Preface to the Third Edition .............................. XIII
Preface to the Second Edition ............................... XV
Preface to the First Edition .............................. XVII
1 Introduction ................................................. 1
2 Electronic and Vibrational Molecular States .................. 9
2.1 Introduction ............................................ 9
2.2 Molecular Schrödinger Equation ......................... 11
2.3 Born-Oppenheimer Separation ............................ 13
2.3.1 Born-Oppenheimer Approximation .................. 15
2.3.2 Some Estimates .................................. 17
2.4 Electronic Structure Methods ........................... 18
2.4.1 The Hartree-Fock Equations ...................... 21
2.4.2 Density Functional Theory ....................... 23
2.5 Condensed Phase Approaches ............................. 24
2.5.1 Dielectric Continuum Model ...................... 25
2.5.2 Explicit Quantum-Classical Solvent Model ........ 31
2.6 Potential Energy Surfaces .............................. 33
2.6.1 Harmonic Approximation and Normal Mode
Analysis ........................................ 35
2.6.2 Operator Representation of the Normal Mode
Hamiltonian
2.6.3 Reaction Paths .................................. 44
2.7 Diabatic versus Adiabatic Representation of the
Molecular Hamiltonian .................................. 50
2.8 Supplement ............................................. 56
2.8.1 The Hartree-Fock Equations ...................... 56
2.8.2 Franck-Condon Factors ........................... 59
2.8.3 The Two-Level System ............................ 60
2.8.4 The Linear Molecular Chain and the Molecular
Ring ............................................ 64
References .................................................. 66
Further Reading ............................................. 66
3 Dynamics of Isolated and Open Quantum Systems ............... 67
3.1 Introduction ........................................... 67
3.2 Time-Dependent Schrödinger Equation .................... 74
3.2.1 Wave Packets .................................... 74
3.2.2 The Interaction Representation .................. 78
3.2.3 Multidimensional Wave Packet Dynamics ........... 80
3.3 The Golden Rule of Quantum Mechanics ................... 83
3.3.1 Transition from a Single State into
a Continuum ..................................... 84
3.3.2 Transition Rate for a Thermal Ensemble .......... 87
3.3.3 Green's Function Approach ....................... 91
3.4 The Nonequilibrium Statistical Operator and the
Density Matrix ......................................... 94
3.4.1 The Density Operator ............................ 94
3.4.2 The Density Matrix .............................. 97
3.4.3 Equation of Motion for the Density Operator ..... 99
3.4.4 Wigner Representation of the Density
Operator ....................................... 100
3.4.5 Dynamics of Coupled Multilevel Systems in
a Heat Bath .................................... 103
3.5 The Reduced Density Operator and the Reduced Density
Matrix ................................................ 107
3.5.1 The Reduced Density Operator ................... 107
3.5.2 Equation of Motion for the Reduced Density
Operator ....................................... 108
3.5.3 Mean-Field Approximation ....................... 109
3.5.4 The Interaction Representation of the Reduced
Density Operator ............................... 111
3.5.5 The Projection Superoperator ................... 112
3.5.6 Second-Order Equation of Motion for the
Reduced Density Operator ....................... 115
3.6 The Reservoir Correlation Function .................... 117
3.6.1 General Properties of Cuv(t) ................... 117
3.6.2 Harmonic Oscillator Reservoir .................. 120
3.6.3 The Spectral Density ........................... 122
3.6.4 Linear Response Theory for the Reservoir ....... 125
3.6.5 Classical description of Cuv(t) ................ 127
3.7 Quantum Master Equation ............................... 128
3.7.1 Markov Approximation ........................... 130
3.8 Reduced Density Matrix in Energy Representation ....... 134
3.8.1 The Quantum Master Equation in Energy
Representation ................................. 134
3.8.2 Multilevel Redfield Equations .................. 136
3.8.3 The Secular Approximation ...................... 141
3.8.4 State Expansion of the System-Reservoir
Coupling ....................................... 142
3.8.5 From Coherent to Dissipative Dynamics:
A Simple Example ............................... 144
3.8.6 Coordinate and Wigner Representation of the
Reduced Density Matrix ......................... 150
3.9 Generalized Rate Equations: The Liouville Space
Approach .............................................. 153
3.9.1 Projection Operator Technique .................. 154
3.9.2 Generalized Rate Equations ..................... 155
3.9.3 Rate Equations ................................. 157
3.9.4 The Memory Kernels ............................. 158
3.9.5 Second-Order Rate Expressions .................. 160
3.9.6 Fourth-Order Rate Expressions .................. 162
3.10 The Path Integral Representation of the Density
Matrix ................................................ 168
3.11 Quantum-Classical Hybrid Methods ...................... 174
3.11.1 The Mean-Field Approach ........................ 174
3.11.2 The Surface Hopping Method ..................... 176
3.11.3 Partial Wigner Representation as a Quantum-
Classical Hybrid Method ........................ 179
3.12 Supplement ............................................ 183
3.12.1 Different Equations of Motion for the Reduced
Density Operator
3.12.2 Limit of Ultrashort Reservoir Correlation
Time ........................................... 187
3.12.3 Markov Approximation and the Factorized Part
of the Reservoir Correlation Function .......... 188
References ................................................. 189
Further Reading ............................................ 389
4 Interaction of Molecular Systems with Radiation Fields ..... 191
4.1 Introduction .......................................... 191
4.2 Absorption and Emission of Light ...................... 196
4.2.1 Linear Absorption Coefficient .................. 196
4.2.2 Dipole-Dipole Correlation Function ............. 197
4.2.3 Field Quantization and Spontaneous Emission
of Light ....................................... 199
4.3 Nonlinear Optical Response ............................ 202
4.3.1 Nonlinear Response Functions ................... 205
4.4 Laser Control of Molecular Dynamics ................... 206
4.4.1 Introduction ................................... 206
4.4.2 Optimal Control Theory ......................... 212
References ................................................. 219
Further Reading ............................................ 220
5 Vibrational Dynamics: Energy Redistribution, Relaxation,
and Dephasing .............................................. 221
5.1 Introduction .......................................... 221
5.2 Intramolecular Vibrational Energy Redistribution ...... 225
5.2.1 Zeroth-Order Basis ............................. 225
5.2.2 Golden Rule and Beyond ......................... 228
5.3 Intermolecular Vibrational Energy Relaxation .......... 232
5.3.1 Diatomic Molecule in Solid State Environment ... 233
5.3.2 Diatomic Molecules in Polyatomic Solution ...... 238
5.4 Polyatomic Molecules in Solution ...................... 243
5.4.1 System-Bath Hamiltonian ........................ 243
5.4.2 Higher-Order Multiquantum Relaxation ........... 245
5.5 Quantum-Classical Approaches to Relaxation and
Dephasing ............................................. 250
5.6 Supplement ............................................ 253
5.6.1 Coherent Wave Packet Motion in a Harmonic
Oscillator ..................................... 253
References ................................................. 254
Further Reading ............................................ 254
6 Intramolecular Electronic Transitions ...................... 255
6.1 Introduction .......................................... 255
6.1.1 Optical Transitions ............................ 256
6.1.2 Internal Conversion Processes .................. 261
6.2 The Optical Absorption Coefficient .................... 262
6.2.1 Golden Rule Formulation ........................ 262
6.2.2 The Density of States .......................... 265
6.2.3 Absorption Coefficient for Harmonic Potential
Energy Surfaces ................................ 268
6.2.4 Absorption Lineshape and Spectral Density ...... 271
6.3 Absorption Coefficient and Dipole-Dipole Correlation
Function .............................................. 276
6.3.1 Absorption Coefficient and Wave Packet
Propagation .................................... 276
6.3.2 Cumulant Expansion of the Absorption
Coefficient .................................... 281
6.3.3 Absorption Coefficient and Reduced Density
Operator Propagation ........................... 282
6.3.4 Mixed Quantum-Classical Computation of the
Absorption Coefficient ......................... 285
6.4 The Emission Spectrum ................................. 287
6.5 Optical Preparation of an Excited Electronic State .... 288
6.5.1 Wave Function Formulation ...................... 289
6.5.2 Density Matrix Formulation ..................... 293
6.6 Pump-Probe Spectroscopy ............................... 294
6.7 Internal Conversion Dynamics .......................... 298
6.7.1 The Internal Conversion Rate ................... 298
6.7.2 Ultrafast Internal Conversion .................. 300
6.8 Supplement ............................................ 302
6.8.1 Absorption Coefficient for Displaced Harmonic
Oscillators .................................... 302
6.8.2 Cumulant Expansion for Harmonic Potential
Energy Surfaces ................................ 305
References ................................................. 307
Further Reading ............................................ 307
7 Electron Transfer .......................................... 309
7.1 Classification of Electron Transfer Reactions ......... 309
7.2 Theoretical Models for Electron Transfer Systems ...... 321
7.2.1 The Electron Transfer Hamiltonian .............. 322
7.2.2 The Electron-Vibrational Hamiltonian of
a Donor-Acceptor Complex ....................... 327
7.2.3 Electron-Vibrational State Representation of
the Hamiltonian ................................ 331
7.3 Regimes of Electron Transfer .......................... 332
7.3.1 Landau-Zener Theory of Electron Transfer ....... 337
7.4 Nonadiabatic Electron Transfer in a Donor-Acceptor
Complex ............................................... 341
7.4.1 High-Temperature Case .......................... 342
7.4.2 High-Temperature Case: Two Independent Sets
of Vibrational Coordinates ..................... 346
7.4.3 Low-Temperature Case: Nuclear Tunneling ........ 349
7.4.4 The Mixed Quantum-Classical Case ............... 352
7.4.5 Description of the Mixed Quantum-Classical
Case by a Spectral Density ..................... 354
7.5 Nonadiabatic Electron Transfer in Polar Solvents ...... 355
7.5.1 The Solvent Polarization Field and the
Dielectric Function ............................ 357
7.5.2 The Free Energy of the Solvent ................. 360
7.5.3 The Rate of Nonadiabatic Electron Transfer in
Polar Solvents ................................. 363
7.6 Bridge-Mediated Electron Transfer ..................... 367
7.6.1 The Superexchange Mechanism .................... 369
7.6.2 Electron Transfer through Arbitrary Long
Bridges ........................................ 371
7.7 Nonequilibrium Quantum Statistical Description of
Electron Transfer ..................................... 375
7.7.1 Unified Description of Electron Transfer in
a Donor-Bridge-Acceptor System ................. 376
7.7.2 Transition to the Adiabatic Electron
Transfer ....................................... 379
7.8 Heterogeneous Electron Transfer ....................... 380
7.8.1 Nonadiabatic Charge Injection into the Solid
State Described in a Single-Electron Model ..... 381
7.8.2 Nonadiabatic Electron Transfer from the Solid
State to the Molecule .......................... 385
7.8.3 Ultrafast Photoinduced Heterogeneous Electron
Transfer from a Molecule into
a Semiconductor ................................ 388
7.9 Charge Transmission through Single Molecules .......... 390
7.9.1 Inelastic Charge Transmission .................. 393
7.9.2 Elastic Charge Transmission .................... 396
7.10 Photoinduced Ultrafast Electron Transfer .............. 402
7.10.1 Quantum Master Equation for Electron Transfer
Reactions ...................................... 408
7.10.2 Rate Expressions ............................... 412
7.11 Controlling Photoinduced Electron Transfer ........... 414
7.12 Supplement ........................................... 417
7.12.1 Landau-Zener Transition Amplitude .............. 417
7.12.2 The Multimode Marcus Formula ................... 419
7.12.3 The Free Energy Functional of the Solvent
Polarization ................................... 420
7.12.4 Second-Order Electron Transfer Rate ............ 423
7.12.5 Fourth-Order Donor-Acceptor Transition Rate .... 425
7.12.6 Rate of Elastic Charge Transmission through
a Single Molecule .............................. 428
References ................................................ 431
Further Reading ............................................ 432
8 Proton Transfer ............................................ 435
8.1 Introduction .......................................... 435
8.2 Proton Transfer Hamiltonian ........................... 440
8.2.1 Hydrogen Bonds ................................. 440
8.2.2 Reaction Surface Hamiltonian for
Intramolecular Proton Transfer ................. 444
8.2.3 Tunneling Splittings ........................... 445
8.2.4 Proton Transfer Hamiltonian in the Condensed
Phase .......................................... 450
8.3 Adiabatic Proton Transfer ............................. 453
8.4 Nonadiabatic Proton Transfer .......................... 456
8.5 The Intermediate Regime: From Quantum to Quantum-
Classical Hybrid Methods .............................. 458
8.5.1 Multidimensional Wave Packet Dynamics .......... 458
8.5.2 Surface Hopping ................................ 461
8.6 Infrared Laser-Pulse Control of Proton Transfer ....... 463
References ................................................. 466
Further Reading ............................................ 466
9 Excitation Energy Transfer ................................. 467
9.1 Introduction .......................................... 467
9.2 The Aggregate Hamiltonian ............................. 474
9.2.1 The Intermolecular Coulomb Interaction ......... 477
9.2.2 The Two-Level Model ............................ 481
9.2.3 Single and Double Excitations of the
Aggregate ...................................... 484
9.2.4 Introduction of Delocalized Exciton States ..... 490
9.3 Exciton-Vibrational Interaction ....................... 494
9.3.1 Exclusive Coupling to Intramolecular
Vibrations ..................................... 495
9.3.2 Coupling to Aggregate Normal-Mode Vibrations ... 495
9.3.3 Coupling to Intramolecular Vibrations and
Aggregate Normal-Mode Vibrations ............... 497
9.3.4 Exciton-Vibrational Hamiltonian and Excitonic
Potential Energy Surfaces ...................... 498
9.4 Regimes of Excitation Energy Transfer ................. 500
9.4.1 Quantum Statistical Approaches to Excitation
Energy Transfer ................................ 501
9.5 Transfer Dynamics in the Case of Weak Excitonic
Coupling: Förster Theory .............................. 503
9.5.1 The Transfer Rate .............................. 503
9.5.2 The Förster Rate ............................... 505
9.5.3 Nonequilibrium Quantum Statistical
Description of Förster Transfer ................ 508
9.6 Transfer Dynamics in the Case of Strong Excitonic
Coupling .............................................. 514
9.6.1 Rate Equations for Exciton Dynamics ............ 515
9.6.2 Density Matrix Equations for Exciton
Dynamics ....................................... 516
9.6.3 Site Representation ............................ 519
9.6.4 Excitation Energy Transfer among Different
Aggregates ..................................... 521
9.6.5 Exciton Transfer in the Case of Strong
Exciton-Vibrational Coupling ................... 522
9.7 The Aggregate Absorption Coefficient .................. 526
9.7.1 Case of no Exciton-Vibrational Coupling ........ 529
9.7.2 Inclusion of Exciton-Vibrational Coupling ...... 532
9.8 Excitation Energy Transfer Including Charge Transfer
States ................................................ 536
9.9 Exciton-Exciton Annihilation .......................... 540
9.9.1 Three-Level Description of the Molecules in
the Aggregate .................................. 542
9.9.2 The Rate of Exciton-Exciton Annihilation ....... 543
9.10 Supplement ............................................ 544
9.10.1 Photon-Mediated Long-Range Excitation Energy
Transfer ....................................... 544
9.10.2 Fourth-Order Rate of Two-Electron-Transfer-
Assisted EET ................................... 553
References ................................................. 557
Further Reading ............................................ 558
Index ...................................................... 559
|
