Preface ........................................................ IX
1 Introduction ................................................. 1
1.1 The Adiabatic Description of Molecules .................. 1
1.1.1 Preliminaries .................................... 1
1.1.2 The Born-Oppenheimer Approximation ............... 3
1.1.3 The Crude Born-Oppenheimer Basis Set ............. 6
1.1.4 Correction of the Crude Adiabatic
Approximation .................................... 7
1.2 Normal Coordinates and Duschinsky Effect ................ 9
1.3 The Vibrational Wavefunctions .......................... 13
1.4 The Diabatic Electronic Basis for Molecular Systems .... 14
1.4.1 Preliminaries ................................... 14
1.4.2 Conical Intersection Between the States
 2B2/2A' and Ã2A1/2A' of H2O+ ..................... 16
1.4.3 The Linear Model for Conical Intersection ....... 18
2 Formal Decay Theory of Coupled Unstable States .............. 21
2.1 The Time Evolution of an Excited State ................. 21
2.1.1 Some Remarks About the Decay of a Discrete
Molecular Metastable State ...................... 26
2.2 The Choice of the Zero-Order Basis Set ................. 27
3 Description of Radiationless Processes in Statistical
Large Molecules ............................................. 31
3.1 Evaluation of the Radiationless Transition
Probability ............................................ 31
3.2 The Generating Function for Intramolecular
Distributions 11 and l2 ................................ 36
3.2.1 The Generating Function G2(w1,w2,z1,z2) .......... 36
3.2.2 Properties of δμ1μ2 v1v2, aμ1μ2 v1v2 and
bμ1μ2 v1v2 ........................................ 41
3.2.3 Case W1 = w2 = 0 ................................ 42
3.2.4 Case W1 ≠ w2 ≠ 0 ................................ 42
3.2.5 Symmetry Properties of I2 ....................... 45
3.2.6 Case Φ = 0 ...................................... 47
3.3 Derivation of the Promoting Mode Factors Kn(t) and
In(t) .................................................. 48
3.4 Radiationless Decay Rates of Initially Selected
Vibronic States in Polyatomic Molecules ................ 52
4 Calculational Methods for Intramolecular Distributions
I1, I2, and IN ............................................... 57
4.1 The One-Dimensional Distribution I1(0, n; a, b) ........ 57
4.1.1 The Addition Theorem ............................ 60
4.2 The Distributions I1(m, n; a, b) ....................... 61
4.2.1 Derivation of I1(m, n; a, b) .................... 61
4.2.2 The Addition Theorem for I1(m, n; a, b) ......... 65
4.2.3 The Recurrence Formula .......................... 65
4.2.4 Case b = 0 ...................................... 67
4.2.5 Case b ≠ 0 ...................................... 68
4.2.6 Numerical Results ............................... 69
4.3 Calculation of the Multidimensional Distribution ....... 71
4.3.1 Preliminary Consideration ....................... 71
4.3.2 Derivation of Recurrence Equations .............. 75
4.3.3 The Calculation Procedure ....................... 78
4.3.3.1 Some Numerical Results ................. 79
4.4 General Case of N-Coupled Modes ........................ 82
4.4.1 The Generating Function GN ...................... 82
4.4.2 Properties of δμv, aμv and
bμv .................. 87
4.4.3 The Distribution and its Properties ............. 89
4.4.3.1 Symmetry Property of IN ................ 91
4.4.4 A Special Case .................................. 92
4.4.5 Concluding Remarks and Examples ................. 93
4.4.6 Recurrence Relations ............................ 94
4.4.7 The Three-Dimensional Case ...................... 96
4.4.8 Some Numerical Results .......................... 97
4.5 Displaced Potential Surfaces .......................... 102
4.5.1 The Strong Coupling Limit ...................... 102
4.5.2 The Weak Coupling Limit ........................ 106
4.6 The Contribution of Medium Modes ...................... 107
5 The Nuclear Coordinate Dependence of Matrix Elements ....... 111
5.1 The q-Centroid Approximation .......................... 111
5.2 Determination of the q-Centroid ....................... 123
6 Time-Resolved Spectroscopy ................................. 129
6.1 Formal Consideration .................................. 129
6.2 Evaluation of the Radiative Decay Probability of
a Prepared State ...................................... 131
6.3 The Sparse Intermediate Case .......................... 137
6.3.1 Preliminary Consideration ...................... 137
6.3.2 The Molecular Eigenstates ...................... 139
6.4 Radiative Decay in Internal Conversion by
Introduction of Decay Rates for {Ψ1} .................. 142
6.5 Dephasing and Relaxation in Molecular Systems ......... 145
6.5.1 Introduction ................................... 145
6.5.2 Interaction of a Large Molecule with a Light
Pulse .......................................... 146
6.5.3 Free Induction Decay of a Large Molecule ....... 149
6.5.4 Photon Echoes from Large Molecules ............. 151
7 Miscellaneous Applications ................................. 155
7.1 The Line Shape Function for Radiative Transitions ..... 155
7.1.1 Derivation ..................................... 155
7.1.2 Implementation of Theory and Results ........... 160
7.1.2.1 Excited-State Geometry ................ 169
7.2 On the Mechanism of Singlet-Triplet Interaction ....... 171
7.2.1 Phosphorescence in Aromatic Molecules with
Nonbonding Electrons ........................... 171
7.2.2 Radiative T1 (ππ*) → S0 Transition ............. 172
7.2.3 Nonradiative Triplet-to-Ground State
Transition ..................................... 178
7.2.3.1 Theory and Application ................ 179
7.2.4 Remarks on the Intersystem Crossing in
Aromatic Hydrocarbons .......................... 183
7.3 Comment on the Temperature Dependence of
Radiationless Transition .............................. 184
7.4 Effect of Deuteration on the Lifetimes of
Electronic Excited States ............................. 186
7.4.1 Partial Deuteration Experiment ................. 186
7.5 Theory and Experiment of Singlet Excitation Energy
Transfer in Mixed Molecular Crystals .................. 191
7.5.1 Transport Phenomena in Doped Molecular
Crystals ....................................... 191
7.5.2 The System Pentacene in p-Terphenyl ............ 191
7.5.3 Techniques ..................................... 194
7.5.4 Nature of the Energy Transfer: Theory .......... 198
7.5.5 Time Evolution of the Guest Excitations ........ 201
7.5.6 The Decay of the Transient Grating Signal ...... 208
7.6 Electronic Predissociation of the 2B2 State of H20+ .... 211
7.6.1 Evaluation of the Nonadiabatic Coupling
Factor ......................................... 211
7.6.2 The Basis State Functions ...................... 216
7.6.2.1 The Initial-State Wavefunction χi ..... 216
7.6.2.2 The Final Vibrational Wavefunction
χƒ- The Closed Coupled Equations ...... 217
8 Multidimensional Franck-Condon Factor ...................... 225
8.1 Multidimensional Franck-Condon Factors and
Duschinsky Mixing Effects ............................. 225
8.1.1 General Aspects ................................ 225
8.1.2 Derivation ..................................... 228
8.2 Recursion Relations ................................... 238
8.3 Some Numerical Results and Discussion ................. 241
8.4 Implementation of Theory and Results .................. 244
8.4.1 The Resonance Raman Process and Duschinsky
Mixing Effect .................................. 244
8.4.2 Time-Delayed Two-Photon Processes:
Duschinsky Mixing Effects ...................... 247
8.4.3 Results ........................................ 249
8.5 The One-Dimensional Franck-Condon Factor (N = 1) ...... 255
Appendices .................................................... 259
Appendix A: Some Identities Related to Green's Function ....... 261
A.l The Green's Function Technique ........................ 261
A.2 Evaluation of the Diagonal Matrix Element of Gss ...... 264
Appendix B: The Coefficients of the Recurrence Equation ....... 267
Appendix C: The Coefficients of the Recurrence Equations ...... 272
Appendix D: Solution of a Class of Integrals .................. 273
Appendix E: Quantization of the Radiation Field ............... 277
Appendix F: The Molecular Eigenstates ......................... 281
Appendix C: The Effective Hamiltonian and Its Properties ...... 285
Appendix H: The Mechanism of Nonradiative Energy Transfer ..... 287
H.l Single-Step Resonance Energy Transfer ................. 287
H.2 Phonon-Assisted Energy Transfer ....................... 289
Appendix I: Evaluation of the Coefficients bμv, cμv, and
bμ in the Recurrence Equations 8.28 and 8.29 ...... 293
H.1 Application ........................................... 294
Appendix J: Evaluation of the Position Expectation Values
of χsm(qS) ........................................ 299
Appendix K: Vibronic Coupling Between Two Electronic
States: The Pseudo-Jahn-Teller Effect ............. 301
References .................................................... 313
Index ......................................................... 327
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