Electron Paramagnetic Resonance of d Transition Metal Compounds (eBook)

Front Cover 1
Electron Paramagnetic Resonance of d Transition Metal Compounds 4
Copyright Page 5
Table of Contents 6
Preface 18
Chapter 1. 22
1.1 THE ELECTRON PARAMAGNETIC RESONANCE EXPERIMENT 22
1.2 THE BASIC COMPONENTS OF AN E.P.R. SPECTROMETER AND THEIR FUNCTIONS 22
1.3 THE EFFECTS OF INSTRUMENTAL SETTINGS ON E.P.R. SPECTRA 29
1.4 SOME EFFECTS OF SAMPLE CHARACTERISTICS ON E.P.R. SPECTRA 37
1.5 SOME EFFECTS OF MICROWAVE FREQUENCY 40
References 41
Chapter 2. SPIN DOUBLETS IN AN APPLIED MAGNETIC FIELD A QUALITATIVE TREATMENT
2.1 ENERGY LEVELS AND SPECTRA FOR A FREE ELECTRON 42
2.2 SPECTRA OF ISOLATED SINGLE PARAMAGNETS 44
2.3 SPECTRA OF RANDOM COLLECTIONS OF PARAMAGNETS: POWDERS AND GLASSES 53
Chapter 3. THE QUANTITATIVE DESCRIPTION OF THE SPECTRA FROM SPIN DOUBLETS INTERACTING WITH AN APPLIED MAGNETIC FIELD ONLY 66
3.1 THE INTERACTION OF THE ELECTRON WITH A MAGNETIC FIELD 66
3.2 THE ESSENTIALS OF PERTURBATION THEORY 67
3.3 THE APPLICATION OF PERTURBATION THEORY TO SPIN DOUBLETS 71
3.4 THE DETERMINATION OF THE PRINCIPAL g TENSOR ELEMENTS FROM SINGLE CRYSTAL SPECTRA 83
References 101
Chapter 4. THE SPECTRA FROM SPIN DOUBLETS INTERACTING WITH A NUCLEAR SPIN: A QUALITATIVE TREATMENT 103
4.1 INTRODUCTION 103
4.2 ISOTROPIC PARAMAGNETS 103
4.3 ANISOTROPY IN METAL HYPERFINE INTERACTIONS 122
4.4 ANISOTROPY IN LIGAND HYPERFINE INTERACTION 139
References 145
Chapter 5. SPECTRA OF SPIN DOUBLETS INTERACTING WITH A NUCLEAR SPIN: A QUANTITATIVE TREATMENT 146
5.1 INTERACTION WITH A METAL NUCLEAR SPIN 146
5.2 THE DETERMINATION OF THE g AND A TENSORS FROM SINGLE CRYSTAL STUDIES 180
5.3 SPIN DOUBLETS INTERACTING WITH A LIGAND NUCLEAR SPIN ONLY 193
5.4 INTERACTION WITH BOTH A METAL NUCLEAR SPIN AND LIGAND NUCLEAR SPINS 206
References 209
Chapter 6. NUCLEAR QUADRUPOLE AND NUCLEAR ZEEMAN EFFECTS IN SPIN DOUBLETS 210
6.1 QUALITATIVE ASPECTS OF METAL NUCLEAR ZEEMAN AND NUCLEAR QUADRUPOLE INTERACTIONS 210
6.2 QUALITATIVE ASPECTS OF LIGAND NUCLEAR QUADRUPOLE AND NUCLEAR ZEEMAN INTERACTIONS 216
6.3 QUANTITATIVE ASPECTS OF THE METAL NUCLEAR ZEEMAN INTERACTION 216
6.4 QUANTITATIVE ASPECTS OF THE METAL NUCLEAR QUADRUPOLE INTERACTION 218
6.5 OTHER METHODS FOR MEASURING QUADRUPOLE INTERACTIONS 236
References 237
Chapter 7. SPECTRUM SIMULATION FOR SPIN DOUBLETS 239
7.1 PURPOSE OF SIMULATING E.P.R. SPECTRA 239
7.2 THE ESSENTIAL STEPS IN SPECTRUM SIMULATION 244
7.3 LINESHAPES AND LINEWIDTHS 256
7.4 THE CONSTRUCTION AND PRESENTATION OF A SPECTRUM 261
7.5 THE EFFECTS OF g STRAIN AND A STRAIN 294
7.6 ADDITIONAL SIMULATION DEVICES 296
7.7 DETAILED TREATMENTS OF SOME SIMULATION SOFTWARE 298
7.8 SIMULATION SOFTWARE 333
References 334
Chapter 8. METAL IONS IN CUBIC AND AXIAL LIGAND FIELDS 340
8.1 INTRODUCTION 340
8.2 TERM ENERGIES AND WA VEFUNCTIONS IN CUBIC CRYSTAL FIELDS 352
8.3 TERM SPLITTINGS AND WA VEFUNCTIONS IN AXIAL DISTORTIONS FROM CUBIC SYMMETRIES 356
References 358
Chapter 9. THE RELATIONSHIP BETWEEN THE SPIN-HAMILTONIAN PARAMETERS AND THE ELECTRONIC STRUCTURES OF SPIN DOUBLET PARAMAGNETS 359
9.1 SPIN-ORBIT COUPLING 360
9.2 THE COMPARISON OF THE SPIN-HAMILTONIAN AND THE COMPLETE-HAMTLTONIAN FOR ORBITAL SINGLETS 366
9.3 LIGAND CONTRIBUTIONS TO THE METAL SPIN-HAMILTONIAN PARAMETERS 381
9.4 ORBITALLY DEGENERATE GROUND TERMS 393
9.5 THE METAL g AND A TENSORS FOR SELECTED STEREOCHEMISTRIES 399
9.6 THE LIGAND HYPERFINE TENSOR 448
9.7 SOME EMPIRICAL OBSERVATIONS CONCERNING g AND A VALUES 455
References 460
Chapter 10. PARAMAGNETS WITH S > ½ .
10.1 ISOTROPIC PARAMAGNETS 466
10.2 THE SPIN-HAMILTONIAN FOR PARAMAGNETS WITH S > ½.
10.3 PERTURBATION EQUATIONS 470
10.4 SINGLE CRYSTAL SPECTRA 478
10.5 INTERPRETATION OF SPIN-HAMILTONIAN PARAMETERS 480
References 486
Chapter 11. MONOMERIC SPIN TRIPLETS: QUALITATIVE AND QUANTITATIVE ASPECTS. 487
11.1 SPECTRA OF ISOLATED PARAMAGNETS 487
11.2 POWDER OR FROZEN GLASS SPECTRA 490
11.3 THE DETERMINATION OF SPIN-HAMILTONIAN PARAMETERS 491
11.4 THE INTERPRETATION OF SPIN-HAMILTONIAN PARAMETERS 501
11.5 ADDITIONAL TERMS IN THE SPIN-HAMILTONIAN 511
References 512
Chapter 12. MONOMERIC SPIN QUARTET PARAMAGNETS 601
12.1 SPECTRA OF ISOLATED PARAMAGNETS 602
12.2 SPECTRA FROM POWDER SAMPLES 606
12.3 THE DETERMINATION OF SPIN-HAMILTONIAN PARAMETERS FROM EXPERIMENTAL SPECTRA 607
12.4 THE INTERPRETATION OF SPIN-HAMILTONIAN PARAMETERS 616
References 622
Chapter 13. MONOMERIC SPIN QUINTETS: QUALITATIVE AND QUANTITATIVE ASPECTS 737
13.1 SPECTRA OF ISOLATED PARAMAGNETS 737
13.2 POWDER AND FROZEN GLASS SPECTRA 739
13.3 THE DETERMINATION OF SPIN-HAMILTONIAN PARAMETERS 740
13.4 THE INTERPRETATION OF SPIN-HAMILTONIAN PARAMETERS 747
References 753
Chapter 14. MONOMERIC SPIN SEXTET PARAMAGNETS 836
14.1 SPECTRA OF ISOLATED PARAMAGNETS 837
14.2 SPECTRA FROM POWDER SAMPLES 840
14.3 THE DETERMINATION OF SPIN-HAMILTONIAN PARAMETERS FROM EXPERIMENTAL SPECTRA 843
14.4 REFINEMENTS TO THE SPIN-HAMILTONIAN 852
14.5 INTERPRETATION OF THE SPIN-HAMILTONIAN PARAMETERS 855
14.6 METAL HYPERFINE AND QUADRUPOLE INTERACTIONS 858
References 858
Chapter 15. POLYNUCLEAR TRANSITION METAL COMPOUNDS 976
15.1 INTRODUCTION 976
15.2 A MATHEMATICAL MODEL FOR THE SPIN STATES OF POLYNUCLEAR TRANSITION METAL COMPOUNDS 979
15.3 WEAK EXCHANGE IN POLYNUCLEAR COMPOUNDS 992
15.4 PATHWAYS FOR EXCHANGE 995
15.5 THE SPIN-HAMILTONIAN PARAMETERS . 996
g, D, AND J. . 996
15.6 SOME SIMULATED POWDER SPECTRA FOR PARAMAGNETS WITH S > 5/2.
15.7 SPIN FRUSTRATION 1003
References 1004
Chapter 16. SIMULATION OF SPECTRA FOR PARAMAGNETS WITH MULTIPLE UNPAIRED ELECTRONS 1022
16.1 INTRODUCTION 1022
16.2 THE RESONANCE FIELD 1023
16.3 DETERMINING RESONANCE CONDITIONS IN THE GENERAL CASE 1028
16.4 OTHER METHODS OF PRESENTATION 1040
16.5 FREQUENCY INDEPENDENT RESONANCE (FIR) DIAGRAMS 1047
16.6 HYPERFINE SPLITTING INTERACTIONS 1051
16.7 OTHER FACTORS IN THE SIMULATION OF S > ½ SPECTRA.
16.8 MODELLING VARIABLE TEMPERATURE SPECTRA 1056
16.9 SIMULATION ARTEFACTS 1066
16.10 HOW TO APPROACH A SIMULATION 1081
16.11 COMPUTER HARDWARE CONSIDERATIONS 1099
16.12 COMPUTER SOFTWARE CONSIDERATIONS 1099
References 1163
Chapter 17. EXTENDED ELECTRON EXCHANGE IN CRYSTALS 1168
17.1 INTRODUCTION 1168
17.2 WEAK EXTENDED EXCHANGE IN ONE AND TWO DIMENSIONS 1171
17.3 EXCHANGE NARROWING 1181
17.4 THE EFFECT OF EXCHANGE AND UNRESOLVED HYPERFINE STRUCTURE 1183
References 1185
Chapter 18. RELAXATION, LINEWIDTHS, DETERMINATION OF CONCENTRATIONS, AND MICROWAVE POWER SATURATION 1186
18.1 RELAXATION 1186
18.2 QUALITATIVE ASPECTS OF LINE BROADENING 1188
18.3 LINESHAPE FUNCTIONS AND FREQUENCY TO FIELD CONVERSION 1190
18.4 THE RELATIONSHIP BETWEEN THE INTENSITY OF AN EXPERIMENTAL SPECTRUM AND THE CONCENTRATION OF THE PARAMAGNET 1197
18.5 LINEWIDTHS IN FLUID SOLUTIONS AND IN SOLIDS 1199
18.6 SPIN-LATTICE RELAXATION PROCESSES 1203
18.7 MICROWAVE POWER SATURATION 1205
18.8 THE ESTIMATION OF RELAXATION TIMES FROM PROGRESSIVE SATURATION STUDIES 1208
References 1209
Appendix 1. Some physical properties of selected solvents 1211
Appendix 2. Physical constants and conversion factors 1212
Appendix 3. Spin-Hamiltonians, Operator Equivalents and Some Relationships Between Angular Momentum Operators 1213
A3.1 Spin-Hamiltonians 1213
A3.2 Operator equivalents 1214
A3.3 Some relationships between angular momentum operators 1215
Appendix 4. Direction cosines and transformation of axes 1217
A4.1 Relationship between direction cosines 1217
A4.2 Transformations involving two sets of orthogonal Cartesian axes 1218
A4.3 Transformations using Eulerian Angles 1220
Appendix 5. Some useful mathematical relationships 1222
A5.1 Complex numbers 1222
A5.2 Trigonometric relationships 1222
A5.3 Determinants 1223
A5.4 Matrices 1225
A5.5 Some standard integrals 1227
A5.6 Vectors 1228
Appendix 6. 1230
A6.1 Some properties of nuclei with non-zero nuclear spin 1230
A6.2 Hyperfine interaction parameters 1235
Appendix 7. Polar coordinates, Cartesian coordinates, wavefunctions, orbitals 1237
A7.1 Polar coordinates, Cartesian coordinates 1237
A7.2 Wavefunctions and orbitals 1238
Appendix 8. Determinantal wavefunctions 1241
Appendix 9. Inter-electron repulsion calculations 1243
Appendix 10. The effect of operators such asR^/3x. 1248
Appendix 11. Dipole-dipole interactions and the point-dipole approximations 1249
A11.1 The classical description of dipole-dipole interactions 1249
Al 1.2 The quantum mechanical description of dipole-dipole interactions 1249
Al 1.3 Some calculations involving dipole-dipole interactions 1250
Appendix 12. Expanded FIR diagrams for S = 1, 3/2, 2,5/2, 3,7/2, 4,9/2. 1257
Appendix 13. Mean values of functions and the method of moments 1326
A 13.1 Mean values of functions 1326
A13.2 The method of moments 1326
SUBJECT AND KEYWORD INDEX 1328
CHEMICAL INDEX 1342