Molecular Symmetry and Spectroscopy
- 1st Edition - March 28, 1979
- Imprint: Academic Press
- Author: Philip Bunker
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 4 3 1 2 2 7 - 2
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 1 5 0 2 5 - 5
Molecular Symmetry and Spectroscopy deals with the use of group theory in quantum mechanics in relation to problems in molecular spectroscopy. It discusses the use of the molecular… Read more
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Request a sales quoteMolecular Symmetry and Spectroscopy deals with the use of group theory in quantum mechanics in relation to problems in molecular spectroscopy. It discusses the use of the molecular symmetry group, whose elements consist of permutations of identical nuclei with or without inversion. After reviewing the permutation groups, inversion operation, point groups, and representation of groups, the book describes the use of representations for labeling molecular energy. The text explains an approximate time independent Schrödinger equation for a molecule, as well as the effect of a nuclear permutation or the inversion of E* on such equation. The book also examines the expression for the complete molecular Hamiltonian and the several groups of operations commuting with the Hamiltonian. The energy levels of the Hamiltonian can then be symmetrically labeled by the investigator using the irreducible representations of these groups. The text explains the two techniques to change coordinates in a Schrödinger equation, namely, (1) by using a diatomic molecule in the rovibronic Schrödinger equation, and (2) by a rigid nonlinear polyatomic molecule. The book also explains that using true symmetry, basis symmetry, near symmetry, and near quantum numbers, the investigator can label molecular energy levels. The text can benefit students of molecular spectroscopy, academicians, and investigators of molecular chemistry or quantum mechanics.
Preface
Acknowledgments
Introduction
Bibliographical Notes
1. Permutations and Permutation Groups
Permutations
The Successive Application of Permutations
Permutation Groups
The Complete Nuclear Permutation Group of a Molecule
Bibliographical Notes
2. The Inversion Operation and Permutation Inversion Groups
The Inversion Operation and Parity
Combining Permutations with the Inversion
The Detailed Effects of P and P* Operations
Summary
3. Rotation Groups and Point Groups
Rotational Symmetry and the Rotation Group
Reflection Symmetry and the Point Group
The Point Group Symmetry of Molecules
The Rotation Group Symmetry of Molecules
Discussion
Bibliographical Notes
4. Representations of Groups
Matrices and Matrix Groups
Isomorphism and Faithful Representations
Homomorphism and Unfaithful Representations
Equivalent and Irreducible Representations
Reduction of a Representation
Conjugate Elements and Classes
Bibliographical Notes
5. The Use of Representations for Labeling Molecular Energy Levels
A Molecular Schrödinger Equation in (X, Y, Z) Coordinates
The Effects of Nuclear Permutations and the Inversion on the Schrödinger Equation
The Symmetry of a Product
The Use of Symmetry Labels and the Vanishing Integral Rule
Diagonalizing the Hamiltonian Matrix
Appendix 5-1: Proof That the Matrices D[R] Generated in Eq. (5-49) Are Representations
Appendix 5-2: Projection Operators
Appendix 5-3: Addendum to Problem 5-2
Bibliographical Notes
6. The Molecular Hamiltonian and its True Symmetry
The Molecular Hamiltonian
The Full Symmetry Group of the Molecular Hamiltonian
Basis Functions and Basis Function Symmetry
Discussion
Bibliographical Notes
7. The Coordinates in the Rovibronic Schrödinger Equation
The Rovibronic Schrödinger Equation
Two Methods for Changing Coordinates in a Schrödinger Equation
Introduction to the Molecule Fixed Axis System
The Diatomic Molecule
Rigid Nonlinear Polyatomic Molecules
Bibliographical Notes
8. The Rovibronic Wavefunctions
The Born-Oppenheimer Approximation
The Electronic Wavefunctions
The Rotation-Vibration Schrödinger Equation
The Rigid Rotor Schrödinger Equation
The Harmonic Oscillator Schrödinger Equation
Summary
Bibliographical Notes
9. The Definition of the Molecular Symmetry Group
The Complete Nuclear Permutation Inversion Group
The Molecular Symmetry Group
The Character Tables and Correlation Tables of MS Groups
The MS Group for Levels of More Than One Electronic State
Summary
Bibliographical Note
10. The Classification of Molecular Wavefunctions in the Molecular Symmetry Group
The Classification of the Complete Internal Wavefunction
The Classification of the Nuclear Spin Wavefunctions and the Determination of Nuclear Spin Statistical Weights
The Classification of the Rotational Wavefunctions
The Classification of the Vibrational Wavefunctions
The Classification of the Electronic Orbital Wavefunctions
The Classification of the Electron Spin Wavefunctions
The Classification of Rotational Wavefunctions Having Half-Integral J
Summary
Bibliographical Notes
11. Near Symmetry, Perturbations, and Optical Selections Rules
Near Symmetry
Near Quantum Numbers
Nonvanishing Perturbation Terms
Perturbations between States
Optical Selection Rules and Forbidden Transitions
Magnetic Dipole and Electric Quadrupole Transitions
Multiphoton Processes and the Raman Effect
The Zeeman Effect
The Stark Effect
Summary
Bibliographical Notes
12. Linear Molecules and Nonrigid Molecules
Linear Molecules
Nonrigid Molecules
Discussion and Summary
Appendix A. The Character Tables
Appendix B. The Correlation Tables
References
Index
- Edition: 1
- Published: March 28, 1979
- Imprint: Academic Press
- No. of pages: 440
- Language: English
- Paperback ISBN: 9780124312272
- eBook ISBN: 9780323150255
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