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 representations -- 2.8 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 groups -- 5.3 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 molecules -- 8.1 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 groups -- 10.2 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 -- 12.4 Definition of the rotational motion -- 12.5 Selection of physically meaningful states -- 12.6 Symmetry methods in the description of intramolecular dynamics -- 12.7 Geometric symmetry and definitions of nonrigid motions -- 12.8 Nuclear statistical weights -- 12.9 Conclusions -- 13 Molecules with transitions of the exchange and nonexchange types between equivalent configurations -- 13.1 Extended point groups -- 13.2 Methanol molecule CH3OH -- 13.3 Methylamine molecule CH3NH2.

13.4 Cyclopentane molecule C5H10 -- 13.5 Conclusions -- 14 On the construction of extended point groups -- 14.1 Hydrogen fluoride dimer (HF)2 -- 14.2 Ionic complexes ArH+3 andArD+3 -- 14.3 Carbocation C2H+3 -- 14.4 Conclusions -- 15 Nonrigid molecular systems with continuous axial symmetry groups -- 15.1 Systems of the HCN/HNC type -- 15.2 Complexes of the XCO type -- 15.3 Nonrigid water molecules H2O -- 15.4 Conclusions -- 16 Molecules with different isomeric forms in a single electronic state -- 16.1 Distorted molecular systems -- 16.2 The methanol molecule CH2DOH -- 16.3 The ethane molecule CH2D-CH2D -- 16.4 The ethanol molecule CH3CH2OH -- 16.5 The cyclobutane 1,1-d2 molecule -- 16.6 The tetrahydrofuran molecule C4H8O -- 16.7 Conclusions -- 17 Molecules with different isomeric forms in different electronic states -- 17.1 Formaldehyde molecule H2CO -- 17.2 The ethylene molecule CH2-CD2 -- 17.3 Conclusions -- 18 Algebraic models of the global description of molecular spectrum -- 18.1 The rigid water molecule H2O -- 18.2 The nonrigid methanol molecule CH3OH -- 18.3 The nonrigid water molecule H2O -- 18.4 Conclusions -- 19 Description of the Zeeman and Stark effects -- 19.1 External field and symmetry of the stationary states -- 19.2 The Zeeman effect in the case of a rigid molecule -- 19.3 The Zeeman effect in the case of a nonrigid molecule -- 19.4 The Stark effect in the case of a rigid molecule -- 19.5 The Stark effect in the case of a nonrigid molecule -- 19.6 Conclusions -- 20 Additional remarks on describing intramolecular dynamics -- 20.1 The nonrigid trimethylborane molecule B(CH3)3 -- 20.2 Hyperfine interactions in the methane molecule CH4 -- 20.3 Parity violation effects in molecules with stereoisomers.

20.4 Parity violation effects in the molecules without stereoisomers -- 20.5 Conclusions -- Conclusion -- Appendices -- Bibliography -- Index.