for the steroids 28 and 29 are A, = 253 + (4 x 5) + (2 x 5 ) = 283 nm and 214 + (3 x 5) + 5 = 234 nm, respectively, again in excellent agreement with the experimental data (282 nm and 234 nm, respectively). Similar rules for estimating the absorption maxima of unsaturated carbonyl compounds have been proposed by Fieser et al. (1948); see Table 2.6.

Table 2.6 lncrement Rules for Enone Absorption (Adapted from Scott, 1964)

if the substituent orbital is lower in energy than the hom*o, that is, if x, > x,; if x, < x,, x, in the nominator has to be .replaced by - x,. In any case, the mesomeric effect always produces a bathochromic shift and is additive for individual substituents, as long as no new rings are being formed and the change of the coefficients (;,, due to substituents can be neglected. Example 2.9:

The discussion given earlier for weak mesomeric effects offers an explanation for the empirical increment rules proposed by Woodward (1942) for estimating the absorption maxima of dienes and trienes. The distinct values for the hom*oand heteroannular arrangement of the double bonds illustrate the configurational influence on the polyene spectra that has been discussed in Example 2.2. From the data collected in Table 2.5 the absorption of methylenecyclohexene (27) with an exocyclic double bond and two alkyl substituents is calcu-

Table 2.5 Increment Rules for Diene Absorption (Adapted from Scott, 1964)

Acyclic 217 nm

hom*oannular 253 nm Increments for: Double bonds extending conjugation Exocyclic double bond Alkyl group, ring residue 0-alkyl Polar groups: 0-ac y l S-alkyl N(alkyl), CI Br

Heteroannular 214 nm

207 nm

215 nm

193 nm

Increments for: Double bonds extending conjugation Exocyclic double bond hom*odiene component a y Substituents in

R CI Br OH OR OAc N R,

10 I5 25 35 35 6

12 12 30 30 30 6

17 6

+ 30 nm + 5 nm + 39 nm 6

position

18 50 31 6

In general, substituents are neither purely inductive nor purely mesomeric; rather they possess some inductive as well as some mesomeric character. From Equations (2.19) and (2.24) it is seen that inductive as well as mesomeric effects on the hom*o and LUMO are proportional to the square ci of the LCAO coefficient at the substituted center g. It is therefore difficult to differentiate between these two effects from the absorption spectra. This is possible, however, by means of the MCD spectra that depend essentially on the difference Ahom*o - ALUMO. (Cf. Section 3.3.) In the case of uncharged (4N + 2)-electron perimeteri and especially benzene, perturbations due to purely inductive substituents always yield Ahom*o = ALUMO to first order in perturbation theory. Due to the energy difference in the denominator of Equation (2.24). however, Ahom*o and ALUMO can be quite different in the case of mesomeric substituents, depending on the energy

114

ABSOKIyI'ION St'EC'fKA OF ORGANIC MOLECULES

2.4

SUBSTITUENT EFFECTS

of the substituent orbital, as has been demonstrated in Figure 2.32. By correlating the MCD spectra with the difference Ahom*o - ALUMO, it could be shown that hyperconjugation is most important in describing the substituent effects of methyl groups, so that for spectroscopic purposes the methyl group is best considered as a mesomeric substituent. (See Example 3.10.) Example 2.10: In nonalternant systems, (c;,,, - c:.,~) can be positive or negative, depending on the position g. Purely inductive substituents can therefore produce a shift of the HOM-LUMO transition to higher or lower energies. In this way, the spectra of methyl-substituted azulenes, for instance, have been analyzed assuming an essentially inductive substituent effect of the methyl group (Heilbronner, 1%3). Displacements of the longest-wavelengths band calculated from Equation (2.19) are compared with experimental values in Table 2.7 and give a satisfactory agreement. If, on the other hand, the substituent effect of the methyl group is assumed to be essentially hyperconjugative, the displacements have to be estimated from Equation (2.25), using appropriate values for the energy difference in the denominator. Assuming that (E,., - E,) is approximately twice the size of (E,,,, - E,). one obtains the values given in the last column of Table 2.7. The agreement with experimental data is even better, especially for 6-methylazulene. Table 2.7 Observed" and CalculatedbSubstituent Effect in Methyl-SubstitutedAzulenes AiJ,">,. Substitution

I-Methyl2-Methyl4-Methyl 5-Methyl 6-Methyl

v,,

17.240 16,450 17,670 17.610 16,890 17.700

Experiment 0 - 790 + 430 + 370 - 350 + 460

Effect

0 - 944 + 106 t 154 ( - 350) + 288

+ M Effect 0

- 958 + 163 278 ( - 350) + 428

Figure 2.33. Schematic representation of the highest occupied n MOs a) of aniline and b) of dimethylaniline (adapted from Kobayashi et al., 1972).

A very strong mesomeric effect is present in aniline (30). From the photoelectron (PE) spectra it is known that the highest occupied M O is largely localized in the benzene ring, whereas in dimethylaniline (31) it is more concentrated on the nitrogen. Thus, it follows that the p, orbital energy of the amino group is very close to the energy of the degenerate JC MOs of benzene (see Figure 2.33) and that the longest-wavelength transition of dimethylaniline should have a strong intramolecular C T (charge transfer) contribution.

After Heilbronner. 1%3. Calculated from Equations (2.19) and (2.25). respectively, using AG = -350 cm-' for S-methylazulene as reference value.

The more pronounced the n donor strength of a substituent, the greater will be its contribution t o the hom*o of the substituted molecule. Excitation from such an orbital into an MO essentially localized in the perimeter will therefore be associated with a charge shift from the substituent into the ring and will thus possess partly some 'La and partly some C T (charge transfer) character. (Cf. Section 2.6.) For a high-lying substituent orbital &, the mixing with the perimeter MOs & and @,, can be of comparable importance.

Perturbation theory is also applicable to substituents with a strong mesomeric effect, but it is t o be expected that results gradually become less reliable a s the substituent strength increases. Two main models have been proposed for the analysis of strong substituent effects in molecules such a s aniline (Godfrey and Murrell, 1964). The localized orbital model makes use of the n MOs of benzene and the p, orbital of the amino group. (Cf. Figure 2.33.) The energy of the intramolecular C T transition may be estimated from the I P of the donor (10.15 eV for aniline), the EA of the acceptor orbital ( - 1.6 eV for benzene), and the Coulomb interaction J between the positive charge at the substituent and the charge distribution on the acceptor. For

116

ABSORPTION SPECTRA OF ORGANIC MOLECULES

2.4

SUBSTITUENT EFFECTS

the degenerate MOs @4 and cp5 of benzene and a C-N distance of 146 pm one obtains the following values for J:

h Inml LOO

300

250

log E

The CT transition is therefore expected to have a transition energy of 3

and should be found at shorter wavelengths than the 'L, band of benzene (4.75 eV). The 'L, band is polarized perpendicular to the long axis of the molecule, the CT band parallel to this axis. The second model makes use of the fact that aniline is isoelectronic with the benzyl anion. From the HMO coefficients it can be seen that the longestwavelength transition from the doubly occupied nonbonding MO into the lowest antibonding MO is polarized perpendicular to the long axis of the molecule. The transition into the following antibonding MO is polarized parallel to this axis. While both transitions are forbidden in the localized-orbital model, oscillator strengths off = 0.15 and f = 1.05, which are much larger than the experimental values, are calculated from the isoconjugate hydrocarbon model. The data collected in Table 2.8 show that the observed oscillator strengths lie between those estimated from the two models. The same is true for the excitation energies and for the ground- and excited-state dipole moments. Both models can be extended. The localized orbital model is improved by allowing for the interaction between the locally excited benzene states and the CT state, and the isoconjugate hydrocarbon model is improved by taking into account the electronegativity change upon the replacement of the C atom in the benzyl anion by an N atom in aniline. Good agreement with experiment is obtained in both cases. Both models are useful, but the localized orbital model has the advantage that it is more easily extended to more complicated molecules. The C1 Table 2.8 Comparison of Different Models for Estimating the Substitwnt Effect in Aniline (Adapted from Murrell, 1963) 1st Excited State

2nd Excited State

Model

Ground state: p(D)

AE(eV)

p(D)

AE(eV)

p(D)

Benzyl anion Localized orbital Experiment

5.76 0 1.02

2.18 4.71 4.35

0.15 0 0.03

13.44 0 6.0

3.87 5.75 5.30

1.05 0 0.17

9.74

4.44

Figure 2.34. Comparison o f the absorption spectra o f various monosubstituted benzenes (by permission from DMS-UV-Atlas, 1966-71).

method based on this model is also known as the MIM (molecules-in-molecules) method of Longuet-Higgins and Murrell (1955). Using energies of locally excited states of fragments and of charge-transfer states, as well as the interactions between these states, the spectra of complex molecules can be calculated by means of the MIM method as shown for aniline composed of the fragments benzene and ammonia. In Figure 2.34 the spectra of some monosubstituted benzenes are shown. From these spectra it is evident that there is a continuous change from a weakly perturbed benzene spectrum to a strongly perturbed one, such as that of aniline. Example 2.11: It is possible to draw Kekule structures a s well a s polar quinoid resonance structures for isomeric disubstituted benzenes with a donor and an acceptor

300

ABSOKI'I ION SI'CC 1 KA Ot C)KC;ANIC MOLECULES

275

A lnml ,250

225

200

2.5

MOLECULES WITH w n * TRANSITIONS

119

addition to n-n* transitions, molecules with the latter type of heteroatoms may therefore exhibit also n-n* transitions from a doubly occupied n orbital into a n* orbital. The most important classes of compounds with n-llr transitions are carbonyl compounds, azo compounds, and nitrogen heterocycles.

2.5.1 Carbonyl Compounds The simplest example of a carbonyl compound is formaldehyde. Like the spectrum of ethylene, its spectrum is not yet completely understood, in spite of many elaborate investigations. Only one of the transitions that are t o be expected from the orbital energy level diagram shown in Figure 2.36 has been observed in the accessible region of the spectrum, namely, the transition from the ground state into the 'A,(n, n*)state. The 3A,(n, llr) and

Comparison of the absorption spectra of isomeric benzenes with one donor and one acceptor substituent (by permission from Grinter and Heilbronner, 1%2).

Figure 2.35.

group in the o- or p-position to each other, whereas for the m-derivative only Kekule structures are possible. Thus, one could expect that the spectra of the o- and p-derivatives would be very similar, and that the m-derivative should absorb at shorter wavelengths. From Figure 2.35 it is seen, however, that this expectation is not confirmed by experiment. Quantum chemical calculations also give a higher transition energy for the p-derivative and similar energies for the o- and m-derivatives, in agreement with experimental observation (Grinter and Heilbronner, 1%2). This example emphasizes that caution is necessary in discussing excited states on the basis of just a few resonance structures.

2.5 Molecules with n-+# Transitions Many heteroatoms carry lone pairs of electrons. Sometimes these are of n symmetry and form a part of the conjugated system. a s in aniline (Kasha's I electrons). but in other cases their symmetry is a (Kasha's n electrons). In

Figure 2.36. Orbital energy level diagram of formaldehyde and qualitative contour diagrams of some MOs.

120

AaSORPTlON SPECTRA OF ORGANIC MOLECULES

3A1(n,11')states can be detected under special conditions. According to calculations of Colle et al. (1978) the IA,(n, 11')state is dissociative, and this may be the reason why it has not yet been observed. The n+fl transition in the 230-253-nm region has been studied in detail. From vibrational analysis it follows that the CO bond is lengthened from 120.3 pm in the ground state to 132 pm in the IA,(n, n*) state, while the CH, group is bent out of the molecular plane by 25-30'. (Cf. Table 1.4, Section 1.4.1 .) The barrier to inversion is small and gives rise to a prominent inversion doubling with 5 = 356 cm-I (Moule and Walsh, 1975). The extinction coefficient, E = 20, is very small. The low intensity is typical for most ~ 1 1transitions ' of carbonyl compounds and can be explained on the basis of the local symmetry. In the case of formaldehyde, which has C,, symmetry, an electronic transition from the n orbital (b,) into the 11'MO (b,) is dipole forbidden. This is no longer true for carbonyl compounds of lower symmetry such as acetaldehyde (C,). Here the n orbital is still essentially of p character, so that the overlap density is approximately p:p, and still has practically no dipole moment. An intensity enhancement has been observed for B,y-unsaturated carbony1 compounds such as 32, which is due to R-n interactions in the nonplanar system of reduced symmetry (Labhart and Wagniere, 1959). In the series of polyene aldehydes, A,, of the n-fl transition increases with in-

2.5

creasing number of double bonds faster than that of the n-11' transition (see Figure 2.37), so that the PT* band becomes swamped by the more intense ~ c - band * ~ if the conjugated chain gets long enough. (Cf. Das and Becker, 1978.)

Example 2.12:

In glyoxal and other dicarbonyl compounds the lone-pair orbitals n, and n? at the two carbonyl groups can interact. This results in orbital splitting that can be observed in PE spectra (Cowan et at., 1971). Either the combination n, = (n, - n,) or n, = (n, + n,) is higher in energy, depending on whether throughspace or through-bond interactions dominate. The data collected in Table 2.9 show the close relationship between the energies of the orbitals n, and n,, which are given by Koopmans' theorem as E~ = - IP,, and the wave number of the longest-wavelength transition in the absorption spectrum. Azo compounds also have two lone pairs of electrons that can interact through space or through bond. Azomethane 33 (R = CH,) has been studied in detail. In the cis form 33a the n, orbital is below the n, orbital and the n,+n* transition at 353 nm is allowed, E = 240. In contrast, the energy order of the n orbitals is reversed in the trans compound 33b, as is to be expected from the negative overlap of the sp2-hybridizedn orbitals. The n p n * transition at 343 nm is therefore symmetry forbidden, as is seen from the value E = 25 (Haselbach and Heilbronner, 1970). For azobenzene 33 (R = Ph) the corresponding

Table 2.9

PE and W M S Data of Dicarbonyl Compounds

Compound

IP(n,)

10.41

10.1 I f

499'

Turner ct al.. 1970. Arnett et al., 1974.

Cowanetal.. 1971. Figure 2.37. Absorption spectra of polyene aldehydes (by permission from Blout and Fields. 1948).

121

MOLECULES WITH w n * TRANSITIONS

' *

Gleiter ct al., 1985. Martin el al., 1978. l.;nlrr ct i l l . . 1975. b1:11ti11 :III,! W:I,II ION'

V ,,

20,000

2.6

data are A = 430 nm ( E = 1.500) for the cis compound and A = 440 nm 500) for the trans compound (Griffiths, 1972).

2.5.2 Nitrogen Heterocycles Whereas for the aza analogues of benzene and naphthalene the n-n* transitions can be observed as separate bands or as shoulders on the n+n* transitions, they are usually hidden by n+n* transitions in higher aromatics. They are about ten times as intense as the n-n* bands of carbonyl compounds since the n orbital is sp2 hybridized, and the intraatomic transition moment, which depends on the s character of the nonbonding orbital, no longer vanishes. The n+n* band is shifted to longer wavelengths as a larger number of nitrogen atoms are introduced into the molecule (Table 2.10). This is due to two factors: the n* orbital is lowered in energy by the nitrogen replacement, and the n orbitals can interact through space and through bonds. From firstorder perturbation theory, the stabilization of the n* MO is seen to be proportional to the sum of the squares Xcii of the LCAO coefficients of all nitrogen positions p. If allowance is made for an additional bathochromic shift

Table 2.10 w n *Absorptions of Some Aza Derivatives of Benzene and Sum of the Squared HMO Coefficients of the hom*o at Positions p of the Nitrogens; as Most wd Absorptions Show Up in the Spectra Only as Shoulders of the n+n* Bands, Their Location has been Characterized by the Wave Number V ( E = 20) for Which the Extinction Coefficient is E = 20 (Adapted from Mason, 1962) t(&= 20)

Compound Pyridine (34) I'yridazinc (35) Pyrimidine (36) Pyrazine (37) syr~r-Triazine(38) sy~n-Tetrazine(39)

Position p

(cm '1

Ccihom*o P

34,500 26.600 30,600 29,850 3 1.500 17.100

0.333 0.500 0.500 0.667 0.500 1 .OOO

2.3 2.6 l,4 1.3.5 2. 3. 5 . 6

SYSTEMS WITH CT TRANSITIONS

123

of approximately 6,000 cm - ' for two nitrogen atoms adjacent to one another, allowing their n orbitals can interact strongly as described in Example 2.12, a good proportionality between theoretical expectations and experimentally observed bathochromic shifts is obtained.

The extent of the n orbital interactions can again be determined experimentally using PE spectroscopy. It has been shown that in most cases the IPS corresponding to the n orbitals are higher than those of the highest occupied n MO (Brogli et al., 1972). The fact that the n-n* transitions are nevertheless observed at longer wavelengths than the n+-n* transition may be due to the exchange integrals that co-determine the singlet-triplet separation. Like the transition intensity, these exchange integrals depend on the overlap density @,&, , and K,. < K.,

2.6 Systems with CT Transitions Solutions of a mixture of an electron donor D, such as hexamethylbenzene (40). and an electron acceptor A, such as chloranil (41), often exhibit an

absorption band that is not present in solutions of the pure components. This band has been assigned to an electron transfer from the donor to the acceptor and is therefore referred to as a donor-acceptor or a CT (charge transfer) transition. Mulliken (1952) has developed a theory of CT transitions which can be summarized as follows: If the ground configuration and the polar configuration produced by electron transfer are described by wave functions 4 ,, and 4,,,, respectively, the interaction of these two configurations yields a weakly stabilized ground state and an excited state where A and p are small compared with I . The CT absorption is then associated with a transition from the ground state Tointo the excited state q,.

124

ABSORPTION SPECTRA OF ORGANIC MOLECULES

Under the assumption that the ZDO approximation is valid for an MO description of the components, the excitation energy of the CT band is easy to estimate. For the transition of an electron from the hom*o of the donor into the LUMO of the acceptor

= E W , ) - E(*o) =

~ U M O

GOMO - C = IPD - EAA - J

+ 2K

(2.30)

where IP, is the ionization potential of the donor, EAAthe electron affinity of the acceptor and C = J the electrostatic interaction between the ions formed by electron transfer. The exchange term K is nearly equal to zero due to the small value of the overlap density. Experimentally, CT transitions may be identified by their broad band shape devoid of vibrational fine structure, and by the sensitivity of their wavelength to the polarity of the solvent, which is to be expected from the highly polar nature of the excited state. (See Section 2.7.) The band shape may be explained by the fact that the binding energies are usually rather small and the minima on the ground-state potential energy surface correspondingly shallow, so in solution many different configurations of the complex exist in equilibrium with one another. Also, the equilibrium intermolecular separations in the excited state undoubtedly are smaller than in the ground state, and the vibrational frequency for this motion is very low.

~amcyclophanesprovide the opportunity to fix the donor and acceptor molecules in a definite geometric structure in order to study the dependence of

donor-acceptor interactions on geometric factors. This concept has been pursued intensely by Staab et al. (1983). Figure 2.38 shows the spectra of the isomeric quinhydrones of the [3.3]paracyclophane series, in which the transannular distance of 310-330 pm is comparable to intermolecular donor-acceptor distances. For the psr~rdo-gc.minulcompound 42 the overlap density is large since the location of nodal planes is the same for the hydroquinone hom*o and the quinone LUMO, which are even identical to a first approximation. This compound exhibits a strong CT band near 500 nm. For the pseudo-ortho derivative 43, however, the overlap density is small due to dissimilar orientation of the nodal planes and the large distance of the oxygen atoms, where the LCAO coefficients of this MO are largest. Only a low-intensity shoulder for 43 is observed in this region, but an additional strong band appears near 360 nm, and has been assigned to a second CT transition.

For complexes combining different donors with the same acceptor a linear relation between the ionization potential IP, of the donor and the wave number of the CT band has been observed. (See Figure 2.39.) This correlation is much better than expected; it requires that the Coulomb term C is either constant or proportional to the donor ionization potential IP,. In many series the intensity of the CT band increases as the complex becomes more stable. This can be explained by using the wave functions L5

Acceptor: Trinitrobeniene

-m

8 -

Cy cl ohesene

Mesliylene Phenanthrene Naphthalene

I> OAnnl ine

30 -

7.0

Figure 2.38. Absorption spectra of isomeric [3.3]paracyclophane-quinhydrones in dioxane (by permission from Staab et al., 1983).

8.0 8.5 IP lev1

9.0

9.5

Figure 2.39. Relation between the wave number of the CT band and the ionization potential IP, of the donor for DA complexes with trinitrobenzene (adapted from Brieglieb and Czekalla. 1960; IPS from more recent PE data).

2.7

STERlC EFFECTS AND SOLVENT EFFECTS

given in Equation (2.28) and Equation (2.29) to calculate the transition moment which then becomes

Since the first integral vanishes if use is made of the ZDO approximation, the intensity is seen to be essentially due to the dipole moment of the polar CT configuration, and the transition moment is proportional to the coefficient A. But in reality the situation is much more complicated, as can be seen from the fact that the intensity can be markedly different from zero even in cases where the ground-state stabilization is very weak and A is therefore approximately zero. The reason may be that the wave functions Equation (2.28) and Equation (2.29) neglect locally excited states (Dewar and Thompson, 1966). Furthermore, it might be important, at least in cases of weak interaction, to take into account the overlap between donor and acceptor orbitals in calculating the transition moment from Equation (2.31). If a molecule consists of several weakly coupled chromophores it may be advantageous to speak of intramolecular CT transitions. The MIM method for calculating the absorption spectra of complex molecules, which has been mentioned in the discussion of substituent effects in Section 2.4.2, is based on this idea.

2.7 Steric Effects and Solvent Effects

Hypsochromic shift

Bothochrorn~cs h ~ f t

Hypsochromic and bathochromic shift due to steric hindrance; the white arrows indicate the steric strain and the black arrows the strain release by molecular deformations (twisting of bonds).

Figure 2.40.

ground state often have a high n bond order in the excited state, that is, a high double-bond character, the twisting is energetically less favorable in the excited state. Steric hindrance is therefore most often expected to result in a hypsochromic shift of the absorption band. (See Figure 2.40.) However, there are also molecules in which the steric strain can be relieved only by twisting formal double bonds. In this case then, the destabilization of the ground state is larger than that of the excited state, where the double-bond character of the bond to be twisted usually is weaker. This effect, which can be used to explain the longer-wavelength absorption of N,N-dimethylindigo (44, A, = 670 nm) compared to indigo (A,, = 610 nm) (Klessinger, 1978), is sometimes referred to as the Brunings-Corwin effect.

So far, the discussion has been confined to isolated planar n systems. However, intramolecular and intermolecular interactions, such as steric effects and solvent effects, may influence the spectra considerably. In this section, some examples are discussed as a review of some of the more important aspects of such effects.

2.7.1 Steric Effects Steric interactions between bulky groups may cause deformations of the geometric structure of a molecule. Of these, twisting of single bonds is by far the most important structural change. This is so because torsion around a single bond by 5" requires less than 0.2 kcdmol of energy, compared to the 4-8 kcallmol that is necessary for stretching a bond by I pm. (Cf. Rademacher, 1988.) Thus, in general steric strain in n systems is relieved by rotation around formal single bonds. This stabilizes the ground state with respect to the strained, untwisted system. Since bonds that have a low n bond order in the

The effect of bond twisting on the orbital energy first-order perturbation theory from the relation

may be estimated by

by allowing fiId6,, of the twisted bond to decrease in absolute magnitude or even to vanish (90"twist). E; becomes more positive if cPiand c, are of equal sign, and more negative if they are of opposite sign. For alternant hydrocarbons one of the paired MOs is always stabilized and the other one destabilized, and a hypsochromic shift of the HOM-LUMO transition results if the hom*o is antibonding in the twisted bond. If it is bonding in this bond, a bathochromic shift is produced. Both possibilities are illustrated in Figure

128

ABSORPTION SPECTRA OF ORGANIC MOLECULES LUMO

-..

-.~AE

2.7

STERIC EFFECT5 AND S ~ L V E ~EFFECTS T

129

some of the methyl derivatives substituted in positions 2 , 6 , 2 ' , and 6' shown in Figure 2.42. The 250 nm band of biphenyl provides an example of a hypsochromic shift with increasing steric hindrance due to a twisting of the central bond for which the hom*o is antibonding. Example 2.14:

hom*o F i 2.41. Effect of bond twisting on the hom*o and LUMO energies of biphenyl (twisting of a formal single bond) and biphenylquinodimethane (twisting of a formal double bond).

The symmetric cyanine dyes are isoelectronic with anions of odd alternant hydrocarbons. Because of bond equalization in these systems it is a reasonable assumption that steric hindrance will cause all bonds to rotate by roughly the same amount. To a first approximation, the energy of the hom*o will not be affected by such a twist as it is nonbonding in all bonds. Since the LUMO is predominantly antibonding, a uniform rotation of all bonds will lower its energy. Thus, steric hindrance in symmetric cyanine dyes is expected to cause a bathochromic shift, as has in fact been observed for the dyes 47 and 48 (Griffiths, 1976).

2.41, where a schematic representation of the hom*o and LUMO of biphenyl (45) and of biphenylquinodimethane (46) is given together with the change in orbital energies due to twisting of the central bond. The hypsochromic and bathochromic shifts that are t o be expected from these arguments are in very good agreement with experimentally observed changes in the spectra. This is demonstrated by the spectra of biphenyl and R = H R = CH,

A-

= 520 nm = 527 nm

R = H R = CH,

A-

= 604 nm = 640 nm

Merocyanine dyes and unsy rnmetrical cyanine dyes, however, have alternating bonds and exhibit in general a hypsochromic shift on steric hindrance; 49 is an interesting dye that, depending on the solvent, shows for R = CH, either a bathochromic or a hypsochromic shift with respect to the parent compound with R = H. This effect will be explained in the following section. (Kiprianov and Mikhailenko. 1991.)

2.7.2 Solvent Effects

The effect of steric hindrance by methyl groups on the absorption spectrum of biphenyl (by permission from DMS-UV-Atlas 1966-71).

Figure 2.42.

Light absorption by organic molecules may be influenced by the solvent through either specific o r nonspecific interactions between the solute and solvent molecules. In trying t o account for the effect of the solvent on the spectrum of a given molecule, one has to evaluate the change in the solutesolvent interaction upon excitation. This change may involve many factors such as dispersion, polarization, and electrostatic forces, and charge-transfer interactions. Dispersion forces are the weak London-van der Waals

130

AUSoI iequal s to the imaginary part of the the real vector M,, magnetic transition moment. The prediction of optical activity for a transition is therefore straightforward if the two transition moments are known. It vanishes if a least one of the transition moments is equal to zero or if both are nonzero but perpendicular to each other. This is always the case if an improper rotation axis S, is present. As already mentioned, optical activity cannot occur in molecules that belong to one of the corresponding point groups. Although the Rosenfeld formula looks very simple, it is by no means easy to predict the length and the relative orientation of the two vectors theoretically. The results are very sensitive to the quality of the wave functions Yo and Y,, and it is the wave function Y, of the excited state that is particularly difficult to calculate. In general, the CD spectrum is measured in the UV and the visible region; Y, is then the wave function of an electronically excited state. Recently, CD measurements in the IR region became feasible as well; Y, is then a vibrationally excited state. (Cf. Mason, 1981.) According to Moffitt and Moscowitz (1959) two classes of chiral molecules can be distinguished, that is: Molecules with an inherently chiral chromophore Molecules in which the chromophore is achiral but is located in a chiral environment within the molecule In both classes there may be molecules that contain two (or more) identical or similar chromophores in a chiral arrangement. For each of these cases a different theoretical method of computation has proven useful. It is possible to calculate, using, for example, the MO-CI method, Yoand qffor the complete molecule. Although this procedure can in principle be applied to every molecule, it is particularly suited for inherently dissymmetric chromophores. The method is very demanding as far as computing is concerned. Its main disadvantage, however, is that every molecule represents a special case, so each additional molecule requires a brand-new calculation. General trends or relationships between molecules in hom*ologous series are then difficult to recognize. For molecules with an achiral chromophore located in a chiral environment that is transparent in the region of the spectrum characteristic of the chromophore, it is advantageous to consider the effect of the chiral environment on the transition moments M, and M,, of the achiral chromophore

NATURAL CIRCULAR DlCHROlSM

147

as a perturbation of the localized wave functions Yo and Y, of the chromophore. An important example of such an achiral chromophore is the carbonyl group that occurs in a large number of chiral ketones. The complete mathematical description of the influence of a chiral environment on the optical activity of a chromophore is rather complex and contains, apart from possible inherent contributions, quite a number of contributions that may be divided into various groups that correspond to different "mechanisms" of inducing optical activity. The "one-electron" mechanism is based on a mixing of various transitions of the chromophore induced by the chiral environment and is somewhat comparable to vibronic coupling (Section 1.3.4). Interactions between electric transition dipoles of groups in a chiral arrangement with a central chromophore may be described as coupled oscillators. The interaction of an electric transition dipole moment with a magnetic transition dipole moment or an electric transition quadrupole moment forms the basis of the "electromagnetic" mechanism of induced optical activity. In general, contributions from all different mechanisms have to be considered. In practice, however, quite often one of the mechanisms predominates to such an extent that all other mechanisms can be neglected. It is therefore possible to speak of a one-electron model of optical activity, or of the exciton-chirality model, which forms a special case of the model of coupled oscillators, etc. Finally, the optical activity of polymers that contain a very large number of inherently achiral chromophores in a chiral arrangement may be treated by methods developed in solid-state physics, like the other optical properties of polymers. The resulting theoretical description can be viewed as a generalization of the exciton-chirality model.

3.2.3 CD Spectra of Single-Chromophore Systems The field of natural products has beqn particularly fertile for the application of CD spectra to structural elucidation. The method has proven especially useful for carbonyl compounds. These have been investigated very thoroughly and will therefore be discussed here in some detail. Other important naturally occurring chromophores such as alkenes, dienes, disulfides, and aromatics will be mentioned more briefly. For a carbonyl group in a C,, symmetry environment, such as in formaldehyde, the dipole approximation for the n + ~transition yields M,, S= 0 and M ,, = 0. Although the transition is magnetically strongly allowed and polarized along the CO axis, it is electrically forbidden. The absorption therefore is of very weak intensity and the rotational strength is equal to zero. Perturbations by vibrations or by an achiral solvent can affect Yo and Y, to such an extent that a small nonzero electric dipole transition moment results; but again this produces only a very small absorption intensity and

OPTICAL ACTIVITY

Figure 3.4. The octant rule. a) Subdivision of the space into "octants" and sign of the contribution of a group in each octant to the CD effect of the v 1 1 c transition of the carbonyl group. b) Computed position of the octant planes (adapted from Bouman and Lightner, 1976).

no optical activity. This requires a chiral perturbation. As the magnetic dipole moment is already inherently large it will be hardly affected by the perturbation. Thus, the optical activity is essentially due t o the fact that the chiral perturbation induces a component of the electric transition moment in the direction of the CO axis, either parallel o r antiparallel t o the magnetic transition moment. The optical activity of carbonyl compounds has been studied using various methods. The first analyses of the perturbation of the symmetrical carbony1 chromophore by groups in a chiral arrangement led t o the so-called octant rule (Moffitt et al., 1%1; see also Wagniere, 1966). According t o this rule the sign of the rotatory strength of the n+3t* transition depends in the following way on the spatial coordinates of the groups that produce the chiral perturbation: If a right-handed Cartesian coordinate system is placed with its origin in the center of the C = O bond such that the z axis points from the carbonyl carbon toward the oxygen and the y axis is in the plane of the carbonyl chromophore, space is divided into eight octants. A sign is associated with each octant and corresponds t o the sign of the product xyz of the coordinates of the points in that octant. (Cf. Figure 3.4a.) The sign of each octant then gives the sign of the contribution t o the rotatory strength by a group located in this octant. Groups that are located in the xy, yz, o r vr plane d o not contribute t o the rotatory strength. Example 3.2:

In Figure 3.5 the application of the octant rule to (+ )-3-methylcyclohexanone is demonstrated. In the boat form as well as in the chair form the methyl group is located in a positive octant if it is in an equatorial position and in a negative

3.2

NATURAL CIRCULAR DlCHROlSM

Figure 3.5. Projections of (+)-3-methylcyclohexanone into the octants a) for the chair form and b) for the boat form.

octant if it is in an axial position. Since all other groups are located in either the yz or the xz plane or pairwise in octants with opposite signs, they do not contribute to the rotatory strength. Decisive therefore is the difference between the methyl group in a positive octant and the hydrogen atom in a negative one. As the effect of the methyl group is stronger, a positive rotatory strength is expected for the more stable conformation with the methyl group in the equatorial position. This in fact is what has been found experimentally. This example illustrates how the octant rule permits one to either establish the absolute configurdtion of compounds with rigid structure and known conformation or to determine the conformation of compounds of known absolute configuration. However, it is not possible to determine the absolute configuration and the conformation at the same time in this way. If viewed from the oxygen, most optically active carbonyl compounds have their substituents only in the rear octants. The appearance of the plane that separates the rear octants from the front octants is not determined by the symmetry of the isolated chromophore. Calculations have shown that it has approximately the shape depicted in Figure 3.4b. Many examples have verified the validity of the octant rule, but there are also cases where it is not applicable, at least not in its original, simple form. This is true for ketones with a cyclopropane ring in the a,@position and for fluorosubstituted ketones, for which the experimentally observed sign can be reproduced only if the perturbation due t o the fluorine atom is assumed to be smaller than that due t o the hydrogen atom. More recent detailed calculations solved some of these problems. (Cf. Charney, 1979.) The CD effect of simple alkenes occurs at shorter wavelengths and is therefore more difficult to measure. The spectra are usually interpreted on the basis of a modified octant rule. The interpretation is much less reliable,

3.2

however, because in the spectral region of interest at least two transitions overlap. Dienes are inherently chiral if they are twisted around the central CC bond. This produces a rotational strength that is positive if the twisted butadiene chromophore forms a right-handed helix. But since this inherent effect is not always predominant, contributions of other substituents have t o be taken into account as well in order to be able to predict the CD spectrum. Substituents in allylic positions are frequently most important. The first absorption band of disulfides corresponds t o an excitation from the energetically higher combination of the two 3p AOs of the sulfur lone pairs of electrons into the antibonding a* orbital of the S - S bond. This is again an inherently dissymmetric chromophore. In this case, however, the expected sign of the CD effect depends not only o n whether the R,-S-S-R, helix forms a right-handed o r a left-handed screw, but also on whether the dihedral angle is smaller o r larger than 90". For dihedral angles of approximately 90" the energies of the plus and minus combinations of the lone pair orbitals on the two sulfur atoms are more o r less equal, and a s a result the longest-wavelength absorption band near 250 nm is approximately degenerate. The rotatory strengths of the two transitions are of the same magnitude but of opposite sign, s o they just cancel each other. For dihedral angles of 0" o r 180" the first band is nondegenerate and at long wavelengths (A = 350 nm) but the inherent contribution to the rotatory strength is again very small. In these cases, the resultant optical activity is frequently determined by chiral perturbations due t o other atoms. If the helix forms a righthanded screw the rotatory strength of the first band is large and positive for acute dihedral angles (0" < q, < 90") but negative for obtuse angles (90" < q, < 180") (Linderberg and Michl, 1970). This has been used to investigate disulfide bridges in proteins (Niephaus et al., 1985).

NATURAL CIRCULAR DICHROISM

Figure 3.6. The chiral disulfide chromophore with a positive torsional angle q, < 90": a) orbitals involved in the w a * transition; b) transition density with

positive and negative regions corresponding to overlap of orbitals with equal or opposite signs shown light and shaded, respectively, as well as the transition dipoles resulting from taking into account the negative charge of the electron: C) right-hand rule and the resulting magnetic transition dipole (by permission from Snatzke, 1982).

Example 3.3:

If the absorption responsible for the CD effect can be described with sufficient accuracy as an electronic transition from MO @i into MO @k, the orientation of the electric and the magnetic transition moments may be derived from the nodal properties of these MOs, thus giving the sign of the CD effect. This will be demonstrated using an inherently chiral disulfide as an example. In Figure 3.6, the orbitals involved in the excitation as well as the overlap densities are given for the case of a positive torsional angle q, < 90". Taking into account the negative charge of the electron. the direction of the transition dipole may be derived from the overlap densities. [Cf. Equation (1.391.1 The right-hand rule yields the direction of the magnetic transition dipole if the p A 0 components of the initial orbital @i are rotated by the smaller one of the two possible angles in such a way that they are converted into the p A 0 components of the final MO Using this procedure it is easy to show (Figure 3 . 6 ~ that ) the components of the magnetic transition dipole moment are arranged along the S R , and S-R2 bonds such that the total magnetic transition dipole. which is given

as their sum, is parallel to the electric transition dipole. The CD effect for this conformation of the disulfide chromophore is therefore positive, in agreement with experimental results for 2.3-dithia-a-steroids (1).

Typical for aromatic hydrocarbons and their derivatives are the IL,, IL,, IB,, and 'B, bands. Chirally twisted aromatic compounds, for example, hexahelicene (2), are inherently dissymmetric n chromophores. The rotatory strength of the various transitions can be calculated by means of the common n-electron methods.

152

OPTICAL ACTIVITY

More numerous, however, are aromatic compounds with an effectively planar n system, the optical activity of which comes from chiral perturbations. Benzene derivatives such as phenylalanine (3) are particularly important. The 'L, band of the benzene chromophore (A = 260 nm) is neither magnetically nor electrically allowed. The symmetry selection rule may be broken by vibronic interactions or due to substituents. The interpretation of the observed rotatory strength is not easy, but empirical sector rules have been proposed. (Cf. Charney, 1979; Pickard and Smith, 1990.)

3.2

NATURAL CIRCULAR DlCHROlSM

153

where R,, is the vector from the center of one chromophore to the center of the other chromophore and R12= (R12J. The rotational strengths %+ and 3-of these two transitions are of the same magnitude but of opposite sign:

In applications of this relation, the contribution from the coupling with the magnetic transition moments M, = is often neglected. The sign of the rotational strength of the lower-energy transition is then the same as the chiral sign for a two transition dipole moment system. A right-handed screw (clockwise rotation) is here considered as positive and a left-handed screw (counterclockwiserotation) as negative. The CD spectrum then shows

3.2.4 Two-Chromophore Systems For the description of the CD spectra of molecules with two (or more) identical or at least similar chromophores in a chiral arrangement the method of coupled oscillators (exciton chirality method) has proven particularly successful. Such systems can occur either as chiral "dimers," or they can be obtained by introducing suitable chromophores into a chiral molecule. The best-known example is given by the dibenzoates derived from 1,2-cyclohexanediol of the general formula 4:

In all these cases it is possible to derive from the CD spectrum the absolute spatial orientation of the electric transition dipoles of the two chromophore's. If the direction of the transition dipole.within the chromophore is known, the absolute stereochemistry of the compound may be determined using these methods. If @ , and @, ( k = 1, 2) are localized ground- and excited-state wave functions of the chromophores k, the ground state of the two-chromophore @ ,,, whereas the excited states Ti = system may be described by To= @ N ,(@,@, + @,,,@,,) are degenerate in zero-order approximation. The exciton-chirality model only takes into account the interaction between the transition dipole moments M Iand M2localized in the chromophores. Thus, the interaction gives rise to a Davydov splitting by 2V,, of the energies of com0 of locally excited states. From the dipole-dipole apbinations T,?and ' proximation one obtains

Figure 3.7. C D spectrum of cholest-5-ene-3/3,4/l-bis@-chlorobenzoate); contributions of the two transitions with Davydov splitting AA (----), sum curve (-), and observed curve (-.---I (by permission from Hnrada and Nakanishi, 1972).

3 .

a combination of a positive and a negative CD band (a "couplet"). The sign of the longer-wavelength band is the same as the sign of the chirality. Example 3.4:

The transition moment of the strong absorption band at 230 nm of the benzoyloxychromophore is directed roughly along the long axis; in a benzoate it is therefore approximately parallel to the C--0 bond of the alcohol, irrespective of the conformation relative to rotation around the C - 0 bond. (Cf. 4.) This is also true for p-substituted benzoyloxy derivatives with a long-wavelength shift of this band. which then usually overlaps much less with other transitions. Figure 3.7 shows a part of the CD spectrum of the bis(p-chlorobenzoate)of the vicinal diol5. a steroid with negative chirality of the C - 0 bonds. As expected, the CD band at longer wavelengths is negative, and the one at shorter wavelengths is positive. This method has been used to determine the absolute configuration of quite a number of natural products.

3.3 Magnetic Circular Dichroism (MCD)

MAGNETIC CIRCULAR DlCHROlSM

155

An MCD spectrum is measured in the same way as a CD spectrum, except that the sample is placed inside the coil of a superconducting magnet or between the poles of an electromagnet in which holes have been bored to permit the light beam to pass through. Only that component of the magnetic field that is parallel to the beam of light contributes to the effect. Reversal of the field direction changes the sign of the measured ellipticity, providing a simple method to cancel out the natural CD effect. Like U V absorption and natural CD spectra, the MCD spectrum observed in the UV/VIS region is a superposition of contributions from all electronic transitions in the molecule. Whereas in ordinary isotropic absorption spectra or in natural CD spectra each transition can be characterized by its band shape and a single scalar quantity, the oscillator strength or the rotatory strength, three numbers, A,, B,, and Ci, are necessary to describe the contribution of each electronic transition i to the MCD spectrum of an isotropic sample. The three numbers are known as the A term, the B term, and the C term of the i-th transition. The contributions of the B term and of the C term to the MCD curve [8l,(fi) have the shape of an absorption peak, which in the simplest case has a Gaussian profile as shown in Figure 3.8. They differ insofar as the contribution of the B term is temperature independent, whereas that of the C term is inversely proportional to the absolute temperature and can therefore dominate the spectra at very low temperatures. If nonzero B and C terms are both present, a measurement of the temperature dependence of the spectrum is needed to separate them. An MCD band can be either positive or negative just as in natural CD spectra. According to the nomenclature accepted in organic MCD spectros-

3.3.1 General Introduction In an external magnetic field all matter becomes optically active. This observation was first made by Faraday in 1845; the magnetically induced rotation of the plane of polarized light is therefore referred to as the Fcrrtrdlry cfli~ct.In recent years, the common mode of study of this phenomenon has been the measurement of magnetic circular dichroisrn (MCD). Similarly to natural circular dichroism, magnetic circular dichroism is defined as the difference be = E,, - E~ of the extinction coefficients for left-handed and righthanded circularly polarized light as caused by the presence of a magnetic field directed parallel to the light propagation direction. To a very good approximation, the effect is proportional to the strength of the magnetic field. A common mode of display of MCD spectra is a plot of magnetically induced molar ellipticity [el,, normalized for unit strength [ I Gauss (G) = 10 - 4 Tesla (T)] of the magnetic field. against wavelength A or wave number c. This quantity is related to AE in the same way as shown in Equation (3.3) for natural CD. It is a good approximation to say that for chiral samples that are naturally optically active, the magnetically induced effect is superimposed in an additive fashion onto their natural CD effect.

Gaussian profile of a MCD band corresponding to a nonzero B or C term (-) and its derivative, which is the band shape of contributions from the A term (...I. Figure 3.8.

156

OPTICAL ACTIVITY

copy, a B term or a C term is called positive if it corresponds to a negative ([el, < O), and negative if it corresponds to a positive MCD peak. The contributions from the A term do not have the shape of an absorption peak, but rather that of the derivative of an absorption peak, which resembles a letter S on its side; this is shown schematically in Figure 3.8 by the dotted curve. The A term is called positive if [8],(5) is negative at lower wave numbers and positive at higher wave numbers; it is called negative if the contributions to the [0],(C) curve are positive at lower and negative at higher ij values. At the absorption maximum the contribution from the A term vanishes. If A and B (or C') terms are both nonzero the resulting band shape is a superposition of the various contributions. In order to obtain a simple mathematical description of the total contribution of the i-th electronic transition to the MCD spectrum, a normalized line-shape function gi(S) and its derivative J(5) are defined. The total spectrum may then be written as a sum over all electronic transitions as

MCD peak

where k is Boltzmann's constant and T the absolute temperature. Common units are D2& for Ai and D2fleIcm-'for Bi and for CiIkT, where D stands for Debye and Be for Bohr magneton. The value of Ci is zero unless the ground state is degenerate. This is very rare for organic molecules, so the MCD spectra of organic molecules are in general temperature independent except for cases where conformational changes or similar temperature-dependent processes change the molecule itself. In the following it will be assumed that all C terms vanish. In that case the A term of an electronic transition is nonzero only if the excited state is degenerate.* This can happen in highly symmetrical molecules with an axis of rotation C, of order n r 3. Again, such molecules are more numerous in inorganic chemistry than in organic chemistry. If the Ai term is sufficiently large compared to the Bi term, both a positive and a negative MCD peak are observed. In all other cases each absorption peak corresponds exactly to an MCD band. Since relative intensities of the various bands in the absorption and MCD spectra, just as in the CD spectra, can be very different, it is possible to use MCD spectroscopy in order to detect transitions that are absent or difficult to recognize in the absorption spectrum. MCD spectroscopy and polarization spectroscopy are in many cases complementary in this respect, since transitions with identical polarizations may have B terms of opposite signs

If the ground state is degenerate the A term i s nonzero even if the excited state i s nondegenerate.

Figure 3.9. Magnetic circular dichroism (top) and absorption polarized along the z axis (-1 and along the y axis (---) of a) acenaphthylene and b) pleiadiene (by permission from Kolc and Michl, 1976, and from Thulstrup and Michl, 1976).

158

OI'I'ICAL AC'I'IVI'I'Y

3.3

MAGNETIC CIRCULAR DlCHROlSM

and transitions with B terms of equal sign may differ in the polarization direction.

, 05

Example 3.5: Figure 3.9 shows the MCD spectra of acenaphthylene and pleiadiene. The second and the third absorption bands overlap strongly. They are the N, or L, and N, or L, bands, which differ in the sign of the B term and are therefore easy to recognize in the MCD spectra. For comparison the linearly polarized spectra, obtained from measurements on stretched sheets, are also shown. They also make it possible to distinguish the two bands, since they have different polarization directions.

500

LOO

300

250

200

-0.5 -

Another spectroscopic application of MCD spectroscopy is important for highly symmetrical molecules. The ptesence of nonzero A terms reveals clearly which transitions are degenerate and which are not. This distinction is in general not possible from ordinary absorption spectra, even if no bands overlap. The magnetic moment of the excited state may be derived from the A, value by means of the relationship where D, is the dipole strength of the transition i. The sign of the magnetic moment corresponds to that excited state that is being generated by lefthanded circularly polarized light. A positive value means that the projection of the magnetic moment onto the direction of the light is positive. Values of the A,, B,, and Ci terms are most easily obtained if the bands belonging to different transitions overlap as little as possible. In this case one can integrate over the transition in question and obtain the following expressions in the usual units given above and in DZfor Di:

log€ L

60 30V (103cm-'l

Figure 3.10. MCD spectrum (top) and absorption spectrum (bottom) of the croconate dianion C,0,2@(by permission from West et al., 1981).

group Dsh;the first excited singlet state is degenerate. This can be verified from the fact that the first band in the MCD spectrum exhibits a positive A term. Numerical integration gives Ai and Divalues, from which the magnetic moment of the excited state can be derived as p = -0.25 PC.

Here, 5 is the wave number of the center of the absorption band and [elM and E are measured in the usual units (deg L m - I mol - I G - I or L molcm--',respectively).

Example 3.6: The MCD spectrum of the croconate dianion C,O,Z@is shown in Figure 3.10. The molecule possesses a fivefold symmetry axis and belongs to the point

If two or more transitions overlap, the quantitative interpretation of the MCD spectrum becomes much more difficult and computational curve fitting that requires simple band shapes is needed. Often, the vibrational structure of the MCD spectrum, which will in general be different from the one in the absorption spectrum, will be so pronounced that this assumption is not fulfilled. Although uncommon, there are some cases known where some sections of the vibrational envelope associated with a single electronic transition are positive and some negative. Thus, the appearance of both positive and negative MCD peaks in a spectral region does not necessarily mean that

160

OPTICAL ACTIVITY

a degenerate electronic state is involved or that more than one electronic transition is present in the region. Reliable assignment of the number of electronic transitions usually requires a painstaking analysis of a number of different kinds of spectra. The resulting detailed information is extremely useful for the spectroscopist. For applications in organic chemistry, on the other hand, knowledge of the symmetries of excited states, of the energy ordering of the orbitals, or of the relative magnitude of orbital coeficients is of primary interest. Such. applications of the MCD method require at least a superficial understanding of the fundamental theory.

3.3.2 Theory The quantum mechanical expressions for the Ai and Ci terms of the electronic transition i derived by means of perturbation theory are relatively simple, whereas the expression for the B, term is much more complicated in that it involves two infinite summations over all electronic states 9,of the molecule. Using Greek indices to distinguish different components of degenerate electronic states, the various terms may be written as follows:

dependent contributions from the C terms. If, on the other hand, the excited state is degenerate, one component of this state will be excited by lefthanded and the other one by right-handed circularly polarized light. Depending on which of these components is shifted to lower energies by the Zeeman splitting in the magnetic field, AE will become initially either positive or negative as the wave number C increases, so a negative or a positive A term results. Sometimes it is possible to predict the sign by means of group theory and in this way to obtain an assignment of state symmetries. This is particularly true for those molecules to which the perimeter model discussed in Section 2.2.2 is applicable. Some of the results of the perimeter model, which are essential for the following discussions, are briefly repeated in Figure 3.1 1, which is basically a portion of Figure 2.1 1 : For a (4N + 2)-electron perimeter (N # 0) hom*oS @,and @-, and LUMOs @+,, and @-,-, occur as degenerate pairs. On the average, an electron in @&(k = N, N f 1) is found to move counterclockwise along the perimeter when viewed from the positive end of the z axis and an electron in @-, tends to move clockwise. Since it is negatively charged, an electron in with a positive angular momentum produces a negative z component of the magnetic moment K and an electron in @-, a positive z comrequires a photon of ponent of equal magnitude. The transition @e@N+l left-handed circularly polarized light that corresponds to a counterclock,.,I requires a wise-rotating electromagnetic field. The transition @ _+@ photon of right-handed circularly polarized light. From the orbital magnetic moments produced by electron circulation in the various orbitals, the z component of the magnetic moment resulting for each electron configuration may be derived. A degenerate state whose components are connected with magnetic moments pL and -p:, respectively, undergoes a Zeeman splitting in the magnetic field. If B: is the component of the magnetic field in the direction of the light beam, the interaction is given by -B,p,. Thus, the component with positive will be stabilized, and that with negative pz will be destabilized. Depending on whether the

Here, g is the degree of degeneracy of the ground state, E, is the energy of the state Qj, and M and are the operators of the electric and magnetic dipole moments, respectively. The wave functions of the ground state 'Po,of over which the the final state Qi,as well as that of the intermediate state 9,. summation runs, are unperturbed wave functions defined in the absence of the magnetic field. The physical meaning of these terms is easy to comprehend qualitatively. They are based on the Zeeman effect, which results in a magnetic-fieldinduced splitting of degenerate states. This depends on the magnitude of the magnetic field strength and on the magnetic dipole moment of the molecule. If the ground state of the free molecule is degenerate, the population of the individual components, which in the presence of the magnetic field are no longer degenerate, depends on temperature and results in temperature-

Figure 3.11. hom*o and LUMO o f an [nlannulene with 4N + 2 electrons. The sense o f electron circulation in these MOs and the resulting orbital magnetic moments are shown schematically (by permission from Souto et al., 1980).

3.3

energetically more stable component will be produced by left-handed or by right-handed circularly polarized light, a positive o r a negative A term results.

Example 3.7: The first singlet excitation of the hypothetical unsubstituted cyclobutadiene dication C4H,'@ ( 6 4 corresponds to an electronic transition from the lowest molecular orbital @o into the degenerate nonbonding a MOs @,, 4-,. Similarly, the first singlet excitation of the hypothetical unsubstituted cyclobutadiene dianion C4H,Z@(6b) corresponds to an electronic transition from the nonbonding n MOs @,, @.. into the antibonding n MO @2 (which is identical with @-,). (Cf. Figure 3.12.) In both molecules this transition is allowed and degenerate and should therefore give rise to an A term in the MCD spectrum. The ground states of C4H4?@ and C4H,2@are nondegenerate and have no magnetic moment, but in the excited states the magnetic moment is no longer zero. In C4H,2@one electron remains in @,,and contributes nothing to the orbital magnetic moment, but the other one will be either in the 4, or 4- ,, depending on whether a lefthanded or a right-handed circularly polarized photon has been absorbed. It thus produces either a negative (+,) or a positive (@-,) contribution to the z component of the magnetic moment. In C,H,2@the electron that has been pro-

MO (left) and state (right) energies for a 2n-electron annulene (top) and for a 2n-hole annulene (bottom). Full arrows indicate the two possible one-electron promotions (left) leading to an excitation from the ground state G to the two components B, and B, of the degenerate excited state (right). The required photon is right-handed (R) or left-handed (L). Double arrows show the Zeeman shifts (adapted from Michl, 1984). Figure 3.12.

MAGNETIC CIRCULAR DlCHROlSM

163

moted to q5, (= @-,I contributes nothing to the magnetic moment. Depending on whether one electron has been promoted by the absorption of a left-handed photon from 4, to @2 or by a right-handed photon from @-, to @, the positive contribution of one of the two electrons in @-, or the negative contribution of one of the two electrons in @, to the z component of the magnetic moment is no longer compensated. Thus, the absorption of a left-handed circularly polarized photon by C4H,Z@produces an excited state with a negative z component of the magnetic moment, whereas absorption by C4H,2@produces one with a positive z component. Signs of the z components are reversed for the absorption of a right-handed circularly polarized photon. The component with positive will be stabilized by the Zeeman splitting. In C4H,2@,that is the component that has been produced by a right-handed photon; in C,H,2@it is the one that has been produced by a left-handed photon. Consequently for C4H,2@,E, will differ from zero for lower and E, for higher photon energies, whereas for C4H,2@the opposite is true. The MCD spectrum is a plot of E ~ -E,, SO for C4H,2@one anticipates an MCD curve that first dips to negative values and then becomes positive as the photon energy increases. This corresponds to a positive A term. For C4H,2@the MCD curve should have the opposite shape, so a negative A term is to be expected. Similar arguments apply to other highly symmetrical aromatic compounds with only two n electrons or two a "holes." Thus, the positive A term of the croconate dianion C,0,2@ (7) may be rationalized by realizing that it can be formally written as a five times deprotonated pentahydroxy derivative of the trication C,H,'@. (Cf. Example 3.6.)

The origin of the B terms is more complex. The two infinite sums come from a perturbation of the molecule by the magnetic field. This perturbation mixes the ground state as well as the final state with all other electronic states. Due t o the energy difference in the denominator the mixing is particularly effective if both states are close t o each other in energy. The second sum, which involves the mutual mixing of excited states, is therefore generally more important than the first one. The mixing of two states qi and qj is dictated by the coupling matrix element < W M I ~ ~ > This . is small unless the states V: and qj can be expressed predominantly by configurations that differ only in promotions of a single electron and that show the appropriate symmetries. Furthermore, it is necessary that the transition moments and relative to the magand ALUMO) and negative-hard (Ahom*o 4 ALUMO), since additional perturbations have only a small effect on the relative values of Ahom*o and ALUMO, and thus their MCD signs are hard though not impossible to modify. A pictorial way of understanding the origin of these so-called p+ contributions, which are proportional to the sum p N + , + pN of the magnetic moments of the perimeter orbitals involved, is given in Figure 3.13. Since the two perimeter orbitals @k and I#-,(k = N, N + I) are exactly degenerate in the absence of a magnetic field, they will enter with exactly equal weights into each of the two MOs that result from their mixing, s o the z components of the angular momentum just cancel each other. The perturbation is said to quench the angular momentum. In the magnetic field the degeneracy of @A and @-, will be removed by Zeeman splitting, and depending on the ratio of the Zeeman splitting to the total splitting, their relative weights in the perturbed MOs will be different, and the angular momentl~mwill be correspond-

Origin of the ,u+ contributions to the B term. The broken horizontal lines indicate the energies of the complex MOs in the absence of the magnetic field, the double arrows give the Zeernan splittings and the round arrows show the sense of electron circulation (viewed from the positive z axis). The canonical MOs of the perturbed annulene, whose energies are given by full lines, result from a pairwise mixing of the perimeter MOs, whose relative weights are indicated by the thickness of the round arrows (by permission from Michl, 1978). Figure 3.13.

ingly less completely quenched. This is indicated in Figure 3.13 by the varying thickness of the round arrows. The MCD sign can be immediately verified from this diagram. When Ahom*o = ALUMO, the p + contributions to the B terms vanish. The latter is then determined only by the so-called p- contributions, which are proportional to the difference p N + - pNin the magnetic moments of the perimeter orbitals involved in the transition and are therefore primarily determined by the nature of the perimeter and not the nature of the perturbation. For positively charged and uncharged perimeters four MCD bands with +, - in the order of increasing transition energies are to be signs +, expected. The p - contributions to the first two B terms are very weak and may even vanish depending on the perturbations. MCD chromophores of this type are called soft because of the ease with which the MCD signs can be changed by minor further perturbations that remove the equality of Ahom*o and ALUMO. When Ahom*o and ALUMO differ only slightly, the p + contributions are nonzero, but they may easily be s o small that the p - contributions are significant a s well. This is particularly true for the two B bands whose p - contributions are relatively large.

Exampk 3.8:

Acenaphthylene is a negative-hard chromophore (Ahom*o < ALUMO); pleiadiene is a positive-hard one (Ahom*o > ALUMO). The MCD spectra of these pclri-condensetl ;tromittics were .;hewn in Figr~re3 . 9 . The relative m:tgnituctc of

167

MAGNFI'IC CIRCULAR DlCHROlSM

3.3

Ahom*o and ALUMO may be derived from a perturbational treatment of the union of the [I llannulenyl cation and C@or of the [13lannulenide anion and C@, respectively. This also shows that these molecules have further excited states in addition to those derived from a (4N + 2)-electron perimeter. This is true for the longest-wavelength transitions of both molecules, which therefore cannot be labeled within the framework of Platt's nomenclature. Hence, a prediction of their MCD sign on the basis of the perimeter model is also impossible. However, the next two bands correspond to the 'L, and 'L, states of a (4N+2)-electron perimeter and show the expected behavior in the MCD spectra. In acenaphthylene the order of the B terms is - , + and in pleiadiene + , - . These signs are not changed by perturbing substituents since the difference between Ahom*o and ALUMO is too large. Both molecules represent hard chromophores. The situation is different for pyrene. This is an alternant hydrocarbon for which Ahom*o = ALUMO must hold to a first approximation (cf. Section 2.2). so the p+ contributions, which usually are dominant, vanish. The MCD of the 'L bands of pyrene is not only very weak but is also affected even by very small perturbations. This is evident from the MCD spectra of I-methylpyrene and 2-methylpyrene shown in Figure 3.14, from which it is easy to recognize that the signs of the 'L, and 'La bands of these two compounds are reversed. The fact that Ahom*o is somewhat larger than ALUMO in 1-methylpyrene, but somewhat smaller than ALUMO in 2-methylpyrene, can be understood easily using arguments based on perturbation theory. This problem will be discussed again in a more general way in Example 3.1 1.

3.3.4 Cyclic JC Systems with a 4N-Electron Perimeter Although the description of electronic states by means of the perimeter model is somewhat less satisfactory for molecules that can be derived formally from an antiaromatic 4N perimeter than for aromatic molecules, simple statements about MCD signs are still possible. While nothing can be said about the S and D bands, which according to the perimeter model have zero electric transition moments and which experimentally are found to be very weak (the latter is normally inobservable), predictions are possible for the strong absorptions that are referred t o as the N l , N2, PI, and P2 bands according to the nomenclature given in Section 2.2.7. The parameters that are essential for the MCD spectra of systems derived from a 4N-electron perimeter are

AHL = AH

- AL

AHSL = (

(3.19)

and

Figure 3.14. MCD (top) and absorption (bottom) spectra of a) I-methylpyrene and b) 2-methylpyrene (by permission from Michl. 1984).

-~EN.~

- EN+,)

s ~ hl> - I,,

(3.20)

where according to Figure 2.22, AH and AL are hom*o and LUMO splitt i n g ~ respectively, , and /I,, s,, and I, denote the shifts of average energies of the two components of the hom*o, SOMO, and LUMO, respectively, which were degenerate in the unperturbed perimeter. The values ei are the

OPTICAL ACTIVITY

Positive +- +

Figure 3.15. B term signs of the N and P bands of n systems derived from a 4NeleCtron perimeter as a function of AHL and AHSL. In soft chromophores the intensity of the two longer-wavelength MCD bands is nearly zero. In hard chromophores with 1 AHSL I # ] AHL I this is true for the third band. No B terms but rather two A terms are to be expected for the unperturbed perimeter, of which the first is zero and the second positive, indicated by [OO] and [ + -1, respectively (by permission from H6weler et al., 1989).

The first weak band of both molecules is an S band for which no prediction of the MCD sign can be made. The next two bands, which according to Platt's nomenclature are the 'L, and IL, bands, are now labeled N, and N2.From Figure 3.15 the signs of the B terms are -, + for acenaphthylene and +, for pleiadiene in the order of increasing excitation energies, in agreement with the MCD spectra in Figure 3.9. Thus, the application of the perimeter model to these species, viewed once as derivatives of [4N 2lannulenes and once as derivatives of [4N]annulenes, results in different nomenclature for their absorption bands but in the same predictions for the signs of their B terms. Not all cyclic conjugated n systems can be formally derived from a (4N + 2)electron perimeter as well as from a 4N-electron perimeter. Examples are pentalene (8) and heptalene (9) whose MCD spectra could not yet be measured because of the great instability of these hydrocarbons. Pentalene and heptalene are obtained from the corresponding annulene by symmetrical introduction of a single cross-link, which is an even perturbation and yields AHL = 0 and IAHSLI 4 IAHLI. From the signs of the MO coefficients, which may easily be derived as indicated in Section 2.2.5, it is seen that AHSL is negative for pentalene and positive for heptalene. Hence both molecules are hard chromophores and the expected signs of the B terms of the N,, N,, and P, bands are -, , + for pentalene and , -, - for heptalene. The MCD spectra of simple derivatives of pentalene and heptalene are shown in Figure 3.16. They both start with an extremely weak low-energy band assigned to the S transi-

orbital energies of the unperturbed perimeter, so for uncharged 4N perimeters the pairing theorem yields (2&, - E,-I - +&, ,) = 0. AHSL = AHS ASL is therefore a measure of the asymmetry between the hom*o-SOMO separation AHS and the SOMO-LUMO separation ASL that is due to a shift in the average energies of the MO pairs upon perturbation, whereas AHL measures the asymmetry of the splitting of these orbital pairs. In hard chromophores, AHL and AHSL differ markedly from each other. The cases for which either AHL or AHSL is nearly zero are particularly important. When AHL and AHSL are of similar magnitude, the chromophore is soft. For the unperturbed perimeter one has AHL = AHSL = 0. The signs of the first three N and P bands expected for different situations can be taken from Figure 3.15. They are independent of the ordering of the transitions, Nl, N,, PI,as usual, or Nl, PI, N,. The P, transition is in general below 200 nm and is therefore difficult to observe. Example 3.9: The n systems of acenaphthylene and pleiadiene may not only be formally derived from (4N + 2)-electron perimeters as in Example 3.7, but just as well from 4N-electron perimeters. Simple perturbational arguments for the union of the [I llannulenyl anion with C@and of the [13]annulenyl cation with CQ, respectively, yield relative values for the parameters AHL and AHSL. For acenaphthylene one finds AHL .- 0 and AHSL < 0; hence it is a negative-hard chromophore; pleiadiene with AHL = 0 and AHSL > 0, on the other hand, is positive-hard.

Figure 3.16. MCD and absorption spectra of a) I ,3-di-I-butyl-pentalene-4.5dicarboxylic ester and b) 3.8-dibromoheptalene (by permission from H6weler et al., 1989).

3 .

lion, and at higher energies contain the stronger N , and N, bands, which show the expected signs.

3.3.5 The Mirror-Image Theorem for Alternant JZ Systems Due to the pairing theorem, the absorption spectra and transition polarization directions of two mutually paired alternant systems should be identical, as shown in Figure 2.25 for the radical anion and the radical cation of tetracene. Under the same conditions (i.e., 3,/ = 0 if p and v are nonneighbors), it can be shown that the MCD spectra of mutually paired alternant n systems should be mirror images of each other (Michl, 1974~). From this mirror-image theorem it follows that MCD spectra of uncharged alternant systems that are paired with themselves should be zero. This is only true within the confines of the above approximations, in which the p- contributions to the MCD are neglected. The p + contributions are in fact zero for uncharged alternant hydrocarbons since from the pairing theorem it follows that Ahom*o = ALUMO. . The originally only theoretically derived mirror-image theorem for MCD

MAGNETIC CIRCULAR DlCHROlSM

171

spectra of paired n systems has been confirmed experimentally on several examples. One of these is shown in Figure 3.17. The fact that the benzyl anion and benzyl cation should have opposite MCD signs according to the mirror-image theorem makes it easy to understand why benzene derivatives with mesomeric donor substituents, which are isoelectronic with the benzyl anion, and benzene derivatives with mesomeric acceptor substituents, which are isoelectronic with the benzyl cation, show opposite MCD signs. This fact can be used for a qualitative and even a quantitative characterization of mesomeric substituent effects. (See also Section 2.4 and Example 3.10.)

3.3.6 Applications MCD measurements are useful not only in purely spectroscopic investigations, for example, in the detection of hidden absorption bands or for the identification of degenerate absorptions, but also in structural organic chemistry. There is, for instance, a rule that describes the influence of the molecular environment on the MCD effect of the n - 4 band of a ketone (Seamans et al., 1977; Linder et al., 1977). However, the method is clearly most useful for investigating cyclic conjugated n systems. All of the examples selected here to illustrate the utility of MCD spectroscopy are based on systems that may be formally derived from a (4N+ 2)electron perimeter. For such systems the MCD effect is most simply and lucidly connected through the quantities Ahom*o and ALUMO with the form and the ordering of the molecular orbitals. It can therefore be used to draw conclusions regarding the electronic and chemical structure of the system under investigation. A structural class for which the perimeter model analysis has been particularly fruitful is that of the porphyrins (Goldbeck, 1988) and related macrocycles (Waluk et al., 1991; Waluk and Michl, 1991).

Applications become particularly simple if a series of such derivatives is studied that can all be derived from the same n system by introducing structural perturbations. The prediction of changes in the MCD spectrum as a function of such perturbation requires the knowledge of three factors:

I. The nature of the perturbation 2. The location of the perturbation on the molecular framework 3. The energy ordering of the four frontier orbitals derived from the (4N + 2)-electron perimeter and defined by their nodal properties

Figure 3.17. MCD and absorption spectra of a) diphenylmethyl cation and b) diphenylmethyl anion (by permission from Tseng and Michl. 1976).

A knowledge of all three factors permits a correct prediction of MCD effects, as has been shown in the previous sections. Conversely, if only two of the three factors are known and the MCD spectra are measured, it is possible to draw conclusions concerning the unknown third factor. For most aromatic systems the appearance of the four frontier orbitals, that is, their nodal properties and the relative magnitude of the LCAO coef-

172

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ficients as well as their energy ordering, is well known. When substituents are introduced into such a system at known locations, MCD spectroscopy can be used to investigate the nature of the electronic perturbation caused by the substituent by examining changes in the relative magnitude of Ahom*o and ALUMO. The effects are particularly pronounced for systems for which Ahom*o = ALUMO, that is, for alternant hydrocarbons. From the data in Example 3.10 it can be seen that even very weak hyperconjugative effects of substituents like SiH, and CH, may be assessed quantitatively. Example 3.10: Since for benzene the MOs are well known and all positions are equivalent the MCD spectra of monosubstituted benzene derivatives are particularly suited for a determination of substituent constants. A more quantitative analysis on the basis of the perimeter model neglecting the p- contributions yields the following result for the B term of the 'L, transition of substituted benzenes:

3.7 x 10-'L(Ahom*o+ ALUMO)(Ahom*o - ALUMO)

' (Weeks

where B is in units of D2PJcm and Ahom*o and ALUMO are in cm

--'*,J-,'i

ALUMO

! $ 'a

Ahom*o

,!'T;: E

-M 'r

ALUMO

#'I

,'! ALUM0

.. ..

Ahom*o

Figure 3.18. Effect of a substituent containing both a donor and an acceptor orbital of n symmetry on the energies of the frontier orbitals of a (4N+2)electron annulene perimeter (schematic). Strong interactions are indicated by dashed lines, weak interactions by dotted lines (by permission from Michl, 1984).

3.3

MAGNETIC CIRCUIAR DlCHROlSM

Table 3.1 B Terms of the 'L,Transition of Substituted Benzenes C@&

(in

Units of 10- 5 WD2B,/cm-I)"

CH,CMe, CH,SiMe, CH?GeMe, CH,SnMe, SiH, SiH,Me SiHMe, SiMe, CMe, SiMe, GeMe, SnMe, * From Michl (1984); the values shown have been normalized against benzene as the standard LY@Jcm-l. by subtracting 3 x

et al., 1986). For a series of weak substituents the percentage changes in (Ahom*o + ALUMO) will be much smaller than those in the much smaller quantity (Ahom*o - AI-UMO). To a good approximation the former can therefore be absorbed in the proportionality constant; at least for weak substituents the B term will then be proportional to Ahom*o - ALUMO. In a better approximation for strong substituents, variations of the proportionality factor 3.7 x 10-l2 (Ahom*o + ALUMO) with substituent strength have to be considered as well. Since to first order in perturbation theory, Ahom*o ALUMO does not depend on the a effect of a substituent (cf. Section 2.4), the B value may be considered a fair measure of Ahom*o - ALUMO and will therefore be a suitable approximate measure of the net n-electron-donating and -accepting ability of a substituent. Some substituents may act simultaneously as both n donor and n acceptor. When both effects are equal, Ahom*o = ALUMO (Figure 3.18) and the B term vanishes as in benzene itself. This is the case for a vinyl substituent on benzene, and the B term of the 'L, band of styrene is in fact very small. If the n donor effect of the substituent is stronger than the n acceptor effect, Ahom*o > ALUMO is obtained according to Figure 3.18 and the B term will be more positive as the donor strength of the substituent becomes more pronounced. If, on the other hand, the substituent is predominantly a n acceptor rather than a n donor, Ahom*o < ALUMO is to be expected from Figure 3.18 and the resultant B term will be a measure of the acceptor strength of the substituent. Table 3.1 summarizes the results obtained in this way for a series of hyperconjugative substituents. The nonvanishing B term of benzene itself, due to vibronically borrowed intensity, is assumed to be invariant in all of the cases listed and has been subtracted. If the a and n effects of the substituents are known, the substitution pattern may be determined in the same way a s described in Example 3.1 1 for ~ l t - for rn:lnv h c t e r o c v c l i c c o m p o ~ r n d \ I-rncthvl and ? - n ~ t ~ f h \ , l n ~ , r ( -'3inc.c

3.3

Ahom*o and ALUMO are not very different from each other, the same procedure can be applied to such compounds in order to gain information about the protonation site, for example, in the various aza analogues of indolizine (lo), or about the tautomerism in heterocycles as exemplified by the lactamlactim isomerism in Zpyridone (11) and about positional isomerism such as in the tautomeric 3 3 - and 3,6-diazaindoles (12, 13). This is possible since the protonation of a nitrogen o r the replacement of a carbon by a heteroatom can be viewed as a special case of substitution. H

Example 3.11: According to Figure 3.14, the MCD spectra of I-methyl- and Zmethylpyrene differ in the sign of the first B term, which is either positive or negative, depending on whether Ahom*o - ALUMO is larger or smaller than zero. The relative magnitude of the LCAO coefficientsof the two highest occupied and the two lowest occupied MOs of pyrene may be estimated from Figure 3.19. For a n donor such as the methyl group, the influence of the unoccupied fron-

MAGNETIC CIRCULAR DlCHROlSM

175

tier orbitals may be assumed to be negligible compared to the occupied frontier MOs, which are energetically much closer to the donor orbital of the substituent. The interaction with the donor orbital will cause a shift of the occupied orbitals to higher energies that is approximately proportional to the square of the coefficient at the position of the substituent. Hence, it follows that for I-methylpyrene the antisymmetric MO is more strongly raised than the symmetric one, and Ahom*o increases. Methyl substitution in the Zposition, however, raises only the symmetric orbital, since the antisymmetric orbital has a node at this position; Ahom*o then decreases. Therefore, 1-methylpyrenewill have a positive first B term because Ahom*o - ALUMO > 0, whereas for 2-methylpyrene Ahom*o - ALUMO < 0 and the B term will be negative. If the position of the substituents had not been known in advance, the two isomers could have been easily assigned by means of the MCD spectra.

Finally, if the perturbation due to the substituent as well as its position in the molecular framework is known, MCD spectroscopy can be used to investigate the nature and the ordering of the frontier orbitals. In this way, the relative importance of transannular interactions compared to substituent effects and geometrical distortions for the electronic structure of bridged annulenes such as 1,&methano[IO]annulene (14) may be assessed by determining the energy ordering of the frontier orbitals of substituted derivatives of 14 from their MCD spectra. This is shown in detail in Example 3.12.

Example 3.12: From a schematic representation of the frontier orbitals &, ips, +%. of the [IOlannulene perimeter shown in Figure 3.20 it is easy to recognize that trans-

The real form of the four frontier orbitals of the 14 n-electron [14]annulene perimeter and the effect of bridging by an ethylene unit (by permission from Michl. 1984).

Figure 3.19.

Figure 3.20.

perimeter.

Nodal properties of the four frontier orbitals of the [IOIannulene

bl a2 _+t

a,+

a1 - t t

a,-~-

bb2

a2 -t+

al*

OPTICAL ACTIVITY

bl b2 a1 -Ha2-H-

SUPPLEMENTAL READING

177

annular interaction, that is, direct through-space interaction between the bridgehead carbons in 1,6-methano[lO]annulene,will not affect the energies of the MOs @a and +,,, that have a nodal plane through the bridgehead carbons but that has no node across the new resonance integral, will stabilize the MO and destabilize the 4,. that has a node across the new resonance integral. Thus the anticipated orbital arrangement is @s below @a in energy. All other possible unchanged, therefore producing the perturbations destabilize @, and leave opposite ordering of the occupied orbitals. with below For instance, dihedral twisting of the partial double bonds in the molecule results in a reduction of the resonance integrals for the four n bonds originating at the bridgewhich is binding head carbon atoms, and will therefore destabilize the MO in these bonds. In order to derive the orbital ordering from the MCD spectrum, use can be made of the fact that according to Figure 3.20 the LCAO coefficients of the MOs 4, and 4,. are larger in absolute value in position 3 than in position 2, whereas the opposite holds for and Therefore, all that needs to be done in order to determine the order of the four frontier orbitals is to measure the B term of the 'L, band of some derivatives of 1,6-methano[lO]annulene with substituents in positions 2 or 3. The theoretically expected shapes for the dependence of the B term of the IL, band on substituent strength for both positions of substitution are shown in the upper part of Figure 3.21 for four possible orbital orderings. The measured B terms for various substituents are displayed in the lower part of Figure 3.21. The resulting shapes show unambiguously that the orbital ordering is that expected only if transannular interaction is the dominant effect; that is, @, (labeled a, in Figure 3.21) below @a (a2) and +a. (b,) below (b2). +$

+,.

+*,

+,.

Supplemental Reading General Caldwell, D.J., Eyring, H. (1971), The Theory of Optical Activity; Wiley-Interscience: New York.

Natural Circular Dichroism Barron, L.D. (1982). Molcculur Light Scattering and Optical Activity; Cambridge University Press: Cambridge. Charney, E. (1979), The Molecular Basis of Opricul Activity; Wiley: New York.

Figure 3.21. Determination of the transannular interaction in 1,6-methano[lO]annulene from an analysis of substituent effects on the MCD spectra: a) theoretically expected dependence of the B term of the 'L,transition on substituent strength ( + M corresponds to a A donor and - M to a n acceptor) for four possible arrangements of the frontier orbitals that are labeled according to the C,, symmetry of the parent compound, and b) observed B terms of the 'L, transition for different substituents in units of lo-' W@Jcm-I. The solid horizontal lines indicate the B term of the unsubstituted hydrocarbon (-4-lo-' W@Jcm-I) (by permission from Klingensmith et al., 1983).

Mason, S.F. (1982), Molecular Optical Activity and the Chiral Discriminations; Cambridge University Press: Cambridge. Nakanishi. K.. Berova, N . , Woody, R. W. ( 1994). Circrrlrr Dichroism: Principlc,~crnd Applications; VCH Publishers. Inc.: New York. Snatzke. G. (1979). "Circular Dichroism and Absolute Conformation-Application of Qualitative MO Theory to Chiroptical Phenomena", Angew. Chem. Inr. Ed. Engl. 18, 363.

Exciton Chirality Model Harada, N., Nakanishi, K . (1983). Circrrlor Dichroic. Spcc.troscopy; University Science Books: New York.

178

OPTICAL ACTIVITY

CHAPTER

Magnetic Circular Dichroism Michl, J. (1984), "Magnetic Circular Dichroism of Aromatic Molecules", Tetrahedron 40, 3845. Michl, J . (1978). "Magnetic Circular Dichroism of Cyclic .rr-Electron Systems", J . Am. Chem. Soc. 100,6801, 6812,6819. Piepho, S.B., Schatz, P.N.(1983). Group Theory in Spectroscopy; Wiley: New York.

Potential Energy Surfaces: Barriers, Minima, and Funnels

The theoretical treatment of photophysical and photochemical processes within the framework of the Born-Oppenheimer approximation requires knowledge of the potential energy surfaces of the ground state and of one or more excited states, and a qualitative understanding of the way in which these surfaces govern nuclear motion. Some of the fundamental principles necessary for such a discussion are presented in the first section of this chapter. There follows a brief outline of correlation diagrams, which in many cases provide very illuminating qualitative descriptions of the essential characteristics of potential energy surfaces. Detailed quantum chemical calculations of such surfaces for low-symmetry systems of interest to organic chemists have very recently become feasible, but the high dimensionality of the problem makes the searches for the topologically relevant features of the surfaces relatively demanding. Many fundamental problems can be solved using simpler model systems and these have provided a useful and intuitively satisfying basis for a general discussion of complex photoprocesses. This is illustrated in the last two sections of this chapter.

4.1 Potential Energy Surfaces 4.1.1 Potential Energy Surfaces for Ground

and Excited States Within the Born-Oppenheimer approximation-that is, after se.parating off the nuclear motion-adiabatic potential energy surfaces are obtained by

180

POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

solving the electronic Schrodinger equation for a great number of nuclear geometries. A plot of the lowest energy E(Q) as a function of all geometrical variables (combinations of bond lengths, angles, etc.) Ql, Q 2 , . . . , Q, Q provides an F-dimensional surface for the ground state in a space that also contains the energy as an additional dimension. This is sometimes referred to as an F-dimensional hypersurface in an (F+1)-dimensional hyperspace. All isomers that can be formed from a given collection of atomic nuclei and electrons have a common ground-state surface and correspond to minima therein. Since the SchrOdinger equation has an infinite number of solutions at each nuclear geometry Q, an infinite number of Born-Oppenheimer surfaces can be obtained in principle. Among these, however, usually only the ground-state surface and the lowest few excited-state surfaces are of interest. The potential energy surfaces form the basis for a detailed description of the reaction process. Its quantum mechanical treatment requires a solution of the time-dependent nuclear Schrodinger equation with E(Q) as the potential. Classically, nuclear motion is handled by finding the classical trajectory of a point that moves without friction on the surface E(Q). The forces that operate on the molecule at a given nuclear arrangement Q are given by the steepest slope on the surface at that particular point (i.e., by minus the gradient of the surface at that point). When there are no interactions with the environment, the total energy is constant, but the kinetic and the potential energy fractions vary continuously as the point moves along the surface. Most often, we display only one vibrational mode at a time in a plot of energy against displacement in nuclear configuration space. In such a drawing, the potential energy is represented by the potential energy curve and the amount of kinetic energy residing in this particular mode is shown by the height of a point above the surface. Although the total energy of the molecule is constant, its distribution among the various modes of nuclear motion varies in time, and so does the height of the point that represents the molecule in this two-dimensional plot. Travel over barriers is possible only occasionally, when the mode happens to have acquired enough kinetic energy and the point is high enough to pass over the barrier. The following discussion makes frequent use of such one-dimensional cross sections through potential energy surfaces. The reaction coordinate Q used as the abscissa often remains unspecified in schematic representations. Caution is required in interpreting such cross sections. What appears as a minimum, barrier, or saddle point in one cross section may look quite different in another one. A typical example is a maximum of a reaction profile, which appears as a minimum in a cross section perpendicular to the reaction coordinate. Since spin-orbit coupling is normally not included in the Born-Oppenheimer Hamiltonian, singlet and triplet states can be distinguished. In a discussion of photochemical processes, large areas of the nuclear configuration space are of interest, and it is useful to label the energy surfaces in a way that differs from the one conventionally t l s e d hy $pectro.;copi.;t\ A t :In\,

4.1

POTENTIAL ENERGY SURFACES

Schematic representation of Born-Oppenheimer potential energy surfaces. Using the photochemical nomenclature, the ground-state surface of a closedshell system, which is the lowest singlet surface, is labeled So, followed by S,, S,, etc. in order of increasing energies. The triplet surfaces are similarly labeled T,, T,, etc. Figure 4.1.

geometry, states of a given multiplicity are labeled sequentially in the order of increasing energies. Surfaces of different multiplicity can cross freely; such crossings do not disturb the labeling of the surfaces by So, S,, S,, . . . and T,, T,, T,, . . . On the other hand, if states of the same multiplicity do cross, they exchange their labels as defined by the convention used here. (See Figure 4.1 .) Therefore, the surface S,, (T,,)can touch the surfaces S,, (TI,-,) and S,,, (T,+ ,) but cannot cross them. The situation depicted in Figure 4.1 corresponds to a touching of s,,and s , , S, and s,, and TI and T,. In polyatomic molecules, such touching of surfaces of identical spin and spatial symmetry is allowed (v. Neumann and Wigner, 1929; Teller, 1937; Herzberg and Longuet-Higgins, 1963; Salem, 1982), although along many paths "intended" touchings are still avoided. (Cf. Example 4.1 .) The convenience gained by the use of the "photochemical" nomenclature is that all isomers of the same formula have a common ground-state surface So. In the spectroscopist's convention, labels of crossing surfaces are kept and So of one isomer could lie above S, at the geometry of another isomer or even above itself, at the same geometry, provided two or more surfaces cross in an appropriate manner in several dimensions.*

*Figure 4.2b (Section 4. I .2) demonstrates that in this convention S,, can lie above itself. Both surfaces would have to be labeled S, if one followed a cut from the minimum in S, t o the intersection and further up. and then sideways and back to the original geometry. avoidin11 I I I I ! ~ llic i n t ~ * ~ . \ tt i.8 2) the unavoided touching of states of equal electronic symmetry is actually quite common (Bernardi et al., 1990b; Xantheas et al., 1991), hence that the earlier belief in its scarcity was wrong. The dimensionality of the subspace in which the energies of the two touching states are equal (the intersection coordinate subspace) is F - 2. In the remaining two dimensions (x,, x,) of the total F-dimensional nuclear configuration space, which define the branching space, the touching is at least weakly avoided. In the immediate vicinity of a touching point, a plot of the surface energies has the form of a double cone. At the cone touching point, the two states are degenerate, and a s one moves away by an infinitesimal amount in the x,, x, plane, the degeneracy is lifted. Thus, at most points in the total F-dimensional space, the touching is avoided, but in an ( F - 2)-dimensional "hyperline," it is not (Atchity et al., 1991). Example 4.2:

In the adiabatic basis obtained by the diagonalization of A, the vector x, is defined as the gradient difference

184

POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

and in this direction the difference in the slopes of the upper and the lower surface is the largest. The vector x2 is given by

and this is the direction of nuclear displacement that mixes the two adiabatic electronic wave functions of the cone point the best. If the electronic wave functions TI and Y2are of different symmetries at the cone point, x2 is the symmetry-lowering nuclear coordinate that permits them to mix. (Cf. Figure 4.2b.) The vectors x, and xz are in general not collinear and often are close to orthogonal.

Efficient algorithms have been developed for locating conical intersections and for locating the points of minimum energy within the ( F - 2)dimensional intersection coordinate subspace: that is, the true bottom of the funnel (Yarkony, 1990; Ragazos et al., 1992; Bearpark et al., 1994), and in recent years, quite a few have been found. (See Chapter 7.) Note that the gradient on neither of the touching potential energy surfaces is zero at the minimum energy point of the intersection, as it would be in a true stationary point. Rather, it is only the projection of the gradient into the (F - 2)dimensional intersection coordinate subspace that is zero. Therefore, the bottom of the funnel is not a ininimum in the sense of having a zero gradient but only in the sense of having the lowest energy (except if the funnel is very tilted). Thus, gradient-based search routines will not recognize this minimum in the F-dimensional space as such. Unlike the general case of conical intersection in polyatomic molecules, which occurs between states of equal electronic symmetry and has not been well documented until relatively recently, the special case in which the condition H I , = 0 (Example 4.1) is enforced by a difference of symmetries of the two states has been well known and studied for a long time. This class of conical intersections is much easier to access computationally and to predict from correlation diagrams. The reaction path along which high symmetry is preserved, and along which H I , vanishes, corresponds to x , . The symmetry-lowering direction that makes H I , nonzero, and thus induces a mixing of the two zero-order states, corresponds to x, (Figure 4.2). The expression "avoided state touching (crossing)" can refer to one of two situations (Salem et al., 1975). First, an avoided touching can be encountered along paths that pass close to a real state touching but miss the tip of the cones and do not quite reach the required values of x , and x, to enter the (F - 2)-dimensional intersection coordinate subspace. An example would be a path that does not quite preserve the high symmetry that is characteristic of some conical intersections. Second, it can be encountered upon improvement of a simpler quantum mechanical approximation in which a

crossing was unavoided because H I , was approximated by zero or in which H I , and H,,were set equal. The wave functions of the states we have dealt with so far diagonalize the complete electronic Hamiltonian and are called adiabatic. As we shall discuss in more detail in Section 6.1, they govern the nuclear motion if it is sufficiently slow. For description of fast motion on surfaces, it is sometimes an advantage to work with surfaces that do not diagonalize the electronic Hamiltonian and therefore cross, such as those obtained in the approximate treatments referred to above. Such states are called diabatic or nonadiabatic. They are described by wave functions that do not greatly change their physical nature at the crossing. Thus, in the region of an avoided crossing, those two parts of the adiabatic potential energy surface that in the nonadiabatic approximation correspond to the same surface (e.g., the parts of the surfaces at the upper left and lower right of Figure 4.3). will be described by very similar wave functions, whereas the character of the wave function changes appreciably along the adiabatic potential surface. If the nuclei are moving so fast that the electronic motion cannot adapt instantaneously to the nuclear configuration as required in the adiabatic limit, the molecule may follow the nonadiabatic surface instead; that is, a jump from one to another adiabatic state may occur. In many dimensions, the situation is more complicated, but in general, arrival of a nuclear wave packet into a region of an unavoided or weakly avoided conical intersection means that the jump to the lower surface will occur with high probability upon first passage. The expression "funnel" is used for regions of a surface in which passage to another surface is so fast that there is no time for vibrational equilibration before the jump, and it can refer both to an unavoided and to a weakly avoided conical intersection (Section 6.1). In perturbation theory language, one can say that the adiabatic BornOppenheimer states are a good zero-order approximation for describing nuclear motion if the non-Born-Oppenheimer corrections are small. This is

Figure 4.3. Schematic representation of adiabatic and diabatic (nondiabatic) potential energy surfaces S, and S,(adapted from Michl, 1974a).

4.1

because Inrge terms that cause the crossing to be avoided-for example, electron repulsion-are already included in the description of the Born-Oppenheimer states. Diabatic states, on the other hand, are a good zero-order approximation in the opposite case.

4.1.3 Spectroscopic and Reactive Minima in Excited-State Surfaces A qualitative anticipation of the location of minima and funnels on excitedstate potential energy surfaces, in particular the S, and TI surfaces, is in general more difficult than the estimation of the minima on the ground-state surface So that correspond to stable ground-state species. There are three basic types of geometries where one would intuitively expect minima andlor funnels in S, and T,-namely, near ground-state equilibrium geometries, at exciplex and excimer (complex) geometries, and at biradicaloid geometries. Minima on excited-state surfaces in the region of ground-state equilibrium geometries may be referred to as spectroscopic minima. Spectroscopic transitions from the ground state to such minima or vice versa are in general easy to observe, even if the probability may be somewhat constrained by the Franck-Condon principle. Excitation from the ground state to spectroscopic minima is approximately vertical. Generally, upon return from these minima to the ground state by fluorescence, phosphorescence, or radiationless processes, an excited molecule will end up in the initial minimum of So, and the excitation-relaxation sequence corresponds to a photoptlysical process without chemical conversion. In particular in larger molecules such as naphthalene, the promotion of an electron from a bonding into an antibonding MO causes such a small perturbation of the total bonding situation that its effect on the equilibrium geometry of the excited state is relatively small. It can, however, also be more significant. Thus, formaldehyde is pyramidal in the I(n,n*) as well as in the '(n.n*) state, and not planar as in the ground state. (Cf. Section 1.4.1 .) Exciplex minima can be viewed as a particular case of spectroscopic minima. Their presence in the excited surfaces reflects the fact that molecules are more polarizable. more prone to charge-transfer processes, and generally "stickier" in the excited state. These minima occur at geometries that correspond to a fairly close approach of two molecules at their usual groundstate geometries, for example, the face-to-face approach of two n systems generally associated with excimers and exciplexes. The ground-state surface normally does not have a significant minimum at the complex geometry when the very shallow van der Waals minimum is disregarded, except in the so-called charge-transfer complexes and similar cases. Radiative or nonradiative return from this type of minimum in an excited state to the ground state leads to the reformation of the two starting molecules in an overall photophysical process.

I'OTENI'IAL ENERGY SURFACES

187

If a pair of nearly degenerate approximately nonbonding orbitals is occupied with a total of only two electrons in the simple MO picture of the ground state, the molecule is called a biradical or a biradicaloid. Various types of biradicals and biradicaloids will be discussed in some detail in Section 4.3. A usual prerequisite for the presence of degenerate orbitals is a specific nuclear arrangement that is referred to as biradicaloid geometry. Minima and funnels at such biradicaloid geometries, that is, biradicaloid minima or funnels, normally are reactive minima or funnels. They are typically characterized by a small or zero (in the case of critically heterosymmetric biradicaloids, see Section 4.3.3) energy gap between the potential energy surfaces; a usually fast radiationless transition from the excited state to the ground state; and normally a shallow minimum in the ground-state surface, if any. A molecule in a biradicaloid minimum generally is a very short-lived species. After return to So, deeper minima at geometries other than the initial one will usually be reached, so the net process corresponds to a photochemical conversion. The relevance of biradicaloid minima for photochemical reactivity was first pointed out by Zimmerman (1%6, 1969) and van der Lugt and Oosterhoff (1969). They represent funnels or leaks in the excited-state potential energy surface (Michl, 1972, 1974a). Biradicaloid geometries are in general highly unfavorable in the ground state, since the two electrons in nonbonding orbitals contribute nothing to the number of bonds. As a result, the total bonding is less than that ordinarily possible for the number of electrons available. When the geometry is distorted to one in which the two orbitals are forced to interact, a stabilization will result. This is evident from Figure 4.4, which shows that the two orbitals combine into one bonding and one antibonding orbital, and both

Figure 4.4.

Orbital energy scheme for two orbitals, cp, and q2,which are occupied with a total of two electrons: a) for biradicaloid geometries cp, and cp, are degenerate; from the three possible singlet configurations only one is shown; b) if the degeneracy is removed the ground state will be stabilized; c) excited configurations will usually be destabilized. The doubly excited configuration and the triplet configuration will be destabilized correspondingly.

188

POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

electrons can occupy the bonding orbital. In the excited state, however, any distortion from a biradicaloid geometry that causes the two orbitals to interact, and split into a bonding and an antibonding combination, is likely to lead to destabilization, since only one of the two electrons can be kept in the bonding MO, while the other one is kept in the antibonding MO, and the destabilizing effect of the latter predominates. Here, we consider the two simplest and most fundamental cases of biradicaloid geometries, reached from ordinary geometries by stretching a single bond or by twisting a double bond. These two cases together underlie much of organic photochemistry. The stretching of an H, molecule provides an illustration of the dissociation of a prototypical single bond (see Figure 4.5): The minimum in Sooccurs at small internuclear distances (74 pm) and is definitely not a biradicaloid minimum since the a, MO is clearly bonding and the a,*.MO clearly antibonding at this geometry. In the dissociation limit, the So state corresponds to a pair of H atoms coupled into a singlet and has a high energy, the same as the TI state. In the latter, the coupling of the electron spins is different, but this has no effect on the energy since the H atoms are far apart. The TI

Figure 4.5. Energies a) of the bonding MO a,and the antibonding MO a:, as well as b) of the electronic states of the H,molecule as a function of bond length (schematic). On the left, the states are labeled by the MO configuration that is dominant at the equilibrium distance; on the right, they are labeled by the VB structure that is dominant in the dissociation limit. Rydberg states are ignored (by permission from Michl and BonaCiC-Kouteckv, 1990).

4.1

POTENTIAL ENERGY SURFACES

189

state has its minimum at the infinite separation of the two H atoms where both MOs are nonbonding. The fully dissociated geometry thus clearly corresponds to a biradicaloid minimum. The S, state has a minimum at 130 pm, that is, at intermediate nuclear separations. For this geometry the MOs a, and c$ are much less bonding and antibonding, respectively, than for the ground-state geometry, so the minimum can also be referred to as biradicaloid. The difference in the minimum geometry of TI and S, is easily understood when it is realized that S, and S, are of zwitterionic nature and may be described by the VB structures HGH@and H@H@.(See Example 4.3.) The location of the minimum in S, represents a compromise between the tendency to minimize the energy difference between a, and a:, favoring a large internuclear distance, and to minimize the electrostatic energy corresponding to the charge separation in the zwitterionic state, favoring a small internuclear distance. Even though H, may not appear to be of much interest to the organic chemist, the importance of Figure 4.5 cannot be overemphasized, and we shall refer to it frequently in the remainder of the text. This is because it represents the dissociation of a single bond in its various states of excitation, and the breaking of a single bond, usually aided by the bond's environment, underlies most chemical reactions. In a sense, Figure 4.5 represents the simplest orbital and state correlation diagrams, to which Section 4.2 is dedicated. Introduction of perturbations by the environment of the bond converts its parts a and b, respectively, into correlation diagrams for the orbitals (e.g., Figures 4.10 and 4.1 I ) or the states (e.g., Figure 4.13) of systems of actual interest for the organic photochemist. In Section 4.3 we shall examine the wave functions of an electron pair in its various states of excitation in more detail, and shall describe the relation between the MO-based description (left-hand side of Figure 4.5b) and the VB-based description (right-hand side of Figure 4.5b). A recent illustration of the same principle in the case of a C--C bond, more directly relevant to organic photochemistry, is provided by the contrast between the Franck-Condon envelopes of the So-S, and the So-T, transitions in [I. I . l]propellane (1) (Schafer et al., 1992). These make it clear that the length of the central bond is nearly the same in the ground state and the '(a,#) excited state, which can be thought of as a contact ion pair. In contrast, in spite of the constraint imposed by the tricyclic cage, the central bond is substantially longer in the '(a@) state, which can be thought of as a repulsive triplet radical pair.

However, it is also important to note the essential limitations of the diagrams presented in Figure 4.5: they apply to the dissociation of single bonds

190

POTENTIAL ENERGY SURFACES: BAKHIEKS, MINIMA, AND FUNNELS

4.1

POTENTIAL ENERGY SURFACES

191

that ( I ) are nonpolar and (2) connect atoms neither of which carries lonepair AOs or empty AOs nor is involved in multiple bonds to other atoms. Thus, as we shall see later (Section 6.3.3), they apply to what is known as nonpolar bitopic bond dissociation. For example, Figure 4.5 applies to the dissociation of the Si-Si bond in a saturated oligosilane (see Section 7.2.3), but not to the dissociation of the C-SO bond in an alkylsulfonium salt, to the dissociation of the C--0 bond in an alcohol (see Section 6.3.3), or to the dissociation of the C--C bond adjacent to a carbonyl group. (See Section 6.3.1 .) Introduction of an electronegativity difference between the two bond termini causes changes in the course of the correlation lines in Figure 4.5 and is discussed in Section 4.3. Introduction of lone pairs, empty orbitals, or adjacent multiple bonds introduces new low-energy states and is discussed in Section 6.3.3. The twisting of the ethylene molecule provides an illustration of a prototypical n bond dissociation (Figure 4.6): The minimum in So occurs at a planar geometry (twist angle of 0") and is definitely not a biradicaloid minimum since the nuMO is clearly bonding and the $ MO clearly antibonding at this geometry. In contrast, the TI, S,, and S, states have a minimum at 90" twist, where both MOs are nonbonding. This obviously is a biradicaloid min-

imum, and the wave functions of the molecular states are analogous to those discussed above for the case of H,.The Soand TI states are represented by VB structures containing a single electron in each of the carbon 2p orbitals of the original double bond, prevented from interacting by symmetry, and not by distance as in the Hzcase. The S, and S, states are of zwitterionic nature and are represented by VB structures containing both electrons in one of these orbitals and none in the other. Unlike the biradicaloid minima located along the dissociation path of a a bond, one of which occurred at a loose (TI)and one at a tight (S,) geometry, those located along the dissociation path of a n bond are at nearly the same geometry. The reason for this difference can be readily understood in terms of the simple model of biradicaloid states outlined in Section 4.3. Figure 4.6 again represents a very simple correlation diagram, and is of similar fundamental importance for reactions involving the dissociation of a n bond as Figure 4.5 is for reactions in which a a bond dissociates. It underlies correlation diagrams such as that for the cis-trans isomerization of stilbene (Figure 7.3). Its use is subject to similar limitations as the use of Figure 4.5: ( I ) The course of the potential energy curves changes when the electronegativity of the two bond termini differs (e.g., Figures 4.22 and 7.6), and such modifications are essential for the understanding of the relation of the potential energy diagrams of protonated Schiff bases and TICT (twisted internal charge transfer) molecules to those of simple olefins. (2) The number of low-energy potential energy surfaces increases when one or both bond termini carry lone pairs or empty orbitals, or if they engage in additional multiple bond formation. Examples of such situations are the cis-trans isomerization of Schiff bases (Figure 7.8) and azo compounds (Figures 7.10 and 7.11). A more complete discussion of the results embodied in Figures 4.5 and 4.6 than can be given here is available elsewhere (Michl and BonaCiC-Kouteckl, 1990). Geometries with large distances between the radical centers such as the TI state of Hzare called loose biradicaloid geometries; those with small distances such as the Sl state of Hzare called tight biradicaloid geometries. Since biradicaloid minima in TI occur preferentially for loose geometries, whereas those in Sl occur for tight geometries, return from the S, and T, to the ground state So will frequently take place at different geometries. This presumably quite general behavior may be one of the primary reasons for the difference in the photochemistry of molecules in the singlet and triplet states (Michl, 1972; Zimmerman et al., 1981).

Figure 4.6. Energies a) of the bonding MO n and the antibonding MO n* and b) of the n-electronic states of ethylene as a function of the twist angle 8. On both sides the states are labeled by the MO configuration dominant at planar geometries; in the middle, they are labeled by the VB structure that is dominant at the orthogonally twisted geometry (by permission from Michl and BonaCiC-Kouteckg, 1990).

Example 4.3: The simplest model to describe a a a s well as a n bond is the two-electron twoorbital model, which will be used frequently in the remainder of the text. The MO and the VB treatment of the H, molecule may serve as an example. In the

192

POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

simple MO picture the singlet states G, S, and D are approximated by the configurations

and respectively. In the first of these, the bonding MO @, = a, (hom*o) is doubly occupied. In the second, 4, and the antibonding MO @2 = a : (LUMO) are both singly occupied, and in the third, @2 is doubly occupied. The triplet state T may be written as In the basis of orthogonalized AOs x,, and xb, the "VB" structures for the singlet states are

4.2

CORRELATION DIAGRAMS

193

ionic structures (xi) and (xi) and their increase with increasing internuclear distance are plausible as a result of charge separation, and the rise of all curves at short internuclear distances is clearly due to poorly screened internuclear repulsion. While the bond in the S, state is covalent, the bond in the S, (and S,) state is purely electrostatic, as in a contact ion pair. At large internuclear separations, the singlet ground configuration I@, is a very poor approximation for the true ground-state function, and its energy is much higher than that of the triplet state. In summary, the simple MO description is useful at short distances, where individual configurations represent reasonable approximations to electronic states. However, at intermediate and larger internuclear separations (biradicaloid geometries), introduction of configuration interaction into the MO picture is absolutely necessary. In this region, the VB description provides a more intuitive rationalization of the shapes of the energy curves. In the case of twisted ethylene the wave functions of the molecular states are quite analogous to those of Hz, with the carbon 2p AOs of the original double bond at 90" twist being prevented from interacting by symmetry, and ,case. not by distance as in the H-

and

4.2 Correlation Diagrams and for the triplet state It can be verified by direct insertion of @, = (Xu + xb)lfl and &

= (K,

- x,)l

a that the relation between the MO configurations and the "VB" structures is

and Note that the triplet MO configuration is equal to the triplet "VB" structure and that in the case of nonpolar bonds the singly excited MO configuration is equal to the zwitterionic "VB" structure (xj - X 2 , ) l ~Configuration . mixing provides a better description of the states G = 'ao- It@, and D = 'a2+ I1Q0,whose ionic character can vary from purely covalent to purely ionic as the value of A changes. A transformation to standard VB theory based on nonorthogonal AOs is also possible but is more complicated (Michl and BonaCiCKoutecky, 1990: Section 4.1). Whereas simple MO theory does not provide any clue as to why the S state and even the D state of a a bond with the antibonding MO & singly and doubly occupied. respectively. are bound and not dissociative like the T state. these minima are readily understood on the basis of VB structures. which'closely approximate the actual state wave functions: The high energy of the zwitter-

Valuable information concerning the excited-state potential energy surface areas where minima o r barriers are t o be expected can be obtained from state correlation diagrams. Such diagrams are a very useful tool in discussing photochemical reaction mechanisms, in spite of their shortcomings. In particular, they are frequently the easiest t o construct along reaction paths that preserve some symmetry elements, and yet, minima in S, and So-S, touchi n g ~are most likely to occur at geometries devoid of all symmetry. Correlation diagrams usually provide only an approximate guide to the location of these important topological features.

4.2.1 Orbital Symmetry Conservation An orbital correlation diagram for a reaction path is obtained if the (qualitative) orbital energy schemes at both ends of the path are known and if energy levels of corresponding orbitals are connected o r correlated. The already familiar Figure 4.5a, which shows the energies of the bonding a and the antibonding dr orbitals for H, at the equilibrium geometry o n the left and for two infinitely separated hydrogen atoms on the right, may serve as an example. Each of the various assignments of electrons t o orbitals corresponds to a different electron configuration. From the orbital correlation diagram one can thus deduce which reactant and product configurations correlate with each other and obtain a configuration correlation diagram. If correlation lines of equal symmetry cross in this diagram, the noncrossing rule is vio-

194

POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

lated. These crossings will usually be avoided when configuration interaction is taken into account, and a state correlation diagram is obtained. Such a state correlation diagram can be interpreted as a cross section through the various potential energy surfaces of the system, and gives at least a qualitative description of the location of energy maxima and minima along the reaction path. Figures 4.5b and 4.6b are examples of state correlation diagrams. In Figure 4.7 the orbital correlation diagram for the concerted disrotatory ring opening of cyclobutene to butadiene is given together with the resulting configuration and state correlation diagrams as an example of a groundstate-forbidden reaction. According to the principle of conservation of orbital symmetry, those reactant and product orbitals associated with the reaction were correlated that show the same symmetry behavior (S = symmetric, A = antisymmetric) with respect to a symmetry element that is preserved along the reaction path. In the case in question, this is the symmetry plane bisecting the butadiene C 2 - 4 3 bond and perpendicular to the molecular plane. The hom*o-LUMO crossing in the orbital correlation diagram induces a crossing in the configuration correlation diagram, which is avoided in the state correlation diagram since both configurations that cross contain only doubly occupied orbitals, and are therefore totally symmetric. It should be noted, however, that the real photochemical reaction is not likely to follow a path that preserves any symmetry. Removal of the exact degeneracy

Figure 4.7. Disrotatory ring opening of cyclobutene to butadiene; a) orbital correlation diagram, b) configuration correlation diagram (dotted lines) and effect of configuration interaction, which converts the diagram into a state correlation diagram (solid lines). The triplet state is indicated by a broken line.

4.2

CORRELATIONDIAGRAMS

i 95

of the nonbonding orbitals at the biradicaloid geometry by a suitable symmetry-lowering distortion has the potential for reducing the So-S, gap to zero. (Cf. the discussion of critically heterosymmetric biradicaloids in Sections 4.3 and 4.4.) The resulting conical intersection represents a very efficient funnel for returning the excited molecules back to the ground-state surface. The appearance of this correlation diagram is very typical for a symmetrical ground-state-forbidden concerted reaction path. At the midway point, the crossing of a doubly occupied and an unoccupied MO results in two orbitals of equal energy that are occupied by a total of two electrons, thus producing a biradical at half-reaction. As mentioned earlier, reduction of symmetry has the potential to reduce the So-S, gap to zero, but it is not clear whether the energy of the point of intersection lies below or above that of the lowest S, energy at the symmetrical geometries shown in Figures 4.7 and 4.8. Except in the case of very exothermic reactions (cf. Example 6.7), molecules that have traveled from the reactant geometry to the biradicaloid minimum will have little chance of reaching the product geometry on the same surface, because the return to So from the pericyclic minimum or a nearby conical intersection will be very efficient. As shown in the correlation diagram in Figure 4.7b, the T, state is not affected by first-order configuration interaction. It is therefore very likely that along the reaction path there are no other minima than the spectroscopic

Figure 4.8. Calculated state correlation diagram for the disrotatory ring opening o f cyclobutene to butadiene (by permission from Grimbert et al., 1975).

? 96

POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

4.2

CORRELATION L)IA(%AMS

197

are no other important correlation-imposed barriers between the planar reactant geometry and the pericyclic minimum, and because the return to So is remarkably efficient,neither reactant fluorescence nor the formation of a fluorescent product can be observed. Finally, it is seen from the diagram that a concerted ring opening of cyclobutene in its triplet state TI is not to be expected (Grimbert et al., 1975). In Figure 4.9 the conrotatory ring opening reaction of cyclobutene is shown as a typical example of an orbital correlation diagram for a groundstate-allowed pericyclic reaction and of the resulting configuration and state correlation diagrams. In this case the spectroscopic product minimum is not separated by a funnel from the initial geometry, so at a first glance it should be easily accessible. However, the concerted reaction path in S, shows a correlation-imposed barrier that inhibits the formation of the product.

4.2.2 Intended and Natural Orbital Correlations a) Orbital correlation diagram, b) configuration correlation diagram (dotted lines); and state correlation diagram (solid lines) for the conrotatory ring opening of cyclobutene as an example for a pericyclic reaction that is allowed in the ground state. Triplet states are indicated by broken correlation lines.

Fipre 4.9.

minima near the reactant and product geometries. In particular, a pericyclic minimum is not to be expected on the TI surface in this case (uncharged perimeter). If no other reaction path is available and if the reactant geometry is energetically more favorable than the product geometry, the molecule will stay in this geometry after excitation into the triplet state and will only undergo photophysical processes; that is, it will return to the initial minimum in the ground-state surface, either by emission or via radiationless processes. If, however, the triplet minimum at the product geometry is lower, triplet excited product may be formed. This can be detected by triplet-triplet absorption spectroscopy. If phosphorescence can compete with radiationless deactivation, product emission can be also observed. Systems derived from a charged perimeter are different in that a special stabilization of T, is expected at the pericyclic geometry, and a minimum is probably present. (See Michl and BonaCiC-Koutecky, 1990.) Example 4.4:

Calculated potential energy curves for the symmetrical disrotatory ring-opening path from cyclobutene to butadiene are shown in Figure 4.8. It is seen that the biradicaloid minimum for this reaction occurs on a surface S , whose wave function is similar to that of the S1,surface at the reactant geometry. This is due to a touching of the potential energy surfaces of the first two excited singlet states. This touching is avoided in the absence of full symmetry. Since there

Difficulties are often encountered in constructing orbital correlation diagrams because no symmetry element is conserved during the reaction, or because the relative energies of reactant and product orbitals are not known. In these cases a two-step procedure has proven very helpful (Michl, 1972; 1973; 1974b). This is based on the decomposition of a relatively complicated system into simpler subunits. First, a correlation diagram is constructed for the noninteracting subunits, and in a second step, interaction between the subunits is added. This will be illustrated using the disrotatory and the conrotatory ring opening of cyclobutene, shown in Figures 4.10 and 4.1 1 as an example. First, the breaking of the a bond is considered with the assumption that an imaginary wall prevents interaction of this subunit with the remainder of the system. Then ring opening leads to two nonbonding hybrid AOs from the aand d MOs, whereas the R orbitals (and all other orbitals not explicitly treated here) remain unaffected. In the second step the imaginary wall is removed so that orbitals with comparable nodal properties can interact with each other. In this way the orbitals of the biradical formed during the first step are converted into the orbitals of the more stable butadiene. In estimating the effects of orbital interaction it has to be remembered that they will become larger as the energy difference between the orbitals of interest becomes smaller and as the LCAO coefficients at the interacting centers become larger. From a comparison of Figures 4. IOa and 4.1 la it is evident that the nodal properties of the newly generated n components of the original a and dr combinations are opposite to each other for the disrotatory and the conrotatory ring opening. The n* MO of the ethylenic bond has a node across the bond and is suitable for interaction with the n component of the original cr* combination if the opening is disrotatory (Figure 4. IOa) and with the n com-

198

POTENTIAL ENERGY SURFACES: BAKKIEKS, MINIMA, AND FUNNELS

4.2

CORRELATION DIAGRAMS

Figure 4.10, 1 Two-step procedure for the derivation of the orbital correlation diagram of the L : ~ L Iotatory ring opening of cyclobutene; a) "intended" orbital correlation that results i t l rhe absence of interaction between orbitals of the a bond that is being broken and o itals of the n bond. The schematic representation of the orbitals shows that due to di erent nodal properties only u-n and 8-n* MO interactions are possible. Orbita1,symmetry labels n and aapply strictly only at the planar cyclobutene and butadienb geometries. Dark and light arrows indicate the magnitude of these interactions, /which are switched on in the second step and produce the orbital correlation diagtam shown in b); labels S and A or solid and broken lines, respectively, indicate the different symmetry properties with respect to the symmetry plane that is preserved along the reaction path (by permission from Michl, 1974b).

a* correlation lines cross in the first step, whereas the crossing is avoided if

ponent of the original a combination if the opening is conrotatory (Figure 4.1 la). The R orbital has no node across the bond, so here the situation is reversed; In Figures 4.10a and 4.1 l a the resulting interactions are indicated by arrods, and in Figures 4. lob and 4. I l b the final orbital correlation diagrams ate shown. It can be seen that the stabilization of the biradical by orbital iqteraction is much more efficient for the conrotatory opening of cyclobuteqe than for the disrotatory reaction. As a consequence of the hom*oLUMO crossing, the latter has to pass through a biradicaloid geometry in spite of the potentially stabilizing interaction. Since the two-step derivation of the orbital correlation diagram with the help of the imaginary wall makes use only of orbital nodal properties, it is generally applicable, even in those cases where no symmetry element is preserved during the reaction. Relations obtained in the first step can be referred to a s "intended" correlations; they demonstrate how the original orbitals would change during the reaction if n o other relations could be established through additional interactions. Thus, in the case of the disrotatory ring opening shown in Figure 4.10a, the R and uas well as the I1C and

interactions are taken into account. From the correlation lines shown in Figure 4.10b this avoided crossing can still be visualized; and since orbital interactions can be assessed a s described earlier, the shape of the correlation lines is not arbitrary. In the following section it will be shown that such avoided crossings in the orbital correlation diagram may in fact show up on potential energy surfaces. If a correlation diagram is constructed by connecting reactant and product orbitals of equal symmetry that are localized in the same spatial region of the molecule and that show the same sign relations for the LCAO coefficients, crossings of correlation lines of equal symmetry may occur. The natural orbital correlations (Devaquet et al., 1978) obtained in this way are very similar to the intended correlations described earlier. The main difference is that in the first step the orbitals of the product are now not taken to be the AOs of the bond that is being broken, but rather MOs constructed from them. In Figure 4.12 the natural orbital correlation is shown once again for the disrotatory ring opening of cyclobutene. The R and Ic* MOs correlate with the butadiene MOs #, and A, for which the LCAO coefficients are largest for the two inner carbon atoms and have either equal o r opposite signs, re-

Figure 4.11. Derivation of the orbital correlation diagram for the conrotatory ring opening of cyclobutene; a) intended correlation, b) correlation including interaction between aand n* and between nand a* MO's, respectively. Orbital symmetry labels n and aapply strictly only at the planar cyclobutene and butadiene geometries. Labels S and A, or solid and broken correlation lines; respectively, indicate the symmetry behavior with respect to the twofold-symmetry axis (by permission from Michl, 1974b).

200

POTENTIAL ENERGY SURFACES: BAfUUERS, MINIMA, AND FUNNELS

Natural orbital correlation for the disrotatory ring opening of cyclobutene to'butadiene (by permission from Bigot, 1980). Figure 4.12.

spectively. Similarly, the a and dr MOs correlate with the contributions from the end atoms dominate.

and

cp3for which

Figure 4.13. Configuration correlation diagram (dotted lines) and the r&sultingstate correlation diagram (solid and broken lines, respectively) for the disrotatory ring from opening of cyclobutene, based on natural orbital correlations (by perhission I Bigot, 1980).

4.2.3 State Correlation Diagrams If intended o r natural correlations are used, one has the choice either to switch on the interaction between subunits first and then to construct the configuration and state correlation diagrams, o r to construct the configuration correlation diagram first and then to add the interaction. The first alternative is identical with the procedure described in Section 4.2.2; the second one is illustrated in Figure 4.13, once again using the disrotatory ring opening of cyclobutene a s an example. It is seen that due to the natural correlation of the a and fl MOs of cyclobutene with the antibonding butadiene MOs t$3 and $., and of the n and a* MOs with the bonding MOs $, and $2, the correlations starting at the ground configuration and at the JZ-fl excited configuration of cyclobutene go uphill, whereas those starting at the -8 excited configurations go downhill. Hence, the avoided crossings produce barriers in the lowest triplet state as well a s in the two lowest singlet states that are not obtained if ordinary symmetry correlations are used. The calculated potential energy surfaces show similar barriers, which have their origin in the fact that the MOs "remember" the intended o r natural correlation. This becomes evident when Figure 4.13 and Figure 4.8 are compared. The situation is complicated by the fact that sometimes it proves useful to derive the orbital correlations not on the basis of MOs but rather on the

basis of AOs, within the framework of a VB description of the wave function. Altogether there are the following possibilities, which are collect d in Figure 4.14: On the one hand, with the help of the imaginary wall w ich prevents orbital interaction, configurations of a system can be con~tructed either from the interaction-free AOs o r from the MOs obtained from these AOs. The configurations and states of interest are then obtained bq turning on the interaction, that is, by removing the imaginary wall. This corr/xponds to the use of interaction-free one-electron functions for constructink manyelectron wave functions in the framework of the V B o r MO theory bnd taking into account the interactions at the level of the many-electron wape functions, that is, either at the MO configuration o r V B structure correlation level o r even at the state correlation diagram level, which is often F r y useful. On the other hand, the interaction may be switched on alreadk at the level of one-electron functions; this leads to MOs with interactions iqcluded, which are then used to construct the many-electron wave functions of configurations and states. In principle, all these procedures will give the same results, but depending on the problem in question, one o r another prpcedure will prove advantageous.

202

I'OTENTIAL ENERGY SURFACLS: BAKKIEKS. MINIMA, AND FUNNELS

noninteracting

Orbitals

,--. \

( AOS)::::~

--/

;'--'-

O ~

'.--a I

C_-_----------

Many-electron functions

interacting

;' VB structure;';

:,--Configurations,,' _ - - _ - _ -----I I

v r---------

States - 1I -----------

i I

& p6-q II

Figure 4.14. Schematic representation of the different possibilities for constructing state correlation diagrams by switching on the orbital interaction at various levels.

Example 4.5: The orbital correlation diagram for the concerted dimerization of ethylene to form cyclobutane or for the reverse reaction, the fragmentation of cyclobutane into two ethylenes, may be obtained most easily by applying the principle of conservation of orbital symmetry. A mirror plane perpendicular to the molec-

Figure 4.15. Symmetry-based orbital correlation of the orbitals involved in the fragmentation of cyclobutane into two ethylene molecules. Indicated is the symmetry behavior (S or A) with respect to a symmetry plane perpendicular to the molecular plane and cutting the ethylene bonds into halves.

4.2

CORRELATION DIAGRAMS

203

ular plane and either across the a bonds that will break, or across the n bonds that will be formed, is used as the symmetry element. It is easily seen that both choices give the same result. Next, we notice that the a and 8 MOs of cyclobutane are stronger bonding and antibonding, respectively, than the n and n* MOs of ethylene, and obtain the orbital correlation diagram of Figure 4.15. The corresponding MO correlation diagram for the fragmentation of cyclobutenophenanthrene into phenanthrene and acetylene is most easily obtained if in a first step the orbital correlation diagram of Figure 4.15 is superimposed on the n MO energy-level diagram of biphenyl and in a second step interactions between orbitals of equal symmetry (S and A with respect to the mirror plane perpendicular to the molecular plane of phenanthrene) are introduced, as shown in Figure 4.16. In hydrogen atom abstraction by a ketone the following orbitals are important: for the reactant R;CO + RH, the orbitals a,, and a:, of the R-H bond to be broken and the orbitals n,,, rc,,, and $O of the ketone chromophore. : a of the newly formed For the product R;COH + .R, the orbitals a(,, and , OH bond, plus the orbitals n,,and n;. of the protonated ketyl radical and the orbital p, of the odd electron on the residue R. Their relative energies can be easily estimated qualitatively. Since both no and a,, are essentially localized

Figure 4.16. Derivation of the correlation diagram for the concerted fragmentation of cyclobutenophenanthrene from the orbital energy-level scheme of biphenyl and the orbital correlation diagram for the fragmentation of cyclobutane into two ethylenes. (The additional double bond has been neglected in the simplified treatment.) The arrows indicate the magnitude of orbital interactions between the two superimposed systems (by permission from Michl. 1974b).

2?4

POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

4.3

BIKADICALS AND UIKADICALOIDS

205

on the oxygen atom, and u,., and p,. are on the carbon atom of the residue R , the natural orbital correlation shown in Figure 4.17a is obtained. This leads to the configuration correlation diagram shown in Figure 4.18 by dotted lines. From this the state correlation diagram shown in solid and broken lines is obtained by taking into account the avoided crossings, which produce barriers in the S, and T, correlation lines, and which correspond closely to those obtained through detailed calculations of the relevant potential curves (Bigot, 1980). If, however, the interaction is already introduced at the orbital correlation level, so that a,, correlates with a,, and n, with p, (Figure 4.17b). a state correlation diagram without barriers and minima resulting from the avoided crossing is obtained. This is in agreement with the Salem diagram derived on the basis of VB structures, which will be discussed in Section 6.3.2.

4.3 Biradicals and Biradicaloids

&'O CI O

k h

H-

Figure 4.17. a) Natural orbital correlation diagram for hydrogen atom abstraction by a carbonyl compound and b) orbital correlations after introducing interactions between orbitals of equal symmetry.

In the beginning of this chapter it was mentioned that biradicaloid minima are of great importance in photochemical reactions. Due t o their very short lifetime, molecules in biradicaloid minima are usually not a s easy to observe as molecules in spectroscopic minima with ordinary geometries. This is particularly true in the singlet state, whose decay is not slowed down by the need for electron spin inversion. Much of the knowledge of reactive minima is therefore based primarily on theoretical arguments, some of which will be considered in this section. (Cf. BonaCliC-Koutecky et al., 1987; Michl 1991.)

4.3.1 A Simple Model for the Description of Biradicals For the discussion of potential energy surfaces of excited states it is particularly important that at appropriate geometries closed-shell molecules can turn into biradicaloids. We have already seen briefly in Section 4.1.2 that such biradicaloid geometries can be derived from equilibrium geometries by suitable distortions such a s the stretching of a single bond (a), twisting of a double bond (b), o r bending of a triple bond (c). T h e "antiaromatic" geometry found along the concerted path of groundstate-forbidden pericyclic reactions, which is topologically equivalent to an 2]annulene, is a particantiaromatic Hiickel [4n]annulene o r Mobius [4n ularly interesting type of biradicaloid geometry. (Cf. Section 4.4.) Other biradicaloid geometries and combinations of those mentioned are equally possible. Whereas at equilibrium geometries the electronic structures of even-electron molecules are in general quite well described by a single closed-shell

State correlation diagram for hydrogen atom abstraction by a carbonyl compound derived from the natural orbital correlations. The configuration correlations are shown by dotted lines, taking into account the interaction yields the correlations shown by solid and broken lines for singlet and triplet states, respectively. Figure 4.18.

206

POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

configuration, this is not so at biradicaloid geometries. At the latter, only two electrons occupy two nearly degenerate approximately nonbonding orbitals in all low-energy states, and as a minimum, one needs to consider all configurations that result from the various possible occupancies of these two orbitals. If the active space is restricted to these two nonbonding orbitals, chosen to be orthogonal and labeled g, and g,', these are the following configurations:

with both orbitals singly occupied and

with one of them doubly occupied. (Cf. Example 4.3.) In the simplest model for the electronic structure of biradicaloids, attention is limited to these three singlet configurations and one triplet configuration, so only three singlet states and one triplet state result (Salem and Rowland, 1972; Michl, 1972; BonaCiC-Kouteckg et at., 1987; Michl, 1988). Before comparing with experiment, it has to be remembered that upon going to a more accurate description by taking into account all interactions with other configurations, the four states of this model can be influenced differentially. Such interactions, including effects known as "dynamic spin polarization" (Kollmar and Staemmler, 1978), may thus change the energetic order of closely spaced states. Nevertheless, those aspects of the model that do not depend on small energy differences are generally correct, and it provides a very pictorial description of many of the interesting properties of biradicaloids. If, for instance, the orthogonal nonbonding orbitals are AOs xa and 2, located at the atoms A and B and prevented from interacting either by excessive separation, as in a dissociated single bond, or by symmetry, as in a twisted double bond-that is, if rp = xa and rp' = xb-the configurations given in Equations (4.1) and (4.2) are the VB structures which may be r e p resented by the formulae 2-7. A - I3 or .AB. A -6 : :A-B ('38)

(z,)

(z2)

4.3

BlRADlCALS AND BlRADlCALOlDS

207

-AB., respectively. Because of their "double radical" appearance, they will be referred to as "dot-dot". structures. Sometimes they are also called biradical structures, or covalent structures. The label covalent is derived from the Heitler-London description of a covalent bond, and is therefore somewhat inappropriate in the case of the triplet, which does not correspond to a bond at all, but to an antibond. The polarized structures Z, and Z, may be represented by the formulae A@B@ and A@B@,respectively, and will be referred to as hole-pair structures. In the case of dissociated H, and twisted ethylene, they are zwitterionic. Because of the charge separation, their energy is high. In general, however, there is no simple relation between the dot-dot or hole-pair nature of these VB structures and their zwitterionic nature. For instance, in the twisted aminoborane (10) the dot-dot structure @.BH,-NH,@. is zwitterionic and high in energy, whereas the hole-pair , no formal charges, and is of structure Z, corresponds to B H ~ N H ,carries low energy. In singly charged systems such as 11-13, neither the dot-dot structure 'B nor the hole-pair structure Z, is zwitterionic, and their energies can be quite comparable.

It is not necessary to choose the orthogonal orbitals g, and g,' to be the most localized ones, as we have done in our discussion so far. Since in the simple model we consider all configurations that can be constructed from the two nonbonding orbitals by any permissible electron occupancy, the energies and wave functions of the resulting states are invariant to any mixing of these orbitals. Thus, we may equally well choose them to be the most delocalized orthogonal molecular orbitals, related to the most localized ones by and

For systems such as a dissociated H, molecule (8)or twisted ethylene (9) the .;tr,lctrlre.; ' R ; ~ n t l'I3 ;rrc nonpolar and can be represented as A-B and

or to be the complex orthogonal orbitals defined in Figure 7.53. In addition to these three canonical choices of orthogonal orbital pairs, an infinite numher of others are available (BonatiC-Kouteckg et al., 1987; Michl, 1991,

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POTENTIAL ENERGY SURFACES:BARRIERS, MINIMA, AND FUNNELS

1992). The appearance of the final singlet-state wave functions is different ("open-shell," "closed-shell") when expressed through one or another choice of orthogonal orbitals, even though they remain the same wave functions. By a suitable choice of one of the canonical orbital sets, any one of the three resulting singlet states can be made to have an "open-shell" ("dotdot") appearance, with two singly occupied orbitals. For instance, the "open-shell" configuration 'B = I(@,@,) in the most delocalized orbital (MO) basis is identical with the combination of two "closed-shell" ("hole-pair") structures in the localized ("VB") basis, X2, - A, whereas Z, - Z, = & & in the delocalized basis is identical with the "open-shell" structure '(xUxb) in the localized basis. (Cf. Example 4.3.) The triplet-state wave function has the same open-shell appearance in all possible orbital bases. Although the various choices of orthogonal orbital basis are all equivalent in principle, often one or another is more convenient to use. In general, the most delocalized choice provides more physical insight for molecules at ordinary geometries, and the most localized choice for molecules at biradicaloid geometries. It was for this reason that we used MO-based labels for the states of the ordinary H2 and ethylene molecules on the left-hand sides of Figures 4.5 and 4.6, respectively, and VB-based labels for the states of the dissociated H,and twisted ethylene molecules in the same figures. At times, it is best to work in the basis of nonorthogonal orbitals (GVB calculations), but we shall not use it here.

4.3

BIKAL)ICALS AND BIKADICALOIDS

Figure 4.19. Wave functions and energy levels of a perfect biradical (center), constructed from the most localized orbitals X, and X, (left) and from the most delocalized orbitals 9, and $2 (right) (adapted from BonaCiC-Kouteckf et al., 1987).

Starting from delocalized orbitals @, and @2,and introducing K,, and K;, = (Jll + J2,)/2 - J,, as the corresponding electron repulsion integrals,

4.3.2 Perfect Biradicals In a perfect biradical, the orthogonal nonbonding orbitals g, and rp' have the same energy and do not interact, no matter how they are chosen. Examples are provided by the earlier cases of fully dissociated H, and 90"-twisted ethylene. The energy-level diagram for a perfect biradical is characterized by only two parameters, the exchange integrals K and K', and is shown in Figure 4.19. The energy diagram may be derived equally well starting with any orbital choice, but the three canonical ones are the simplest to use. We shall outline the derivation starting with the most localized orbitals. If for the moment xb(l)xb(2),xa(1)xb(2),and spin is ignored, the four configurations xU(1)xu(2), xb(1)xa(2)would have the same energy in the absence of electron repulsion (HMO approximation). Electron repulsion is much higher for the chargeseparated functions of the hole-pair type than for those of the dotdot type and causes a symmetric splitting of their energies by 2KAb = (Jaa+ JJ2 Jabwith respect to the average energy E,, where Jab= (aalbb) is the usual Coulomb integral. Finally, when the properly symmetry-adapted combina] I used, ~ tions [xa(1)xu(2) x b ( 1 )~b(2)1/@and [xu(I )~b(2)2 x b ( 1) X U ( ~ )are the in-phase (plus) combinations are destabilized and the out-of-phase (minus) ones are stabilized by Kt,,. Here, Kub= (ablab) is the usual exchange integral. Thus, the resulting four energy levels are E, + KiIb-+ K,,,.

and

(cf. Equation 4.3), one obtains similar results (Figure 4.19). The overlap density yg,' is smaller for the localized orbitals X, and xb, which occupy as distinct parts of space as at all possible, than for the delocalized orbitals @, and tp,, so and The wave function [xa(1)xb(2)- xb(l )xU(2)]/flis antisymmetric with respect to an interchange of electrons 1 and 2 and needs to be multiplied with one of the three symmetric two-electron spin functions to describe a triplet state T. The other three functions are symmetric, need to be multiplied with the antisymmetric two-electron spin function, and describe three singlet states, So, S , and S,. The amusing isomorphism of the two-electron ordinary and spin functional space has been discussed elsewhere (Michl, 1991, 1992).

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POTENTIAL ENEKGY SURFACES: UAKKIEHS, MINIMA, AN0 FUNNELS

Since both K,,, and K;, are non-negative, in this model the triplet state T is the most stable of all four states. From Figure 4.19 it is also clear that (I) the wave function (x: + X-) = (& + &) represents the least stable of the four states, S,; (2) the wave function (x: - xi), or '(@,@,), represents S,; and (3) the wave function '(x,~,,),or (& - @$), represents So. In the general case K;, and KO,are different from each other, so the energies of the four states, T, So, S,, and S, are all different. Biradicals with K,, = 0 are referred to as pair biradicals, since the condition can be strictly satisfied only if the separation between the centers A and B is infinite so that the biradical in fact consists of a pair of distant radical centers. In practice, even twisted ethylene already is very nearly an ideal pair biradical. In pair biradicals, So and T as well as S, and S, are pairwise degenerate. Example 4.6:

On the basis of the two-electron two-orbital model it is easy to understand the differences in the potential energy curves describing the dissociation of a a bond and a n bond. The H, molecule at infinite internuclear separation (righthand side of Figure 4.5) and the ethylene molecule at 90" twist (center of Figure 4.6) are perfect biradicals. The former is a perfect pair biradical (K,,, = 0 ) ; the latter is a nearly perfect one (small K,,,). This difference is reflected in perfect TS, and S,-S,degeneracies in the former and only near degeneracies in the latter within the framework of the siinple model. However. upon going to a more accurate calculation, the state order within both nearly degenerate state pairs of the twisted ethylene changes, for reasons that are now well understood (Mulder. 1980; Buenker et al., 1980).

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211

between the eigenfunctions of the perfect biradical is due to interaction elements introduced by the perturbation that converted it into a biradicaloid. In hom*osymmetric biradicaloids, a bonding interaction between the most localized orbitals is the only perturbation ("covalent perturbation"). Its magnitude is described by y, approximately equal to twice the resonance integral of simple theories. Its presence causes a mixing of the state functions '(x,x,) and (x: + X-) of the perfect biradical, which stabilizes its ground state Soand destabilizes its S, state relative to the triplet state, whose energy we take as a reference (Figure 4.20a). When y is large enough, an ordinary nonpolar covalent bond results, with a large percentage of dot-dot character, '(x,~,), and a small amount of symmetrized hole-pair character, (x: + x:), so that an ordinary molecule is formed (Figure 4.20a). The S, state is not affected, and the energy gap AE between the Soand the S, state increases with increasing interaction. Stretched H, and twisted ethylene again may serve as examples. As the H-H separation decreases, and as the twist angle in ethylene decreases, the covalent perturbation y increases in absolute magnitude. In both cases, this results in a stabilization of the So state (bond formation) relative to the antibonding T state. It also results in the stabilization of the S, and S, states of Hz, although in the usual description the first of these states has as many electrons in the antibonding as in the bonding orbital, and the second only

Biradicals for which K;, = K,,, are referred to as axial hiradicals and in these, Soand S, are degenerate. This condition is normally enforced by the presence of a threefold or higher axis of symmetry (e.g., in 0, and the pentagonal cyclopentadienyl cation), but alone, this is not sufficient (e.g., square cyclobutadiene is almost a pair biradical).

4.3.3 Biradicaloids Imperfect biradicals, for which at least one of the necessary conditions for perfect biradicals is not fulfilled, are called biradicaloids. In the general case they are nonsymmetric biradicaloids. In these, the localized orbitals X, and x,, have different energies (electronegativities)and also interact. An example is propene partially twisted about its double bond. In hom*osymmetric biradicaloids the localized orbitals X, and X, have equal energies, but interact. An example is partially twisted ethylene. In heterosyrnmetric biradicaloids the localized orbitals xu and x,, have different energies, but do not interact. An example is 90"-twisted propene. In the simple model, the triplet state of a biradicaloid is still described by the wave function '(qq'), but the singlet wave functions no longer are those given in Figure 4.19. The mixing (CI)

The two-electron two-orbital model a) for a hom*osymmetric biradicaloid and b) for a heterosymmetric biradicaloid: schematic representation of state energies, relative to the T state, as a function of the interaction integral y or as a function of the electronegativity difference6 of the orbitals X, and X, (by permission from Michl and BonaCiC-Kouteckq, 1990). Figure 4.24.

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POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

has electrons in the antibonding orbital, and thus neither might be expected to be bound. In this regard, the effect of untwisting the ethylene molecule, which results in an energy increase for both the S, and S, states, is comforting. The difference is clearly due to the fact that along the ethylene twisting path, K:, hardly changes as Id grows, so the magnitude of y alone dominates the state energies, while along the H,association path, K;, drops dramatically as the charge separation energy decreases at shorter distances, so it counteracts the effect of the growing 14. The bonding in S, and S, is not covalent; rather, it is similar to bonding in an ion pair. In order to understand the concurrent changes in the energy of the reference state T within the simple model, it is necessary to consider overlap explicitly (BonaCiC-Koutecky et al., 1987). As the overlap between the nonorthogonal AOs grows, the energy of the orthogonalized localized orbitals xa and X, increases, and so does the energy of the T state. In heterosymmetric biradicaloids, the only perturbation is an electronegativity difference between the two most localized orbitals ("polarizing perturbation"). This is described by their energy difference 6, equal to half the energy difference between the structures xt, and xi. Its presence causes the in-phase and out-of-phase combinations of the hole-pair structures, (x: + xi) and (d - xi), to mix. This results in an increase in the energy of the former (S,), dominated by the less stable of the two hole-pair structures, and a decrease in the energy of the latter (S,), dominated by the more stable holepair structure, relative to the energy of the triplet state. The dot-dot structure '(xaxb)remains an eigenstate of the system, independent of 6. In perfect biradicals with a small K,,, close to the pair biradical limit (e.g., twisted ethylene), the S, and S, states are nearly degenerate, and even a weak polarizing perturbation 6 causes an essentially complete uncoupling of the hole-pair configurations and xi. This imparts a highly polar character to the S, and S, states and underlies an effect that is known in the literature as sudden polarization (BonaCiC-Koutecky et al., 1975). Example 4.7: The sudden polarization of the zwitterionic state of a nonsymmetric biradicaloid, starting with a perfect biradical, requires the presence of a small polarizing perturbation 6 and the presence of a covalent interaction y whose magnitude can be varied from well above 6 to less than 6. As long as y is much larger than S, the effect of the latter on the composition of the eigenstates is essentially nil, and the S, and S2states are represented by nearly exactly balanced mixtures of the hole-pair structures. As y becomes smaller than 6, the situation changes abruptly, and now the effect of 6 dominates the composition of the wave functions: the S, and S, states are each nearly exactly represented by a single hole-pair structure. The results of ab initio calculations for the charge distribution in the S,state plotted in Figure 4.21 as a function of the twist of s-cis-s-trans-1,3,5-hexatriene

4.3

BlRADlCALS AND BlRADlCALOlDS

Figure 4.21. Charge separation Aq in the excited singlet state S, of twisted scis-s-trans-l,3,5-hexatriene as a function of the twist angle 8 (by permission from BonaCiC-Koutecky et al., 1975).

angle 8, which controls the magnitude of the covalent perturbation y, make this evident. For nearly all values of 8 the charge is distributed evenly among the two allylic units according to the ionic structures 14a c* 14b. If the allylic groups are nearly at right angles to each other (0 = 90°), the covalent perturbation vanishes and sudden polarization occurs as a consequence of the small asymmetry S between the cis- and trans-connected allyl groups (BonaCiC-Koutecky et al., 1975).

The fact that the S, state rather than the S, state of a perfect biradical is stabilized upon polarizing perturbation has an important consequence. When the perturbation becomes strong enough, it causes a surface crossing as indicated in Figure 4.20b. The degeneracy of the S, and S, states has important consequences for photochemistry, since it provides a facile point of return for singlet excited molecules to the ground state. (See Chapter 6.) The point at which the states So and S, are degenerate is given by the relation

Three important situations are of interest. For 6 < 6, the biradicaloid is weakly heterosymmetric. The lowest singlet, S,, similar to that of the perfect

214

POTENTIAL ENEKCY SUKFACES: BAKKIEKS, MINIMA, AND FUNNELS

biradical, is represented by '(x,~,),and its separation from the T state is unaffected by 6. The S, state is represented by a mixture of hole-pair configurations, (x:) and (xi), with (xi) dominant. This situation, which corresponds to a large energy gap AE, is usually encountered if the dot-dot structure involves no formal charges. Examples are unsymmetrical 90"-twisted double bonds, such as twisted propene, or twisted ethylene pyramidalized at one carbon. For 6 > 6, the biradicaloid is referred to as strongly heterosymmetric. In the lowest singlet So,represented nearly exclusively by the more stable of the hole-pair configurations, both electrons are kept virtually exclusively in the more stable orbital X, localized on the center B, often as a "lone pair," while the less electronegative orbital X, is empty. If (xi) involves formal separation of charge, such species are usually referred to as zwitterions or ion pairs, with a positive charge on center A and a negative charge on B. However, really large 6 values are normally encountered in systems in which the dot-dot structure '(x,~,)carries separated formal charges, while the holepair configurations (xi) does not. Examples of strongly heterosymmetric biradicaloids are molecules containing a noninteracting donor-acceptor pair, such as the 90'-twisted aminoborane (10);the TlCT (twisted internal charge transfer) states represented by the zwitterionic excited state S, of these biradicaloids lead to a very pronounced solvent dependence of the emission wavelength (Grabowski and Dobkowski, 1983; Lippert et al., 1987). Finally, a species with 6 = 6, is a critically heterosymmetric biradicaloid. In this case, the dot-dot structure has the same energy as the more stable of the hole-pair structures, and the simple model predicts S, and S, to be degenerate. This situation is most readily obtained if neither '(xJ,,) nor (xi) involves formal charge separation, that is, in charged biradicaloids where excitation results only in a translocation of formal charge. These arguments are in good agreement with detailed calculations for the ethyleneiminium ion CH-FNH,~, for which the energy gap AE(S, - So) is just equal to zero in the 90"-twisted geometry. (See Section 7.1.5.) These results are equally applicable to a and n bond dissociations, and suggest the general rule that the Soand S, hypersurfaces of a biradicaloid are expected to closely approach each other and to touch if the energies of the dot-dot (A-B) and hole-pair VB structures (AB:) are equal and if the two structures cannot interact. The energy equality can be reached by an appropriate choice of atoms or groups A and B, including the choice of substituents and their orientation (e.g., by choosing the particular double bond in a conjugated sequence around which the molecule will be twisted), the choice of transannular interactions in pericyclic biradicaloids, and the choice of the solvent (BonaCiC-Kouteckget al., 1984; BonatiC-Kouteckg and Michl, 1985b). We can now return to the bond dissociation diagrams in Figures 4.5 and 4.6 and generalize them from the nonpolar case (6 = 0) to a polar case. A

4.3

BIKADICALS AND BlRADlCALOlDS

iis

major change will occur in the dissociated (biradicaloid) limit, since the state energies plotted there apply for 6 = 0 and will change in the manner shown in Figure 4.20b as 6 increases. The results are shown in Figure 4.22 for the dissociation of a a bond and Figure 4.23 for the dissociation of a n bond. In the case of a a bond, the bond length is plotted from left to right so that the dissociated limit ( R = m) is on the right, with the energy of the dotdot singlet and triplet states independent of 6 and the energy of the hole-pair state dropping as 6 increases toward the viewer, as expected from Figure 4.20b. The back side of the plot shows the nonpolar dissociation curves already familiar from Figure 4.5, and cuts at constant 6 taken closer to the viewer provide dissociation curves at increasing values of 6. Clearly, the major change is that the S, state becomes dissociative, and at 6 = 6, goes to the same dissociative limit as the triplet. This situation is nearly reached for the charged bonds such as C-No, for which the dot-dot and the holepair dissociation limits differ by charge translocation rather than charge separation, and have comparable energies. For even larger values of 6, the nature of the ground state changes. It is increasingly well described by a single hole-pair structure, and the entity in question can be called a dative bond, or a charge-transfer complex. The

Figure 4.22. Schematic representation of the state energies of a dissociating a bond. Shown are the So, S , , and TI energies a s a function o f the bond length R and the electronegativity difference 6 of orbitals x,, and X, (by permission from Michl and BonaCiC-Kouteckg. 1990).

216 . ,.

POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

Figure 4.23. Schematic representation of the state energies of a dissociating a bond as an example of a heterosymmetric biradicaloid. Shown are the So, S,, and T, energies as a function of the twist angle 8 and the electronegativitydifference 6of orbitals x and xb (by permission from BonaCiC-Kouteckg and Michl, 1985b).

singlet excited state is zwitterionic, and the S,-T singlet-triplet splitting is small. A simple example is @H,N-BHP. In organic chemistry, this situation is frequently encountered in donor-acceptor pairs. In most cases, the donor, the acceptor, or both have a complicated internal structure and possess lowlying locally excited states that need to be added for a complete description, using the techniques of Section 4.2. While the nonpolar case (6 = 0) of S, dissociation clearly applies to an isolated H, molecule, Figure 4.22 suggests that such a symmetrical dissociation path is probably followed by no others. In polyatomic molecules, the two bond termini always have an opportunity to acquire different electronegativities (a nonvanishing 6 value), by intramolecular means such as changes in the degree of pyramidalization or of conjugation with adjacent groups, or by intermolecular means such as unsymmetrical solvation. Since such a reduction of symmetry will permit an uncoupling of the two holepair configurations (cf. Example 4.7). permitting a decrease in the energy of the S, state, it is hard to imagine circ*mstances under which it would fail to occur. One can therefore expect single bond dissociations in S, to proceed along unsymmetrical pathways and to produce contact ion pairs, even in the nominally nonpolar cases such as Si-Si bond dissociation. Internal conversion to s,,corresponds to back electron transfer and may be

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BlKADlCALS AND BlKADlCALOlDS

217

slow if the excitation energy is high. Fluorescence, intersystem crossing, and attack by external or intramolecularly present nucleophiles or electrophiles on the ion pair may then compete successfully, and it is indeed possible to account for most if not all of the singlet photochemistry of organooligosilanes on this basis. It is not known to what degree this is correct, and to what degree their reactions involve motion into those parts of the potential energy surfaces where the S, state is of a dot-dot character. (See Section 4.4.) Figure 4.23 is exactly analogous but deals with the dissociation of a n bond. The energies of the So, S,, and T states are shown as a function of the twist angle 8 and the electronegativity difference 6. The nonpolar case, 6 = 0, is shown in front and corresponds to the potential energy curves of Figure 4.6. A cut through the surfaces at 8 = 90' yields the curves familiar from Figure 4.20b: the singlet and triplet dot-dot structures are nearly degenerate since K,, is small, and do not change their energy as 6 is increased, while one of the hole-pair structures is stabilized until it meets the dot-dot singlet at 6 = do, and thereafter its energy descends further below that of the dotdot structures. Cuts through the surfaces of Figure 4.23 at various constant values of 6 give the rc-bond dissociation curves of polar bonds. The different values of 6 could be achieved intramolecularly, by a suitable variation of the molecular geometry, or intermolecularly, by changes in the molecular environment, or even by such modifications in the molecular composition itself as changes in the substituents on the double bond or in the nature of the doubly bonded atoms. The cut at 6, contains a critically heterosymmetric biradicaloid and a S,-So touching. This situation is normally encountered with charged n bonds, for example, protonated Schiff bases and many cationic dyes. (See Section 7.1.5 and Figure 7.6.) Inasmuch as a variation of 6 can be accomplished by geometrical distortions of a molecule, Figure 4.23 can be viewed as depicting a funnel in its S, potential energy surface. This provides a nice illustration of the physical significance of the vectors x, and x, (Section 4.1.2) in the nuclear configuration space that define the branching space of a conical intersection corresponding to a critically heterosymmetric biradicaloid: x, is the 6 coordinate (i.e., the direction of the fastest change in the energy difference between the two "nonbonding" orbitals) and x, is the y coordinate (i.e., the direction of the fastest change in the degree of interaction between these two orbitals). Recall that the electronic energy that is converted into nuclear kinetic energy by downhill motion on the S, surface toward the tip of the cone usually tends to accelerate the nuclei in the direction of x, (since that is usually the steepest slope on the upper cone); the electronic energy that is converted into nuclear kinetic energy by a jump to the lower surface accelerates the nuclei in the direction x2. The paths followed after return to So through a "critically heterosymmetric" funnel are therefore likely to

218

PO'SENI'IAL ENERGY SUKFACES: UAtU, weighted by its spin-orbit coupling parameter I , and this clearly reflects the "heavy atom effect." However, it indicates equally clearly that a contribution from an atom does not need to be large just because the atom is heavy: the vector contribution from that atom might have a small length or an unfortunate direction that cancels contributions from other atoms. (Note that "inverse" heavy atom effects are therefore possible; cf. lhrro et al., 1972b.) This brings us to the last factor to consider-the size and direction of the atomic vector contributions <xUl@lXb>. The size can only be significant if the coefficients of the 2p orbitals located on atom p in at least one of the most localized orbitals X, and xb are large (and indeed, in the first approxi-

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BlRADlCALS AND BlWlCALOlDS

225

mation only the two atoms carrying the radical centers were considered, Salem and Rowland, 1972), but this condition is not sufficient. Specifically, in view of Equation (4.13), the z component of the vector contribution from atom p consists of two parts that are added algebraically. The first will be large when the coefficient on the p,, orbital in 2, is large, and when one or more of the atomic orbitals that have a large overlap with p, (including p, itself) have large coefficients in xu. The second will be large when the coefficient on the p, orbital in xb is large, and when one or more of the atomic orbitals (including p,,) that have a large overlap with p,, have large coefficients in xu. The signs of the two contributions are dictated by the signs of the orbital coefficients, by the signs in Equation (4.13), and by the signs of the overlaps. Similar results hold for the x and y contributions to the atomic vector provided by atom p. Example 4.10:

The atomic vectors <X,l@"'Xb> contain through-space and through-bond contributions. Their origin is most easily visualized for conformations in which the axes of the singly occupied orbitals at the two radical centers are mutually perpendicular. It is somewhat unfortunate that these are often just the conformations at which the covalent perturbation y of a perfect biradical is zero, making C,., vanish, and causing the So-T, spin-orbit mixing to be negligible even if the resultant of the atomic vectors is large (it is then the experimentally uninteresting S2-T, coupling that is large). This is indeed the case in both of the following simple examples.

Figure 4.25.

Sum-over-atoms factor in the spin-orbit coupling vector HSo a) in orthogonally twisted ethylene and b) in (0.90") twisted trimethylene biradical, using Equation (4.12) and (4.13); most localized orbitals x,,. xh and nonvanishing atomic vectorial contributions from x,, (white: through-space, black: through-bond).

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I'WEN'I'IAL ENERGY SUKI.'t\CCS: UAKKIL..IIS, M I N I M , AND FUNNELS

In orthogonally twisted ethylene, the localized orbitals X,and X, are related by symmetry. Each is primarily located on a free p orbital of one CH, group and is hyperconjugatively delocalized into the CH bonds of the other CH, group (Fig. 4.25a). The principal axes of the zero-field-splitting tensor are dictated by symmetry. Only the z component of the atomic vectors <X.191'lX,>, directed along the CC axis, is different from zero, and spin-orbit coupling will mix S , with only one of the three triplet components. TI:. We can therefore locate the x and y axes arbitrarily as long as all three axes are mutually orthogonal, and we choose them to lie in the planes of the two CH, groups. The nonbonding orbitals then have the form

where c, c,, c, > 0. The resulting atomic vectors for the hydrogen atoms are negligible; those for the two carbon atoms (p = 1,2)are large and equal. We illustrate the evaluation <xnI9!Ixb>: <x'Je:lxh>

4.3

BlRADlCALS AND BIRADICALOIDS

227

is sensitive to the details of the structure, and so is the relative sign of the through-space and through-bond contributions. For instance, in orthogonally twisted H,N-BH,, the empty orbital located on boron does not have such a node, and the dominant through-bond contribution, due to the one-center term on the N atom, now has the same sign as the through-space contribution. The through-bond terms will not always dominate, but are likely to be quite generally important. In our second example, a singly twisted 1,3-trimethylene biradical (Figure 4.25b), the leading term ( p = 3) arises from the hyperconjugation of the singly occupied orbital of the CH, group on C(l), whose hydrogens are twisted out of the CCC plane, with the C(2)C(3)bond. In the coordinate system of Figure 4.25b. chosen so as to diagonalize the zero-field splitting tensor, X, then contains small contributions from the p3, and p, orbitals on C(3). an atom on which X, has its dominant component, p,,. The action of either the 9; or the operator rotates p,: into overlap with x,. As a result, both the x and y components of the atomic vector <X,1931X,,> are nonzero, and the through-bond mechanism of spin-orbit coupling will be the primary cause of the mixing of both TI, and TI, with So.

- cl('2

- c,c,

+ stnull icrtns

where the small terms either contain a product of two small coefficients, clc3. andlor contain no atomic orbitals located on C(I) (e.g., clc,). The first term on the right-hand side is of the through-space type. It would be present even if there were no hyperconjugation, that is, even if the nonbonding orbitals were strictly localized on C(1) and C(2), respectively (c, = 1, cz = c, = 0). The second and third terms would vanish in this limit and are of the through-bond type. The action of the operator 9: on a n-symmetry orbital on its right is to rotate it by 90" around the z axis in the clockwise sense when viewed against the direction of z (cf. Equation 4.13); for instance,

Thus, the through-space term makes a positive contribution to the z compoand the two through-bond terms make nent of the atomic vector <Xe1911~b>. negative contributions. I t is impossible to evaluate the sign of the resultant without at least a rough numerical evaluation of the opposing contributions: the through-space term contains the overlap integral S,, as a relatively small multiplier while the through-bond terms contain the small coefficient c, or c, as a multiplier, but there are more of them. In a minimum basis set approximation, a computation shows that the through-bond terms dominate. Inclusion of the two-electron part of the spin-orbit operator in the calculation reduces the magnitude of the result by a factor of about two. hut does not change its sign. Note that the opposed signs of the through-space and through-bond contributions are a result of the nodal properties of the orbitals x,, and xb. As is seen in Figure 4.25a, they have a node separating the main part of the orbital from the minor conjugatively delocalized part. However. the presence of the node

Example 4.11: The magnitude of the total spin-orbit coupling strength can change dramatically as a function of biradical conformation (Carlacci et al., 1987). The throughspace part can be roughly approximated by where w is the acute angle between the axes of the p orbitals containing the unpaired electrons and S is their overlap integral. The overlap S is related to the resonance integral between these two orbitals and thus to the coefficient of the in-phase combination of the two hole-pair functions in the So wave function, Co.+.The factor sin w originates from the operator 9~in the matrix element which rotates the orbital xhaccording to Equation (4.13) before its overlap with x,, is taken. No such simple generally valid approximation is currently available for the through-bond part of the spin-orbit coupling strength, which results from the delocalization of even the most localized form of the nonbonding orbitals into the a skeleton, onto nearby carbon atoms p located between the radical centers. This produces nonzero coefficients on the p orbitals on these atoms and permits them to contribute to the sum in Equation (4.12). A similar mechanism operates when atoms carrying lone pairs, such as oxygen. are located between the radical centers. The low-lying electronic states of biradicals of this type are more numerous and the spin-orbit coupling is less likely to be properly described by the simple model that led to this equation. The availability of additional states involving promotion from the lone pairs appears to make spinorbit coupling particularly effective. Note that the placement of lone-pair carrying or heavy atoms into positions that do not lie between the two radical centers cannot be expected to have much effect, since then only one of the most localized nonbonding orbitals has significant coefficients on their orbitals.

<X,,lefillxb>.

228

POTENTIAL ENERGY SURFACES: BARRIERS, MINIMA, AND FUNNELS

As discussed in Example 4.9, the probability of the intersystem crossing to the singlet will be determined by the weight of the singlet spin function in the "impure" triplet at a time when the molecular motion brings its geometry to a region in which the singlet-triplet splitting increases significantly, so that a decision between an essentially pure triplet and an essentially pure singlet state must be made. If it occurs, further nuclear motions will be dictated by the So surface, and if it does not, the biradical will continue its conformational motion in the impure triplet state. The geometries at which the singlet-triplet splitting becomes large are those at which the covalent interaction between the two localized singly occupied orbitals, described in the simple model by the quantity y, is large. At many of these, the spin-orbit coupling is also large. At these geometries, the Sosurface will typically slope steeply toward a product minimum, with no barrier in the way, and the probability that a newly formed singlet molecule might escape the likely fate of falling into this abyss is undoubtedly minimal. The somewhat startling conclusion, that intersystem crossing in triplet biradicals can and normally does produce closed-shell singlet products and not floppy singlet biradicals, was initially suggested by Closs. It has been gradually gaining recognition (De Kanter and Kaptein, 1982; Wagner, 1989; Wagner et al., 1991). Indeed, intersystem crossing caused by random spin relaxation at the two independently acting radical centers, which can be accelerated by the addition of paramagnetic impurities, and which would be expected to generate floppy singlet biradicals at a variety of geometries, yields different product ratios (Scaiano, 1982). Geometries expected to be favorable for intersystem crossing are those at which both the covalent interaction y as well as the spin-orbit coupling strength become large. This requires that the two most localized singly occupied orbitals overlap enough to establish a significant covalent perturbation of the biradical, and that they are mutually oriented in such a manner that they still overlap after the action of the angular momentum operator 8' on one of them, that is, after a 90" rotation of the p orbital around an axis that passes through its center (particularly if it is located on an atom of a high atomic number). If the orbitals overlap through space, the likely singlet reaction is covalent bond formation between the two radical centers, as exemplified in Figure 4.26a for n. bond formation in 1,2-biradicals by planarization, and in Figures 4.26b and c for disrotatory and conrotatory a bond formation in 1,n-biradicals by radical recombination. It also occurs when they interact in a through-bond fashion, for example, in I,Cbiradicals, in which case the likely singlet reactions are disproportionation or fragmentation, depending on the details of the geometry as indicated in Figures 4.26~4 and e. In order to understand the rate of intersystem crossing and the nature of the products, it is therefore essential to consider not only the shape of the T potential energy surface, which determines the occupancy of the various conformer minima and the frequency with which the various molecular ge-

4.4

PEKlCYCLlC FUNNELS (MINIMA)

Examples of biradicaloid geometries expected to be favorable for spinorbit coupling: overlap leading to covalent interaction y between the localized nonbonding orbitals (full lines) and nonzero overlap after the action of the angular momentum operator k on one of them (dotted lines); a) partial double-bond twist, b) disrotatory, and c) conrotatory ring closure, d) disproportionation, and e) fragmentation. Figure 4.26.

ometries are visited, but also the magnitude of the spin-orbit coupling element and of the singlet-triplet splitting as a function of geometry. To summarize the result of the simple theory, an admixture of Socharacter into the triplet wave function of a biradical is expected to be large at those geometries at which covalent interaction and spin-orbit coupling are both simultaneously large, that is, at which the most localized singly occupied orbitals overlap sufficiently before as well as after a 90" rotation of one of the important p orbitals. A jump to an essentially pure singlet, followed by motion on the So surface, occurs upon excursion of the biradical geometry into an area of strong covalent perturbation (large singlet-triplet splitting, singlet stabilization), with a probability dictated by the degree of admixture of singlet character into the triplet wave function. The simple theory of spin-orbit coupling in biradicals has been found useful for the interpretation of the lifetimes of triplet biradicals as a function of their structure and conformation (Johnston and Scaiano, 1989; Adam et al., 1990) and of the stereochemistry of their reaction products (Chapter 7).

4.4 Pericyclic Funnels (Minima) The global term "pericyclic funnel" will be used to refer to the funnel or funnels in the S, surface that occur at the critically heterosymmetric biradicaloid geometries reached near the halfway point along the path of a thermally forbidden pericyclic reaction, and the minima in S, that are encountered along one-dimensional cuts along reaction paths that miss the conical intersections (in particular, those along high-symmetry paths, which pass

23fj

POTENTIAL ENERGY SUItFACES: BAKKIEIIS, MINIMA, AND FUNNELS

through the geometry of a perfect biradical, and in which the S I S otouching is therefore avoided). This region of the S, surface was usually called "pericyclic minimum" because it was thought that the touching is most likely weakly avoided everywhere. Thanks to the extensive recent work of the groups of Bernardi, Olivucci, and Robb (Bernardi et al., 1990a-c. 1992a-c; Olivucci et al., 1993, 1994a,b) this is now known not to be so (cf. Section 4.1.3). and for quite a few reactions the exact location of the bottom of this funriei has been determined in considerable detail. An understanding of the electtonic states in the region of the pericyclic funnel is of fundamental signitlc,~ncein many photoreactions such as ground-state-forbidden cycloadditionc, electrocyclic reactions, or sigmatropic rearrangements, and it appears assential to discuss these states in some detail. We skiall base the discussion on an analysis of a simple four-electron-fourorbital ibodel, exemplified by H, (the "20 x 20 CI model"), which contains all the dssential ingredients (Gerhartz et al., 1976, 1977), as shown by the more redent calculations on actual molecules (two of these are discussed in more deliail in Section 6.2.1). Although it might thus appear that an understanding~of the electronic states of a tetraradical is necessary, we shall see that alreddy an understanding of the states of biradicals and biradicaloids at the level k>f the two-electron-two-orbital ("3 x 3 CI") model (Section 4.3) is immen$ely helpful, although not quite a substitute for the full 20 x 20 CI descriptign. For those familiar with valence-bond theory, an even simpler "2 x 2" VB model (Bernardi et al., 1988, 1990b) will be described, and the strengths and weaknesses of the 3 x 3 and 2 x 2 models will be compared.

4.4.1 bhe Potential Energy Surfaces of Photochemical [2, + 2,) andxI2, I

+ 2,1 Processes

Pericyclic brocesses involving interactions of four electrons in four overlapping orbitab arranged in a cyclic array (A, C, D, B, labeled clockwise along the perimetqr) correspond in general to the switching of two bonds originally connecting oms A with B and C with D, in the reactants to connect atoms A with C an B with D in the final product (Scheme 1). Examples are the conversion i f butadiene into cyclobutene (cf. Section 4.2.2) or norbornadiene (15) ingo quadricyclane (16):

4.4

PERlCYCLlC FUNNELS (MINIMA) + 2.4

7 B

+ 2~

A-C

B-D

Scheme 1

Analogous processes in which the final product has atom A attached to D and atom B attached to C (cross-links in the perimeter) are also known (Scheme 1) and could be called cross-pericyclic (the term "cross-cycloaddition" is relatively common in the literature). An example is the conversion of 1,3-butadiene to bicyclobutane (17). If the new bonds are formed in a suprafacial way, the process is referred to as x[2, + 2,]. The singlet states of the hypothetical H, molecule at triply right tetrahedral geometries calculated by Gerhartz et al. (1977) can be thought of as a simple model for the electronic states involved. The results of model 20 x 20 CI calculations on H, led to the proposal (Gerhartz et al., 1977) that the [2, + 2,] and x[2, + 2,] processes proceed through the same pericyclic funnel in the S, state. This has been supported by recent more realistic calculations (Olivucci et al., 1993, 1994b), and the two processes are therefore best discussed together. To simplify a relatively complex situation, we shall however first pretend that only a relatively high-symmetry version of the [2, + 2,] path is accessible, in which the four orbitals in question (modeled by the four H atoms) are located at the corners of a rectangle. Halfway along this reaction path, they are located at the corners of a square. At this point we shall find a fairly strongly avoided touching of the S, and So states and a "pericyclic minimum" in the S, state. Of course, in H,, this is not at all a minimum, since several types of distortion, such as an increase in the size of the square, lower the energy. A realistic example of such a path is the one used in the correlation diagrams in Figures 4.7 and 4.8. Subsequently, we shall relax the condition that all four H atoms have to be in the same plane, and we shall find a downhill path that leads from this pericyclic "minimum" to an S , S , conical intersection as the square is puckered and the two diagonals, AD and BC, shortened. A real molecule is likely to follow a lower-symmetry path straight to this "cross-bonded" pericyclic conical intersection. Once on the So surface, it will end up as a [2, + 2,], as an x[2, + 2,1 product, or as the starting material. Figure 4.27 is based on the results of a full 20 x 20 C1 calculation for H, and shows the energies calculated for the lowest singlet states of the reaction H, + Hi 2HH' with geometries corresponding to the hypothetical best ground-state rectangular path. The nomenclature used to label the states refers to the whole H, system or "supermolecule." The singly excited S state correlates smoothly from left to right without a barrier; the calculation produces, however, a broad minimum at the biradicaloid geometry. We shall see

If the new bonds are formed in a suprafacial way, the process is referred to as [2, + 2,]. The singlet states of the hypothetical H, molecule at square geometries cgculated by Gerhartz et al. (1976) can be thought of as a simple model for the/ electronic states involved.

XPS

A=.[0,] = lo7-I@ s-I, so the oxygen effect becomes noticeable when ksr = 10' or smaller (Stevens and Algar, 1967).

The density of states is approximately given by the number of ways of distributing A E over the normal modes of vibration. Because of many low-frequency modes, the number of these overtones and combinations is enormous: there are as many as -3 x 10' states per cm-I in the St-T, case ( A E = 8,500 cm - I ) of benzene with 30 normal modes of vibration.

I'll( 1 OIJll\rSlCAL PKOCESSES

5.2

RADIATIONLESS DEACTIVATION

259

Figure 5.6. Nonradiative conversion in polyatomic molecules. Due to the difference k,, k,,,,, and the tranin state density of the initial state Vli and the final state q,. sition is practically irreversible.

The influence of the energy gap between the states involved on the rate constant of radiationless transitions may be clarified with the aid of Equations (5.15) and (5.16) as follows: According to Figure 5.6, the density of states Q, in the final state increases with an increasing energy gap. The electronic excitation energy, which has to be converted into vibrational motion of the nuclei, increases at the same time. The larger the difference in vibrational quantum numbers, the smaller the overlap of the vibrational wave functions. Thus, the expected increase of the rate constant k of a radiationless transition with increasing energy gap A E due to the density of states is overcompensated by a decrease due to increasingly unfavorable FranckCondon factors. Theoretical arguments lead to an exponential dependence of the Franck-Condon factors on the energy gap (Siebrand, 1966; Englman and Jortner, 1970). According to Equation (5.15)- the rate constant for a transition from the higher to the lower state is larger than that of the reverse transition. This is because for a given energy the density of states Q, of the lower state is larger than the density of states of the higher state. as can be seen from Figure 5.6. Also, the rate-determining transition between approximately isoenergetic levels of close-lying states is followed by a very fast dissipation of the vibrational energy. This prevents the back reaction and makes radiationless transitions into lower states virtually irreversible. (Cf. Figure 5.6.) Example 5.4: Figure 5.7 gives a schematic representation of the potential energy curves for two states of a diatomic molecule. Depending on the relative positioning of these curves different probabilities for radiationless transitions result because the Franck-Condon factors can differ appreciably. If the energy difference between the two states is large. as is generally the case for Soand S,, the zerovibrational level (v' = 0) of S, overlaps with a higher vibrational level (e.g., v = 12) of Soin a region close to the equilibrium geometry, where the kinetic energy of the nuclear motion is large and the probability x:, is small. The overlap integral <X,J~,,.> is therefore close to zero (Figure 5.7a) and the FranckCondon factor makes the transition very unlikely. If the states are energetically closer to each other, such as S2and S,, or if the potential energy curves cross,

Figure 5.7. Franck-Condon factors for radiationless transitions between different potential energy curves of a diatomic molecule; a) for a large and b) for a small energy gap, such as those observed, for instance, between S, and Soor between S, and S,, respectively, and c) for the case that the potential energy curves (e.g., S, and TI)cross. as may be the case for S, and T,, the overlap <x,Jx,,> between the zero-vibrational level of the higher state and the isoenergetic vibrational level of the lower state will be much larger (Figure 5.7b and c). Radiationless transitions between these states are therefore much more likely. According to Figure 5.7, the rate of radiationless transitions depends not only on the energy gap, but also on the equilibrium geometries of the states involved. Thus, rigid n systems such as condensed aromatic hydrocarbons possess only a relatively small energy gap between S, and So,but the bonding characteristics in the ground state and in the first excited (a,*) state differ so little that the potential energy surfaces of these states are nearly parallel. Since the amplitudes of the vibrational wave functions X, of the higher excited vibrational levels of S, oscillate very quickly around zero near the equilibrium geometry, integration results in very small Franck-Condon factors. Therefore. in these systems fluorescence can compete with radiationless deactivation.

Example 5.5: In radiationless transitions from the triplet state to the ground state of aromatic hydrocarbons, the excess electronic energy goes predominantly into the CH stretching vibrations. Being of high frequency (C .= 3,000 cm-I), they are widely spaced and much smaller vibrational quantum numbers are required than for other normal modes of vibration whose wave numbers are at most half

260

PHOTOPHYSICAL PROCESSES

5.3

EMISSION

this size. Indeed, the triplet lifetime of naphthalene increases from t = 2 s to t = 20 s on perdeuteration. The energy gap AE(T, - S,,)is virtually the same for the deuterated and the undeuterated compound, but higher numbers of vibrational quanta are necessary to overcome this gap because the frequencies of the CD vibrations are smaller by roughly 30%. Hence, the Franck-Condon factors are much less favorable for the deuterated than for the protiated compounds (Laposa et al., 1%5).

Stokes shift I

0-,o

t r a n s ~ion t

5.3 Emission

Emission of a photon from an electronically excited state is referred to as luminescence. Fluorescence and phosphorescence can be differentiated depending on whether the transition is between states of equal or different multiplicity and hence spin-allowed or spin-forbidden. (Cf. Section 5.1.1 .) Thus, for molecules with singlet ground states fluorescence constitutes a pathway for deactivating excited singlet states whereas phosphorescence is observed in the deactivation of triplet states.

5.3.1 Fluorescence of Organic Molecules According to the results presented in the last section, a fraction of the energy that a malecule acquires through absorption of a light quantum is dissipated in condensed phases very rapidly via radiationless deactivation and thermal equilibration. In general, the rate of energy loss by emission is comparable with the rate of radiationless deactivation only for the lowest excited singlet state S, or the lowest triplet state T,. As a rule, therefore, the energy of the emitted radiation is lower than that of the absorbed radiation by the amount of energy that has been dissipated nonradiatively. The resulting emission is of longer wavelengths than the absorbed light. As a further consequence of thermal equilibration the intensity distribution in fluorescence and phosphorescence spectra is independent of the exciting wavelength. The shapes of absorption and emission bands are determined in the same way by Franck-Condon factors. The shift of the emission maximum with respect to the absorption maximum, which is referred to as Stokes' shifr, increases with the increasing difference between the equilibrium geometries of the ground and the excited states. This is schematically shown for a diatomic molecule in Figure 5.8; the maximum intensity of absorption will be observed for the vertical transition v = 0 + v' = n, whereas emission will occur after vibrational relaxation, with the highest probability for the transition form v' = 0 to a different ground-state vibrational level, v = m.

Often the 0-0 transitions of absorption and emission do not coincide, and a " 0 4 gap" results. This is referred to as anomalous Stokes shifr and is due

Stokes shift; a) definition and b) dependence on the difference in equilibrium geometries ofground and excited states. Shown is the probability distribution in various vibrational levels, which is proportional to the square of the vibrational wave function (adapted from Philips and Salisbury, 1976).

Figure 5.8.

to different intermolecular interactions in the ground and excited states. The energy of the excited-state molecule decreases during its lifetime through reorientation of the surrounding medium, so fluorescence is shifted to longer wavelengths. As an example the difference of the 0-0 transitions in the absorption and in the fluorescence of p-amino-p'-nitrobiphenylis shown in Figure 5.9 as a function of solvent polarity. In solid solutions at low temperatures the motion of solvent molecules can be slowed down to such an extent that no reorganization occurs and the anomalous Stokes shift disappears. Frequently, the fluorescence spectrum is the mirror image of the absorption spectrum, as exemplified for perylene in Figure 5.10. This spectral symmetry is due to the fact that the excited-state vibrational frequencies, responsible for the fine structure of the absorption band, and the ground-state vibrational frequencies. which show up in the fluorescence band, are often

5.3

Fluorescence-

--- - - - o--

,, /

Absorption

Benzene

Figure 5.9.

50 d i o x a n e [vol.%l

100

Anomalous Stokes shift illustrated by displacements of 0-0 transitions

in absorption and fluorescence of p-amino-p'-nitrobiphenylin benzeneldioxane as a

function of the dioxane content (by permission from Lippert, 1%6).

A Inrnl

263

EMISSION

quite similar. According to Figure 5.8 the intensity distribution given by the Franck-Condon factors for absorption and emission are also comparable. This is particularly true in those cases where electronic structures and equilibrium geometries of the ground and excited states differ very little, as for instance in n-n* transitions of delocalized n systems. In biphenyl, however, which is less twisted around the central single bond in the excited than in the ground state (cf. Section 1.4. I ) , the absorption and fluorescence spectra differ appreciably, and vibrational structure is observed only in emission. Another example of the mirror-image relation between absorption and fluorescence spectra is provided by anthracene (Figure 5.1 I). In this particular case the situation is complicated by vibronic coupling; the 'Laand 'L, bands overlap in the absorption spectrum, and the location of the 'L, origin has been inferred from the substituent effects evident from the MCD spectrum (Steiner and Michl, 1978). The relationship between the quantum yield of fluorescence and molecular structure is determined to a large extent by the structural dependence of the competing photophysical and photochemical processes. Thus, for most rigid aromatic compounds fluorescence is easy to observe, with quantum yields in the range 1 > @, > 0.01. This may be explained by the fact that the Franck-Condon factors for radiationless processes are very small because changes in equilibrium geometry on excitation are small; thus internal conversion becomes sufficiently slow. (Cf. Calzaferri et al., 1976.) A fundamental factor that determines the fluorescence quantum yield is the nature of the lowest excited singlet state-that is to say, the magnitude of the transition moment between S,,and S,. If the SO+Sl transition is symmetry forbidden, as in benzene, k,: is small compared to x k i for the comI

A Inrnl 700 600 500 LOO

Fluorescence

Absorption and fluorescence spectrum of perylene in benzene (by permission from Lakowicz, 1983).

Figure 5.10.

Figure 5.11.

Turro, 1978).

Absorption and emission spectra of anthracene (by permission from

264

PHOTOPHYSICAL PROCESSES

peting processes and only minor quantum yields of fluorescence are observed. If due to substitution the intensity of the S,,+S, transition becomes larger, as in aniline, the fluorescence yield increases. Most compounds whose lowest excited singlet state is an (n,n*) state exhibit only very weak fluorescence. The reason is that due to spin-orbit coupling, intersystem crossing into an energetically lower triplet state is particularly efficient. (Cf. Section 5.2.2.) Heavy atoms in the molecule (e.g., bromonaphthalene) or in the solvent (e.g., methyl iodide) may favor intersystem crossing among (n,n*) states to such an extent that fluorescence can be more or less completely suppressed. At low temperatures, photochemical deactivation and energy-transfer processes involving diffusion and collisions become less important, and low-frequency torsional vibrations that are particularly efficient for radiationless deactivation are suppressed, so fluorescence quantum yields increase. For instance, for trans-stilbene (7), @, = 0.05 at room temperature, but @, = 0.75 at 77 K. If the stilbene chromophore is fixed in a rigid structural frame as in 8, @, equals 1 .O independent of temperature (Sharafy and Muszkat, 1971; Saltiel et al., 1968).

5.3

EMISSION

Figure 5.12. Qualitative state diagram for the fluorescence quenching of benzene by radiationless transition into one of the higher vibrational levels of the isomeric

benzvalene. The back reaction is a hot ground-state reaction.

1990 for leading references) thus involves no special mechanism of nonradiative decay.

The quantum yield of fluorescence from unsaturated compounds is independent of the exciting wavelength, unless photochemical reactions originating from higher excited singlet states or intersystem crossing compete with internal conversion. A good example is benzene in the gas phase at low pressure (less than 1 torr): on excitation of the S, state at I = 254 nm fluorescence occurs with a quantum yield of @, = 0.4. This decreases if higher vibrational levels of this state are excited, and at A < 240 nm no emission can be detected at all. It is assumed that a radiationless transition is possible from the higher vibrational levels of the S, state of benzene into very highly excited vibrational levels of the ground state of the isomeric benzvalene (9), as shown in the schematic representation in Figure 5.12. Benzvalene can either be stabilized by vibrational relaxation or can undergo a hot groundstate reaction and return to the benzene ground state (Kaplan and Wilzbach, 1%8). Calculations shdw that a funnel in S, (conical intersection of S, and So),separated from the vertical geometry by a small barrier to isomerization, provides a mechanism for an ultrafast return to So, as soon as the molecule has sufficient vibrational energy to overcome the barrier (Palmer et al., 1993; Sobolewski et al., 1993). The so-called "channel 3" effect (see Riedle et al.,

By measuring the fluorescence intensity of sufficiently dilute solutions as a function of the exciting wavelengths afluorescence excitation specrrum is obtained. Such a measurement represents a remarkably sensitive method for investigating the absorption spectrum. With I, and IFbeing the intensities of the absorbed light and of the light emitted as fluorescence, respectively,

where I, is the intensity of the exciting light, E the extinction coefficient, c. the concentration of the sample, and d the optical path length. (Cf. Section 1.1.2.) If the absorbance A = ~ c isd smaller than say 0.2-0.3, a series expansion of the exponential function ec" = 1 - x + . . . , with neglect of the higher powers of x, yields

and as a result, for a given @, and I,, the fluorescence intensity reflects the wavelength or wave-number dependence of the extinction coefficient E.

I'Hc YI'OI'HYSICAL PROCESSES

5.3

EMISSION

267

5.3.2 Phosphorescence Because internal conversion and vibrational relaxation are very fast, phosphorescence corresponds to a transition from the thermally equilibrated lowest triplet state TI into the ground state So and the phosphorescence spectrum is approximately a mirror image of the So+T, absorption spectrum, which is spin forbidden and therefore difficultto observe because of the low intensity. This mirror-image symmetry is evident from the singlet-triplet absorption and phosphorescence spectra of anthracene shown in Figure 5.1 1. In general the TI state is energetically below the S, state, and phosphorescence occurs at longer wavelengths than fluorescence, as shown in Figure 5.11. Since the transition moment of the spin-forbidden T,-*So transition is very small, the natural lifetime t,Pof the triplet state is long. Consequently, radiationless processes can compete with phosphorescence in deactivating the T, state. Of particular importance are collision-induced bimolecular processes (cf. Section 5.4), and phosphorescence of gases and liquid solutions is relatively difficult to observe (Sandros and Backstrom, 1962). An exception is biacetyl with a very short TI lifetime t:. (Cf. Figure 5.3.) Phosphorescence spectra are commonly measured using samples in solvents or mixed solvents that form rigid glasses at 77 K (such as EPA = ether-pentane-alcohol mixture). (Cf., however, Example 5.6). The natural lifetime of the triplet state t,P = Ilk, may be estimated from the observed lifetime and the quantum yields of fluorescence and phosphorescence. According to Equation (5.1 1)

Figure 5.13. Various possiblities for the disposition of the lowest singlet and triplet (n,lc*) and (n,n*) states of organic molecules (adapted from Wilkinson, 1968).

If internal conversion and all energy-transfer processes and photochemical reactions are negligible, q, = 1 - QF, and one obtains 1 - aF -

to' = t p

s and many seconds. The natural lifetime $ varies between The rate constant ksT of intersystem crossing depends on the energy gap AEsT between the singlet and triplet states and in particular on spin-orbit coupling. The difference in the magnitude of spin-orbit coupling contributes greatly to the fact that the quantum yield as,of triplet formation is small for aromatic hydrocarbons, but nearly unity for carbonyl compounds. (Cf. the El-Sayed rules, Section 5.2.2.) In discussing the energy gap dependence of the intersystem crossing rate one has to note that the triplet state closest to

S, can be one of the higher triplet states T,, such as is the case for anthracene (cf. Example 5.3), and that in molecules with lone pairs of electrons either TI or T, may be of the same type as S,. This is illustrated in Figure 5.13, where various possibilities for the energy order of the (n,n*) and (n,n*) states are displayed schematically. Not all the situations shown are equally probable; it is, for instance, very unlikely that the singlet-triplet splitting of the (n,fl) states could be appreciably larger than that of the (n,llL)states, as shown in Figure 5.13f.

268

PHOTOPHYSICAL PROCESSES

The relative position of the excited states of benzophenone (10) is shown in Figure 5.13a. Intersystem crossing leads from a '(n,*) state to a '(n,n*) state; this type of transition is favored by spin-orbit coupling to such an extent that as, = I and no fluorescence is observed. If, however, S, and TI are (n,n*) states and are disposed as in Figure 5.13b, a, is so small that practically no phosphorescence can be observed although the molecule has rr-** transitions. The relative disposition of (n,llr) and (n,n*) states may be changed by solvent effects and the rate constants of the various photophysical and photochemical processes can be drastically altered. Thus lone pairs of electrons in molecules such as quinoline (11) may be stabilized by hydroxylic solvents to such an extent that the (n,lt*) states become higher in energy than the (n,*) states, as shown in Figure 5.13d and e. Phosphorescence would predominate in the former case, fluorescence in the latter. As a result of the heavy-atom effect or the effect of paramagnetic molecules such as 02,which both enhance S,l+T,, absorption (cf. Section 1.3.2). phosphorescence TI+Stl as well as the rate constants k,., and k.,., of intersystem crossing will be Favored. The consequence according to Equation (5.1 I ) is an increase in qlsc, whereas r], will increase or decrease depending on which of the two processes, radiationless deactivation of the triplet state or phosphorescence, is more strongly favored. Frequently, an increase in the

5.3

EMISSION

269

quantum yield a, of phosphorescence by the heavy-atom effect is observed. For example, free-base porphine (12) exhibits practically only fluorescence in a neon matrix and practically only phosphorescence in a xenon matrix (Figure 5.14). It has been concluded that the phosphorescence rate constant is enhanced by at least two orders of magnitude by the heavy-atom effect (Radziszewski et al., 1991).

Example 5.6: The heavy-atom effect can be utilized for measuring phosphorescence in solution. In Figure 5.15 the luminescence spectrum of 1.4-dibromonaphthalene

Ar -NZ purged -----Aerated

Figure 5.14. Luminescence of free-base porphine (12) in N e (4 K) and X e (12 K). The former is totally dominated by fluorescence (left) and the latter by phosphorescence (right) (by permission from Radziszewski et al., 1991).

Figure 5.15.

Luminescence spectrum of 1.4-dibromonaphthalene in acetonitrile with and without purging with NZ(by permission from Turro et al., 1978).

PHO'I'OPHYSICAL PROCESSES

5.3

EMISSION

271

fluorescence excitation spectra and has been discussed in detail in Section 5.3.1. The use of a heavy-atom solvent such as ethyl iodide and of an intense light source permits the direct measurement of S,+T, transitions by this method. This technique may be used even when the compound itself is nonphosphorescent by having present a phosphorescent molecule of lower triplet energy that is excited by energy transfer (see Section 5.4.5) from the nonphosphorescent triplets. Example 5.7: The phosphorescence excitation spectrum may be used to decide whether the lowest triplet state is a '(n,n*) or a '(n,n*) state, if measurements are carried out in two different solvents with or without the heavy-atom effect, respectively. The intensity of the phosphorescence excitation spectrum will in general increase due to the heavy-atom effect if T, is a '(n,n*) state as in p-hydroxyacetophenone. However, no intensity increase is observed if T, is a '(n,fl) state as in benzophenone, since spin-orbit coupling associated with a n+n* transition is already so strong that the additional solvent effect is negligible. The spectrum in Figure 5.17 illustrates the intensity increase expected for a '(n,n*) state.

Figure 5.16. Luminescence spectra of naphthalene and triphenylene in 1,2dibromoethane (by permission from Turro et al.. 1978).

is shown as an example of the "internal heavy-atom effect." The spectra of naphthalene and triphenylene in Figure 5.16 demonstrate the "external heavyatom effect" due to the solvent I .2-dibromoethane. For such measurements it is important to use highly purified and deoxygenated solvents since otherwise phosphorescence is too weak to be detected, as is evident from Figure 5.15 (Turro et al., 1978).

When a, is independent of the excitation wavelength the extreme sensitivity associated with emission spectroscopy can be utilized to obtain So-T absorption spectra by measuring phosphorescence excitation spectra (Marchetti and Kearns, 1967). The principle of the method is the same as for

Figure 5.17. Phosphorescence excitation spectrum of p-hydroxybenzophenone in an ether-toluol-ethanol mixture with (-) and without (---) the addition of ethyl iodide. The curves are normalized in such a way that the S T excitation of the '(n,lr*) state shows about the same intensity in both solvents (by permission from Kearns and Case, 1%6).

272

PHOTOPHYSICAL PROCESSES

5.3.3 Luminescence Polarization A light quantum of appropriate energy can be absorbed by a molecule fixed in space only if the light electric field vector has a component parallel to the molecular transition moment. If the directions of the transition moment and of the electric field vector form an angle 9,the absorption probability is proportional to cos29.(Cf. Section 1.3.5.) The light quanta of luminescence are also polarized, with the intensity again proportional to cosZq. The polarization direction of an electronic transition may be determined by measurement of the absorption of polarized light by aligned molecules. (Cf. Michl and Thulstrup, 1986.) Orientation may be achieved in a number of ways. When single crystals are used or when the molecules of interest are incorporated into appropriate single crystals, a very high degree of orientation can be obtained if the crystal structure is favorable. Other methods accomplish orientation by embedding the molecules in stretched polymer films (polyethylene, PVA; Thulstrup et al., 1970)or in liquid crystals; further possibilities are orientation by an electric field (Liptay, 1963), or, in the case of polymers such as DNA, by a flow field (Erikson et al., 1985). The relative polarization directions of the different electronic transitions of a molecule may be determined by exciting with polarized light and analyzing the degree of polarization of the luminescence, referred to briefly as luminescence polurizution. When a solution of unoriented molecules is exposed to plane-polarized light of a wavelength appropriate for a specific electronic transition, only those molecules that have their transition moment oriented parallel to the electric field vector absorb with maximum probability. Using this selection process, known as photoselection, an effective alignment of the excited molecules is achieved. Only excited molecules can emit, and the directions of the transition moment of emission [in general M(S,-*S,) or M(T,-*S,,)] and the transition moment of absorption M(S,+S,,) will form an angle a. If rotation of the excited molecules during their lifetimes is prevented by high viscosity of the solution, the emission will also be polarized. The degrt~ec?f'polurizc~tion is defined as

while the degree of anisotropy, which sometimes leads to simpler formulas (cf. Michl and Thulstrup, 1986), is defined as

R =

Ill - 1, I,, + 21,

Here Ill and I , are the intensities of the components of the emitted light parallel and perpendicular to the electric vector of the exciting light, respectively. The curves P(A) or P(5) are called the polarization spectrum. Depending on whether the measurement is carried out with constant excitation

5.3

EMISSION

273

wavelength A, or at constant luminescence wavelength A2, different polarization spectra result. Using excitation light of fixed wavelength A, a fluorescence polarization spectrum (FP) or a phosphorescence polarization spectrum (PP), respectively, is obtained. Measurement at a constant emission wavelength yields an absorption-wavelength-dependent polarization spectrum of either fluorescence [AP(F)I or phosphorescence [AP(P)]. The relationship between the degree of polarization P and the angle a between the transition moments of absorption and emission is given by

Ideally, P can assume values ranging between P = 0.5 (corresponding to a = 0") and P = -0.33 (corresponding to a = 90'). If a molecule possesses a symmetry axis of order n > 2 and absorption and emission are isotropically polarized in a plane perpendicular to this axis, P = const = 0.14 (Dorr and Held, 1960). The value of P is affected by the overlap of different electronic transitions and also reflects the orientational dependence of the transition moment on vibronic mixing with nonsymmetrical vibrations. Under favorable conditions it is therefore possible not only to determine the relative directions of electronic transition moments from the polarization spectra but also to locate bands hidden in the absorption spectrum and to ascertain the symmetry of the vibrations giving rise to the fine structure. Energy migration (repeated intermolecular energy transfer) causes depolarization; such measurements have therefore to be carried out in dilute solutions.

In ~ i i u r 5.18 e the absorption and emission spectra of azulene are shown. The anomalous fluorescence of azulene from the S, state is easy to recognize. The AP(F) spectrum exhibits a deep minimum at 33,900 cm-I. The small peak in the absorption spectrum at the same wave number is therefore not duk to vibrational structure but rather to another electronic transition, the polarization of which had been predicted by PPP calculations. Figure 5.19 shows all four types of polarization spectra of phenanthrene. FP becomes negative at the vibrational maxima of the fluorescence; the most intense vibration is not totally symmetric, in contrast to the one which shows up weakly. For all absorption bands, AP(P) = -0.3. The polarization direction of phosphorescence is perpendicular to the transition moments of all n-n* transitions lying in the molecular plane and is therefore perpendicular to the molecular plane. One observes PP = -0.3 as well, with a modulation due to vibrations. The observed phosphorescence polarization direction may be accounted for by the fact that singlet-triplet transitions acquire their intensity by spin-orbit coupling of the Sostate with triplet states and particularly, of the T, state with singlet states. (Cf. Section 1.3.2.) Under usual conditions the phosphorescence is an unresolved superposition of emissions from the three components of the triplet state, which in the absence of an external magnetic field are described

PHO'fOPHYSICALPROCESSES

5.3

EMISSION

A lnml 1000 1

700 600 500 I

LOO 350

300 I

250 1

Figure 5.18. Absorption (A) and fluorescence spectrum (F) of azulene in ethanol at 93 K. FP and AP(F) denote the polarization spectrum of fluorescence and the excitation-polarization spectrum of fluorescence, respectively (by permission from DOrr, I%@.

by the spin functions 8,, a,, and 63, [cf. Equation (4.7)] and have the same symmetry properties as the rotations A,,,fi,, and fi: about the molecular symmetry axes. In general they belong to different irreducible representations of the molecular point group and therefore mix with different singlet states under the influence of the totally symmetric spin-orbit coupling operator. The transition moments of the different admixed singlet states then determine the intensity and polarization direction of emission from the various components of the TI state. In the case of phenanthrene. the triplet component with the transition moment perpendicular to the molecular plane contributes most of the states with pointensity. since spin-orbit coupling of this component to '(u,lr*) larization direction perpendicular to the plane predominates over the spin-orbit coupling of the other components. The TI-S, transition steals its intensity from such S,+S, transitions. In Figure 5.20, the emission spectrum of triphenylene is shown: P = 0.14 in the FP spectrum due to the threefold symmetry axis perpendicular to the molecular plane, which is also the polarization plane for all n-n* transitions.

600 500 I

LOO I

350 I

300 I

250 I

200

Figure 5.19. Absorption (A) and emission spectra ( F and P) of phenanthrene in ethanol at 93 K. FP and PP denote the polarization spectra of fluorescence and phosphorescence, AP(F) and AP(P) the excitation polarization spectra of fluorescence and phosphorescence, respectively (by permission from M r r , 1966).

The phosphorescence polarization direction is again perpendicular to the molecular plane and is modified by out-of-plane vibrations.

If the excited molecules merely return to their ground state by radiative or nonradiative processes, no permanent orientation remains after the photoselective irradiation is terminated. However, when the excited molecules undergo a permanent chemical change, photoselection leads to a lasting alignment of that portion of the reactant molecules that remain when the irradiation is interrupted. Sometimes, the product molecules are aligned as well, depending on the degree of correlation between the average orientation of the parent reactant and the daughter photoproduct molecules in space (Michl and Thulstrup, 1986). Samples oriented by photoselection have been used for studies of molecular anisotropy by polarized absorption spectroscopy. For instance, the

PHOTOPHYSICAL PROCESSES

5.4

BIMOLECULAR DEACTIVATION PROCESSES

277

that involve the transfer of excitation energy from one molecule to another. These processes are generally referred to as quenching processes. The suppression of emission by energy-transfer processes is in particular referred t o a s luminescence quenching (quenching in the strict sense). If it is not the deactivation that is of principal interest during a bimolecular process but rather the excitation of the energy acceptor molecule, the process is referred to a s sensitizution. States that otherwise would be accessible only with difficulty o r even not at all may be populated through sensitized excitation.

5.4.1 Quenching of Excited States Fluorescence quenching is a very general phenomenon that occurs through a variety of different mechanisms. All chemical reactions involving molecules in excited states can be viewed as luminescence quenching. Such photochemical reactions will be dealt with in later chapters. Photophysical quenching processes that d o not lead t o new chemical species can in general be represented as

Figure 5.20. Emission spectra (F and P) of triphenylene in ethanol at 93 K. FP and PP denote the polarization spectra of fluorescence and phosphorescence, respectively (by permission from D6rr, 1966).

symmetries of all IR-active vibrations of free-base porphine (12) have been measured on a sample photooriented with visible light in a rare-gas matrix (Radziszewski e t al., 1987, 1989). Photoorientation of the major and the minor conformer of 1,3-butadiene in rare-gas matrices was used t o determine the directions of the IR-transition moments in both, which revealed that the latter is planar in these media (i.e., s-cis and not gauche), and yielded the average relation between the orientation of the s-cis reactant and that of the s-trans photoproduct (Arnold et at., 1990, 1991).

where M' is the ground state o r another excited state of M. According t o whether the quencher Q is a molecule M of the same kind o r a different molecule self-quenching o r concentration quenching can be distinguished from impurity quenching by some other chemical species. Most intermolecular deactivation processes are based on collisions between an excited molecule M* and a quencher Q. They are subject to the Wigner-Witmer spin-conservation rule according to which the total spin must not change during a reaction (Wigner and Witmer, 1928). Example 5.9: In order that the products C and D lie on the same potential energy surface as the reactants A and B, the total spin has to be conserved during the reaction. The spins S, and S, 01' the reactants may be coupled according to vector addition rules in such a way that the total spin of the transition state can have the following values: (SA

In addition t o monomolecular processes such as emission and radiationless deactivation there are very important bimolecular deactivation mechanisms

(SA

+ s, - 1).

, IS, - S,(

Similarly, the spins S, and S,, of the products may be coupled to give one of the total spin values (Sc

5.4 Bimolecular Deactivation Processes

+ S,).

+ Sn). (Sc + Sn -

1),

- .-

ISc - SDI

A reaction is allowed according to the Wigner-Witmer spin-conservation rule if the reactants can form a transition state with a total spin that can also be obtained by coupling the product spins, that is. if the two sequences above have a number in common.

I'H( ) I'OPHYSICAL PROCESSES

5.4

BIMOLECULAR DEACTIVATION PROCESSES

Thus, for S, = S, = 0 the reaction is allowed if S,. = S,, = 0, but not if S,. = I, S, = 0 since in the latter case S, and S, can be coupled only to the total spin (S,. + S,) = IS,. - S,I = 1. Therefore, the singlet-singlet energy transfer

ID*

+ [ A-, ID + 'A*

is allowed. Similarly, the triplet-triplet energy transfer

is seen to be allowed. For the reaction of two molecules in their triplet states one has S, = S, = 1 and the total spin can take the values 2, 1, and 0. Triplettriplet annihilation Figure 5.21.

MO scheme of excimer and exciplex formation.

thus gives one molecule in a singlet state while the other one may be in a singlet, a triplet, or a quintet state.

Except for some long-distance electron-transfer and energy-transfer mechanisms bimolecular deactivation involves either an encounter complex (M* . . . Q), or an exciplex (MQ*) or excimer (MM)*. An exciplex or an excimer has a binding energy larger than the average kinetic energy (312)kT and represents a new chemical species with a more or less well-defined geometrical structure corresponding to a minimum in the excited-state potential energy surface. This is not true for an encounter complex in which the components are separated by widely varying distances and have more random relative orientations. Encounter complexes, exciplexes, and excimers can lose their excitation energy through either fluorescence or phosphorescence, by decay into M + Q* which corresponds to an energy transfer, by electron transfer to give Mm + Q" or M@ + Q@,by internal conversion, and by intersystem crossing (Schulten et al., 1976b). All these processes lead to quenching of the excited state M* and are therefore referred to as quenching processes.

occupied. This gives rise to the relative minimum of the excimer '(MM)*on the excited-state potential energy surface. (Monomer Fluorescence)

. .

i'"

(Excimer Fluorescence)

(MM)

In Section 4.4 it was shown for the (H2 + H?) system that interaction and q M results in exciton between locally excited states described by qMM.

5.4.2 Excimers Frequently, it is observed that an increase in the concentration of a fluorescent species such as pyrene is accompanied by a decrease in the quantum yield of its fluorescence. This phenomenon is called self-quenching or concentration quenching and is due to the formation of a special type of complex formed by the combination of a ground-state moIecule with an excited-state molecule. Such a complex is called an excimer (excited dimer) (Forster and Kaspar, 1955). Whereas for a system M + M of two separate ground-state molecules all interactions are purely repulsive except for those yielding the van-der-Waals minima observed in the gas phase, stabilizing interactions are possible according to Figure 5.21 if one of the molecules is in an excited state and the hom*o and LUMO of the combined system are only singly

Schematic representation of the potential energy surfaces for excimer formation and of the difference between monomer fluorescence and excimer fluorescence (adapted from Rehm and Weller, 1970a). Figure 5.22.

PHOTOPHYSICAL PROCESSES

h Inml 500 a)

L50

LOO

3 50 I

5.4

BIMOLECULAR DEACTIVATION PROCESSES

281

in Figure 5.22. From this diagram it is evident that excimer fluorescence is to be expected at longer wavelengths than monomer fluorescence and that the associated emission band should be broad and generally without vibrational structure, being due to a transition into the unbound ground state. The spectrum of pyrene in Figure 5.23 is the perfect confirmation of these expectations. Excimer formation is observed quite frequently with aromatic hydrocarbons. Excimer stability is particularly great for pyrene, where the enthalpy of dissociation is AH = 10 kcallmol (Fdrster and Seidl, 1965). The excimers of aromatic molecules adopt a sandwich structure, and at room temperature, the constituents can rotate relative to each other. The interplanar separation is 300-350 pm and is thus in the same range as the separation of 375 pm between the two benzene planes in 4,4'-paracyclophane (13), which exhibits the typical structureless excimer emission. For the higher hom*ologues, such as 5,S'-paracylophane, an ordinary fluorescence characteristic of p-dialkylbenzenes is observed (Vala et al., 1965).

Calculations based on a wave function corresponding to Equation (5.22) also indicate a sandwich structure and an interplanar distance of 300-360 pm (Murrell and Tanaka, 1964).

5.4.3 Exciplexes Figure 5.23. Absorption (..,) and fluorescence spectrum (-) of pyrene a) lo-' moll L in ethanol, b) 10-2 mol/L in ethanol, and c) absorption and emission (---) of crystalline pyrene (adapted from Farster and Kaspar, 1955).

states. The magnitude of the interaction is a measure of the energy transfer from one molecule to the other. (Cf. the Forster mechanisms of energy transfer, Section 5.4.5.) Interaction with ion-pair or CT states further stabilizes the lower of the exciton states, so the excimer can be described by a wave function of the form Whether the stabilization is given by a plus or minus combination depends on the orientation of M* relative to M. (For a more detailed treatment see Michl and BonaCiC-Koutecky, 1990.) The potential energy surfaces of the ground state M + M and the ercited state M* + M resulting from these arguments are represented schematically

%o different molecules M and Q can also form complexes with a definite stoichiometry (usually I: I). If complexation is present already in the ground state and leads to CT absorption (Section 2.6), which is absent in the individual components, the complex is referred to as a charge-transfer or donoracceptor complex. If, however, the complex shows appreciable stability only in the excited state, it is called an exciplex (excited complex): 'M' (Monomer Fluorescence)

- h"

l(~a)*

(Exclplex Fluomsconce)

(Ma)

The spectra of anthracene-dimethylaniline shown in Figure 5.24 exemplify the new structureless emission at longer wavelengths due to the formation of an exciplex. This fluorescence is very similar to excimer fluorescence. Contrary to the situiition for excimers, one component of the exciplex acts predominantly as the donor (D); the other one acts as the acceptor (A).

5.4

Fluorescence and exciplex emission from anthracene in toluene (3.4.10 ' mol/L) for various concentrations c., of dimethylaniline (by permission from Weller, 1968).

UIMOLECULAK L)EACSIVA'SION PROCESSES

283

Figure 5.24.

If use is made of this fact in the notation. one obtains instead of Equation (5.22) the wave function

Figure 5.25. Exciplex formation by charge transfer a) from the donor to the excited acceptor and b) from the excited donor to the acceptor. Exciplex emission is indicated by a broken arrow (by permission from Weller, 1%8).

Exciplexes and excimers appear to be involved in many photochemical processes; in particular, they are probably involved in many quenching and charge-transfer processes and in many photocycloadditions.

where c, # c, and c, # c,; the third term corresponds to a charge-transfer

(CT) excited state (cf. Section 4.4) and is by far the most important one, and the exciplex corresponds to a contact ion pair. Experimentally the chargetransfer character is revealed by the high polarity, with exciplexes from aromatic hydrocarbons and aromatic tertiary amines having dipole moments p(AD)* > 10 D (Beens et al., 1967; cf. Section 1.4.2). From a simple MO treatment it follows that the electron transfer leading to exciplex formation can occur either from an excited donor to an acceptor or from a donor to an excited acceptor. (See Figure 5.25.) In both cases, the singly occupied orbitals of the resulting exciplex correspond to the hom*o of the donor and the LUMO of the acceptor. Neglecting solvent effects, the energy of exciplex emission is therefore given by where IP, and EAAare the ionization potential of the donor and the electron affinity of the acceptor, and C describes the Coulomb attraction between the components of the ion-pair D@A@.

5.4.4 Electron-Transfer and Heavy-Atom Quenching According to the following scheme, electron transfer, intersystem crossing and energy transfer can all compete with fluorescence in deactivating an exciplex '(DA)* formed from the molecules A and D.

In polar solvents, polar exciplexes (contact ion pairs) dissociate into nonfluorescent radical ions (loose ion pairs or free ions) due to the stabilization of the separated ions by solvation. It has been observed that exciplex emission decreases with increasing polarity of the solvent and that at the same

284

PHOTOPHYSICAL PROCESSES

5.4

BIMOLECULAR UI~.AC'I'IVA'I'IONI'KOCESSES

time the free-radical ions DO and A@can be identified by flash spectroscopy (Mataga, 1984). Assuming the existence of a quasi-stationary state the rate constant of an exothermic electron-transfer reaction can be written as kdiR,k,, k-dirr,and k-, are the rate constants for diffusion, forward electron transfer from D to A, for the dissociation of the encounter complex to A and D, and for the back electron transfer from A o to DO, respectively. The terms with k - , have been neglected since k-, e k, can be assumed for exothermic reactions. According to the Marcus theory (1964) a relationship of the form exists for adiabatic outer-sphere electron-transfer reactions* between the free enthalpy of activation AGt and the free enthalpy of reaction AG. A in Equation (5.25) is the reorganization energy essentially due to changes in bond distances and solvation. As a consequence of this relation, the rate constant should first increase with increasing exothermicity until the value AG = -A is reached and then decrease again. The dependence of log kc on AG obtained in this way is shown in Figure 5.26 by the dashed curve; the region of decreasing rate for strongly exergonic electron-transfer reactions (AG < A) is referred to as the Marcus inverted region. The temperature dependence of electron-transfer rate constants is interesting. In the normal region, it shows an activation energy as predicted from simple Marcus theory. In the inverted region, the activation energy is very small or zero. This agrees with the quantum mechanical version of the theory (Kestner et al., 1974; Fischer and Van Duyne, 1977), which makes it clear that the transition from the upper to the lower surface behaves just like ordinary internal conversion. Studies of the fluorescence quenching in acetonitrile have shown that the electron-transfer reaction

Figure 5.26. Dependence of the rate constant log k for electron-transfer processes on the free reaction enthalpy AG, Rehm-Weller plot (-) and Marcus plot (---) for I = 10 kcal/mol (adapted from Eberson, 1982).

leading to a radical ion pair is diffusion controlled if the free enthalpy of this reaction is AG I- 10 kcal/mol, and that in contrast to the Marcus theory it remains diffusion-controlled even for very negative values of AG. Therefore, Rehm and Weller (1970b) proposed the empirical relationship AGt = AGl2

+ [(AG/2)' + (A/4)2]"2

(5.27)

which adequately describes the experimentally observed data, as can be seen from the solid curve in Figure 5.26. The free enthalpy of electron transfer AG can be estimated according to Weller ( 1982a) from the equation where E;il(D) and E.sd(A)are the half-wave potentials of the donor and acceptor, AE,,,(A) is the (singlet or triplet) excitation energy of the acceptor, and AEcoUlis the Coulombic energy of the separated charges in the solvent in question. The authors suggested that the disagreement with the Marcus theory is due to fast electron transfer occurring via exciplex formation (Weller, 1982b), as shown in the following reaction scheme: Encounter complex (d = 700 pm)

* Redox processes between metal complexes are divided into outer-sphere processes and inner-sphere processes that involve a ligand common to both coordination spheres. The distinction is fundamentally between reactions in which electron transfer takes place from one primary bond system to another (outer-sphere mechanism) and those in which electron transfer takes place within a primary bond system (inner-sphere mechanism) (Taube, 1970).

'A*

kI *I + 'D .--( A + ID)

Exciplex

(d -300 pm)

'(A*D)

i I

/'ti( I'OIJHYSICAL PROCESSES

Experimental values of k,E,:;indicate that dissociation of weakly solvated dipolar exciplexes into a strongly solvated radical ion pair requires charge separation against the Coulomb attraction as well as diffusion of solvent molecules during resolvation (Weller, 1982b). More recent investigations of rigidly fixed donor-acceptor pairs, for example, of type 14 with different acceptors A (Closs et al., 19861, and also of free donor-acceptor systems (Gould et al., 1988) have shown, however, that rates of strongly exothermic electron-transfer reactions in fact decrease again, as is to be expected for the Marcus inverted region. The deviation of the original Weller-Rehm data from Marcus theory at very large exothermicities may well be due to the formation of excited states of one of the products, for which the exothermicity is correspondingly smaller, and to compensating changes in the distance of intermolecular approach at which the electron transfer rate is optimized. Recently a number of covalently linked porphyrin-quinone systems such as 15 (Mataga et al., 1984) or 16 (Joran et al., 1984) have been synthesized in order to investigate the dependence of electron-transfer reactions on the separation and mutual orientation of donor and acceptor. These systems are also models of the electron transfer between chlorophyll a and a quinone molecule, which is the essential charge separation step in photosynthesis in green plants. (Cf. Section 7.6.1 .) Photoinduced electron transfer in supramolecular systems for artificial photosynthesis has recently been summarized (Wasielewski, 1992).

5.4

BIMOLECULAR DEACTIVATION PROCESSES

287

occurring via a highly excited triplet exciplex -'(MO,)** that undergoes internal conversion to the lowest triplet exciplex '(MO,)* and decays into the components:

The net reaction consists of a catalyzed intersystem crossing which is spin allowed as opposed to the simple intersystem crossing (Birks, 1970). Triplet states may also be quenched by oxygen, but triplet-triplet annihilation (cf. Section 5.4.5.5) seems to be the predominant mechanism.

5.4.5 Electronic Energy Transfer If an excited donor molecule D* reverts to its ground state with the simultaneous transfer of its electronic energy to an acceptor molecule A, the process is referred to as electronic. energy trunsfer: The acceptor can itself be an excited state, as in triplet-triplet annihilation. (Cf. Section 5.4.5.5.) The outcome of an energy-transfer process is the quenching of the emission or photochemical reaction associated with the donor D* and its replacement by the emission or photochemical reaction characteristic of A*. The processes resulting from A* generated in this manner are said to be sensitized. Energy transfer can occur either radiatively through absorption of the emitted radiation or by a nonradiative pathway. The nonradiative energy transfer can also occur via two different mechanisms-the Coulomb or the exchange mechanism.

5.4.5.1 Radiative Energy Transfer Radiative energy transfer is a two-step process and does not involve the direct interaction of donor and acceptor: Heavy-atom quenching occurs if the presence of' a heavy-atom-containI SC

ing species enhances the intersystem crossing '(MQ)* +'(MQ)* to such an extent that it becomes the most important deactivation process for the exciplex. Since the triplet exciplex is normally very weakly bound and dissociates into its components, what one actually observes in such systems is Luminescence quenching by oxygen appears to be a similar process with = ?02. The process is diffusion-controlled. and it may be thought of as

The efficiency of radiative energy transfer, frequently described as "trivial" because of its conceptual simplicity (Forster, 1959). depends on a high quantum efficiency of emission by the donor in a region of the spectrum where the light-absorbing power of the acceptor is also high. I t may be the dominant energy transfer mechanism in dilute solutions, because its probability decreases with the donor-acceptor separation only relatively slowly as compared with other energy-transfer mechanisms. When donor and acceptor are identical and emission and absorption spectra overlap sufficiently, radiative

288

PHOTOPHYSICAL PROCESSES

trapping may occur through repeated absorption and emission that increases the observed luminescence lifetime.

5.4

BIMOLECULAK L)CACI'IVAI'ION PROCESSES

289

tor absorption, respectively, are normalized to a unit area on the wave-number scale, that is

5.4.5.2 Nonradiative Energy Transfer The nonradiative energy transfer is a single-step process that requires that the transitions D*+D and A-A* be isoenergetic as well as coupled by a suitable donor-acceptor interaction. If excited-state vibrational relaxation is faster than energy transfer, and if energy transfer is a vertical process as implied by the Franck-Condon principle, the spectral overlap defined by

is proportional to the number of resonant transitions in the emission spectrum of the donor and the absorption spectrum of the acceptor. (Cf. Figure 5.27). The spectral distributions iD(s)and zA(fi)of donor emission and accepEmission

Absorption

This clearly reflects the fact that J is not connected to the oscillator strengths of the transitions involved. The coupling of the transitions is given by the interaction integral

6 = lli\i,>n

1:1t*,-

(',>~lcli~io '' ~( '~ I I \, , I I I

/?,,I,.

77. 793.

Closs. G.L.. C;llcatcrra. L.T.. Grcen. N.J.. Penfield. K.W.. Miller, J.R. (1986). "Distance, Stereoelectronic Effects. and the Miircus Inverted Region in Intramolecular Electron Trilnsfer in Organic Radical Anions." J . Pliys. Clicrt~.90. 3673.

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PHOTOPHYSICAL PROCESSES

CHAPTER

Eberson, L. (1987), Electron Transfer Reactions in Organic Chemistry; Springer: Berlin, Heidelberg, New York. FOX, M.A.. Ed. (1992). "Electron Transfer: A Critical Link between Subdisciplines in Chemistry," thematic issue of Chem. Rev. 92, 365-490. Fox, M.A., Chanon, M., Eds. (1988). Plzotoindrtced Electron Trctnsfc,r, Vol. 1-4, Elsevier: Amsterdam.

Photochemical Reaction Models

Gould, I.R., Farid, S. (1988). "Specific Deuterium Isotope Effects on the Rates of Electron Transfer within Geminate Radical-Ion Pairs," J. Am. Chem. Soc. 110, 7883. Kavarnos, G.J. (1993). Fundamentals of Photoinduced Electron Transfer; VCH Inc.: New York. Kavarnos, G.J., Turro, N.J. (1986), "Photosensitization by Reversible Electron Transfer: Theories, Experimental Evidence, and Examples," Chem. Rev. 86, 401. Marcus, R.A., Sutin, N. (1985), "Electron Transfers i n Chemistry and Biology," Biochirn. Biophys. Actcr 81 1. 265. Mattay, J., Ed. (1990-92). "Photoinduced Electron Transfer, Vol. I-IV," Chemistry. 156, 158. 159, 163; Springer: Heidelberg.

Topics of Current

Salem. L. (1982). Elc,c.trons in Chcmic~crlRt,uctiorl.s:First I'rinc.ip1e.s; Wiley: New York. Weller, A. (1968). "Electron Transfer and Complex Formation in the Excited State," Pure Appl. Chem. 16, 115.

Energy Transfer Closs, G.L., Johnson, M.D., Miller, J.R., Piotrowiak, P. (1989). "A Connection between Intramolecular Long-Range Electron, Hole, and Triplet Energy Transfers," J. Am. Chem. Soc. 111, 3751. Lamola, A.A. (1969). "Electronic Energy Transfer i n Solution: Theory and Applications" in Techniques of Organic Chemistry 14; Weisberger, A., Ed.; Wiley: New York. Turro, N.J. (1977), "Energy Transfer Processes." Pure Appl. Chrm. 49,405. Yardley, J.T. (1980), Introduction to Molecular Energy Transfer; Academic Press: New York.

Ground-state reactions are easily modeled using the absolute reaction-rate theory and the concept of the activated complex. The reacting system, which may consist of one or several molecules, is represented by a point on a potential energy surface. The passage of this point from one minimum to another minimum on the ground-state surface then describes a ground-state reaction, and the saddle points between the minima correspond to the activated complexes or transition states. For a theoretical discussion of photochemical reactions at least two potential energy surfaces are required: the ground-state surface with reactant and product minima as well as the excited-state surface on which the photoreaction is launched. Furthermore, the theoretical model must be capable of describing what happens between the time of light absorption by a molecule in its electronic ground state and the appearance of the product molecule, also in its electronic ground state, and in thermal equilibrium with its surroundings.

6.1 A Qualitative Physical Model for Photochemical Reactions in Solution A starting point for the discussion of experimental results in mechanistic photochemistry is the knowledge of the shapes of the ground-state (S,,)and

310

I'HO'fOCHLMICAI> KFA(1ION MODELS

first excited-state (S,) singlet surfaces and the lowest triplet-state surface (TI).Three steps can then be distinguished: First, minima and funnels in S, and TI have to be located. Then, it must be estimated which minima (funnels) are accessible, given the reaction conditions, and which ones will actually be populated with significant probabilities. Finally, from the shape of the ground-state surface So it must be determined what the products of return from these important minima (funnels) in S, and TI will be. This simple model ignores molecular dynamics problems as well as information on additional excited states, density of vibrational levels, vibronic coupling matrix elements, etc., which are required in more sophisticated advanced applications.

6.1.1 Electronic Excitation and Photophysical Processes According to the Franck-Condon principle, light absorption is a "vertical" process. Consequently, immediately after brief excitation with broad-band light the geometry of the system is virtually identical with that just before excitation. Subsequently, however, the motions of the nuclei are suddenly governed by a new potential energy surface, so the geometry of the system will change in time. In solution, the surrounding medium will act as a heat bath and efficiently remove excess vibrational energy. In a very short time, on the order of a few (5-50) picoseconds, thermal equilibrium will be established and the molecule will be sitting in one or another of the numerous minima in the excited-state surface. (Cf. Section 4.1.3.) If, due to the initial kinetic energy of the nuclei, the molecule can cross barriers before reaching this minimum, the process is referred to as a reaction of "hot molecules in an excited state" or simply as a hot c~xcited-stuterecrction. (See Section 6.1.3.) If the initial excitation was not into the lowest excited state of given multiplicity, a fast crossing to that state will occur via internal conversion, that is, typically to the S, or TI state (Kasha's rule, cf. Section 5.2.1). In some cases a funnel in S, is accessible and internal conversion from S, to Socan be so fast that the first thermal equilibration of the vibrational motion in these molecules is achieved in a minimum in the So state. Such a process is referred to as a direct reccc.rion. Here as well. the excess kinetic energy of the nuclei may take the molecule over barriers in the So state into valleys other than the one originally reached; analogous to the above-mentioned reactions, such processes are referred to as hot grorrnd-stare reacrions. Finally, in the presence of heavy atoms or in other special situations (cf. Section 4.3.4) intersystem crossing may proceed so fast that it is able to

6.1

A QlJALlTATlVE PHYSICAL MODEL

311

compete with vibrational relaxation. The first thermally equilibrated species formed may then be found in a minimum on the T, surface, even if the initial excitation was into S,. TI may also be reached via sensitization, that is, by excitation energy transfer from another molecule in the triplet state. (Cf. Section 5.4.5.) In one way or another, picoseconds after the initial excitation, the molecule will typically find itself thermally equilibrated with the surrounding medium in a local minimum on the S,, TI, or So surfaces: in S, if the initial excitation was by light absorption, in TI if it was by sensitization or if special structural features such as heavy atoms were present, and in So if the reaction was direct. Frequently, the initially reached minimum in S, (or TI)is a spectroscopic minimum located at a geometry that is close to the equilibrium geometry of the original ground-state species, so no net chemical reaction can be said to have taken place so far. Slower processes are the next to come into play. The most important among these are: First, thermally activated motion from the originally reached minimum over relatively small barriers to other minima or funnels, representing the adiabatic photochemical reaction proper. Second, intersystem crossing that takes the molecule from the singlet to the triplet manifold and thus eventually to a new minimum in TI. Third, fluorescence or phosphorescence that return the molecule to the ground-state surface So. Fourth, radiationless conversion from S, or TI to So,which is usually not competitive unless the energy gap AE(Sl - So)or AE(Tl - So)between the S, or TI and So states in the region of the minimum is small. (Cf. Section 5.2.3.) In this case, a "hot" molecule is produced, and a hot ground-state reaction can take place before removal of the excess energy. Other processes are also possible. These are, for example, further photon absorption (cf. Example 6. I), or either excitation or deexcitation via energy transfer, such as triplet-triplet annihilation or quenching. (Cf. Section 5.4.) A complex reaction mechanism that consists either of a two- or three-quantum process. depending on the temperature, will be discussed in Example 7.18. Example 6.1:

The photochemical electrocyclic transformation of the cyclobutene derivative 1 to pleiadene (2) does not proceed from the thermalized S, and TI states. At room temperature, the reaction cannot compete with fluorescence or intersystem crossing (ISC) due to high intervening barriers. However, these can be overcome by excitation to higher states, populated starting from Soeither by excitation with a single photon of sufficiently high energy (A < 214 nm) or in a rigid glass at 77 K by subsequent two-photon excitation. In the latter case U V absorption followed by intersystem crossing yields the long-lived TIstate. This intermediate can absorb visible light corresponding to a TI+-T, transition (Castellan et al., 1978). The situation is illustrated in Figure 6.1. Experimentally, it was not possible to distinguish between a reaction from one of the higher ex-

312

PHOTOCHEMICAL REACTION MODELS

6.1

A QUALITATIVE I'HYSICAL MODEL ~

Figure 6.2. Schematic representation of the jump from an excited-state surface (S, or TI)to the ground-state surface a) without chemical conversion and b) in the region

of a "continental divide" with partial conversion.

Figure 6.1. Photophysical processes and photochemical conversion of

6b,lob-dihydrobenzo[3,4]cyclobut[I,2-ulacenaphthylene. The numbers given are quantum yields of processes starting at levels indicated by black dots (by permissign from Castellan et al., 1978). cited S, or T, states and a reaction of vibrationally "hot" molecules in one of the lower excited states, possibly even Sl or TI.

excitation at least for some of the molecules, and the process is considered photochemical. The description given so far is best suited for unimolecular photochemical reactions. As mentioned above, if the process is bimolecular, both components together must be considered as a "supermolecule." The description given here remains valid except that some motions on the surface of the supermolecule may be unusually slow since they are diffusion-limited.

6.1.2 Reactions with and without Intermediates

No matter whether the eventual return to Sowill be radiative or radiationless, its most important characteristic is the geometry of the species at the time of the return, that is, the location of the minimum in S, or TIfrom which the return occurs. If the returning molecule reaches a region ofthe Sosurface that is sloping down to the starting minimum as shown in Figure 6.2a, the whole process is considered photophysical, since there is no net chemical change. If the return is to a region of S,, that corresponds to a "continental divide" (cf. Figure 6.2b) or that clearly slopes downhill to some other minimum in s,, a net chemical reaction will have occurred as a result of the initial

Figure 6.3 shows a schematic representation of two surfaces of the ground state (S,) and of an excited state (S, or TI)and of various processes following initial excitation. The thermal equilibration with the surrounding dense medium requires a sojourn in some local minimum on the surface for approximately I ps or longer. This may happen for the first time while the reacting species is still in an electronically excited state (Figure 6.3, path c), or it may occur only after return to the ground state (Figure 6.3, path a). In the former case, the reaction mechanism can be said to be "complex," in the latter, "direct." Direct reactions such as direct photodissociations cannot be quenched. The first ground-state minimum in which equilibrium is reached need not correspond to the species that is actually isolated. Instead, it may correspond to a pair of radicals or to some extremely reactive biradical, etc. (Figure 6.3, path k). Ncvertheless, this seems to be a reasonable point at which the photochemical reaction proper can be considered to have been

0.1

A QUALI'IXI'IVE PHYSICAL MODEL

315

Example 6.2: I'assage of a reacting system to the S,,surface through a funnel in the S, surface

is common in organic photochemical reactions, but the quantitative description of such an event is not easy. Until recently, it was believed that the funnels mostly correspond to surface touchings that are weakly avoided, but recent work of Bernardi, Olivucci, Robb, and co-workers (1990-1994) has shown that the touchings are actually mostly unavoided and correspond to true conical intersections. This discovery does not have much effect on the description of the dynamics of the nuclear motion, since the unavoided touching is merely a limiting case of a weakly avoided touching. Only when the degree of avoidance becomes large, comparable to vibrational level spacing, does the efficiency of the return to So suffer much. The expression "funnel" is ordinarily reserved for regions of the potential energy surface in which the likelihood of a jump to the lower surface is so high that vibrational relaxation does not compete well. The simplest cases to describe are those with only one degree of freedom in the nuclear configuration space. In such a one-dimensional case, the probability P for the nuclear motion to follow the nonadiabatic potential energy surface

Figure 6.3. Schematic representation of potential energy surfaces of the ground state (S,,) and an excited state (S, or TI) and of various processes following initial excitation (by permission from Michl. 1974a).

completed, even though the subsequent thermal reactions may be ofdecisive practical importance. If return t o So from the minimum in S , o r T , originally reached by the molecule is slow enough for vibrational equilibration in the minimum to occur first, the reaction can be said to have an excited-sttrte intermediate. The sum of the quantum yields of all processes that proceed from such a minimum, that is, from an intermediate, cannot exceed one. Those minima in the lowest excited-state surface that permit return t o the ground-state surface so rapidly that there is not enough time for thermal equilibration are termed "funnels." (Usually. they correspond to conical intersections, cf. Section 4.1.2.) By definition, direct photochemical reactions without an intermediate proceed through a funnel. Sometimes, a funnel may be located on a sloping surface and not actually correspond t o a minimum. Since different valleys in S,, may be reached through the same funnel depending on which direction the molecule first came from, the sum of quantum yields of all processes proceeding from the same funnel can differ from unity. The reason for the difference between an intermediate and a funnel is that a molecule in a funnel is not sufficiently characterized by giving only the positions of the nuclei-the directions and velocities of their motion are needed a s well (Michl, 1972).

Figure 6.4. Schematic representation of potential energy surfaces So and S, as well as So+S, excitation (solid arrows) and nuclear motion under the influence of the potential energy surfaces (broken arrows) a) in the case of an avoided crossing, and b) in the case of an allowed crossing (adapted from Michl, 1974a).

316

PHUrOCHEMICAL KEACTION MODELS

(i.e., to perform a jump from the upper to the lower adiabatic surface) is given approximately by the relation of Landau (1932) and Zener (1932): P = exp [ ( - n2/h)(AEZIvAS)]

Here, AE is the energy gap between the two potential energy surfaces at the geometry of closest approach, AS is the difference of surface slopes in the region of the avoided crossing, and v is the velocity of the nuclear motion along the reaction coordinate. Thus, the probability of a "jump" from one adiabatic Born-Oppenheimer surface to another increases, on the one hand, with an increasing difference in the surface slopes and increasing velocity of the nuclear motion, and on the other hand, with decreasing energy gap AE. The less avoided the crossing, the larger the jump probability; when the crossing is not avoided at all, AE = 0 and therefore P = 1. This is indicated schematically in Figure 6.4. In the many-dimensional case, the situation is more complicated (Figure 6.5). The arrival of a nuclear wave packet into a region of an unavoided or weakly avoided conical intersection (Section 4.1.2) still means that the jump to the lower surface will occur with high probability upon first passage. However, the probability will not be quite 100%. This can be easily understood qualitatively, since the entire wave packet cannot squeeze into the tip of the cone when viewed in the two-dimensional branching space, and some of it is forced to experience a path along a weakly avoided rather than an unavoided crossing, even in the case of a true conical intersection. An actual calculation of the S,+S, jump probability requires quantum mechanical calculations of the time evolution of the wave packet representing the initial vibrational wave function as it passes through the funnel (Manthe and

Figure 6.5. Conical intersection of two potential energy surfaces S, and So; the coordinates x, and x, define the branching space, while the touching point corresponds to an (F - 2)-dimensional "hyperline." Excitation of reactant R yields R*, and passage through the funnel yields products P, and P, (by permission from Klessinger, 1995).

Koppel, 1990), or a more approximate semiclassical trajectory calculation (Herman, 1984). In systems of interest to the organic photochemist, ~ i r ~ ~ t i l t a neous loss of vibrational energy to the solvent would also have to be included, and reliable calculations of quantum yields are not yet possible. I t is perhaps useful to provide a simplified description in terms of classical trajectories for the simplest case in which the molecule goes through the bottom of the funnel, that is, the lowest energy point in the conical intersection space. The trajectories passing exactly through the "tip of the cone" (Figure 6.5) proceed undisturbed. They follow the typically quite steep slope of the cone wall, thus converting electronic energy into the energy of nuclear motion. This acceleration will often be in a direction close to the x, vector, that is, the direction of maximum gradient difference of the two adiabatic surfaces. (Cf. Example 4.2.) Trajectories that miss the cone tip and go near it only in the twodimensional branching space have some probability of staying on the upper surface and continuing to be guided by its curvature, and some probability of performing a jump onto the lower surface and being afterward guided by it. However, in this latter case, an amount of energy equal to the "height" of the jump is converted into a component of motion in a direction given by the vector X, (direction of the maximum mixing of the adiabatic wave functions, cf. Example 4.2), which is generally not collinear with x, and is often approximately perpendicular to it (Dehareng et al., 1983; Blais et al., 1988). After the passage through the funnel, motion in the branching space, defined by the x,, xz plane, is most probable. Of course, momentum in other directions that the nuclei may have had before entry into the funnel will be superimposed on that generated by the passage through the funnel.

Figure 6.6. Schematic representation a) of the transition state of a thermal reaction and b) of the conical intersection as a transition point between the excited state and the ground state in a photochemical reaction. Ground- and excited-state reaction paths are indicated by dark and light arrows, respectively (adapted from Olivucci et al., I994b).

ti. 1

A bifurcated reaction path will probably result, and several products are often possible as a result of return through a single funnel. (Cf. Figure 6.5.) In summary, the knowledge of the arrival direction, the ~nolecularstructure associated with the conical intersection point, and the resulting type of molecular motion in the x,, x, plane centered on it provide the information for rationalizing the nature of the decay process, the nature of the initial motion on the ground state, and ultimately. after loss of excess vibrational energy, the distribution of product formation probabilities. Depending on the detailed reaction dynamics, the sum of the quantum yields of photochemical processes that proceed via the same funnel could be as low as zero or as high as the number of starting points. To appreciate the special role of a conical intersection as a transition point between the excited and the ground state in a photochemical reaction, it is useful to draw an analogy with a transition state associated with the barrier in a potential energy surface in a thermally activated reaction (Figure 6.6). In the latter, one characterizes the transition state with a single vector that corresponds to the reaction path through the saddle point. 'The transition structure is a minimum in all coordinates except the one that corresponds to the reaction path. In contrast, a conical intersection provides two poss~blelinearly independent reaction path directions.

Often. the minimum in S, or TI that is originally reached occurs near the ground-state equilibrium geometry of the starting molecule (Figure 6.3. path c); the intermediate corresponds to a vibrationally relaxed approximately vertically excited state of the starting species, which can in general be identified by its emission (fluorescence or phosphorescence, Figure 6.3, path d). Quenching experiments can help decide whether the emitting species lies on the reaction path or represents a trap that is never reached by those molecules that yield products. However, often the minimum that is first reached is shallow and thermal energy will allow the excited species to escape into other areas on the S, or TI surface before it returns to So(Figure 6.3, path e). This is particularly true for the TI state due to its longer lifetime. In the case of intermolecular reactions the rate also depends on the frequency with which diffusion brings in the reaction partner. The presence of a reaction partner may provide ways leading to minima that were previously not accessible, for example, by exciplex formation. Other possibilities available to a molecule for escaping from an originally reached minimum are classical energy transfer to another molecule, absorption of another photon (cf. Example 6.1), triplet-triplet annihilation (cf. Example 6.4), and similar processes.

A QUALII'A'rIVEPHYSICAL MODEL

'(n,n*) state (S,)to the CC double bond, whereas intersystem crossing into the '(n,n*) state (T,) prevents oxetane formation. The '(n,n*) state is quenched by triplet energy transfer to the diene, which then undergoes a sensitized transcis isomerization to 7 (Hautala et al., 1972).

Example 6.4:

A well-studied example of a photoreaction involving excimers is anthracene dimerization (Charlton et al., 1983). Figure 6.7 shows part of the potential energy surfaces of the supermolecule consisting of two anthracene molecules. Singlet excited anthracene ('A* + 'A) can either fluoresce (monomer fluores-

Example 6.3:

For reactions proceeding from the S, state. intersystelli crossing is frequently a dead end. Thus. irradiation of truru-2-methylhexadiene (4) in acetone (3) yields the oxetanes 5 and 6 through stereospecific addition of the ketone in its

319

Figure 6.7. Schematic potential energy curves for the photodimerization of anthracene (adapted from Michl. 1977).

320

PHOTOCHEMICAL REACTION MODELS

cence hv,), intersystem cross to the triplet state ('A* + 'A), or undergo a bimolecular reaction to form an excimer I(AA)*, which can be identified by its fluorescence (hv,). Starting from the excimer minimum and crossing over the barrier, the molecule can reach the pericyclic funnel and proceed to the ground-state surface leading to the dimer (24%) or to two monomers (76%). In this case intersystem crossing to the triplet state does not necessarily represent a dead end, because two triplet-excited anthracene molecules may undergo a bimolecular reaction to form an encounter pair whose nine spin states are reached with equal probability. (Cf. Section 5.4.5.5.) One of these is a singlet state '(AA)**that can reach the pericyclic funnel without forming the excimer intermediate first. The experimentally observed probability for the dimer formation via triplet-triplet annihilation agrees very well with the spin-statistical factor (Saltiel et a)., 1981). From Example 6.4 it can be seen that the molecule may also end up in a minimum o r funnel in S, o r T, that is further away from the geometry of the starting species. This then corresponds t o a "nonspectroscopic" minimum o r funnel (Figure 6.3, minimum f) such a s the pericyclic funnel of the anthracene dimerization in Figure 6.7, o r even to a spectroscopic minimum of another molecule o r another conformer of the same molecule (Figure 6.3, minimum i). Reactions of the latter kind can sometimes be detected by product emission (Figure 6.3, path j). (Cf. Example 6.5.) In many photochemical reactions return t o the ground-state surface S, occurs from a nonspectroscopic minimum (Figure 6.3, path g) that may be reached either directly o r via one o r more other minima (Figure 6.3, sequence c,e).

6.1.3 "Hot" Reactions Even in efficient heat baths, there are usually several short periods of time during a photochemical reaction when the reactant vibrational energy is much higher than would be appropriate for thermal equilibrium. One of these occurs at the time of initial excitation, unless the excitation leads into the lowest vibrational level of the corresponding electronic state. The amount of extra energy available for nuclear motion is then a function of the energy transferred t o the molecule in the excitation process, that is, a function of the exciting wavelength. Further, such periods occur during internal conversion (IC) o r intersystem crossing (ISC), when electronic energy is converted into kinetic energy of nuclear motion, o r after emission that can lead t o higher vibrational levels of the ground state. The length of time during which the molecule remains "hot" for each of these periods clearly depends on the surrounding thermal bath. In ordinary liquids at room temperature it appears to be of the order of picoseconds. (Cf. Section 5.2.1 .) Although short, this time period permits nuclear motion during lo2-1W vibrational periods. During this time, a large fraction of the mol-

ecules can move over potential energy barriers that would be prohibitive at thermal equilibrium. Since the vibrational energy may be concentrated in specific modes of motion, a molecule can move over barriers in these favored directions and not move over lower ones in less-favored directions. Chemical reactions (i.e., motions over barriers) that occur during these periods are called "hot. " Example 6.5:

Reactions of hot molecules are known for the ground state as well as for excited states. Thus, after electronic excitation of 1,Cdewarnaphthalene (8) in a glass at 77 K emission of 8 as well as of naphthalene (9) produced in a photochemical electrocyclic reaction is observed. The intensity of fluorescence from 9 relative to that from 8 increases if the excitation wavelength is chosen such that higher vibrational levels of the S, state of 8 are reached. This suggests that there is a barrier in S,. (Cf. Example 6.1.) If some of the initial vibrational energy is utilized by the molecule to overcome the reaction barrier before it is lost to the environment, 9 is formed and can be detected by its fluorescence. If the energy is not sufficient or if thermal equilibrium is reached so fast that the barrier can no longer be overcome, fluorescence of 8 is observed. The situation is even more complicated because at very low temperatures a quantum mechanical tunneling through the small barrier in S, of 8 occurs (Wallace and Michl, 1983).

Thermal o r quusi-equilibrium reactions, as opposed to hot ones, can be usefully discussed in terms of ordinary equilibrium theory a s a motion from one minimum t o another, using concepts such as activation energy, activation entropy, and transition state, as long as the motion remains confined t o a single surface. "Leakage" between surfaces can be assigned a temperature-independent rate constant. In this way jumps from one surface to another through a funnel may be included in the kinetic scheme in a straightforward manner.

Example 6.6: For the photoisomerization of 1.4-dewarnaphthalene (8) to naphthalene already discussed in Example 6.5 the following efficiencies could be measured in an N, matrix at 10 K (Wallace and Michl, 1983): q1.(8)= 0.13, qsT(8)= 0.29, qR. = 0.14, qRd+ qrcl = 0.44, qJ9) = 0.047, and qrs(9) = 0.95. Here, the indices Ra and Rd refer to the adiabatic and diabatic reaction from the singlet state, ret refers to the nonvertical return to the ground state of 8, and TS refers to the intersystem crossing to the ground state of 9. M;~kingthe plausible assumption that triplet 8 is converted to triplet 9 with lo()%efficiency. these data

Figure 6.8. Schematic representation of the potential energy surfaces relevant for the photochemical conversion of 1.4-dewarnaphthalene to naphthalene. Radiative and nonradiative processes postulated are shown and probabilities with which each path is followed are given (by permission from Wallace and Michl, 1983).

may be combined to produce the graphical representation shown in Figure 6.8. Here the probabilities with which each path is followed after initial excitation of a molecule of 8 into the lowest vibrational level of its IL, (S,) state are shown. Using the values r,.(8) = 14.3 ? I ns and T , (9) = 177 ? 10 ns for the fluorescence lifetimes, rate constants can be derived f~.omEquation (5.8) for the various processes. Thus, one obtains k,. = qlltl = 9.1 x 10" s ' for the fluorescence of 8 and k, = (q,, + qWd+ vrr,)ltk= 4.1 x 10' s I for the rate of passing the barrier.

6.1.4 Diabatic and Adiabatic Reactions The description of the course of photochemical processes outlined s o far implies that there is a continuous spectrum of reactions from unequivocally diahatic ones that involve a nonradiative jump between surfaces t o unequiv-

QLII~LI1AI IVE PHYSICAL MODEL

323

ocally udic1hatic ones that proceed on a single surface (Forster, 1970). The dicrhatic liinit is represented by reactions in which return to the ground state occurs at the geometry of the starting material. The rest of the reaction then occurs in the ground state and the reaction must be a hot ground-state one; otherwise the ground-state relaxation would regenerate the starting material, resulting in no net chemical change. The other extreme, a prrrely udiahutic reaction, is represented by reactions that proceed in an electronically excited state all the way to the ground-state equilibrium geometry of the final product. Here the excited state converts to the ground state via emission of light o r by a radiationless transition. In both these limiting cases, the return to the ground state occurs from a spectroscopic minimum at an ordinary geometry. In addition to such minima the lowest excited states tend t o contain numerous minima and funnels a t biradicaloid geometries, through which return to the ground state occurs most frequently. Most photochemical reactions then proceed part way in the excited state and the rest of the way in the ground state, and the fraction of each can vary continuously from case to case. (Cf. Figure 6.3, path a.) It is common to label "adiabatic" only those reactions that produce a "spectroscopic" excited state of the product (cf. Figure 6.3, path h), s o distinction between diabatic and adiabatic reactions would appear to be sharp rather than blurred. But this is only a n apparent simplification, since it is hard to unambiguously define a spectroscopic excited state. A second obvious problem with the ordinary definition of adiabatic reactions is the vagueness of the term "product." If the product is what is actually isolated from a reaction flask at the end, few reactions are adiabatic. (Cf. Example 6.7.) If the product is the first thermally equilibrated species that could in principle be isolated a t sufficiently low temperature, many more can be considered adiabatic. A triplet Norrish 11 reaction is diabatic if an enol and an olefin are considered as products. It would have to be considered adiabatic, however, if the triplet 14-biradical, which might easily be observed, were considered the primary photochemical product. (See Section 7.3.2.) Example 6.7:

For a photochemical conversion to be adiabatic. the excited-state surface has to exhibit an overall downhill slope from reactant to product geometries and must not contain unsurmountable barriers or local minima by which the reacting molecules get trapped and funneled off to the ground-state surface before reaching the product geometry. For instance, the photochemical conversion of 1.4-dewarnaphthalene to naphthalene is so strongly exothermic that the pericyclic minimum is without doubt shallow enough to facilitate efficient escape on the excited surface. (Cf. Figure 6.8; for a semiempirical calculation of the potential energy curves, see Jug and Bredow. 1991.) The result is that a portion of the reactants proceeds along the adiabatic path. An example of this behavior

324

PHOTOCHEMICAL KWC'I'ION M0l)t:LS

is the photochemical decomposition of the benzene dimers 10 and 11, which yields excited benzene efficiently. Since the benzene excited state lies at 110 kcaVmol and the wavelength of the exciting light was 335 nm, corresponding to 85.3 kcallmol, the result clearly demonstrates that a part of the chemical energy stored in the reactant is utilized in the adiabatic process to generate electronic excitation in the product (Yang et al., 1988).

The situation is different for the valence isomerization of the metacyclophanediene 12 to the methano-cis-dihydropyrene 13, which also proceeds adiabatically (Wirz et al., 1984). In this case reactant and product hom*oS correlate with each other in the same way as the corresponding 1,UMOs. The reaction is therefore allowed in the ground state. Nevertheless, the excited state has no correlation-imposed barrier, although the photochemical reaction should be forbidden by the simple Woodward-Hoffmann rules. (See also Example 7.18.) Other examples for adiabatic reactions may be found among triplet reactions, as funnels do not exist in the triplet surface, and return to the singlet ground state requires spin inversion. The ring opening of 1,4-dewarnaphthalene to naphthalene is an example of such a case. (See Figure 6.8.)

6.1.5 Photochemical Variables In addition to concentration there are essentially four reaction variables that can be relatively easily controlled and that may have a considerable effect on the course of a photochemical reaction; these are the reaction medium and temperature, and the wavelength and intensity of the exciting light. In addition, magnetic field and isotope effects may come into play.

6.1.5.1 m e Effecto f the Reaction Medium Medium effects can be divided into two classes: those that directly modify the potential energy surfaces of the molecule, such a s polarity o r hydrogen bonding capacity, affecting through strong solvation in particular the (n,n*) as opposed to the (n,n*)state energies, and those that operate in a more subtle manner. Examples of the latter are microscopic heat conductivity,

which determines the rate of removal of excess vibrational energy, the presence of heavy atoms, which enhance rates of spin-forbidden processes, o r viscosity, which affects diffusion rates and thus influences the frequencies of bimolecular encounters. Through these, it may also control triplet lifetimes o r the competition between monomolecular and birnolecular processes. Very high solvent viscosity, encountered in crystalline and glassy solids, also effectively alters the shape of potential energy surfaces by making large changes in molecular geometry either difficult o r impossible. This increases the probability that the excited molecule will not greatly change the initial geometry and will eventually emit light rather than react. The structural dependence of biradicaloid minima discussed in Section 4.3.3 on an example of twisting of a double bond A=B can be extended to take solvent effects into account. Not only the nature of the atoms A and B but also polar solvents and counterions affect the stability of zwitterionic states and states of charged species. Then, depending on the solvent, a biradicaloid minimum can represent either an intermediate o r a funnel for a direct reaction. Example 6.8:

If light-induced electron transfer is the crucial step in a photochemical reaction, the solvent dependence expected for this process (cf. Section 5.5.3) may carry over to the whole reaction. An example is the reaction of I-cyanonaphthalene (14) with tlonor-substituted acetic acids such asp-methoxyphenylacetic acid (15).

ti. l

QUALI'TA'rIVE PHYSICAL MODEL

I n polar solvents such as acetonitrile, electron transfer occurs followed by proton transfer from the radical cation to the radical anion with concurrent loss of CO?.The radicals collapse to addition products such as 16 or 17. Alternatively, the radical pair may escape the solvent cage to give, after hydrogen abstraction from a suitable hydrogen source, the reduction product 18. In nonpolar solvents such as benzene, however. electron transfer is not possible; only exciplex emission and no chemical reaction are observed (Libman, 1975).

6.1S.2 Temperature Effects Temperature can have an essential effect on the course of a photochemical reaction because it can affect the rates at which molecules escape from minima in S, or TI. At very low temperatures, even barriers of a few kcal/mol are sufficient to suppress many photochemical processes more or less completely. Processes such as fluorescence, which were too slow at room temperature, may then be able to compete. (Cf. Example 6.5.) At times, the excited molecule has the choice of reacting in two or more competing ways. and the competition between them can also be temperature dependent. An example is the temperature dependence of the diastereoselectivity and regioselectivity of the cycloaddition of' menthyl phenylglyoxylate 19 to tetramethylethylene (20) and to ketene acetal 21 (Buschmann et al., 1991):

Temperature dependence of the diastereoselectivity of oxetane formation (22: @, 23: A, 24: m) by cycloaddition of menthyl phenylglyoxalate (19) to tetramethylethylene (20) and ketene acetal (21) (hy permission from Huschmann et al., 1991).

Figure 6.9.

temperatures the benzene oxide predominates in the benzene oxide-oxepin equilibrium, and only the photochemistry of this tautomer is observed. At higher temperatures, however, the photochemical reactions of the oxepin (26), present in the equilibrium, prevail due to its considerably higher extinction coefficient E at the wavelength of irradiation (Holovka and Gardner, 1%7).

6.1.5.3 Effectsof Wauelength and Intensity of the Exciting Light Figure 6.9 shows a plot of In klk' versus T-I, where k and k' are the overall formation rate constants for the major and the minor oxetane isomer, respectively. The diastereomeric excess (% dc) can either increase or decrease with decreasing temperature. Changes in temperature generally affect ratios of conformer concentration of the starting ground-state molecules and also their distribution among individual vibrational levels, thus codetermining the nuclear configuration of the average molecule just after excitation. The equilibrium between valence tautomers is also affected by temperature changes, and a temperature effect on the photochemical reactivity may result. 'I'hus, irradiation of benzene oxide (25) at room temperature produces the furan 27, whereas irradiation at -80°C gives 11% 27. 74% phenol and 15% benzene. At lower

Changes in light wavelength determine the total amount of energy initially available to the excited species. As pointed out in Section 5.2.1, in dense media part of this energy is rapidly lost and after 10- "-10 - l 2 s the molecule reaches either one of the minima on the S , or T I surfaces, or in the case of a direct reaction through a funnel, one of the minima on the S,, surface. Since internal conversions need not be "vertical" the probability that one or another minimum is reached may change drastically as the energy of the starting point changes. In general, one can imagine that a higher initial energy will allow the molecule to move above barriers that were previously forbidden. and that additional minima will become available. Whether the additional energy is actually used for motion toward and above such barriers or whether it is used for motion in "unproductive" directions and eventually lost as heat could be a sensitive function of the electronic state and vibra-

328

PHOTOCHEMICAL KEACI'ION M0I)I::LS

6.1

A QUALII'A'I'IVI; I'I IYSICAL. MOI)I 24 kcal/mol no dimerization has been observed. (Cf. Section 7.4.2.)

6.2.4 Normal and Abnormal Orbital Crossings The initial problem in constructing a correlation diagram for a thermally forbidden pericyclic reaction is in the identification of those orbitals that are most responsible for the ground-state energy barrier. In particular, it is necessary to actually identify the originally bonding orbital of the reactant, say @ i , which becomes antibonding (or at least nonbonding) in the product, and the originally antibonding reactant orbital, say which becomes bonding in the product, in order to completely specify the "characteristic configuration." The second step in the argument consists of an assignment of states of both the reactant and the product to specific configurations, and may require a consultation of spectroscopic data and some CI calculations. In many cases @, is the hom*o and @, the I,UMO ofthe reactant, and its they cross along the reaction coordinate, GI becomes the LUMO and @, the hom*o of the product. This kind of crossing will be referred to as "normal orbital crossing." Although the crossing may be avoided in systems of low symmetry, the arguments do not change. An "abnormal orbital crossing" occurs if at least one of the crossing orbitals and @, is neither the hom*o nor LUMO of the reactant. In this case, already at the stage of the configuration correlation diagram, more or less significant barriers have to be expected on the S, and TI surfaces. This becomes apparent from the following argument: The characteristic , of the reactant will correlate with the configuration @l,i configuration, @ of the product and this will be the lowest-energy configuration likely to remain at approximately constant energy along the path. If the crossing is of the normal type, this configuration most often predominates in the lowest excited singlet and triplet states S, and TI of both the reactant and the product, with the result that no barriers due to correlation are imposed starting on either side. If instead, either due to abnormal orbital crossing or due to configuration interaction effects, it predominates in one of the higher excited

+,,

states, other configurations necessarily represent the lowest excited state,

S, or TI. This then rises along the reaction path until it meets the state primarily represented by the characteristic configuration, and barriers are imposed on the excited-state surfaces. In the case of many aromatics, the lowest singlet excited state is not represented by the hom*o-LUMO excited configuration ('La) but rather by a +,, and Q i - I,A ('L,, cf. Section 2.2.2), and a barrier is exmixture of @ pected in the excited state S,. Since the difference in the S, and S, energies is usually quite small the resulting barrier will be small. (See Example 6.12.) In the triplet state, no barriers of this origin are expected since even in these cases the triplet represented by the hom*o-+LUMO excitation is lowest.

Example 6.12: Figure 6.18a gives a schematic representation of the orbital correlation diagram for the thermally forbidden conversion of one alternant hydrocarbon into another one. The following configuration correlations are easily verified from this diagram: ct)" @l-I,

-9

@';7;: +

+ -*

@;-I.

I-?'

@';z):

Figure 6.18. Excited-state barriers: a) orbital correlation diagram for a thermally forbidden conversion of an alternant hydrocarbon; b) the corresponding configuration ;~nd state correlation diagram for the case that the HOMChLUMO exciti~tiondoes not represent the longest-wavelength absorpt ion.

6.2

where (I,and cD' may refer either to reactant or to product. The ground state -I.. which i n i~roniatichydrocarbons as well as the mixture of cD,-_,. and represents the 'L, state. correlates with high-lying doubly excited states. Assuming that both in the reactant and the product the 'L, state is below the 'La state, which corresponds to the hom*o-+I,UMOexcit;~lion, the state correlation diagriun shown in 1:igurc 0.IXh is obtained, which irlrcady takes into consideration the avoided crossings between singlet states o f equal symmetry. From the derivation of this diagram it is evident that a barrier in the S, state is to be expected in all those cases i n which the lowest excited singlet state is not represented by the hom*o-2LUMO excitation, but is symmetrical with respect to the symmetry element that is being conserved during the correlation, like the ground state. A n example of the situation discussed here is given by the conversion of dewarnaphthalene into naphthalene. (Cf. Example 6.5.) The corresponding correlation diagram was already shown in Figure 6.8.

I'ERICYCLIC REACTIONS

347

that interacts strongly with the antibonding combination (a*)will be If #i is the hom*o of the original molecule and #, the LUMO. the orbital crossing is normal; otherwise it is abnormal. Example 6.13: 120rcyclobutenopheni~nthrcnc(50) two dill'crcnt photochcmici~lreaction pathways are conceivable (Michl, 1974b); the electrocyclic opening o f the cyclobutene ring to form 51 and the cycloreversion reaction to give phenanthrene and acetylene. The HMO coefficients of the 2 and 2' positions in biphenyl have opposite signs in the hom*o and equal signs in the LUMO. Thus, the hom*o

From the generitl form of the correlation diagram in Figure 6.18 it is evident that since barriers can be overcome with the aid of thermal energy the initial excitation need not be into that state that is represented by the characteristic configuration. In this case low temperature can prevent the reaction from taking place. Excitation of higher vibrational levels of one-andthe-same absorption band can enable the nuclei to move over the barrier in a hot reaction. In the case of an abnormal orbital crossing, a straightforward consideration of frontier orbitals would be misleading. Examples of high barriers due to abnormal orbital crossing have been observed in the electrocyclic ring opening of cyclobutenoacenaphthylene (47) and similar compounds (cf. Example 6.1 and Figure 6. I ) (Michl and Kolc, 1970; Meinwald et al., 1970). An example of a low barrier due to abnormal orbital crossing that can be overcome using thermal energy has been reported for the cycloreversion reaction of heptacyclene 48 to two acenaphthylene molecules (49) (Chu and Kearns, 1970).

In deciding whether a normi11 or an abnornial orbital crossing is to be expected for an electrocyclic process, the two-step procedure for constructing qualitative orbital correlation diagrams described in Section 4.2.2 has proven very useful. The least-bonding MO of the reactant that interacts strongly with the bonding combination (a)of the AOs on the two carbons originally joined by a single bond will be Q,,and the least-antibonding MO

Figure 6.19. State correlation diagram for the fragmentation o f cyclobutenophenanthrene. The straight arrows indicate absorption o f light of a given wavelength; the wavy lines indicate how the barriers i n S, (full lines) and in TI (broken lines) can be overcome when sufficient energy is available (by permission from Michl, 1974b).

348

PHOTOCHEMICAL KEACI'ION M0L)CIS cannot interact with the bonding combination and the L U M O cannot interact with the antibonding combination o f the AOs o f the original cr bond during the disrotatory opening of the cyclobutene ring in 50. This results in an abnormal orbital crossing. This reaction has i n fact so far not been detected. Experimentally known, however, is the cycloreversion to give phenanthrene and acetylene. This is assumed to be concerted in the singlet state and stepwise in the triplet state as indicated in Figure 6.19. The orbital correlation diagram for the concerted reaction has been derived in Example 4.5 and exhibits a normal orbital crossing. (See Figure 4.16.) Since the 'I,, band that is represented by the hom*o-+LUMO transition corresponds to an excitation from S,, to S2in biphenyl as well as i n phenanthrene, a barrier i n S, results, as shown for the general case in Figure 6.18. However, the triplet reaction is expected to be endothermic and the molecules will sooner or later again collect in the T, minimum for the starting geometry. Also indicated in Figure 6.19 is the nonconcerted p;~thwayfor which a barrier in 1'' is to he expected, since the TI is o f i t n-n* niiture while the chiu-;~cteristicconfiguration for reaching the openchain minimum i s of ;Ic ~ c P nature. (Cf. Figure 6.20.)

avoided and results in a barrier separating two minima on the TI surface (Figure 6.20). The minimum, which is essentially represented by the '(n,n*) configuration, is a spectroscopic minimum, into which initial excitation occurs, either by energy transfer (triplet sensitization) or indirectly by intersystem crossing (ISC) from the singlet manifold. The minimum represented by the '(0,d) configuration, on the other hand, is a reactive minimum, from which the actual dissociation takes place. Similarly, the characteristic state for an a cleavage in a ketone triplet is of (0.8)nature, whereas the excitation is into the (n,n*) state. The spectroscopic minimum preserves the excited molecule until it can escape toward the reactive minimum. Its role is particularly crucial in bimolecular processes, where this escape has to wait for diffusion to introduce a reaction partner. A high barrier separating the spectroscopic minimum and the reactive minimum is to be expected if the orbitals @, and which represent the characteristic configuration, do not interact with the orbitals involved in the electronic transition into the lowest excited state; the crossing between the potential energy curve that goes up in energy along the reaction coordinate and the one that comes down in energy would then not be avoided. Examples of this situation are the dissociation of an aromatic CH bond in toluene or the cleavage of a CC bond in a ketone that is rather far away from the carbonyl group. No doubt such reactions will show minima in the S, or TI surface. But they are separated by unsurmountable barriers, so these reactions cannot be observed.

6.3 Nonconcerted Photoreactions 6.3.1 Potential Energy Surfaces for Nonconcerted Reactions Most known photochemical processes are not pericyclic reactions. Even in many of these cases correlation diagrams can be helpful in estimating the location of minima and barriers on excited-state surfaces. (Cf. Section 4.2.2.) The derivation of these correlation diagrams, however, is often more difficult, not only because of lack of symmetry, but also because it may be difficult to identify any one excited state as the characteristic state, particularly in large molecules. For example, many of the cwd" excited states of toluene will have some contribution from the v r r * bond orbital excitation in one of the three C-H bonds in the methyl group. Often, however, it is sufficient to distinguish between rr* and n* orbitals in order to decide whether a barrier is likely to occur. For instance, the T, surface of toluene along the path of nuclear geometries that leads to dissociation to C,H,CH2. + H- can be viewed as originating from interaction of a locally excited '(n,n*)configuration of the benzene chromophore and a locally excited '(0.d) configuration of the CH bond. The former is of lower energy at the initial geometries, as is the latter at the final geometries; somewhere along the way they intend to cross, but the crossing is

Figure 6.20. bhcrgies of zclcctcd st;llcb tlur-ing dis\oci;~tionof ;I h c r ~ ~ y l('ti i c hol~d in toluene as ;Ifiinction of thc rc;lction coonlin;~tc(hy pcrnlis\io~lI.roln Michl. 1073;1).

6.3

However, when the orbitals of the characteristic configuration can interact with the orbitals involved in excitation, as is the case for the cleavage of the benzylic C-H bond in toluene or the a CC bond in a ketone, the crossing will be avoided and the barrier will be lowered depending on the interaction. The magnitude of the interaction is rather difficult to predict without a detailed calculation. In the particular case of the photolytic dissociation of the benzylic CH bond in toluene, the barrier separating the two minima is so high that the reaction proceeds on absorption of a single photon only if light of sufficiently short wavelengths is used. With light of longer wavelengths another photon is needed to overcome the barrier. (Cf. Johnson and Albrecht, 1968 as well as Michl, 1974a.) Example 6.14: Except for the relief of ring strain, similar harrier heights are to be expected for the triplet-sensitized photochemical ring opening of benzocyclobutene (52) to form o-xylylene (53) and for the dissociation of the benzylic C--C bond in ethylbenzene leading to a benzyl and methyl radical. Since the energy of the characteristic configuration may be lowered by additional substituents, this may favor the interaction with the orbitals involved in the initial excitation and thus reduce the barrier height. In fact, for a,a,a'af-tetraphenylbenzocyclobutene (54)a photochemical ring opening has been observed. whereas under similar conditions of low-temperature irradiation benzocyclobutene is inert (Quinkert et al., 1969: Flynn and Michl, 1974).

NONCONCEKTED PHOTOREACTIONS

351

to be expected on the basis of orbital symmetry, the interaction between these configurations is likely to be strong, so the barrier resulting from the avoided crossing may not be high. The results of ab initio calculations for hydrogen abstraction by ketones according to

represented in Figure 6.21, in fact show small barriers in the '(n,n*) and 3(n.n*) excited states, which indicate that the MOs apparently "remember" the natural or intended correlation. (Cf. Figure 4.18.) Another barrier on the T, surface is observed for hydrogen abstraction by ketones whose 3(n,n*) state is of lower energy than the '(n,n*) state. From Figure 4.17 it is seen that the >(n,n*)state goes up in energy while the '(n,n*) state comes down in energy along the reaction coordinate or at least remains more or less constant (Figure 6.21), and a crossing of the corresponding potential energy surfaces will occur at a geometry intermediate between that of the reactant and a biradical. For nonplanar arrangements of the nuclei this crossing will be avoided and will produce a barrier. This amounts to 5 kcallmol in the case of the hydrogen abstraction in the naphthyl

In the case of dissociation of the various methyl-substituted anthracenes to form the corresponding anthrylmethyl radicals the relative magnitude of the interaction between the a orbitals of the characteristic configuration and the n and n* orbitals involved in the excitation may be estimated quite easily. Assuming that the interaction is proportional to the square $,of the LUMO coefficient of the carbon atom adjacent to the methyl group, the lowest barrier is expected for the Pmethyl derivative and the highest one for the 2-methyl derivative, as may be seen from the squared coefficients given in formula 55.

1.3

Bo"

50 H

151

122~90"

'GJ

In Section 4.2.2 it has been shown that due to intended or natural orbital correlations, crossings may occur in the configuration correlation diagram that are avoided in the state correlation diagram. If no avoided crossing is

109 ,H H-C 109 5O vH VH

Figure 6.21. Sti~tecor1~1:rtion diagram for the photochemical hydrogen abstraction, as calculated for the system formirldehyde + methane (by permission from Devaquet et ;)I.. 1978).

352

PHOTOCHEMICAL REAC'TION M0L)EU;

ketone 56 to form 57, an example in which the '(n,n*) is higher in energy by 9 kcallmol than the '(n,n*) state. Besides, this is an abstraction of the 6-H atom that makes a nonplanar reaction path very likely (De Boer et al., 1973).

The picture becomes somewhat more complex if the a cleavage of ketones is considered.

If all atoms involved in the reaction lie in the same plane, the unpaired electron of the acyl radical may be either in an orbital that is symmetric with respect to this plane or in an orbital that is irntisymmctric-that is, either in 21 a or in a n orbital, whereas only a cr orbital is avirilable for the unpaired electron of radical K. Instead of just one singlet and one triplet covalent biradicaloid structure (Figure 4.5). there are now two of each. which may be denoted as I - % , , ,and , , '.'B,,,,,, respectively. Similarly, there are also different zwitterionic structures to be expected. The increase in complexity and the number of states that results from the presence of more than two active orbitals on the atoms of a dissociating bond has been formalized and used for the development of a classification scheme for photochemical reactions ("topicity"), as is outlined in more detail in Section 6.3.3. As shown in Figure 6.22 in the example of the formyl radical, the a acyl radical prefers a bent geometry with the unpaired electron in an approxi-

1SO0

ii HCO

Figure 6.22. Qualitative representation of the energy o f the o and n formyl radical as a function of the HCO angle.

mately sp"ybrid AO that has some s character and thus is energetically more favorable than a pure p AO. In contrast, the n acyl radical prefers a linear geometry, since it has its unpaired electron in the n* orbital; the p,. A 0 starts empty and overlaps with the doubly occupied n,, A 0 to form a doubly occupied MO. Since at linear geometries three electrons in one n system are equivalent to three electrons in two p AOs orthogonal to this n system, the aand the n acyl radical states have the same energy, that is, are degenerate. In discussing the rciiction it is helpfill to use bond dissociation and bond angle variation in the reaction product as independent coordinates. In this way the potential energy surfaces of the type shown in Figure 6.23 for the a-cleavage reaction of formaldehyde are obtained. Such a three-dimensional diagram is difficult to construct without calculations, and an initial analysis can be based on a conideration of the reactions to linear and bent products separately as shown in Figure 6.24. Sometimes the two reaction paths are plotted superimposed, with only the a states of the acyl radical shown for the bent species and only the n states shown for the linear species (Salem, 1982). but such plots can be easily mistrnderstood and we avoid them. We shall return to these issues in connection with applications of these diagrams

Figure 6.23. Potential energy surfaces for the a-cleavage reaction of formaldehyde as a function of the CH, distance and the OCH, angle; formaldehyde states are in the front left corner, correlation to the front right corner corresponds to cleavage of the a bond with bond angles kept constant, and correlation from here to the right rear corner corresponds to linearization of the formyl radical. Correlation between states of formaldehyde and of the linear biradical results from a cross section through these surfaces approximately long the diagonal from the front left to the rear right corner (by permission from Reinsch et al., 1987).

6.3

Figure 6.24. State correlation diagram for the n cleavage of saturated ketones. The path to a bent acyl radical is shown on the right, that to 21 linear acyl radical to the left. The right-hand part of the diagram corresponds to the front face of the threedimensional representation in Figure 6.23; the left-hand part corresponds to the cross section along the diagonal in Figure 6.23.

180

aOCH 1°1

120 110

300

110

Rcn Ipml

300

NONCONCERTED PHOTOREACTIONS

355

Figure 6.26. Potential energy curves for the a-cleavage reaction of formaldehyde. Part a) represents a cross section through the surfaces of Figure 6.23 approximately along the QOCH = 130" line, forming a bent acyl radical, and part b) a cross section along the minimum energy path on the (n,n*)excited surfaces S, and T;,,forming a linear acyl radical.

in Section 7.2.1. It is important to remember that the two parts of Figure 6.24 do not represent different reactions but rather correspond to different reaction paths on the same potential energy surfaces. This becomes particularly evident from the contour diagrams shown in Figure 6.25. For the potential energy surfaces of Figure 6.23 these diagrams show the reaction path to the bent acyl radical, which is the minimum energy path in the ground state and in the -'(n,n*) state (Soand T,), and the alternative reaction path to the linear acyl radical, which is more favorable in (n,n*) states ( S t ,and T,). Cross sections through the surfaces of Figure 6.23 along these reaction paths are depicted in Figure 6.26. Figure 6.26a corresponds to the right-hand side of the correlation diagram shown in Figure 6.24, and Figure 6.26b to the lefthand side.

6.3.2 Salem Diagrams

Contour diagrams of the potential energy surfaces for the a-cleavage reaction of formaldehyde shown in Figure 6.23. The broken lines indicate the reaction paths to the bent ( A ) and the linear ( B ) acyl radical ( b y permission from Reinsch et ;)I.. 1987). Figure 6.25.

In f;ivorable cases state correlation diagrams of the type shown in Figure 6.2 1 and Figure 6.24 may be obtained simply from the leading VB structures of the reactant and the biradici~loidproduct. The molecular plane is chosen as the symmetry elenlent-that is. one considers coplan;u- reactions, and any deviation from coplanarity may possibly be taken into account as an additional perturbation. As tr orbitals are symmetric and n orbitals antisymmetric with respect to the molecular plane, symmetries of the various states may be obtained by simply counting the number of a and n electrons in a VB structure. A single structure is in general not sufficient to describe an electronic state accurately. but all contributing V B structures have the same symmetry, so the inclusion of just some of them is sufficient to establish a correlation diagram. The use of VB structures in the consideration of photochemical reaction paths was pioneered by Zimmerman (1969). The use of

PHOTOCHEMICAL REACTION M0L)EL.S

Figure 6.27. Salem diagram for hydrogen abstraction by a carbonyl compound. The biradicaloid product states are denoted by '.'B (dot-dot, covalent)and Zl,z(hole-pair, zwitterionic),respectively (by permission from Dauben et at., 1975).

VB correlation diagrams for this purpose was developed by Salem (1974) and collaborators (Dauben et al., 1979, and they are commonly referred to as Salem diugrtrnzs. The photochemical hydrogen abstraction by carbonyl compounds, which has already been discussed in the last section, will be used to illustrate the procedure. The left-hand side of Figure 6.27 shows the dominant VB structures of the ground state and of the excited (n,n*) and (n,n*) states of the reactants. Only the electrons directly involved in the reaction are considered. In the ground and the (n,n*) states, the numbers of a and n electrons are 4 and 2, respectively, and these states are symmetric relative to reflection in the mirror plane. In the (n,n*) states, both numbers are equal to 3. and these states are antisymmetric. The right-hand side shows the analogous VR structures for the various states of the biradicaloid system formed as a primary product. Dot-dot (covalent) states are denoted by % and ' B and holepair (zwitterionic) states by 2, and Z2, using the nomenclature introduced in Section 4.3.1. The energy of these states depends on the nature of radical centers A and B as has also been discussed in Section 4.3.1. In the present case both radical centers are C atoms, so the dot-dot states are clearly lower in energy than the charge-separated hole-pair ones. Since the electron count gives 30, 3n for the dot-dot and 40, 2n for the hole-pair states, correlation lines can be drawn immediately as shown in Figure 6.27. Thus, a diagram is obtained that is basically identical to the results represented in Figures 4.18 and 6.21 except for the barriers revealed by natural orbital correlations.

6.3.3 Topicity The differences between the correlation diagrams for the dissociation of the H-H or Si-Si single bond (Figure 4.5) and for the dissociation of the C--C

single bond in the Norrish type I process (Figure 6.24) are striking. In particular, in the former case, only the triplet state is dissociative, while in the latter case, a singlet state is as well. We have already seen in Section 4.3.3 that the correlation diagram for the dissociation of a single bond can change dramatically when the electronegativities of its termini begin to differ significantly. Now, however., both bonds to be cleaved are relatively nonpolar. The contrast is clearly not due to the differences in the properties of silicon and carbon, either. Rather, it is due to the fact that in one case a double bond is present at one of the termini of the bond that is being cleaved. This causes an increase in the number of low-energy states and changes the correlation diagram. This role of the additional low-energy states has been formalized in the concept of topicity (Salem, 1974; Dauben et al., 1975), which was generalized by its originators well beyond simple bond-dissociation processes. We believe th:lt this concept is most powerful and unambiguous in the case of reactions in which only one bond dissociates, and shall treat this situation only. Simple bond-dissociation reactions are classified as bitopic, tritopic, tetratopic, etc., according to the total number of active orbitals at the two terminal atoms of the bond. Active orbitals at an atom (AOs or their hybrids) are those whose occupiincy is not always the same in all V B structures that are important for the description of the low-energy states that enter the correlation diagram for the bond-dissociation process. These are obviously the two orbitals needed to describe the bond to be cleaved, so the lowest possible topicity number ib two, but possibly also other orbitals located at the two atoms: those containing lone pairs out of which excitation is facile (e.g., oxygen 2p), those that are empty such that excitation into them is facile (e.g., boron 2p), and those participating in multiple bonds adjacent to the bond being cleaved (e.g., carbonyl in the rx-cleavage reaction). I t is now clear that the dissociation 01' the H-H bond and of the Si-Si bonds in saturated oligosilanes are bitopic processes. The Norrish type I a cleavage is an example of a tritopic process, sometimes subclassified further as a a(a,n) tritopic process to specify that one terminal carries an active orbital of a symmetry and the other two active orbitals, one of o and one of n symmetry. Other examples of tritopic reactions are the dissociation of the C-N bond in a saturated amine and the dissociation of the C--0 bond in a saturated alcohol (the oxygen 2s orbital is very low in energy, doubly occupied in all important stiltes, and not counted as active). Figure 6.28 shows the correlation diagram for the dissociation of the C--0 bond in methanol. Diagrams for such simple dissociations are not necessarily of use in themselves, not only since these reactions require high-energy excitation and are relatively rarely investi~dtedby organic photochemists. but primarily because the lowest excited states of fully saturated organic molecules are usually of Rydberg ch:tracter while only valence states are shown in the diagrams. Thus. at least one side of the dii~gram is quite unrealistic. Experimental (Keller el ;ti.. 1992; .lensen et a1.. 1993) and theol-elical (Y;II--

Supplemental Reading

75';)

\C S m G , d:

loo*

"g2,

P3 q)

I k ~ u h c n .W.G.. S;~lcni.I... '1'11rro. N.J. (1975). " A CI ; ~.s. s' "~ l l c a t i oonf I'horochemical Re;~clions," Ac.c.. ('hc,rn. Rc,s. 8 . 41. Dougherty. R.C. (1971). "A Perturbation Molecular Orbital Treatment of Photochemical Reactivity. The Nonconservation o f Orhital Symmetry in I'hotochcmic:~l Pericyclic Re. 93. 7187. actions." J. Am. C l i c ~ i i.Yo(,. Fijrster. Th. (1970). "Diabatic and Adiabatic Processes in Photochemistry," Pure Appl. Clrc~rn.24, 443. Gerhartz, W., Poshusta. R.D., Michl, J. (1976). "Excited Potential Energy Hypersurfaces for H, at Trapezoidal Geometries. Relation to Photochemical 2s + 2s Processes," J. A m . ('ltc,rn. Soc.. 98. 6427. Michl, J. (1974). "Physical I h s i s of Qualitative MO Arguments in Organic I'hotochemistry," Fortsc.l~r.Clrenr. Forsclr. 46, I. Michl, J., BonaCiC-Kouteckg. V. (19901, Elc~c.trotiicAspc,c~tsof Orgtrnic. Phofochemistry; Wiley: New York. Salem. 1,. (1976). "Theory of Photochemical Reactions." Scic,ricx, 191. 822. Salem. L. (1982). E1c~c.trotr.sin Clrc~~nic.ul Recrc~1ion.s:First Princ.iplc,.s; Wiley: New York.

Figure 6.28. VB structure (dotted lines) and state (full lines) correlation diagram for the dissociation of the C--0 bond in methanol (by permission from Michl and BonaEiC-Kouteckv, 1990).

kony, 1994) investigations of Rydberg-valence interitctions in the processes CH,SH -+ CH, + SH and CH,SH -+ CH,S + H exemplify this situation. Although diagrams such as that of Figure 6.28 are useless for the understanding of molecules such as CH,OH or CH,SH themselves, they are still useful for the derivation of orbital correlation diagrams for bond dissociation reactions of molecules with unsaturated chromophores, using the stepwise procedure described in Section 4.2.2. Thus, Figure 6.28 forms the basis for the understanding of reactions such as the photo-Fries and photo-Claisen rearrangements discussed in Section 7.2.1; it applies to the ring opening reactions of oxiranes, etc. Examples of tetratopic reactions are the C-N bond dissociation in azo compounds, discussed in Section 7.2.2, C-X bond dissociation in alkyl halides, and the 0--0 bond dissociation in peroxides. Examples of pentatopic reactions are the dissociation of the C-X bond in vinyl halides, of the C=C bond in ketenes, and of the C=N bond in diazoalkanes. An example of a hexatopic bond dissociation is the fragmentation of an alkyl azide to a nitrene and Nz.A verification of the topicity rules at a semiempirical level was reported (Evleth and Kassab, 1978). and a detailed description of the electronic structure aspects of bond dissociations characterized by various topicity numbers, with references to the original literature. has appeared recently (Michl and BonatiC-Kouteckjj, 1990).

Turro, N.J.. McVey, J.. Ramamurthy, V., Cherry, W., Farneth, W. (1978), "The Effect of Wavelength on Organic Photoreactions in Solution. Reactions from Upper Excited States," Chc,m. Rc,v. 78. 125. Zimmerman, H.E. (19761, "Mechanistic and Explaratory Organic Photochemistry," Science 191, 523. Zimmerman. H . E . (1982). "Some Theoretical Aspects of Organic Photochemistry," Acc. Chem. Res. 15, 312.

CHAPTER

Organic Photochemistry

Examples of photoreactions may be found among nearly all classes of organic compounds. From a synthetic point of view a classification by chromophore into the photochemistry of carbonyl compounds, enones, alkenes, aromatic compounds, etc., or by reaction type into photochemical oxidations and reductions, eliminations, additions, substitutions, etc., might be useful. However, photoreactions of quite different compounds can be based on a common reaction mechanism, and often the same theoretical model can be used to describe different reactions. Thus, theoretical arguments may imply a rather different classil'ication, based, for instance, on the type of excitedstate minimum responsible for the reaction, on the number and arrangement of centers in the reaction complex, or on the number of active orbitals per center. (Cf. Michl and BonaCik-Kouteckq, 1990.) Since it is not the objective of this chapter to give either a complete review of all organic photoreactions or an exhaustive account of the applicability of the various theoretical models, neither of these classifications is followed strictly. Instead, the interpretation of experimental data by means of theoretical models will be discussed for selected examples from different classes of compounds or reaction types in order to elucidate the influence of molecular structure and reaction variables on the course of a photochemical reaction.

7.1

CIS-TRANS ISOMERIZATION OF DOUBLE BONDS

Cis-trans Isomerization of Double Bonds

Cis-trans photoisomerizations have been studied in great detail and can serve as an instructive example for the use of state correlation diagrams in discussing photochemical reactions. They have been observed for olefins, a7c*r;iethines,and azo compounds.

71. I .1 Mechanisms of cis-trans Isomerization Po4srlde cis-trans isomerization mechanisms of isolated double bonds can using ethylene as an example. A state correlation diagram for is shown in Figure 4.6. (Cf. also Figure 2.2.) This diagram the strongly avoided crossing that gives rise to a biradicaloid minlrnum in the S, surface (Cf. Section 4.3.2). This is surely not a minimum with I.-spect to distortions other than pure twisting (see below). The diagram also ci'splays the biradicaloid minimum in the TI surface, where T I and S, are ~ieitrlydegenerate. rding to the MO model, both the hom*o and the LUMO are singly in the T, state by electrons of parallel spin. The minimum in this state {hen arises from the fact that the destabilizing effect of the n* MO (LUYO) is stronger than the stabilizing effect of the n MO (hom*o) if overlap oflthe AOs is taken into account. For the biradicaloid geometry, however, t)ie overlap vanishes and its destabilizing effect disappears. (Cf. Section 4.3.2.) From the state energies of a hom*osymmetric biradicaloid shown in Figure 4.20, the energy difference between the S, and TI states is expected to be copstant; Figure 4.6 indicates that this is true to a good approximation. Since forla twisting of the double bond the internuclear distance is more or less fixed by the abond. there are in this case no lome geometries that could favor the 'I", state. Similar arguments apply to the S, state. Since twisted ethylene is a hom*osymmettic biradicaloid, this state is described by configurations that correspond tolcharge-separated structures in the VB picture, such as

\0 /

c-c;

,c-c;

0 ,

(cf. Sectio 4.3.1 ). It has been proposed that charge separations of this type, which ma bring about very polar excited states if the symmetry is perturbed (srqdden pollrrizcrtion effect, cf. Section 4.3.3). may also be important in photochemical reactions (Bruckmann and Salenl, 1976). but no experimental evidence supports this so far. At thejlevel of the 3 x 3 CI model, heterosymmetric perturbations 6 that introducd an energy difference between the two localized nonbonding orbitals of the twisted double bond may reduce the s,-s,,gap to zero and provide a very efficient relaxation path. (Cf. Section 4.3.3.) Calculations show that pyramidalization of one of the methylene groups alone does not represent a

Figure 7.1. Geometry of the S,-So conical intersection of ethylene calculated at the CASSCF level, indicating the possibility of cis-trans isomerization and [ I ,2] hydrogen shift; a) side view, b) Newman projection with localized nonbonding orbitals (Freund and Klessinger, 1995).

perturbation S sufficient for reaching a critically heterosymmetric biradicaloid geometry (real conical intersection). However, this is accomplished by an additional distortion of one of the CH bonds toward the other carbon atom (Ohmine, 1985; Michl and BonaCiC-Kouteckq, 1990). The geometry of the resulting conical intersection calculated at the CASSCF level is shown in Figure 7.1. Thus it is most likely that ethylene cis-trans isomerization and 11.21 hydrogen shift occur via the same funnel. (Cf. Section 6.2.1.) Two essentially different cis-trans isomerization mechanisms may be derived from the state correlation diagram of ethylene: I. Through absorption of a photon, the molecule reaches the biradicaloid minimuni in S, via one of the excited singlet states; return from this minimum to the ground state S, at the pericyclic funnel region close to the orthogonal geometry can then lead to either of the planar geometries. Heterosymmetric perturbations that introduce an energy difference between the two localized nonbonding orbitals of the twisted form reduce the So-S, gap, possibly to zero, and provide very efficient relaxation paths. (Cf. Section 4.3.3.) 2. Energy transfer from a triplet sensitizer produces the TI state; return to the ground state So occurs again for a twisted geometry. T, has a minimum near 0 = 90". but spin-orbit coupling is inefficient at this geometry (cf. Section 4.3.4). and the return to S,, most likely occurs at a smaller twist angle. The advantage of sensitization is that it is readily applicable to monoolefins, which require very high energy radiation for singlet excitation. Furthermore, competing reactions of the S, state such as valence isomerizations, hydrogen shifts, and fragmentations are avoided. Given suitable reaction partners, the TI state of the olefin may also be reached via an exciplex and a radical ion pair (see Section 7.6. I), which may undergo ISC and subsequent reverse electron transfer (Roth and Schilling, 1980).

364

ORGANIC PHOTOCHEMISI'UY

Additional mechanisms that have been established may be termed photocatalytic. One of these is the Schenck mechanism, which involves an addition of the sensitizer (Sens) to the double bond and formation of a biradicaloid intermediate that is free to rotate about the double bond and subsequently collapses to the sensitizer and olefin: Sens

7.1

365

CIS-TRANS ISOMERIZATION OF DOUBLE BONDS

In protic solvents, strained truns-cycloalkenes such as methylcyclohexene (3) give an adduct according to the following scheme (Kropp et al., 1973):

hv + senso

Obviously, the reaction can proceed according to this mechanism even if the triplet energy of the sensitizer is below that of the olefin (Schenck and Steinmetz, 1962). Instead of the sensitizer, a photolytically generated halogen atom can also add to the olefin and produce a radical, which may then rotate about the double bond:

7.1.2 Olefins Cis-trans isomerization of simple nonconjugated olefins is difficult to achieve by direct irradiation because such high energy is required for singlet excitation (A < 200 nm). Cis-trans isomerization via the S, state has been observed for 2-butene (1) (Yamazaki and CvetanoviC, 1969); at higher concentrations a photochemical [2 + 21 cycloaddition comes into play. (See Section 7.4.1 .) Cis-trans isomerizations of cycloalkenes clearly demonstrate the influence of ring strain: trans-cycloalkenes are impossible to make with unsaturated small rings; with six- and seven-membered rings the trans products can be detected at low temperatures (cf. Bonneau et al., 1976; Wallraff and Michl, 1986; Squillacote et al., 1989), whereas larger rings give transcycloalkenes that are stable at room temperature. trtrns-Cyclooctene (2) has been obtained on direct as well as on sensitized irradiation (Inoue et al., 1977). Enantioselective cis-trans isomerization with very high optical purities (64%) has been obtained for cyclooctene (2) by triplex-forming sensitizers (Inoue et al., 1993).

From the state correlation diagram of cis-trans isomerization in Figure 4.6, it is seen that the crossing is strongly avoided with a large energy difference A E between S,, and S, for the biradicaloid geometry ( 8 = 90"). The energy gap AE will be reduced at less symmetrical geometries, where the electronegativities of the two termini of the double bond will differ. (Cf. Section 4.3.3.) Still, in simple olefins the result could well be a biradicaloid minimum rather than a funnel, and this suggests the occurrence of an intermediate. In the earlier literature this intermediate is referred to as phantom stcrte 'P* (Saltiel et al., 1973). Therefore the fraction P of molecule$ in the biradicaloid minimum that reach the ground state of the truns-olefin is independent of the initial isomer. At a given wavelength A the cis and the trans isomers c and t are formed in a constant ratio, and after a certain peiiod of time a photo.sttrlioncrr~~ sttrte (PSS) is reached. The composition of tue photostationary state is given by

where &(A)is the extinction coefficient at wavelength A and Q, is the iuantum yield of the photochernical conversion. (See Example 7.1 .) If thdre are no competing reactions one has 4,,, = /? and ,-

00 75k[r\

SY isomers

q; 0.2.kSy lo7 S-' 56 kcallrnd

0.06

Scheme 5

tion as exemplified in Scheme 6, whereas disproportionation would require a change in conformation and is therefore in general not observed (Cohen and Zand, 1962).

Figure 7.19. Jablonski diagram and photochemical parameters of 7,8-diazatetracycl0[3.3.0.0~4.0'.~]oct-7-ene(by permission from Turro, 1978).

Sl+Tl intersystem crossing and therefore enhances the formation of diazacyclooctatetraene on direct irradiation. (Mlproport.1

Scheme 6

Example 7.5: Compound 19, which yields the valence isomers of benzene on direct irradiation, and diazacyclooctatraene (20) as the major product upon triplet sensitization, is an interesting example of the different reactivity of the S, and TI states of azo compounds (Turro et al.. 1977a):

The photochemical parameters for 19 are summarized in Figure 7.19. From these data it is apparent that at low temperatures diazacyclooctatetraene becomes the exclusive product, since the loss of N,from the '(n,lr*)state requires an activation energy of 5-6 kcal/mol. Oxygen has a catalytic effect on the

The photoextrusion of N, from cyclic azo compounds is a very useful way of producing strained ring systems such as 21 (Snyder and Dougherty, 1985) or 22 (Liittke and Schabacker, 1966). Unstable species such as the o-quinodimethanes 23 (Flynn and Michl, 1974) and 24 (Gisin and Wirz, 1976), and biradicals such as 25 (Gisin and Wirz, 1976), 26 (Watson et al., 1976), 27 (Platz and Berson, 1977), 28 (Dowd, 1966), and 29 (Roth and Erker, 1973), can also be generated in a matrix by this route and spectroscopically identified.

392

ORGANIC PHOTOCHEMISTRY

7.2

PHOTODISSOCIAI'IONS

Some azo' compounds undergo the usual photolysis (A > 300 nm) only to a minor degree or not at all and are therefore dubbed "reluctant azoalkanes." These are cyclic azo compounds such as 30,31, and 32.

Photolysis of such compounds can be accelerated by employing elevated temperatures or by introducing substituents that stabilize the radicals formed. (Cf. Engel et al., 1985.) Short-wavelength irradiation (A = 185 nm) also enhances photodissociation. Bridgehead azoalkanes such as 33 are also reluctant compounds and undergo photochemical trans-cis isomerization (Chae et al., 1981). Loss of nitrogen and formation of bridgehead radicals are observed upon excitation to the second singlet state (S,) of the trans or the cis isomer, with quantum yields of cD, = 0.3 and @, = 0.16, respectively (Adam et al., 1983).

tion reactions, but not as dissociation reactions, since more than one single or double bond is broken in these processes. They are closely related to the pericyclic processes discussed in Sections 7.4 and 7.5 and are formally isoelectronic with other excited-state-allowed four-electron pericyclic reactions, such as cheletropic elimination of CO from cyclopropanone and disrotatory electrocyclic ring closure in butadiene. The analogy of the chainabridgement reaction to the latter is illustrated in Figure 7.20, which shows the orbitals involved in the two reactions.

7.2.3 Photofragmentation of Oligosilanes and Polysilanes Alkylated and arylated oligosilanes and polysilanes, the silicon analogues of alkanes and of polyethylene, have recently attracted considerable attention (Miller and Michl, 1989). Unlike saturated hydrocarbons, these materials absorb in the near UV region. The reasons for this are related to the electropositive nature of silicon and can be understood in simple terms (Michl, 1990). Their excited states bear considerable similarities to those of polyenes, but also exhibit significant differences (Balaji and Michl, 1991). Upon irradiation, oligosilanes (Ishikawa and Kumada, 1986) and particularly polysilanes (Trefonas et al., 1985), readily fragment to lower-molecular-weight species, and polysilanes show promise as photoresists. Three distinct photochemical processes have been identified as shown in Scheme 7: (1) chain abridgement by silylene extrusion, (2) chain cleavage by silylene elimination, and (3) chain cleavage by hom*olytic scission (Miller and Michl, 1989). The two silylene-generating processes are believed to occur in the singlet excited state in pericyclic fashion, while the radical-pair-forming hom*olytic cleavage process is believed to occur in the triplet state (Michl and Balaji, 1991), as would be expected from Figure 4.5. According to the definition given in the beginning of this section, the singlet I , l-elimination (reductive elimination) processes qualify as fragmenta-

Figure 7.20. Comparison of the A 0 interactions in the photochemical chain abridgement in a polysilane (top) and in the disrotatory electrocyclic ring closure of butadiene (bottom) (by permission from Michl and Balaji, 1991).

394

()I(n,n*)state proceed over a barrier. The triplet reaction then reaches the 'B,,, state of the biradical, which is just

ORGANIC PHOTOCHEMISTRY

7.3

HYDROGEN ABSTRACTION REACTIONS

401

tones with a chiral y-C atom such as 41, which competes with the hydrogen abstraction (Yang and Elliott 1969):

The reaction is not concerted and does not yield a triplet olefin, even when this process would be exothermic, as in the case of 42. Triplet stilbene decays to a 60:40 mixture of cis- and trans-stilbene, but in the reaction of 42,98.6% trans-stilbene was observed (Wagner and Kelso, 1969).

Schematic representation of energies of stationary points for the Norrish type 11 reaction of butanal. The diagram corresponds to a projection of multidimensional potential energy surfaces into a plane. The two energies given for the biradical on the Sosurface correspond to a geometry optimized for So(front bottom) and optimized for S, (middle rear), respectively. A broken line (---) is used for the TI surface and a broken-dotted line (-.-.-)for the S, surface. The relative energies of T,, Soand S, for the geometry of the funnel are not known (by permission from Dewar and Doubleday, 1978). Figure 7.24.

barely above the ground state. In the correlation diagram, this is apparently the point that corresponds to the crossing of the levels connected to the ground state and to the I(n,n*) state of the ketone. From this funnel the system can return to the initial geometry or proceed either to the singlet biradical or to the products (cyclobutanol or enol + olefin). The reaction path toward the elimination products passes through a geometry that is effectively the same as that of the transition state for cleavage of the singlet biradical and is stereospecific; that is, the stereochemistry of the initial ketone is preserved in the products. The calculated activation energies of 9 and 12 kcal/mol for the singlet and the triplet reaction, respectively, and of 10 kcallmol for cleavage of the singlet biradical are presumably too high by 3-5 kcallmol, but the relative values appear to be correct. Evidence that the triplet reaction is not concerted, but rather proceeds via the 1,Cbiradical, has been obtained from the photoracemization of ke-

Intersystem crossing to the So surface is believed to occur at the 1,4-biradical stage, and to yield one of the three possible types of singlet product (reactant, olefin, cycloalkanol) depending on the geometry at which it occurs, as discussed in Section 4.3.4. The singlet reaction also proceeds at least partially via a biradical, as was shown indirectly. If the reaction of 43 were concerted, the transfer of H should yield the deuterated cis isomer and the transfer of D the nondeuterated trans isomer:

With piperylene as the triplet quencher, 10% deuterated trans olefin is found, which must result from rotation about the /3,y bond of the singlet biradical (Casey and Boggs, 1972). If a molecule has two y hydrogens available, in the Norrish type I1 reaction the transfer proceeds over the lower of the two barriers, and according to Scheme 10 a preference for cleavage of the weaker secondary CH bond results (Coxon and Halton, 1974).

OK(;ANIC PHOTOCHEMISTRY (Hatransf.) CHI-CH=CH-CHI

+ CH3-CH=O (Major route)

c~,cH:,

(libtransf.)

(mrwr r v l

An increase in temperature or in photon energy reduces the selectivity. For alkyl aryl ketones electron-releasing substituents in the p position decrease the rate constant and quantum yields for type I1 cleavage. p-OH, p-NH,, and p-phenyl substituents inhibit the reaction completely. Similarly as in the: case of intermolecular hydrogen abstraction, this effect is thought to be a consequence of the 3(n,llc) state no longer being the lowest triplet state, resulting in a larger barrier. The rario of olefin to cyclobutanol product yield often depends on substitution. In order to understand this in detail, more would need to be known about the conformational dependence of the spin-orbit coupling matrix element. The present qualitative understanding (Section 4.3.4, Figure 4.26) of the critical intersystem crossing step suggests that it occurs at geometries at which the 2p orbitals of the two radical ends interact through a nonzero resonance integral while their axes lie approximately orthogonal to each other, such that after a 90-degree rotation of one of the orbitals about its center there still is a nonzero resonance integral with the other. According to this analysis a gauche conformation, in which the orbitals interact primarily through space (Figure 7.25a), and an anti conformation, in which they interact primarily through bonds (Figure 7.25b), can both be favorable, provided that the end groups are twisted properly. After intersystem crossing, the former is expected to yield the cyclobutanol, and the latter the fragmentation products, essentially instantaneously. The relative energies of the two types of conformation should be sensitive to the steric demands of substituents.

Stereoelectronic effects on the Norrish type 11 reaction. Presumed o p timal orbital alignments a) for cyclization and b) for elimination. Figure 7.25.

7.3

403

HYDROGEN ABSTRACTION REACTIONS

The cyclobutanol-forming path is diastereoselective, for example, a-methylbutyrophenone (44) and valerophenone (45) prefer to place the methyl and the phenyl groups on opposite sides of the four-membered ring (Scheme 11). Such steric discrimination on the T surface may already be present in the open-chain triplet biradical or become felt gradually as the radical ends approach each other and develop the covalent perturbation that leads to intersystem crossing (see Section 4.3.4), and both cases are known and exemplified by the two reactions in Scheme 1I. The high stereoselectivity of 44 is believed to be due to a repulsive interaction of the phenyl and the a-methyl groups in the 1,4-biradical (Figure 7.25a). The interaction between the phenyl and the y-methyl group in the biradical from 45 should be small until after the intersystem crossing has taken place and the 1,4-bond is almost completely formed (Lewis and Hilliard, 1972).

Scheme 11

Abstraction of a 6 hydrogen normally competes only when a y hydrogen is not available, and produces a 1,5-biradical. There are only two choices: return to the starting materials, or cyclization to a cyclopentanol. For instance, a-(0-ethylpheny1)acetophenone (46) yields 1-methyl-2-phenyl-2-indanol (47):

Diastereoselection is again observed and can be understood in terms of the relative energies of the two conformations that are ideally set up for intersystem crossing by spin-orbit coupling (Section 4.3.4). As is seen in Scheme 12, in the favored conformation, a hydroxyl, and in the disfavored conformation, a phenyl, have to be accommodated close to a benzene ring (Wagner et al., 1991).

ORGANIC PHOTOCHEMISTRY

7.4 Cycloadditions 7.4.1 Photodimerization of Olefins According to the Woodward-Hoffmann rules, the concerted cycloaddition + 2J of two olefins to afford a cyclobutane is allowed photochemically as reaction and thermally as the + J,] reaction. The different modes of addition give rise to products with different stereochemical structures as indicated in Figure 7.26. If the reaction does not follow a concerted pathway

Fipre 7.26. Stereochemical consequences of thermal and photochemical [2 cycloaddition.

but rather proceeds by a multistep process, and if ring closure of the intermediate is not very rapid compared with bond rotation, rotations about the CC bonds may occur, with subsequent loss of stereospecificity. Recent calculations for the [2 + 21 photoaddition of two ethylene molecules (Bernardi et al., 1990a,b) demonstrated that the bottom of the pericyclic funnel on the S, surface does not lie at the often assumed highly symmetrical rectangular geometry; instead, it is distorted to permit stabilization by diagonal interaction (cf. Section 6.2. l), as suggested by model calculations on H,(Gerhartz et al., 1977). Moreover, the calculations show that the S , S otouching is not even weakly avoided but actually is a conical intersection. These features, a rhomboidal distortion and a conical intersection, are likely to be general for photocycloadditions. Photodimerization often involves an excimer that can be treated as a supermolecule. (Cf. Section 6.2.3.) Then, the state correlation diagram for the singlet process (Figure 7.27a) ordinarily calls for a two-step return from S, to So along the concerted reaction path. First, an excimer intermediate E* is formed. Second, a thermally activated step takes the system to the diagonally distorted pericyclic funnel P* (cf. Section 4.4. l), and the return to So that follows is essentially immediate. The reaction will be stereospecific and concerted in the sense that the new bonds form in concert. However, it will not be concerted in the other sense of the word, in that it involves an intermediate E*. There may well be systems in which the excimer minimum occurs in the S, rather than the S, surface (Figure 7.27b). The approach to the pericyclic funnel P* on S, may then be barrierless, and an excimer intermediate will

Fipre 7.27. Schematic representation of the state correlation diagram for a groundstate-forbidden pericyclic reaction with an excimer minimum E* a) at geometries well before the pericyclic funnel P* is reached, and b) at geometries similar to those of P*.

not be detectable. (For a possible example of the latter case, see Peters et al., 1993.) These concepts are in very good agreement with experimental findings. There are relatively few examples of photodimerization of simple nonconjugated acyclic olefins because these compounds absorb at very short wavelengths. Irradiation of neat but-Zene, however, yields tetramethylcyclobutane with a quantum yield Q, = 0.04. For very low conversion, the observed stereochemistry of the adducts is the stereospecific one expected from Scheme 13 for a concerted [J, + J,] cycloaddition. However, since the major pathway is cis-trans isomerization with a quantum yield @ = 0.5 (cf. Section 7.1.2), it has been concluded that the molecules that undergo cistrans isomerization are not involved in photodimerization (Yamazaki et al., 1976).

Small-ring cyclic alkenes cannot deactivate by cis-trans isomerization. For instance, in contrast to acyclic alkenes, cyclopentene (48) therefore undergoes photosensitized [2 + 21 cycloaddition. For cycloalkenes with a six-membered or larger ring, a trans form becomes possible; for molecules such as cyclooctene (2), photosensitized cis-trans isomerization is the more efficient reaction path. (Cf. Section 7.1.2.)

Since most simple alkenes have a high triplet energy (ET = 75-78 kcall mol), triplet sensitizers have to be chosen accordingly to prevent oxetane formation (see Section 7.4.4), as shown in Scheme 14 for norbornene with acetophenone (ET = 75 kcallmol) and benzophenone (ET = 69 kcal/mol), respectively, as sensitizers (Arnold et al., 1965):

Scheme 13

In simple olefins, direct excitation of the triplet state and intersystem crossing from an excited singlet state to a triplet state do not play an important role. A sensitized reaction of the triplet state is possible and could in principle also be concerted. However, in the triplet state loose geometries with two separate radical centers are energetically more favorable than tight pericyclic geometries with cyclic interaction (cf. Section 6.2.1); it is most probable that one of these favorable minima will be reached prior to return to So. This tendency then favors a nonconcerted mechanism with the two new bonds formed in separate reaction steps. Formation of the first bond takes place on the TI surface, while the second one will close after the molecule has reached the So surface. The nature and stereochemistry of the product that results from the triplet species upon return to the Sosurface, in particular cyclobutane formation or back reaction to two olefins, is believed to be dictated by the geometry at which the conversion to Sotook place. The relative efficiencies are determined by the rates of the various processes, which in turn depend on such factors as the populations of the various conformers in TI and the size of the T , S o spin-orbit coupling matrix element, the geometrical dependence of which was discussed in detail in Section 4.3.4.

Scheme 14

phAph

Finally, it should be remembered that excimer minima E* and pericyclic funnels P* of different energies can result if different mutual arrangements of the reactants can lead to cycloaddition, as indicated in Scheme 3 in Section 6.2.3. The related issues of regio- and stereoselectivity of singlet photocycloaddition are dealt with in Section 7.4.2. Example 7.8: Sensitized irradiation of cyclohexenes and cycloheptenes in protic media results in protonation. This phenomenon, which is not shared by other acyclic or cyclic olefins, has been attributed to ground-state protonation of a highly strained trans-cycloalkene intermediate. In aprotic media, either direct or triplet-sensitized irradiation of cyclohexene produces a stereoisomeric mixture of [2 + 21 dimers 49-51 as the primary products, with 50 predominating. The reaction apparently involves an initial cis-trans photoisomerization of cyclohexene followed by a nonstereospecific nonconcerted ground-state cycloaddition, promoted by the high degree of strain involved. In contrast, cycloheptene undergoes only a slow addition to the p-xylene used as sensitizer,

408

ORGANIC PHOTOCHEMISTRY

presumably because the trans isomer is not sufficiently strained to undergo the nonconcerted cycloaddition. Copper(1)-catalyzed photodimerization of cyclohexene and cycloheptene affordsthe product expected for [2, + 2,] cycloaddition of the trans isomer to the cis isomer within a cis,trans complex 52. Stereospecificity is high in the former case and complete in the latter. (Kropp et al., 1980.)

Irradiation of butadiene in isooctane yields the isomeric 1,2-divinylcyclobutanes 53a and 53b and various other products, dependent on reaction conditions. The triplet-sensitized photoreaction yields 4-vinylcyclohexene (54) in addition to the divinylcyclobutanes fcf. Example 6.1 I), and the product ratio depends on the triplet energy of the sensitizer:

agonal bonds, to yield the x[2 + 21 product in one case; in the other case, there is preservation of perimeter bonding and eventual production of the [2 + 21 product. (Cf. Figure 6.1.5). Which product will be formed depends on the number of methylene groups between the double bonds. If either one or three CH, groups are present, the common [2 + 21 cycloaddition is observed; with two CH, groups x[2 + 21 cycloaddition predominates. For cyclic dienes the dependence of the reaction product on the number of CH, groups is even more pronounced; 1,5-cyclooctadiene (56) yields the product 57 exclusively (Srinivasan, 1963).

These findings have been rationalized by the rule offive (Srinivasan and Carlough, 1967), according to which five-membered cyclic biradicals are preferentially formed, as shown in Scheme 15. (Cf. also the Baldwin rules for radical cyclizations, Baldwin, 1976.)

Scheme 15

When ET is in excess of 60 kcal/mol, s-trans-butadiene (ET = 60 kcall @),which strongly predominates in the thermal equilibrium, is excited and produces mainly divinylcyclobutanes. When the E, of the sensitizer is not high enough to excite s-trans-butadiene, energy transfer to s-cis-butadiene (E, = 54 kcallmol) occurs instead, yielding vinylcyclohexene. If ET < 50 kcavmol, nonvertical energy transfer to a twisted diene triplet is believed to occur (Liu et al., 1x5). Intramolecular photoadditions can also occur as so-called x[2 + 21 cycloadditions, as demonstrated for 1,5-hexadiene (55): the terminal carbon atom of each double bond adds to the internal carbon atom of the other double bond in such a way the resulting a bonds cross each other.

It is likely that [2 + 21 and x[2 + 21 cycloadditions proceed through the same type of diagonally distorted pericyclic funnel (Section 4.4.1) with a preservation of the diagonal interaction, and eventual production of two di-

Gleiter and Sander (1985) proposed that the reaction is not concerted and that the different reaction course is due to differences in through-bond interactions. (Cf. Gleiter and Schafer, 1990.) Depending on the number of methylene groups between the double bonds, these through-bond interactions may change the orbital ordering. If such an interaction reverses, the "natural" ordering of n orbitals imposed by through-space interaction, the excited-state barrier for the x[2 + 21 cycloaddition will be lower than that for the [2 + 21 cycloaddition. Evidence for the deleterious effect of the reversal of orbital order on the [2 + 21 process is provided by cases in which the x[2 + 21 reaction is sterically impossible and the [2 + 21 reaction fails to proceed (Example 7.9). However, it is also possible that the reaction is concerted in its initial stages, and that the difference in the relaxation paths after return to So through a distorted pericyclic funnel is dictated by the steric requirements imposed by the alkane chains. Example 7.9: Tricyclo[4.2.0.0~~510ctadiene (58) does not undergo (2 cubanr,

although its ec~ornetr\rappc>:rr.; to he

+ 21 photocyclization to

ideally Yet tip for it. In thi.; mol-

sensitized mixed cycloadditions are summarized in Scheme 16 (Scharf, 1974). D l .

Scheme 16

The addition of trans-stilbene to 2,3-dimethylbutene-2 appears to be a singlet reaction: Figure 7.28. Correlation of the n orbitals of two cyclobutene molecules (left) with those of 58 (center) and 59 (right) (by permission from Gleiter, 1992).

ecule, the interaction of the normally more stable in-phase combination of the two n orbitals, a+ = (n,+ n,)lfl, with the two doubly allylic a bond orbitals is very strong and pushes its energy above that of the out-of-phase combination, n - = (n, - n,)lfl, inverting the natural orbital order (Figure 7.28). This converts the normal orbital crossing characteristic of ordinary [2 + 21 cycloadditions into an abnormal orbital crossing, so that the characteristic configuration no longer is the lowest in energy, and a barrier in the potential energy surface results for this reaction path. (See Section 6.2.4.)

Furthermore, [2 + 21 cycloadditions to N=N and C=N double bonds have been described (Prinzbach et al., 1982; Albert et al., 1984). The regioselectivity of the addition of electron-rich olefins to cyclic ketoiminoethers such as 60 may be rationalized using perturbation theory (Fabian, 1985):

7.4.2 Regiochemistry of Cycloaddition Reactions

In the quadruply bridged derivative 59, the [2 + 21 photocycloaddition proceeds. This can be understood as due to the restoration of the natural order of the orbital energies, n+ below n-,by the effect of the propano bridges (Figure 7.28). These can be expected to bring the two double bonds closer in space, increasing the through-space interaction, and to introduce additional throughbond interaction opposed in sign to the interaction through the doubly allylic bonds (Gleiter and Karcher, 1988).

Mixed cycloadditions between different olefins are also observed. The regiochemistry follows a pattern that has been rationalized by consideration of the HMO coefficients (Herndon, 1974). Some typical examples of triplet-

An important aspect of photocycloaddition consists of its regio- and stereoselectivity. Thus, dimerization of substituted olefins generally yields head-to-head adducts 61a and 61b in a regiospecific reaction, while head-totail dimen 63 are obtained from 9-substituted anthracenes (62) in polar solutions (Applequist et al., 1959; cf. Kaupp and Teufel, 1980).

412

ORGANIC PHOTOCHEMISTKY

The portion of the head-to-head product increases in nonpolar solvents and in micelles (Wolff et at., 1983). The regioselectivity of 9-methylanthracene is temperature dependent, and a photochemical equilibrium exists between the two isomers (Wolff, 1985). Singlet acenaphthylene (64) stereospecifically gives the syn dimer 65a, while in the TI reaction the anti dimer 65b predominates. The syn-anti ratio can be influenced by solvents with heavy-atom effect (Cowan and Drisco, 1970b), as well as by micellar solvents (Ramesh and Ramamurthy, 1984). Secondary orbital interactions (broken arrows) in the photochemical dimerization of acenaphthylene. The primary orbital interactions are indicated by full double arrows. Figure 7.29.

Triplet quenchers such as 0, or ferrocene inhibit formation of the anti dimer, while the formation of the syn dimer is hardly affected. The syn-anti ratio in the triplet reaction was determined by comparing the outcome of the reaction with and without use of a quencher (Cowan and Drisco, 1970a). Many factors must be considered to explain these facts, not least the relative stabilities of the various possible excimers or exciplexes and the accessibility of the pericyclic funnels. (Cf. Scheme 3 in Section 6.2.3.) In addition, the geometrical structure at the funnel and the ground-state relaxation pathways originating in the decay region determine which products will be formed. Excimer and exciplex formation will mainly influence the excited-state reaction path. Simple perturbation theory suggests that in concerted singlet photocycloadditions, electronic factors always favor the most highly symmetric excimer affording head-to-head regiochemistry and syn or cis stereochemistry, since hom*o-hom*o and LUMO-LUMO interactions are decisive in excimer formation according to Section 5.4.2. (Cf. Figure 5.21.) Interaction between centers whose LCAO coefficients are either both large or both small, that is, the head-to-head addition, is then favored:

head-to-head addition

head-to-tail addition

Similarly, secondary orbital interactions favor the syn arrangement of two acenaphthylene molecules, as illustrated in Figure 7.29.

The formation of head-to-tail dimers such as those of 9-substituted anthracenes and similar species can be rationalized by the conjecture that in this case it is not the most favorable excimer that determines the stereochemical outcome of the reaction but rather, the most readily reached pericyclic funnel. This can be understood if the effect of substituents on the pericyclic funnel is first considered at the simple two-electron-two-orbital model level (3 x 3 CI, Section 4.3.1). The discussion of cyclodimerization of an olefin is restricted to the four orbitals directly involved in the reaction. To simplify the presentation, we shall initially ignore the possible effects of a diagonal distortion. Then, the localized nonbonding orbitals at the rectangular pericyclic geometry have equal energies. They correspond to the degenerate n MOs $9 and $, of cyclobutadiene.

Since they are occupied with a total of two electrons, the system is a perfect biradical (6 = 0) and the energy splitting A E between Soand S, is relatively large. (Cf. Figure 4.19.) Substitution in positions 1,3 or 2,4 removes the degeneracy (Section 6.2.1). and the biradical is converted into a heterosymmetric biradicaloid (6 # 0). According to the results in Section 4.3.3, this brings the S, and So states closer and is likely to reduce the energy of the S, state. For instance, ab initio calculations on perturbed cyclobutadienes indicate that the splitting vanishes almost completely when two CH groups on diagonally opposite corners of the cyclobutadiene (positions 1 and 3) are replaced by isoelectronic NH@groups, yielding a critically heterosymmetric biradicaloid (BonaOiC-Kouteckyet at., 1989). As a result of the rectangular geometry, the pericyclic "minimum" at the head-to-tail dimerization path, which corresponds to a 1,3-disubstituted heterosymmetric biradicnloid, is likely to be deeper than that at the head-

to-head reaction path. This in turn should reduce the barriers around the minimum and thus make it easier to reach the head-to-tail rectangular "minimum" from the excimer. These arguments would suggest that head-to-tail regiochemistry is favored when access to the pericyclic "minimum" determines the product formation, while the head-to-head product is expected if the energy of the excimer intermediate is decisive for the reaction path (BonaCiC-Koutecky et al., 1987). Next, we consider also the effects of rhomboidal distortions, which permit a diagonal interaction. These may either reinforce or counteract the effect of the substituents, depending on which of the two diagonals has been shortened. For a head-to-tail approach of two substituted ethylenes, there will be two funnels corresponding to 1,3-disubstituted critically heterosymmetric biradicaloids, one at less and one at more diagonally distorted geometry than for the unsubstituted ethylene. This is confirmed by the results of calculations shown in Figure 7.30. In agreement with expectations from the two-electron-two-orbital model (lower part of Figure 7.30), the effect of donor substituents reinforces the orbital splitting produced by a 1.3-diagonal interaction, which brings the

a=24.5 ' E,I = 0.0

a=-15.S0

a =11.7'

Ere,= 22.0

Ercl = 15.2

a=-221' Ere, = 0.0 kcallmol

2.4 interaction

1.3 interaction

2.4 interact~on

1.3 interaction

Figure 7.30. Geometries of the conical intersections for the syn head-to-tail [2 + 21 cycloaddition of two aminoethylene molecules (left) ant1 of two acrylonitrile molecules (right), and a schematic representation of the energies of the cyclobutadienelike "nonbonding" biradicaloid orbitals. The effect of the donor (D) and acceptor (A) substituents on orbital energies is incorporated in the levels shown in the center of each half of the diagram. The effect of the diagonal interaction required to reach the critical value of the orbital energy difference (6,. cf. Section 4.3.3) is indicated by broken arrows.

substituted atoms closer to each other, while the effect of acceptor substituents opposes that of the 1,3 interaction. The opposite is true for the 2,4 interaction, which places the substituted atoms apart. As a result, a small rhomboidal distortion is sufficient to reach the "critically biradicaloid" geometry at which S, and Soare degenerate when the l ,3 diagonal is short for donor substituents and when the 2,4 diagonal is short for acceptor substituents. A large distortion is needed for donor substituents if the short diagonal is 2,4 and for acceptor substituents if it is 1,3. Numerical calculations yield a lower energy for the conical intersection when the substituent effect is opposed to that of the rhomboidal distortion, that is, at the more strongly distorted geometries (Klessinger and Hoinka, 1995). For small rhomboidal distortions, the peripheral bonding will dominate at the funnel geometry after return to So, and the formation of the head-to-tail product is likely to be favored. The diagonal bonding will dominate for large distortions, however, and head-to-head product could possibly be formed by x[2 + 21 cycloaddition-that is, by formation of one diagonal bond and subsequent closure of the other. Thus, the result of the photoaddition will depend on the distorted rhomboidal geometries, that is, on the relative heights of the barriers that lead to the various funnels, typically via an excimer or exciplex minimum. That is where steric effects as well as abnormal orbital crossing effects (cf. Example 7.9) may come into play. Finally, as we pointed out in Example 6.2, a number of different groundstate trajectories leading to one or the other of the possible photoproducts may emanate from the apex of the cone. This is illustrated schematically in Figure 7.31, which shows energy contour maps for the S, and So states of the syn head-to-tail approach of two acrylonitriles. Three valleys starting at the conical intersection are seen on the ground-state surface (Figure 7.31b), one leading to the cyclobutane minimum (B), the other one to the diagonally bonded product (D), and a broad slope back to the reactants (R). The steric outcome of the reaction will depend on the way in which the system enters the funnel region (Figure 7.3la) and on the dynamics of the passage through the cone. A model for estimating the barrier height between the excimer minimum and the pericyclic minimum for a given geometrical arrangement of the adducts, which ignores the effects just mentioned, was introduced in Section 6.2.3. The resonance integral fir,) for the bonds formed in the cycloaddition reaction may be estimated according to Equation (6.3) from the singlet and triplet excitation energies and the HMO coefficients of the hom*o and LUMO. A small absolute value will correspond to early surface crossings (cf. Figure 6.17) and thus to low barriers, and high reactivity. Table 7.2 summarizes some results obtained from this model. I t is seen that aromatic compounds and olefins undergo facile dimerizations when 1 P(rc)I < 20 kcaltmol, while for 1 f i r ) 1 = 20-24 kcaltmol the reactivity is moderate, and for 1 firc) 1 2 24 kcaltmol dimerizations have so far not been reported.

Table 7.2

Dimerization of Olefins and Aromatic Compounds: Singlet and Triplet Excitation Energies Es and E,, and Interaction Integral I Kr,) I (kcaVmol) ET

ICs

Anthracene Stilbene 1.3-Cyclohexadiene Simple alkenes Acenaphthylene Naphthalene Pyrene Phenanthrene

75.6 85.3 91.3

42.6 49 53

121 61.1 90.9

78 43--47 60.9

77.0 82.4

48.3 61.7

Caba

+ +

1.55* 1.55 2.88* 1.98 4.04 1.45 1.41* 0.98 0.72 1.41

I++

C a b = C (awob, en

+ aw,b,,)

for [2

+ 21 or (4

other reactions

Exp.

+ 41 cycloadditions; asterisks indicate result~for

the latter (adapted from Caldwell, 1980).

In discussing the state correlation diagram of the H, H,reaction, which can serve as a model for ethylene dimerization, it has been pointed out that the doubly excited state corresponds in the limit to an overall singlet coupling of two initial molecules 'M*in their triplet-excited states. As a consequence, the pericyclic minimum should be accessible not only from the excimer minimum but also directly through triplet-triplet annihilation. This was demonstrated for anthracene dimerization by determining the quantum yield as a function of the light intensity. The probability of excimer formation by triplet-triplet annihilation was determined experimentally as p l = 0.115, which is in good agreement with the spin statistical factor 119 and is accounted for by noting that apart from the singlet complex, triplet and quintet complexes are also formed upon triplet-triplet encounter. (Cf. Section 5.4.5.5.) Only the singlet species can yield the pericyclic intermediate, whereas the other complexes decay into monomers in the ground state or in a singlet- or triplet-excited state (Saltiel et al., 1981). It is likely that triplet-triplet annihilation also plays a role in other photochemical reactions. This is especially true at high concentrations and high intensities of the exciting light. The sensitized photodimerization of anthracene presumably proceeds entirely through triplet-triplet annihilation.

7.4.3 Cycloaddition Reaction of Aromatic Compounds Energy contour maps for the face-to-face [2 + 21 cycloaddition of two acrylonitrile molecules in the syn head-to-tail arrangement, showing (a) the lowest excited state S, and (b) the ground state So. Possible reaction paths via the low-energy conical intersection are indicated by arrows. Figure 7.31.

416

Photodimerizations are observed not only for olefins, but also for aromatic compounds, allenes, and acetylenes. The photodimerization of anthracene,

which may be considered to be a ground-state-forbidden [,4, + ,4,1 cycloaddition, was in fact described as early as in 1867 (Fritsche, 1867). Example 7.10: Much information about the detailed mechanism of anthracene dimerization was gained in the study of intramolecular photoreactions of linked anthracenes such as a,w-bis(9-anthryl)alkanes (66). I t was shown that luminescence and cycloaddition are competing pathways for the deactivation of excimers. In compounds with sterically demanding substituents R and R' that impair the cycloaddition reaction, the radiative deactivation is enhanced (H.-D. Becker, 1982).

The [2 + 21 cyclodimerization of benzene has been studied theoretically (Engelke et al., 1984) and used practically in the synthesis of polycyclic hydrocarbons such as 69 (Fessner et al., 1983). This represents a first step in the synthesis of the undecacyclic hydrocarbon pagodane (70), which in turn can be isomerized to give dodecahedrane (Fessner et al., 1987).

Mixed photocycloadditions of anthracene and conjugated polyenes yield products that correspond to a concerted reaction path, as well as others that are Woodward-Hoffmann-forbidden and presumably result from nonconcerted reactions. For example, the reaction of singlet-excited anthracene with 1,3-cyclohexadiene yields small quantities of the [,4, + ,2,] product 72 ,4,] product 71. in addition to the allowed [,4, Photocyclization of bis(9-anthryl)methane (67) and the corresponding photocycloreversion were shown by picosecond laser spectroscopy to have a common intermediate whose electronic structure is different in polar or nonpolar solvents as judged by different absorption spectra in various solvents (Manring et al.. 1985). a,af-Disubstituted bis-9-anthrylmethyl ethers (68) are characterized in their meso form by mirror-plane symmetry (a)and perfectly overlapping anthracene moieties (68a). The corresponding racemic diastereomers (68b) assume a conformation having a twofold axis of symmetry (CJ. Both the meso and racemic diastereomers cyclomerize. However, whereas the meso compounds are virtuall y nonfluorescent, the racemic diastereomers deactivate radiatively both from the locally excited state and from the excimer state. Thus, in the emitting excimer state of linked anthracenes the aromatic moieties overlap only partially. Apparently, the formation of luminescent excimers from bichromophoric aromatic compounds is associated with perfectly overlapping n systems only when intramolecular cycloaddition is an inefficient process (H.-D. Becker, 1982).

The yield of 71 increases with increasing polarity of either the solvent or the substituent X in the 9-position of anthracene. This result has been explained by invoking a stabilization of the exciplex, which should reduce the barrier between the exciplex minimum and the pericyclic minimum. The observation that in the presence of methyl iodide 72 becomes the major product for X = H, due to the heavy-atom effect, is compatible with the obvious assumption that the multistep process is a triplet reaction. However, if X = CN, no methyl iodide heavy-atom effect is observed (N. C. Yang et al., 1979, 1981).

420

ORGANIC PHOTOCHEMIS'I'KY

Addition of an alkene to benzene can occur in three distinct ways indicated in Scheme 17: ortho, meta, or para.

In general, dienophiles produce the ortho product in addition to small amounts of the para product. Maleic anhydride gives the 1:2 adduct 73 (Gilbert, 1980). Maleimides undergo analogous reactions. Both classes of compounds form CT complexes with benzene and its derivatives, and the reaction can be initiated by irradiation into the CT band (Bryce-Smith, 1973). Alkylethylenes, on the other hand, produce the meta adducts.

Figure 7.32. Orbital energy diagram for the photocycloaddition of excited benzene to an olefin a) with an electron-donating substituent X and b) with an electron-withdrawing substituent Z (adapted from Houk, 1982).

The selectivity may be explained by a consideration of the possible interactions of the degenerate benzene hom*o, &, and LUMO, $,., &,. (cf. Section 2.2.5 and Figure 2.33), with the ethylene n and n* MOs (Houk, 1982). In the ortho approach, the benzene MOs @a and &,. can interact with the ethylene MOs n and n*, while in the meta approach, and @a. can interact with nand d.Therefore, the configuration. , @ , is predicted to be energetically favored along the ortho cycloaddition path, while the configuration. , @ , is stabilized for the ortho and particularly the meta cycloaddition path. The magnitude of the stabilization depends on orbital overlap and relative orbital energies. The former factor favors the ortho approach and the latter the meta approach of the reactants. Altogether, one arrives at the prediction that for the addition of ethylene to the S, ('B,,) state of benzene, whose wave function can be written as (a,,. - @,,,.)/fl, comparable amounts of ortho and meta adducts should be formed, while the meta addition should dominate whenever' the alkene MOs n and n* are close in energy to the benzene MOs &, and @,., &..

+,,

The presence of substituents alters the situation in that charge transfer between the reaction partners may become significant, and ortho addition should then be preferred over meta addition. For electron-rich alkenes or electron-poor arenes, the ethylene IT MO lies at much higher energy than the singly occupied bonding MO of the excited arene ($a for the ortho path), and thus charge transfer from the alkene to the arene will take place. For an electron-poor alkene or an electron-rich arene, charge transfer from the arene to the alkene will occur (Figure 7.32). This analysis does not require a specification of the timing of the bondforming events. This could correspond (1) to a fully concerted, synchronous pathway, (2) to the cyclization of benzene to a biradical referred to as prefulvene followed by addition of the olefin, or (3) to the bonding of the olefin to meta positions and subsequent cyclopropane formation, as indicated for the case of meta cycloaddition in Scheme 18. Mechanism 2 of Scheme 18, which was first proposed in 1966 (BryceSmith et al., 1966), has been discarded because recent experimental evidence excludes the intermediacy of prefulvene (Bryce-Smith et al., 1986). Mechanism 3 is presently favored. Experimental and theoretical results sup-

( ) I \ ,rU\1IC I'HO'I'OCHEMISI'KY

dition is expected. Ortho cycloaddition is favored for AGE, values up to about 1.4-1.6 eV, and meta cycloaddition for more strongly positive values (Scheme 20).

port the notion that the a bonds between the reactants are formed during the initial stage of the reaction, while the cyclopropane ring closure is not expected until crossing to the ground-state energy surface (De Vaal et al., 1986; van der Hart et al., 1987). A fully concerted process (mechanism 1 in Scheme 18) is considered unlikely. An argument against it, and in favor of mechanism 3, is provided by independent photochemical generation of the proposed biradical intermediate (Scheme 19), which yields the same product ratio as is obtained from the corresponding arene-alkene photocycloaddition at low conversions (Reedich and Sheridan, 1985).

Scheme 20

Regioselectivity in the meta cycloaddition to substituted benzenes has been assumed to depend on charge polarization in the biradical intermediate shown in Scheme 21 (van der Hart et al., 1987). The theoretical calculations mentioned earlier, however, point out that in the early stage of the reaction the excited state has appreciable polar character that disappears as the reaction proceeds; the biradical itself does not have any particular polarity.

Irradiation of mixtures of various acetylenes with benzene gives cyclooctatetraenes, presumably via an intermediate ortho adduct 74 (Bryce-Smith et al., 1970). For acetylenes with bulky substituents, the bicyclooctatriene intermediate is sufficiently stable for a subsequent intramolecular photocycloaddition to a tetracyclooctene (75) (Tinnemans and Neckers, 1977):

Furthermore, the occurrence of an exciplex intermediate is assumed; an empirical correlation based on the AGE, values calculated from the Weller relation, Equation (5.28), has been established which allows the prediction of mode selectivity for a wide range of arene-alkene photocycloadditions (Mattay, 1987). For negative or very small values of AGE,, addition is preferred over cycloaddition. This is the case for the reactions of certain electron-rich alkenes with excited arenes. For positive values of AGE,, cycload-

ORGANIC PHOTOCHEMISTRY

424

7.4.4 Photocycloadditions of the Carbonyl Group Another photocycloaddition reaction that has been known for a long time is the Paterno-Buchi reaction, which involves the formation of oxetanes through the addition of an excited carbonyl compound to olefins:

As far as the addition of aromatic carbonyl compounds is concerned, only the triplet state is reactive, and hydrogen abstraction occurs as a side reaction. Another competing reaction path involves energy transfer (cf. Section 7.1.2); efficient oxetane formation is therefore observed only when the triplet energy of the carbonyl compound is not high enough for sensitized triplet excitation of the olefin. As is to be expected from the loose geometry of a triplet biradical intermediate, the reaction is not stereospecific; the same mixture of oxetanes 76 and 77 is produced at low conversion by irradiating cis- or trans-2-butene with benzophenone (Turro et al., 1972a; Carless, 1973): Figure 7.33. Mechanism of the photochemical oxetane formation: k,, k,,, and kc are rate constants of triplet biradical formation, intersystem crossing, and cyclization; kipand k, correspond to the formation of a contact ion pair and solvent-separated ion pairs; and kS and k,, are rate constants of the back reaction of the singlet biradical and back-electron transfer, respectively (by permission from Buschmann et al., 1991).

That the reaction is partly regiospecific, as indicated in Scheme 22, has been attributed to the differing stabilities of the biradical intermediates (Yang et al., 1964).

pair may also dissociate to a solvent-separated ion pair (k,) or return to the reactants by back-electron transfer (k,,). The triplet biradical intermediate was identified by picosecond spectroscopy (Freilich and Peters, 1985). A mechanism involving the formation of polar exciplexes in the first step, as well as electron-transfer processes, has been invoked in the interpretation of biacetyl emission quenching by electron-rich alkenes (Mattay et al., 1984b; Cersdorf et al., 1987). Diastereomeric oxetanes are formed from chiral carbonyl compounds such as menthyl phenylglyoxylate (78) (Buschmann et al., 1989).

Scheme 22

The mechanism of the photochemical oxetane formation is summarized in Figure 7.33. The 3(n,n*) excited state of the ketone produced by light absorption and subsequent intersystem crossing (ISC) attacks the olefin to form a triplet 1,Cbiradical (k,,). Intersystem crossing (kist) to the singlet, either directly or via a contact ion pair (kip),leads to ring closure (kc)to form the oxetane, or to /3 cleavage to re-form the reagents (k8). The contact ion I

The general kinetic scheme (Fig. 7.34) displays two stages of diastereoselection: (1) a preferred formation of that of the two diastereomeric 1,4-

0I:CANIC PHOTOCHEMISTRY

e ndo

Figure 7.35. Preferred conformations for intersystem crossing during the diastereoselective oxetane formation (adapted from Griesbeck and Stadtmiiller, 1991).

Figure 7.34. A simplified kinetic scheme for the diastereoselective oxetane formation in the Paterno-Bilchi reaction (k, and k; as well as k, and k; include intersystem crossing steps) (by permission from Buschmann et al., 1989). biradicals (k, > k;) which leads to the majority oxetane product, and (2) a preferred /3 cleavage of the biradical that leads to the minority oxetane product (k; > &,), or a preferred ring closure of the biradical, which leads to the majority oxetane product (k, > k;). Upon continued irradiation, the Pcleavage products reenter the reaction cycle, establishing a "photon-driven selection pump." The Arrhenius plot for the diastereoselectivity (cf. Section 6.1.5.2) contains two linear regions, one with a positive and one with a negative slope, changing into each other at the "inversion temperature," Tin,. Each region selection has a different dominant selection step. At temperatures above Tin", is driven primarily by enthalpy, as expected for an early transition state in the bond cleavage in the energy-rich biradical intermediate. Below Ti,,,selection is driven primarily by entropy, as expected for an early transition state in the bond-forming step in the formation of the biradical from the energy-rich reactants (Buschmann et al., 1989). Example 7.11: An interesting example of diastereoselectivity is provided by the photocycloaddition of aromatic aldehydes to electron-rich cyclic olefins such as 2.3dihydrofuran (79):

The stereochemistry of the reaction can be accounted for by the conformational dependence of .;pin-orhit cor~plinpelements dihc~~rred in Section 4.3.4.

Figure 7.35a shows the postulated geometry of favored intersystem crossing in the biradical derived from an unsubstituted cycloalkene; bond formation following spin inversion is faster than conforrnational changes, and the endo adduct is formed from the less sterically hindered conformation. The exoselectivity observed in I-substituted cycloalkenes is explained by increasing gauche interactions with the Balkoxy group that favor the biradical conformations shown in Figure 7.35b (Griesbeck and Stadtmiiller, 1991). The photoaddition of a furan and an aldehyde can serve as a photochemical version of a stereoselective aldol reaction, since the photoadduct can be viewed as a protected aldol, as indicated in Scheme 23 (Schreiber et al., 1983).

Scheme 23

For aliphatic ketones, the situation is complicated by less efficient intersystem crossing, thus permitting reaction of the '(n,n*) as well as the '(n,llr) state of the carbonyl compound, as revealed by the use of triplet quenchers. The S, reaction is more stereospecific, presumably because of the tight geometry of the singlet biradical, and yields less cis-trans isomerization by a competing path. Thus, the stereochemistry of cis-I-methoxy-I-butene (80) is partially retained when acetone singlets attack the olefin, but it is almost completely scrambled in the reaction of triplet acetone (Turro and Wriede, 1970):

ORGANIC PHOTOCHEMISTRY

428

The situation is different with electron-poor olefins such as 1,2-dicyanoethylene. Only the S, state of acetone forms oxetanes, and the reaction is highly stereospecific, as indicated in Scheme 24. The competing cis-trans isomerization of the olefin arises exclusively from the triplet state (Dalton et al., 1970).

Scheme 24

+ NCAcN

The specificity of this reaction has been used to chemically rirrate both the excited-singlet acetone and the triplet acetone produced through thermal decomposition of tetramethyl-1,2-dioxetane.(Cf. Section 7.6.4.) For this purpose the thermolysis was carried out in the presence of trans-1 ,Zdicyanoethylene, and the quantities of singlet and triplet acetone formed were obtained from the yields of dioxetane and cis-1,2-dicyanoethylene, respectively (Turro and Lechtken, 1972). The various reactions of excited carbonyl compounds with olefins may be rationalized on the basis of correlation diagrams. In principle, four different pathways have to be discussed: the perpendicular and the parallel approaches (Figure 7.36) and the initial formation of a CO and a CC bond, yielding a C,C-biradical and C,O-biradical, respectively:

However, only three out of these four possibilities are realistic, since there is no carbonyl group orbital available for a perpendicular approach a ~ ford mation of a CC bond. Formation of a C,O-biradical is therefore possible only through a parallel approach.

Perpendicular approach

Parallel approach

The perpendicular and the parallel approach for the interaction of an mn*excited ketone with a ground-state olefin.

Figure 7.36.

Correlation diagram a) for the perpendicular approach of ketone and olefin, and for the parallel approach resulting in b) a C,C-biradical and c) a C,Obiradical. Figure 7.37.

From Figure 7.37a, the perpendicular approach leading to a C,C-biradical is seen to be electronically allowed. Since, however, the two p AOs of the unpaired electrons are oriented perpendicular to each other, a rotation of the CH, group of the ketone is required prior to cyclization both for the singlet biradical and for the triplet biradical, which assume similar geometries and therefore can each give an oxetane. Small rotations in the less sterically hindered direction to optimal geometries for ISC and subsequent reaction may lead to stereospecific oxetane formation from the triplet state. (Cf. Example 7.11 .) Correlation diagrams for the two modes of parallel approach are shown in Figures 7.37b and 7.37~.If the CO bond is formed first, the (n,n*) excited reactant states correlate with highly excited (n,aGo) states of the products and a correlation-induced barrier results. Hence this reaction is electronically forbidden (Figure 7.37b). If, however, the CC bond is formed first, the unpaired electron at the oxygen can be localized in a p A 0 with either a or n symmetry, that is, either in the fco MO or in the no orbital. Since the '.3(n,n*)reactant states correlate with the 'v3B,,., product states, no correlation-induced barrier is to be expected, and the reaction is likely to be exothermic (Figure 7.37~).In contrast to the perpendicular approach, the triplet biradical of the parallel approach will have a loose geometry and should result in cis-trans isomerization of the olefin. The conclusions from the correlation diagrams have been nicely confirmed by early ab initio calculations for the carbon-xygen attack of formaldehyde on ethylene (Salem, 1974)and by more recent calculations on the same model reaction considering both modes of attack. (Palmer et al., 1994).

The results for the carbon-oxygen attack are summarized schematically in Figure 7.38. The excited-state branch of the reaction path terminates in a conical intersection point at a CO distance of 177 pm before the biradical is fully formed (cf. Figure 7.37a). Thus the system can evolve back to the reactants or produce a transient C,C-biradical intermediate that is isolated by small barriers (< 3 kcallmol) to fragmentation (TS,) or to rotation and ring closure to oxetane (TS,). The singlet and triplet biradical minima are essentially coincident. A schematic representation of the surfaces for the carbon-carbon attack is shown in Figure 7.39. The very flat region of the S,, surface (barriers of the order of I kcallmol) corresponds to the '.3B,., C.0-biradical. The '.3B,, biradical has a CC bond length of 156 pm and corresponds to a conical intersection geometry in the case of the singlet, and to a minimum in the case of the triplet. Thus for the singlet photochemistry the decay to So occurs close to the products, and the reaction appears to be concerted. Since, however, the formation of the singlet biradical is also possible from the same funnel, a certain fraction of photoexcited reactant can evolve via a nonconcerted route. Figure 7.39. Photoaddition of formaldehyde and ethylene. Schematic representation of the carbondxygen attack as a function of the C,C distance R,, and the dihedral angle rp between the formaldehyde and ethylene fragments (by permission from Palmer et al., 1994).

Photocycloaddition of formaldehyde and ethylene. Schematic representation of the surfaces involved in the carbon-oxygen attack as a function of the C,O distance R, and the dihedral angle rp between the formaldehyde and ethylene fragments. )( and denote the parallel and perpendicular approach of the reactants, respectively; CI marks the conical intersection (by permission from Palmer et al., 1994). Figure 7.38.

The overall nature of the singlet reaction path is determined by whether the system returns to S,, through an early funnel along the path of carbonoxygen attack to produce a C,C-biradical intermediate (Figure 7.38) or through a late funnel along the path of carbon-carbon attack to produce oxetane in a direct process (Figure 7.39). The stereochemistry and efficiency of the reaction will depend on which of these two excited-state reaction paths is followed. Conclusions similar to those obtained from the correlation diagrams can be reached by means of either PMO theory (Herndon, 1974) or simple frontier orbital theory, as indicated in Figure 7.40. Orbital energies may be estimated from the assumption that the olefinic n MOs will be stabilized by electron-withdrawing substituents and destabilized by electron-releasing ones. The hom*o energy of an electron-rich olefin will then be comparable to that of the carbonyl n orbital, whereas the LUMO of electron-poor olefins will be similar in energy to the n* MO of the carbonyl group. Interactions between orbitals of comparable energy require a parallel approach in the case of electron-poor olefins and result in CC bond making and formation of a C,O-biradical. Perpendicular attack is required for electron-rich olefins and yields a C,C-biradical by CO bond formation.

ORGANIC PHOTOCHEMISTRY

7.4.5 Photocycloaddition Reactions of a,&Unsaturated Carbonyl Compounds Intermolecular photoadditions of a,@unsaturated carbonyl compounds can take place either at the CC or at the CO double bond. Photodimerizations with formation of a cyclobutane ring are quite common. In cases such as cyclopentenone (811, head-to-head as well as head-to-tail dimers are produced.

Electron-pwr olef ins

Electron - rich olef ins

Figure 7.40. Frontier orbitals for oxetane formation. Interaction of one of the halffilled carbonyl orbitals with the LUMO of electron-poor olefins (left) and with the hom*o of electron-rich olefins (right).

The magnitude of the LCAO MO coefficients of the interacting orbitals permits a prediction of the expected oxetane regiochemistry. Both in the hom*o of a donor-substituted olefin and in the LUMO of an acceptor-substituted olefin, the coefficient of the unsubstituted carbon atom is the larger one in absolute value. Therefore, electron-poor olefins regioselectively afford the oxetane with the substituted carbon next to the oxygen. (Cf. Barltrop and Carless, 1972.) In contrast, an electron-rich olefin predominantly yields the oxetane with the unsubstituted carbon next to the oxygen. (Cf. Scheme 22.) Finally, Figure 7.40 permits the conclusion that oxetane formation can be considered to be either a nucleophilic attack by a ketone on an electronpoor olefin or an electrophilic attack by a ketone on an electron-rich olefin, corresponding to the predominant interaction of a half-filled carbonyl orbital either with the empty n* MO or with the doubly filled rc MO of the olefin.

While double-bond cis-trans isomerization in Esubstituted a,&enones occurs at both 313 and 254 nm, oxetene forms only when short wavelengths are used (Friedrich and Schuster, 1969, 1972). This differentiation has been explained on the basis of calculations that revealed a S,-So conical intersection lying 15 and 10 kcallmol above the '(n,n*) minimum of s-trans- and scis-acrolein, respectively (Reguero et at., 1994). Oxabicyclobutane, however, has not been detected. This behavior of a,@enones is in contrast with that of butadiene, where cyclobutene and bicyclobutane are formed simultaneously. (Cf. Sections 6.2.1 and 7.5.1.) Mixed cycloadditions, for example, between cyclopentenone and ethyl vinyl ether, have also been observed frequently (Schuster, 1989). As indicated in Scheme 25, attack of the 3(3t.,n*)excited state of the enone on the olefin will give a triplet 1,4-biradical that ultimately yields cyclization and disproportionation products (Corey et at., 1964; De Mayo, 1971). The regio-

7.5

selectivity of the reaction, which was explained earlier in terms of an initial interaction of the enone triplet with an alkene to give an exciplex, can alternatively be accounted for by the relative efficiencies with which each of the isomeric biradical intermediates proceeds to the annelation products (as opposed to reverting to the ground-state enone). While the structural isomers 84 and 85 are produced in a ratio 1.0 : 3.1, trapping with hydrogen selenide H,Se indicates that the biradicals 82 and 83 are formed in the ratio 1 .O: I .O (Hastings and Weedon, 1991). Kinetic studies indicating that triplet 3-methylcyclohex-2-en-1-one (86) reacts with maleic or fumaric dinitrile directly to yield triplet 1,4-biradicals argue against the intermediacy of an exciplex (Schuster et al., 1991a). Dynamical properties of enone '(n,n*) states have been determined and discussed; torsion around the olefinic bond is the principal structural parameter that affects their energies and lifetimes (Schuster et a]., 1991b). Twisting around the C==C bond causes an increase in energy on the Sosurface and a concomitant decrease in energy on the '(n,n*) surface (cf. Figure 4.6). This reduces the TI-S,, gap and facilitates T,-S,, radiationless decay in a process dominated by spin-orbit coupling (Section 4.3.4). Average energies and lifetimes of the mixture of head-to-head and head-to-tail 1,Cbiradicals have been determined by photoacoustic calorimetry (Kaprinidis et al., 1993).

REARRANGEMENTS

435

characterized by a number of thermal as well as photochemical electrocyclic reactions and sigmatropic shifts, some of which are as follows:

Ergosterol

Precalciferol

Pyrocalciferol

The number of photoreactions that proceed in agreement with the Woodward-Hoffmann rules (Table 7.3) is very large. Some examples are collected in Scheme 26.

Synthetic applications of [2 + 21 cycloadditions of a#-unsaturated carbonyl compounds are numerous. The synthesis of cubane (Eaton and Cole, 1964), in which cage formation is achieved by the following photochemical reaction step, is an example: Scheme 26

7.5 Rearrangements 7.5.1 Electrocyclic Reactions Electrocyclic ring-opening and -closure reactions represent another important field in which the Woodward-Hoffmann rules apply. These rules were in fact derived as a rationalization of the chemistry of vitamin D, which is

Table 7.3 Orbital Symmetry Rules for Thermal (A) and Photochemical (hv) Electrocyclic Reactions Number of n Electrons in Open-Chain Polyene Reaction

4n Conrotatory Disrotatory

Disrotation Conrotation

436

ORGANIC PHOTOCHEMISTRY

The important role of avoided crossings and the resulting pericyclic minima for the mechanisms of photochemical reactions was first pointed out on the example of the butadiene-cyclobutene conversion (van der Lugt and Oosterhoff, 1969).

While the Oosterhoff model that follows from the state correlation diagrams discussed in Section 4.2.3 describes the stereochemistry of electrocyclic reactions correctly and in agreement with the Woodward-Hoffmann rules, it is oversimplified in that it does not attempt to actually locate the bottom of the pericyclic minimum and simply assumes a planar carbon framework. It therefore predicts a nonzero S,-So gap at perfect biradicaloid geometry. As discussed earlier (cf. Sections 4.4.1, 6.2.1, etc.) symmetry-lowering distortions that remove the exact degeneracy of the nonbonding orbitals at the perfect biradical geometry by introducing a heterosymmetric perturbation 6 lower the energy of the S, state and reduce the S,-So gap. Recent calculations on butadiene (Olivucci et al., 1993) have demonstrated that the gap is actually reduced to zero and that the funnel corresponds to a true S,-So conical intersection at geometries with pericyclic and diagonal interactions. According to these calculations, the ring closure of butadiene to form cyclobutene proceeds through the same funnel as the cis-trans isomerization, and the stereochemical decision is taken mainly on the excitedstate branch of the reaction pathway, where the low-energy pathway corresponds to disrotatory motion, as discussed in detail in Section 6.2.1. In fact, an excited-state cis-butadiene enters the conical intersection region in a conformation already consistent with the production of only one ground-state cyclobutene isomer (Figure 7.41). However, not all reactions that follow a Woodward-Hoffmann allowed path are necessarily stereospecific. (Cf. Clark and Leigh, 1987). Irradiation

Figure 7.41. Schematic representation of the geometry changes of excited state scis-butadiene a) entering the conical intersection region b) and producing groundstate cyclobutene c). Light and dark arrows indicate excited-state and ground-state pathways, respectively (adapted from Olivucci et al., 1993).

of bicyclo[4.2.0]oct-7-enes (87) yields the products shown in Scheme 27 (Leigh et al., 1991). Recent calculations suggest that the motion on the S, surface is disrotatory, as demanded by the Woodward-Hoffmann rules, and that a loss of steric information results from motion on the ground-state surface after return through the pericyclic funnel (Bernardi et a]., 1992~).The mechanism of the fragmentation step (also shown in Scheme 27) has not yet been elucidated in a definitive fashion.

Irradiation of s-cis-2,3-dimethylbutadieneyields both electrocyclic ring closure and double-bond isomerization products (Scheme 28). While the ring closure in s-cis-butadiene, isoprene, 2-isopropylbutadiene, and 1,3-pentadiene is considerably less efficient than s-cis-s-trans isomerization, in s-cis2,3-dimethylbutadiene it is about 50 times faster (Squillacote and Semple, 1990). This effect is counterintuitive, since the two methyl groups appear to hinder the rotation about the central C--C bond in butadiene.

Example 7.12: According to ab initio calculations of Olivucci et al., (1994b), the presence of the methyl substituents in s-cis-2,3-dimethylbutadienedoes not alter the nature of the pathway on S, to the pericyclic funnel. In both the parent and the dimethyl derivative, the atoms attached in positions 2 and 3 remain eclipsed. The different behavior could therefore be due to differences in the region of the Sosurface explored after return through the funnel, or to differences in the kinematics caused by the larger inertia of the methyl groups compared to hydrogen. The latter explanation is favored by Olivucci et al., but dynamical calculations are needed to settle the issue.

438

ORGANIC PHOTOCHEMISTRY

At the conical intersection the C,-C2-C3valence angle o is close to 90°, suggesting that in strained systems, where this value is hard to reach, the excited-state barrier on the pathway to the conical intersection o r the conical intersection itself may be s o high in energy that the photoreaction cannot take place. The quantum yields for cyclobutene formation in dimethylenecycloalkanes summarized in Scheme 29 (Aue and Reynolds, 1973; Leigh and Zheng, 1991) are in agreement with this expectation.

7.5

REARRANGEMENTS

439

Example 7.13:

The photochemical reaction network and photoequilibrium involved in the commercial synthesis of vitamin D using the photochemical electrocyclic ring opening of ergosterol to give precalciferol, which subsequently undergoes a thermal [1,7]-H shift to produce vitamin D itself (cf. Jacobs and Havinga, 1979). has been studied using a combination of molecular mechanics and simple 2 x 2 VB methods (Bernardi et al., 1992b). The results are summarized in Figure 7.42. The focal feature of the reaction network centered on precalciferol is the existence of three funnels analogous to those discussed for the cis-trans isomerization of cis-hexatriene in Section 7.1.3, except that there are two conical intersections CIZr and CIS for the s-cis-s-trans isomerization (c-t)since the

Bicyclo[l .l .O]butane is usually a side product of the photocyclization of butadiene to cyclobutene (Srinivasan, 1963); in isooctane, the quantum yield ratio is I : 16 (Sonntag and Srinivasan, 1971). It becomes the major product in systems in which the butadiene moiety is constrained near an s-trans conformation and bond formation between the two terminal methylene groups that leads to cyclobutene is disfavored. An example is the substituted diene 88 in Scheme 30, for which the bicyclobutane is the major product; a nearly orthogonal conformation should result from the presence of the 2,3-di-t-butyl substituents (Hopf et al., 1994).

HO Ergosterol

Me Toxisterol C2

Mechanistic scheme for the precalciferol reaction network including the three conical intersection regions CIA, CI; and CI,.,. Dark arrows indicate ground-state pathways, while light arrows indicate pathways on the excited-state surface (by permission from Bernardi et al., 1992b). Figure 7.42.

ORGANIC PHOTOCHEMISTRY

The electrocyclic ring-closure reaction proceeds exclusively in the S, state and yields solely the trans product by a conrotatory mode of reaction, as is to be expected from Table 7.3 for a 6n-electron system. Competing reactions are cis-trans isomerization (cf. Section 7.1.4) and intersystem crossing to T,. From the T, state, generally only cis-trans isomerization is observed. Stilbenes with substituents that enhance spin inversion, such as Br, RCO, and NO,, do not undergo the cyclization reaction efficiently. This reaction is not limited to stilbene itself. Whether a diarylethylene may be cyclized, and if so, in which way, can be predicted from the sum F* = 6' of the free valence numbers $*= fl - CQ; calculated for tre reacting positions Q and o of the hom*o-LUMO excited reactant. Here, C a is the sum of excited-state n-bond orders for all bonds p-g' originating from atom e. Laarhoven (1983) derived the following rules:

c*+

Figure 7.43. Illustration of the NEER principle: interconversion of the excited-state conformers of precalciferol is prohibited by the high probability of decay to the ground state through the conical intersection CI,., (by permission from Bernardi et al., 1992b). s-cis-Z-s-cis isomer of precalciferol has two diastereomers, which may be denoted as cZc + and cZc - . The possibility of bifurcation of the reaction path on the So surface corresponding to the various possible bond-forming schemes (indicated in Figure 7.42 by dark arrows) and the existence of several pathways in the S , state (light arrows) are the reasons for the great diversity of photoproducts from precalciferol. In agreement with the existence of three ground-state conformers cZc+, cZc- and cZt of precalciferol, there are three excited-state minima, cZc+*, cZc-*, and cZt*. Search for transition structures between these excited-state minima led toward the funnels Cl;, and C I , . This work explains the short singlet lifetime of an excited-state conformer, as well as the inability of excited conformers to interconvert, as stated by the NEER (nonequilibration of excited rotamers) principle. (Jacobs and Havinga, 1979; see also Example 6.9.) The interconverting conformer (e.g., cZc*) will have high probability of decaying to the ground state through the conical intersection CI,., before the barrier for interconverting to cZt* could be completely overcome. This is illustrated qualitatively in Figure 7.43.

The photocyclization of cis-stilbene gives dihydrophenanthrene (5), which may be thermally or photochemically converted back to cis-stilbene or oxidized to phenanthrene (Moore et al., 1963; Muszkat, 1980).

d=i

I . Photocyclizations do not occur when F; < 1 .O.

2. When two or more cyclizations are possible in a particular compound, only one product arises if one value is larger by at least 0.1 than all the others. 3. When planar as well as nonplanar products (pentahelicene or higher helicenes) can be formed, the planar aromatic will in general be the main product regardless of rule 2, provided rule 1 is fulfilled for its formation. The application of these rules is illustrated in the following example.

Example 7.14:

The excited-state n-bond orders of an alternant hydrocarbon are given by

where pw, is the n-bond order of the bond between atom e and its neighbor g', while cflo and c~.,, are the corresponding LCAO coefficients of the hom*o. Using q'= fl - 1.282 = 0.450, 4*= 0.620,and 6,.= 0.491, F ; , = 0.941, and 4;. = 1.1 1 1 are found for compound 89. From rule I only ring closure between positions 4 and 2' to yield the hydrocarbon 91 is expected, and no formation of 92 by ring closure between positions 2 and 2' should occur. ,. = 1.095 and = 1.188; from rule I, formation Similarly, for 90 one has & of both 91 and 92 could be expected, but since 91 is nonplanar, 92 should be the main product according to rule 3. Experimental results show that only products allowed by rules 1-3 are formed: 89 gives 91 in 60% yield and 90 yields only the planar compound 92, in 75% yield (Laarhoven, 1983).

e,;,.

7.5

REARRANGEMENTS

443

A situation similar to that of stilbene is found for dimethyldihydropyrene (%), which is converted into the dimethyl-substituted metacyclophanediene

97 by irradiation with visible light (A = 465 nm); complete back reaction to the reactants is achieved either with lower wavelength light (A = 313 nm) or thermally.

The analogous photocyclization of N-methyldiphenylamine has been studied in detail (Forster et al., 1973; Grellmann et al., 1981) and utilized synthetically (Schultz, 1983). In contrast to stilbene, the reaction proceeds from the triplet state of the amine by an adiabatic conrotatory ring closure to give a dihydrocarbazole (93), in accordance with the Woodward-Hoffmann rules. After return to the ground state, the initial product is oxidized to a carbazole (Scheme 31):

The two systems differ insofar as for stilbene the thermodynamic stability of the "open" form is greater, while for dihydropyrene the "ring-closed" form is more stable. The thermal back reaction 97 -, 96, which requires an activation energy of 22 kcal/mol, is apparently a symmetry-forbidden concerted reaction. An estimate of the ground-state barrier based on EHT calculations yields values that are in good agreement with experimental activation energies (Schmidt, 1971). In general, electrocyclic ring-closure and ring-opening reactions are singlet processes, believed to proceed via tight biradicaloid geometries. In contrast, triplet excitation frequently yields five-membered rings (see the rule of five, Section 7.4.1) via loose biradicaloid intermediates. For example, singlet cyclohexadiene gives bicyclo[2.2.0]hexene (98) and hexatriene, while triplet hexatriene yields bicyclo[3.1.O]hexene (99) (Jacobs and Havinga, 1979):

I Scheme 31

CH3

This reaction is of special interest because it is a stereospecific triplet reaction. Another known example is the ring opening by CC bond cleavage of the heterocyclic three-membered rings aziridine (94), oxirane (95). etc. (Huisgen, 1977; Padwa and Griffin, 1976). These reactions are believed to proceed through a cyclic antiaromatic triplet minimum which is isoelectronic with C,H,@; this in turn is an axial biradical with E(T,)< E(S,). (Cf. Section 4.3.2.) It has been suggested that the unusual degree of triplet stabilization at the tight pericyclic geometry in axial biradicals is responsible for the stereospecific course of the reaction (Michl and BonaCiC-Kouteckg, 1990).

The reactions of butadiene are very typical. As indicated in Scheme 32, direct irradiation yields predominantly cyclobutene; in the presence of Cu(1) or Hg, however, bicyclobutane formed by an x[2 + 21 process is the major product, with minor products formed through [2 + 21 cycloaddition. (Cf. Section 7.4.2.)

m--> Scheme 32

- la*1-hv

1 '*I

444

ORGANIC PHOTOCHEMISTRY

Example 7.15: Direct irradiation of myrcene (100) gives the cyclobutane derivative 101 by an electrocyclic ring-closure reaction, together with Ppinene (102) formed in a [2 21 cycloaddition process. The sensitized reaction, however, yields the bicyclic compound 103.

biradical and products of its further transformation. These are indeed not observed.

7.5.2 Sigmatropic Shifts

The triplet reaction is assumed to proceed as a two-step process with the most stable five-ring biradical as intermediate according to the "rule of five" (cf. Section 7.4.1) (Liu and Hammond, 1%7).

The kinetics of the photochemical ring opening of cyclic dienes and trienes such as 1,3,5-cyclooctatriene (104) were determined by picosecond time-resolved UV resonance Raman spectroscopy (Ried et al., 1990) and provide excellent direct support for the Woodward-Hoffmann rules. The photochemical ring opening of cyclohexa-1,3-diene involves a rapid (10 fs) radiationless decay of the initially excited 1B, spectroscopic state to the lower 2A,, presumably through an S,-S, conical intersection reached by a conrotatory motion, in agreement with Woodward-Hoffmann rules (Trulson et al., 1989). According to the latest calculations (Celani et al., 1994), this is followed by further conrotatory motion on the 2A, surface along a pericyclic path distorted in the usual diagonal way from twofold symmetry, to a shallow minimum located most of the way toward the ringopen geometry of s-cis-Z-s-cis-hexatriene. As judged by the experimentally observed 6 ps appearance time of the ground-state 1,3,5-hexatriene product (Reid et al., 1993), the molecule has the time to equilibrate vibrationally in this shallow minimum before it decays to the ground state, presumably mostly via thermal activation to a more strongly diagonally distorted pericyclic conical intersection area located only about 1 kcallmol higher in energy. As is common for pericyclic funnels, this return to So is about equally likely to be followed by relaxation to the starting 1,3-cyclohexadiene and to the product, s-cis-Z-s-cis-hexatriene. The calculations assign little if any importance to an alternative ground-state relaxation path that would preserve the diagonal 1,5 interaction and lead to the 5-methylenecyclopent-2-en-I-yl

Sigmatropic shifts represent another important class of pericyclic reactions to which the Woodward-Hoffmann rules apply. The selection rules for these reactions are best discussed by means of the Dewar-Evans-Zimmerman rules. It is then easy to see that a suprafacial [1,3]-hydrogenshift is forbidden in the ground state but allowed in the excited state, since the transition state is isoelectronic with an antiaromatic 4N-Hiickel system (with n = I), in which the signs of the 4N AOs can be chosen such that all overlaps are positive. The antarafacial reaction, on the other hand, is thermally allowed, inasmuch as the transition state may be considered as a Mobius system with just one change in phase.

suprafacial

antarafacial

[I .3]hydrogen shift

For sigmatropic shifts of organic groups other than hydrogen, inversion of configuration at the migrating site is possible and introduces another change in phase. No phase change occurs if the configuration is retained. The resulting rules are summarized in Table 7.4.

Table 7.4 Orbital Symmetry Rules for Thermal (A) and Photochemical (hv) Sigmatropic [i, j1 Shifts Reaction

I + j = 4 n

supra Inv." antara Ret. supra Ret . antara Inv.,'

+ + + +

i + j = 4 n supra-antara antara-supra supra-supra antara-anlara

" Hydrogen shifts with inversion are not possible.

I + j = 4n 2

+ srrprcc + Ret . untara + Inv." supra + lnv." onrara + Ret.

i+j= 4n + 2 sicpru-srrpra antara-untura supra-antarc1 anrura-supra

Interesting examples of sigmatropic shift reactions are provided by the rearrangements of 1,5-dienes, which, as indicated in Scheme 33 for geranonitrile (105), undergo a [3,3] shift (Cope rearrangement) in the ground state and a [1,3] shift in the singlet-excited state, while the triplet excited state undergoes an x[2 + 21 addition via a biradical, in agreement with the rule of five (Section 7.4.1). Stereospecificity of the singlet reaction, as well as results of deuterium labeling experiments, verify the expectations from the selection rules for concerted photochemical reactions (Cookson, 1968).

Scheme 33

(1 9%)

(8 1%)

However, mixtures of [I ,2]- and [I .3]-shift products may be obtained by irradiating the same reactant, as shown in Scheme 34 for the direct irradiation of 1,5-hexadienes (Manning and Kropp, 1981). Configuration and state correlation diagrams for the [I ,3] shift show that a pericyclic geometry in S, is indeed present, making the excited-singlet reaction quite analogous to the disrotatory interconversion of butadiene and cyclobutene discussed in the preceding section. Appropriate diagonal distortions of the pericyclic geometry may again lower the excited-state energy and possibly produce a conical intersection. The [1,2] or pseudosigmatropic shift, on the other hand, involves a cyclic array of an odd number of interacting orbitals that is isoelectronic with a generalized fulvene, and the reaction is always ground-stateforbidden because the product is a biradical.

[1,2] and [1,3] pathways is consistent with a suprafacial process and retention of configuration at the migrating carbon (Bernardi et al., 1992a).

The irradiation of diisopropylidenecyclobutane (106) causes an allowed antarafacial [ I ,5] shift (Kiefer and Tanna, 1969). For cycloheptatriene (107), a suprafacial [1,7] sigmatropic shift (Roth, 1963) and formation of bicyclo[3.2.0]hepta-2,6-diene (108) by intramolecular cyclization (Dauben and Cargill, 1961) are observed. Both these reactions originate from the 2A' excited state, which is reached from the optically prepared IA" state via an S,S, conical intersection, as has been suggested from lifetime measurements (Borell et al., 1987; Reid et al., 1992, 1993) and confirmed by theoretical calculations. The latter also showed that no such conical intersection exists for dibenzosuberene (109), and the relaxed S, minimum is still of A" symmetry (Steuhl and Klessinger, 1994). This state exhibits excited-state carbon acid behavior, showing that in fact the HOM-LUMO excited-singlet state of ground-state antiaromatic carbanions is stabilized compared to the excited state of ground-state aromatic carbanions (Wan and Shukla, 1993).

A formal [I ,5] hydrogen shift occurs in photoenolization of compounds such as o-methylacetophenone (110). The reaction proceeds in the triplet state by way of hydrogen abstraction and involves biradical intermediates and an equilibrium of the triplet states of Z- and E-en01 (Haag et al., 1977; Das et al ., 1979). These expectations have been confirmed by recent theoretical investigations on methyl shifts in but-I-ene (Scheme 35). The results demonstrate the existence of a funnel on the S, surface at a geometry from which travel on the ground-state surface can produce either a [1,2] or a [1,3] sigmatropic shift. The geometry and orientation of the migrating CH, radical along the

448

ORGANIC PHOTOCHEMISI'UY

cis-Crotonaldehyde (111) has been used as a model for the theoretical investigation of photoenolization reactions (Sevin et al., 1979; Dannenberg and Rayez, 1983).

Compound 112 represents an example of a photochromic material in which the colored enol is stabilized through hydrogen bonding and by the phenyl groups (Henderson and Ullmann, 1965).

7.5.3 Photoisomerization of Benzene The photochemical valence isomerizations of benzene summarized in Scheme 36 are wavelength-dependent singlet reactions. The first excited singlet state gives benzvalene (115) and fulvene (116); prefulvene (117), which had been postulated to be involved in the addition of olefins to benzene (cf. Section 7.4.3), was suggested to be an intermediate for both isomers (BryceSmith, 1968). The second excited singlet state leads to the formation of dewarbenzene (113) in addition to benzvalene (115) (Bryce-Smith et al., 1971) and fulvene (116); prismane (114) is not produced directly from benzene but rather results from a secondary reaction of dewarbenzene. (Cf. Bryce-Smith and Gilbert, 1976, 1980.) The conversion of dewarbenzene into prismane may be treated as a L2, + ,2,] cycloaddition.

The formation of benzvalene is formally an x[2 + 21 cyclo-addition. The S, (B,,) reaction path from benzene toward prefulvene starts at an excitedstate minimum with D,, symmetry and proceeds over a transition state to the geometry of prefulvene, where it enters a funnel in S, due to an S,-So conical intersection and continues on the So surface, mostly back to benzene, but in part on to benzvalene (Palmer et al., 1993; Sobolewski et al., 1993). At prefulvene geometries, So has a flat biradicaloid region of high energy with very shallow minima whose exact location depends on calculational details (Kato, 1988; Palmer, et al., 1993, Sobolewski et al., 1993). Fulvene has been proposed to be formed directly from prefulvene or via secondary isomerization of benzvalene (Bryce-Smith and Gilbert, 1976). Calculations support the former pathway with a carbene intermediate (Dreyer and Klessinger, 1995). The conversion of' benzene into dewarbenzene can be formally considered to be a disrotatory 4n ring-closure reaction; thus it is not surprising that it is forbidden in the ground state and allowed in the excited state. The correlation diagrams in Figure 7.44 indicate that the reaction proceeds from the S, state (at vertical geometries this is 'B,,, but it soon acquires E,, character as motion along the reaction path occurs). (Cf. Example 7.16.) The best currently available calculations (Palmer et al., 1993) suggest that the molecule moves downhill on the S, surface to an S,-S, conical intersection and

Figure 7.44. Benzene-dewarbenzene valence isomerization; a) orbital correlation diagram (C,,symmetry) and b) state correlation diagram, devised with the help of Table 7.5 and experimental state energies.

reaches the S, surface at a geometry where S,, too, has a funnel. This is caused by an S , S oconical intersection and provides further immediate conversion to the So state. Thus, there is no opportunity for vibrational equilibration in the S, state. The biradicaloid geometry at which these stacked funnels are located is calculated to be such that relaxation in Socan produce dewarbenzene, benzvalene, or benzene. In low-temperature argon matrices, dewarbenzene has been shown to be a primary product of benzene photolysis at 253.7 nm (Johnstone and Sodeau, 1991). Hexafluorobenzene yields hexafluorodewarbenzene upon irradiation in the liquid or vapor phase (Haller, 1967). Isomerization reactions of benzene that result in "scrambling" of hydrogen and carbon atoms presumably involve a benzvalene intermediate and thermal or photochemical rearomatization; depending on which of the CC bonds indicated in Scheme 37 by a heavy or a broken line is cleaved, either the rearranged product is formed or the reactant is recovered (Wilzbach et al., 1968).

Scheme 37

The major product of the direct irradiation of dewarbenzene is benzene, while some prismane is produced via an intramolecular [2 + 21 cyclization, which involves a funnel that lies between the geometries of dewarbenzene and prismane (Palmer et al., 1992). The electronic factors that control the existence of this funnel are the same as those for the intermolecular [2 + 21 cycloaddition of two ethylenes. (Cf. Sections 6.2.1 and 7.4.1 .) An important difference is due to the strong steric strain that arises in the cagelike a-bond framework as a diagonal distortion is introduced, producing a high-energy ridge along the rhomboidal distortion coordinate. This moves the conical intersection to higher energies, but it apparently remains accessible. Furthy strain may locate the bottom of the pericyclic funnel at a less diagonally distorted structure, where the S o S , touching is still weakly avoided. Triplet sensitization (ET> 66 kcallmol) exclusively yields triplet excited benzene in an adiabatic reaction. According to Scheme 38, this catalyzes the conversion of dewarbenzene into benzene. The reaction thus proceeds as a chain reaction with quantum yields of up to aIi,= 10 (Turro et al., 1977b).

Scheme 38

3[o[a -- 0 '[or +

The major reaction to result from direct excitation of benzvalene is a degenerate [1,3] sigmatropic shift as indicated in Scheme 39. The same reaction is observed upon sensitized triplet excitation if the triplet energy of the sen-

sitizer ET is below 65 kcal/mol. If, however, ET exceeds 65 kcal/mol, reversion to benzene takes place. The latter is an adiabatic hot triplet reaction, which proceeds from one of the higher excited triplet states (T,) of benzvalene and produces triplet excited benzene. It results in a chain reaction with QIi, 2: 4, similar to the reaction of dewarbenzene shown in Scheme 38 (Renner et al., 1975).

Scheme 39

Direct irradiation as well as sensitized triplet excitation of prismane results in rearomatization to produce benzene and in isomerization to form dewarbenzene, which predominates even in the triplet reaction. An adiabatic rearrangement to excited benzene is not observed (Turro et al., 1 977b). Benzene valence isomers undergo thermal rearomatization to form benzene rather easily. Half-times of dewarbenzene and benzvalene at room temperature are approximately 2 and 10 days, respectively. Ythough all these reactions are strongly exothermic, chemiluminescence (cf. Section 7.6.4) is observed only for the thermal ring opening of dewarbenzene. This reaction produces triplet excited benzene in only very small amounts. While benzene phosphorescence is undetectable in fluid solution near room temperature, triplet-to-singlet energy transfer with 9,lO-dibromoanthracene as acceptor, followed by fluorescence, leads to a readily detectable indirect chemiluminescence (Lechtken et al., 1973; Turro et al., 1974). --

Example 7.16: The experimental results on valence isomerization of benzene can be rationalized by means of correlation diagrams that were first discussed for hexafluorobenzene by Haller (1967). The orbital correlation diagram for the conversion of benzene to dewarbenzene (Figure 7.44a) has been constructed on the basis of a classification of the benzene n MOs according to C,, symmetry. The full symmetry of benzene is D,. The symmetry elements common to both point groups C,, and D, are E, C,, and a,(x,z) = al'),which is the plane through

Table 7.5 Interrelations between Irreducible Representations of Point Croups C , and D ,

ORGANIC PHOTOCHEMISfKY While the electrocyclic ring opening to o-quinodimethanes is the major reaction pathway in the irradiation of substituted benzocyclobutenes (cf. Example 6.14), the irradiation of unsubstituted benzocyclobutene yields 1,2dihydropentalene (119) and 13-dihydropentalene (120) a s major products. The mechanism shown with "prebenzvalene" (118) as primary photochemical intermediate has been proposed to explain the formation of the isomeric dihydropentalenes (Turro et al., 1988). Supporting calculations that yield the same mechanism for the benzene-to-fulvene transformation have been published (Dreyer and Klessinger, 1995).

Figure 7.45. Benzene-prismane valence isomerization; a) orbital correlation diagram (C,, symmetry) and b) state correlation diagram, devised with the help of Table 7.5 and experimental state energies.

atoms C-l and C-4, and d,(yz) or a:1', perpendicular to the former plane. From symmetry behavior with respect to these elements, interrelations between irreducible representations of the two point groups may be derived as indicated in Table 7.5. Making use of experimental singlet and triplet excitation energies and of the relative ground-state energies (cf. Turro et al., 1977b). one can obtain the state correlation diagram of the benzene-dewarbenzene interconversion shown in Figure 7.44b; according to Table 7.5 the 'B,state of dewarbenzene correlates with the 'B,,state of benzene, located 5.% eV above the ground state. This explains why dewarbenzene is formed only by short-wavelength excitation (Scheme 36). In agreement with the ab initio results discussed earlier, both an S 2 4 ,conical intersection and an S , 4 , funnel are easily recognized, although the calculated intersections occur at geometries of lower symmetry, as is to be expected from the discussion in Section 6.2.1. The rearomatization observed on singlet excitation and the adiabatic formation of triplet excited benzene observed for sensitized triplet excitation are apparent from this diagram. It is also seen that correlations can be drawn such that the So and TI lines cross, permitting chemiluminescence to occur. (Cf. Section 7.6.4.) Corresponding correlation diagrams for the benzene-prismane interconversion in Figure 7.45 explain why the direct irradiation of benzene does not produce prismane, while the reverse reaction is quite efficient. Correlation diagrams for the other benzene valence isomerization reactions can be derived in a similar way. (See also Halevi, 1977.)

7.5.4 Di-n-methane Rearrangement 1,4-Dienes and related compounds undergo a photochemical rearrangement reaction known as the di-n-methane or Zimmerman rearrangement (Zimmerman et al., 1966, 1980; Hixson et al., 1973). The reaction occurs also with B,y-unsaturated carbonyl compounds and is then called the oxa-di-nmethane rearrangement. (See Section 7.5.5.) According to Scheme 40, the reaction formally involves a [I ,2] shift, but the second double bond between carbons C-1 and C-2 is apparently also involved in the reaction process. The most favorable structural feature for di-n-methane rearrangement is an interaction of the C-2 and C-4 centers of the I ,4-diene in a way that permits a stepwise reaction involving a I ,4-biradical and a 1,3-biradical, as formulated in Scheme 40. In contrast to experimental results (Paquette and Bay, 1982), a b initio calculations suggested that the 1,4-biradical may be a true intermediate (Quenemoen et al., 1985).

Scheme 40

1.4-Biradlcal

1.3-Blradicai

7.5

However, more recent calculations for the excited-singlet reaction of 1,4pentadiene (Reguero et al., 1993) suggest that the preferred relaxation from S, to So occurs via a funnel that corresponds to a 1,2 shift of a vinyl group (see Section 7.5.2) and produces the 1,3-biradical, avoiding the formation of the 1,4-biradical intermediate altogether. The 1,3-biradical is unstable and undergoes a ground-state barrierless ring-closure process to yield the final vinylcyclopropane product. In particular, three funnels have been found: one structure with both double bonds twisted, which would lead only to cistrans isomerization or back to the starting material (cf. Section 7.1.3); one rhomboidal structure similar to the conical intersection for the ethylene + ethylene [2, + 2,] cycloaddition, which would lead to cycloaddition products or to the I ,4-biradical (which arises from an asynchronous [2 + 21 addition, cf. Section 7.4.2); and the lowest-energy conical intersection (23 kcallmol lower in energy than the first and 31 kcallmol lower than the second), which corresponds to the sigmatropic [1,2] shift and would produce the 1,3-biradical. A ground state reaction path emanating from the geometry of this funnel leads to vinylcyclopropane. From the stereochemistry at C-1 and C-5, it has been concluded that the ring closure occurs in a disrotatory way and anti with respect to the migrating vinyl group, as shown in Scheme 41. Only when the anti-disrotatory ring closure is not possible for steric reasons is a stereochemistry that corresponds to a syn-disrotatory mode of reaction observed.

8, hv

Scheme 41

Both reaction paths that involve breaking of one a and two n bonds and the making of three new bonds are in agreement with the Woodward-Hoffmann rules. According to Figure 7.46, the disrotatory ring closure between C-3 and C-5 requires the orbitals D and F to overlap anti or syn with respect to the bond between C-2 and C-3 which is being cleaved; overlap of orbitals C and B produces the new bond between C-2 and C-4, and orbitals A and E form the new n bond between C-l and C-2. The rearrangement may therefore be formulated as a Qa+ 2,+ 2,1, or a [J, + 3, + ,2,] reaction, for the anti- or syn-disrotatory mode of reaction, respectively. Both cases correspond to ground-state-forbidden, photochemically allowed reactions. The

REARRANGEMENTS

Orbital interactions at the di-n-methane rearrangement a) anti-disrotatory mode (G [J, + 2, + 3 [,2, + 2,]), b) syn-disrotatory mode (e tn2, + 2,+ 2.1, e 3 [J, + 2 3

Figure 7.46.

s,],+

same conclusion may be reached by the observation from Figure 7.46 that the relevant orbitals form a (4N + 2)-Mobius system, since signs of the six orbitals can be chosen in such a way that just one overlap is negative. Inversion of configuration at C-3, which is expected for an anti-disrotatory reaction path, has been observed, for instance, for the acyclic chiral I ,4-diene 121.

The stereochemistry of the di-n-methane rearrangement has thus been shown to be in complete agreement with a concerted reaction course (Zimmerman et al., 1974). The Qa + s , ] or L2, + J,] mode has the same stereochemical consequences. However, this mechanism, which does not involve the n bond between C-1 and C-2, was excluded because no di-n-methane rearrangement is observed upon irradiation of compound 122, which contains only one double bond.

For acyclic and monocyclic 1,4-dienes, the di-n-methane rearrangement occurs in general from the singlet excited state, since loose geometries are favored in the triplet state and cis-trans isomerization is the preferred reaction, as shown in Scheme 42.

ORGANIC PHOTOCHEMISTRY

Scheme 42

For singlet reactions, the direction of ring closure is the one that involves the most stable 1,3-biradical, as shown in Scheme 43. This is equivalent to the assumption that in a concerted mode of reaction the bond between centers C-3 and C-5 is only weakly formed during the initial stages of the reaction.

7.5

REARRANGEMENTS

457

(cf. Scheme 40) occurs during the evolution of the conical intersecction structure toward the 1,3-biradical structure, as was shown by reaction path calculations: the a bond between the two terminal methylene radical centers is formed via a barrierless process on the side of the --CH, fragment opposite to the initial position of attachment of the migrating vinyl radical. The triplet reaction probably proceeds by a different mechanism, likely to involve a I ,Cbiradical intermediate. In an elegant study of the rearrangement of deuterated m-cyanodibenzobarrelene (124) to the corresponding semibullvalene 125, it was in fact shown that the 1 ,Cbiradical is the productdetermining intermediate (Zimmerman et al., 1993).

A large number of rearrangements such as 126 -+ 127 can be classified as belonging to the di-n-methane type even though the molecules do not formally contain a 1 ,4-diene unit, since in these cases an aryl ring can take the place of one of the olefinic bonds. The di-n-methane rearrangement is not confined to acyclic and monocyclic systems. Bicyclic 1,Cdienes such as barrelene (123) also rearrange, but they do so upon triplet sensitization (Zimmerman and Grunewald, 1966). In all probability, the built-in geometry constraint of a bicyclic molecule does not allow for the loose geometries otherwise characteristic of the triplet state, while in the singlet state other reactions such as [2 + 21 cycloaddition predominate.

Substituent effects have been studied in detail and have been rationalized on the basis of the proposed mechanism (Zimmerman, 1980). Example 7.17:

Donor-substituted benzonorbornadienes 128 generally yield the product of a di-n-methanerearrangement corresponding to m-bridging, while acceptor-substituted compounds 129 give the p-bridged product: All these experimental features are consistent with a concerted pathway that passes through a funnel for a [1,2] vinyl shift and leads to the 1,3biradical region (Reguero et al., 1993). First, the regiospecifity is readily rationalized via the different accessibility of the two conical intersections leading to the 1,3-biradicals (Scheme 43): the one with the most stable substituted radical moiety will be lower in energy, and the vinyl radical without radical stabilizing substituents will migrate. Second, the double bond in the migrating vinyl radical retains its original configuration along the excitedstate-ground-state relaxation path. Third, inversion of configuration on C-3

01-:tiANIC PHOTOCHEMISTRY

Figure 7.47.

Orbital ordering in donor- and acceptor-substituted benzenes.

If the triplet states of 128 and 129 involve mainly single configurations with a half-occupied hom*o and a half-occupied LUMO. the pronounced regioselectivity may be rationalized on the basis of an interaction of the half-occupied LUMO of the aromatic moiety with the vacant LUMO of the ground-state ethylene moiety. Substitution removes the degeneracy of the benzene LUMO, and the product formed (meta or para) depends on the magnitude of the LCAO coefficients of the lower of these MOs. From Example 3.10 the @., MO is known to be the LUMO in acceptor-substituted benzenes, while @,,. is the LUMO in donor-substituted benzenes. (Cf. Figure 3.18.) This is shown again in Figure 7.47, together with the labeling of the MOs corresponding to C,, symmetry; in the b, MO the LCAO coefficient of the para position is largest in absolute value, while in the a, MO the meta coefficient is larger than the para coefficient (Santiago and Houk, 1976).

Example 7.18: The complex mechanism of the rearrangement of metacyclophanediene 130 into dihydrocyclopropapyrene 136 was elucidated by Wirz et al. (1984) and is 131 are symshown in Figure 7.48. Valence isomerization of the type 130 metry-allowed ground-state reactions and are extraordinarily fast. The adiabatic formation of 131* was mentioned in Example 6.7.

7.5

REARRANGEMENTS

459

Figure 7.48. Mechanism of the transformation of metacyclophane 130 into dihydrocyclopropapyrene 136 with intermediates 1321133 and 1341135. The suggested position of the original methano bridge is marked by a bullet. The hatched arrows indicate the two-quantum process that occurs at room temperature and does not involve the ground-state intermediate 134 (adapted from Wirz et al., 1984).

Below - 30°C the reaction path consists of a three-quantum process involving two thermally stable, light-sensitive isomers 132 and 134. The first two steps from 130 to 133 may formally be viewed as di-n-methane rearrangements (cf. Scheme 40, the carbon marked with a bullet in Figure 7.48 corresponds to C3 in Scheme 40). while the last step from 134 to 136 represents a [1,7] hydrogen shift. At room temperature the reaction proceeds as a two-quantum process, bypassing the ground-state intermediate 134.

A related reaction, the "bicycle rearrangement," is schematically shown in Scheme 44: A carbon with substituents R'and RZconnected to a n system by two hybrid AOs moves along the molecule as if the hybrid AOs were the wheels and the substituents the handlebars of a bicycle.

An example is the rearrangement of 2-methyleneJ,6-diphenylbicyclo[3.l .O]hexene (137). which yields 1,5-diphenylspiro[2.4]-4,6-heptadiene

460

ORGANIC PHOTOCHEMISTRY

7.5

REARRANCEMENI'S

(138). The shift does not proceed over two bonds as depicted in Scheme 44, but over three bonds (Zimmerman et al., 1971):

The reaction proceeds in the singlet state and is stereospecific in that the configuration of the "handlebars" is retained for migrations of up to three bonds. Both the mechanism of the di-a-methane rearrangement and that of the 2,5-cyclohexadienone rearrangement (dealt with in Section 7.5.9, involve a step that may be formulated as a bicycle rearrangement (Zimmerman, 1982).

7.5.5 Rearrangements of Unsaturated Carbonyl Compounds In addition to the normal photochemical reactions of saturated ketones, P,yunsaturated carbonyl compounds undergo carbonyl migration via a [1,3] shift. Compound 139 in Scheme 45 represents a typical example. Compounds with an alkyl substituent in the /? position such as 140 may also undergo a Norrish type I1 reaction (Kiefer and Carlson, 1%7), while for ketones with electron-rich double bonds such as 141, oxetane formation is also observed (Schexnayder and Engel, 1975).

a Cleavage is much faster for F,y-unsaturated ketones than for saturated ketones. This can be rationalized by the relative stability of the acyl-ally1 radical pair, which can experience an additional stabilization by simultaneous bonding interaction of the acyl radical with the y carbon (Houk, 1976). Whether this interaction is large enough to render the [I ,3] shift a concerted

Figure 7.49. Possible mechanisms of the [I ,3] shift of P,y-unsaturated ketones: a) concerted, b) concerted with inclusion of carbonyl orbitals, c) biradical intermediate, and d) radical pair intermediate (adapted from Houk, 1976).

reaction, or whether a mechanism involving a cleavage and subsequent radical recombination prevails, cannot be generally decided. Four different mechanisms can be envisioned as indicated in Figure 7.49: the [I ,3] shift may be concerted and can be classified either as a [,2, + ,2,] reaction (Figure 7.49a) or with inclusion of the acoand no orbitals in the orbital array (Figure 7.49b). Two stepwise mechanisms, one involving the formation of a biradical, the other of a radical pair, can also be formulated (Figure 7.49c,d). Since the [I ,3] shift is a ground-state forbidden by orbital symmetry, the ground-state surface will have a saddle point at a geometry approximating the transition state of this reaction, while the S, surface will have a minimum or a funnel at a nearby geometry. Thus, whether a biradicaloid intermediate or a radical pair will be involved, or whether the reaction will be concerted, depends on the magnitude of a,y interaction or on the degree to which the crossing is avoided. For the '(n,n*) state of a B,y-unsaturated ketone to undergo radical a cleavage or a [I ,31 shift, the a bond must be approximately parallel to the n orbital, since only then can ally1 resonance stabilize the biradical and the carbonyl orbital overlap with the a system at the y terminus. These geometrical requirements are not fulfilled for the aldehyde 142, and intersystem crossing dominates a cleavage and [I ,3] shift (Baggiolini et al., 1970). The triplet photochemistry of P,y-unsaturated carbonyl compounds depends very much on tl-cir electronic configuration. The '(n,n*) state under-

OIIl A N I C PHOTOCHEMISTRY

7.5

REARRANGEMENTS

463

[I ,3] shift (Barber et al., 1969) has been observed for cyclopentenones (143). Radical stabilizing substituents in the 5-position, as in 144, favor formation of cyclopropyl ketenes (Agosta et al., 1969). goes a [1,3] shift, presumably via a radical pair. In most p,y-unsaturated carbonyl compounds, however, the lowest triplet state is the 3(n,n*) state, for which a [1,2] shift termed the oxa-di-n-methane rearrangement is characteristic (Schaffner and Demuth, 1986). Concerted mechanisms as well as biradical intermediates may be formulated for this reaction, in a way analogous to the di-n-methane rearrangement. Although the problem has not yet been solved generally, evidence in favor of a stepwise reaction path has been obtained-for instance, for the reaction shown in Scheme 46 (Dauben et al., 1976). This contrasts with the corresponding results for the di-n-methane rearrangement of the hydrocarbon 121, which occurs in the singlet state.

Scheme 49

144

' ~ h

For cyclohexenones, only [1,2] shifts are typical. According to Scheme 50, two types of [1,2] shift with ring contraction can occur: one through rearrangement of the ring atoms (type A), the other through migration of a ring substituent (type B) (Zimmerman, 1964): Scheme 48

Because the intersystem crossing probability is low, the triplet reaction can in general be initiated only by sensitization. The difference between singlet and triplet reactions can be utilized synthetically, as indicated in Scheme 47 (Baggiolini et al., 1970; Sadler et al., 1984):

Scheme 47

@gib-sh

~ y pe

R' 'R'

~yp A

Scheme 50

Photochemical ring opening of linearly conjugated cyclohexadienones affords dienylketenes (145), which react in one of the following ways: recyclization to the original or to a stereoisomeric cyclohexadienone, formation of bicyclo[3.l.O]hexenones (146), or addition of a protic nucleophile to yield substituted hexadienecarboxylic acids (147) (Quinkert et al., 1979).

In addition to the reactions discussed in Section 7.4.5, a,&unsaturated ketones undergo isomerization to give the deconjugated p,y-unsaturated compound. According to Scheme 48, this reaction may be analyzed as a Norrish type I1 reaction with cleavage of a n bond instead of a a bond. However, it may also be interpreted as a photoenolization. (Cf. Section 7.5.2.)

Scheme 48

JyeDeyJeJy

Cyclic enones and dienones undergo a number of photorearrangements. As indicated in Scheme 49, both ring contraction via a [1,2] shift (Zimmerman and Little, 1974) and formation of cyclopropanone derivatives via a

In addition to these reactions typical of the '(n,n*) state, 6-acetyloxycyclohexadienones (0-quinol acetates) form phenols from the 3(n,n*)state. These results are summarized in Figure 7.50 (Quinkert et al., 1986). Dienylketenes are produced irrespective of whether irradiation occurs into the n-n* or n-n* band, and phenols can be formed not only through triplet

464

ORGANIC PHOTOCHEMISTRY

OAc

.XYCH3

Figure 7.50. Schematic state correlation diagram for o-quinol acetate photoreactions. Wavy arrows designate physical as well as chemical radiationless processes (by permission from Quinkert et al., 1986).

sensitization (ET > 42 kcal/mol, corresponding to the Yrc,n*)state), but also by extended direct irradiation in aprotic solvents if the quinol acetate is regenerated from the kinetically unstable dienylketene.

7.6 Miscellaneous Photoreactions 7.6.1 Electron-Transfer Reactions

7.6

MISCELLANEOUS PHOTOREACTIONS

465

From Scheme 51 it is seen that an exciplex with a certain degree of charge-transfer character can be formed either from an excited donor molecule ID* and an acceptor molecule 'A or from an excited acceptor molecule 'A* and a donor molecule ID. Both alternatives have been observed experimentally. Thus, the use of diethylaniline as donor and either biphenyl or anthracene as acceptor yields exciplexes that can be identified by the typical structureless fluorescence at long wavelengths. This corresponds to the two possibilities depicted in Figure 5.25a and b, excitation of the donor in the first case and of the acceptor in the second case. The charge-transfer character of the complex causes the wavelength of its fluorescence to be highly sdvent dependent, and the value of p = 10 D has been derived for the dipole moment (Beens et at., 1967). Electron transfer then gives a radical ion pair ( D e A e ) , which for k, > k, decays to the reactants by back electron transfer; this corresponds overall to an electron-transfer quenching. (Cf. Section 5.4.4.) However, if fast secondary reactions lead to product formation, k, %k,, the process becomes a photoinduced electron-transfer reaction, and this can be utilized synthetically. Example 7.19: As an example, photochemical excitation of donor-acceptor complexes may be considered. Irradiation into the CT band of the anthracene-tetracyanoethylene complex leads directly to the radical ion pair, the components of which are identifiable from their UV-visible spectra. The transient absorptions decay in -60 ps after excitation, as the radical ion pairs undergo rapid back electron transfer to afford the original donor-acceptor complex (Hilinski et al., 1984). With tetranitromethane as acceptor, however, an addition product is obtained in both high quantum and chemical yield. This is due to the fact that the tetranitromethane radical anion undergoes spontaneous fragmentation to a NO2 radical and a trinitromethyl anion, which is not able to reduce the anthracene radical cation (Masnovi et al., 1985):

It has become evident only fairly recently that photochemical electron-transfer processes (PET) play an important role in many reactions. In this connection it is of great importance that in an excited state a molecule can be a better oxidant as well as a better reductant than in the ground state. For instance, after H O M b L U M O excitation the half-occupied hom*o can readily accept another electron, while the single electron from the LUMO can readily be transferred to an acceptor. (Cf. Figure 5.25.)

A detailed study showed that after dissociation of the radical anion a contact ion pair [Dm C(NO,)f)] in a solvent cage is initially formed. It transforms into

OK(;ANIC PHOTOCHEMISTRY a solvent-separated ion pair within a few ps, which in turn converts into the free ions within a few ns. Both processes follow first-order kinetics. The free ions then form the adduct in a second-order process (Masnovi et al., 1985).

The photoreduction of carbonyl compounds or aromatic hydrocarbons by amines was one of the early electron-transfer reactions to be studied. Observation of products from primary electron transfer depends on the facility of a deprotonation of the amine, which must be fast compared to back electron transfer. For amines without a hydrogens, quenching by back electron transfer is observed exclusively (Cohen et al., 1973). The solvent plays a quite important role since it determines the yield of radical ion pairs formed from the exciplex (Hirata and Mataga, 1984). As a typical example the photoreduction of naphthalene by triethylamine (Barltrop, 1973) is shown in Scheme 52. The radicals generated by a deprotonation couple to the products 148 and 149, and disproportionate to the reduction product 150.

7.6

more readily from the conformationally favored transition state 152 rather than from 153 (Lewis et al., 1981):

While electron-transfer reactions of aromatic hydrocarbons are in general reactions of the (n,n*) state, electron transfer in carbonyl compounds can be into the (n,n*) as well as into the (n,n*) state. Correlation diagrams may be constructed for these reactions and are fully equivalent to the corresponding diagrams for hydrogen abstraction. (Cf. Section 7.3.1 .) From such diagrams it is, for instance, evident that coplanar electron transfer (attack of the amine within the plane of the carbonyl group) is symmetry allowed in the (n,n*) state but symmetry forbidden in the (n,rt*) state. Photoreduction of benzophenones and acetophenones by amines has been studied in detail. A mechanism has been derived for the reaction of benzophenone with N,N-dimethylaniline that involves a triplet exciplex in the formation of the radical ion pair, as indicated in Scheme 49.

t PhN(CH& 140

Scheme 52

With singlet excited trans-stilbene (151) and tertiary alkyl amines only products characteristic for radical coupling are observed (Lewis et al., 1982).

With unsymmetrical trialkylamines selective formation of the least-substituted a-amino radical is observed. The, stereoselectivity is thought to be stereoelectronic in origin, as can be most easily seen in highly substituted amines such as diisopropylmethylamine, where a deprotonation occurs

467

MISCELLANEOUS PHOTOREACTIONS

+ Ph2C=0

.O P~N(CHJ),

+ P~,CO 0

Scheme 53

Subsequent proton transfer yields the ketyl radical and the usual products. (Cf. Section 7.3.1.) This mechanism was confirmed by CIDNP measurements. At the same time it was proven that on excitation of the amine, electron transfer occurs from the singlet excited amine to the ground-state ketone (Hendricks et al., 1979). The exact time scale for those processes that follow the electron transfer was studied by picosecond spectroscopy (Peters et al., 1982). Photochemical addition reactions may also occur as electron-transfer reactions involving a radical ion pair. An illustrative example is the photochemical reaction of 9-cyanophenanthrene(154) with 2,3-dimethyl-2-butene, which, in nonpolar solvents, gives good yields of a [2 + 21 cycloadduct via a singlet exciplex, while in polar solvents radical ions are formed in the primary photochemical process. The olefin radical cation then undergoes deprotonation to yield an allyl radical or suffers nucleophilic attack by the solvent to produce a methoxy alkyl radical. Coupling of these radicals with

468

ORGANIC PHOTOCHEMISTRY

7.6

MISCELLANEOUS PHOTOREACTIONS

the aromatic radical anion produces acyclic adducts such as 156 in addition to the cycloaddition and reduction products (Lewis and Devoe, 1982).

Formation of cycloadducts can be completely quenched by conducting the experiment in a nucleophilic solvent. This intercepts radical cations so rapidly that they cannot react with the olefins to yield adducts. In Scheme 54 the regiochemistry of solvent addition to 1-phenylcyclohexene is seen to depend on the oxidizability or reducibility of the electron-transfer sensitizer. With I-cyanonaphthalene the radical cation of the olefin is generated, and nucleophilic capture then occurs at position 2 to afford the more stable radical. Electron transfer from excited 1,4-dimethoxynaphthalene, however, generates a radical anion. Its protonation in position 2 gives a radical that is oxidized by back electron transfer to the sensitizer radical before being attacked by the nucleophilic solvent in position 1. Thus, by judicious choice of the electron-transfer sensitizer, it is possible to direct the photochemical addition in either a Markovnikov (157) or anti-Markovnikov (158) fashion (Maroulis and Arnold, 1979).

Electron transfer can also induce valence isomerizations such as the transformation of hexamethyldewarbenzene (159) to hexamethylbenzene. The quantum yield of this reaction is larger than unity; a chain reaction mechanism is therefore assumed (Jones and Chiang, 1981).

Spectroscopic studies with photo-CIDNP techniques revealed the existence of two distinct radical cations generated from hexamethyldewarbenzene, presumably rapidly interconverting. In one of these, the central carbon-carbon bond is significantly stretched and bears the unpaired spin density. In the second. the spin density is confined to one of the olefinic bonds. This example is the first to show conclusively that two different radical ion structures can correspond to a single minimum on the ground-state surface of the neutral (Roth et al., 1984). Quadricyclanes (160) also undergo a valence isomerization to norbornadienes if irradiated in the presence of electron acceptors such as fumaronitrile (Jones and Becker, 1982). Two distinct radical cation structures are observed for the hydrocarbon, corresponding roughly to the bonding patterns of norbornadiene and quadricylane, respectively (Roth et al., 1981).

Quadricyclane in Csl or KBr matrices, prepared by deposition in the salt under conditions that yield single-molecule isolation, is rapidly converted into norbornadiene under conditions that induce color center formation in the alkali halide: rapid-growth vapor deposition, or U V or X-ray irradiation. The reaction proceeds only at temperatures at which color centers of the "missing electron" type (H center) are mobile. At lower temperatures (T < 90 K), UV irradiation of norbornadiene converts it into quadricyclane in the usual fashion (Kirkor et al., 1990). The electron-transfer sensitized interconversion of trans- (161) and cis1.2-diphenylcyclopropane (162) (Wong and Arnold, 1979) is thought to proceed via the radical ion pair from which back electron transfer generates a triplet biradical that undergoes geometric isomerization; the corresponding ring-opened radical cations 163are conformationally stable (Roth and Schilling, 1981). Cycloadditions of carbonyl compounds to olefins generally involve exciplexes and biradicals. (Cf. Section 7.4.4.) While normal olefins frequently yield a number of products, photoinduced electron transfer may be utilized in the case of electron-rich olefins to influence the regioselectivity. Thus, irradiation of the ketene acetal 165 and biacetyl (164) yields exclusively the oxetane 167. Since the radical cation 166 could be trapped, electron transfer

OKtiANIC PHOTOCHEMISTRY

470

7.6

MISCELLANEOUS PHOTOREACTIONS

is assumed to be the photochemical primary step. As the regioisomeric oxetane 168 is generated by a thermal process involving a dipolar intermediate, this reaction constitutes a case of reversal ("Umpolung") of the carbonyl reactivity by photoinduced electron transfer (Mattay et al., 1984a).

6~ Ph Scheme 56

In the photoinduced singlet dimerization of indene shown in Scheme 55, the endo head-to-head dimer expected from the more favorable excimer geometry is the preferred product. With electron-transfer sensitization, the less sterically hindered exo head-to-head dimer is formed (Farid and Shealer, 1973).

Scheme 55

170

The [4 + 21 cycloaddition of electron-rich dienes to electron-rich dienophiles in nonpolar solvents can be catalyzed by electron-poor arene sensitizers (Calhoun and Schuster, 1984). The proposed mechanism involves a triplex (ternary complex) formed by the reaction of the diene with an exciplex composed of the sensitizer and the dienophile. Using a chiral sensitizer, ( - )-I, 1 '-bis(2,4-dicyanonaphthyl), an enantioselective cycloaddition was observed as shown in Scheme 57. In the case of 1,3-cyclohexadiene and trans-/?-methylstyrene, the enantiomeric excess was 15 2 3% (Kim and Schuster, 1990). (Cf. the enantioselective cis-trans isomerization via a triplex discussed in Section 7.1.2.)

Besides cyclobutane formation, alternative ring closures are sometimes observed. One example is the 9,lO-dicyanoanthracene sensitized dimerization of 1,l-diphenylethylene (169). The six-membered ring is formed via the 1 ,4-radical cation, which results from the addition of the free radical cation to diphenylethylene as indicated in Scheme 56, while the l,4-biradical generated by back electron transfer from the radical ion pair yields tetraphenylcyclobutane (170) (Mattes and Farid, 1983).

Products resulting from photolysis of alkyl iodides indicate that according to Scheme 58 hom*olysis of the C-X bond is followed by electron transfer, which results in an ion pair in a solvent cage (Kropp, 1984). In the case of norbornyl iodide (171) and other bridgehead iodides, bridgehead cations re-

ORGANIC PHOTOCHEMISTRY

472

sult; these are difficult to obtain from solvolytic reactions. In other cases Wagner-Meerwein rearrangements of the ionic intermediates have been observed.

OCH,

Scheme 58

A particularly important photoinduced electron-transfer process occurs in photosynthesis in green plants. The overall process amounts to the splitting of water by sunlight into oxygen and metabolically bound hydrogen, and this forms the basis for the existence of higher organized living systems on earth (Kirmaier and Holten, 1987; Feher et al., 1989; Boxer, 1990). In contrast to simpler photosynthetic bacteria that have only one photosystem and are not able to oxidize water, two quanta of light are used by plants to split water by means of two photosystems (PS I and PS 11). This proceeds via a sequence of redox processes, indicated schematically in Figure 7.5 1. Photosynthesis may be formally described as charge separation induced by electron transfer with the positive charge (electron defect) being used for

PS 1

("P700") @--

-----r

7.6

MISCELLANEOUS PHOTOREACTIONS

473

oxidation of H,O (or H,S) and the negative charge for reduction of CO,, according to the overall equation

However, the saccharides (CH20), are not produced by the photoreaction but by a subsequent dark reaction of the photochemically generated hydrogenated nicotinamide adenine dinucleotide phosphate (172) (NADPB-H,). The energy absorbed by pigment-protein complexes in the light-gathering antennae, which also contain carotenoids as triplet quenchers, is transferred to the photochemically active reaction center and produces the excited singlet state of pigment P680 absorbing at 680 nm, which constitutes a special dimer complex of chlorophyll a (173) referred to as the special pair. The oxidation potential of excited P680 is sufficient to remove one electron from water; an electron is transferred from the excited special pair, via a primary electron acceptor, possibly a pheophytin a molecule (an Mg-free chlorophyll a), to a plastoquinone (174). From Figure 7.52 it is seen that after these two electron-transfer processes the ground state of P680 is regenerated; P680 thus acts as a photocatalyst for the transfer of an electron from water to plastoquinone.

"P 870"

H20 oxidation

PS2 ("P680") Figure 7.51. Schematic representation of charge separation in the photosynthetic cycle a) in green plants involving photosystems PS I1 and PS I and b) in photosynthetic active bacteria (by permission from Rettig, 1986).

(In bacteriochlorophyll C3 carries a COCHI group and the C7-C8 double bond is hydrogenated)

Plastoquinone in turn is a reductant for excited WOO of photosystem PS I, which operates similarly to the system PS I1 and has a reduction potential sufficient for an electron transfer to the iron-sulfur complex of ferredoxin and finally to N A D P . producing [emailprotected].

ORGANIC PHOTOCHEMISTRY

- -

Chl a*

I +'- - - -+3' H20

+ S t + H~O?

Chl a

7.6

MISCELLANEOUS PHOTOREACTIONS

475

in meta positions, and strong electron-releasingsubstituents such as 4 C H 3 behave as activating substituents and direct incoming nucleophiles to the ortho and para positions. The photoreactions of the three nitroanisoles with @CN are collected in Scheme 59 to illustrate this behavior (Letsinger and McCain, 1969).

PQ?

Redox process of photosystem PS I1 during electron transfer from water to plastoquinone.

Figure 7.52.

The protein matrix essentially determines the properties and the n-electron redox chemistry of the reaction center and has to be considered an apoenzyme of this functional unit. The geometrical arrangement of the chromophores in the reaction center of the purple bacterium Rhodopseudomonas viridis has been elucidated using X-ray crystallographic analysis (Deisenhofer et al., 1985). On the basis of these structures, several mechanisms have been proposed to explain the primary electron-transfer event (Bixon et al., 1988; Bixon and Jortner, 1989; Marcus, 1988). The special pair in this system consists of a bacteriochlorophyll dimer that transfers an electron from the excited singlet state via a bacteriopheophytin to an ubiquinone (175). The high symmetry of this arrangement and the small overlap of the chromophores in the reaction center are apparently essential for the high efficiency of the system, as has been concluded from a comparison with TICT states, or "sudden polarization" states (cf. Section 4.3.3) (Rettig, 1986). In solution, electron transfer from a metal porphyrin to benzoquinone is, in fact, efficient only in the triplet state, and in the singlet state back electron transfer predominates (Huppert et al., 1976). INDOIS calculations demonstrate that the observed charge separation can be reproduced only by including the effects of the protein; utilizing the selfconsistent reaction field solvent model dramatically lowers the energy of all the charge-transfer states (Thompson and Zerner, 1991).

7.6.2 Photosubstitutions Many aromatic compounds undergo heterolytic photosubstitution on irradiation. Nucleophilic aromatic substitutions are particularly frequent. The orientation rules are reversed compared to those known for ground-state reactivity; that is, electron-withdrawing substituents orient incoming groups

Aromatic photosubstitution can proceed by various mechanisms. Electron-withdrawing substituents presumably include a S,2 3Ar*mechanism involving a a complex of the triplet excited aromatic moiety with the nucleophile, as indicated in Scheme 60.

Scheme 60

This mechanism has been proven conclusively for the CH30@exchange reaction of nitroanisoles and similar compounds. Attack by the nucleophile occurs at the position with the highest calculated positive charge in the triplet state. The directing effect of the nitro group can also be described by hom*o and LUMO charge densities but the activating influence is difficult to rationalize on the basis of charge densities. This has been explained by the fact that the excited triplet and the ground-state potential energy surfaces are particularly close to each other at the geometry of the a complex for meta substitution, which is very unfavorable in the ground state (Van Riel et al., 1981). The activating effect of methoxy groups and similar substituents has been explained by an SRoNljAr* mechanism with the formation of a radical cation through electron transfer as the principal step as shown in Scheme 61 (Havinga and Cornelisse, 1976):

ORGANIC PHOTOCHEMISTRY

7.6

MISCELLANEOUS IJHOI'OKEACI'IONS

Route I:

Scheme 61

Route II:

For halobenzenes an SRoNlAr* mechanism with the formation of a radical anion by electron transfer as shown in Scheme 62 has been discussed (Bunnett, 1978):

Aliphatic and alicyclic molecules such as cyclohexane undergo photosubstitution with nitrosyl chloride (Pape, 1967). The reaction is of considerable industrial importance in the synthesis of E-caprolactam, an intermediate in the manufacture of polyamides (nylon 6). (Cf. Fischer, 1978.) At long wavelengths a cage four-center transition state between alkane and an excited nitrosyl chloride molecule is involved, as indicated in Scheme 63. In contrast to light-induced halogenation, photonitrosation has a quantum yield smaller than unity, and is not a chain reaction.

Scheme 83

7.6.3 Photooxidations with Singlet Oxygen Under photochemical conditions oxygen can insert itself into a substrate with the formation of hydroxyhydroperoxides (176), hydroperoxides (177), peroxides (178), and dioxetanes (179). There are essentially two different reaction courses, involving either a photochemically generated radical reacting with ground-state oxygen or a ground-state substrate molecule reacting with singlet oxygen. (Cf. Example 7.20.) Some typical examples are summarized in Scheme 64.

Formation of endoperoxides of type 178 can be interpreted as a + ,?,I cycloaddition that involves singlet oxygen and therefore constitutes a photochemical reaction. Similarly, formation of hydroperoxides from nonconjugated olefins with an allylic hydrogen generally appears to be a concerted ene reaction as indicated in Scheme 65. Other mechanisms have

k4,

(

478

) I . II\IVIC I7 I 0 10CHCILIIb I KL

been proposed, and according to Scheme 65 involve a biradical or a perepoxide 180. Ab initio calculations favor the biradical mechanism, at least in the gas phase (Harding and Goddard 111, 1980), while semiempirical calculations suggest the perepoxide to be a genuine intermediate (Dewar and Thiel, 1977). Reactions of singlet oxygen are characterized by low activation energies and very fast reaction times. Therefore, a detailed mechanism is in general difficult to establish. Many experimental findings suggest, however, that an interaction with charge-transfer character occurs at the initial stages of reaction, with the stereochemistry given by the hom*o of the olefin as the electron donor and the n* LUMO of the oxygen (Stephenson et al., 1980). This is exemplified in Scheme 66 for the hom*o-LUMO interaction of 2-butene with oxygen.

7.6

MISCELLANEOUS PHOTOREACTIONS

St ate

Complex Orbitals

Real Orbitals

Figure 7.53. Spin-orbital diagrams for the lowest molecular oxygen states (by permission from Kasha and Brabham, 1979).

Scheme 6c

Some substituted alkenes react with singlet oxygen to form a dioxetane in a [ J , + ,2,] cycloaddition reaction. Most dioxetanes readily decompose to carbonyl compounds in an exothermic reaction that is accompanied by a bluish luminescence. The chemiluminescence will be dealt with in more detail in Section 7.6.4.

Example 7.20: The ground state of molecular oxygen is a 'I:; state according to Hund's rule, and the MOs n, and n,,, which are degenerate by symmetry, are singly occupied by electrons with parallel spin. The corresponding singlet state 'X: is higher in energy by 35 kcallmol. Between these two I: states there is a degenerate 'A8 state, 22 kcallmol above the 'I:; ground state. This 'Agstate is generally referred to as singlet oxygen. The description of these states becomes particularly intelligible if it is recognized that the 0, molecule is a perfect axial biradical. especially if the symmetry-adapted complex n MOs n , = (JZ,+ in,)/ and n = (n,- in,)lfi are used. Figure 7.53 gives a schematic representation of the wave functions of the lowest states of molecular oxygen expressed in terms of complex and real orbitals, with MOs doubly occupied in all states not shown. In an axial biradical, all possible real combinations of the degenerate orbitals are localized or delocalized to the same degree. (Cf. Section 4.3.2.) Potential energy curves of molecular oxygen are shown in Figure 7.54.

Figure 7.54. Potential energy curves for the lowest molecular oxygen states (adapted from Herzberg, 1950).

ORGANIC PHOTOCHEMlSTRY

480

7.6

MISCELLANEOUS I'HUI'OKEAC'I'IONS

Singlet oxygen can be generated either by thermal or by photochemical methods. The most general and synthetically useful method is photosensitization with a strongly absorbing dye such as Rose Bengal or methylene blue, which can be used advantageously as a polymer-bound sensitizer (Schaap et al., 1975). Singlet oxygen is generated by triplet-triplet annihilation according to Sens + hv + 'Sens* -,3Sens* 'Sens* + '0, + Sens + '0, The thermal generation of singlet oxygen from hydrogen peroxide and hypochlorite presumably involves the chloroperoxy anion; other synthetically useful examples involve decomposition of phosphite ozonides or endoperoxides, as indicated in Scheme 67 (cf. Murray, 1979).

Figure 7.55.

Orbital correlation diagram for endoperoxide formation.

Figure 7.56.

Schematic state correlation diagram a) for a singlet photoreaction and

Example 7.21: The orbital correlation diagram for the [4 is shown in Figure 7.55 for the reaction

+ 21 cycloaddition of singlet oxygen

The ordering of the reactant orbitals is obtained from ionization potentials of molecular oxygen and butadiene. The reactant configuration with singly occupied MOs $ and ('0,)correlates with a highly excited product configuration, while the configuration with doubly occupied or MOs correlates with the product peroxide in'the ground state. Due to perturbation by the reaction partner, the configuration develops as the reaction proceeds.

< ~

7.6.4 Chemiluminescence From the schematic representation in Figure 7.56 it is seen that chemiluminescence can be described as a reverse photochemical reaction. Chemiluminescence is afforded by a transition from the ground-state potential energy surface to an isoenergetic vibrational level of an excited-state surface and

b) for a singlet chemiluminescent process.

7.6

by escape over a small barrier into a deeper well. If the separation of the ground-state and excited-state surfaces has increased in the process as shown in Figure 7.46b, the resulting excited molecule can reveal its presence by emission. Oxidation of luminol (see Example 7.22) and thermolysis of endoperoxides or I ,Zdioxetanes provide important examples of chemiluminescent reactions. Tetramethyl-1,Zdioxetane(181) has been studied in great detail; the thermolysis is clearly first order and the activation enthalpy in butyl phthalate is AHS= 27 kcallmol. The enthalpy difference between the reactants and ground-state products is AH,, = -63 kcallmol.

The sum -AH,, + AHt is greater than the excitation energies of the TI (n,n*) state (A& = 78 kcallmol) as well as the S, (n,n*) state (AEs = 84 kcallmol) of acetone. Both states can be formed exothermally from the transition state for thermolysis (Lechtken and Hohne, 1973). It could be shown independently that triplet excited acetone ()A*) is produced directly with a quantum yield Q, = 0.5. Singlet excited acetone ('A*) is formed with a quantum yield = 0.005.

MISCELLANEOUS PHOTOREACTIONS

483

These results have been rationalized by means of the correlation diagram shown in Figure 7.57 (Turro and Devaquet, 1975). The ground state of tetramethyl-1,tdioxetane correlates with a doubly n+n* excited state of the supermolecule consisting of two acetones, while the ground state of the latter correlates with a doubly v d r excited state of the dioxetane. The (n,n*) states of acetone will correlate directly with excited dioxetane states of appropriate symmetry, probably with the (n,dr) states, which are antisymmetric with respect to the reaction plane. The crossing between So and T, will be weakly avoided due to spin-orbit coupling, and a "surface jump" to the TI product surface ('A* + A,) can occur. The origin of spin-orbit coupling that makes the crossing avoided may be visualized by means of the schematic diagram given in Figure 7.57, which represent the electronic structure of the reaction complex for different stages of the reaction: To the left of the transition state, the 0-0 bond has lengthened with the "unpaired" electrons in orbitals of a symmetry; at the product side, however, one of the unpaired electrons is in a n* MO of one of the carbonyl groups. That a reaction of the type So+ TI + Sois not observed may be due to the fact that the first crossing can be reached many times until spin inversion finally takes place, while the second crossing is passed only once. Probabilities are therefore much lower for the TI -* Sotransition than for the So+ T, transition. The situation is somewhat different in the case of dewarbenzene, which undergoes an electrocyclic ring opening to give triplet excited benzene. (Cf. Example 7.16.) In contrast to I ,2-dioxetanes, this reaction possesses a very low chemiluminescence efficiency. The reason is thought to be the low intersystem crossing probability, which is due to the very weak spin-orbit coupling inherent in hydrocarbon systems. Thus, although the available energy is very favorable for chemiluminescence, the rearrangement proceeds as a ground-state reaction. Example 7.22: It is generally agreed that the excitation-producing step in the oxidation of luminol(182) is decomposition with loss of nitrogen of the dianion of an azoendoperoxide produced by the action of a base and oxygen:

Figure 7.57. State correlation diagram for the chemiluminescence reaction of tetramethyl-] ,Zdioxetane (by permission from Turro, 1978).

This can be viewed as an allowed [2, + 2, + 2,J pericyclic reaction, and it is not obvious that there should be an avoided or unavoided touching of Sowith S, that could provide an easy "surface jump" to the S, surface along the way.

484

ORGANIC PHOTOCHEMISTRY

The following alternative mechanism may well provide an explanation of luminol chemiluminescence:

The first step is analogous to the easy retro-Diels-Alder reaction of 1.4-dihydrophthalazine (183). whose A I F is 15 kcavmol (Flynn and Michl, 1974). The ground state of the resulting energy-rich peroxide dianion has 18 n electrons. Stretching of the 0-0 bond converts it into a much more stable aminophthalate dianion product, whose ground state, however, has only 16 n electrons. It therefore does not correlate with the ground state, but with a doubly n-dc excited state of the peroxide. The 18 n-electron ground state of the peroxide correlates with a doubly n-n* excited state of the aminophthalate dianion product. At high symmetries, the crossing of the two states will be avoided. In the first approximation, the splitting will be given by twice the exchange integral between the two orbitals that cross (cf. Section 4.2.3). One of these is a

415

SUPPLEMENTAL READING

n-type orbital, the other an n-type orbital, and the overlap density and the exchange integral will therefore be only very small. It is likely that an S , S , conical intersection can be reached when the symmetry is lowered, and this ought to provide a facile radiationless crossing between the two surfaces as indicated in Figure 7.58 (Michl, 1977).

Several additional chemiluminescence mechanisms have been described, which are based on excited-state generation by electron transfer in a radical ion pair according to where D@ + A- constitutes an excited state of the system D + A. The radical ion pair may be produced either electronically or chemically by electron transfer to a peroxide that subsequently rearranges and loses a neutral molecule. An example of this CIEEL (chemically induced electron-exchange luminescence) mechanism is provided by the thermal reaction of diphenoyl peroxide (184) (Koo and Schuster, 1977):

184

ACT = activator, for example, aromatic hydrocarbon.

Supplemental Reading Barltrop, J.A., Coyle, J.D. (1975),Excited States in Organic Chemistry; Wiley: London. Coyle, J.D., Ed. (1986), Pholochemistry in Organic Synthesis, Special Publ. 57; The Royal Soc. Chem.: London. Cowan, D.O., Drisko, R.L. (1976). Elerrrents New York.

c?f

Organic Photochemistry; Plenum Press:

Coxon, J.M., Halton, B. (1974), Organic Photochemistry; Cambridge University Press: Cambridge. Gilbert, A., Baggott, J. (1991). Essentials of Molecular Photochemistry; CRC Press: Boca Raton. Horspool, W.M., Ed. (1984). Synthetic Organic Photochemistry; Plenum Press: New York. Reactant

Product

Figure 7.58. Schematic state correlation diagram for the chemiluminescence of a strongly exothermic reaction forbidden in the ground state (adapted from Michl, 1977).

Kagan. J. (1993), Organic Photochemistry: Principles and Applications; Academic Press: London. Kopecky, J. (1992), Organic Photochemistry: A Visual Approach; VCH: New York Ramamurthy, V.,Turro, N.J.,Eds. (1993). "Photochemistry," thematic issue of Chem. Rev. 93, 1-724.

486

UI, I;IWIC PHOTOCHEMISTRY

Scaiano, J.C., Ed. (1989), Handbook of Organic Photochentistry; CRC Press: Boca Raton, Vols. I and 11.

Houk, K.N. (1976). "The Photochemistry and Spectroscopy of B,y-Unsaturated Carbonyl Compounds," Chem. Rev. 76. I .

Turro, N.J. (1978), Modern Molecular Photochemistry; BenjaminICummings Publ.: Menlo Park.

Kramer, H.E.A. (1990). "Salicylates, Triazoles, Oxazoles," in Photochromism, Molecules and Systems; Durr, H., Bouas-Laurent, H., Eds.; Elsevier: Amsterdam.

Wayne, R.P. (19881, Principles and Applications of Photoclremistry; Oxford University Press.

Sammes, P.G. (1986), "Photoenolization." Acc. Chem. Res. 4, 41.

Collin, G.J. (1987). "Photochemistry of Simple Olefins: Chemistry of Electronic Excited States or Hot Ground State?", Adv. Photochem. 14, 135.

Schuster. D.I. (1980). "Photochemical Rearrangements of Enones," in Rearrangements in Ground and Excited States, 3; de Mayo, P., Ed.; Academic Press: New York.

Dauben, W.G., McInnis, E.L., Michno, D.M. (1980). "Photochemical Rearrangement in Trienes," in Rearrangements in Ground and Excited state.^. 3; de Mayo. P., Ed.; Academic Press: New York.

Turro. N.J., Dalton, J.C., Dawes, K., Farrington, G., Hautala, R., Morton. D., Niemczyk, M., Schore, N. (1972)- "Molecular Photochemistry of Alkanones in Solution: a-Cleavage, Hydrogen Abstraction, Cycloaddition, and Sensitization Reactions," Acc. Chem. Res. 5, 92.

Gorner, H., Kuhn. H.J. (1995). "Cis-trans Photoisomerization of Stilbene and Stilbene-Like Molecules," Adv. Photochem. (Neckers, D.C., Volman, I1.H.. von Bunau, G., Eds.) 19, 1. Jacobs, H.J.C.. Havinga, E. (1979). "Photochemistry of Vitaniin D and Its Isomers and of Simple Trienes," Adv. Photochem. 11,305. Saltiel, J.. Sun. Y.-P. (1990). "Cis-trans Isomerization of C=C Double Bonds," in Photochromism, Molecules and Systems; Dilrr. H.. Bouas-Laurcnt, H., Eds. ; Elsevier: Amsterdam. Saltiel, J.. Sun, Y.-P. (1989). "Application of the Kramers Equation to Stilbene Photoisomerization in n-Alkanes Using Translational Diffusion Coefficients to Define Microviscosity," J. Phys. Chem. 93, 8310.

Azoalkanes and Azomethines Adam, W., De Lucchi, 0. (1980). "The Synthesis of Unusual Organic Molecules from Azoalkanes." Angew. Chem. Int. Ed. Engl. 19, 762.

Schaffner, K., Demuth, M. (1980). "Photochemical Rearrangements of Conjugated Cyclic Dienones," in Rearrangements in Ground and Excited States. 3; de Mayo, P., Ed.; Academic Press: New York.

Wagner, P.J. (1980). "Photorearrangements via Biradicals of Simple Carbonyl Compounds," in Rearrangements in Ground and Excited States. 3; de Mayo, P., Ed.; Academic Press: New York. Wagner. P.J., Park. B.-S. (1991). "Photoinduced Hydrogen Atom Abstraction by Carbonyl Compounds." Org. Photochem. (Padwa, A., Ed.) 11, I I!.

Photocycloadditions Arnold, D.R. (1968). "The Photocyloaddition of Carbonyl Compounds to Unsaturated Systems: The Syntheses of Oxetanes," Adv. Photochem. 6, 301. Becker, H.-D. (1990). "Excited State Reactivity and Molecular Topology Relationships in Chromophorically Substituted Antracenes," Adv. Photochem. 15, 139. Bernardi, F., Olivucci, M.. Robb, M. A. ( 1990). "Predicting Forbidden and Allowed Cycloaddition Reactions: Potential Surface Topology and Its Rationalization," Acc. Chem. Res. 23,405.

Durr, H., Ruge, B. (1976). "Triplet States from Azo Compounds," Topics Curr. Chem. 66, 53. Engel. P.S. (1980), "Mechanism of the Thermal and Photochemical Decomposition of Azoalkanes," Chem. Rev. 80.99.

Bouas-Laurent. H.. Desvergne, J.-P. (1990). "Cycloaddition Reactions Involving 4n.Electrons: [4 41 Cycloaddition Reactions Between Unsaturated Conjugated Systems," in Photochromism. Molecrtlrs and Systems; Diirr. H., Bouas-Laurent, H., Eds.; Elsevier: Amsterdam.

Meier, H.. Zeller, K.-P. (1977). "Thermal and Photochemical Elimination of Nitrogen," Angent. Chem. Int. Ed. Engl. 16,835.

Caldwell, R.A., Creed, D. (1980). "Exciplex Intermediates in [2 Acc. Chem. Res. 13,45.

Paetzold, R., Reichenbticher, M. Appenroth, K. (1981). "Die Kohlenstoff-Stickstoff-Dop pelbindung: Spektren, Struktur, thermische und photochemische EIZ-lsomerisierung," Z. Chem. 12.42 1.

Cornelisse, J. (19931, "The Meta Photocycloaddition of Arenes to Alkenes," Chem. Rev. 93,615.

Rau, H. (1990). "Azo Compounds" in Photochromism. Molec.rrles and Systems; DOrr. H.. Bouas-Laurent, H., Eds.; Elsevier: Amsterdam. Wentrup. C. (1984). Reactive Molecules; Wiley: New York.

Carbonyl Compounds Cohen, S.G., Parola, A., Parsons Jr., G.H. (1973). "Photoreduction by Amines." Chem. Rev. 73, 141.

+ 21 Photocyloadditions,"

Crimmins, M.T. (1988). "Synthetic Applications of Intramolecular Enone-Olefin Photocycloadditions," Chem. Rev. 88. 1453. Desvergne, J.-P.. Bouas-Laurent. H. (1990). "Cycloaddition Reactions Involving 4n Electrons: [2 + 21 Cycloadditions; Molecules with Multiple Bonds Incorporated in or Linked to Aromatic Systems," in Photochromism, Molecrtles and Systems; Durr, H., BouasLaurent, H., Eds.; Elsevier: Amsterdam. Jones, 11. G. (1990). "Cycloaddition Reactions Involving 4n Electrons: [2 + 21 Cycloadditions; Photochemical Energy Storage Systems Based on Reversible Valence Photoiso-

ORGANIC PHO'I'OCHEMISTRY SUPPLEMENTAL READING merization" in Photochromism, Molecules und Systems; Diirr, H., Bouas-Laurent, H., Eds.; Elsevier: Amsterdam.

489

Photosubstitution

Laarhoven. W.H. (1987), "Photocyclizations and intramolecular Cycloadditions of Conjugated Olefins," Org. Photochem. (Padwa, A., Ed.) 9, 129.

Cornelisse, J., Havinga, E. (1975). "Photosubstitution Reactions of Aromatic Compounds," Chem. Rev. 75, 353.

McCoullough, J.J. (1987). "Photoadditions of Aromatic Compounds," Chem. Rev. 87, 81 1.

Davidson, R.S., Gooddin, J.W., Kemp, G. (1984). "The Photochemistry of Aryl Halides and Related Compounds," Adv. Phys. Org. Chem. 20, 191.

Schuster, D.I. (1993). "New Mechanism for Old Reactions: Enone Photocycloaddition," Chem. Rev. 93, 3. Wagner-Jauregg, T. (1980). "Thermische und photochemische Additionen von Dienophilen an Arene und deren Vinyloge und Hetero-Analoge." Synthesis 165.769. Wender, P.A. (1986). "Alkenes: Cycloaddition," in Photochemistry in Orgunic Synthesis, Special Publ. 57; Coyle, J.D., Ed.; The Royal Soc. Chem.: London. Wender, P.A., Siggel, L.. Nuss, J.M. (1989). "Arene-Alkene Photocycloaddition Reactions." Org. Photochem. (Padwa, A., Ed.) 10, 356.

Rearrangement Reactions Arai, T., Tokumaru, K. ( 1993). "Photochemical One-way Isomerization of Aromatic Olefins," Chem. Rev. 93. 23. Bryce-Smith. D., Gilbert, A. (1980). "Rearrangements of the Benzene Ring," in Reurrungements in Ground and Excited Stutes. 3; de Mayo, P., Ed.; Academic Press: New York: Demuth, M. (1991), "Synthetic Aspects of the Oxadi-n-Methane Rearrangement," Org. Photochem. (Padwa, A., Ed.) 11.37.

Havinga, E., Cornelisse, J . (1976), "Aromatic Photosubstitution Reactions." Pure Appl. Chem. 47, 1. Kropp, P.J. (1984). "Photobehavior of Alkyl Halides in Solution: Radical, Carbocation, and Carbene Intermediates," Arc. Chem. Res. 17, 131.

Singlet Oxygen Foote, C.S. (1968). "Photosensitized Oxygenations and the Role of Singlet Oxygen," Acc. Chem. Res. 1 , 104. Lissi, E., Encinas, M.V., Kubio, M.A. (1993). "Singlet Oxygen Bimolecular Photoprocesses," Chem. Rev. 93, 698. Stephenson, L.M., Grdina, M.J., Orfanopoulos, M. (1980), "Mechanism of the Ene Reaction between Singlet Oxygen and Olefins," Acc. Chem. Res. 13,419. Wasserman, H.H., Murray, K.W. (1979). Singlet Oxygen; Academic Press: New York.

Chemiluminescence

Leigh, W.J. (1993). "Techniques and Applications of Far UV Photochemistry. The Photochemistry of the C,H, and C,H, Hydrocarbons," Chem. Rev. 93,487.

Gundermann, K.-D., McCapra, F. (1987). Chemiluminescence in Orgunic Chemistry; Springer: Berlin.

Zimmerman, H.E. (1991). "The Di-v-Methane Rearrangement," Org. Photochem. (Padwa, A., Ed.) 11, I .

Schuster, G.B., Schmidt, S.1'. (1982). "Chemiluminescence of Organic Compounds," Adv. Phys. Org. Chem. 18, 187.

Electron-Transfer Reactions Davidson, R.S. (1983). "The Chemistry of Excited Complexes: a Survey of Reactions," Adv. Phys. Org. Chem. 19. 1. Eberson, L. (1987). Electron Transfer Reactions in Orgunic Chemistry; Springer: Berlin.

Turro, N.J., Ramamurthy, V. (1980). "Chemical Generation of Excited States"; in Rrcrrrungements in Ground ctnd Excited Stutes, 3; de Mayo, P., Ed.; Academic Press: New York.

Various

FOX,M.A., Ed. (1992). "Electron-Transfer Reactions," Chem. Rev. 92,365.

Balzani, V., Scandola, F. (1991). Suprumolecular Photochemistry; Ellis Horwood: New York.

Fox, M.A. (1986). "Photoinduced Electron Transfer in Organic Systems: Control of the Back Electron Transfer," Adv. Photochem. 13,237.

BUnau, G. von, Wolff, T. (1988). "Photochemistry in Surfactant Solutions," Adv. Pl~otochem. 14,273.

Julliard, M., Chanon, M. (1983). "Photoelectron-Transfer Catalysis: Its Connections with Thermal and Electrochemical Analogues." Chem. Rev. 83,425.

Dbrr, H., Bouas-Laurent, H.. Eds. 0990). Photochromism, Molecrtles ctnd Systems; Elsevier: Amsterdam.

Kavarnos, G.J., Turro, N.J. (1986). "Photosensitation by Reversible Electron Transfer: Theories, Experimental Evidence, and Examples." Chem. Rev. 86,401.

Guillet, J. (19851, Polymer Photophysics and Photochemistry; Cambridge University Press: Cambridge.

Mariano, P.S., Stavinoka, J.L. (1984). "Synthetic Aspects of Photochemical Electron Transfer Reactions," in Synthetic Organic Photochemistry; Horspool. W.M., Ed.; Plenum Press: New York.

Platz, M.S., Leyva, E., Haider, K. (1991). "Selected Topics in the Matrix Photochemistry of Nitrenes, Carbenes, and Excited Triplet States," Org. Photochem. (Padwa, A., Ed.) 11,367.

Mattay, J. (1987). "Charge Transfer and Radical Ions in Photochemistry,"Angew. Chem. Int. Ed. Engl. 26, 825.

Turro, N.J., Cox. G.S., Paczkowski, M.A. (19851, "Photochemistry in Micelles," Top. Curr. Chem. 129.57.

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Epilogue

In the preceding seven chapters, we have gradually developed the framework necessary for a qualitative understanding of the photophysical and photochemical behavior of organic molecules in terms of potential energy surfaces. After introducing the basics of electronic spectroscopy, ordinary and chiral, and the fundamental concepts of photophysics in Chapters 1 4 , we described the basic notions of organic photophysics and photochemistry in Chapter 5 and 6, and illustrated their utility on a fair number of specific examples in Chapter 7. Throughout, we have attempted to concentrate on the key concepts provided by the quantum theory of molecular structure, and to relate these to experimental observations. In a sense, this text aspires to being a textbook of both theoretical and mechanistic photochemistry but it makes no pretext of providing practical experimental information on light sources and the like. More than anything else, our goal has been to introduce the reader to a way of thinking about problems in photophysics and photochemistry. Although many additional organic photochemical processes could be added to Chapter 7, we have chosen not to do so. Instead, we hope that the reader will be able to apply the understanding of the material that we have chosen to present as he or she approaches the study of additional reactions.

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Index

A term, 155-56, 158, 163 quantum mechanical expression, 160 Ab initio calculations, absorption spectra, 58-60 acetaldehyde, 380 benzene valence isomeriziltion, 449 butadiene, 60, 338-39,436-37 but-I-ene, methyl shift, 446-47 di-n-methane-rearrangement, 453, 45657 2.3-dimethylbutadiene, 437 electron transfer, 292 ethylene, cis-trans isomerization, 363 dimerization, 405 formaldehyde-methane. 395.429-3 1 H,. 235. 332-33 hexatriene. 36748 hydroperoxide formation. 478 methyl mercaptane, 358 Paterno-BUchi reaction, 429-3 1 perturbed cyclobutadienes, 4 13 Absorbance, 7,8, 265 Absorption coefficient, 7 Absorption spectrum. See ulso Spectrum; Polarization spectrum ab initio calculations, 58-60 anthracene, 19,72, 263 aromatic hydrocarbons, 7 1-76 4- and 5-azaazulene, 104, 106

azulene, 33-34, 106, 273-74 benzene, 37-38,86, 107 benzyl radical, 102 biphenyl. 128 biphenylene, 98-99 @carotene, 66 croconate dianion, 159 cyclooctetraene dianion, 86 3,8-dibromoheptalene, 169 1.3-di-t-butylpentalene-4.5-dicarboxylate, 99, 169 diphenylmethyl anion and cation, 170 I,4-disilabenzene, 105, 107 ethylene, 64-65 isoquinoline, 104, 106 1- and 2-methylpyrene, 166 naphthalene, 33.42, 104, 106 N-nitrosodimethylaniline, 133-34 octahydrobenzoquinoxaline, 144-45 [3,3]paracyclophane-quinhydrone,124 pentalene, 99 perylene, 261-62 phenanthrene, 8, 19, 273, 275 polyene aldehyde, 120 polyenes, 65-7 1 pyrene, 40,280-81 quinoline, 104, 106 rotational fine structure, 9

518

Absorption spectrum (conr.) silabenzene, 105, 107 substituted benzenes, 1 15-17 tetracene, 72, 103 tetracene radical anion and cation, 103-4 triphenylene, 274, 276 tropylium ion, 86 vibrational structure, 9 Acceptor, 1 19, 123-25, 173,464-65. See also Electron transfer; Exciplex Acenaphthylene, 165, 168, 346 dimerization, 412-13 MDC spectrum and polarized absorption, 157-58 perimeter model, 87 Acenes, 7 1-73 Acetaldehyde, 1 19-20, 380-82 Acetone, chemical titration, 428 oxetane formation, 3 18,427 singlet and triplet states, 382. 428 Acetophenone. 407. 467 Acetylene. 203. 348 cycloaddition. 4 16.423 excited state geometry. 4 5 4 6 2-Acetylnaphthalene, 398 6-Acetyloxycyclohexadienones, 463 Acidity, excited states, 48-52 Acrolein, 34, 38243,433 Acrylonitrile, 328,414-15,417 Activation energy. 38243,400 Acyl radical, 352-55, 380432,460 Adiabatic. See Potential energy surface; Reaction; Wave function Alkene, photocycloaddition, 366,420-23 addition to benzene, 420 substituted, 432 Alkyl amines, tertiary, 466 Alkyl aryl ketones, 399. 402 Alkylethylenes, 420 Alkylidenecyclopropene, 57-58 N-Alkylimines, 375 Alkyl iodide, 471 Alkyl methyl ketones, 383-84 Alkyl radical, 380 Allene, 416 Allyl radical. 102,460 All yl resonance, 46 1 Alternant hydrocarbons, 33.86.97. 1 12, 127, 167.441 n-bond order, 441 excited states, 17 first order Ci, 17, 54, 70 longest-wavelength transition, 74-75

INDEX mirror image theorem, 170-7 1 pairing theorem, 17, 90, 103 plus and minus states, 17, 18, 33, 54 radicals and radical ions, 101-104 topology and geometry, 70 Aminoborane, twisted, 207,214,218,226 Aminoethylene. 4 14 Aminophthalate dianion, 484 p-Amino-p'-nitrobiphenyl, 26142 Ammonia-borane adduct, 216, 218 Ammonium and sulfonium salts. 379 Angular momentum, 76.81, 161, 164 z component. 77.81. 164 operator, 223. 229 orbital, 28, 29, 76-78, 81 quantum number, 77.81 spin, 28, 29 Aniline. 52, 1 15-16, 264 Anils, 375 [nIAnnulene, 78.85, 161, 164. See also 4Nand (4N + 2)-electron perimeter [ IO]Annulene, 83 nodal properties of frontier orbitals, 92, 175 perimeter, 175 [8]Annulene dianion. frontier orbitals, 90 [I4]Annulene perimeter, 87, 174 Annulene, perimeter model, 78, 85 antiaromatic. 167, 205,445 bridged. 70 2n-electron and k-hole, 162-63 substituent effects on frontier orbitals, 172-73 [I I] and [13]Annulenyl ion, 87, 167-68 Anthracene. absorption spectrum, 19.72, 263 delayed fluorescence, 296-97 dimerisation. 3 19-20,416,418 electron transfer, 465 fluorescence and phosphorescence, 263, 266, 282 internal conversion, 253 intersystem crossing rate, 256,266 hom*o+LUMO transition, 19, 20 'La and 'L, band, 94, 263 linked, 418 methyl substituted, 350 orbital energy levels, 18 oscillator strength, 253 perimeter model, 93-94 photocycloaddition, 419 substituted, 302.41 1,413,419 triplet-triplet annihilation, 29697,320

INDEX

Anthracene-dimethylaniline exciplex, 28182 Anthracene-tetracyanoethylene complex, 465 Anthrylmethyl radical, 350 Aromatic hydrocarbons. 92, 151 absorption spectrum, 71-76 barrier in the S, state, 34546 condensed. 73-76.259 electron transfer reactions. 467 energy gap, 254-56 excimer formation, 281 intersystem crossing, 255-56 radiationless transition, 254, 259 Aromatic molecules, B term, 164 cycloaddition, 416-23 derived from (4N + 2)-electron perimeter, 87 dimerization, 415-19 electron-poor and electron-rich, 421 photosubstitution, 474 Arrhenius plot. 426 Atomic orbital (AO), 1 1 Atomic vector contributions. See Spinorbit coupling Azaazulene, absorption spectra, 104, 106 Aziridine. 442 Azoalkanes, 37677,392 Azobenzene. 121, 377-78 Azo compounds, 1 19, 121,358 cis-trans isomerization, 376-78 cyclic and bicyclic. 389-92 N2elimination, 387-92 reluctant, 392 Azo dye, 133 Azoendoperoxide dianion, 483 Azomethane, 121,376 Azomethines, 374-76 Azulene, absorption and emission spectra, 33-34, 104-106, 1 14,273-74 anomalous fluorescence, 253-54.27374 hom*o-LUMO transition, 33, 91 'L, band. 91-92 perimeter model, 83.88, 91-92 substituent effect. 1 14 triplet quencher. 37 1 0 term. 155-58. 163-67 11 and ~c - contribution. 164-67 quantum mechanical expression. 160 substituted benzenes, 172-73 sign. 156, 164, 167, 169 +

Back electron transfer, 2 16, 284, 363,425, 46546,46869,474 Bacteriochlorophyll, 474 Bacteriopheophytin, 474 Baldwin rules, 409 Band shape, 2 1-44 CD band, 143 MDC band, 155-56 ORD band, 143 'B, and 'B, band, 71-76 'B, and 'B, state, 79-81, 83,92 Barrelene, 456 Barrier, 180,200,232, 31 1, 318, 321, 34144,415 abnormal orbital crossing, 345 a cleavage, 380 correlation induced, 197, 324, 345, 380, 398.429 excited state, 328, 370. 388 natural correlation, 35 1 photodimerization, 342-44 Basicity, excited states, 48-52 Bathochromic shift, 104-105, 1 12, 123 solvent effect, 132 by steric hindrance, 127-28 Benzaldehyde, 299, 381-83 Benzene, absorption spectrum, 37-38.69. 73.86. 94-96 aza derivatives, 122-23 cyclodimerization, 4 19 density of states, 257 dimers, 324,419 excited state geometry, 43-44 fluorescence, 264-65 frontier orbitals, 32. 80. 90, 420 Ham effect, 134 highest resolution spectra, 43 'L, transition, 172-73 phosphorescence, 45 1 photoc ycloaddition, 420-23 rate constants of unimolecular photophysical processes, 250 rotational constants, 44 selection rules, 32 substituent effects on the intensity, 109 substituted. 115-18.458 transition densities, 80 transition moments, 95 triplet excited, 45 1, 483 two-photon spectrum, 43 valence isomerization, 26465, 302, 448-53 vibronic coupling, 32, 37-38, 96

INDEX Benzene oxide-oxepin equilibrium, 326-27 Benzhydrol, 397 Benzocyclobutene, 350,453 Benzonorbonadienes, substituted, 457 Benzophenone, 26748,407,424,467 Jablonski diagram, 252 oxetane formation, 407,424 photoreduction, 397-98,467 as sensitizer, 294, 367, 407 substituted, 52 Benzopinacol, 397 Benzoylox y chromophore, 154 Benzvalene, 264-65, 302,448-5 1 Benzyl anion and cation, 171 Benzyl radical, 102 Biacetyl, 266,291,425, 469 Jablonski energy diagram, 25 1 9,9'-Bianthryl, 48 Bichromophoric system, 305-6,418 Bicycle rearrangement, 459 Bicyclobutane, 23 1, 333, 336, 339, 34 1, 36647,433.438.443 Bicyclo[3.2.0]hepta-2.6-diene, 447 Bicyclo[2.2.O]hexene, 443 Bicyclo[3. l .O]hexene. 368.443 Bicyclo[3. I .O]hexenones, 463 Bicyclononadiene, 329 Bicyclooctatriene, 423 Bicyclo[4.2.0]oct-7-enes,437 Bimolecular process, 244,276-301, 313, 34 1 Biphenyl, 45, 203, 348 absorption spectrum, 128 electron transfer, 465 fluorescence spectrum, 263 hom*o and LUMO energy, 128 methyl derivatives, 128 Biphenylene, 98 Biphenylquinodimethane, 128 Biphenylyl t-butyl ketone, 383, 397 1 $3-Biradical,453-54, 456-57 1,4-Biradical, 236, 400,424,433-34,45354,457,470 l ,n-Biradical, 389 C,O- and C,C-Biradical, 428-3 1 Biradical, 187, 195, 197,205-10,2 19-230, 342.35 1, 391,430,434,461. See also Biradicaloid; ~o-electron-twoorbital model axial, 1 10, 210,442,478 cyclobutadiene like, 334 intermediates, 423-24.447, 461 magnetic field effect, 33 1

pair, 98, 210, 212, 231-32 perfect, 208-10,212, 223, 225,231-32, 234,236, 334,413,436 spin-orbit coupling, 219-29 triplet, 229, 323,403,424,469 wavefunctions and energy levels, 206, 208-2 12 Biradicaloid, 187.205.2 10-30,461. See also Biradical; Geometry; Minimum; Structure; Two-electron-two-orbital model critically heterosymmetric. 195, 214. 217. 228-29. 334. 338. 363 heterosymmetric. 2 10-19. 213. 236. 303. 334.413-15 hom*osymmetric. 2 10-12. 224. 234. 362 nonsymmetric. 210. 212.224 ( - 1- I . I '-Bis(2.4-dicyanonaphthyl). 47 1 ct.co-Bis(9-anthryl)alkanes. 4 18 Bis(9-anthry1)methane.4 18 Bis-9-anthrylmethyl ethers, a,a'disubstituted, 418 Bitopic, 190. 357. 379. See ulsn Topicity Blue shift, 133 Boltzmann's Law, 6 Bond dissociation. See Dissociation Bond order-bond distance relation, 45 Bond order, excited state, 441 Born-Oppenheimer approximation, 10, 34, 179,328 Hamiltonian, 180 states. 185-86 surface, 180-81. 316 Bracket notation, 5 Branching space, 183, 217,31617,339 Bridging, 87. 175. See also Perturbation, hierarchy of Brillouin's theorem, 54 I -Bromonaphthalene, 255,264 Brooker dyes, 135 Butadiene, 230-3 1, 336-39, 341, 366,408, 433,443 ab initio calculations, 43637 ab initio state energies, 60 HMOs, 26,3 1 isomerization, 333, 336-39, 366-67 ring closure, 332-33,43637 s-trans- and s-cis-, 2627, 31-32, 70, 276, 338,366,409,436 twisted, 341 Butanal, Norrish type I1 reaction, 399-400 l -Butene, 446 2-Butene, 364,406,424,478 r-Butyl ketones, 383

IZCisotope enrichment, 385 C term, 155-56, 158 quantum mechanical expression, 160 Cage effect, 385 Caldwell model, 343-44.415. 417 E-Caprolactam, 476 Carbazole. 442 Carbonyl compounds, 1 19-2 1, 365 aromatic, 92, 151, 3% chiral, 425 a cleavage, 380-87 dipole moment, 47-48 intersystem crossing, 29 optical activity, 147-49 photocycloaddition, 424-32 photoreduction, 466 rearrangement reactions, 460-64 solvatochromism, 133 spin-orbit coupling, 29-30 a,/?-unsaturated, 433-34.46263 #3.y-unsaturated, 120.453.460-62 singlet and triplet reactions, 462 /?-Carotene, absorption spectrum, 66 Carotenoids, 473 CASSCF, 58.363 Cationic dye, 217 CD spectrum, 147-50 cholest-5-ene-3#3,4/?-bis(p-

chlorobenzoate), 153-54 octahydrobenzoquinoxaline, 144

single chromophore systems. 147-52 two-chromophore systems, 152-54 CH and CD vibrations, 259-60 Characteristic configuration. 344-46. 349, 410 Charge-transfer (CT), 239, 421. See ulso Charge translocation; Electron transfer; Excimer; Exciplex band, 1 16, 125,420 character, 1 14, 282,465,478 complex, 34, 186,215, 34 1,420,465 configuration, 126 interaction, 238 intramolecular, 115, 126, 303 state, 1 16,238,474 transitions, 32, 115, 123-26 Charge translocation, 214-15 Chemical titration, 428 Chemically induced electron-exchange luminescence (CIEEL), 485 Chemiluminescence, 451-52,478,480-85 Chirality, 143-46, 150 Chiroptical measurements. 141-43

Chloranil, 123 I -Chloronaphthalene. 252 Chlorophyll a, 286,473 Cholest-5-ene-3#3,4/?-bis( p-chlorobenzoate), 153 CI. See also Configuration interaction 3 x 3, 230,232-33, 236, 334,336 20 x 20, 23633,235, 237, 336 . CIDNP, 220,469 CI matrix, perimeter model, 78-79,82,84, 93,97-99 Circular birefringence, 139, 141 Circular dichroism, 139, 141-42 magnetic, 154-77 natural. 143-54 Circularly polarized light, 139-4 1 Cis-band, 67 Cis-trans isomerization, 319, 329, 333, 336, 362-78, 388,406-7,427-29,433, 436-37.441.454-55. See also Synanti isomerization; State correlation diagrams azo compounds, 376-78 azomethines, 374-76 benzophenone sensitized, 367 butadiene, 367,437 cycloal kene. 364-65 dienes and trienes, 366-69 diimide, 376-77 double bonds, 362-78 enantioselective, 364 ethylene. 36243 heteroatom, substituent and solvent effects, 372-73 cis-hexatriene, 439 mechanisms, 36264 olefin, 364-66 Schiff base, 191, 373 stilbene, 369-72 triplet-sensitized, 363, 367 Clar's nomenclature, 20 Classification of photoreactions, 361 a Cleavage, carbonyl compounds, 352-55, 380-87.460-6I c yclobutanone. 386 ester, amide, 387 formaldehyde, 353-55 potential energy surfaces, 353, 355 state correlation diagram, 354 /? Cleavage, 425-26 CNDOIS method, 55 Collisional frequency, 247 Color center, 469

522

INDEX

Cone. 183,217. 316-17.366.415 Configuration, 12, 23 1-32 closed-shell. 205 electronic, 16-20, 193 excited, 12, 54, 58 ground, 12, 16, 54, 77 orbital, II Configuration correlatien diagram. 193. See also Correlation diagram Configuration interaction. 13. 16-20. 24. oI 52, 56, 72, 192. See ~ I s C complete. 55-57, 69 doubly excited (DCI, SDCI), 55, 57, 69 first-order, 16-17, 54, 70, 78, 102, 195 H4,234 second-order, 16 singly excited (SCI). 55-57. 70 Configurational functions, 11, 12, 17, 53 Conical intersection. 195, 2 17. 229. 23 1. 236-37.254, 315-18, 333-38, 363, 366-68. 375, 381.405.414-15.417, 430,433,43640,444,446-47.44950,452,454,457 true and weakly avoided, 182-86 Conjugated n systems. See cilso Polyenes; Annulenes; Aromatic hydrocarbons cyclic. 71-101, 171 linear, 63-70 Conrotatory. See Electrocyclic reactions; Reaction pathway Contact ion pair, 283,424-25,465 Continental divide, 3 12-1 3 Cope rearrangement, 446 Correlation diagram, 179, 184, 193-205, 23 1-32. 332, 334. 366,405,428-3 1, 449. 451-52. See ulso Orbitalcorrelation diagram: State correlation diagram Correlation, dynamic. 233 intended, 197-200, 35 1, 379 natural, 197-200, 204-5, 351, 383, 39697 Correlation effects, 56 Coulomb energy, 336 Coulomb gauge, 22 Coulomb integral. 14-15. 88. 97. 104. 208. 237 Couplet. 154 Covalent. See Perturbations; Structure Croconate dianion. 158-59 Crossing, Set. trlso Surface touching allowed. 3 16. avoided. 184-85. 200. 205. 23 1-32. 3 15-16. 777. 746. 10F 700 3 0 % -175 76 JX7

(.is-Crotonaldel~yde.448 Cross-link. 87. Y I. 101. 109. 169. Set' (IISO Perturbation. hierarchy o f CT. See Charge transfer Cubane. 409.434 Cyanethylene + NH,.304 Cyanine dye. 16. 69, 129. 218, 373 i n stretched poly(viny1 alcohol), 39 m-Cyanodibeniobarrelene. 457 I~cyanoheptalene,329-30 I-cyanonaphth;~lcne, 325, 468 9-cyanophenani hrene, 467 Cyclic n Systcnis. See ulso Annulene; Conjugated n Systems. Perimeter with a 4N-electron perimeter. 96-101. 167-70 with a ( 4 N + 2)-electron perimeter, 81-96. 16447 Cyclization. Sc,c Photocyclization Cycloaddition. 404-35. See also photocycloaddition aromatic compounds, 4 16-23 carbonyl group. 424-33 crossed. 23 1. 340. 342 enantioselect ive. 47 1 formaldehyde + ethylene, 430 ground-state forbidden, 230. 341 mixed. 410.4 19,433 photosensitized. 470-71 regiochemistry. 4 17-23 two ethylene molecules. 202-3. 237. 33336. 339. 417 c1.l-i-unsaturitrcd carbonyl compounds. 433-34 Cycloaddition. 12 + 21. 23 1. 237. 334-36. 364. 404-1 1. 414.417.443-44.448. 450.454-56. 461.467.478 N = N and C = N double bonds. 4 1 1 [4 + 2j.419, 471.477. 480 [4 + 41. 418-19 (2 + 2 21.455 .r[2 + 21. 23 1. 237. 333. 335.408-9.415. 443.446. 449 Cycloalkene. 30445. 407 I-Cycloalkenes. substituted. 427 Cyclobutadiene. 233. 236. 334.4 13 Cyclobutadienc dianion and dication. 16243 Cyclobutane. 404. 406. 415. 433. 444 fragmentatioii. 202-3 Cyclobutanol. JOO, 402-3 Cyclobutanone. 386 Cyclobutene, 230, 323-33, 336, 339, 36667. 410. .133. 436. 447

INDEX conrotatory ring opening. 196, 199 disrotatory ring opening, 194-201, 340 Cyclobutenophenanthrene, 203,34648 Cyclodecapentaene, even and odd perturbation, 9 1-92 Cycloheptatriene. 447 Cycloheptene, 407 Cyclohexadiene, 4 19, 443-44.47 1 Cyclohexadienone. 460,463 Cyclohexane. 476 1.2-Cyclohexanediol. 152 Cyclohexanone. 386 Cyclohexene. 407 Cyclohexenones, 463 Cyclononatriene. 329 1.5-Cyclooctadiene, 409 Cyclooctatetraene. 236. 423 dianion, 90 1.3.5-Cyclooctatriene. kinetics o f ring opening. 444 Cyclooctene, 364. 407 Cyclopentene. 407 Cyclopentenone, 433. 463 C yclopropane, 42 1-22 Cyclopropanone, 463 Cyclopropyl ketenes. 463 Cycloreversions. 347

1.4-Dibromonaphthalene, 269 Dicarbonyl compounds, PE and U V data, 121 9.10-Dicyanoanthracene, 470 I,2-Dicyanoethylene, 428 Dielectric constant, 13 1 Diene, 112, 444, 446. 453, 455 acyclic chiral. 455 bicyclic, 456 cis-trans isomerization. 366-369 Dienones. 462 Dienophil, 420 Dienylketenes, 4 6 3 4 4 Diethylaniline. 465 Differential overlap. Sot) Zero differential overlap hb. IOb-Dihydrobenzol3,4jcyclobutI I-2-trji~ccnaphthylene.3 12 Dihydrocarbi~zole.442 Dihydrocyclopropapyrene. 458-59 2.3-Dihydrofuran. 426 Dihydropentalene. 453 Dihydrophenanthrene. 37 1,440 1.4-Dihydrophthalazine, 484 Dihydropyrene. 443 Diimide. 376-77, 388-89 Diisopropylamine. 398 Diisopropylidenecyclobutane. 447 Davydov splitting. 152-53 Diisopropylmethylamine, 466 De Broglie relationship. 15 Dimer, syn and anti. 412 rrcrtts-Decalin. 292 head-to-head and head-to-tail. 41 1-14, Decarbonylation, 385 470 Degree o f anisotropy, 272 Dimerization, acenaphthylene, 4 12-1 3 Degree o f polarization. 272 ethylene. 202-3. 339. 416 Density o f states. 244. 257-58. 290 indene. 470 Deuterium labeling. 446 olefins and aromatic compounds, 415 Dewarbenzene. 448-52.483 I-4-Dimethoxynaphthalene, 468 Dewar-Evans-Zimmerman rules, 445 p-I)imethylaminohenzonitrilc, 303 I,4-Dewarnaphthalene. 32 1-23, 328. 346 Dimethylaniline. 115. 467 Di-n-methane rearrangements. 453-60. 462 9.10-Dimethylant hracene. 247 Diabatic. See Reaction; States Dimethylbutadiene, 367, 437 Diarylethylene. 44 1 2.3-Dimethyl-2-butene. 299, 41 1, 467 Diastereoselecti v i t y, 403 Dimethylcyclopropene. 367 oxetane formation. 326-27. 425-27 Dimethyldihydropyrene, 443 Diazabic yclooc tene, 292 Dimethylenecycloalkane, 438 Diazacyclooctatetraene, 390 2.5-Dimethyl-2.4-hexadiene. 3 0 - 1 3.5- and 3.6-Diazaindoles, 174 N.N-Dimethylindigo. 127 7.8-Diazatetracyclo[3.3.0.0~~4.0'~hJoct-7-ene,Dimethylketyl radical. 397 39 1 Dioxetane. 428. 476. 478. 482-83 Dibenzosuberene. 447 Diphenoyl peroxide. 485 Dibenzyl ketone. 385 Diphenyl amine. 340 9, !0-Dibromoanthracene, 256.45 1 9.10-Diphenylanthracene, 330 1.2-Dibromoethane. 270 Diphenylcarbene, 330 3.8-Dibrc~mnheptalcr~n. I69 1.2-Diphcnylcyclopropane. 469-70

INDEX Diphenyldiazomethane, 330 l-Diphenylethylene, 470-7 1 Diphenylketyl radical, 397 Diphenylmethyl anion and cation, 170 9, I0-Diphenylphenanthrene,330 1.5-Diphenylspiro[2.4]-4.6-heptadiene, 459 Dipole-dipole interactions, 290 Dipole field, 131 Dipole length formula. 23, 56-58 Dipole moment, 465. See also Electric dipole moment; Magnetic dipole moment exciplex, 282 excited-state, 47-48, 132 induced, 130 permanent. 130-3 1 Dipole strength, 158 Dipole velocity formula, 2, 56-57 Direct reaction. See Reaction 1,4-Disilabenzene, 105-7 Disproportionation, 228-29, 380, 390,433 Disrotatory. See Electrocyclic reaction; Reaction pathway Dissociation benzylic C-X bond, 379, 387 C-H bond, 348-49 a bond, 188-90, 210, 214-15, 356-57 n bond, 190-91, 210, 214, 216-17 B-N bond, 2 19 C-C bond, 190,350 C-N bond, 358, 380. 387-92 C-Ne bond, 215. 219 C - 0 bond, 190, 357-58 C-S@bond, 190 double bond, 378 H-H bond, 188-89, 356 polar bond, 2 17 single bond, 188-90, 378-79 Si-Si bond, 190, 216, 356, 379 toluene, 348-49 Distortion, diagonal, 333, 339-42, 413, 444, 446,450 rhomboidal, 334-35.405.4 14-1 5,450, 454 Disulfides. 150-5 1 1.3.-Di-~-butyl-pentaIcnt'-4.5-di~i1rboxylic ester. 169 2.3-Dithia-cr-steroids. I5 I 1.2-Divinylcyclobutanes. 408 Dodecahedrane, 4 19 Donor, 110-11, 114, 123-24, 135, 173,421, 465 Donor-acceptor chromophores, 134, 2 18 Donor-acqeptor complex, 28 1,465

Donor-acceptor pairs, 123-24, 2 14, 2 16, 218, 286. See also Charge transfer; Exciplex rigidly fixed, 286, 305 Doppler broadening, 42-43 Double bond. twisted. 188,205, 218. See crlso Ethylene; Propene Dynamic correlation, 232 Dynamic spin polarization, 206 Dynamical memory. 373 Dynamics of nuclear motion, 3 15.415.437 Efficiency, 247-49, 32 1, 406, 43 1 EHT calculation, 443 Einstein probability, 245 Electric dipole moment operator, 5, 13, 15, 23, 25 Electric quadrupole moment operator. 5, 13, 25 Electrocyclic reaction. 321,434-44 Electrocyclic ring-closure, 430,434,43637.44 1,443-44.456 conrotatory. 442 disrotatory. 436.449.454-55 Electrocyclic ring opening. 434. 443-44. 453.483 conrotatory, 196, 199, 338,439,444 cyclobutenoacenaphthylene, 347 disrotatory, 194-201, 340 kinetics, 444 Electromagnetic spectrum, 1-2 Electron affinity, 53, 282 interaction, 14, 52 Electronegativity, 191, 212, 218, 365, 372 Electron energy loss spectroscopy, 28 Electronic energy transfer. See Energy transfer Electronic excitation, 3 10 MO models, 9-2 1 quantum chemical calculations, 52-60 Electronic transitions, intensity, 21-27 notation schemes, 20 polarization, 38-40 selection rules, 27-34 Electron repulsion. 53. 55, 74.78. 234 Electron transfer, 123, 28347,292,398. 425,475-76,485 dependence on solvation, 304-6 free enthalpy. 285 light induced, 286, 304, 325,464-75 reactions, 464-75 sensitization, 468-70 Ellipticity, 140, 142, 154 El Sayed's rules, 255,257,266

INDEX Emission, 244-45, 260-76, 3 18, 323. See also Fluorescence; Luminescence; Phosphorescence Encounter complex, 278. 285. 29 1, 34 1 Endoperoxide. 477,480-8 1 Ene reaction, 477 Energy gap, 218, 255-56.258-59. 266, 316, 328.365, 372 law, 247, 254 Energy transfer, 277-78, 283. 287-97, 3 18, 363, 365.424.45 1 Coulomb and exchange mechanism, 290-95 nonvertical, 408 radiative and nonradiative. 287-88 Z- and E-enol, 447 Enthalpy and entropy control. 426 Environmental effects, 3 0 1 4 Ergosterol, 439 Ether-pentane-alkohol mixture (EPA). 250. 266 Ethylbenzene, 350 Ethylene. 64-65. 218. 420-21. 429-31.450. 454 cis-trans isomerization. 362-63 correlation diagram. I90 dimerization. 202-3. 236. 335. 339. 404. 416.454 electronic states. 64 [1,2] hydrogen shift, 363 MO diagram, 64-65 N t V transition, 24, 64 Rydberg orbitals, 5 9 4 , 64 spectrum, 64 substituted, 334 twisted, 190, 193, 206-14, 325-26, 36243 Ethyleneiminium ion, 2 14 a-(o-Ethy1phenyl)acetophenone.403 Ethyl vinyl ether, 433 Exchange energy, 287 Exchange integral. 14-15, 121, 208-10, 237, 289, 335-36.484 Excimer, 238,278-81, 335. 341-43.405, 412-13.418 fluorescence, 27940,418 intermediate, 405,414 minimum, 186,232,238-39. 279,320, 341-42,405,407,415 MO scheme, 279 wave function, 280 Exciplex, 48, 238, 278, 281-83, 285, 335, 342, 363, 366,412,419, 425,434, 46547,469 emission. 282. 3054. 326

intermediate, 422,434,444 minimum, 186, 341-43,405,415,419 triplet, 444, 467 wave function, 282 Excitation, electronic, 13, 310-13 Excitation energy, 13-14. 56. 93 HMO model. 13 quantum chemical calculation. 5 2 4 0 semiempirical calculations. 53-56 Excitation polarization spectra, 273-75 Excited State, 44-52, 263. See also Acidity; Basicity; Dipole Moment; Geometry n-bond order, 44 1 carbon acid. 447 degenerate, 156, 161-62 magnetic moment, 158-59 potential energy surfaces, 179-82 vertically. 3 18 Exciton-chirality model, 147, 152 Exciton state. 238, 280 Exo-selectivit y. 427 Exponential decay. 246 Extinction coefficient, 8, 21, 40, 139, 143, 265, 327. 365 Face-to-face approach, 186, 333.4 17 Faraday effect, 154 Far-UV region. 9 FEMO model, 15-16.67-68. 76-77 Fermi golden rule, 223, 255, 257, 290 Ferredoxin. 473 Fluorene, 238. 330 Fluorescence, 2 17, 244-45, 260-65, 282, 3 1 1, 320. 465 anomalous, 254, 273 benzene, 264-65 benzenoid aromatics, higher excited states, 253 delayed, e-type and p-type, 245, 295 donor-acceptor pair, 304-5 excimer, 238,279-8 1, 320 exciplex, 282, 304-5, 326 intensity, 32 1 lifetime. 47. 322 polarization, 39, 272-76 quantum yield, 248-49, 263-64 quenching, 277. 283 rate constant, 322 stilbene, 264, 370 Fluorescence excitation spectrum, 265, 27 1, 367 Fluorescence polarization spectrum, 272-73

INDEX

Fluorescence quenching. 277-78, 283 benzene. 265 diazabicyclooctene. 292 10-methylacridinium ion. 300-1 Fluorescence spectrum. anthracene. 263 anthracene + dimethylaniline. 282 azulene. 273-74 perylene. 2 6 1 4 2 phenanthrene. 273-75 porphine. 2 6 8 4 9 pyrene. 280-8 I triphenylene. 274. 276 Formaldehyde. excited state geometry. 45. 120. 186 barrier t o inversion. 120 energy level diagram. 119 solvent effect. 132-33 ethylene. 429-31 Formaldehyde Formaldehyde + methane. 351. 395-96 Formaldimine. 374-75 Formaldiminii~mion. 373 Formyl radical, 252 Forster cycle, 49. 51 Fiirster mechanism. 280. 290-91 Fragmentation. 228-29 Franck-Condon envelope. 189 Franck-Condon factor. 34-35. 223. 25840. 263 Franck-Condon principle. 34-36. 13 1. 186. 288. 310 Franck-Condon region. 254 Free-electron model, 15-16. 76 Free-valence number. 44 1 Frontier orbital. 432 Fulvene. 448-49 Fumaronitrile, 434 Funnel. 18246. 195. 197. 314-15. 317. 3202 1. 325-27. 332-33.336. 338-39. 342. 363. 36547.414.436.439-40.446. 449-50.452.454.456.461 bottom. 184. 230. 236. 317. 333. 366.436 pericyclic. 229-39. 332-39. 363. 36647. 407. 412. 437. 450 diagonally di5tortcd. 342. 366. 405. 408-409. 4 13. 444. 450 region. 335. 338-39. 3 6 6 4 7 . 4 15 }:our-clectrc)n-four-orhit;il model. 230. 232. 333 Furiin. 427

g Value. 220 0-0 Gap. 260 S,-S,, gap. 2 18

Gaussian linesh;~pe. 143. 155 Geometry. antiiiromatic, 205 biradicaloid. 187-88, 191, 193, 198,205, 208. 228. 13 1. 323. 339-4 1. 362-369. 449-50 excited states. 44-47. 56. 186 loose and tight. 191. 339-41. 362. 399. 406.424. 429.442-43 pericyclic. 33.1. 334. 337.442.446 rhomboidal. 2 36. 335-36 Gcrade and ung[.ri~de.30-3 1. 4 1. S ~ itl.~c) C Parity Geranonitrile. 4 I 0 Glyoxal, 121 Gradient. 180. 133-84. 317 Guanosine-5'-moncjphosphate.300-1 Hl molecule. INS-93 correlation di;~gritm.232 dissociated. 207. 216 electronic cibr~figuratians.64 M O and VR t tci~tment.191-93 H, H?. 231-32. 232-36. 238.279.295. 333-34.4 17 H,. 230-38.333. 336. 342.405 Hairpin polyenes. 70 Half-times. den :irhenzene and benzvalene. 45 1 Half-wave potc~~ti;ils. 285 Hiim effect. 134 Hiimiltonian. 14. 2 1. 78-79. 180 electronic. 10. IHO. 184 H M O model. I 3 spin-orbit c o ~ ~ p l i n g28. vibr;.rtioni~l. I I Hiird and soft cl~roniophore. 1 6 4 4 8 Harmonic oscill,rtor eigenfunction. 36 Hartree-Fock approximation. 52 Heavy atom effect. 28. 223-24.255.264. 269-70. 306. 412. 419 external and internal. 270 Heitler-London. 237 Helicene. I 5 I.44 I Hematoporphy rin. 295 Heptacyclene. 3-46 Heptalene. 169 Hcrzberg-Tcllc~vibronic coupling. 37 flcteroatom replacement. 8748,91, 109. See ctlso I'erturhat ion. hierarchy of Hetero-TTA. 2'h-97 Hexacene. 254 1.5-Hexadiene. -108. 446 2.4-Hexadicne. 16%

INDEX

Hexadienecarboxylic acids, 463 Hexafluorobenzcne. 450-5 1 Hexafluorodewarhenzene. 450 Hexahelicene. 15 1 Hexamethylbcnzcne. 126. 468 Hexamethyldewarbenzene. 468 Hexatriene. 46. 212-13. 329. 36748.439. 444 Highest resolution spectrii. 42. 44 AHI.. AHSI.. 1 0 7 4 9 H M O approuiniiit ion. 208 H M O model. 13-14. 17. 09. 74. 77. 8%. 332 coefficients. 410. 415 excitation energy. 13.73-75 polyenes. 67-68 radical ions. 102- 103 Hole transfer. 292 hom*o. 13. 43 1-32. 441. 428 Ahom*o. 82. 84. 10%. 110-I I. 164-67. 170. 172-75 l1OMO-hom*o ititcr;rction. 343. 411 hom*o-L-UMO crossing. 194. 198.376 H O M O - L U M O excitation. 75. 77. 345.441. 447 hom*o-1,UMO intcraction. 478 hom*o-1,UMO splitting. 91. 105 hom*o-.I,UMO tr;~nsition. 13-14. 16-17. 26. 31. 33-34. 65. 72. 91. 114. 127. 34% polyencs. 62. 69-70 s ~ ~ h s t i t u c cfl'cc't. nt 105 IIOMO-SOMO tran\ilion. I 0 1 Hot molcculcs. 252. 3 10-1 2. 373. 45 1 Hot I-c;~cticbn. 330-22. Scco crl.\ct Reactions cxcitcd stiitc. 301. 210 g r o t ~ n dsti~te.204. 310-1 1. 38% Hund's rule. 37% Hydrocarbon. Sclc~trlso Alternant hydrocarbon cata-condensed. 7 1-72.95 nonalternant. 104 Hydrogen abstraction. 203-4. 380. 395403,424.447 carbonyl compound. 35 1-52, 395-99.424 intramolecular, 399-403 in-plane iind perpcndiceliir attack. 39697 natural orhitill correlittion dii~griini.204 Hydrogen sclcnide, 434 [ I .2j-Hydrogen shift. 363 11.31-Hydrogen shift. 445 II.5 ]-Hydrogen shift. 447 [1.7]-Hydrogen shift. 439. 447. 459 Hydroperoxidcs. 476-77

p-Hydroxyacetophenone. 27 1 o- and p-Hydroxyaryl ketones. 387 4-H ydroxybenzophenone. 398 Hydroxyhydroperoxides. 476 3-Hydroxyquinoline. 50-5 1 Hyperconjugation. 88. 114. 173.227 Hyperfine interaction. 220-21. 331, 385 Hypsochromic shift, I04 solvent effect. 132 hy steric hindrance. 127-28 Increment rules. diene absorption. 112 enone absorption. 1 13 Indene, 470 Indicator equilibrinm, 48 I N DOlS method. 55.474 Indole. perimeter niodel. 88. 91 Indolizine. 174 Inductive effect. 104-9 In-plane inversion. 374 Intensity. 21-44 acene, 95 'B,. 'B?. 'L,. 'L?transitions. 85 benzene. 95-96, 108-9 borrowing. 37.96 Cl calculation. 57-58 CT band. 126 electronic transitions. 2 1-27 emission. 245-46 exciting light. 327-30 integriited. 246 I~itcriiction.t c . y. 461. Sc#t*crlso Throt~ghhond: -1'hrough-spircc . tliagoniil. 239. 334-39. 30647. 405. 4 1415.444 Intcrniediirtc. hir;~dical. 423-24. 447. 46 1 excimer. 405. 4 14 exciplex. 422. 434. 444 excited state. 3 14 pericyclic. 4 16 triplet. 368 Internal conversion (IC). 2 16. 244-45. 25254, 264. 287. 310. 320. 366 intersection coordinate suhspace, 183-84 Intersystem crossing (ISC). 30. 244-45. 254-56. 264. 266. 283. 286-87. 295. 302. 3 10- II 320. 328. 340. 349, 363. 382. 384. 396.401-3.406.424.42629.441.461-62 aromatic hydrocarbons, 255 biradicals and biradicaloids. 219-29 hyperfine coupling mechanism, 220-21 spin orbit coupling mechanism, 221-27

Inversion temperature, 426 Ionization potential, 53, 282 I o n pair, 424-25.47 1. See ulso Contact ion pair; Radical ion pair states, 238 Isoconjugate hydrocarbon model, 116 Isoquinoline, 104, 106, 109 Isoprene, 437 2-Isopropylbutadiene, 437 Isotope effects, 33 1, 385 Jablonski diagram, 243-45, 25 1-52 Jahn-Teller distortion. 96, 98 Kasha's rule. 253, 3 10 Ketene, 380, 386 acetal, 326-27, 469 Ketoiminoether, 4 1 1 Ketone. See ulso Carbonyl compounds aldol reaction, 427 excited state basicity. 52 K e t y l radical, 397-98. 467 Kinetics o f photophysical processes, 250. 297-30 1 Koopmans' theorem. 14, 12 1

'L, and 'L, band. 52. 7 1-76, 167, 173 IL, and 'L2band, 169 'L,, IL,, 'B,, 'B, states, 83, 86, 92-93, 167 Laarhoven rules, 441 Lactam-lactim isomerism. 174 Lambert-Beer law, 7-8, 366 Landau-Zener relation. 3 16 Langevin dipoles solvent model, 133 Laser spectroscopy. 4 18, 425, 444 Lifetime, 369, 434 excited singlet and triplet states. 245 higher excited states, 253 natural and observed, 245-47. 249-50. 253,266 triplet biradicals,, 229 Light absorption, 5-9 M O models. 11-13 Light, circularly polaridzed, 41, 139-44, 154, 158, 162-63 elliptically polarized, 139-43 linearly polarized, 1-3. 5.. 38-4 1, 139-4 1 Light-gathering antennae, 473 Linear momentum operator, 22,24, 56, 145 Line-shape function, 156 Liquid crystals, 272 Localized orbital model, 115-16

Locally excited states. 116 London formula, 237 Luminescence, 244, 260,418,478. See cilso Emission; Fluorescence; Phosphorescence Luminescence polarization. 272-76 Luminescence quenching, 293 by oxygen, 286 Luminescence spectrum, 1.4dibromonaphthalene, 269 free-base porphine. 268 naphthalene and triphenylene, 270 1.uminol. 482-84 I.UMO. 13. 43 1-32. 458 A12UM0. 82. 84. 110-1 1. 16447. 170. 17275 l . U M 0 - 1 - U M O interirctions. 343. 412 Magnetic circular dichroism (MCD), 142, 154-77 Magnetic dipole moment operator, 5, 13, 25, 145, 160 Magnetic field effects, 33 1 Magnetic moment, 77, 331-32, 385 z component. 1 6 1 6 3 p' and y - contributions, 164-65, 170 excited state. 158-59 Magnetic optical rotary dispersion (MORD), 142 Maleic anhydride, 420 Maleic dinitrile, 434 Maleimide, 420 Marcus inverted regicin, 284. 286 Marcus theory. 284-86 Markovnikov and anti-Markovnikov, 468 Mataga-Nishimoto formula, 53, 55 M C D spectrum, acenaphthylene, 157-58, 169 anthracene. 263 applications, 17 1-77 croconate dianion, 159 3.8-dibromheptalene, 169

1,3-Di-t-butylpentalene-4.5-dicarboxylic ester, 169 diphenylmethyl anion and cation, 170 4N-electron perimeter, 167-70 ( 4 N 2)-electron perimeter, 164-67 I- and 2-methylpyrene, 166-67 monosubstituted benzenes, 114, 172 mutually paired alternant systems, 169 orbital ordering. 175 pleiadiene. 157-58, 169

mirror image law, 170-7 1 temperature dependence, 155 vibrational structure, IS9 Mechanism cis-trans isomerization, 302-64 energy transfer, 287-91 oxetane formation. 425 photocatalytic, 364 photosubstitution, 474-76 [I,3] shift 6, y-unsaturated ketones, 461 transformation o f metacyclophane, 459 Menthyl phenylglyoxylate. 326-27.425 Merocyanine, 129, 135 Mesomeric effect, 109-18. 171 Meta c ycloaddition, 420-23 Metacyclophanediene, 324.443.458-59 I,6-Methano[lO]annulene. 175-77 Methano-cis-dihydropyrene, 324 I-Methoxy-l -butene, 427 p-Methoxyphenylacetic acid. 325 o-Methylacetophenone, 447 10-Methylacridinium chloritle, 300-1 Methylamine, protonated. 2 18 9-Methylanthracene, 403 Methylbicyclo[3. I.O]hexenc , 329 a-Methylbutyrophenone, 403 ( )-3-Methylcyclohexanon~.,148-49 Methylcyclohexene, 365 3-Methylcyclohex-?-en- l-one. 434 I-Methylcyclopropene, 336 N-Methyldiphenylumine. 4-12 Methylene blue. 295. 480 Methylenecyclohexene, I12

2-Methylene-5.6-diphenylbicyclo(3.1.0]hexene, 459 Methyl ethyl ketone, 384 2-Methylhexadiene, 3 18 Methylhexatriene- l,2,4, 329 Methyl iodide, 264, 419 4-Methylphenyl benzyl ketone, 385 I-Methyl-2-phenyl-2-indanol, 403 I-and 2-Methylpyrene, 166-67. 1?4-75 Methyl shift, 446 PMethylstyrene, 47 1 Methylvinylcyclobutene, 329 Micellar solvents, 412 Micelle, 384435.4 12 MIM (Molecules-in-Molecules), 117, 126 MIND013 calculations, 399 Minimum, antiaromatic, 442 biradicaloid, 187-91, 195-96, 205, 325, 36263, 365, 370-7 1

excimer, 186, 232, 238-39, 279, 320, 34142,405,407,415 exciplex, 186, 341-44,405,415, 419 excited state, 186-93 pericyclic, 195-96, 229-39, 320, 332-33, 338-44, 349-50, 370,419,436 reactive, 186-93, 349-50 spectroscopic, 186-93, 3 11, 320, 323, 349-50, 370 Minus states, 18-19, 27, 33, 54, 70 Mirror-image, absorption-emission, 260-63, 266 Mirror-image theorem (MCD), 170-7 1 M N D O C method. 56.383 M O (Molecular Orbital). II.See also Orbital M O configuration. 187-90. 192. 101. 131 M O model. electronic excitation, 9-21 light absorption. 1 1-13 Mobius array. 205. 329.445. 455 Molecular dynamics simulations. 132-33. 339 Molecular mechanics, 439 MRD-CI method, 58 Multiplicity, 12, 28-29, 180-81. 244. 247. 253. 257, 379 Mutually paired systems, 104, 170 Myrcene. 444 N and P transitions. 99-100, 167-69 N, Elimination from azo compounds. 38792 Naphthalene, 256, 321-24, 328, 346 absorption spectrum, 33. 42, 72. 104. 106 aza derivatives. 122 electron affinity and ionization potential. 14 excited state geometry, 44-45 HOM-LUMO transition, 14-55. 33 luminescence spectrum, 270 perimeter model, 83, 88, 91-92 photoreduction, 466 sensitization, 294-95 transition density. 33 triplet lifetime, 260 two-photon absorption spectrum, 41-42 Naphthalene- I-carboc ylic acid, 50 Naphthalene, 2-substituted. 84 I-Naphthol, 50 Naphthyl ketones, 351-52, 398 N E E R (non-equilibrium o f excited rotamers), 440

Nicotinamide adenine dinrtcleotide phosphirte (NAIII'). 473 Nitroanisoles. 475 Nitrogen heterocycles, 122-23 N-Nitrosodimethylamine, 133-34 Nitrosyl chloride. 476 Noncrossing rule. 182-83. 193 Norbornadiene. 230. 469 Norbornene. 407 Norbornyl iodide. 47 1 Norrish type Ireaction. 357. 380-97 Norrish typc II reaction. 323, 395. 399-404. 460,462 Nuclear kinetic energy. 217 N ~ ~ c l c o p h i laromatic ic substittrtions. 47476 Number o f active orbitals. 357. 379 Numbering systeni o f orbiti~ls.17 Nylon 6. 476 Octirhydrobenzoquinoxirline. 144 Octant rule. 148-49 Octatetraene. 70 Olefin. 363-66. 4 1 1. 4 12. Sc*cncilso Alkene cis-trans isomcrizirtion. 3 6 4 4 6 electron-poor. 42 1.428.43 1-32 elect ron-rich, 42 1, 423, 432 photodimerization. 404-1 1 Oligosilanes. 217. 302. 357. 392-94 One-electron model. 13-16 Oosterhoff modcl. 332. 335. 436 Optical activity, 140-54 exciton-chirality model. 147. I52 one-electron model. 147 Optical density, 7 Optical rotatory dispersion (ORD). 142-43 Orbital. See c11so AO: MO: Spin orbital active. 357, 379 canonical. 207 complex. 77. 79-81. 207. 478-79 c yclobutadiene-like, 334.4 14 degenerate, 187,413.420.458 frontier. 17. 90. 1 1 1. 17 1. 174-77. 292. 43 1 lone-pair. I 2 I. 150 most delocalized. 207-9. 478 nlost localized. 207-9. 225. 232. 334, 36243.413-14.478 nonbonding. 206. 232, 236. 334. 362-63. 413-14.436 nonort hogonal. 208 orthogonal, 206. 208 perimeter. 76. 89. 97

Orhitirl correlillion diagram. 189. 333 alternant hydl ocarbon. 345-46 benzene valc~rceisomerization. 449. 452 o bond dissociation. 188-89 n bond dissociirtion. 190-91 cubane. 410 cyclobutene. conrotatory r i n g opening. 196-97. 1'19 cyclobutenc. tlisrotatory ring opening. 194-98. ZcH) cyclohutenopl~cnirnthrene. 203 diimide. u-clc;~virge.3 8 7 4 9 cis-trans-i\c~merization. 377 endoperoxid lormation. 480-8 1 ethylene dinicrizirtion. 202-3. 333 hydrogen ab\t rirction. 204-5. 397 Iwo-step procedure. 197-W. 346 0rbit;rl crossiny. normal and abnormal. 344-48. 4o9-10.415 Orbital energy. 13-15. 104 perimeter niotlcl. 77 Orbital energy diagram. anthracene and phenantht-cne. 18 benzene pholocycloaddition. 42 1 two orbital s!,\tcni. 187 Orbital interacliun. 197-99,201-3.342.455 secondary. 4 1 2- 13 Orbital labeling system. 17 Orbital magnetic moment. 77. 161 Orbital ordering. 376.409-10.458 Orbital symmet I y. 193-97. 202.435 Orientation field. 131 Oriented molec~tles,38-40 Orlandi-Siebratid diagram. 369 Ortho cycloaddit ion. 420-23 Oscillator strength. 21-24. 38. 56-57. 67. 116. 246. 253. 289-Yo Outer-sphere clcctrcm-transfer reactions. 284 Overlap charge density. 26. 33 Overlap densit). 14. 79. 125. 150,209.485 Overlap integrirl. 237. 362 Overlap selection rule, 32-33 Oxabicyclobutatic. 433 Oxacarbene. 380 Oxa-di-n-met h;111crearrirngement 453. 462 Oxepin. 326 Oxctanc. 299. 3 19. 3M. 407.424-32. 460. 470 kinetic schcnit.. 426 Oxelene. 433 Oxirirnc. 340. 7 F X . 442

Oxygen effect. 256 Oxygen wave functions. 478-79. See crlso Singlet oxygen Pagodane$ 419 Pairing theorem. 17. 33. 90. 170. See ulso Alternant hydrocarbon Para cycloaddition. 420 Paracyclophanc, 124. 281 Parity. 3 1 Paterno-Riichi reaction. 424-32 carbon-carbon attitck. 43 1 carbon-ox ygen attack. 429-3 1 parallel and perpendicular approach. 428-30 PE (Photoelectron) spectra. IIS. 121. 376 Pentacene isomers, 94-95 Pentadiene. 367.437. 454 Pentahelicene, 44 1 Pentalene, 169. 236 Perepoxide. 478 Pericyclic reactions. 205. 230. 235. 238-39. 332-48, 393. Sene cilso Cycloaddition: Elect roc yclic reaction ground-state allowed. 197 ground-state forbidden. 194-95. 202. 229. 332. 344.454 spectroscopic nature o f states. 238-39 Perimeter modcl, 76-101. 161-70. 236 applications. 87-92. 17 1-77 C I matrix. 79. 82. 84. 97 complex MOs. 76 generalization. 81-101 Perimeter. 4N-electron. 96-101. 167-70, 445 charged. 98. 340 perturbation-induced orbital splitting. I00 substituent-induced perturbation. 108 uncharged, 97-98. 340 Perimeter ( 4 N + 2)-electron. 77.81. 85-87. 90. 92. 109-10. 161. 164-67. 171 charged, 78.8247 uncharged. 78.90.92 Peripheral bonding. 337. 367. 415 Peroxides. 338. 480 Perturbation. chiral. 147 covalent ( y ) . 21 1-13. 220-21. 224-25. 228-29, 332. 339. 366 hierarchy of. 87 polarizing ( 0 ) .212-13. 218. 224. 236. 332. 334. 339. 36243.436 structural. 82

theory, 2 1. 37. 104. 122. 127. Set. erlso PMO method time-dependent. 2 1 Perylene. 262 Phantom state, 365. 371.413 Phase angle, perimeter model, 82-83, 9192.97 Phase difference. 140 Phase polygon. 79-80 Phenanthrene, 203. 348. 440 absorption spectrum. 19 H M O orbital energy levels. 18 perimeter model, 93-94 polarization spectra. 275 Phenes. 71 Phenol. 52. 463 Phenylalanine. 152 I-l'henylcyclohexene. 468 I - and 2-Phenylnaphthirlene. 46-47 I'heophytin a. 473 I'hosphoresccnce. 244-45. 266-71. 2W. 31 1 I'hosphot-escence cxcitirtion spectrum. 27071 p-hydroxybenzophenone. 27 1 Phosphorescence polirriz:rtion spectrum. 273-76 Phosphorescence spectrum. Scp crlso Luminescence Spectrum anthracene. 263. 266 porphine. 268 Photoacoustic calorimetry. 434 Photocatalyst. 364. 473 Photochemical electron transfer (PET). See Electron transfer Photochemical nomenclature. 18 1 Photochemical reaction models. 309-32 Photochemical variables. 324-3 1 pitrirmcters. 3%) I'hotochromic material. 448 Photo-Claisen. photo-Fries. 358. 379, 387 Photocyclization. N-methyldiphenylamine. 340,442 ( Z ) -I.3.5-hexatriene. 229 cis-stilbene. 238, 440 Photocycloadditions. 341-43. 404-5. See also Cycloaddition arene-irl kene. 422 carbonyl group. 424-32 excited benzene to olefin. 42 1 ground-state forbidden, 341 n./l-unsaturated cirrhonyl compounds. 433-34 Photocycloreversion. 4 18

INDEX Photodimerization, 34 1-44, 405. See ulso Dimerization acenaphthylene, 413 anthracene, 341, 416 Copper(1) catalyzed, 408 olefins, 344, 404.41 1 schematic potential energy curves, 343 Photodissociation, 378-94. See also Dissociation Photodissociation spectroscopy, 238 Photodynamic tumor therapy, 295 Photoenolization, 447-48, 462 Photofragmentation o f oligosilanes and polysilanes, 392-94 Photoinduced electron transfer, 286, 466, 470, 472. See crlso Electron transfer Photoisomerization, 32 1, 368. 388 o f benzene, 448-53 Photon-driven selection pump, 426 Photonitrosation. 476 Photoorientation, 276 Photooxidations with singlet oxygen, 47680 Photophysical parameters, 249 Photophysical process, 179, 186, 196, 243306, 310-13 i n gases and condensed phases, 301-2 lifetime, 2 4 8 4 9 quantum yield, 248-50 rate constant, 249-50 temperature dependence, 302-3 Photoracemization o f ketones, 400 Photorearrangements. See Rearrangement reactions Photoreduction, 395-99 benzophenone, 395,397-98 benzophenones and acetophenones, 467 carbonyl compounds, 466 naphthalene by triethylamine, 466 Photoselection, 272, 275 Photosensitization, 292, 407. See ~ l s o Sensitization Photostationary state. 329. 365. 371 Photosubstitutions, 444-76 Photosynthesis, 286,472-74 Photosystem Iand 11,472-74 Pigment P680 and P700.472-74 Pinacol, 397-98 ppinene, 444 Piperylene, 299, 367, 401 pK value, 49-52 Plastoquinone, 473 Platt's nomenclature, 21, 79, 91, 167, 169

Pleiadene, 165, 168, 3 1 1 M C D spectra, 157-58 polarized absorption, 157-58 Plus and minus states, 18-19, 27, 33, 54, 70 PMO method, 75, 88-89, 343. 431 Polarization degree, 41 Polarization direction, 2, 3 8 4 0 , 57, 272, 274 absolute and relative, 6 'L,, 'L,, 'B, , 'B2 band, 86-92-93. 109 N a n d P bands. 100 substituent effect, 109 Polarization. electronic transition, 38-40 Polarization spectrum, 273-76 acenaphthylene, 157 azulene, 274 cyanine dye. 39 o f fluorescence and phosphorescence, 273-76 phenanthrene. 273 pleiadicnc. 157 pyrcne. 40 triphenylene. 276 Polyacene, 92-96 Polyamides, 476 Polyene aldehydes, 120 Polyenes, 48. 54. 65-71, 370 'A, state, 70 alternating double and single bonds, 67-68 dimethyl and diphenyl, 67 Polysilane, 392-94 Porphine, free base, 268, 276 Porphyrin-quinone systems, 286 Porphyrins, 171, 295,474 expanded, 296 Potential energy curves. ethylene, 66, 373 diatomic molecule, 36, 259 formaldimine, 374-75 formaldiminium ion, 373 molecular oxygen, 478-79 SiH, elimination, 394 Potential energy surfaces, 179-93, 309, 3 14 acetaldehyde, a cleavage, 38 1-82 acrolein, a cleavage. 382 adiabatic and diabatic; 179, 185-86, 315-16 anthracene dimerization. 3 19 benzaldehyde, a cleavage, 38 1-82 chemiluminescence, 48 1 1.4-dewarnaphthalene, photoisomerization, 322

INDEX diimide, cis-trans isorneriration, 377 excimer formation, 279 excited states, 179-8 1 , 186-93 formaldehyde, a cleavage, 353-55 nonconcerted reactions. -349-55 12 + 2) and .r[2 + 2) processes. 230-38 PPP met hod. 17-1 8. 53-55. 70-7 1. 102-3. 273. 332 Prebenzvalene, 453 Precalciferol, 4 3 9 4 0 Prefulvene. 42 1-22.44849 Prismane. 448.450.452 2-Propanol, 398 [ I.I.ljpropellane. 189 Propene. twisted, 210, 214 Proton transfer, 49 Protonation site, 174 Pseudosigmatropic shift, 446 Purple bacterium Rhodopseudomonas viridis, 472 Pyramidalization. 2 18, 362 Pyrene. 87. 134. 256. 280-8 1. 295 absorption and fluoresce~icespectra. 280 2-Pyridone, 174 Quadricyclane, 230,469 Quantum yield, 247-50, 3 17-18, 365, 367. 378,406,416,438 benzvalene isomerization. 45 1 chemiluminescence, 483 cyclobutene formation. 438 dewarbenzene isomerization, 450 differential, 248 emission, 253 fluorescence, 248-50, 263, 266, 297, 30 1-2 hexamethyldewarbenzenc valence isomerization, 468 hydrogen abstraction, 398 internal conversion, 248-49 intersystem crossing. 248 -49 N?elmination, 392 Norrish type 11 reaction, 399 oxetane formation, 299 phosphorescence. 248-50, 266, 269 photodimerization, 406 photonitrosation, 476 radiationless deactivation, 249 stilbene isomerization. 370-71 temperature dependence, 373 total, 248 triplet formation, 249 Quartet state, 102

Quencher, 298 triplet, 371, 398. 412, 473 Quenching. 3 1 1,425 concentrat ion, 277-78 diffusion-controlled, 299 dynamic and static, 299-301 electron-transfer, 283-87, 465 excited states, 277-78 heavy atom, 283-87 impurity, 277 oxygen, 286-87 rate constant, 298 Quinhydrones o f the [3.3]paracyclophane series. 124 o-quinodimethanes, 391, 453 o-quinol acetate, 463-64 Quinoline. 104. 106, 26748, 303 Quinone, 100. 286 Radiation, electromagnetic, I intensity. 4 interaction with molecule. 21 Radiationless deactivation, 245, 249, 25260. 31 1 processes. 244, 253. 263 transition, 253-54, 257-60 Radical anion, 476 Radical cation. 467. 469-70. 475 Radical. doublet and quartet configuration, 102 odd alternant, 101-3 Radical ion pair, 285-86, 363, 465-67, 46970.485 Radical ions. 284 alternant hydrocarbons. 102 pairing theorem, 103 Radical pair, 33 1, 460-62 Rate constant, 248-49 electron transfer processes, 285 fluorescence, 246, 248 internal conversion, 247, 249 intersystem crossing, 247, 249, 266 isomerization, 370 nonradiative energy transfer, 290 phosphorescence. 246. 249 spontaneous emission. 245 triplet-triplet energy transfer. 292, 294 vibrational relaxation, 247 Rate. internal conversion, 247 intersystem crossing, 256 radiationless transitions, 259 unimolecular processes, 245-47 Rate law. exponential. 246. 248

INDEX

534

Reaction, adiabatic and diabatic, 31 I, 32224,450-5 1 antarafacial. 445, 447 complex, 3 13 concerted, 340 direct, 310-1 1. 327 electron-transfer. 464-75 ground-state allowed, 197, 324 ground-state forbidden, 194-97, 205, 229, 405 HI + H,, 230-36, 238, 279. 295, 342, 417 hot, 301, 310-1 1, 320-22, 388 intermolecular, 3 18 nonconcerted, 349-59.406 pericyclic, 205. 320 stereospecific. 340 symmetry forbidden, 443 with and without intermediates, 313-20 Reaction coordinate. 180 Reaction dynamics, 3 18 Reaction field. 130-32. 474 Reaction medium. 324-26 Reaction pathway, 193, 3 18 bifurcated. 3 18, 440 conrotatory. 339. 366 disrotatory, 339, 366-67.436-37 ground-state, 436 rectangular. 235. 335 tetrahedral. 235 Rearrangements. 434-64 unsaturated carbonyl compounds, 460-64 Recombination, 380 Reductive elimination of SiH,, 392-94 Refractive index, 2, 140 Regioselectivity, 326, 407, 410-17, 420, 422-24.432. 434,456,458,469 Rehm-Weller relationship, 285-86 Relaxation. 6 Reorganization energy, 284 Resonance integral, 53, 56, 1 1 I, 2 11, 224, 344. 402,415 Retinal Schiff base, 373 Retro-Diels-Alder reaction, 484 Rhodamine dyes. 250. 373 Rhodopsin. 373 Right-hand rule. 150-51 King opening and closure. S c p IIISO Correlation diagram in hiradicals. 228-29. 430 Ring strain. 350. 364. 438 Rose Bengal, 295,480 Rosenfeld formula. 145-46 Rotation, specific and molar. 142

Rotational barriers. 329 Rotational fine structure, 9, 42-44 Rotational strength. 145-46 Rule of five. 409. 443-44.446 Rydberg orbital. 59-60 Rydberg transition. 2 1 Saccharides. 473 Saddle point. 180. 333 Salem diagram. 205, 355-56 Schcnck mcch;~ni\m.364 Schiff base. 191. 217. 273 Schrodinger equittion. 180 Scrambling of hydrogen. 450 Selection rules. 27-34 Self-consistent field (SCF) methods. 52 Self-consistent reaction field, 131-32. 474 Self-quenching. 277-78 Self-repulsion energy. 33 Semibullvalene. 457 Sensitization. 277. 292-95. 31 1. 364-67. 388-90.407-8, 416.450.456.462-63 Sensitizer. 292. 364. 372. 389.407 chiral. 364, 47 1 Sigmatropic shift, 435. 445-48. See crlso Hydrogen shift [ 1.21, 363, 446. 453-54.456.46243 type A and type B. 463 [ 1,3]. 445-46. 450,46043 (3.31.446 [ij]. 445 antarafacial. 445. 447 degenerate, 450 suprafacial, 23 1. 445, 447 vinyl. 454. 456 Silabenzene, 105-7 Silylene, 392-94 Single bond. dissociation, 188-90 stretching. 205 Singlet, 13. 180 impure. 28 Singlet oxygen. 295,476-80 Singlet-singlet energy transfer. 278. 291 Singlet-triplet splitting. 33-34. 55. 76. 123. 220-2 1. 227, 229. 266, 289 Sing!ct-triplet ~ t i ~disposition. te 267-68 Singlet-triplet tr;lnsitic>n. 29 12 Slater determini~~it. Slater rules. 15, 234 Solvation. 284. 305. 324 Solvatochromisn~.positive or negative, 132-33 Solvent cage, 326, 387, 465, 47 1

INDEX Solvent effect. 48, 129-35, 303-6, 325 continuum and discrete theories, 131 Solvent parameters, 1 3 1 Solvent reorganization, 303. 306 Solvent-separated ion pair, 425 SOMO, 102, 167 SOMO+LUMO excitation. 10? Special pair. 473-74 Spectra, atomic and molecular. 9 Spectral distributions. 288 Spectral ovcrlap, 288-90 Spectroscopist's convention, 181 Spin correlation effect. 389 Spin density. 469 Spin functions, 54, 224, 227. 274 singlet and triplet. 209. 222 Spin inversion, 255, 324, 389. 399,483 Spin orbital, I I, 78, 289,479 Spin-orbit coupling, 28-29. 180, 220-29. 255, 257, 264, 266, 268, 273, 363, 402-3,406,426,434,483 atomic vector contributions. 224-26 operator, 28. 222. 274 parameter, 223-24 strength, 222. 224. 227-28 through-bond. 222. 225-27 through-space. 225-27 vector, 222-23 Spin relaxation. 2 19-20, 228 Spin selection rule, 28. 32, 291 Spin-statistical factor. 320. 416 Spin. z component. 1:' State correlation diagram. 189. 194. 200-5. 446 alternant hydrocarbon, 345 anthracene dimerization. 3 19-20 azobenzene. cis-trans-isomerization. 377-78 benzene valence isomerization. 449. 452 o bond dissociation. 188-89 n bond dissociation. 190-91 butanal. Norrish typ 11. 400 chemiluminescence. 48 1-82 u cleavage, 354-55. 381-82. 388 cyclobutanone. 386 cyclobutene ring opening. 195-99, 201. 436 cyclob~~tenophenanthrenc fragmentation. 347-48 diimide, 376-77, 388-89 ethylene, cis-trans isomerization. 191. 362, 365 dimerization. 334

formaldehyde + methane. 35 1, 395 H4,232-35.416 hydrogen abstraction, 203-4, 35 1, 397 methanol, C - 0 bond dissociation, 358 a-quinol acetate reactions. 464 photodimerization. 403 stilbene. 369 tetraniethyl-1,2-dioxetane,482 State diagram. Sue Jablonski diagram State. electronic. 16-20 degenerate, 159. 161 diabatic. 185-86, 3 17 267disposition of (n,n*) and (n,n*), 68 G . S and D. 98-100. 192 N and P, 99-1 00 Stationary point, 184 Stereochemistry, 404,412,431,436,455 head-to-head and head-to-tail, 334-35, 342.41 1-15.417, 433-34 syn and anti, 342,412,414,417 Stereoelectronic effects. 466 Stereoselectivity, 403. 407, 41 1, 427. 466 Stereospecificity. 4044,428, 442,446 Steric discrimination. 403 Steric effects. 126-29, 450 Stern-Volmer equation. 298 Stern-Volmer plot, 299-301 Steroids, 1 13 Stilbene, 218,401. 41 1,440-43, 466 cis-trans isomerization, 369-72 fluorescence quantum yields. 264 triplet, 401 Stokes shift, 260-62 Stretched polymer films, 39-40, 272 Structure, biradicaloid, 352, 355-56 charge-separated, 362 covalent, 54. 207, 233 dot-dot, 207-8, 21 1-14, 217, 233, 356 hole-pair, 207-8. 2 12-1 8, 223-24, 233, 356 zwitterionic. 189, 191-92. 207. 223. 233-34 Substituent effect, 104-1 18, 172-73.41315.42 1. 438. 453. 457. See crlso Steric effects aniline. 1 15-16 hyperconjugative. 173 MCD signs, 171 methyl group, 1 14. 173-75 Substituent parameter. I I 1 Substituents. acceptor. 414-15, 432, 457-58 &ma-. 414-15.458

INDEX electron-donating and withdrawing, 17172,236, 335,402,421, 431-32 inductive, 104-9 +Mand - M , 110 mesomeric, 109- 1 18 strength, 115 Substitution, 87-88. See also Perturbation, hierarchy of Sudden polarization, 212-13, 218, 317, 362, 474 Supermolecule, 132, 23 1, 3 13, 341, 405 Supersonic jet laser spectroscopy, 44, 367 Surface jump, 2 17, 3 15-17.483 Surface touching, 181-83, 217, 236, 3 15, 333. See also Crossing Symmetry selection rules, 30-32 Syn-anti isomerization, 374-75 Temperature dependence, photophysical processes, 302-3 stereoselectivity, 326-27 Tetra-t-butyltetrahedrane, 385 Tetracene, 254 absorption spectrum, 72, 103 Tetracene radical anion and cation, 103 Tetracyclooctene, 423 Tetramethylcyclobutane, 406 Tetramethyl-l,2-dioxetane,428, 482-83 Tetramethylethylene, 326-27 Tetranitromethane, 465 a,a,a1a'-Tetraphenylbenzocyclobutene. 350 Tetraphenylcyclobutiine, 470 Tetraphenylethylene, 33 1 Tetraradical, 230 Thermal equilibration, 260, 310, 321 Thiobenzophenone, 328 Thiocarbonyl compounds. 254 Third row elements, 105, 107 Three-quantum process, 459 Through-bond interaction, 121, 292, 402, 409- 10 Through-space interaction, 12 1, 177, 402, 409- 10 TICT (twisted internal charge transfer). 191, 214, 218, 303,474 Time-resolved spectroscopy, 250, 444 Toluene, 348-49 Topicity, 190, 352, 356-58, 379 Trajectory, 180, 317,415 Transannular interactions, 175-77 Transient spectrum, 369,465

Transition. See also Electronic transition 0-0, 37. 26162 allowed and forbidden, 27 charge-transfer, 123-26 degenerate, 158 electric dipole, 5 quadrupole. 5 intensity, 21-27 longest-wavelength, alternant hydrocarbons, 74-75 magnetic dipole, 5 n-m*, 1 18-23 carbonyl compounds, 34, 119-22 nitrogen heterocycles, 122-23, 133 solvent effect. 133 radiationless, 323 spin-forbidden, 266 two-photon, 40-42 vertical, 35-36 vibrationally induced. 36-38 Transition density, 25, 34, 79-8 1, I5 1 Transition dipole moment. 23. 32. 37. 56. 85 electronic, 36. 144-46. 150-5 1, 160. 164 magnetic, 144-46, 150-51, 153, 160, 164 Transition moment, 5, 13. 15. 18, 25-27. 29, 126, 246, 263, 266, 272-74, 289, 303 computation. 56-58 direction, 25, 272-73 perimeter model, 79-8 1, 85, 99 solvent effect, 133 tensor, two-photon. 4 1 Transition state, 3 17-18, 334-35 geometry. 384 Translocation of formal charge, 214 Tricyclo[4.2.0.0?']octadiene. 409 Trienes. 1 12. 366.444 Trimethinecyanine, FEMO model, 16 Trimethylene biradical, 225, 227 Trinitrobenzene, DA complex, 125 Triphenylene, 270, 276 Triphenylmethane dyes, 373. , Triple bond. bending, 205 Triplet, 12, 14, 180 impure, 28, 220-21, 227 Triplet energy of sensitizer, 372, 407 Triplet function, 222 Triplet state, aromatics, 76 calculation, 55 ethylene, 64 Triplet-triplet absorption, 256 Triplet-triplet annihilation, 238, 278, 287, 295-97, 31 1, 318, 320, 41617,480

Triplet-triplet energy transfer. 278, 291-94 Triplex, 364, 471 Trisilane, 394 Tritopic. See Topicity Tropylium ion, 86 . Tunneling. 321, 33 1 Two-chromophore system, 152-54 Two-electron-two-orbital model, 191-93, 205-18, 230, 336.413-14 Two-photon excitation, 3 1 I . 370 Two-photon process, 248, 330 Two-photon spectroscopy, 28.40-44. 54, 70 Two-photon spectrum. benzene, 43 naphthalene, 4 1-42 Two-quantum process, 459 Two-step procedure, 198-9. 203, 346 Ubiquinone, 474 Umpolung, 470 Ungerade, 30-3 1 , 4 1. See ulso Parity Unimolecular processes, 243-52, 3 13 Unitary group approach (UGA), 55 Valence isomerization, 324, 329,458,46869 . of benzene, 264-65. 302,448-52 Valence isomers of benzene. 390-91.448 Valence tautomers, 326 Valerophenone, 403 triplet quenching, 300-1 VB (Valence Bond), 208, 230, 232 VB correlation diagram. Src. Salem diagram VB exchange integral, 237 2 x 2 VB model, 230, 232-33, 235-37 VB structure, 189-92, 202, 205-208, 232, 236, 355-56, 362. Set. trlso Structure Vector potential, 22 Vibrational equilibration, 185, 444, 450 Vibrational relaxation, 245, 252, 264-65, 288, 301, 303, 310. 375 Vibrational structure, 9-1 1, 13, 35, 43, 159 Vibronic coupling, 31, 33, 37, 44, 273 benzene, 32,37-38, % Vibronic progression, 38

Vibronically induced transitions, 36-38 2-Vinylbicyclo[l . 1 .O]butane, 368 4-Vinylcyclohexene, 408 Vinylcyclopropane, 454 Vinyl radical, 45657 [I ,21 vinyl shift, 456 Vinyl substituent, l I0 Viscosity, 299-300, 306, 325, 370 Vision, primary steps, 373 Vitamin D. 434-35, 439 Wagner-Meerwein rearrangements, 472 Walsh rules, 44 Wave function, electronic, 10. adiabatic and nonadiabatic, 184 excited state, 53-54 total, 10 vibrational, 10. 23. 35-36 Wave number, 2-3 Wave packet, nuclear, 185, 3 16 Wave vector, 3. 22 Wavelength. 2- 4 Wavelength dependent photoreaction, 302, 327-30,448 Weakly coupled chromophores, 126 Weller equation, 285, 422 Wigner-Witmer rule, 277-78, 291. 295, 384 Woodward-Hoffmann rules, 324, 404, 419, 434-37.442-444-45.454 x , and xz vector, 183-84, 217, 316, 339

Xanthone, 52, 296-97 p-Xylene, 407 o-Xylylene, 350 Zeeman splitting. 160-65 Zero differential overlap (ZDO) approximation, 26, 53, 56, 79, 96, 124, 126, 234 Zero field splitting, 22 1 tensor, 22 1, 225, 227 Zimmerman rearrangement, 453 Zwitterionic character, 54, 207, 214, 23536, 356

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