Symmetry of Intramolecular Quantum Dynamics (eBook)

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Alexander V. Burenin,Institute of Applied Physics, Russian Academy of Sciences, Russia.

Preface 5
I Foundations of the mathematical apparatus 15
1 Basic concepts of group theory 17
1.1 The group postulates 17
1.2 Subgroup, direct product of groups, isomorphism, and homomorphism 20
1.3 Cosets. Semidirect product of groups 21
1.4 Conjugacy classes 23
2 Basic concepts of group representation theory 24
2.1 Linear vector spaces 24
2.2 Operators in configuration and function spaces 27
2.3 Representations of groups 29
2.4 Characters. Decomposition of reducible representations 31
2.5 Direct product of representations. Symmetric power 34
2.6 The Clebsch-Gordan coefficients 37
2.7 Basis functions of irreducible representations 39
2.8 Irreducible tensor operators. The Wigner-Eckart theorem 42
3 The permutation group 45
3.1 Operations in the permutation group. Classes 45
3.2 Irreducible representations. The Young diagrams and tableaux 47
3.3 Basis functions of irreducible representations 49
3.4 The conjugate representation 51
4 Continuous groups 53
4.1 Compact Lie groups 53
4.2 Lie group of linear transformations 55
4.3 Lie algebra. Three-dimensional rotation group 56
4.4 Irreducible representations of a three-dimensional rotation group 60
5 Point groups 65
5.1 Operations in point groups 65
5.2 Discrete axial groups 67
5.3 Cubic groups. Icosahedral groups 68
5.4 Continuous axial groups 70
6 Dynamic groups 72
6.1 Invariant dynamic groups 72
6.2 Noninvariant dynamic groups 73
II Qualitative intramolecular quantum dynamics 79
7 The philosophy of using the symmetry properties of internal dynamics 81
7.1 Symmetry groups of internal dynamics 81
7.2 Significance of the analysis of symmetry properties 87
7.3 On the domain of the point group 90
7.4 The chain of symmetry groups 95
7.5 The concept of the coordinate spin 97
7.6 The influence of numerical methods on the overall description 100
7.7 Conclusions 100
8 Internal dynamics of rigid molecules 103
8.1 Nonlinear molecules without inversion center 103
8.2 Nonlinear molecules with inversion center 115
8.3 Linear molecules 122
8.4 Description of quasidegenerate vibronic states 129
8.5 Conclusions 133
9 Molecules with torsional transitions of the exchange type 137
9.1 Extended point groups. Intermediate configuration 137
9.2 Methanol molecule CH3OH 143
9.3 Ethane molecule C2H6 149
9.4 The molecules of complex hydrides LiBH4 and NaBH4 154
9.5 The molecules of dimethyl ether (CH3)2O and acetone (CH3)2CO 162
9.6 Conclusions 169
10 Molecules with pseudorotations of the exchange type 171
10.1 Extended point groups 171
10.2 Cyclobutane molecule C4H8 173
10.3 Molecules of the XPF4 type 180
10.4 Phosphorus pentafluoride molecule PF5 185
10.5 The separation of internal motions 193
10.6 Conclusions 195
11 Molecules with transitions of the nonexchange type between equivalent configurations 196
11.1 Extended point groups 196
11.2 The ammonia molecule NH3 199
11.3 The peroxide molecule HOOH 203
11.4 The hydrazine molecule N2H4 209
11.5 Conclusions 218
12 On the meaning of the Born-Oppenheimer Approximation 219
12.1 Nondegenerate electronic states 220
12.2 Degenerate electronic states 221
12.3 Internal geometric symmetry of the Hamiltonian 224
12.4 Definition of the rotational motion 230
12.5 Selection of physically meaningful states 233
12.6 Symmetry methods in the description of intramolecular dynamics 237
12.7 Geometric symmetry and definitions of nonrigid motions 240
12.8 Nuclear statistical weights 243
12.9 Conclusions 244
13 Molecules with transitions of the exchange and nonexchange types between equivalent configurations 249
13.1 Extended point groups 249
13.2 Methanol molecule CH3OH 253
13.3 Methylamine molecule CH3NH2 259
13.4 Cyclopentane molecule C5H10 264
13.5 Conclusions 269
14 On the construction of extended point groups 270
14.1 Hydrogen fluoride dimer (HF)2 270
14.2 Ionic complexes ArH+3 andArD+3 275
14.3 Carbocation C2H+3 282
14.4 Conclusions 291
15 Nonrigid molecular systems with continuous axial symmetry groups 292
15.1 Systems of the HCN/HNC type 293
15.2 Complexes of the XCO type 296
15.3 Nonrigid water molecules H2O 297
15.4 Conclusions 304
16 Molecules with different isomeric forms in a single electronic state 305
16.1 Distorted molecular systems 305
16.2 The methanol molecule CH2DOH 307
16.3 The ethane molecule CH2D-CH2D 311
16.4 The ethanol molecule CH3CH2OH 316
16.5 The cyclobutane 1,1-d2 molecule 321
16.6 The tetrahydrofuran molecule C4H8O 329
16.7 Conclusions 341
17 Molecules with different isomeric forms in different electronic states 343
17.1 Formaldehyde molecule H2CO 343
17.2 The ethylene molecule CH2-CD2 350
17.3 Conclusions 362
18 Algebraic models of the global description of molecular spectrum 363
18.1 The rigid water molecule H2O 364
18.2 The nonrigid methanol molecule CH3OH 368
18.3 The nonrigid water molecule H2O 373
18.4 Conclusions 375
19 Description of the Zeeman and Stark effects 377
19.1 External field and symmetry of the stationary states 377
19.2 The Zeeman effect in the case of a rigid molecule 378
19.3 The Zeeman effect in the case of a nonrigid molecule 381
19.4 The Stark effect in the case of a rigid molecule 382
19.5 The Stark effect in the case of a nonrigid molecule 387
19.6 Conclusions 391
20 Additional remarks on describing intramolecular dynamics 393
20.1 The nonrigid trimethylborane molecule B(CH3)3 393
20.2 Hyperfine interactions in the methane molecule CH4 408
20.3 Parity violation effects in molecules with stereoisomers 410
20.4 Parity violation effects in the molecules without stereoisomers 412
20.5 Conclusions 415
Conclusion 417
Appendices 419
Bibliography 431
Index 437

lt;P>"This is a detailed book that is well worth reading. ... One part is a clear presentation of the background theory of symmetry operators and group representations. In this regard it is an excellent reference book and one of the clearest sets of chapters on this standard theory. ..."
Brian L. Burrows, University of Michigan Mathematical Reviews, August 2013

"This book is an excellent one. Using only the basis of the symmetry principles, the author gives a systematic description of intramolecular quantum dynamics. […] For Physicists and Mathematicians on theoretical studies in intramolecular quantum dynamics the book has a very useful reference value. This book can very well be used as graduate student course." Zentralblatt für Mathematik