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Transitions in Molecular Systems

by: Kupka, Hans J.

Transitions in Molecular Systems

by: Kupka, Hans J.

ISBN 13:
9783527410132
ISBN 10:
3527410139
Edition: 1st
Format: Hardcover
Copyright: 08/09/2010
Publisher: Wiley-VCH

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Summary

To understand the full complexity of energy transfer within molecules and apply it to cutting edge research, also more special, but also important processes need to be understood. Especially vibronic (those involving vibration to store energy), nonadiabatic and diabatic couplings and radiationless processes need to be considered. A book is needed covering these in context with one another. This work fills this gap with the necessary mathematical rigor.

Preface	p. IX
Introduction	p. 1
The Adiabatic Description of Molecules	p. 1
Preliminaries	p. 1
The Born-Oppenheimer Approximation	p. 3
The Crude Born-Oppenheimer Basis Set	p. 6
Correction of the Crude Adiabatic Approximation	p. 7
Normal Coordinates and Duschinsky Effect	p. 9
The Vibrational Wavefunctions	p. 13
The Diabatic Electronic Basis for Molecular Systems	p. 14
Preliminaries	p. 14
Conical Intersection Between the States B²B₂/²A′ and Ã²A₁/²A′ of H₂O⁺	p. 16
The Linear Model for Conical Intersection	p. 18
Formal Decay Theory of Coupled Unstable States	p. 21
The Time Evolution of an Excited State	p. 21
Some Remarks About the Decay of a Discrete Molecular Metastable State	p. 26
The Choice of the Zero-Order Basis Set	p. 27
Description of Radiationless Processes in Statistical Large Molecules	p. 31
Evaluation of the Radiationless Transition Probability	p. 31
The Generating Function for Intramolecular Distributions I₁ and I₂	p. 36
The Generating Function G₂(w₁,w₂,z₁,z₂)	p. 36
Properties of ¿_¿₁¿₂ _v₁v₁ a_¿₁¿₂ and b_¿₁¿₂ _v₁v₂	p. 41
Case w₁ = w₂ = 0	p. 42
Case w₁ ≠ w₂ ≠ 0	p. 42
Symmetry Properties of I₂	p. 45
Case ¿ = 0	p. 47
Derivation of the Promoting Mode Factors K_¿(t) and I_¿(t)	p. 48
Radiationless Decay Rates of Initially Selected Vibronic States in Polyatomic Molecules	p. 52
Calculational Methods for Intramolecular Distributions I₁, I₂ and I_N	p. 57
The One-Dimensional Distribution I₁ (0, n; a, b)	p. 57
The Addition Theorem	p. 60
The Distributions I₁(m, n; a, b)	p. 61
Derviation of I₁ (m, n; a, b)	p. 61
The Addition Theorem for I₁(m, n; a, b)	p. 65
The Recurrence Formula	p. 65
Case b = 0	p. 67
Case b ≠ 0	p. 68
Numerical Results	p. 69
Calculation of the Multidimensional Distribution	p. 71
Preliminary Consideration	p. 71
Derivation of Recurrence Equations	p. 75
The Calculation Procedure	p. 78
Some Numerical Results	p. 79
General Case of N-Coupled Modes	p. 82
The Generating Function G_N	p. 82
Properties of ¿_¿,¿, a_¿,¿, and b_¿,¿	p. 87
The Distribution and its Properties	p. 89
Symmetry Property of I_N	p. 91
A Special Case	p. 92
Concluding Remarks and Examples	p. 93
Recurrence Relations	p. 94
The Three-Dimensional Case	p. 96
Some Numerical Results	p. 97
Displaced Potential Surfaces	p. 102
The Strong Coupling Limit	p. 102
The Weak Coupling Limit	p. 106
The Contribution of Medium Modes	p. 107
The Nuclear Coordinate Dependence of Matrix Elements	p. 111
The q-Centroid Approximation	p. 111
Determination of the q-Centroid	p. 123
Time-Resolved Spectroscopy	p. 129
Formal Consideration	p. 129
Evaluation of the Radiative Decay Probability of a Prepared State	p. 131
The Sparse Intermediate Case	p. 137
Preliminary Consideration	p. 137
The Molecular Eigenstates	p. 139
Radiative Decay in Internal Conversion by Introduction of Decay Rates for {¿₁}	p. 142
Dephasing and Relaxation in Molecular Systems	p. 145
Introduction	p. 145
Interaction of a Large Molecule with a Light Pulse	p. 146
Free Induction Decay of a Large Molecule	p. 149
Photon Echoes from Large Molecules	p. 151
Miscellaneous Applications	p. 155
The Line Shape Function for Radiative Transitions	p. 155
Derivation	p. 155
Implementation of Theory and Results	p. 160
Excited-State Geometry	p. 169
On the Mechanism of Singlet-Triplet Interaction	p. 171
Phosphorescence in Aromatic Molecules with Nonbonding Electrons	p. 171
Radiative T₁ (¿¿^*)→S₀ Transition	p. 172
Nonradiative Triplet-to-Ground State Transition	p. 178
Theory and Application	p. 179
Remarks on the Intersystem Crossing in Aromatic Hydrocarbons	p. 183
Comment on the Temperature Dependence of Radiationless Transition	p. 184
Effect of Deuteration on the Lifetimes of Electronic Excited States	p. 186
Partial Deuteration Experiment	p. 186
Theory and Experiment of Singlet Excitation Energy Transfer in Mixed Molecular Crystals	p. 191
Transport Phenomena in Doped Molecular Crystals	p. 191
The System Pentacene in p-Therphenyl	p. 191
Techniques	p. 194
Nature of the Energy Transfer: Theory	p. 198
Time Evolution of the Guest Excitations	p. 201
The Decay of the Transient Grating Signal	p. 208
Electronic Predissociation of the ²B₂ State of H₂O⁺	p. 211
Evaluation of the Nonadiabatic Coupling Factor	p. 211
The Basis State Functions	p. 216
The Initial-State Wavefunction ¿_i	p. 216
The Final Vibrational Wavefunction ¿_f: The Closed Coupled Equations	p. 217
Multidimensional Franck-Condon Factor	p. 225
Multidimensional Franck-Condon Factors and Duschinsky Mixing Effects	p. 225
General Aspects	p. 225
Derivation	p. 228
Recursion Relations	p. 238
Some Numerical Results and Discussion	p. 241
Implementation of Theory and Results	p. 244
The Resonance Raman Process and Duschinsky Mixing Effect	p. 244
Time-Delayed Two-Photon Processes: Duschinsky Mixing Effects	p. 247
Results	p. 249
The One-Dimensional Franck-Condon Factor (N = 1)	p. 255
Appendices	p. 259
Some Identities Related to Green's Function	p. 261
The Green's Function Technique	p. 261
Evaluation of the Diagonal Matrix Element of G_ss	p. 264
The Coefficients of the Recurrence Equation	p. 267
The Coefficients of the Recurrence Equations	p. 271
Solution of a Class of Integrals	p. 273
Quantization of the Radiation Field	p. 277
The Molecular Eigenstates	p. 281
The Effective Hamiltonian and Its Properties	p. 285
The Mechanism of Nonradiative Energy Transfer	p. 287
Single-Step Resonance Energy Transfer	p. 287
Phonon-Assisted Energy Transfer	p. 289
Evaluation of the Coefficients b_¿¿, C_¿¿, and b_¿ in the Recurrence Equations 8.28 and 8.29	p. 293
Application	p. 294
Evaluation of the Position Expectation Values of ¿_sm (q^s)	p. 299
Vibronic Coupling Between Two Electronic States: The Pseudo-Jahn-Teller Effect	p. 301
References	p. 313
Index	p. 327
Table of Contents provided by Ingram. All Rights Reserved.

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Transitions in Molecular Systems

Transitions in Molecular Systems

9783527410132

3527410139

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Table of Contents

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