| Preface | 5 |
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| I Foundations of the mathematical apparatus | 15 |
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| 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 |
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| 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 |
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