Theories of Molecular Reaction Dynamics

Cover Page......Page 1
Title Page......Page 4
ISBN 0199203865......Page 5
Preface......Page 6
Contents (with page links)......Page 10
1 Introduction......Page 14
1.1 Nuclear dynamics: the Schrödinger equation......Page 18
1.2 Thermal equilibrium: the Boltzmann distribution......Page 24
Problems......Page 27
PART I: GAS-PHASE DYNAMICS......Page 30
2 From microscopic to macroscopic descriptions......Page 32
2.1 Cross-sections and rate constants......Page 33
2.2 Thermal equilibrium......Page 39
Problems......Page 45
3 Potential energy surfaces......Page 48
3.1 The general topology of potential energy surfaces......Page 49
3.2 Molecular electronic energies, analytical results......Page 54
Further reading/references......Page 62
Problems......Page 63
4.1 Quasi-classical dynamics......Page 65
4.2 Quantum dynamics......Page 100
Further reading/references......Page 117
Problems......Page 118
5 Rate constants, reactive flux......Page 122
5.1 Classical dynamics......Page 124
5.2 Quantum dynamics......Page 142
Further reading/references......Page 151
6 Bimolecular reactions, transition-state theory......Page 152
6.1 Standard derivation......Page 155
6.2 A dynamical correction factor......Page 158
6.3 Systematic derivation......Page 162
6.4 Quantum mechanical corrections......Page 164
6.5 Applications of transition-state theory......Page 168
6.6 Thermodynamic formulation......Page 174
Problems......Page 177
7 Unimolecular reactions......Page 182
7.1 True and apparent unimolecular reactions......Page 183
7.2 Dynamical theories......Page 189
7.3 Statistical theories......Page 197
7.4 Collisional activation and reaction......Page 210
7.5 Detection and control of chemical dynamics......Page 212
Further reading/references......Page 219
Problems......Page 220
8 Microscopic interpretation of Arrhenius parameters......Page 224
8.1 The pre-exponential factor......Page 225
8.2 The activation energy......Page 226
Problems......Page 233
PART II: CONDENSED-PHASE DYNAMICS......Page 234
9 Introduction to condensed-phase dynamics......Page 236
9.1 Solvation, the Onsager model......Page 238
9.2 Diffusion and bimolecular reactions......Page 242
Further reading/references......Page 252
Problems......Page 253
10 Static solvent effects, transition-state theory......Page 254
10.1 An introduction to the potential of mean force......Page 255
10.2 Transition-state theory and the potential of mean force......Page 258
Further reading/references......Page 274
11 Dynamic solvent effects, Kramers theory......Page 275
11.1 Brownian motion, the Langevin equation......Page 278
11.2 Kramers theory for the rate constant......Page 281
11.3 Beyond Kramers, Grote–Hynes theory and MD......Page 288
Further reading/references......Page 299
Problems......Page 300
PART III: APPENDICES......Page 302
Appendix A: Statistical mechanics......Page 304
A.1 A system of non-interacting molecules......Page 305
A.2 Classical statistical mechanics......Page 310
Further reading/references......Page 316
B.1 Microscopic reversibility......Page 317
B.2 Detailed balance......Page 323
Further reading/references......Page 325
Appendix C: Cross-sections in various frames......Page 326
C.1 Elastic and inelastic scattering of two molecules......Page 327
C.2 Reactive scattering between two molecules......Page 337
D.1 Diagonalization of the internal kinetic energy......Page 342
Further reading/references......Page 349
E.1 Diagonalization of the potential energy......Page 350
E.2 Transformation of the kinetic energy......Page 352
E.3 Transformation of phase-space volumes......Page 353
Further reading/references......Page 355
F.1 Basic axioms of quantum mechanics......Page 356
F.2 Application of the axioms—examples......Page 359
F.3 The flux operator......Page 364
F.4 Time-correlation function of the flux operator......Page 368
Further reading/references......Page 372
Appendix G: An integral......Page 373
Appendix H: Dynamics of random processes......Page 376
H.1 The Fokker–Planck equation......Page 378
H.2 The Chandrasekhar equation......Page 382
Further reading/references......Page 384
Appendix I: Multidimensional integrals, Monte Carlo method......Page 385
I.1 Random sampling and importance sampling......Page 386
Further reading/references......Page 388
F......Page 389
R......Page 390
Z......Page 391