Contents:Preface; I Foundations of the mathematical apparatus; 1 Basic concepts of group theory; 1.1 The group postulates; 1.2 Subgroup, direct product of groups, isomorphism, and homomorphism; 1.3 Cosets. Semidirect product of groups; 1.4 Conjugacy classes; 2 Basic concepts of group representation theory; 2.1 Linear vector spaces; 2.2 Operators in configuration and function spaces; 2.3 Representations of groups; 2.4 Characters. Decomposition of reducible representations; 2.5 Direct product of representations. Symmetric power; 2.6 The Clebsch-Gordan coefficients
2.7 Basis functions of irreducible representations2.8 Irreducible tensor operators. The Wigner-Eckart theorem; 3 The permutation group; 3.1 Operations in the permutation group. Classes; 3.2 Irreducible representations. The Young diagrams and tableaux; 3.3 Basis functions of irreducible representations; 3.4 The conjugate representation; 4 Continuous groups; 4.1 Compact Lie groups; 4.2 Lie group of linear transformations; 4.3 Lie algebra. Three-dimensional rotation group; 4.4 Irreducible representations of a three-dimensional rotation group; 5 Point groups; 5.1 Operations in point groups
5.2 Discrete axial groups5.3 Cubic groups. Icosahedral groups; 5.4 Continuous axial groups; 6 Dynamic groups; 6.1 Invariant dynamic groups; 6.2 Noninvariant dynamic groups; II Qualitative intramolecular quantum dynamics; 7 The philosophy of using the symmetry properties of internal dynamics; 7.1 Symmetry groups of internal dynamics; 7.2 Significance of the analysis of symmetry properties; 7.3 On the domain of the point group; 7.4 The chain of symmetry groups; 7.5 The concept of the coordinate spin; 7.6 The influence of numerical methods on the overall description; 7.7 Conclusions
8 Internal dynamics of rigid molecules8.1 Nonlinear molecules without inversion center; 8.2 Nonlinear molecules with inversion center; 8.3 Linear molecules; 8.4 Description of quasidegenerate vibronic states; 8.5 Conclusions; 9 Molecules with torsional transitions of the exchange type; 9.1 Extended point groups. Intermediate configuration; 9.2 Methanol molecule CH3OH; 9.3 Ethane molecule C2H6; 9.4 The molecules of complex hydrides LiBH4 and NaBH4; 9.5 The molecules of dimethyl ether (CH3)2O and acetone (CH3)2CO; 9.6 Conclusions; 10 Molecules with pseudorotations of the exchange type
10.1 Extended point groups10.2 Cyclobutane molecule C4H8; 10.3 Molecules of the XPF4 type; 10.4 Phosphorus pentafluoride molecule PF5; 10.5 The separation of internal motions; 10.6 Conclusions; 11 Molecules with transitions of the nonexchange type between equivalent configurations; 11.1 Extended point groups; 11.2 The ammonia molecule NH3; 11.3 The peroxide molecule HOOH; 11.4 The hydrazine molecule N2H4; 11.5 Conclusions; 12 On the meaning of the Born-Oppenheimer Approximation; 12.1 Nondegenerate electronic states; 12.2 Degenerate electronic states
12.3 Internal geometric symmetry of the Hamiltonian