Transitions in molecular systems

Title:

Personal Author:

Kupka, Hans J.

Publication Information:

Weinheim : Wiley-VCH, 2010

Physical Description:

x, 331 p. : ill. ; 25 cm.

ISBN:

9783527410132

Subject Term:

Radiationless transitions

Molecular dynamics

Molecular relaxation

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010264242	QD462.6.E53 K87 2010	Open Access Book	Book	Searching... Unknown

Filling the gap for a book covering vibronic, nonadiabatic and diabatic couplings as well as radiationless processes in context, this monograph compiles classic and cutting-edge work from numerous researchers into one handy source.
Alongside a description of radiationless processes in statistical large molecules and calculational methods for intramolecular distributions, the authors also investigate the nuclear coordinate dependence of matrix elements. Whole chapters are devoted to the mathematical description of the lifetime and decay of a prepared states as well as miscellaneous applications. The text is supplemented by a number of appendices for optimum usability.
With its integration of the necessary mathematical rigor, this is primarily intended for graduate students in theoretical physics and chemistry, but is also indispensable reading for those working in molecular physics, physical chemistry and laser physics.

Author Notes

Hans J. Kupka eamed his PhD in Laser Physics at the Technical University of Wroclaw, and from 1968 he researched at the Institute for Low Temperature and Structure Research at the Polish Academy of Science. In 1977, he joined the Heinrich Heine University in Dsseldorf, Germany, before continuing his research at the Max Planck Institute for Radiation Chemistry.
Professor Kupka is the author of many publications in the fields of laser physics, theoretical chemistry, and spectroscopy of organic and anorganic compounds.

Preface	p. IX
1 Introduction	p. 1
1.1 The Adiabatic Description of Molecules	p. 1
1.1.1 Preliminaries	p. 1
1.1.2 The Born-Oppenheimer Approximation	p. 3
1.1.3 The Crude Born-Oppenheimer Basis Set	p. 6
1.1.4 Correction of the Crude Adiabatic Approximation	p. 7
1.2 Normal Coordinates and Duschinsky Effect	p. 9
1.3 The Vibrational Wavefunctions	p. 13
1.4 The Diabatic Electronic Basis for Molecular Systems	p. 14
1.4.1 Preliminaries	p. 14
1.4.2 Conical Intersection Between the States B 2 B 2 / 2 A′ and Ã 2 A 1 / 2 A′ of H 2 O +	p. 16
1.4.3 The Linear Model for Conical Intersection	p. 18
2 Formal Decay Theory of Coupled Unstable States	p. 21
2.1 The Time Evolution of an Excited State	p. 21
2.1.1 Some Remarks About the Decay of a Discrete Molecular Metastable State	p. 26
2.2 The Choice of the Zero-Order Basis Set	p. 27
3 Description of Radiationless Processes in Statistical Large Molecules	p. 31
3.1 Evaluation of the Radiationless Transition Probability	p. 31
3.2 The Generating Function for Intramolecular Distributions I 1 and I 2	p. 36
3.2.1 The Generating Function G 2 (w 1 ,w 2 ,z 1 ,z 2 )	p. 36
3.2.2 Properties of ¿ ¿ 1 ¿ 2 v 1 v 1 a ¿ 1 ¿ 2 and b ¿ 1 ¿ 2 v 1 v 2	p. 41
3.2.3 Case w 1 = w 2 = 0	p. 42
3.2.4 Case w 1 ≠ w 2 ≠ 0	p. 42
3.2.5 Symmetry Properties of I 2	p. 45
3.2.6 Case ¿ = 0	p. 47
3.3 Derivation of the Promoting Mode Factors K ¿ (t) and I ¿ (t)	p. 48
3.4 Radiationless Decay Rates of Initially Selected Vibronic States in Polyatomic Molecules	p. 52
4 Calculational Methods for Intramolecular Distributions I 1 , I 2 and I N	p. 57
4.1 The One-Dimensional Distribution I 1 (0, n; a, b)	p. 57
4.1.1 The Addition Theorem	p. 60
4.2 The Distributions I 1 (m, n; a, b)	p. 61
4.2.1 Derviation of I 1 (m, n; a, b)	p. 61
4.2.2 The Addition Theorem for I 1 (m, n; a, b)	p. 65
4.2.3 The Recurrence Formula	p. 65
4.2.4 Case b = 0	p. 67
4.2.5 Case b ≠ 0	p. 68
4.2.6 Numerical Results	p. 69
4.3 Calculation of the Multidimensional Distribution	p. 71
4.3.1 Preliminary Consideration	p. 71
4.3.2 Derivation of Recurrence Equations	p. 75
4.3.3 The Calculation Procedure	p. 78
4.3.3.1 Some Numerical Results	p. 79
4.4 General Case of N-Coupled Modes	p. 82
4.4.1 The Generating Function G N	p. 82
4.4.2 Properties of ¿ ¿,¿ , a ¿,¿ , and b ¿,¿	p. 87
4.4.3 The Distribution and its Properties	p. 89
4.4.3.1 Symmetry Property of I N	p. 91
4.4.4 A Special Case	p. 92
4.4.5 Concluding Remarks and Examples	p. 93
4.4.6 Recurrence Relations	p. 94
4.4.7 The Three-Dimensional Case	p. 96
4.4.8 Some Numerical Results	p. 97
4.5 Displaced Potential Surfaces	p. 102
4.5.1 The Strong Coupling Limit	p. 102
4.5.2 The Weak Coupling Limit	p. 106
4.6 The Contribution of Medium Modes	p. 107
5 The Nuclear Coordinate Dependence of Matrix Elements	p. 111
5.1 The q-Centroid Approximation	p. 111
5.2 Determination of the q-Centroid	p. 123
6 Time-Resolved Spectroscopy	p. 129
6.1 Formal Consideration	p. 129
6.2 Evaluation of the Radiative Decay Probability of a Prepared State	p. 131
6.3 The Sparse Intermediate Case	p. 137
6.3.1 Preliminary Consideration	p. 137
6.3.2 The Molecular Eigenstates	p. 139
6.4 Radiative Decay in Internal Conversion by Introduction of Decay Rates for {{¿ 1 }}	p. 142
6.5 Dephasing and Relaxation in Molecular Systems	p. 145
6.5.1 Introduction	p. 145
6.5.2 Interaction of a Large Molecule with a Light Pulse	p. 146
6.5.3 Free Induction Decay of a Large Molecule	p. 149
6.5.4 Photon Echoes from Large Molecules	p. 151
7 Miscellaneous Applications	p. 155
7.1 The Line Shape Function for Radiative Transitions	p. 155
7.1.1 Derivation	p. 155
7.1.2 Implementation of Theory and Results	p. 160
7.1.2.1 Excited-State Geometry	p. 169
7.2 On the Mechanism of Singlet-Triplet Interaction	p. 171
7.2.1 Phosphorescence in Aromatic Molecules with Nonbonding Electrons	p. 171
7.2.2 Radiative T 1 (¿¿ * )→S 0 Transition	p. 172
7.2.3 Nonradiative Triplet-to-Ground State Transition	p. 178
7.2.3.1 Theory and Application	p. 179
7.2.4 Remarks on the Intersystem Crossing in Aromatic Hydrocarbons	p. 183
7.3 Comment on the Temperature Dependence of Radiationless Transition	p. 184
7.4 Effect of Deuteration on the Lifetimes of Electronic Excited States	p. 186
7.4.1 Partial Deuteration Experiment	p. 186
7.5 Theory and Experiment of Singlet Excitation Energy Transfer in Mixed Molecular Crystals	p. 191
7.5.1 Transport Phenomena in Doped Molecular Crystals	p. 191
7.5.2 The System Pentacene in p-Therphenyl	p. 191
7.5.3 Techniques	p. 194
7.5.4 Nature of the Energy Transfer: Theory	p. 198
7.5.5 Time Evolution of the Guest Excitations	p. 201
7.5.6 The Decay of the Transient Grating Signal	p. 208
7.6 Electronic Predissociation of the 2 B 2 State of H 2 O +	p. 211
7.6.1 Evaluation of the Nonadiabatic Coupling Factor	p. 211
7.6.2 The Basis State Functions	p. 216
7.6.2.1 The Initial-State Wavefunction ¿ i	p. 216
7.6.2.2 The Final Vibrational Wavefunction ¿ f : The Closed Coupled Equations	p. 217
8 Multidimensional Franck-Condon Factor	p. 225
8.1 Multidimensional Franck-Condon Factors and Duschinsky Mixing Effects	p. 225
8.1.1 General Aspects	p. 225
8.1.2 Derivation	p. 228
8.2 Recursion Relations	p. 238
8.3 Some Numerical Results and Discussion	p. 241
8.4 Implementation of Theory and Results	p. 244
8.4.1 The Resonance Raman Process and Duschinsky Mixing Effect	p. 244
8.4.2 Time-Delayed Two-Photon Processes: Duschinsky Mixing Effects	p. 247
8.4.3 Results	p. 249
8.5 The One-Dimensional Franck-Condon Factor (N = 1)	p. 255
Appendices	p. 259
Appendix A Some Identities Related to Green's Function	p. 261
A.1 The Green's Function Technique	p. 261
A.2 Evaluation of the Diagonal Matrix Element of G ss	p. 264
Appendix B The Coefficients of the Recurrence Equation	p. 267
Appendix C The Coefficients of the Recurrence Equations	p. 271
Appendix D Solution of a Class of Integrals	p. 273
Appendix E Quantization of the Radiation Field	p. 277
Appendix F The Molecular Eigenstates	p. 281
Appendix G The Effective Hamiltonian and Its Properties	p. 285
Appendix H The Mechanism of Nonradiative Energy Transfer	p. 287
H.1 Single-Step Resonance Energy Transfer	p. 287
H.2 Phonon-Assisted Energy Transfer	p. 289
Appendix I Evaluation of the Coefficients b ¿¿ , C ¿¿ , and b ¿ in the Recurrence Equations 8.28 and 8.29	p. 293
I.1 Application	p. 294
Appendix J Evaluation of the Position Expectation Values of ¿ sm (q s )	p. 299
Appendix K Vibronic Coupling Between Two Electronic States: The Pseudo-Jahn-Teller Effect	p. 301
References	p. 313
Index	p. 327

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