THEORY OF MAGNETIC RESONANCE

Transcription

1 THEORY OF MAGNETIC RESONANCE Second Edition Charles P. Poole, Jr., and Horacio A. Farach Department of Physics University of South Carolina, Columbia A Wiley-lnterscience Publication JOHN WILEY & SONS New York Chichester Brisbane - Toronto Singapore

2 CONTENTS 1. Introduction Magnetic Resonance Theories, The Hamiltonian, Atomic Hamiltonian, Spin Hamiltonian, Equivalent Operators, Effective Spin Hamiltonian, 7 2. Mathematical and Quantum-Mechanical Background Introduction, Types of Matrices, Unitary Matrices, Hermitian Matrices, Angular Momentum Operators, Angular Momentum Matrices, Addition of Angular Momentum, Perturbation Theory, General Two-Spin (\, ) System \ Preliminary Remarks, The Hamiltonian, The Secular Equation and Energy Levels^ Eigenfunctions, Transition Probabilities, Conclusions, 35 xi

3 xii CONTENTS 4. NMR Two-Spin (^, \) System Preliminary Remarks, Energy Levels and Line Spacings, Intensities, Limiting Cases, Conclusions, ESR Two-Spin (\,\) System Preliminary Remarks, Energy Levels and Line Spacings, Intensities, Signs of Hamiltonian Terms, Perturbation Solutions, Anisotropic Hamiltonians Introduction, Energy Levels, Intensities, Angular Dependence of the g-factor, Angular Variations of Experimental Spectra, Hyperfine Hamiltonian Matrix, Hyperfine Patterns, Combined g-factor and Hyperfine Anisotropies, Alpha and Beta Protons, Experimental Determination of the g- and T-Tensors, Multispin Systems Introduction, 80 7ч2х Three-Spin Zeeman Interactions, \ General Three-Spin (5,5,5) Case, ^Three-Spin ESR Case > Three-Spin AB 2 NMR Case, T^ree-Spin ABC and ABX NMR Systems, Equivalent Spins, 98

4 CONTENTS 8. High-Spin Systems 8-1. Introduction, 99 \ 8-2. Spin Systems S, = ks 2 = 1, Quadrupole Interactions, Quadrupole Hamiltonian, Quadrupole Moment, 105^ 8-6. Spin / = 1 Energy Levels and Eigenf unctions, Spin / = 1 Zeeman Effect, Quadrupole Energies for / > Г^Ш^ 8-9. Zero Field Splittings, ИЗ Zero Field D Term, Principal Axis Matrices for D and E, Spin 5 = 1 Energy Levels and Eigenf unctions, Triplet States, Transition-Metal Ions, Hyperfine or Spin-Spin Zero Field Limit, Mössbauer Resonance 9-1. Nature of Mössbauer Effect, Hamiltonian Terms, Energy Levels, Hyperfine Field, Isomer Shift, Atomic Spectra and Crystal Field Theory Introduction, Spin-Orbit Coupling, Zeeman Effect, Zeeman Transition Probabilities, Paschen-Bach Effect, Crystal Fields, Crystal Field Potential, Cubic and Lower Symmetry Potentials, Irreducible Tensor Operators, Equivalent Operators, Energies and Wavefunctions for d-electrons, Irreducible Representations and Kramers'Theorem, Calculation of ^-Factors, 166

5 XiV CONTENTS 11. Lineshapes Introduction, Anderson Theory of Exchange Narrowing, Exchange for the Spin-^ Case, Exchange Narrowing with Hyperfine Structure, Exchange Effects on Chemical Shifts, Intrinsic Linewidth, Gaussian and Lorentzian Shapes, Voigt Lineshape, Powder Pattern Lineshapes, Relaxation, Measurement of Relaxation Times, Double Resonance Introduction, Types of Double Resonance, Hamiltonian and Energy Levels, Relaxation Rates, Dipolar Relaxation, Thermal Equilibrium Populations, Dynamic Equilibrium Populations, Dynamic Equilibrium of a Four-Level System, Steady-State Populations, Absorption and Emission, Electron-Nuclear Double Resonance Introduction, Hamiltonian and^ Energy Levels, Master Equations, The ENDOR Experiment, Steady-State ENDC])R, Dynamics of ENDÖR Response, Transient ENDOR, Double ENDOR, Electron-Electron Double Resonance Introduction, Transition Energies, 247

6 CONTENTS XV Master Equations, ELDOR Reduction Factor, The ELDOR Experiment, Steady-State ELDOR, Transient ELDOR, Dynamic Polarization Introduction, The Hamiltonian,N Master Equations, Polarization and Enhancement, Individual Relaxation Paths, Scalar and Dipolar Relaxation, Polarization Via Forbidden Transitions, Transient Nuclear Polarization, Chemically Induced Dynamk>J^uclear^Polarizätion, Chemically Induced Dynamic Electron Polarization, Nuclear-Nuclear Double Resonance Introduction, Producing Nuclear Double Resonance, Nuclear Overhauser Effect, Two-Dimensional Nuclear Overhauser Effect, Hamiltonian with High Radiofrequency Power, Frequency Sweep Double Resonance, Spin Tickling and Spin Decoupling, Acoustic, Muon, and Optical Magnetic Resonance Introduction, Acoustic Magnetic Resonance, Muon Spin Resonance, Optical Double Magnetic Resonance, Spin Labels Introduction, Correlation Times and Lineshapes in Liquids, Line Broadening, 306

7 xvi Saturation Transfer, Nitroxide Spin Labels, Spin Label Lineshapes Due to Molecular Motion, Measuring Molecular Motion with Spin Labels, 1317 CONTENTS 19. Fourier Transform Nuclear Magnetic Resonance Introduction, Fourier Transforms, Lorentzian Lineshapes and Exponential Decay, Gaussian Self-Transform, Free Induction Decay, Spin Echoes, Time Domain NMR Spectra, Two-Dimensional Spectroscopy, 339 Appendix I. Physical Constants and Energy Conversion Factors 346 Index 349