electron paramagnetic resonance - gbv · 2013-01-19 · r. contents . preface xix acknowledgments...
TRANSCRIPT
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ELECTRON PARAMAGNETIC RESONANCE
uion Elementary Theory and first
.g to
iidst Practical Applications~ the and
20th :heir Second Edition iere, leas.
ney, JOHN A. WElL eeds Department of Chemistry, University of Saskatchewan, Saskatoon, way Saskatchewan, S7N OWO Canada -dge
JAMES R. BOLTON Bolton Photosciences Inc., 628 Cheriton Cres. NW, Edmonton, AS T6R 2M5,
CanadaI the
ILEY BICIENTIENNIAL
ARD " . i1807~
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BICENTIlNNIAL
WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
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CONTENTS
PREFACE xix
ACKNOWLEDGMENTS xxiii
1 BASIC PRINCIPLES OF PARAMAGNETIC RESONANCE 1
1.1 Introduction / I
1.2 Historical Perspective / 3
1.3 A Simple EPR Spectrometer / 4
1.4 Scope of the EPR Technique / 7
1.5 Energy Flow in Paramagnetic Systems / II
1.6 Quantization of Angular Momenta / 13
1.7 Relation Between Magnetic Moments and Angular Momenta / 14
1.8 Magnetic Field Quantities and Units / 15
1.9 Bulk Magnetic Properties / 18
1.10 Magnetic Energies and States / 20
1.11 Interaction of Magnetic Dipoles with Electromagnetic Radiation / 21
1.12 Characteristics of the Spin Systems / 23
1.12.1 The g Factor / 23
1.12.2 Characteristics of Dipolar Interactions / 27
1.13 Parallel-Field EPR / 28
vii
viii CONTENTS
1.14 Time-Resolved EPR / 29 References / 79 1.1 S Computerology / 29 Notes / 79 1.16 EPR Imaging / 30 Further Reading / 80 References / 30 Problems / 80 Notes / 32
Further Reading / 34 4 ZEEMAN ENERGY I
Problems / 3S 4.1 Introduction / 8
2 MAGNETIC INTERACTION BETWEEN PARTICLES 36 4.2 Systems with Hil
4.3 Systems with Rh 2.1 Introduction / 36 4.4 Construction of t 2.2 Theoretical Considerations of the Hyperfine Interaction / 38 4.5 Symmetry-Relate 2.3 Angular-Momentum and Energy Operators / 40 4.6 EPR Line Intensi
2.3.1 Spin Operators and Hamiltonians / 41 4.7 Statistically Ranr 2.3.2 Electronic and Nuclear Zeeman Interactions / 43 4.8 Spin-Orbit Coup] 2.3.3 Spin Hamiltonian Including Isotropic Modeling of g /
Hyperfine Interaction / 46 4.9 Comparative OVI 2.4 Energy Levels of a System with One Unpaired Electron
and One Nucleus with I=! / 47
2.5 Energy Levels of a System with S = ! and I = I / 50
References / 111
Notes / 112
Further Reading / 11· 2.6 Signs of Isotropic Hyperfine Coupling Constants / 53 Problems / 114 2.7 Dipolar Interactions Between Electrons / 54
References / 54 5 HYPERFINE (A) ANI Notes / 55 5.1 Introduction / I Further Reading / 56 5.2 Origin of the Ani Problems / 56 Hyperfine Interac
3 ISOTROPIC HYPERFINE EFFECTS IN EPR SPECTRA 58 5.3 Determination an
Hyperfine Matrix 3.1 Introduction / 58 5.3.1 The Anise
3.2 Hyperfine Splitting from Protons / 59 5.3.2 The Case 3.2.1 Single Set of Equivalent Protons / S9 5.3.2.1 I
3.2.2 Multiple Sets of Equivalent Protons / 62 5.3.2.2 '
3.3 Hyperfine Splittings from Other Nuclei with I=! / 68
3.4 Hyperfine Splittings from Nuclei with I > ! / 69
5.3.2.3 '
5.4 Combined g and 3.5 Useful Rules for the Interpretation of EPR Spectra / 74 5.5 Multiple Hyperfii 3.6 Higher-Order Contributions to Hyperfine Splittings / 75 5.6 Systems With I :
3.7 Deviations from the Simple Multinomial Scheme / 77 5.7 Hyperfine Powde 3.8 Other Problems Encountered in EPR Spectra of References / 150
Free Radicals / 77 Notes / 151 3.9 Some Interesting 7T-Type Free Radicals / 78 Further Reading / 15
CONTENTS ix
References / 79
Notes / 79
Further Reading / 80
Problems / 80
4 ZEEMAN ENERGY (g) ANISOTROPY 85
4.1 Introduction / 85
4.2 Systems with High Local Symmetry / 88 36
4.3 Systems with Rhombic Local Symmetry / 90
4.4 Construction of the g Matrix / 92
4.5 Symmetry-Related Sites / 96
4.6 EPR Line Intensities / 97
4.7 Statistically Randomly Oriented Solids / 99
4.8 Spin-Orbit Coupling and Quantum-Mechanical Modeling of g / 105
4.9 Comparative Overview / 110
References / I II
Notes / 112
Further Reading / 114
Problems / 114
5 HYPERFINE (A) ANISOTROPY 118
5.1 Introduction / 118
5.2 Origin of the Anisotropic Part of the Hyperfine Interaction / 120
5.3 Determination and Interpretation of the Hyperfine Matrix / 12258
5.3.1 The Anisotropic Breit-Rabi Case / 122
5.3.2 The Case of Dominant Electron Zeeman Energy / J24
5.3.2.1 General Case / 126
5.3.2.2 The Case of B ~ Bhf / 128
5.3.2.3 The Case of B »»; / 141
5.4 Combined g and Hyperfine Anisotropy / 143
5.5 Multiple Hyperfine Matrices / 144
5.6 Systems With I > ~ / 144
5.7 Hyperfine Powder Lineshapes / 145
References / 150
Notes / 151
Further Reading / 152
X CONTENTS
Problems / 152 References / 221
Notes / 222 6 SYSTEMS WITH MORE THAN ONE UNPAIRED ELECTRON 158 Further Reading / 22:
6.1 Introduction / 158 Problems / 223
6.2 Spin Hamiltonian for Two Interacting Electrons /
6.2.1 Electron-Exchange Interaction / 160
159 8 TRANSITION-GROU
6.2.2 Electron-Electron Dipole Interaction / 162 8.1 Introduction / 2:
6.3 Systems with S = I (Triplet States) / 164 8.2 The Electronic G
6.3.1 Spin Energies and Eigenfunctions / 165 Species / 227
6.3.2 .6.Ms = ±2' Transitions / 172 8.3 The EPR Parame
6.3.3
6.3.4
6.3.5
6.3.6
Randomly Oriented Triplet Systems / 173
Photo-excited Triplet-State Entities / 177
Thermally Accessible Triplet Entities / 182
Ground-State Triplet Entities / 185
6.3.6.1 Carbenes and Nitrenes / 185
6.3.6.2 Dianions of Symmetric Aromatic Hydrocarbons / 187
8.4 Tanabe-Sugano [ Crossings / 240
8.5 Covalency Effect
8.6 A Ferroelectric S
8.7 Some j-Electron :
References / 246
Notes / 248
6.3.6.3 Inorganic Triplet Species / 188 Further Reading / 241
6.4 Interacting Radical Pairs / 189 Problems / 249
6.5 Biradicals / 190 9 THE INTERPRETAT 6.6 Systems with S > I / 195
6.7 High-Spin and High-Field Energy Terms / 196 9.1 Introduction / 2
6.8 The Spin Hamiltonian: A Summing up / 197 9.2 rr-Type Organic.
6.9 Modeling the Spin-Hamiltonian Parameters /
References / 200
Notes / 203
Further Reading / 204
Problems / 205
199 9.2.1
9.2.2
9.2.3
9.2.4
9.2.5
Anions ar and Some
Anions ar
g Factors
Origin of
Sign of th
7 PARAMAGNETIC SPECIES IN THE GAS PHASE 208 9.2.6 Methyl PI
7.1 Introduction / 208
7.2 Monatomic Gas-Phase Species / 209 9.2.7
and Hype
Hyperfine than Prou
7.3 Diatomic Gas-Phase Species / 211 9.2.8 One-Dim 7.4 Triatomic and Polyatomic Gas-Phase Molecules / 217 9.3 a-Type Organic 7.5 Laser Electron Paramagnetic Resonance / 219 9.4 Triplet States ani 7.6 Other Techniques / 219 9.5 Inorganic Radica 7.7 Reaction Kinetics / 220 9.6 Electrically Cone 7.8 Astro-EPR / 220 9.6.1 Metals /
I
xii CONTENTS
9.6.2 Metals Dissolved in Ammonia and 10.
Amine Solutions / 282 10.
9.6.3 Semiconductors / 283 10.5.4 Lir
9.6.4 Graphitic Compounds / 285 Co
9.7 Techniques for Structural Estimates from EPR Data / 285 10.
9.7.1 The Newman Superposition Model / 285 10.
9.7.2 The Pseudo-cube Method / 286 10.5.5 Me
9.7.3 Distances from Parameter D / 286 10,
9.7.4 Eatons' Interspin-Distance Formula / 287 10,
9.7.5 Summary / 287 10.5.6 Ge
References / 287 10.6 Longitudin:
Notes / 291 10.7 Saturation-'
Further Reading / 291 10.8 Time Depe!
Problems / 292 10.8.1 Cc
Appendix 9A Huckel Molecular-Orbital Calculations / 294 10.8.2 Ch
HMO References / 298 Po
HMO Problems / 299 10.9 Dynamic N
10.10 Bio-Oxygei
10 RELAXATION TIMES, L1NEWIDTHS AND SPIN KINETIC 10.11 Summary PHENOMENA 301 References / 348
10.1 Introduction / 30 I Notes / 351
10.2 Spin Relaxation: General Aspects / 302 Further Reading /
10.2.1 Spin Temperature and Boltzmann Distribution / 302 Problems / 353
10.2.2 Spin Dynamics / 303
10.2.3 Mechanisms for T I / 305 11 NONCONTINUOI 10.3
10.4
10.5
Spin Relaxation: Bloch Model / 308
10.3.1 Magnetization in a Static Magnetic Field / 309
10.3.2 Addition of an Oscillating Magnetic Field / 310
10.3.3 Rotating Frame / 311
10.3.4 Steady-State Solutions of Bloch Equations / 312
Linewidths / 316
10.4.1 Homogeneous Broadening / 316
10.4.2 Inhomogeneous Broadening / 316
Dynamic Lineshape Effects / 317
10.5.1 Generalized Bloch Equations / 318
I 1.1 Introduction
11.2 The Idealize
11.3 The Single]
11.4 Fourier-Trar
11.5 Multiple Pul
11.6 Electron Spi
11.7 Advanced T
11.8 Spin Cohere
References / 378
10.5.2
10.5.3
Other Theoretical Models / 322
Examples of Line-Broadening Mechanisms /
10.5.3.1 Electron-Spin Exchange / 323
322
Notes / 380
Further Reading I Problems / 382
10.5.3.2 Electron Transfer / 324
12
r CONTENTS xiii
10.5.3.3 Proton Transfer / 326
10.5.3.4 Fluxional Motion / 326
10.5.4 Linewidth Variation: Dynamic Hyperfine Contributions / 327
10.5.4.1 Single Nucleus / 328
10.5.4.2 Multiple Nuclei / 329
10.5.5 Molecular Tumbling Effects / 333
10.5.5.1 Dipolar Effects / 335
10.5.5.2 Spin-Rotation Interaction / 339
10.5.6 General Example / 340
10.6 Longitudinal Detection / 342
10.7 Saturation-Transfer EPR / 343
10.8 Time Dependence of the EPR Signal Amplitude / 343
10.8.1 Concentration Changes / 343
10.8.2 Chemically Induced Dynamic Electron Polarization / 345
10.9 Dynamic Nuclear Polarization / 347
10.10 Bio-Oxygen / 347
10.11 Summary / 347 301 References / 348
Notes / 351
Further Reading / 352
/ 302 Problems / 353
11 NONCONTINUOUS EXCITATION OF SPINS 357
11.1 Introduction / 357
11.2 The Idealized B, Switch-on / 359o 11.3 The Single B, Pulse / 362
11.4 Fourier-Transform EPR and FID Analysis / 364
11.5 Multiple Pulses / 368
11.6 Electron Spin-Echo Envelope Modulation / 369
11.7 Advanced Techniques / 375
11.8 Spin Coherence and Correlation / 375
References / 378
Notes / 380
Further Reading / 381
Problems / 382
.
xiv CONTENTS
12 DOUBLE-RESONANCE TECHNIQUES 385 13.10.6 R(
13.10.7 Rl12.1 Introduction / 385 13.10.8 S,12.2 A Continuous-Wave ENDOR Experiment / 386 13.10.9 T<12.3 Energy Levels and ENDOR Transitions / 388
12.4 Relaxation Processes in Steady-State ENDOR5 / 392 13.10.10 T<
13.10.11 Tl12.5 CW ENDOR: Single-Crystal Examples / 397 13.10.12 Zi12.5.1 The F Centers in the Alkali Halides / 397
13.11 Liquid Cryst: 12.5.2 Metal-Ion Tetraphenylporphyrins / 401 13.12 "Point" Defe12.6 CW ENDOR in Powders and
Non-Crystalline Solids / 401 13.12.1 Ins
12.7 CW ENDOR in Liquid Solutions / 402 13.
12.8 Pulse Double-Resonance Experiments / 404 13.
12.9 Electron-Electron Double Resonance (ELDOR) / 404 13.12.2 SeT
12.10 Optically Detected Magnetic Resonance / 406 13.13 Polymers /
12.11 Fluorescence-Detected Magnetic Resonance / 407 13.14 Radiation Dc
References / 408 13.15 Spin Labels
Notes / 410 13.16 Spin Traps /
Further Reading / 411 13.17 Trapped Atoi
Problems / 411 APPENDIX A MATHE
13 OTHER TOPICS 414 Al Complex Numbers
13.1 Apologia / 414 A2 Operator Algebra /
13.2 Biological Systems / 414 A2.1 Properties 0
13.3 Clusters / 415 A2.2 Eigenvalues
13.4 Charcoal, Coal, Graphite and Soot / 415 A3 Determinants / 42~
13.5 Colloids / 415 A.4 Vectors: Scalar, Vel
13.6 Electrochemical EPR / 415 A.5 Matrices / 432
13.7 EPR Imaging / 416 A.5.1 Addition ani
13.8 Ferromagnets. Antiferromagnets and A5.2 Multiplicatii Superparamagnets / 416 A5.3 Special Mat
13.9 Glasses / 417 A5.4 Dirac Notati 13.10 Geologic/Mineralogic Systems Matrix Elerr
and Selected Gems / 417 A.5.5 Diagonaliza 13.10.1 Amethyst / 417 A5.6 Matrix Invai 13.10.2 BerylandChrysoberyl / 417 A6 Perturbation Theory 13.10.3 Diamond / 417 A7 Dirac Delta Functioi 13.10.4 Emerald / 418 A8 Group Theory / 45 13.10.5 Opal / 418 References / 450
-------- - -------------
XV
385
414
r CONTENTS
13.10.6 Rock Crystal (a-Quartz) / 418
13.10.7 Ruby / 418
13.10.8 Sapphire / 418
13.10.9 Topaz / 418
13.10.10 Tourmaline / 419
13.10.11 Turquoise / 419
13.10.12 Zircon / 419
13.11 Liquid Crystals / 419
13.12 "Point" Defects / 419
13.12.1 Insulators / 419
13.12.1.1 Alkali Halides / 419
13.12.1.2 Oxides / 419
13.12.2 Semiconductors / 420
13.13 Polymers / 420
13.14 Radiation Dosage and Dating / 420
13.15 Spin Labels / 421
13.16 Spin Traps / 421
13.17 Trapped Atoms and Molecules / 421
APPENDIX A MATHEMATICAL OPERATIONS
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
422
PJ
xvi CONTENTS
Notes / 451 C.2 RH Radicals / 497
Further Reading / 451 C.3 RH2 Radicals / 498
Problems / 451 C.3.l Spin Hamiltoni
C.3.2 EPR Transition APPENDIX B QUANTUM MECHANICS OF ANGULAR
MOMENTUM 455 References /
Notes / 501
501
B.I Introduction / 455 Further Reading / 502 B.2 Angular-Momentum Operators / 457 Problems / 502 B.3 Commutation Relations for General
Angular-Momentum Operators / 458 APPENDIX D PHOTONS
BA '2 ' Eigenvalues of J and J z / 459 0.1 Introduction / 505 B.5 Superposition of States / 464 0.2 The Physical Aspects c B.6 Angular-Momentum Matrices / 464 0.3 Magnetic-Resonance A B.7 Addition of Angular Momenta / 466 References / 510 B.8 Notation for Atomic and Molecular States / 472 Notes / 510 B.9 Angular Momentum and Degeneracy of States / 473
B.IO Time Dependence / 475 APPENDIX E INSTRUMI
B.II Precession / 475 PERFORIIi
B.12 Magnetic Flux Quantization / 477 E.l Instrumental: Backgroi B.13 Summary / 478 E.2 CW EPR Spectrometer References / 479 E.2.l Magnet Systerr Notes / 480 E.2.2 Radiation Sour Further Reading / 480 E.2.3 Microwave Tn: Problems / 481 E.2A Coupling of tlu
Notes for Problem B.12 / 483 E.2.5 Resonator Syst
E.2.6 Field-Modulati
APPENDIX C THE HYDROGEN ATOM AND SELECTED E.2.7 Coupling of tlu
RADICALS RHn 484 E.2.8 Detection Sysn
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
493
E.3 Pulsed EPR Spectrome
E.4 Computer Interfacing ,
E.5 Techniques for Tempel and Control / 531
E.6 Techniques for Pressur
References / 533
Notes / 535
Further Reading / 535
Problems / 536
Perturbation Theory / 495
93
455
r
484
CONTENTS xvii
C.2 RH Radicals / 497
C.3 RH2 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 505
0.1 Introduction / 505
0.2 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
xviii CONTENTS
APPENDIX F EXPERIMENTAL CONSIDERATIONS 537
F.I Techniques for Generation of Paramagnetic Species / 537
F.2 Lineshapes and Intensities / 539
F.2.1 Lineshapes / 539
F.2.2 Signal Intensities and Spin-Concentration Standards / 545
F.3 Sensitivity and Resolution / 548
F.3.1 Optimum Sensitivity / 548
F.3.2 Sample Temperature / 550
F.3.3 Microwave Frequency / 550
F.3A Q Factor of the Resonator / 551
F.3.5 Microwave Power Level and Measurements of B, / 553
F.3.6 Modulation Amplitude / 554
F.3.7 Modulation Frequency / 557 PREFACE FA Measurements / 557
FA.l g Factors and Hyperfine Splittings / 557
FA.2 Relaxation Time / 559
FA.3 Spin-Number Determinations / 561 This book is intended to be an References / 561 resonance (EPR) spectroscop Notes / 564 senior undergraduate or gradi
course or a self-study guide. Further Reading / 565 It would seem fair to dema
Problems / 565 in their first pages some of the understanding of the 'new' m: APPENDIX G EPR-RELATED BOOKS AND in learning mathematical anSELECTED CHAPTERS 567 challenge and enumerate the expect to accrue:
APPENDIX H FUNDAMENTAL CONSTANTS, CONVERSION FACTORS, AND KEY DATA 577 1. Understanding of the fund.
having no previous training APPENDIX I MISCELLANEOUS GUIDELINES 588 netic resonance provide an
ing of this theory. Reader I.l Notation for Symbols / 588 anticipate the acquisition 1.2 Glossary of Symbols / 590 skills, plus powerful exper 1.3 Abbreviations / 600 the interpretation of a wide lA Exponent Nomenclature / 602 2. The reader will be stimulau
solution of problems of int1.5 Journal Reference Style / 602 analytical chemistry; chen ample scope for this, sine Author Index 603 solid, liquid and gaseous S'
3. The reader will have rnaSubject Index 624 of exciting new EPR dev