Contents -- Introduction -- Chapter 1 The Wave Mechanics of Diatomic Molecules -- 1.1 Introduction -- 1.2 The two-body Schrödinger equation -- 1.3 Eigenvalues and eigenfunctions -- 1.4 Angular momentum -- 1.5 Emission and absorption of radiation: Infrared -- 1.6 Emission and absorption of radiation: Raman -- 1.7 Intensities of vibrational transitions -- 1.8 Schrödinger equation in two dimensions -- 1.9 The Schrödinger equation in one dimension and the quasidiatomic model -- 1.10 Representation of molecular spectra by fitting formulas: Dunham expansion of energy levels -- 1.11 Herman-Wallis expansion for intensities -- Chapter 2 Summary of Elements of Algebraic Theory -- 2.1 Lie algebras -- 2.2 Lie subalgebras -- 2.3 Invariant (Casimir) operators -- 2.4 Basis states (representations) -- 2.5 Eigenvalues of the Casimir operators -- 2.6 Algebraic realization of quantum mechanics -- 2.7 Dynamical symmetries -- 2.8 One-dimensional problems -- 2.9 Dunham-like expansion for one-dimensional problems -- 2.10 Transitions in one-dimensional problems -- 2.11 The harmonic limit -- 2.12 The Hamiltonian in three dimensions -- 2.13 Dynamical symmetries for three-dimensional problems -- 2.14 Energy levels: The nonrigid rovibrator -- 2.15 Energy levels: The rigid rovibrator -- 2.16 Dunham-like expansion for three-dimensional problems -- 2.17 Infrared transitions -- 2.18 Electrical anharmonicities -- 2.19 Rotational-vibrational interaction -- 2.20 Raman transitions -- Chapter 3 Mechanics of Molecules -- 3.1 Triatomic molecules -- 3.2 Polyatom Schrödinger equation -- 3.3 One dimensional coupled oscillators -- 3.4 Nonlinear classical dynamics -- Chapter 4 Three-body Algebraic Theory -- 4.1 Algebraic realization of many-body quantum mechanics -- 4.2 One-dimensional coupled oscillators by algebraic methods -- 4.3 The local-mode limit -- 4.4 The normal-mode limit.

4.5 Local-to-normal transition -- 4.6 An example: Stretching vibrations of water -- 4.7 Infrared intensities -- 4.8 Three-dimensional coupled roto-vibrators by algebraic methods -- 4.9 Local basis -- 4.10 The normal-mode basis -- 4.11 Expansion of the coupled basis into uncoupled states -- 4.12 Linear triatomic molecules -- 4.13 Local-mode Hamiltonian for linear triatomic molecules -- 4.14 The normal-mode Hamiltonian for linear triatomic molecules -- 4.15 l-dependent terms -- 4.16 Linear XY[sub(2)]molecules -- 4.17 Majorana couplings (Darling-Dennison couplings) -- 4.18 Quantum number assignment -- 4.19 Fermi couplings -- 4.20 Bent triatomic molecules -- 4.21 Local Hamiltonians for bent triatomic molecules -- 4.22 Linear-bent correlation diagram -- 4.23 The normal mode Hamiltonians for bent triatomic molecules -- 4.24 Bent XY[sub(2)] molecules -- 4.25 Majorana couplings -- 4.26 Higher-order corrections. Linear molecules -- 4.27 Higher-order corrections. Bent molecules -- 4.28 Rotational spectra -- 4.29 Higher-order corrections to rotational spectra -- 4.30 Rotation-vibration interaction -- 4.31 Diagonal rotation-vibration interactions -- 4.32 Nondiagonal rotation-vibration interactions -- 4.33 Properties of nondiagonal rotation-vibration interactions: Linear molecules -- 4.34 Properties of nondiagonal rotation-vibration interactions: Nonlinear molecules -- Chapter 5 Four-Body Algebraic Theory -- 5.1 Tetratomic molecules -- 5.2 Recoupling coefficients -- 5.3 Linear tetratomic molecules -- 5.4 Local Hamiltonian for linear tetratomic molecules -- 5.5 Majorana couplings in linear tetratomic molecules -- 5.6 Vibrational l doubling. Casimir operators -- 5.7 Higher-order terms in tetratomic molecules -- 5.8 Fermi couplings -- 5.9 Amat-Nielsen couplings -- 5.10 Summary of interbond couplings in linear tetratomic molecules.

Chapter 6 Many-Body Algebraic Theory -- 6.1 Separation of rotation and vibration -- 6.2 Internal symmetry coordinates -- 6.3 Quantization of coordinates and momenta -- 6.4 Stretching vibrations -- 6.5 Hamiltonian for stretching vibrations -- 6.6 Higher-order terms -- 6.7 Symmetry-adapted operators -- 6.8 The benzene molecule -- 6.9 Isotopic substitutions. Lowering of symmetry -- 6.10 Infrared intensities -- 6.11 Octahedral molecules -- 6.12 Bending vibrations. The Pöschl-Teller potential -- 6.13 Hamiltonian for bending vibrations -- 6.14 Bending vibrations of benzene -- 6.15 Complete spectroscopy -- 6.16 Removal of spurious states -- 6.17 Complete spectroscopy of benzene -- Chapter 7 Classical Limit and Coordinate Representation -- 7.1 Potential functions -- 7.2 Exact results. One dimension -- 7.3 Exact results. Three dimensions -- 7.4 Geometric interpretation of algebraic models -- 7.5 One-dimensional problems -- 7.6 Intensive boson operators -- 7.7 One-dimensional potential functions -- 7.8 Coupled one-dimensional problems -- 7.9 Potential functions for two coupled one-dimensional problems -- 7.10 Three-dimensional problems -- 7.11 Intensive boson operators in three dimensions -- 7.12 Three-dimensional potential functions -- 7.13 Coupled three-dimensional problems -- 7.14 Potential functions for two coupled three-dimensional problems -- 7.15 Vibrations and the shape of the potential -- 7.16 One-dimensional problems -- 7.17 Three-dimensional problems -- 7.18 Rotations and the equilibrium distance -- 7.19 Coupled problems -- 7.20 Vibrations and the shape of the potential in linear triatomic molecules -- 7.21 Rotations and equilibrium positions -- 7.22 Tetratomic molecules -- 7.23 Higher-order terms -- 7.24 Mean-field theory -- 7.25 Epilogue -- Chapter 8 Prologue to the Future -- APPENDIX A: Properties of Lie Algebras -- A.1 Definition.

A.2 Generators and realizations -- A.3 Cartan classification -- A.4 Number of operators in the algebra -- A.5 Isomorphic Lie algebras -- A.6 Casimir operators -- A.7 Example of Lie algebras -- A.8 Representations -- A.9 Tensor products -- A.10 Branching rules -- A.11 Example of representations of Lie algebras -- A.12 Eigenvalues of Casimir operators -- A.13 Examples of eigenvalues of Casimir operators -- APPENDIX B: Coupling of Algebras -- B.1 Definition -- B.2 Coupling coefficients -- B.3 Addition of angular momenta, SO(3) -- B.4 Properties of Clebsch-Gordan coefficients -- B.5 Tensor operators -- B.6 Wigner-Eckart theorem -- B.7 Tensor products -- B.8 Recoupling coefficients -- B.9 Addition of three angular momenta, SO(3) -- B.10 Properties of 6 - j symbols -- B.11 Addition of four angular momenta -- B.12 Reduction formulas -- B.13 Coupling of SO(4) representations -- B.14 Racah's factorization lemma -- B.15 Coupling coefficients of SO(4) -- B.16 Recoupling coefficients of SO(4) -- APPENDIX C: Hamiltonian Parameters -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Y.