Contents 

1 Introduction 1 
1.1  Origin of EMR 1 
1.2  Experimental apparatus 3 
1.2.1  Microwave source 4 
1.2.2  Resonant cavity and coupling system 5 
1.2.3  Magnet 10 
1.2.4  Detection system 12 
1.2.5  Data treatment system 12 
1.3  Target of research 13 
1.4  Prospects for future 13 References 14 
2 Theoretical basics 16 
2.1  Phenomenal description of EMR 16 
2.2  Angular momentum and magnetic moment 17 
2.2.1  Orbital motion of electron and its magnetic moment 17 
2.2.2  Eigen motion of electrons and its magnetic moment 20 
2.2.3  Spin angular momentum and magnetic moment of atomic nucleus 23 
2.2.4  Electric quadrupole moment of atomic nucleus 25 
2.3  Unit of magnetic field 26 
2.4  The interaction between external fields and magnetic moment 28 
2.5  Interaction of magnetic moment with electromagnetic field in the external magnetic field 30 
2.6  Interaction of nuclear magnetic moment with electron magnetic moment in the external magnetic field 33 References 34 Further reading 34 
3 g-Tensor theory 35 
3.1  Landé factor 35 
3.2  Matrix presentation of g-tensor 37 
3.2.1  g-Tensor of colour center (cubic symmetry and uniaxial symmetry system) 37 
3.2.2  The g-tensor of nonaxisymmetric (lower than uniaxial symmetry) system 39 
VIII Contents 
3.3  g-Tensor of irregular orientation system 46 
3.3.1  g-Tensor of axisymmetric system 46 
3.3.2  g-Tensor of nonaxisymmetric system 50 References 52 Further reading 52 
4 Isotropic hyperfine structure 53 
4.1  Theoretical exploration of hyperfine interaction 53 
4.1.1  Dipole–dipole interaction 53 
4.1.2  Fermi contact interaction 54 
4.2  Energy operator of isotropic hyperfine interaction 55 
4.2.1  Spin operator and hamiltonians 55 
4.2.2  Zeeman interaction of electrons and nuclei 57 
4.2.3  Spin hamiltonian of isotropic hyperfine interaction 59 
4.3  Spectral isotropic hyperfine structure 60 
4.3.1  System with one magnetic nucleus and one unpaired electron 60 
4.3.2  Multimagnetic nuclei with one unpaired electron system 65 
4.3.3  Hyperfine splitting arising from other magnetic nuclei 71 
4.3.4  Encountered problems in isotropic radical spectra 75 
4.4  Hyperfine structure of organic π-free radical spectrum 76 
4.4.1  Hyperfine coupling constant of organic π-radical 76 
4.4.2  McConnell semiempirical formula 76 
4.4.3  Hückel molecular orbital (HMO) theory 77 
4.4.4  Calculation of probability density distribution of unpaired electron 79 
4.4.5  The Q value of the radical with fully symmetrical structure 85 
4.4.6  Hyperfine coupling constant a value of the even alternant hydrocarbons 86 
4.4.7  Hyperfine coupling constant a value of the even alternant heterocyclic hydrocarbons 89 
4.4.8  Hyperfine coupling constant a value of the odd alternant and nonalternant hydrocarbons 90 
4.5  Mechanism of hyperfine splitting in the spectrum of conjugated systems 91 
4.5.1  “Electronic correlation” effect 91 
4.5.2  The sign of proton hyperfine splitting constant 93 
4.5.3  Negative spin density 96 
4.5.4  About the Q value problem 96 
4.5.5  Hyperfine splitting and hyperconjugation effect of methyl protons 98 
4.6  Hyperfine splitting of other (non-proton) nuclei 101 
4.6.1  Hyperfine splitting of 13C nucleus 101 
Contents 
4.6.2  Hyperfine splitting of 14N nucleus 103 
4.6.3  Hyperfine splitting of 19F nucleus 104 
4.6.4  Hyperfine splittings of 17O and 33S nuclei 105 References 105 Further readings 106 
5 Anisotropic hyperfine structure 107 
5.1  Anisotropic hyperfine interaction 107 
5.2  Matrix interpretation of anisotropic hyperfine interaction 110 
5.3  Example demonstration 116 
5.4  Anisotropic hyperfine coupling tensor and structure of radical 122 
5.4.1  Hyperfine coupling tensor of central atom 122 
5.4.2  Hyperfine coupling tensor of α-hydrogen atom 127 
5.4.3  Hyperfine coupling tensor of β-hydrogen atom 130 
5.4.4  Hyperfine coupling tensor of σ-type organic radicals 132 
5.5  Anisotropy of the combination of g-tensor and A-tensor 133 
5.6  Anisotropy of A tensor in the irregular orientation system 133 References 135 Further readings 136 
6 Fine structure 137 
6.1  Zero-field splitting 138 
6.2  Spin hamiltonian of two-electron interaction 140 
6.2.1  Exchange interaction of electron spin 140 
6.2.2  Dipole interaction of electron–electron 144 
6.3  The triplet molecule (S = 1) system 153 
6.3.1  Energy levels and wave functions of triplet molecules under the action of external magnetic field 153 
6.3.2  Examples of triplet state excited by light 156 
6.3.3  Examples of thermal excitation triplet state 157 
6.3.4  Examples of other excited triplet 159 
6.3.5  Examples of ground triplet state 159 
6.4  Triplet system of irregular orientation 162 
6.5  Biradical 166 References 169 Further reading 170 
7 Relaxation and line shape and linewidth 171 
7.1  Model of spin relaxation 171 
7.1.1  Spin temperature and boltzmann distribution 171 
7.1.2  Spin particle transition dynamics 173 
7.1.3  Mechanism of the effect of relaxation time τ1 on linewidth 175 
Contents 
7.1.4  Magnetization in static magnetic field 177 
7.1.5  Bloch equation in the static magnetic field 178 
7.1.6  Bloch equation in the static magnetic field coupled with the oscillating magnetic field 180 
7.1.7  Stationary solutions of bloch equation 181 
7.2  Shape, width, and intensity of spectral line 182 
7.2.1  Line shape function 182 
7.2.2  Linewidth 186 
7.2.3  Line broadening 188 
7.2.4  Line intensity 188 
7.3  Dynamic effects of line shape 189 
7.3.1  Generalized bloch equation 189 
7.3.2  Chemical exchange broadening mechanism 193 
7.3.3  Mechanism of the spectral lines broadening caused by physical motion 200 
7.4  Saturation transfer of spectra 214 
7.5  Intensity of signal dependent on time 214 
7.5.1  Free radical concentration changes with time 214 
7.5.2  Chemical-induced dynamic electron polarization (CIDEP) 215 References 217 Further readings 218 
8 Quantitative determination 220 
8.1  Main factors of influence for quantitative determination 221 
8.1.1  Factors of instrument 221 
8.1.2  Influence of operating factors 228 
8.2  Selection and preparation of standard samples 235 
8.3  Key parameters and its effect on the intensity of EMR signal 237 
8.4  Achievable accuracy of quantitative determination 239 References 240 
9 Paramagnetic gases and inorganic radicals 242 
9.1  Spectra of paramagnetic gases 242 
9.1.1  Monoatomic paramagnetic gases 242 
9.1.2  Diatomic paramagnetic gas 245 
9.1.3  Gaseous molecules of triatom and polyatom 256 
9.2  Expanding of EMR technique for study on paramagnetic gas 257 
9.2.1  Laser electronic magnetic resonance 257 
9.2.2  Magnetic resonance induced by electron 257 
9.3  Inorganic radicals 258 
9.4  Point defects in solid states 261 
9.5  Spectra of conductor and semiconductor 265 
Contents 
9.6  Structure of a molecule structure of a molecule estimated from the data of EMR 268 References 269 Further readings 272 
10 Ions of transition elements and their complexes 273 
10.1  Electron ground state of transition element ion 273 
10.2  Orbital degeneracy is rescinded in ligand field 275 
10.3  Electric potential of ligand field 278 
10.4  Energy-level splitting of transition metal ion in ligand field 282 
10.4.1  P-state ion in octahedron Field (L = 1) 282 
10.4.2  D-state ion 283 
10.4.3  About F-state ion 286 
10.5  Spin–orbit coupling and spin hamiltonian 288 
10.6  Ground-state ion with orbital nondegeneracy 294 
10.6.1  D-state ions of ground-state orbital nondegenerate 295 
10.6.2  F-state ions of ground-state orbital nondegenerate 298 
10.6.3  S-state ions of the ground-state orbital nondegenerate 305 
10.7  Ground-state ions with orbital degeneracy 310 
10.7.1  D-state ions 310 
10.7.2  F-state ions 316 
10.7.3  Jahn–Teller distortion 320 
10.7.4  The palladium group (4d) and platinum group (5d) ions 321 
10.8  EMR spectra of rare earth Ions 321 
10.8.1  Lanthanide ion 321 
10.8.2  Actinide ions 323 
10.9  EMR spectra of transition metal complexes 324 References 325 Further readings 327 
Appendix 1: Extension and expansion of EMR 328 
Appendix 2: Mathematical preparation 399 
Appendix 3: Angular momentum and stable-state perturbation theory in quantum mechanics 421 
Appendix 4: Fundamental constants and useful conversion actors 442 
Appendix 5: The natural abundance, nuclear spin, nuclear magnetogyric ratio of some magnetic nuclei and their hyperfine coupling parameters 445 
Index 451 

Author’s Preface 

“Electron Magnetic Resonance (EMR)” instructive training course was conducted in the Chemistry Department of Tsinghua University during autumn of 1983. I was invited as a chief lecturer. The draft of my lecture then was an original blank of this book. 
In the fall of 1984, I moved to Department of Chemistry, Zhejiang University, as a professor. I also served for two terms in the EMR training course in 1985 and 1986. My lecture drafts at Tsinghua training course in 1983 were printed by mimeograph and were provided to the students to use as teaching material. 
The JEOL Company of Japan printed 200 copies of this material and provided to its users. 
Till my retirement in 1998, graduate students had been provided EMR course every year. It is the main teaching material. Some modifications and compliments to the material have been received from time to time. 
Ten years after my retirement (2008), this draft as a monograph of “Applied Electron Magnetic Resonance Spectroscopy” has been published formally by Science Press (Beijing), funded by the publishing foundation of the Department of Science & Technology. 
And seven years thereon (2015), after receiving opinion of readers, the book has passed through considerable revision and modification, and has been renamed as “Principle of Electron Magnetic Resonance” (Chinese edition), published by Tsinghua University Press. 
In order to satisfy the requirements of international exchange as well as students studying EMR abroad, the English edition of “Electron Magnetic Resonance Principles” is published now. 
The author expresses heartfelt gratitude to Professor Yu. D. Tsvetkov for writing Foreword of this book. 

Professor of Physical Chemistry Yuanzhi Xu