Preface to the Second Edition ................................... v
Preface to the First Edition .................................. vii
Chapter 1 Introduction: What is "Nonadiabatic
Transition" ..................................................... 1
Chapter 2 Multi-Disciplinarity ................................. 7
2.1 Physics .................................................... 7
2.2 Chemistry ................................................. 12
2.3 Biology ................................................... 16
2.4 Economics ................................................. 17
Chapter 3 Historical Survey of Theoretical Studies ............ 19
3.1 Landau-Zener-Stueckelberg Theory .......................... 19
3.2 Rosen-Zener-Demkov Theory ................................. 28
3.3 Nikitin's Exponential Model ............................... 31
3.4 Nonadiabatic Transition Due to Coriolis Coupling and
Dynamical State Representation ............................ 33
Chapter 4 Background Mathematics .............................. 41
4.1 Wentzel-Kramers-Brillouin Semiclassical Theory ............ 41
4.2 Stokes Phenomenon ......................................... 45
Chapter 5 Basic Two-State Theory for Time-Independent
Processes ...................................................... 53
5.1 Exact Solutions of the Linear Curve Crossing Problems ..... 53
5.1.1 Landau-Zener type .................................. 53
5.1.2 Nonadiabatic tunneling type ........................ 61
5.2 Complete Semiclassical Solutions of General Curve
Crossing Problems ......................................... 64
5.2.1 Landau-Zener (LZ) type ............................. 65
5.2.2 Nonadiabatic Tunneling (NT) Type ................... 77
5.3 Non-Curve-Crossing Case ................................... 87
5.3.1 Rosen-Zener-Demkov model ........................... 87
5.3.2 Diabatically avoided crossing model ................ 88
5.4 Exponential Potential Model: Unification of the Landau-
Zener and Rosen-Zener Models .............................. 91
5.4.1 Model 1 - Exact Solution ........................... 91
5.4.2 Model 2 - Exact Solution ........................... 97
5.4.3 Model 3 - Semiclassical Solution ................... 99
5.5 Mathematical Implications ................................ 111
5.5.1 Case (i) .......................................... 112
5.5.2 Case (ii) ......................................... 115
5.5.3 Case (iii) ........................................ 118
Chapter 6 Basic Two-State Theory for Time-Dependent
Processes ..................................................... 121
6.1 Exact Solution of Quadratic Potential Problem ............ 121
6.2 Semiclassical Solution in General Case ................... 126
6.2.1 Two-crossing case: β ≥ 0 .......................... 126
6.2.2 Diabatically avoided crossing case: β ≤ 0 ......... 129
6.3 Other Exactly Solvable Models ............................ 135
Chapter 7 Two-State Problems ................................. 145
7.1 Diagrammatic Technique ................................... 145
7.2 Inelastic Scattering ..................................... 149
7.3 Elastic Scattering with Resonances and Predissociation ... 151
7.4 Perturbed Bound States ................................... 155
7.5 Time-Dependent Periodic Crossing Problems ................ 157
7.6 Time-Dependent Nonlinear Equations Related to Bose-
Einstein Condensate Problems ............................. 160
7.7 Wave Packet Dynamics in a Linearly Chirped Laser Field ... 163
Chapter 8 Effects of Coupling to Phonons and Quantum
Devices ....................................................... 169
8.1 Effects of Coupling to Phonons ........................... 169
8.2 Quantum Devices .......................................... 176
Chapter 9 Multi-Channel Problems ............................. 181
9.1 Exactly Solvable Models .................................. 181
9.1.1 Time-independent case ............................. 181
9.1.2 Time-dependent case ............................... 183
9.2 Semiclassical Theory of Time-Independent Multi-Channel
Problems ................................................. 188
9.2.1 General framework ................................. 191
9.2.2 Numerical example ................................. 197
9.3 Time-Dependent Problems .................................. 206
Chapter 10 Multi-Dimensional Problems ......................... 211
10.1 Classification of Surface Crossing ....................... 212
10.1.1 Crossing seam ..................................... 212
10.1.2 Conical intersection .............................. 213
10.1.3 Renner-Teller effect .............................. 215
10.2 Reduction to One-Dimensional Multi-Channel Problem ....... 216
10.2.1 Linear Jahn-Teller problem ........................ 216
10.2.2 Electronically adiabatic chemical reaction ........ 222
10.3 Semiclassical Propagation Method ......................... 227
10.3.1 Trajectory surface hopping method ................. 228
10.3.2 Semiclassical initial value representation
method ............................................ 232
10.3.3 Semiclassical frozen Gaussian propagation method .. 234
10.4 Nonadiabatic Transition State Theory .................... 241
10.4.1 General formulation ............................... 241
10.4.2 Improvement of the Marcus theory of electron
transfer .......................................... 244
Chapter 11 Complete Reflection and Bound States in the
Continuum ..................................................... 247
11.1 One NT-Type Crossing Case ................................ 247
11.2 Diabatically Avoided Crossing (DAC) Case ................. 254
11.3 Two NT-Type Crossings Case ............................... 260
11.3.1 At energies above the top of the barrier:
(Eu,∞) ........................................... 260
11.3.2 At energies between the barrier top and the
higher crossing: {E+, Eu) ......................... 262
11.3.3 At energies in between the two crossing regions:
(E-, E+) .......................................... 264
11.3.4 At energies below the crossing points: (-∞, E-) ... 265
11.3.5 Numerical examples ................................ 265
Chapter 12. New Mechanism of Molecular Switching .............. 269
12.1 Basic Idea ............................................... 269
12.2 One-Dimensional Model .................................... 270
12.2.1 Transmission in a pure system ..................... 270
12.2.2 Transmission in a system with impurities .......... 278
12.3 Two-Dimensional Model .................................... 287
12.3.1 Two-dimensional constriction model ................ 287
12.3.2 Wave functions, matching, and transmission
coefficient ....................................... 291
12.4 Numerical Examples ....................................... 295
Chapter 13. Control of Nonadiabatic Processes by an External
Field ......................................................... 303
13.1 Floquet Theorem and Nonadiabatic Transitions in a
Quasi-Periodic Field ..................................... 304
13.1.1 Floquet theorem and dressed state representation .. 304
13.1.2 Nonadiabatic transitions in a quasi-periodic
field ............................................. 306
13.2 Control of Nonadiabatic Transitions by Periodically
Sweeping External Field .................................. 308
13.2.1 Basic ideas ....................................... 308
13.2.2 Basic theory of periodic sweeping ................. 313
13.3 Semiclassical Guided Optimal Control Theory .............. 323
13.4 Laser Control of Photodissociation with Use of the
Complete Reflection Phenomenon ........................... 328
Chapter 14. Comprehension of Nonadiabatic Chemical Dynamics ... 333
14.1 Chemical Reaction Dynamics ............................... 333
14.1.1 Three-dimensional chemical reactions .............. 333
14.1.2 Nonadiabatic chemical reactions ................... 341
14.2 Photo-Induced Dynamics ................................... 350
14.2.1 Photo-isomerization of retinal .................... 350
14.2.2 Photo-absorption spectrum ......................... 355
14.3 Electron Transfer ........................................ 358
14.3.1 Normal case ....................................... 358
14.3.2 Inverted case ..................................... 362
Chapter 15. Control of Chemical Dynamics ...................... 365
15.1 Efficient Excitation/De-Excitation by Periodic Chirping .. 365
15.1.1 Spin tunneling by magnetic field .................. 365
15.1.2 Vibrational and tunneling transitions controlled
by laser .......................................... 368
15.1.3 Selective and complete excitation of energy
levels ............................................ 380
15.1.4 Pump and dump of wave packet ...................... 390
15.2 Control of Wave Packet Motion and Transition at Conical
Intersection ............................................. 399
15.2.1 Vibrational isomerization of HCN .................. 399
15.2.2 Giving a pre-determined directed momentum to
wave packet ....................................... 402
15.2.3 Selective Photo-dissociation of OHC1 intoO+HCl .... 405
15.3 Selective Photo-Dissociation with Use of the Complete
Reflection Phenomenon .................................... 407
15.4 Control of 7r-Electron Rotation and Its Coupling
to Molecular Vibration ................................... 423
Chapter 16. Manifestation of Molecular Functions .............. 427
16.1 Molecular Switching ...................................... 428
16.2 Hydrogen Transmission Through Carbon Ring ................ 436
16.3 Photo-Chromic Conversion of Cyclohexadiene to
Hexatriene ............................................... 442
16.4 Molecular Motors ......................................... 449
Chapter 17. Conclusions: Future Perspectives .................. 459
Appendix A. Final Recommended Formulas of the Zhu-Nakamura
Theory for General Time-Independent Two-Channel Problem ....... 463
A.l Landau-Zener Type (see Fig. A.l) ......................... 463
A.l.l E ≥ EX ............................................ 465
A.1.2 E ≤ EX ............................................ 466
A.1.3 Definitions of σzn, δzn and δψ .................... 467
A.1.4 Total scattering matrix ........................... 468
A.2 Nonadiabatic Tunneling Type (see Fig. A.2) ............... 469
A.2.1 E ≥ Eb ............................................ 471
A.2.2 Еb ≥ E ≥ Et ....................................... 472
A.2.3 E ≤ Et ............................................ 473
Appendix B. Time-Dependent Version of the Zhu-Nakamura
Theory ........................................................ 475
References .................................................... 477
Index ......................................................... 495
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