Algebraic Theory of Molecules
1st Edition
Published on 12. January 1995
262 pages
978-0-19-535973-2 (ISBN)
Description
Algebraic Theory of Molecules presents a fresh look at the mathematics of wave functions that provide the theoretical underpinnings of molecular spectroscopy. Written by renowned authorities in the field, the book demonstrates the advantages of algebraic theory over the more conventional geometric approach to developing the formal quantum mechanics inherent in molecular spectroscopy. Many examples are provided that compare the algebraic and geometric methods, illustrating the relationship between the algebraic approach and current experiments. The authors develop their presentation from a basic level so as to enable newcomers to enter the field while providing enough details and concrete examples to serve as a reference for the expert. Chemical physicists, physical chemists, and spectroscopists will want to read this exciting new approach to molecular spectroscopy.
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F. Iachello | R. D. Levine
Algebraic Theory of Molecules
Book
04/1995
Oxford University Press Inc
€256.00
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Content
- Intro
- 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
