Theoretical Foundations of Electron Spin Resonance

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.

Contenu

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 =
   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