Preface .................................................. xix
Chapter 1 Molecular Photochemistry of Organic Compounds:
An Overview .......................................... 1
1.1 What Is Molecular Organic Photochemistry? .................. 1
1.2 Learning Molecular Organic Photochemistry through the
Visualization of Molecular Structures and the Dynamics
of Their Transformations ................................... 3
1.3 Why Study Molecular Organic Photochemistry? ................ 3
1.4 The Value of Pictorial Representations and Visualization
of Scientific Concepts ..................................... 5
1.5 Scientific Paradigms of Molecular Organic Photochemistry ... 6
1.6 Exemplars as Guides to the Experimental Study and
Understanding of Molecular Organic Photochemistry .......... 7
1.7 The Paradigms of Molecular Organic Photochemistry .......... 8
1.8 Paradigms as Guides for Proceeding from the Possible
to the Plausible to the Probable Photochemical Processes ... 8
1.9 Some Important Questions that Will Be Answered by the
Paradigms of Molecular Organic Photochemistry ............. 10
1.10 From a Global Paradigm to the Everyday Working Paradigm ... 11
1.11 Singlet States, Triplet States, Diradicals, and
Zwitterions: Key Structures Along a Photochemical
Pathway from *R to P ...................................... 14
1.12 State Energy Diagrams: Electronic and Spin Isomers ........ 16
1.13 An Energy Surface Description of Molecular
Photochemistry ............................................ 20
1.14 Structure, Energy, and Time: Molecular-Level Benchmarks
and Calibration Points of Photochemical Processes ......... 25
1.15 Calibration Points and Numerical Benchmarks for
Molecular Energetics ...................................... 26
1.16 Counting Photons .......................................... 28
1.17 Computing the Energy of a Mole of Photons for Light of
Wavelength A. and Frequency ............................... 29
1.18 The Range of Photon Energies in the Electromagnetic
Spectrum .................................................. 29
1.19 Calibration Points and Numerical Benchmarks for
Molecular Dimensions and Time Scales ...................... 33
1.20 Plan of the Text .......................................... 36
References ................................................ 38
Chapter 2 Electronic, Vibrational, and Spin Configurations
of Electronically Excited States .................... 39
2.1 Visualization of the Electronically Excited Structures
through the Paradigms of Molecular Organic
Photochemistry ............................................ 39
2.2 Molecular Wave Functions and Molecular Structure .......... 42
2.3 The Born-Oppenheimer Approximation: A Starting Point for
Approximate Molecular Wave Functions and Energies ......... 45
2.4 Important Qualitative Characteristics of Approximate
Wave Functions ............................................ 47
2.5 From Postulates of Quantum Mechanics to Observations of
Molecular Structure: Expectation Values and Matrix
Elements .................................................. 49
2.6 The Spirit of the Use of Quantum Mechanical Wave
Functions, Operators, and Matrix Elements ................. 50
2.7 From Atomic Orbitals, to Molecular Orbitals, to
Electronic Configurations, to Electronic States ........... 51
2.8 Ground and Excited Electronic Configurations .............. 52
2.9 The Construction of Electronic States from Electronic
Configurations ............................................ 56
2.10 Construction of Excited Singlet and Triplet States from
Electronically Excited Configurations and the Pauli
Principle ................................................. 56
2.11 Characteristic Configurations of Singlet and Triplet
States: A Shorthand Notation .............................. 57
2.12 Electronic Energy Difference between Molecular Singlet
and Triplet States of *R: Electron Correlation and the
Electron Exchange Energy .................................. 58
2.13 Evaluation of the Relative Singlet and Triplet Energies
and Singlet-Triplet Energy Gaps for Electronically
Excited States (*R) of the Same Electronic
Configuration ............................................. 60
2.14 Exemplars for the Singlet-Triplet Splittings in
Molecular Systems ......................................... 63
2.15 Electronic Energy Difference between Singlet and Triplet
States of Diradical Reactive Intermediates: Radical
Pairs, I(RP), and Biradicals, I(BR) ....................... 66
2.16 A Model for Vibrational Wave Functions: The Classical
Harmonic Oscillator ....................................... 69
2.17 The Quantum Mechanical Version of the Classical Harmonic
Oscillator ................................................ 75
2.18 The Vibrational Levels of a Quantum Mechanical Harmonic
Oscillator ................................................ 77
2.19 The Vibrational Wave Functions for a Quantum Mechanical
Harmonic Oscillator: Visualization of the Wave Functions
for Diatomic Molecules .................................... 78
2.20 A First-Order Approximation of the Harmonic-Oscillator
Model: The Anharmonic Oscillator .......................... 80
2.21 Building Quantum Intuition for Using Wave Functions ....... 82
2.22 Electron Spin: A Model for Visualizing Spin Wave
Functions ................................................. 82
2.23 A Vector Model of Electron Spin ........................... 85
2.24 Important Properties of Vectors ........................... 85
2.25 Vector Representation of Electron Spin .................... 86
2.26 Spin Multiplicities: Allowed Orientations of Electron
Spins ..................................................... 87
2.27 Vector Model of Two Coupled Electron Spins: Singlet and
Triplet States ............................................ 89
2.28 The Uncertainty Principle and Cones of Possible
Orientations for Electron Spin ............................ 92
2.29 Cones of Possible Orientations for Two Coupled 1/2 Spins:
Singlet and Triplet Cones of Orientation as a Basis for
Visualizing the Interconversion of Spin States ............ 93
2.30 Making a Connection between Spin Angular Momentum and
Magnetic Moments Due to Spin Angular Momentum ............. 94
2.31 The Connection between Angular Momentum and Magnetic
Moments: A Physical Model for an Electron with Angular
Momentum .................................................. 94
2.32 The Magnetic Moment of an Electron in a Bohr Orbit ........ 95
2.33 The Connection between Magnetic Moment and Electron
Spin ...................................................... 97
2.34 Magnetic Energy Levels in an Applied Magnetic Field for
a Classical Magnet ........................................ 99
2.35 Quantum Magnets in the Absence of Coupling Magnetic
Fields ................................................... 101
2.36 Quantum Mechanical Magnets in a Magnetic Field:
Constructing a Magnetic State Energy Diagram for Spins
in an Applied Magnetic Field ............................. 102
2.37 Magnetic Energy Diagram for a Single Electron Spin and
for Two Coupled Electron Spins ........................... 103
2.38 Magnetic Energy Diagrams Including the Electron
Exchange Interaction, J .................................. 104
2.39 Interactions between Two Magnetic Dipoles: Orientation
and Distance Dependence of the Energy of Magnetic
Interactions ............................................. 106
2.40 Summary: Structure and Energetics of Electrons,
Vibrations, and Spins .................................... 108
References ............................................... 108
Chapter 3 Transitions between States: Photophysical
Processes .......................................... 109
3.1 Transitions between States ............................... 109
3.2 A Starting Point for Modeling Transitions between
States ................................................... 111
3.3 Classical Chemical Dynamics: Some Preliminary Comments ... 112
3.4 Quantum Dynamics: Transitions between States ............. 113
3.5 Perturbation* Theory ..................................... 113
3.6 The Spirit of Selection Rules for Transition
Probabilities ............................................ 118
3.7 Nuclear Vibrational Motion As a Trigger for Electronic
Transitions. Vibronic Coupling and Vibronic States:
The Effect of Nuclear Motion on Electronic Energy and
Electronic Structure ..................................... 119
3.8 The Effect of Vibrations on Transitions between
Electronic States: The Franck-Condon Principle ........... 122
3.9 A Classical and Semiclassical Harmonic Oscillator Model
of the Franck-Condon Principle for Radiative
Transitions (R + hv → *R and *R → R + hv) ................ 124
3.10 A Quantum Mechanical Interpretation of the Franck-
Condon Principle and Radiative Transitions ............... 128
3.11 The Franck-Condon Principle and Radiationless
Transitions (*R → R + heat) .............................. 130
3.12 Radiationless and Radiative Transitions between Spin
States of Different Multiplicity ......................... 134
3.13 Spin Dynamics: Classical Precession of the Angular
Momentum Vector .......................................... 135
3.14 Precession of a Quantum Mechanical Magnet in the Cones
of Possible Orientations ................................. 139
3.15 Important Characteristics of Spin Precession ............. 141
3.16 Some Quantitative Benchmark Relationships between the
Strength of a Coupled Magnetic Field and Precessional
Rates .................................................... 142
3.17 Transitions between Spin States: Magnetic Energies and
Interactions ............................................. 144
3.18 The Role of Electron Exchange (J) in Coupling Electron
Spins .................................................... 144
3.19 Couplings of a Spin with a Magnetic Field:
Visualization of Spin Transitions and Intersystem
Crossing ................................................. 146
3.20 Vector Model for Transitions between Magnetic States ..... 148
3.21 Spin-Orbit Coupling: A Dominant Mechanism for Inducing
Spin Changes in Organic Molecules ........................ 149
3.22 Coupling of Two Spins with a Third Spin: T+ → S and
T- → S Transitions ....................................... 157
3.23 Coupling Involving Two Correlated Spins: T0 → S
Transitions .............................................. 158
3.24 Intersystem Crossing in Diradicals, I(D): Radical
Pairs, I(RP), and Biradicals, I(BR) ...................... 159
3.25 Spin-Orbit Coupling in I(D): The Role of Relative
Orbital Orientation ...................................... 160
3.26 Intersystem Crossing in Flexible Biradicals .............. 164
3.27 What All Transitions between States Have in Common ....... 166
References ............................................... 167
Chapter 4 Radiative Transitions between Electronic States .... 169
4.1 The Absorption and Emission of Light by Organic
Molecules ................................................ 169
4.2 The Nature of Light: A Series of Paradigm Shifts ......... 169
4.3 Black-Body Radiation and the "Ultraviolet Catastrophe"
and Planck's Quantization of Light Energy: The Energy
Quantum Is Postulated .................................... 172
4.4 The "Photoelectric Effect" and Einstein's Quantization
of Light—The Quantum of Light: Photons ................... 173
4.5 If Light Waves Have the Properties of Particles, Do
Particles Have the Properties of Waves? - de Broglie
Integrates Matter and Light .............................. 176
4.6 Absorption and Emission Spectra of Organic Molecules:
The State Energy Diagram as a Paradigm for Molecular
Photophysics ............................................. 178
4.7 Some Examples of Experimental Absorption and Emission
Spectra of Organic Molecules: Benchmarks ................. 178
4.8 The Nature of Light: From Particles to Waves to Wave
Particles ................................................ 181
4.9 A Pictorial Representation of the Absorption of Light .... 181
4.10 The Interaction of Electrons with the Electric and
Magnetic Forces of Light ................................. 182
4.11 A Mechanistic View of the Interaction of Light with
Molecules: Light as a Wave ............................... 184
4.12 An Exemplar of the Interaction of Light with Matter:
The Hydrogen Atom ........................................ 185
4.13 From the Classical Representation to a Quantum
Mechanical Representation of Light Absorption by a
Hydrogen Atom and a Hydrogen Molecule .................... 188
4.14 Photons as Massless Reagents ............................. 191
4.15 Relationship of Experimental Spectroscopic Quantities
to Theoretical Quantities ................................ 194
4.16 The Oscillator Strength Concept .......................... 195
4.17 The Relationship between the Classical Concept of
Oscillator Strength and the Quantum Mechanical
Transition Dipole Moment ................................. 196
4.18 Examples of the Relationships of ε, ke0, τe0, <Ψ1|P|Ψ2>,
and f .................................................... 197
4.19 Experimental Tests of the Quantitative Theory Relating
Emission and Absorption to Spectroscopic Quantities ...... 200
4.20 The Shapes of Absorption and Emission Spectra ............ 201
4.21 The Franck-Condon Principle and Absorption Spectra of
Organic Molecules ........................................ 204
4.22 The Franck-Condon Principle and Emission Spectra ......... 208
4.23 The Effect of Orbital Configuration Mixing and
Multiplicity Mixing on Radiative Transitions ............. 210
4.24 Experimental Exemplars of the Absorption and Emission
of Light by Organic Molecules ............................ 214
4.25 Absorption, Emission, and Excitation Spectra ............. 215
4.26 Order of Magnitude Estimates of Radiative Transition
Parameters ............................................... 218
4.27 Quantum Yields for Emission(*R → R + hv) ................. 223
4.28 Experimental Examples of Fluorescence Quantum Yields ..... 230
4.29 Determination of "State Energies" ES and ET from
Emission Spectra ......................................... 234
4.30 Spin-Orbit Coupling and Spin-Forbidden Radiative
Transitions .............................................. 235
4.31 Radiative Transitions Involving a Change in
Multiplicity: S0 ↔ T(n,π*) and S0 ↔ T(π,π*) Transitions
as Exemplars ............................................. 237
4.32 Experimental Exemplars of Spin-Forbidden Radiative
Transitions: S0 → T1 Absorption and T1 → S0
Phosphorescence .......................................... 240
4.33 Quantum Yields of Phosphorescence, ΦР: The T1 → S0 + hv
Process .................................................. 243
4.34 Phosphorescence in Fluid Solution at Room Temperature .... 244
4.35 Absorption Spectra of Electronically Excited States ...... 245
4.36 Radiative Transitions Involving Two Molecules:
Absorption Complexes and Exciplexes ...................... 247
4.37 Examples of Ground-State Charge-Transfer Absorption
Complexes ................................................ 248
4.38 Excimers and Exciplexes .................................. 249
4.39 Exemplars of Excimers: Pyrene and Aromatic Compounds ..... 253
4.40 Exciplexes and Exciplex Emission ......................... 256
4.41 Twisted Intramolecular Charge-Transfer States ............ 257
4.42 Emission from "Upper" Excited Singlets and Triples:
The Azulene Anomaly ...................................... 260
References ............................................... 262
Chapter 5 Photophysical Radiationless Transitions ............ 265
5.1 Photophysical Radiationless Transitions As a Form of
Electronic Relaxation .................................... 265
5.2 Radiationless Electronic Transitions as the Motion of
a Representative Point on Electronic Energy Surfaces ..... 266
5.3 Wave Mechanical Interpretation of Radiationless
Transitions between States ............................... 270
5.4 Radiationless Transitions and the Breakdown of the
Born-Oppenheimer Approximation ........................... 275
5.5 An Essential Difference between Strongly Avoiding and
Matching Surfaces ........................................ 275
5.6 Conical Intersections Near Zero-Order Surface
Crossings ................................................ 275
5.7 Formulation of a Parameterized Model of Radiationless
Transitions .............................................. 276
5.8 Visualization of Radiationless Transitions Promoted by
Vibrational Motion; Vibronic Mixing ...................... 277
5.9 Intersystem Crossing: Visualization of Radiationless
Transitions Promoted by Spin-Orbit Coupling .............. 281
5.10 Selection Rules for Intersystem Crossing in Molecules .... 282
5.11 The Relationship of Rates and Efficiencies of
Radiationless Transitions to Molecular Structure:
Stretching and Twisting as Mechanisms for Inducing
Electronic Radiationless Transitions ..................... 287
5.12 The "Loose Bolt" and "Free-Rotor" Effects: Promoter and
Acceptor Vibrations ...................................... 288
5.13 Radiationless Transitions between "Matching" Surfaces
Separated by Large Energies .............................. 291
5.14 Factors That Influence the Rate of Vibrational
Relaxation ............................................... 293
5.15 The Evaluation of Rate Constants for Radiationless
Processes from Quantitative Emission Parameters .......... 296
5.16 Examples of the Estimation of Rates of Photophysical
Processes from Spectroscopic Emission Data ............... 298
5.17 Internal Conversion (Sn → S1, S1 → S0, Tn → T1) ........... 300
5.18 The Relationship of Internal Conversion to the Excited-
State Structure of *R .................................... 301
5.19 The Energy Gap Law for Internal Conversion (S1 → S0) ..... 303
5.20 The Deuterium Isotope Test for Internal Conversion ....... 304
5.21 Examples of Unusually Slow Sn → S1 Internal
Conversion ............................................... 305
5.22 Intersystem Crossing from S1 → T1 ........................ 306
5.23 The Relationship Between S1 → T1 Intersystem Crossing
to Molecular Structure ................................... 307
5.24 Temperature Dependence of S1 → Tn Intersystem
Crossing ................................................. 308
5.25 Intersystem Crossing (T1 → S0) ........................... 309
5.26 The Relationship between T1 → S0 Intersystem Crossing
and Molecular Structure .................................. 309
5.27 The Energy Gap Law for T1 → S0 Intersystem Crossing:
Deuterium Isotope Effects on Interstate Crossings ........ 310
5.28 Perturbation of Spin-Forbidden Radiationless
Transitions .............................................. 311
5.29 Internal Perturbation of Intersystem Crossing by the
Heavy-Atom Effect ........................................ 312
5.30 External Perturbation of Intersystem Crossing ............ 313
5.31 The Relationship between Photophysical Radiationless
Transitions and Photochemical Processes .................. 314
References ............................................... 315
Chapter 6 A Theory of Molecular Organic Photochemistry ....... 319
6.1 Introduction to a Theory of Organic Photoreactions ....... 319
6.2 Potential Energy Curves and Surfaces ..................... 322
6.3 Movement of a Classical Representative Point on
a Surface ................................................ 323
6.4 The Influence of Collisions and Vibrations on the
Motion of the Representative Point on an Energy
Surface .................................................. 325
6.5 Radiationless Transitions on PE Surfaces: Surface
Maxima, Surface Minima, and Funnels on the Way from *R
to P ..................................................... 325
6.6 A Global Paradigm for Organic Photochemical Reactions .... 326
6.7 Toward a General Theory of Organic Photochemical
Reactions Based on Potential Energy Surfaces ............. 328
6.8 Determining Plausible Molecular Structures and
Plausible Reaction Pathways of Photochemical Reactions ... 330
6.9 The Fundamental Surface Topologies for "Funnels" from
Excited Surfaces to Ground-State Surfaces:
Spectroscopic Minima, Extended Surface Touchings,
Surface Matchings, Surface Crossings, and Surface
Avoidings ................................................ 330
6.10 From 2D PE Curves to 3D PE Surfaces: The "Jump" from
Two Dimensions to Three Dimensions ....................... 333
6.11 The Nature of Funnels Corresponding to Surface
Avoidings and Surface Touchings Involved in Primary
Photochemical Processes .................................. 334
6.12 "The Noncrossing Rule" and Its Violations: Conical
Intersections and Their Visualization .................... 335
6.13 Some Important and Unique Properties of Conical
Intersections ............................................ 337
6.14 Diradicaloid Structures and Diradicaloid Geometries ...... 341
6.15 Diradicaloid Structures Produced from Stretching a
Bonds and Twisting re Bonds .............................. 344
6.16 An Exemplar for Diradicaloid Geometries Produced by
σ-Bond Stretching and Bond Breaking: Stretching of the
σ Bond of the Hydrogen Molecule .......................... 344
6.17 An Exemplar for Diradicaloid Geometries Produced by
π-Bond Twisting and Breaking: Twisting of the π Bond of
Ethylene ................................................. 348
6.18 Frontier Orbital Interactions As a Guide to the Lowest-
Energy Pathways and Energy Barriers on Energy Surfaces ... 351
6.19 The Principle of Maximum Positive Orbital Overlap for
Frontier Orbitals ........................................ 353
6.20 Stabilization by Orbital Interactions: Selection Rules
Based on Maximum Positive Overlap and Minimum Energy
Gap ...................................................... 353
6.21 Commonly Encountered Orbital Interactions in Organic
Photoreactions ........................................... 354
6.22 Selection of Reaction Coordinates from Orbital
Interactions for *R → I or *R → F → P Reactions:
Exemplars of Concerted Photochemical Reactions and
Photochemical Reactions That Involve Diradicaloid
Intermediates ............................................ 357
6.23 Electronic Orbital and State Correlation Diagrams ........ 357
6.24 An Exemplar for Photochemical Concerted Pericyclic
Reactions: The Electrocyclic Ring Opening of
Cyclobutene and Ring Closure of 1,3-Butadiene ............ 358
6.25 Frontier Orbital Interactions Involving Radicals as
Models for Half-Filled Molecular Orbitals ................ 359
6.26 Orbital and State Correlation Diagrams ................... 362
6.27 The Construction of Electron Orbital and State
Correlation Diagrams for a Selected Reaction
Coordinate ............................................... 364
6.28 Typical State Correlation Diagrams for Concerted
Photochemical Pericyclic Reactions ....................... 364
6.29 Classification of Orbitals and States for the
Electrocyclic Reactions of Cyclobutene and
1,3-Butadiene: An Exemplar Concerted Reaction ............ 364
6.30 Concerted Photochemical Pericyclic Reactions and
Conical Intersections .................................... 368
6.31 Typical State Correlation Diagrams for Nonconcerted
Photoreactions: Reactions Involving Intermediates
(Diradicals and Zwitterions) ............................. 368
6.32 Natural Orbital Correlation Diagrams ..................... 368
6.33 The Role of Small Barriers in Determining the
Efficiencies of Photochemical Processes .................. 369
6.34 An Exemplar for the Photochemical Reactions of n,π*
States ................................................... 370
6.35 The Symmetry Plane Assumption: Salem Diagrams ............ 372
6.36 An Exemplar State Correlation Diagram for n-Orbital
Initiated Reaction of n,π* States: Hydrogen Abstraction
via a Coplanar Reaction Coordinate ....................... 372
6.37 Extension of an Exemplar State Correlation Diagram to
New Situations ........................................... 375
6.38 State Correlation Diagrams for α-Cleavage of Ketones ..... 375
6.39 A Standard Set of Plausible Primary Photoreactions for
π,π* and n,π* States ..................................... 378
6.40 The Characteristic Plausible Primary Photochemistry
Processes of π,π* States ................................. 378
6.41 The Characteristic Plausible Primary Photochemical
Processes of n,π* States ................................. 380
6.42 Summary: Energy Surfaces as Reaction Graphs or Maps ...... 381
References ............................................... 382
Chapter 7 Energy Transfer and Electron Transfer .............. 383
7.1 Introduction to Energy and Electron Transfer ............. 383
7.2 The Electron Exchange Interaction for Energy and
Electron Transfer ........................................ 387
7.3 "Trivial" Mechanisms for Energy and Electron Transfer .... 391
7.4 Energy and Electron Transfer Mechanisms: Similarities
and Differences .......................................... 396
7.5 Visualization of Energy Transfer by Dipole-Dipole
Interactions: A Transmitter-Antenna Receiver-Antenna
Mechanism ................................................ 399
7.6 Quantitative Aspects of the Förster Theory of Dipole-
Dipole Energy Transfer ................................... 400
7.7 The Relationship of kET to Energy-Transfer Efficiency
and Separation of Donor and Acceptor RDA ................. 404
7.8 Experimental Tests for Dipole-Dipole Energy Transfer ..... 406
7.9 Electron Exchange Processes: Energy Transfer Resulting
from Collisions and Overlap of Electron Clouds ........... 411
7.10 Electron Exchange: An Orbital Overlap or Collision
Mechanism of Energy Transfer ............................. 411
7.11 Electron-Transfer Processes Leading to Excited States .... 413
7.12 Triplet-Triplet Annihilation (TTA): A Special Case of
Energy Transfer via Electron Exchange Interactions ....... 414
7.13 Electron Transfer: Mechanisms and Energetics ............. 416
7.14 Marcus Theory of Electron Transfer ....................... 424
7.15 A Closer Look at the Reaction Coordinate for Electron
Transfer ................................................. 436
7.16 Experimental Verification of the Marcus Inverted Region
for Photoinduced Electron Transfer ....................... 438
7.17 Examples of Photoinduced Electron Transfer That
Demonstrate the Marcus Theory ............................ 441
7.18 Long-Distance Electron Transfer .......................... 441
7.19 Mechanisms of Long-Distance Electron Transfer: Through-
Space and Through-Bond Interactions ...................... 442
7.20 A Quantitative Comparison of Triplet-Triplet Energy and
Electron Transfer ........................................ 445
7.21 A Connection between Intramolecular Electron, Hole, and
Triplet Transfer ......................................... 446
7.22 Photoinduced Electron Transfer between Donor and
Acceptor Moieties Connected by a Flexible Spacer ......... 447
7.23 Experimental Observation of the Marcus Inversion Region
for Freely Diffusing Species in Solution ................. 448
7.24 Control of the Rate and Efficiency of Electron-Transfer
Separation by Controlling Changes in the Driving Force
for Electron Transfer .................................... 449
7.25 Application of Marcus Theory to the Control of Product
Distributions ............................................ 451
7.26 The Continuum of Structures from Charge Transfer to Free
Ions: Excipfexes, Contact Ion Pairs, Solvent Separated
Radical Ion Pairs, and Free Ion Pairs .................... 454
7.27 Comparison between Exciplexes and Contact Radical Ion
Pairs .................................................... 458
7.28 Energy and Electron-Transfer Equilibria .................. 461
7.29 Energy-Transfer Equilibria ............................... 461
7.30 Electron-Transfer Equilibria in the Ground State ......... 463
7.31 Excited-State Electron-Transfer Equilibria ............... 463
7.32 Excited-State Formation Resulting from Electron-Transfer
Reactions: Chemiluminescent Reactions .................... 464
7.33 Role of Molecular Diffusion in Energy and Electron-
Transfer Processes in Solution ........................... 466
7.34 An Exemplar Involving Energy Transfer Controlled by
Diffusion ................................................ 467
7.35 Estimation of Rate Constants for Diffusion Controlled
Processes ................................................ 469
7.36 Examples of Near-Diffusion-Controlled Reactions:
Reversible Formation of Collision Complexes .............. 472
7.37 The Cage Effect .......................................... 474
7.38 Distance-Time Relationships for Diffusion ................ 476
7.39 Diffusion Control in Systems Involving Charged Species ... 478
7.40 Summary .................................................. 479
References ............................................... 479
Index ......................................................... 483
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