Molecular Symmetry and Spectroscopy

Molecular Symmetry and Spectroscopy

1st Edition - March 28, 1979

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  • Author: Philip Bunker
  • eBook ISBN: 9780323150255

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Description

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 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.

Table of Contents


  • 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

Product details

  • No. of pages: 440
  • Language: English
  • Copyright: © Academic Press 1979
  • Published: March 28, 1979
  • Imprint: Academic Press
  • eBook ISBN: 9780323150255

About the Author

Philip Bunker

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