Download - ELECTRON PARAMAGNETIC RESONANCE - GBV · 2013-01-19 · r. CONTENTS . PREFACE xix ACKNOWLEDGMENTS xxiii 1 BASIC PRINCIPLES OF PARAMAGNETIC RESONANCE 1 1.1 Introduction / I 1.2 Historical

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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~

~ffiWILEY ~ ~: 2 007 ~ _; I> • r

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


Problems / 114

5 HYPERFINE (A) ANISOTROPY 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


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


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


7.2 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


/ 302 Problems / 353

11 NONCONTINUOUS EXCITATION OF SPINS 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


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


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


Problems / 502

APPENDIX D PHOTONS 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


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

Download - ELECTRON PARAMAGNETIC RESONANCE - GBV · 2013-01-19 · r. CONTENTS . PREFACE xix ACKNOWLEDGMENTS xxiii 1 BASIC PRINCIPLES OF PARAMAGNETIC RESONANCE 1 1.1 Introduction / I 1.2 Historical

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