Transitions in Molecular Systems

Transitions in Molecular Systems......Page 1
Contents......Page 7
Preface......Page 11
1.1.1 Preliminaries......Page 13
1.1.2 The Born–Oppenheimer Approximation......Page 15
1.1.3 The Crude Born–Oppenheimer Basis Set......Page 18
1.1.4 Correction of the Crude Adiabatic Approximation......Page 19
1.2 Normal Coordinates and Duschinsky Effect......Page 21
1.3 The Vibrational Wavefunctions......Page 25
1.4.1 Preliminaries......Page 26
1.4.2 Conical Intersection Between the States B2B2/2A' and Ã2A1/2A' of H2O+......Page 28
1.4.3 The Linear Model for Conical Intersection......Page 30
2.1 The Time Evolution of an Excited State......Page 33
2.1.1 Some Remarks About the Decay of a Discrete Molecular Metastable State......Page 38
2.2 The Choice of the Zero-Order Basis Set......Page 39
3.1 Evaluation of the Radiationless Transition Probability......Page 43
3.2.1 The Generating Function G2(w1,w2,z1,z2)......Page 48
3.2.2 Properties of δμ1μ2, ν1ν2, aμ1μ2, ν1ν2, and bμ1μ2, ν1ν2......Page 53
3.2.4 Case w1 ≠  w2 ≠  0......Page 54
3.2.5 Symmetry Properties of I2......Page 57
3.2.6 Case ф = 0......Page 59
3.3 Derivation of the Promoting Mode Factors Kη(t) and Iη(t)......Page 60
3.4 Radiationless Decay Rates of Initially Selected Vibronic States in Polyatomic Molecules......Page 64
4.1 The One-Dimensional Distribution I1(0, n; a, b)......Page 69
4.1.1 The Addition Theorem......Page 72
4.2.1 Derivation of I1(m, n; a, b)......Page 73
4.2.3 The Recurrence Formula......Page 77
4.2.4 Case b=0......Page 79
4.2.5 Case b ≠  0......Page 80
4.2.6 Numerical Results......Page 81
4.3.1 Preliminary Consideration......Page 83
4.3.2 Derivation of Recurrence Equations......Page 87
4.3.3 The Calculation Procedure......Page 90
4.3.3.1 Some Numerical Results......Page 91
4.4.1 The Generating Function GN......Page 94
4.4.2 Properties of δμ,ν, aμ,ν, and bμ,ν......Page 99
4.4.3 The Distribution and its Properties......Page 101
4.4.3.1 Symmetry Property of IN......Page 103
4.4.4 A Special Case......Page 104
4.4.5 Concluding Remarks and Examples......Page 105
4.4.6 Recurrence Relations......Page 106
4.4.7 The Three-Dimensional Case......Page 108
4.4.8 Some Numerical Results......Page 109
4.5.1 The Strong Coupling Limit......Page 114
4.5.2 The Weak Coupling Limit......Page 118
4.6 The Contribution of Medium Modes......Page 119
5.1 The q-Centroid Approximation......Page 123
5.2 Determination of the q-Centroid......Page 135
6.1 Formal Consideration......Page 141
6.2 Evaluation of the Radiative Decay Probability of a Prepared State......Page 143
6.3.1 Preliminary Consideration......Page 149
6.3.2 The Molecular Eigenstates......Page 151
6.4 Radiative Decay in Internal Conversion by Introduction of Decay Rates for {ψ1}......Page 154
6.5.1 Introduction......Page 157
6.5.2 Interaction of a Large Molecule with a Light Pulse......Page 158
6.5.3 Free Induction Decay of a Large Molecule......Page 161
6.5.4 Photon Echoes from Large Molecules......Page 163
7.1.1 Derivation......Page 167
7.1.2 Implementation of Theory and Results......Page 172
7.1.2.1 Excited-State Geometry......Page 181
7.2.1 Phosphorescence in Aromatic Molecules with Nonbonding Electrons......Page 183
7.2.2 Radiative T1 (ππ* ) → S0 Transition......Page 184
7.2.3 Nonradiative Triplet-to-Ground State Transition......Page 190
7.2.3.1 Theory and Application......Page 191
7.2.4 Remarks on the Intersystem Crossing in Aromatic Hydrocarbons......Page 195
7.3 Comment on the Temperature Dependence of Radiationless Transition......Page 196
7.4.1 Partial Deuteration Experiment......Page 198
7.5.2 The System Pentacene in p-Terphenyl......Page 203
7.5.3 Techniques......Page 206
7.5.4 Nature of the Energy Transfer: Theory......Page 210
7.5.5 Time Evolution of the Guest Excitations......Page 213
7.5.6 The Decay of the Transient Grating Signal......Page 220
7.6.1 Evaluation of the Nonadiabatic Coupling Factor......Page 223
7.6.2.1 The Initial-State Wavefunction xi......Page 228
7.6.2.2 The Final Vibrational Wavefunction xf : The Closed Coupled Equations......Page 229
8.1.1 General Aspects......Page 237
8.1.2 Derivation......Page 240
8.2 Recursion Relations......Page 250
8.3 Some Numerical Results and Discussion......Page 253
8.4.1 The Resonance Raman Process and Duschinsky Mixing Effect......Page 256
8.4.2 Time-Delayed Two-Photon Processes: Duschinsky Mixing Effects......Page 259
8.4.3 Results......Page 261
8.5 The One-Dimensional Franck–Condon Factor (N=1)......Page 267
Appendices......Page 271
A.1 The Green's Function Technique......Page 273
A.2 Evaluation of the Diagonal Matrix Element of Gss......Page 276
Appendix B: The Coefficients of the Recurrence Equation......Page 279
Appendix C: The Coefficients of the Recurrence Equations......Page 283
Appendix D: Solution of a Class of Integrals......Page 285
Appendix E: Quantization of the Radiation Field......Page 289
Appendix F: The Molecular Eigenstates......Page 293
Appendix G: The Effective Hamiltonian and Its Properties......Page 297
H.1 Single-Step Resonance Energy Transfer......Page 299
H.2 Phonon-Assisted Energy Transfer......Page 301
Appendix I: Evaluation of the Coefficients bμν, cμν, and bμ in the Recurrence Equations 8.28 and 8.29......Page 305
I.1 Application......Page 306
Appendix J: Evaluation of the Position Expectation Values of xsm(qs)......Page 311
Appendix K: Vibronic Coupling Between Two Electronic States: The Pseudo-Jahn–Teller Effect......Page 313
References......Page 325
Index......Page 339