Electron Spin Resonance: Elementary Theory and Practical Applications

509 Pages·1986·23.351 MB·English

by  John E. Wertz, James R. Bolton (auth.)

TABLE A Fundamental constantst
1. Speed of light
c = (2.9979250 ± 0.0000010) X 10'0 cm S-1
2. Electronic Charge
e = (4.803250 ± 0.000021) X 10-10 esu
3. Electron rest mass
m = (9.109558 ± 0.000054) X 10-28 g
4. Proton rest mass
mp " (1.672614 ± 0.000011) X 10-24 g
5. Planck's constant
h = (6.626196 ± 0.000050) X 10-27 erg s
ft = h/21r = (1.0545919 ± 0.0000080) X 10-27 erg s
6. Bohr magneton
eft
{3 = - = (9.274096 ± 0.000065) X 10-21 erg G-l
2mc
7. Electron free-spin g-factor
g. = 2.0023192778 ± 0.0000000062
8. Electrgo:n magnetic moment
"'. = = (9.284851 ± 0.000065) X 10-21 erg G-l
9. Nuclear magneton
eft
{3N = -- = (5.050951 ± 0.000050) X 10-24 erg G-l
2m c
p
10. "'p = (1.4106203 ± 0.0000099) X 10-23 erg G-l
11. Magnetogyric ratio of proton in spherical water samples
"Yp(corrected for diamagnetism of host compound) = (2.6751965 ± 0.0000082)
X 104 rad S-1 G-l
12. gp(corrected for diamagnetism) = 2",p = 5.585564 ± 0.000017
{3N
13. Magnetogyric ratio of a free electron
"Ye = S1",f.1t = - (1.7608425 ± 0.0000010) X 107 rad 8-. 1 G -1
14. Boltzmann's constant
k = 1.380622 ± 0.000059 X 10-16 erg K-l
t Taken from B. N. Taylor, W. H. Parker and D. N. Langenberg, Rev. Mod. Phys., 41,
375 (1969).
TABLE B Useful conversion factors
L Magnetic field, H (gauss), to el(e!c,t)ro n resonant frequ~ncy, V,l (MHz) and Vel (em-I)
H
(g'~H) (~)
Vel = = 2.80247
(~)
H = 0.356828 Vel
V,l (MHz) = e X 1O-6vel (em-I) = 2.99793 X 104V'1
Vel (em-I) = 0.333564 X 1O-4V,1 (MHz)
2. Magnetic field, H (gauss), to proton resonant frequency, Vp (MHz)
Vp = 4.257708 X 1O-3H
H = 234.868vp
3. Ratio of proton to electron resonant frequency
(~)
vplvel = 1.51927 X 10-3
4. Calculation of g factors
= hVel = 0.714484 Vel (MHz)
g fjH H (G)
= 2-p.p -V,l = 3.042065 X 10-3-V,l
fj ~ ~
5. Hyperfine couplings and hyperfine splittings
(!,)
A (MHz) = 2.80247 a (gauss)
(~)
a (G) = 0.356828 A (MHz)
Ale (em-I) = 0.3g3:3 564 X 1O-4A (MHz)
Ao (MHz) = 8; p.; If.(0)12 = 23.4779 p.; If.(O)12
ELECTRON SPIN RESONANCE
Elementary Theory and
Practical Applications
John E. Wertz
Professor of Chemistry
University of Minnesota
James R. Bolton
Professor of Chemistry
University of Western Ontario
Chapman and Hall
New York • London
First edition published 1972 by
McGraw-Hill Book Company
This reprint published 1986 by
Chapman and Hall
29 West 35th St. New York, N.Y. 10001
Published in Great Britain by
Chapman and Hall Ltd
II New Fetter Lane, London EC4P 4EE
© 1986 Chapman and Hall
Softcover reprint of the hardcover 1st edition 1986
This title is available in both clothbound and paperback editions. The paperback edition is sold
subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or
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All rights reserved. No part ofthis book may be reprinted, or reproduced or utilized in any
form or by any electronic, mechanical or other means, now known or hereafter invented,
inclUding photocopying and recording, or in any information storage and retrieval system,
without permission in writing from the Publisher.
Congress Cataloging-in-Publication Data
Wertz, John E., 1916-
Electron spin resonance.
Reprint. Originally published: New York: McGraw-HilI,
1972.
Bibliography: p.
Includes index.
I. Electron paramagnetic resonance. I. Bolton,
James R., 1937- II. Title.
[QC762.W47 1986] 538'.36 85-29080
ISBN-I3: 978-94-010-8307-2 e-ISBN-I3: 978-94-009-4075-8
DOl: 10.1007/978-94-009-4075-8
Contents
Preface xiii
Chapter 1 Basic Principles of Electron Spin Resonance
1-1 Introduction 1
1-2 Energy of Magnetic Dipoles in a Magnetic Field 7
1-3 Quantization of Angular Momentum 9
1-4 Relation between Magnetic Moments and Angular Momenta 11
1-5 Interaction of Magnetic Dipoles with Electromagnetic Radiation 12
1-6 Characteristics of the g Factor 17
Problems 20
Chapter 2 Basic Instrumentation of Electron Spin Resonance 21
2-1 A Simple ESR Spectrometer 21
2-2 Choice of Experimental Conditions 22
2-3 Typical Spectrometer Arrangement 23
2-3a The Cavity System 23
2-3b The Source 28
2-3c The Magnet System 29
2-3d The Modulation and Detection Systems 30
2-4 Line Shapes and Intensities 32
References 36
Problems 36
Chapter 3 Nuclear Hyperfine Interaction 38
3-1 Introduction 38
3-2 Origins of the Hyperfine Interaction 40
3-3 Energy Levels of a System with One Unpaired Electron and One
Nucleus with 1= t 43
3-4 The Energy Levels of a System with S = t and I = 1 46
3-5 Summary 47
Problems 48
Chapter 4 Analysis of Electron Spin Resonance Spectra of Systems in the
Liquid Phase 49
4-1 Introduction 49
4-2 Energy Levels of Radicals Containing a Single Set of Equivalent
Protons 50
4-3 ESR Spectra of Radicals Containing a Single Set of Equivalent
Protons 52
4-4 ESR Spectra of Radicals Containing Multiple Sets of Equivalent
Protons 57
4-5 Hyperfine Splittings from Other Nuclei with I = t 67
4-6 Hyperfine Splittings from Nuclei with I > t 68
v
vi CONTENTS
4-7 Useful Rules for the Interpretation of Spectra 73
4-8 Other Problems Encountered in the ESR Spectra of Free Radicals 76
4-9 Second-order Splittings 77
Problems 79
Chapter 5 Interpretation of Hyperfine Splittings in 7T-type Organic Radicals· 87
5-1 Introduction 87
5-2 Molecular Orbital Energy Calculations 88
5-3 Unpaired Electron Distributions 95
5-4 The Benzene Anion and Its Derivatives 99
5-5 The Anions and Cations of the Polyacenes 105
5-6 Other Organic Radicals 106
5-7 Summary 107
References-HMO Method 108
Problems 109
Chapter 6 Mechanism of Hyperfine Splittings in Conjugated Systems 112
6-1 Origin of Proton Hyperfine Splittings 112
6-2 Sign of the Hyperfine Splitting Constant 114
6-3 Extension of the Molecular Orbital Theory to Include Electron
Correlation 118
6-4 Alkyl Radicals-A Study of Q Values 121
6-5 The Effect of Excess Charge on the Parameter Q 122
6-6 Methyl-proton Hyperfine Splittings-Hyperconjugation 124
6-7 Hyperfine Splitting by Nuclei Other than Protons 125
Bibliography 128
Problems 128
Chapter 7 Anisotropic Interactions in Oriented Systems with S = t 131
7 -1 Introduction 13 1
7 -2 A Simple Example of Anisotropy of g 13 1
7-3 Systems with Orthorhombic or Lower Symmetry 134
7-4 Experimental Determination of the g Tensor in Oriented Solids 135
7-5 Anisotropy of the Hyperfine Coupling 138
7-6 Origin of the Anisotropic Hyperfine Interaction 140
7-7 Determination of the Elements of the Hyperfine Tensor 144
7-8 Corrections to Hyperfine Tensor Elements 150
7-9 Line Shapes in Nonoriented Systems 154
7-9a Line Shapes for Systems with Axial Symmetry 155
7-9b Hyperfine Line Shapes for an Isotropic g Factor, S = t and
One Nucleus with 1= t 159
Problems 161
Chapter 8 Interpretation of the ESR Spectra of Systems in the Solid State 164
8-1 Generation of Free Radicals in Solids 164
8-2 7T-type Organic Radicals 165
CONTENTS vii
8-2a Identification 165
8-2b Aliphatic Radicals 167
8-2c Radicals from Unsaturated Organic Compounds 173
8-3 a-type Organic Radicals 174
8-4 Inorganic Radicals 175
8-4a Identification of Radical Species 175
8-4b Structural Information 178
8-5 Point Defects in Solids 179
8-5a Generation of Point Defects 179
8-5b Substitutional or Interstitial Impurities 181
8-5c Trapped-electron Centers 184
8-5d Trapped-hole Centers 185
References 186
Problems 187
Chapter 9 Time-dependent Phenomena 192
9-1 Introduction 192
9-2 Spin-lattice Relaxation Time 193
9-3 Other Sources of Line Broadening 196
9-3a Inhomogeneous Broadening 196
9-3b Homogeneous Broadening 196
9-4 Mechanisms Contributing to Line Broadening 197
9-4a Electron Spin-Electron Spin Dipolar Interactions 197
9-4b Electron Spin-Nuclear Spin Interactions 197
9-5 Chemical Line-broadening Mechanisms 198
9-5a General Model 198
9-5b Electron-spin Exchange 201
9-5c Electron Transfer 203
9-5d Proton Exchange 204
9-6 Variation of Linewidths within an ESR Spectrum 204
9-6a Time-dependent Hyperfine Splitting for a Single Nucleus 205
9-6b Time-dependent Hyperfine Splittings for Systems with
Several Nuclei 207
9-7 Spectral Effects of Slow Molecular Tumbling Rates 214
9-8' Spectral Effects of Rapid Molecular Tumbling Rates-Spin-rota
tional Interaction 220
9-9 Summary 221
Problems 221
Chapter 10 Energy-level Splitting in Zero Magnetic Field; The Triplet State 223
10-1 Introduction 223
10-2 The Spin Hamiltonian for S = 1 224
10-3 State Energies for a System with S = I 227
10-4 The Spin Eigenfunctions for a System with S = 1 231
10-5 Electron Spin Resonance of Triplet-state Molecules 232
10-6 Line Shapes for Randomly Oriented Systems in the Triplet State 238
10-7 The "IlMs = 2" Transitions 242
viii CONTENTS
10-8 Triplet Ground States 244
10-9 Carbenes and Nitrenes 246
10-10 Thermally Accessible Triplet States 249
10-11 Biradicals; Exchange Interaction 250
10-12 Systems with S > 1 255
Bibliography 256
Problems 256
Chapter 11 Transition-metal Ions. I. 258
11-1 States of Gaseous Transition-metal Ions 259
11-2 Removal of Orbital Degeneracy in Crystalline Electric Fields 261
11-3 The Crystal Field Potential 263
11-4 The Crystal Field Operators 267
11-5 Crystal Field Splittings of States for P-, D- and F-state Ions 269
11-6 Spin-orbit Coupling and the Spin Hamiltonian 278
11-7 D-and F-state Ions with Orbitally Nondegenerate Ground States 283
11-7a D-state Ions 287
3d1(ttdl + ttgl) in 3d1(cubal + ttgl)
3d7(1s)(oct + ttgl); 3d9(oct + ttgl)
11-7b F -state Ions 289
3d8(oct)
3d2(ttdl)
3d8(oct + ttgl)
3d2(ttdl + ttgl)
3d3(oct)
3 d1(hs)(t td!)
3d3(oct + ttgl)
11-8 S-state Ions 303
3d5(hs)(oct)
3d5(hs)(oct + ttgl)
Problems 310
Chapter 12 Transition-metal Ions. II. Electron Resonance in the Gas
Phase 313
12-1 Ions in Orbitally Degenerate Ground States 313
12-1 a D-state Ions 314
3d1(oct)
3d1(oct + ttgl), ~ » 8 » A
3d1(oct + ttg!), ~ » A = 8
3d1(oct + trgl)
3 d5(ls)( oct + ttgl)
3d9(ttdl + ttgl)
3d6(hs)(oct)
12-1 b F -state Ions 328
3d2(oct)
3d2(oct + trgl)
3d7(hs)(oct)
12-1c lahn-Teller Splitting 334
CONTENTS ix
3d9(oct)
3d7(1s)(oct)
12-2 Elements of the 4d and 5d Groups (Palladium and Platinum
Groups) 335
12-3 The Rare-earth Ions 336
12-4 The Actinide Ions 339
12-5 Deficiencies of the Point-charge Crystal Field Model; Ligand-
Field Theory 340
12-6 Electron Resonance of Gaseous Free Radicals 345
12-7 The Practical Interpretation of ESR Spectra of Ions in the Solid
State 349
Bibliography 351
Problems 351
Chapter 13. Double-resonance Techniques 353
13-1 An ENDOR Experiment 354
13-2 Energy Levels and ENDOR Transitions 356
13-3 Relaxation Processes in Steady-state ENDOR 360
13-4 An ENDOR Example: The F Center in the Alkali Halides 366
13-5 ENDOR in Liquid Solutions 370
13-6 ENDOR in Powders and Nonoriented Solids 373
13-7 Electron-electron Double Resonance 374
Problems 376
Chapter 14. Biological Applications of Electron Spin Resonance 378
14-1 Introduction 378
14-2 Substrate Free Radicals 379
14-3 Flavins and Metal-free Flavoproteins 381
14-4 Photosynthesis 383
14-5 Heme Proteins 386
14-6 Iron-sulfur Proteins 388
14-7 Spin Labels 390
Appendix A. Mathematical Operations 391
A-I Complex Numbers 391
A-2 Operator Algebra 392
A-2a Properties of Operators 392
A-2b Eigenvalues and Eigenfunctions 394
A-3 Determinants 396
A-4 Vectors: Scalar, Vector, and Outer Products 398
A-5 Matrices 400
A-5a Addition and Subtraction of Matrices 400
A-5b Multiplication of Matrices 401
A-5c Special Matrices and Matrix Properties 403
A-5d Dirac Notation for Wave Functions and Matrix Elements 404
A-5e Diagonalization of Matrices 405
A-6 Tensors 408
A-7 Perturbation Theory 414
CONTENTS
A-8 Euler Angles 416
Bibliography 417
Problems 417
Appendix B. Quantum Mechanics of Angular Momentum 419
B-1 Introduction 419
B-2 Angular-momentum Operators 420
B-3 The Commutation Relations for the Angular-momentum
Operators 422
B-4 The Eigenvalues of jz and jz 423
B-5 The Matrix Elements of j +, j _, j x and j y 426
B-6 Angular-momentum Matrices 427
B-7 Addition of Angular Momenta 428
B-8 Summary 433
Bibliography 434
Problems 434
Appendix C. Calculation of the Hyperfine Interaction in the Hydrogen Atom
and in an 'RHz Radical 436
C-l The Hamiltonian for the Hydrogen Atom 436
C-2 The Spin Eigenfunctions and the Energy Matrix for the Hydrogen
Atom 437
C-3 Exact Solution of the Determinant of the Energy Matrix
(Secular Determinant) 438
C-4 Selection Rules for High-field Magnetic-dipole Transitions in the
Hydrogen Atom 439
C-5 The Transition Frequencies in Constant Magnetic Field with a
Varying Microwave Frequency 441
C-6 The Resonant Magnetic Fields at Constant Microwave
Frequency 442
C-7 Calculation of the Energy Levels of the Hydrogen Atom by Pertur-
bation Theory 443
C-8 Wave Functions and Allowed Transitions for the Hydrogen Atom
at Low Magnetic Fields 445
C-9 The Energy Levels of an . RHz Radical 446
Problems 449
Appendix D. Experimental Methods; Spectrometer Performance 450
D-l Sensitivity 450
D-2 Factors Affecting Sensitivity and Resolution 452
D-2a Modulation Amplitude 452
D-2b Modulation Frequency 454
D-2c Microwave Power Level 456
D-2d The Concentration of Paramagnetic Centers 458
D-2e Temperature 458