Charge and energy transfer dynamics in molecular systems

This 3rd edition has been expanded and updated to account for recent developments, while new illustrative examples as well as an enlarged reference list have also been added. It naturally retains the successful concept of its predecessors in presenting a unified perspective on molecular charge and energy transfer processes, thus bridging the regimes of coherent and dissipative dynamics, and establishing a connection between classic rate theories and modern treatments of ultrafast phenomena.

Among the new topics are:
- Time-dependent density functional theory
- Heterogeneous electron transfer, e.g. between molecules and metal or semiconductor surfaces
- Current flows through a single molecule.

While serving as an introduction for graduate students and researchers, this is equally must-have reading for theoreticians and experimentalists, as well as an aid to interpreting experimental data and accessing the original literature.

Author Notes

Volkhard May studied physics at the Humboldt University, Berlin, and received his Ph.D. in Theoretical Physics in 1987, and his habilitation at the College of Education, Custrow, in 1987. He worked in the Department of Biophysics at the Institute of Molecular Biology in Berlin from 1987 to 1991, and has been a senior researcher at the Instiute of Physics, Humboldt University Berlin, since 1992. His current research activities focus on the theory of transfer phenomena in molecular nanostructures.
Oliver Kuhn studied physics at the Humboldt University, Berlin. After receiving his Ph.D. degree in Theoretical Physics in 1995, he worked as a pastdoc first at the University of Rochester, USA, then at Lund University, Sweden. From 1997 to 2007, Prof. Kiihn has been a senior researcher at the Institute of Chemistry, Free University Berlin, where he earned his habilitation in 2000. Since 2008 he has been a Professor of Theoretical Physics at the University of Rostock. His current research interests lie in ultrafast spectroscopy and dynamics of condensed phase systems such as biomolecular hydrogen bonds and excitons in molecular aggregates.

Preface to the Third Edition	p. XIII
Preface to the Second Edition	p. XV
Preface to the First Edition	p. XVII
1 Introduction	p. 1
2 Electronic and Vibrational Molecular States	p. 9
2.1 Introduction	p. 9
2.2 Molecular Schrodinger Equation	p. 11
2.3 Born-Oppenheimer Separation	p. 13
2.3.1 Born-Oppenheimer Approximation	p. 15
2.3.2 Some Estimates	p. 17
2.4 Electronic Structure Methods	p. 18
2.4.1 The Hartree-Fock Equations	p. 21
2.4.2 Density Functional Theory	p. 23
2.5 Condensed Phase Approaches	p. 24
2.5.1 Dielectric Continuum Model	p. 25
2.5.2 Explicit Quantum-Classical Solvent Model	p. 31
2.6 Potential Energy Surfaces	p. 33
2.6.1 Harmonic Approximation and Normal Mode Analysis	p. 35
2.6.2 Operator Representation of the Normal Mode Hamiltonian	p. 39
2.6.3 Reaction Paths	p. 44
2.7 Diabatic versus Adiabatic Representation of the Molecular Hamiltonian	p. 50
2.8 Supplement	p. 56
2.8.1 The Hartree-Fock Equations	p. 56
2.8.2 Franck-Condon Factors	p. 59
2.8.3 The Two-Level System	p. 60
2.8.4 The linear Molecular Chain and the Molecular Ring	p. 64
References	p. 66
Further Reading	p. 66
3 Dynamics of Isolated and Open Quantum Systems	p. 67
3.1 Introduction	p. 67
3.2 Time-Dependent Schrodinger Equation	p. 74
3.2.1 Wave Packets	p. 74
3.2.2 The Interaction Representation	p. 78
3.2.3 Multidimensional Wave Packet Dynamics	p. 80
3.3 The Golden Rule of Quantum Mechanics	p. 83
3.3.1 Transition from a Single State into a Continuum	p. 84
3.3.2 Transition Rate for a Thermal Ensemble	p. 87
3.3.3 Green's Function Approach	p. 91
3.4 The Nonequilibrium Statistical Operator and the Density Matrix	p. 94
3.4.1 The Density Operator	p. 94
3.4.2 The Density Matrix	p. 97
3.4.3 Equation of Morion for the Density Operator	p. 99
3.4.4 Wigner Representation of the Density Operator	p. 100
3.4.5 Dynamics of Coupled Multilevel Systems in a Heat Bath	p. 103
3.5 The Reduced Density Operator and the Reduced Density Matrix	p. 107
3.5.1 The Reduced Density Operator	p. 107
3.5.2 Equation of Motion for the Reduced Density Operator	p. 108
3.5.3 Mean-Field Approximation	p. 109
3.5.4 The Interaction Representation of the Reduced Density Operator	p. 111
3.5.5 The Projection Superoperator	p. 112
3.5.6 Second-Order Equation of Motion for the Reduced Density Operator	p. 115
3.6 The Reservoir Correlation Function	p. 117
3.6.1 General Properties of C uv (t)	p. 117
3.6.2 Harmonic Oscillator Reservoir	p. 120
3.6.3 The Spectral Density	p. 122
3.6.4 Linear Response Theory for the Reservoir	p. 125
3.6.5 Classical description of C uv (t)	p. 127
3.7 Quantum Master Equation	p. 128
3.7.1 Markov Approximation	p. 130
3.8 Reduced Density Matrix in Energy Representation134
3.8.1 The Quantum Master Equation in Energy Representation134
3.8.2 Multilevel Redfield Equations	p. 136
3.8.3 The Secular Approximation	p. 142
3.8.4 State Expansion of the System-Reservoir Coupling	p. 142
3.8.5 From Coherent to Dissipative Dynamics: A Simple Example	p. 144
3.8.6 Coordinate and Wigner Representation of the Reduced Density Matrix	p. 150
3.9 Generalized Rate Equations: The Liouville Space Approach	p. 153
3.9.1 Projection Operator Technique	p. 154
3.9.2 Generalized Rate Equations	p. 155
3.9.3 Rate Equations	p. 157
3.9.4 The Memory Kernels	p. 158
3.9.5 Second-Order Rate Expressions	p. 160
3.9.6 Fourth-Order Rate Expressions	p. 162
3.10 The Path Integral Representation of the Density Matrix	p. 168
3.11 Quantum-Classical Hybrid Methods	p. 174
3.11.1 The Mean-Field Approach	p. 174
3.11.2 The Surface Hopping Method	p. 176
3.11.3 Partial Wigner Representation as a Quantum-Classical Hybrid Method	p. 179
3.12 Supplement	p. 183
3.12.1 Different Equations of Motion for the Reduced Density Operator	p. 183
3.12.2 Limit of Ultrashort Reservoir Correlation Time	p. 187
3.12.3 Markov Approximation and the Factorized Part of the Reservoir Correlation Function	p. 188
References	p. 189
Further Reading	p. 189
4 Interaction of Molecular Systems with Radiation Fields	p. 192
4.1 Introduction	p. 192
4.2 Absorption and Emission of Light	p. 196
4.2.1 linear Absorption Coefficient	p. 196
4.2.2 Dipole-Dipole Correlation Function	p. 197
4.2.3 Field Quantization and Spontaneous Emission of Light	p. 199
4.3 Nonlinear Optical Response	p. 202
4.3.1 Nonlinear Response Functions	p. 205
4.4 Laser Control of Molecular Dynamics	p. 206
4.4.1 Introduction	p. 206
4.4.2 Optimal Control Theory	p. 212
References	p. 229
Further Reading	p. 220
5 Vibrational Dynamics: Energy Redistribution, Relaxation, and Dephasing	p. 222
5.1 Introduction	p. 222
5.2 Intramolecular Vibrational Energy Redistribution	p. 225
5.2.1 Zeroth-Order Basis	p. 225
5.2.2 Golden Rule and Beyond	p. 228
5.3 Intermolecular Vibrational Energy Relaxation	p. 232
5.3.1 Diatomic Molecule in Solid State Environment	p. 233
5.3.2 Diatomic Molecules in Polyatomic Solution	p. 238
5.4 Polyatomic Molecules in Solution	p. 243
5.4.1 System-Bath Hamiltonian	p. 243
5.4.2 Higher-Order Multiquantum Relaxation	p. 245
5.5 Quantum-Classical Approaches to Relaxation and Dephasing	p. 250
5.6 Supplement	p. 253
5.6.1 Coherent Wave Packet Motion in a Harmonic Oscillator	p. 253
References	p. 254
Further Reading	p. 254
6 Intramolecular Electronic Transitions	p. 255
6.1 Introduction	p. 255
6.1.1 Optical Transitions	p. 256
6.1.2 Internal Conversion Processes	p. 261
6.2 The Optical Absorption Coefficient	p. 262
6.2.1 Golden Rule Formulation	p. 262
6.2.2 The Density of States	p. 265
6.2.3 Absorption Coefficient for Harmonic Potential Energy Surfaces	p. 268
6.2.4 Absorption Lineshape and Spectral Density	p. 271
6.3 Absorption Coefficient and Dipole-Dipole Correlation Function	p. 276
6.3.1 Absorption Coefficient and Wave Packet Propagation	p. 276
6.3.2 Cumulant Expansion of the Absorption Coefficient	p. 281
6.3.3 Absorption Coefficient and Reduced Density Operator Propagation	p. 282
63 A Mixed Quantum-Classical Computation of the Absorption Coefficient	p. 285
6.4 The Emission Spectrum	p. 287
6.5 Optical Preparation of an Excited Electronic State	p. 288
6.5.1 Wave Function Formulation	p. 289
6.5.2 Density Matrix Formulation	p. 293
6.6 Pump-Probe Spectroscopy	p. 294
6.7 Internal Conversion Dynamics	p. 298
6.7.1 The Internal Conversion Rate	p. 298
6.7.2 Ultrafast Internal Conversion	p. 300
6.8 Supplement	p. 302
6.8.1 Absorption Coefficient for Displaced Harmonic Oscillators	p. 302
6.8.2 Cumulant Expansion for Harmonic Potential Energy Surfaces	p. 305
References	p. 307
Further Reading	p. 307
7 Electron Transfer	p. 309
7.1 Classification of Electron Transfer Reactions	p. 309
7.2 Theoretical Models for Electron Transfer Systems	p. 321
7.2.1 The Electron Transfer Hamiltonian	p. 322
7.2.2 The Electron-Vibrational Hamiltonian of a Donor-Acceptor Complex	p. 327
7.2.3 Electron-Vibrational State Representation of the Hamiltonian	p. 331
7.3 Regimes of Electron Transfer	p. 332
7.3.1 Landau-Zener Theory of Electron Transfer	p. 337
7.4 Nonadiabatic Electron Transfer in a Donor-Acceptor Complex	p. 341
7.4.1 High-Temperature Case	p. 342
7.4.2 High-Temperature Case: Two Independent Sets of Vibrational Coordinates	p. 346
7.4.3 Low-Temperature Case: Nuclear Tunneling	p. 349
7.4.4 The Mixed Quantum-Classical Case	p. 352
7.4.5 Description of the Mixed Quantum-Classical Case by a Spectral Density	p. 354
7.5 Nonadiabatic Electron Transfer in Polar Solvents	p. 355
7.5.1 The Solvent Polarization Field and the Dielectric Function	p. 357
7.5.2 The Free Energy of the Solvent	p. 360
7.5.3 The Rate of Nonadiabatic Electron Transfer in Polar Solvents	p. 363
7.6 Bridge-Mediated Electron Transfer	p. 367
7.6.1 The Superexchange Mechanism	p. 369
7.6.2 Electron Transfer through Arbitrary Long Bridges	p. 371
7.7 Nonequihbrium Quantum Statistical Description of Electron Transfer	p. 375
7.7.1 Unified Description of Electron Transfer in a Donor-Bridge-Acceptor System	p. 376
7.7.2 Transition to the Adiabatic Electron Transfer	p. 379
7.8 Heterogeneous Electron Transfer	p. 380
7.8.1 Nonadiabatic Charge Injection into the Solid State Described in a Single-Electron Model	p. 381
7.8.2 Nonadiabatic Electron Transfer from the Solid State to the Molecule	p. 385
7.8.3 Ultrafast Photoinduced Heterogeneous Electron Transfer from a Molecule into a Semiconductor	p. 388
7.9 Charge Transmission through Single Molecules	p. 390
7.9.1 Inelastic Charge Transmission	p. 393
7.9.2 Elastic Charge Transmission	p. 396
7.10 Photoinduced Ultrafast Electron Transfer	p. 402
7.10.1 Quantum Master Equation for Electron Transfer Reactions	p. 408
7.10.2 Rate Expressions	p. 412
7.11 ControEing Photoinduced Electron Transfer	p. 414
7.12 Supplement	p. 417
7.12.1 Landau-Zener Transition Amplitude	p. 417
7.12.2 The Multirnode Marcus Formula	p. 419
7.12.3 The Free Energy Functional of the Solvent Polarization	p. 420
7.12.4 Second-Order Electron Transfer Rate	p. 423
7.12.5 Fourth-Order Donor-Acceptor Transition Rate	p. 425
7.12.6 Rate of Elastic Charge Transmission through a Single Molecule	p. 428
References	p. 431
Further Reading	p. 432
8 Proton Transfer	p. 435
8.1 Introduction	p. 435
8.2 Proton Transfer Hamiltonian	p. 440
8.2.1 Hydrogen Bonds	p. 440
8.2.2 Reaction Surface Hamiltonian for Intramolecular Proton Transfer	p. 444
8.2.3 Tunneling Splittings	p. 445
8.2.4 Proton Transfer Hamiltonian in the Condensed Phase	p. 450
8.3 Adiabatic Proton Transfer	p. 453
8.4 Nonadiabatic Proton Transfer	p. 456
8.5 The Intermediate Regime: From Quantum to Quantum-Classical Hybrid Methods	p. 458
8.5.1 Multidimensional Wave Packet Dynamics	p. 458
8.5.2 Surface Hopping	p. 461
8.6 Infrared Laser-Pulse Control of Proton Transfer	p. 463
References	p. 466
Further Reading	p. 466
9 Excitation Energy Transfer	p. 467
9.1 Introduction	p. 467
9.2 The Aggregate Hamiltonian	p. 474
9.2.1 The Intermolecular Coulomb Interaction	p. 477
9.2.2 The Two-Level Model	p. 481
9.2.3 Single and Double Excitations of the Aggregate	p. 484
9.2.4 Introduction of Delocalized Exciton States	p. 490
9.3 Exciton-Vibrational Interaction	p. 494
9.3.1 Exclusive Coupling to Intramolecular Vibrations	p. 495
9.3.2 Coupling to Aggregate Normal-Mode Vibrations	p. 495
9.3.3 Coupling to Intramolecular Vibrations and Aggregate Normal-Mode Vibrations	p. 497
9.3.4 Exciton-Vibrational Hamiltonian and Excitonic Potential Energy Surfaces	p. 498
9.4 Regimes of Excitation Energy Transfer	p. 500
9.4.1 Quantum Statistical Approaches to Excitation Energy Transfer	p. 501
9.5 Transfer Dynamics in the Case of Weak Excitonic Coupling: Forster Theory	p. 503
9.5.1 The Transfer Rate	p. 503
9.5.2 The Forster Rate	p. 505
9.5.3 Nonequilibrium Quantum Statistical Description of Forster Transfer	p. 508
9.6 Transfer Dynamics in the Case of Strong Excitonic Coupling	p. 514
9.6.1 Rate Equations for Exciton Dynamics	p. 515
9.6.2 Density Matrix Equations for Exciton Dynamics	p. 516
9.6.3 Site Representation	p. 519
9.6.4 Excitation Energy Transfer among Different Aggregates	p. 521
9.6.5 Exciton Transfer in the Case of Strong Exciton-Vibrational Coupling	p. 522
9.7 The Aggregate Absorption Coefficient	p. 526
9.7.1 Case of no Exciton-Vibrational Coupling	p. 529
9.7.2 Inclusion of Exciton-Vibrational Coupling	p. 532
9.8 Excitation Energy Transfer Including Charge Transfer States	p. 536
9.9 Exciton-Exciton Annihilation	p. 540
9.9.1 Three-Level Description of the Molecules in the Aggregate	p. 542
9.9.2 The Rate of Exciton-Exciton Annihilation	p. 543
9.10 Supplement	p. 544
9.10.1 Photon-Mediated Long-Range Excitation Energy Transfer	p. 544
9.10.2 Fourth-Order Rate of Two-Electron-Transfer-Assisted EET	p. 553
References	p. 557
Further Reading	p. 558
Index	p. 559

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