Symmetry of Intramolecular Quantum Dynamics

Symmetry of Intramolecular Quantum Dynamics......Page 4
Preface......Page 6
Contents......Page 10
Part I: Foundations of the mathematical apparatus......Page 16
1.1 The group postulates......Page 18
1.2 Subgroup, direct product of groups, isomorphism, and homomorphism......Page 21
1.3 Cosets. Semidirect product of groups......Page 22
1.4 Conjugacy classes......Page 24
2.1 Linear vector spaces......Page 25
2.2 Operators in configuration and function spaces......Page 28
2.3 Representations of groups......Page 30
2.4 Characters. Decomposition of reducible representations......Page 32
2.5 Direct product of representations. Symmetric power......Page 35
2.6 The Clebsch–Gordan coefficients......Page 38
2.7 Basis functions of irreducible representations......Page 40
2.8 Irreducible tensor operators. The Wigner–Eckart theorem......Page 43
3.1 Operations in the permutation group. Classes......Page 46
3.2 Irreducible representations. The Young diagrams and tableaux......Page 48
3.3 Basis functions of irreducible representations......Page 50
3.4 The conjugate representation......Page 52
4.1 Compact Lie groups......Page 54
4.2 Lie group of linear transformations......Page 56
4.3 Lie algebra. Three-dimensional rotation group......Page 57
4.4 Irreducible representations of a three-dimensional rotation group......Page 61
5.1 Operations in point groups......Page 66
5.2 Discrete axial groups......Page 68
5.3 Cubic groups. Icosahedral groups......Page 69
5.4 Continuous axial groups......Page 71
6.1 Invariant dynamic groups......Page 73
6.2 Noninvariant dynamic groups......Page 74
Part II: Qualitative intramolecular quantum dynamics......Page 80
7.1 Symmetry groups of internal dynamics......Page 82
7.2 Significance of the analysis of symmetry properties......Page 88
7.3 On the domain of the point group......Page 91
7.4 The chain of symmetry groups......Page 96
7.5 The concept of the coordinate spin......Page 98
7.7 Conclusions......Page 101
8.1 Nonlinear molecules without inversion center......Page 104
8.2 Nonlinear molecules with inversion center......Page 116
8.3 Linear molecules......Page 123
8.4 Description of quasidegenerate vibronic states......Page 130
8.5 Conclusions......Page 134
9.1 Extended point groups. Intermediate configuration......Page 138
9.2 Methanol molecule CH3OH......Page 144
9.3 Ethane molecule C2H6......Page 150
9.4 The molecules of complex hydrides LiBH4 and NaBH4......Page 155
9.5 The molecules of dimethyl ether (CH3)2O and acetone (CH3)2CO......Page 163
9.6 Conclusions......Page 170
10.1 Extended point groups......Page 172
10.2 Cyclobutane molecule C4H8......Page 174
10.3 Molecules of the XPF4 type......Page 181
10.4 Phosphorus pentafluoride molecule PF5......Page 186
10.5 The separation of internal motions......Page 194
10.6 Conclusions......Page 196
11.1 Extended point groups......Page 197
11.2 The ammoniamolecule NH3......Page 200
11.3 The peroxide molecule HOOH......Page 204
11.4 The hydrazine molecule N2H4......Page 210
11.5 Conclusions......Page 219
12 On the meaning of the Born–Oppenheimer Approximation......Page 220
12.1 Nondegenerate electronic states......Page 221
12.2 Degenerate electronic states......Page 222
12.3 Internal geometric symmetry of the Hamiltonian......Page 225
12.4 Definition of the rotational motion......Page 231
12.5 Selection of physically meaningful states......Page 234
12.6 Symmetry methods in the description of intramolecular dynamics......Page 238
12.7 Geometric symmetry and definitions of nonrigid motions......Page 241
12.8 Nuclear statistical weights......Page 244
12.9 Conclusions......Page 245
13.1 Extended point groups......Page 250
13.2 Methanol molecule CH3OH......Page 254
13.3 Methylamine molecule CH3NH2......Page 260
13.4 Cyclopentane molecule C5H10......Page 265
13.5 Conclusions......Page 270
14.1 Hydrogen fluoride dimer (HF)2......Page 271
14.2 Ionic complexes ArHC3+ and ArDC3+......Page 276
14.3 Carbocation C2HC3+......Page 283
14.4 Conclusions......Page 292
15 Nonrigid molecular systems with continuous axial symmetry groups......Page 293
15.1 Systems of the HCN/HNC type......Page 294
15.2 Complexes of the XCO type......Page 297
15.3 Nonrigid water molecules H2O......Page 298
15.4 Conclusions......Page 305
16.1 Distorted molecular systems......Page 306
16.2 The methanol molecule CH2DOH......Page 308
16.3 The ethane molecule CH2D–CH2D......Page 312
16.4 The ethanol molecule CH3CH2OH......Page 317
16.5 The cyclobutane-1,1-d2 molecule......Page 322
16.6 The tetrahydrofuran molecule C4H8O......Page 330
16.7 Conclusions......Page 342
17.1 Formaldehyde molecule H2CO......Page 344
17.2 The ethylene molecule CH2–CD2......Page 351
17.3 Conclusions......Page 363
18 Algebraic models of the global description of molecular spectrum......Page 364
18.1 The rigid water molecule H2O......Page 365
18.2 The nonrigid methanol molecule CH3OH......Page 369
18.3 The nonrigid water molecule H2O......Page 374
18.4 Conclusions......Page 376
19.1 External field and symmetry of the stationary states......Page 378
19.2 The Zeeman effect in the case of a rigid molecule......Page 379
19.3 The Zeeman effect in the case of a nonrigid molecule......Page 382
19.4 The Stark effect in the case of a rigid molecule......Page 383
19.5 The Stark effect in the case of a nonrigid molecule......Page 388
19.6 Conclusions......Page 392
20.1 The nonrigid trimethylborane molecule B(CH3)3......Page 394
20.2 Hyperfine interactions in the methane molecule CH4......Page 409
20.3 Parity violation effects in molecules with stereoisomers......Page 411
20.4 Parity violation effects in the molecules without stereoisomers......Page 413
20.5 Conclusions......Page 416
Conclusion......Page 418
Appendix I: Tables of characters of the permutation group π2-π8......Page 420
Appendix II: Tables of characters of point groups......Page 423
Appendix III: Tables of nuclear statistical weights......Page 427
Appendix IV: Classification of normal vibrations of nonrigid molecules......Page 429
Appendix V: Action of the direction cosines on the rotational unit vectors......Page 431
Bibliography......Page 432
Index......Page 438