Theoretical Foundations of Electron Spin Resonance

Physical Chemistry: A Series of Monographs

1st Edition - January 28, 1978

Author: John E. Harriman

Editor: Ernest M. Loebl

eBook ISBN:

9 7 8 - 1 - 4 8 3 1 - 9 1 6 6 - 9

Theoretical Foundations of Electron Spin Resonance deals with the theoretical approach to electron paramagnetic resonance. The book discusses electron spin resonance in… Read more

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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.

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