ELECTRON PARAMAGNETIC RESONANCE Elementary Theory and Practical Applications
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1 ELECTRON PARAMAGNETIC RESONANCE Elementary Theory and Practical Applications Second Edition JOHN A. WElL Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan, S7N OWO Canada JAMES R. BOLTON Bolton Photosciences Inc., 628 Cheriton Cres. NW, Edmonton, AS T6R 2M5, Canada BICIENTIENNIAL ". i1807~ ~ffiwiley ~ ~: ~ _; I> r BICENTIlNNIAL WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
2 PREFACE ACKNOWLEDGMENTS xix xxiii 1 BASIC PRINCIPLES OF PARAMAGNETIC RESONANCE Introduction / I 1.2 Historical Perspective / A Simple EPR Spectrometer / Scope of the EPR Technique / Energy Flow in Paramagnetic Systems / II 1.6 Quantization of Angular Momenta / Relation Between Magnetic Moments and Angular Momenta / Magnetic Field Quantities and Units / Bulk Magnetic Properties / Magnetic Energies and States / Interaction of Magnetic Dipoles with Electromagnetic Radiation / Characteristics of the Spin Systems / The g Factor / Characteristics of Dipolar Interactions / Parallel-Field EPR / 28 vii
3 viii 1.14 Time-Resolved EPR / S Computerology / EPR Imaging / 30 References / 30 Notes / 32 Further Reading / 34 Problems / 3S 2 MAGNETIC INTERACTION BETWEEN PARTICLES Introduction / Theoretical Considerations of the Hyperfine Interaction / Angular-Momentum and Energy Operators / Spin Operators and Hamiltonians / Electronic and Nuclear Zeeman Interactions / Spin Hamiltonian Including Isotropic Hyperfine Interaction / Energy Levels of a System with One Unpaired Electron and One Nucleus with I=! / Energy Levels of a System with S =! and I = I / Signs of Isotropic Hyperfine Coupling Constants / Dipolar Interactions Between Electrons / 54 References / 54 Notes / 55 Further Reading / 56 Problems / 56 3 ISOTROPIC HYPERFINE EFFECTS IN EPR SPECTRA Introduction / Hyperfine Splitting from Protons / Single Set of Equivalent Protons / S Multiple Sets of Equivalent Protons / Hyperfine Splittings from Other Nuclei with I=! / Hyperfine Splittings from Nuclei with I >! / Useful Rules for the Interpretation of EPR Spectra / Higher-Order Contributions to Hyperfine Splittings / Deviations from the Simple Multinomial Scheme / Other Problems Encountered in EPR Spectra of Free Radicals / Some Interesting 7T-Type Free Radicals / 78
4 ix References / 79 Notes / 79 Further Reading / 80 Problems / 80 4 ZEEMAN ENERGY (g) ANISOTROPY Introduction / Systems with High Local Symmetry / Systems with Rhombic Local Symmetry / Construction of the g Matrix / Symmetry-Related Sites / EPR Line Intensities / Statistically Randomly Oriented Solids / Spin-Orbit Coupling and Quantum-Mechanical Modeling of g / Comparative Overview / 110 References / I II Notes / 112 Further Reading / 114 Problems / HYPERFINE (A) ANISOTROPY Introduction / Origin of the Anisotropic Part of the Hyperfine Interaction / Determination and Interpretation of the Hyperfine Matrix / The Anisotropic Breit-Rabi Case / The Case of Dominant Electron Zeeman Energy / J General Case / The Case of B ~ B hf / The Case of B»»; / Combined g and Hyperfine Anisotropy / Multiple Hyperfine Matrices / Systems With I > ~ / Hyperfine Powder Lineshapes / 145 References / 150 Notes / 151 Further Reading / 152
5 X Problems / SYSTEMS WITH MORE THAN ONE UNPAIRED ELECTRON Introduction / Spin Hamiltonian for Two Interacting Electrons / Electron-Exchange Interaction / Electron-Electron Dipole Interaction / Systems with S = I (Triplet States) / Spin Energies and Eigenfunctions / M s = ±2' Transitions / Randomly Oriented Triplet Systems / 173 Photo-excited Triplet-State Entities / 177 Thermally Accessible Triplet Entities / 182 Ground-State Triplet Entities / Carbenes and Nitrenes / Dianions of Symmetric Aromatic Hydrocarbons / Inorganic Triplet Species / Interacting Radical Pairs / Biradicals / Systems with S > I / High-Spin and High-Field Energy Terms / The Spin Hamiltonian: A Summing up / Modeling the Spin-Hamiltonian Parameters / 199 References / 200 Notes / 203 Further Reading / 204 Problems / PARAMAGNETIC SPECIES IN THE GAS PHASE Introduction / Monatomic Gas-Phase Species / Diatomic Gas-Phase Species / Triatomic and Polyatomic Gas-Phase Molecules / Laser Electron Paramagnetic Resonance / Other Techniques / Reaction Kinetics / Astro-EPR / 220
6
7 xii Metals Dissolved in Ammonia and Amine Solutions / Semiconductors / Graphitic Compounds / Techniques for Structural Estimates from EPR Data / The Newman Superposition Model / The Pseudo-cube Method / Distances from Parameter D / Eatons' Interspin-Distance Formula / Summary / 287 References / 287 Notes / 291 Further Reading / 291 Problems / 292 Appendix 9A Huckel Molecular-Orbital Calculations / 294 HMO References / 298 HMO Problems / RELAXATION TIMES, L1NEWIDTHS AND SPIN KINETIC PHENOMENA Introduction / 30 I 10.2 Spin Relaxation: General Aspects / Spin Temperature and Boltzmann Distribution / Spin Dynamics / Mechanisms for T I / 305 Spin Relaxation: Bloch Model / Magnetization in a Static Magnetic Field / Addition of an Oscillating Magnetic Field / Rotating Frame / Steady-State Solutions of Bloch Equations / 312 Linewidths / Homogeneous Broadening / Inhomogeneous Broadening / 316 Dynamic Lineshape Effects / Generalized Bloch Equations / Other Theoretical Models / 322 Examples of Line-Broadening Mechanisms / Electron-Spin Exchange / Electron Transfer /
8 xiii Proton Transfer / Fluxional Motion / Linewidth Variation: Dynamic Hyperfine Contributions / Single Nucleus / Multiple Nuclei / Molecular Tumbling Effects / Dipolar Effects / Spin-Rotation Interaction / General Example / Longitudinal Detection / Saturation-Transfer EPR / Time Dependence of the EPR Signal Amplitude / Concentration Changes / Chemically Induced Dynamic Electron Polarization / Dynamic Nuclear Polarization / Bio-Oxygen / Summary / 347 References / 348 Notes / 351 Further Reading / 352 Problems / NONCONTINUOUS EXCITATION OF SPINS Introduction / The Idealized B, Switch-on / The Single B, Pulse / Fourier-Transform EPR and FID Analysis / Multiple Pulses / Electron Spin-Echo Envelope Modulation / Advanced Techniques / Spin Coherence and Correlation / 375 References / 378 Notes / 380 Further Reading / 381 Problems / 382
9 xiv 12 DOUBLE-RESONANCE TECHNIQUES Introduction / A Continuous-Wave ENDOR Experiment / Energy Levels and ENDOR Transitions / Relaxation Processes in Steady-State ENDOR 5 / CW ENDOR: Single-Crystal Examples / The F Centers in the Alkali Halides / Metal-Ion Tetraphenylporphyrins / CW ENDOR in Powders and Non-Crystalline Solids / CW ENDOR in Liquid Solutions / Pulse Double-Resonance Experiments / Electron-Electron Double Resonance (ELDOR) / Optically Detected Magnetic Resonance / Fluorescence-Detected Magnetic Resonance / 407 References / 408 Notes / 410 Further Reading / 411 Problems / OTHER TOPICS Apologia / Biological Systems / Clusters / Charcoal, Coal, Graphite and Soot / Colloids / Electrochemical EPR / EPR Imaging / Ferromagnets. Antiferromagnets and Superparamagnets / Glasses / Geologic/Mineralogic Systems and Selected Gems / Amethyst / BerylandChrysoberyl / Diamond / Emerald / Opal / 418
10 XV Rock Crystal (a-quartz) / Ruby / Sapphire / Topaz / Tourmaline / Turquoise / Zircon / Liquid Crystals / "Point" Defects / Insulators / Alkali Halides / Oxides / Semiconductors / Polymers / Radiation Dosage and Dating / Spin Labels / Spin Traps / Trapped Atoms and Molecules / 421 APPENDIX A MATHEMATICAL OPERATIONS 422 Al Complex Numbers / 422 A.2 Operator Algebra / 423 A.2.1 Properties of Operators / 423 A.2.2 Eigenvalues and Eigenfunctions / 426 A.3 Determinants / 428 A.4 Vectors: Scalar. Vector, and Outer Products / 430 A5 Matrices / 432 A.5.1 Addition and Subtraction of Matrices / 434 A5.2 Multiplication of Matrices / 434 A.5.3 Special Matrices and Matrix Properties / 438 A5.4 Dirac Notation for Eigenfunctions and Matrix Elements / 438 A.5.5 Diagonalization of Matrices / 440 A.5.6 Matrix Invariants / 446 A6 Perturbation Theory / 446 A.7 Dirac Delta Function / 449 A.8 Group Theory / 450 References / 450
11 xvi Notes / 451 Further Reading / 451 Problems / 451 APPENDIX B B.I Introduction / 455 QUANTUM MECHANICS OF ANGULAR MOMENTUM 455 B.2 Angular-Momentum Operators / 457 B.3 Commutation Relations for General Angular-Momentum Operators / 458 BA '2 ' Eigenvalues of J and J z / 459 B.5 Superposition of States / 464 B.6 Angular-Momentum Matrices / 464 B.7 Addition of Angular Momenta / 466 B.8 Notation for Atomic and Molecular States / 472 B.9 Angular Momentum and Degeneracy of States / 473 B.IO Time Dependence / 475 B.II Precession / 475 B.12 Magnetic Flux Quantization / 477 B.13 Summary / 478 References / 479 Notes / 480 Further Reading / 480 Problems / 481 Notes for Problem B.12 / 483 APPENDIX C THE HYDROGEN ATOM AND SELECTED RADICALS RH n 484 C I Hydrogen Atom / 484 CI.I Spin Hamiltonian / 484 CI.2 The Spin Eigenkets and Energy Matrix / 485 CI.3 Exact Solution for the Energy Eigenvalues / 487 CIA Energy Eigenstates and Allowed Transitions / 489 CI.5 Resonant Frequencies in Constant Magnetic Field / Cl.6 Resonant Magnetic Fields at Constant Excitation Frequency / 493 C.1.7 Calculation of Spin Energy Levels by Perturbation Theory /
12 xvii C.2 RH Radicals / 497 C.3 RH 2 Radicals / 498 C.3.1 Spin Hamiltonian and Energy Levels / 499 C.3.2 EPR Transitions / 499 References / 501 Notes / 501 Further Reading / 502 Problems / 502 APPENDIX D PHOTONS Introduction / The Physical Aspects of Photons / 505 OJ Magnetic-Resonance Aspects / 508 References / 510 Notes / 510 APPENDIX E INSTRUMENTATION AND TECHNICAL PERFORMANCE 512 E.I Instrumental: Background / 512 E.2 CW EPR Spectrometers / 515 E.2.1 Magnet System / 516 E.2.2 Radiation Source / 517 E.2.3 Microwave Transmission / 518 E.2.4 Coupling of the Source to the Resonator / 519 E.2.5 Resonator System / 520 E.2.6 Field-Modulation System / 525 E.2.7 Coupling of the Resonator to the Detector / 525 E.2.8 Detection System / 526 E.3 Pulsed EPR Spectrometers / 529 E.4 Computer Interfacing with EPR Spectrometers / 530 E.5 Techniques for Temperature Variation and Control / 531 E.6 Techniques for Pressure Variation / 532 References / 533 Notes / 535 Further Reading / 535 Problems / 536
13 xviii APPENDIX F EXPERIMENTAL CONSIDERATIONS 537 F.I Techniques for Generation of Paramagnetic Species / 537 F.2 Lineshapes and Intensities / 539 F.2.1 F.2.2 Lineshapes / 539 Signal Intensities and Spin-Concentration Standards / 545 F.3 Sensitivity and Resolution / 548 FA F.3.1 F.3.2 F.3.3 F.3A F.3.5 F.3.6 Optimum Sensitivity / 548 Sample Temperature / 550 Microwave Frequency / 550 Q Factor of the Resonator / 551 Microwave Power Level and Measurements of B, / 553 Modulation Amplitude / 554 F.3.7 Modulation Frequency / 557 Measurements / 557 FA.l FA.2 g Factors and Hyperfine Splittings / 557 Relaxation Time / 559 FA.3 Spin-Number Determinations / 561 References / 561 Notes / 564 Further Reading / 565 Problems / 565 APPENDIX G EPR-RELATED BOOKS AND SELECTED CHAPTERS 567 APPENDIX H FUNDAMENTAL CONSTANTS, CONVERSION FACTORS, AND KEY DATA 577 APPENDIX I MISCELLANEOUS GUIDELINES 588 I.l Notation for Symbols / Glossary of Symbols / Abbreviations / 600 la Exponent Nomenclature / Journal Reference Style / 602 Author Index 603 Subject Index 624
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