Theoretical Foundations of Electron Spin Resonance

Theoretical Foundations of Electron Spin Resonance

Physical Chemistry: A Series of Monographs

1st Edition - January 28, 1978

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  • Author: John E. Harriman
  • eBook ISBN: 9781483191669

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Description

Theoretical Foundations of Electron Spin Resonance deals with the theoretical approach to electron paramagnetic resonance. The book discusses electron spin resonance in applications related to polyatomic, probably organic, free radicals in condensed phases. The book also focuses on essentially static phenomena, that is, the description and determination of stationary-state energy levels. The author reviews the Dirac theory of the electron in which a four-component wave function is responsible for the behavior of the electron. The author then connects this theory with the nonrelativistic wave function theory. The book also addresses the relationship between spin Hamiltonian parameters and observable energy levels, as well as the expressions for specific spin Hamiltonian parameters concerning operators and wave functions. The book discusses wave- functions for open-shell systems; as well as how to extract values of spin Hamiltonian from information related to wave functions. The author then examines empirically adjusted parameters that can determine the wave function itself. This book can prove valuable for scientists involved with nuclear physics, molecular physics, and researchers in chemical physics.

Table of Contents


  • Preface

    Acknowledgments

    Chapter 0. Review of Elementary Electron Spin Resonance

    Systems Studied by Electron Spin Resonance

    The Basic Electron Spin Resonance Experiment

    Relaxation and Lineshape

    The Spin Hamiltonian

    The Electronic Zeeman Interaction

    Magnetic Hyperfine Interactions

    Equivalent Nuclei and Intensity Patterns

    Other Interactions

    Chapter I. The Origin of Magnetic Energy Levels

    1. The Dirac Electron

    Origin of the Dirac Equation

    Some Properties of the Dirac Equation and Dirac Operators

    Solutions of the Dirac Equation

    Perturbations of the Dirac Hydrogen Atom

    Other Calculations with Four-Component Functions

    Summary of Section 1

    2. The Relationship between Relativistic and Nonrelativistic Theories

    Characteristics of and Criteria for Transformations

    The Foldy-Wouthuysen Transformation

    Foldy-Wouthuysen Transformation with Electric Fields Present

    Partitioning of the Dirac Equation

    Discussion of Terms Occurring in the Hamiltonian

    Hydrogenic Ion Results

    Summary of Section 2

    3. Radiative Corrections

    Quantum Electrodynamics

    Anomalous Magnetic Moment

    Modification of the Dirac Equation

    Reduction to Nonrelativistic Form

    Summary of Section 3

    4. Relativistic Many-Electron Theories

    The Bethe-Salpeter Equation

    The Breit Equation

    Reduction to Nonrelativistic Form

    Other Methods

    Discussion of Results

    Extension to Many Electrons

    Summary of Section 4

    5. Effects of Nuclear Structure

    Nuclear Size

    Nuclear Moments

    Summary of Section 5

    6. The Separation of Nuclear and Electronic Motions

    Center of Mass in Relativistic Quantum Mechanics

    Nonrelativistic, One-Electron Atoms

    Effect on Relativistic Corrections for One-Electron Atoms

    Other Systems

    Summary of Section 6

    Chapter II. The Description of Magnetic Energy Levels

    7. The Spin Hamiltonian as a Summary of Experimental Data

    Isotropic Spin Hamiltonian for S = ½

    Nearly Degenerate Electronic States

    Nonisotropic Spin Hamiltonians

    Powder Spectra

    Summary of Section 7

    8. The Relationship of the Spin Hamiltonian to Calculated Energy Levels

    Partitioning Treatment

    Spin Hamiltonian

    States with Additional Degeneracies

    Summary of Section 8

    9. Perturbation Expressions for Spin Hamiltonian Parameters

    Form of the Spin Hamiltonian

    Spin Hamiltonian Parameters

    Orientation Dependence of Spin Hamiltonian Parameters

    Summary of Section 9

    10. Summarizing Calculated Data in Terms of Density Matrix Components

    Spin Components of Reduced Density Matrices

    Relationship to Spin Hamiltonian Parameters

    Summary of Section 10

    Chapter III. Calculations

    11. Wave Functions for Open-Shell Systems

    Spin Couplings and Antisymmetry

    Spin Eigenfunctions

    The Interaction of Space and Spin via Permutational Symmetry

    Comparison of Functions of Different Types

    Other Methods of Calculation

    An Example: Lithium Atom

    Summary of Section 11

    12. Evaluation of Spin Hamiltonian Parameters

    Operators Involved

    Basis Functions

    Integrals

    Summary of Section 12

    13. Semiempirical Methods

    Atomic Orbital Spin Density

    All-Valence-Electron Semiempirical Methods

    Pi-Electron Methods

    Simple Valence Bond Treatments

    Summary of Section 13

    14. External Perturbations

    Static and Dynamic Effects

    Nature of the Interaction

    Perturbation Treatments

    Semiempirical Methods

    Summary of Section

    Appendices

    Appendix A Classical Mechanics and Fields including Relativistic Forms; Units

    Classical Mechanics of Particles

    Electromagnetic Fields and Potentials

    Charged Particles in Fields

    Four-Vectors and Lorentz Transformations

    Units

    Appendix B Gauge Transformations in Nonrelativistic Quantum Mechanics

    Appendix C Rotations, Tensors, Angular Momentum, and Related Topics

    Angular Momentum Operators

    Angular Momentum Eigenfunctions

    Matrices of Angular Momentum Operators

    Coupling of Angular Momenta

    Time Reversal, Complex Conjugation, and Kramers Conjugation

    Rotations

    Tensors and Tensor Operators

    Appendix D Reduced Density Matrices

    Appendix E Some Useful Operator Identities and Matrix Relationships

    Inverse of Operator Sum

    Exponential Operators

    Eigenvalues and Eigenvectors of a Complex Hermitian Matrix

    Diagonalization and Inversion of 2 X 2 Matrices

    Commutators of Spin-Dependent Operators with L2

    Appendix F Summary of Terms in the Hamiltonian

    References

    Index

Product details

  • No. of pages: 416
  • Language: English
  • Copyright: © Academic Press 1978
  • Published: January 28, 1978
  • Imprint: Academic Press
  • eBook ISBN: 9781483191669

About the Author

John E. Harriman

About the Editor

Ernest M. Loebl

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