Theories of molecular reaction dynamics: the microscopic foundation of chemical kinetics/ Niels E. Henriksen and Flemming Y. Hansen

1 Introduction 1
1.1 Nuclear dynamics: the Schr6dinger equation 5
1.2 Thermal equilibrium: the Boltzmann distribution 11
Further reading/references 14
Problems 14
PART I GAS-PHASE DYNAMICS
2 From microscopic to macroscopic descriptions 19
2.1 Cross-sections and rate constants 20
2.2 Thermal equilibrium 26
Further reading/references 32
Problems 32
3 Potential energy surfaces 35
3.1 The general topology of potential energy surfaces 36
3.2 Molecular electronic energies, analytical results 41
Further reading/references 49
Problems 50
4 Bimolecular reactions, dynamics of collisions 52
4.1 Quasi-classical dynamics 52
4.2 Quantum dynamics 87
Further reading/references 104
Problems 105
5 Rate constants, reactive flux 109
5.1 Classical dynamics 111
5.2 Quantum dynamics 129
Further reading/references 138
6 Bimolecular reactions, transition-state theory 139
6.1 Standard derivation 142
6.2 A dynamical correction factor 145
6.3 Systematic derivation 149
6.4 Quantum mechanical corrections 151
6.5 Applications of transition-state theory 155
6.6 Thermodynamic formulation 161
Further reading/references 164
Problems 164
7 Unimolecular reactions 169
7.1 True and apparent unimolecular reactions 170
7.2 Dynamical theories 176
7.3 Statistical theories 184
7.4 Collisional activation and reaction 197
7.5 Detection and control of chemical dynamics 199
Further reading/references 206
Problems 207
8 Microscopic interpretation of Arrhenius parameters 211
8.1 The pre-exponential factor 212
8.2 The activation energy 213
Problems 220
PART II CONDENSED-PHASE DYNAMICS
9 Introduction to condensed-phase dynamics 223
9.1 Solvation, the Onsager model 225
9.2 Diffusion and bimolecular reactions 229
Further reading/references 239
Problems 240
10 Static solvent effects, transition-state theory 241
10.1 An introduction to the potential of mean force 242
10.2 Transition-state theory and the potential of mean force 245
Further reading/references 261
11 Dynamic solvent effects, Kramers theory 262
11.1 Brownian motion, the Langevin equation 265
11.2 Kramers theory for the rate constant 268
11.3 Beyond Kramers, Grote-Hynes theory and MD 275
Further reading/references 286
Problems 287
PART III APPENDICES
Appendix A Statistical mechanics 291
A.1 A system of non-interacting molecules 292
A.2 Classical statistical mechanics 297
Further reading/references 303
Appendix B Microscopic reversibility and detailed balance 304
B.1 Microscopic reversibility 304
B.2 Detailed balance 310
Further reading/references 312
Appendix C Cross-sections in various frames 313
C.1 Elastic and inelastic scattering of two molecules 314
C.2 Reactive scattering between two molecules 324
Appendix D Classical mechanics, coordinate transformations 329
D.1 Diagonalization of the internal kinetic energy 329
Further reading/references 336
Appendix E Small-amplitude vibrations, normal-mode coordinates 337
E.1 Diagonalization of the potential energy 337
E.2 Transformation of the kinetic energy 339
E.3 Transformation of phase-space volumes 340
Further reading/references 342
Appendix F Quantum mechanics 343
F.1 Basic axioms of quantum mechanics 343
F.2 Application of the axioms-xamples 346
F.3 The flux operator 351
F.4 Time-correlation function of the flux operator 355
Further reading/references 359
Appendix G An integral 360
Appendix H Dynamics of random processes 363
H.1 The Fokker-Planck equation 365
H.2 The Chandrasekhar equation 369
Further reading/references 371
Appendix I Multidimensional integrals, Monte Carlo method 372
I.1 Random sampling and importance sampling 373
Further reading/references 375
Index 376