General Appendices

Tables G1–G5 and G7 below were adapted from the Appendix in [Anders Lund,Masaru Shiotani and Shigetaka Shimada: Principles and Applications of ESRSpectroscopy (Springer, 2011)] with permission from Springer.

Table G1 Fundamental constantsa

Quantity Symbol Value SI unit

Speed of light c 2.997 924 58 108 m s�1

Elementary charge e 1.602 176 10�19 CFaraday constant FDNAe 9.648 456 104 C mol�1

Boltzmann constant k 1.380 65 10�23 J K�1

Gas constant RDNAk 8.314 47 J K�1 mol�1

Planck constant h 6.626 068 10�34 J s„D h/2 1.054 571 10�34 J s

Avogadro constant NA 6.022 14 10�23 mol�1

Atomic mass unit u 1.660 54 10�27 kgMass

Electron me 9.109 38 10�31 kgProton mp 1.672 62 10�27 kgNeutron mn 1.674 93 10�27 kg

Vacuum permittivity "0D 1/c2�0 8.854 188 10�12 F m�1

aCODATA recommended values of the fundamental physical constants2006, National Institute of Standards and Technology, Gaithersburg, Mary-land 20899–8420, USA; http://physics.nist.gov/cuu/Constants/

A. Lund and M. Shiotani (eds.), EPR of Free Radicals in Solids I, Progressin Theoretical Chemistry and Physics 24, DOI 10.1007/978-94-007-4893-4,© Springer ScienceCBusiness Media Dordrecht 2003,2013

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394 General Appendices

Table G2 Magnetic constants in SI unitsa

Quantity Symbol Numerical value Unit

Magnetic constant �0D 4 10�7 12.566 370 10�7 N A�2

Bohr magneton �B (ˇe) 927.400 915 (23) 10�26 J T�1

Nuclear magneton �N (ˇN) 5.050 783 24(13) 10�27 J T�1

Electron g-factor ge 2.002 319 304 361 7(15)Electron gyromagnetic ratio e 1.760 859 770 (44) 1011 s�1 T�1

�B/h �B/h 13.996 246 4(35) 109 Hz T�1

�B/hc �B/hc 46.686 451 5(12) m�1 T�1

�N/h �N/h 7.622 593 84(19) MHz T�1

aCODATA recommended values of the fundamental physical constants 2006, National Instituteof Standards and Technology, Gaithersburg, Maryland 20899–8420, USA; http://physics.nist.gov/cuu/Constants/

Table G3 Conversion factors for EPR (ESR) coupling constantsa, b

Unit MHz mT cm�1

MHz 1 0.071 447 66/g 0.333 564 095 10�4

mT 13.996 25�g 1 4.668 645 10�4 �gcm�1 2.997 924 58 104 0.214 194 9 104/g 1

A coupling given in a unit of the 1st column is calculated in other units bymultiplication with the factor in the corresponding row.Calculations of g from measured values of microwave frequency �e (GHz) andresonance field B (T), of resonance field, and of nuclear frequency �N (MHz):

g D h�B� �eBD 0:071447656

�e .GH z/B.T /

, B.T / D h�B� �egD 0:071447656

�e .GH z/g

�N .MHz/ D �Nh� gNB D 7:62259384 � gNB.T /

aThe factors were obtained from CODATA recommended values of the constants inTable G1; http://physics.nist.gov/cuu/Constants/bMohr PJ, Taylor BN, Newell DB (2008) Rev Mod Phys 80:633; J Phys Chem Ref.Data 37:1187

Table G4 Other usefulconversion factors 1 eV 1.602 18 10�23 J

96.485 kJ mol�1

8065.5 cm�1

1 cal 4.184 J1 atm 101.325 kPa1 cm�1 1.986 4 10�23 J1 D (Debye) 3.335 64 10�30 C m1 A 10�10 m1 T 10�4 G (or gauss)1 L atm D 101.325 J� /ıC D T/K � 273.15

General Appendices 395

Table G5 Symbols, variables and units in EPR (ESR)

Symbol Name or description Unit and/or value

A, a Hyperfine coupling (splitting) constant MHz, mT (milli-Tesla)D Zero-field splitting, Fine structure cm�1, MHz, mTB (H) External magnetic field T (Tesla)e Electron charge 1.602 177 10�19 A.sg g-factor DimensionlessG Radiation yield �mol�J�1

h Planck constant 6.626 068 10�34 J.sI Nuclear spin angular momentum J.sI Nuclear spin quantum number DimensionlessJ Heisenberg exchange coupling cm�1, MHz, mTk Boltzmann constant 1.380658 10�23 J.K�1

L Orbital angular momentum J.sl Orbital quantum number Dimensionlessme Electron mass 0.910939 10�30 kgmI Nuclear magnetic quantum number DimensionlessmS Electron magnetic quantum number DimensionlessP Microwave power J.s�1

Q Nuclear quadrupole coupling cm�1, MHz, mTS Electron spin angular momentum J.sS, s Electron spin quantum number Dimensionlessv Speed m.s�1

œ Spin-orbit coupling constant cm�1

� Magnetic moment A.s�B, (ˇe) Bohr magneton 9.274015 10�24 J.T�1

�N, (ˇN) Nuclear magneton 5.050787 10�27 J.T�1

� Frequency Hz

Table G6 Abbreviations

Abbreviation Name or description

Magnetic resonance:ADMR Absorption detected magnetic resonanceALC-MuSR Avoided level crossing MuSRBP Breit-PauliCPMG Carr-Purcell-Meiboom-GillCW, cw Continuous waveDEER Double electron electron resonanceDQC-ESR (EPR) Double quantum coherence ESR (EPR)ED-EPR (EchoEPR) Echo-detected EPRELDOR Electron electron double resonanceEMR Electron magnetic resonanceENDOR Electron nuclear double resonanceENTOR Electron nuclear triple resonanceEPR Electron paramagnetic resonance

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396 General Appendices

Table G6 (continued)

Abbreviation Name or description

EPR-COSY EPR correlation spectroscopyEPR-SECSY EPR spin echo correlated spectroscopyESE Electron spin echoESEEM Electron spin echo envelope modulationESR Electron spin resonanceESTN Electron spin transient nutationFID Free induction decayFT Fourier transformHF, hf HyperfineHF-EPR (ESR) High frequency EPR (ESR)HFC, hfc (Hfi or Hfs) Hyperfine coupling (interaction or structure)HYSCORE Hyperfine sublevel correlationIHC Isotropic hyperfine couplingLF-MuSRx Longitudinal (magnetic) field muon spin-relaxationMIDP Microwave induced delayed phosphorescenceMRFM Magnetic resonance force microscopyMW, mw Micro waveMuSR (�SR) Muon spin rotationNMR Nuclear magnetic resonanceNMRD Nuclear magnetic relaxation dispersionNQC, Nqc Nuclear quadrupole couplingOD(N)MR Optically detected (nuclear) magnetic resonancePELDOR Pulsed electron electron double resonanceQC-ENDOR (NMR) Quantum computing ENDOR (NMR)QTM Quantum tunneling of magnetizationRF, rf Radio-frequencySHF, shf Super-hyperfineSMM Single-molecule magnetSO(MF) Spin-orbit (meanfield)SOO Spin-other-orbitSS/EPR dosimeters Solid state EPR dosimetersTF Transverse-fieldTPPI Time proportional phase increment

Quantum chemistry:AMFI Atomic mean fieldB3LYP Becke, three-parameter, Lee-Yang-ParrCAS Complete active spaceCC Coupled-clusterCI Configuration interactionCNDO Complete neglect of differential overlapCP Car–ParrinelloCP(CM) Conducter-like polarized (continuum method)CP(KS) Coupled-perturbed (Kohn-Sham)DFT Density functional theoryDIM Diatomics-in-moleculesDKH Douglas-Kroll-Hess

(continued)

General Appendices 397

Table G6 (continued)

Abbreviation Name or description

DZ(P) Double-zeta (plus polarization)GGA Generalized gradient approximationsGIAO Gauge including atomic orbitalsHDV Heisenberg-Dirac-Van VleckHF Hartree-FockHOMO Highest occupied molecular orbitalIEF Integral equation formalismIGLO Individual gauges for localized orbitalsINDO Intermediate neglect of differential overlapJ-T Jahn-TellerL(S)DA Local (spin) density approximationLUMO Lowest unoccupied molecular orbitalMCSCF Multi-configuration SCFMD Molecular dynamicsMM Molecular mechanicsMO Molecular orbitalMP Møller-PlessetMRCI Multi-reference configuration-interactionMRMP2 Second-order multi-reference Møller–PlessetNBMO Non-bonding molecular orbitalNDDO Neglect of diatomic differential overlapPCM Polarizable continuum modelsQM/MM Quantum-mechanics/molecular-mechanics(Q)RO (Quasi) restricted orbitalROHF Restricted open-shell Hartree-FockSAC-CI Symmetry-adapted cluster configuration interactionSCF Self-consistent fieldSCIPCM Self-consistent isodensity PCMSCRF Self-consistent reaction fieldSD(T) Single, double (and perturbative triple)SECI (CIS) Single excitation configuration interactionSO-CI Spin–orbit configuration interactionSOMO Singly occupied molecular orbitalSOS Sum-over-statesTZ Triple-zetaUDFT Uncoupled density functional theoryUHF Unrestricted Hartree-FockZFS Zero-field splittingZORA Zero order regular approximationZPVE Zero point vibrational energy

Chemistry and biochemistry:2-MTHF 2-MethyltetrahydrofuranAlPO4 Aluminum orthophosphateArO Phenoxidea-Si:H Hydrogenated amorphous silicon

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398 General Appendices

Table G6 (continued)

Abbreviation Name or description

BQ 1,4-BenzoquinoneBSS Benzylsuccinate synthaseCU Coupling unitCuHis Copper(II)-histidineCyt CytochromeDCMU 3-(3,4-Dichlorophenyl)-1,1-dimethylureaDMBQ 2,3-Dimethyl-1,4-benzoquinoneDMC 2,3-Dimethylenecyclohexane-1,4-diylDME DimethyletherDMEQ 2,3-Dimethyl-5-ethyl-1,4-benzoquinoneDMNQ 2,3-Dimethyl-1,4-naphthoquinoneDPNO DiphenylnitroxideDQ Duroquinone: 2,3,5,6-tetramethyl-1,4-benzoquinoneDTBN di-tert-Butyl nitroxideEt3N TriethylamineFA Ferredoxin AFB Ferredoxin BFreon-11 Fluorotrichloromethane (CCl3F)Freon-113 1,1,2-Trifluoro-1,2,2-trichloroethane (CCl2FCClF2)Freon-114B2 1,2-Dibromotetrafluoroethane (CF2BrCF2Br)GO Galactose oxidaseGT Gauche-transHAS Human serum albuminHCA II Human carbonic anhydrase IIIN IminonitroxideMES 2-(n-Morphorino)ethansulfonic acidMTBE Methyl tert-butyl etherNADP Nicotinamide adenine nucleotide phosphateNAG n-Acetyl-glycine radicalNN Nitronyl nitroxideNO tert.-Butyl-nitroxideNQ 1,4-NaphthoquinoneOEC Oxygen-evolving complexP680 Pigment 680 nmP700 Pigment 700 nmPE PolyethylenePFL Pyruvate formate lyasePQ PlastoquinonePr3N TripropylaminePS Photosynthetic reaction centerQ QuinoneQK PhylloquinoneQOX Quinol oxidaseRg Rare gasesRNR Ribonucleotide reductaseRO• Alkoxy radicals

(continued)

General Appendices 399

Table G6 (continued)

Abbreviation Name or description

RO2• Organic peroxyl radicalRps RhodpseudomonasSH2 Bimoleclar homolytic substitutionTempone 4-Oxo-2,2,6,6-tetramethylpiperidine-N-oxylTME TetramethyleneethaneTMM TrimethylenemethaneTMQ 2,3,5-Trimethyl-1,4-benzoquinoneTMS TetramethylsilaneTPA TriphenylamineTPM TriphenylmethylTris Tris(hydroxylmethyl)aminomeethaneTrp TryptophanUSQ UbisemiquinoneVCP Vinyl cyclopropaneV-O Vacancy-oxygen (complex)VOCs Volatile organic compoundsVP Versatile peroxidaseVZ VerdazylWOC Water oxidizing complexZSM Zeolite socony mobilOthers:CNOT Controlled-notCORBA Common object request broker architectureETE Extended time excitationEXAFS Extended X-ray absorption fine structureFCC (fcc) Face centered cubicFFT Fast Fourier transformFTIR Fourier transform infraredHCP, hcp Hexagonal closed-packedIAEA International atomic energy agencyIDAS International dose assurance serviceIP Ionization potentialLET Linear energy transferMBE Molecular beam epitaxyNIST National institute for standards and technologyNPL National Physical LaboratoryNSERC Natural Sciences and Engineering Research Council of CanadaPL Photo-luminescencePPTV (pptv) Parts-per-trillion-by-volumeQC Quantum computingQIP Quantum information processingSDC Super dense codingSQUID Superconducting quantum interference deviceSS/ES Solid state electron spectroscopyUV/VIS Ultraviolet ultraviolet/visible (absorption spectroscopy)XANES: X-ray absorption near edge structure

400 General Appendices

Table G7 Magnetic properties of stable isotopes a, b, c

IsotopeAtomicnumber (Z)

Naturalabundance (%)

Nuclearspin (I)

Nuclearg-factor (gN)

1H 1 99.985 0.5 5:585692H 1 0.0148 1 0:857443He 2 0.00014 0.5 �4:255256Li 3 7.5 1 0:822057Li 3 92.5 1.5 2:170969Be 4 100 1.5 �0:78510B 5 19.8 3 0:6002211B 5 80.2 1.5 1:7924213C 6 1.11 0.5 1:4048214N 7 99.63 1 0:4037615N 7 0.366 0.5 �0:5663817O 8 0.038 2.5 �0:7575219F 9 100 0.5 5:2577321Ne 10 0.27 1.5 �0:441223Na 11 100 1.5 1:4783925Mg 12 10 2.5 �0:3421827Al 13 100 2.5 1:456629Si 14 4.67 0.5 �1:110631P 15 100 0.5 2:263233S 16 0.75 1.5 0:4291135Cl 17 75.77 1.5 0:5479237Cl 17 24.23 1.5 0:4560839K 19 93.26 1.5 0:2609940K 19 0.0117 4 �0:3245341K 19 6.73 1.5 0:1432543Ca 20 0.135 3.5 �0:3764145Sc 21 100 3.5 1:3590647Ti 22 7.4 2.5 �0:3153949Ti 22 5.4 3.5 �0:3154850V 23 0.25 6 0:5565951V 23 99.75 3.5 1:4683653Cr 24 9.5 1.5 �0:314755Mn 25 100 2.5 1:381957Fe 26 2.15 0.5 0:180659Co 27 100 3.5 1:31861Ni 28 1.13 1.5 �0:5000163Cu 29 69.2 1.5 1:48465Cu 29 30.8 1.5 1:58867Zn 30 4.1 2.5 0:3503169Ga 31 60.1 1.5 1:3443971Ga 31 39.9 1.5 1:7081873Ge 32 7.8 4.5 �0:1954475As 33 100 1.5 0:9596577Se 34 7.6 0.5 1:0693

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General Appendices 401

Table G7 (continued)

IsotopeAtomicnumber (Z)

Naturalabundance (%)

Nuclearspin (I)

Nuclearg-factor (gN)

79Br 35 50.69 1.5 1:4042781Br 35 49.31 1.5 1:5137183Kr 36 11.5 4.5 �0:215785Rb 37 72.17 2.5 0:5412587Rb 37 27.83 1.5 1:8342787Sr 38 7 4.5 �0:2429189Y 39 100 0.5 �0:2748491Zr 40 11.2 2.5 �0:5214593Nb 41 100 4.5 1:371295Mo 42 15.9 2.5 �0:365697Mo 42 9.6 2.5 �0:373499Ru 44 12.7 2.5 �0:249101Ru 44 17 2.5 �0:279103Rh 46 100 0.5 �0:1768105Pd 46 22.2 2.5 �0:256107Ag 47 51.83 0.5 �0:22725109Ag 47 48.17 0.5 �0:26174111Cd 48 12.8 0.5 �1:19043113Cd 48 12.2 0.5 �1:2454113In 49 4.3 4.5 1:22864115In 49 95.7 4.5 1:23129115Sn 50 0.38 0.5 �1:8377117Sn 50 7.75 0.5 �2:00208119Sn 50 8.6 0.5 �2:09456121Sb 51 57.3 2.5 1:3455123Sb 51 42.7 3.5 0:72876123Te 52 0.89 0.5 �1:4736125Te 52 7 0.5 �1:7766127I 53 100 2.5 1:1253129Xe 54 26.4 0.5 �1:55595131Xe 54 21.2 1.5 0:46124133Cs 55 100 3.5 0:73785135Ba 56 6.59 1.5 0:55884137Ba 56 11.2 1.5 0:62515138La 57 0.089 5 0:74278139La 57 99.911 3.5 0:7952141Pr 59 100 2.5 1:6143Nd 60 12.2 3.5 �0:3076145Nd 60 8.3 3.5 �0:19147Sm 62 15.1 3.5 �0:2322149Sm 62 13.9 3.5 0:1915151Eu 63 47.9 2.5 1:389153Eu 63 52.1 2.5 0:6134155Gd 64 14.8 1.5 �0:1723

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402 General Appendices

Table G7 (continued)

IsotopeAtomicnumber (Z)

Naturalabundance (%)

Nuclearspin (I)

Nuclearg-factor (gN)

157Gd 64 15.7 1.5 �0:2253159Tb 65 100 1.5 1:342161Dy 66 19 2.5 �0:189163Dy 66 24.9 2.5 0:266165Ho 67 100 3.5 1:192167Er 68 22.9 3.5 �0:1618169Tm 69 100 0.5 �0:466171Yb 70 14.4 0.5 0:9885173Yb 70 16.2 2.5 �0:27195175Lu 71 97.39 3.5 0:63943176Lu 71 2.61 7 0:452177Hf 72 18.6 3.5 0:2267179Hf 72 13.7 4.5 �0:1424181Ta 73 99.9877 3.5 0:67729183W 74 14.3 0.5 0:23557185Re 75 37.4 2.5 1:2748187Re 75 62.6 2.5 1:2878187Os 76 1.6 0.5 0:1311189Os 76 16.1 1.5 0:488191Ir 77 37.3 1.5 0:097193Ir 78 62.7 1.5 0:107195Pt 78 33.8 0.5 1:219197Au 79 100 1.5 0:09797199Hg 80 16.8 0.5 1:01177201Hg 80 13.2 1.5 �0:37348203Tl 81 29.5 0.5 3:24451205Tl 81 70.5 0.5 3:2754207Pb 82 22.1 0.5 1:1748209Bi 83 100 4.5 0:938235U 92 0.72 3.5 �0:11aRaghavan P (1989) At. Data Nucl. Data Tables 42:189bhttp://ie.lbl.gov/toipdf/mometbl.pdfcValues for the isotropic and anisotropic hyperfine couplings of theisotopes are reported in (Weil JA, Bolton JR (2007) Electron paramag-netic resonance: elementary theory and practical applications, 2nd ed.Wiley)

Index

AAb initio, 110, 139, 144, 146, 173, 191, 195,

198, 202, 203, 206, 209, 286, 287, 289,291–293, 300, 310, 311, 323–352, 365,371, 380, 384

Ab initio MO calculations, 191, 203Activation energy, 32–34, 37, 109, 110, 113,

126, 210, 214Active space, 342, 370, 372, 375, 383, 384Adiabatic, 125, 127, 128, 154, 156, 157Adiabatic part, 125, 128, 156, 157Adsorption-desorption, 3, 37Adsorption strength, 37Alfa-proton methyl rotor, 133A1-lines, 174, 176A2-lines, 176Alkyl-substituted cyclohexanes, 201Allowed �mI D 0 transitions, 6Aluminosilicate and aluminophosphate

sodalite, 76Amino acids, 80, 286, 295–304, 319, 324, 332,

340, 350radicals, 80, 295–304, 317, 319, 324, 332

Ammonium tartrate, 77, 78, 81Amorphous, 3, 15–17, 25, 70, 114, 115, 156,

215glassy, 114, 156

Analysisof powder spectra, 15–26of saturation curves, 3, 31

Angular selection, 16, 18, 20–22, 25, 26Anisotropic exchange, 225, 227, 230, 236, 268,

273–274Anisotropic hyperfine coupling constants

(HFCCs), 268, 288, 289, 292, 301Antisymmetric exchange, 225, 236, 279Apical (“a”) site, 189, 191–193

Ar matrix, 134, 142, 143, 173–175, 178–182Arrhenius

barrier, 113fit, 113law, 105, 123parameters, 113plot, 34, 210, 214, 215

a-Si:H. See Hydrogenated amorphous silicon(a-Si:H)

Asymmetrically distorted structure(s), 173,192, 206–211

Asymmetric catalysts, 90A-type spins, 79Automatic fitting, 25, 26Axially symmetric 1H hfc tensor, 20Axial symmetry, 14, 21, 39–41, 137, 142, 224,

241, 366

BBandwidth, 55, 65, 73, 82, 88, 152Barriers of rotation, 135Basis set, 38, 65, 139, 286, 287, 289–293, 295,

304, 310–312, 317, 318, 328–331, 336,338, 339, 342, 344, 372, 375

Becke’s three-parameter hybrid exchangefunctional, 292

Bimolecular homolytic substitution (SH2)reactions, 173, 211–215

Biological radicals, 285–352Biradicals, 79, 189, 273, 366, 385Blue copper proteins, 90Blue ultramarine pigments, 92Boltzmann distribution, 198, 203, 206Boson, 134, 146, 175, 182BP Hamiltonian. See Breit-Pauli (BP)

Hamiltonian

A. Lund and M. Shiotani (eds.), EPR of Free Radicals in Solids I, Progressin Theoretical Chemistry and Physics 24, DOI 10.1007/978-94-007-4893-4,© Springer ScienceCBusiness Media Dordrecht 2003,2013

403

404 Index

Branching, 60Breit-Pauli (BP)

Hamiltonian, 325, 326, 367, 372spin-orbit coupling Hamiltonian, 369

Brownian diffusion, 149

CCancellation of errors, 287, 293, 304–305, 371,

375Carotenoid radical cations, 91Car-Parrinello molecular dynamics, 311,

313–315Carr and Purcell, 73Carr-Purcell-Meiboom-Gill (CPMG), 71–75CASPT2, 329, 352, 371CASSCF, 368, 370, 372–375, 378, 380–384CC. See Coupled-cluster (CC)cC6. See Cyclohexane (cC6)cC6C. See Cyclohexane radical cation (cC6C)cC6-1,1,3,3-d4

C, 202–206cC6-1,1,4,4-d4

C, 202, 205, 206CD3 (radical), 123, 133, 134, 141, 145–147,

174–178, 191–193, 195, 212, 213CD4

C, 189–191, 200CD2H2

C, 189–191CDH3

C, 189–191CD3HC, 189–191, 212CD3OCD3

C, 195–198, 200CD3OCH3

C, 195–198, 200CD3OCHD2

C, 195–198, 200CD3OCH2DC, 195–198, 200CH3 (radical), 104, 105, 114, 115, 130, 133,

134, 137–145, 172–179, 183, 184, 192,195, 196, 200, 212–215, 342

CH4C, 189–191, 200

CH2D, 134, 146, 172, 174–178, 195, 196CHD2, 134, 146, 174–178, 195–19812CH2DFC, 199C2h distorted structure, 202–203CH2DOHC, 199, 200Chemical exchange, 3, 32, 111, 119–123, 148Chemical reorganization, 119, 12112CH3FC, 19913CH3FC, 199, 200CH3OCH3

C, 195–198CH3OCH2DC, 195–198C2H5 radical, 184CH3SiD3, 212–214CH3SiH2 radical, 212CI. See Configuration interaction (CI)Classical equation of magnetization, 53Classical relaxation theory, 125, 135Classical rotor(s), 105, 132

Cluster chemical model, 313Coalescence, 120Coherences, 52, 59–62, 80, 83–85, 87, 262,

263Coherent, 58, 124, 135Composite approaches, 311–313Computational efficiency, 292, 330Computational scheme, 287, 295–296, 303,

305Computational time, 242, 247, 249, 250, 253,

256, 257, 304Concanavalin, 91Configuration interaction (CI), 291, 328, 329,

335, 352, 368, 370, 371, 377, 382, 384Conformational search, 295, 296, 303Continuous wave EPR (CW-EPR), 1–39, 52,

55, 56, 65, 67, 71, 74, 76, 78, 81, 108,111, 112, 116, 117, 133, 136, 151, 157,236

Convergence of DFT-based methods, 292Correction of ENDOR frequencies, 10Correlation(s) functional, 291, 292, 329, 345,

371, 377Correlations time(s), 92, 93, 106, 107, 111,

112, 116, 118, 120, 125–128, 134, 138,140, 141, 149, 157, 255

Coulomb interactions, 384Counterions, 81, 384Coupled-cluster (CC), 286, 293, 304, 329, 352,

371Coupled-perturbed (CP), 333, 371–373CPMG. See Carr-Purcell-Meiboom-Gill

(CPMG)C60

C radicals, 70Cross-relaxation, 148, 161Cryocrystal(s), 104, 141Cryogenic temperatures, 76, 104, 105, 173,

179, 212Crystal-lattice vibrations, 123Crystalline environment, 302Crystal plane(s), 8, 10, 13, 39, 41cSiC5. See Silacyclohexane (cSiC5)cSiC5-2,2,6,6-d4C, 206, 208, 210Cu(II), 70, 76, 80, 91, 256, 261

complexes, 70, 256, 261C2v symmetry, 191, 194, 195C2v type geometrical structure, 189CW-ENDOR, 87, 89, 147, 148CW-EPR. See Continuous wave EPR

(CW-EPR)CW microwave saturation measurements, 28Cyclic nitroxides, 106, 107, 109–110Cyclohexane (cC6), 32, 173, 201–211

cation (cC6C), 173, 201– 206

Index 405

DDalton program, 368D and E values, 256, 366Davies ENDOR, 82, 88, 89, 236D���CD3, 177, 178D���CH2D, 177, 178[D2(H2)D2]C, 186D���D2 complex, 182Decay of photoexcited species, 68DEER. See Double electron electron resonance

(DEER)DEERAnalysis software, 79Degenerate HOMOs, 199, 201, 202Density functional (calculations), 292, 304,

311, 314, 318, 323–352, 372Density functional theory (DFT) (calculations),

19, 139, 173, 190, 192–195, 198, 202,203, 206, 286, 287, 290–293, 295,303–305, 310, 312–313, 315, 317, 325,327, 329–347, 349, 351, 352, 365, 368,369, 371, 375, 376, 384

Density matrix, 32, 58–64, 73, 83, 119, 121,122, 261–263, 289, 332, 368, 382

D-E strain, 255, 256Detection, 53, 59, 67, 69, 76, 79, 87, 88, 236,

240, 261, 263, 364, 378Deuterated methane radical cations, 189, 200Deuteriated methyl rotor, 113, 134Deuterium (D) isotope effects, 172, 173,

188–200, 202–206, 214–215Deuterium labeling, 171–215DFT. See Density functional theory (DFT)Diffuse functions, 290, 293, 295, 311Diffusional (rotor), 105, 110, 132, 135Diffusion limit, 105Diffusion of radicals, 35–371,1-Dimethylcyclohexane (1,1-Me2-cC6), 201,

206Dimethylether (DME), 173, 195, 198, 203,

204radical cations, 173, 195–200, 203

Dipole-dipole, 154, 225, 227, 236, 241,267–269, 271, 279

interaction, 225, 227, 236, 241, 278mechanism, 154

Direct field (effect), 6, 17Direction cosines, 4, 10, 11, 40, 83, 255Direct process, 66, 70, 124Disordered system, 2, 19–20, 148Distant ENDOR, 89Distorted structures, 173, 192, 201–203,

206–211Distribution, 28, 36, 52, 66, 67, 70, 74, 76–81,

92, 111, 116, 138–141, 146, 148, 160,

177, 198, 203, 206, 227, 242, 247, 248,253, 255, 256, 270, 272, 275, 286, 291,304, 317, 323, 341, 366, 376, 384

DKH Hamiltonian. See Douglas-Kroll-Hess(DKH) Hamiltonian

D-labeledmethane radical cations, 189–191methyl radicals, 172–174, 177radicals, 172, 208

D-labeling and quantum effects, 179D-labeling study (studies), 172, 173, 184,

211–215DME. See Dimethylether (DME)�ms D˙1 transition, 177�ms D˙2 transition, 177DNA, 36, 81, 286, 287, 296, 310, 315Double electron electron resonance (DEER),

52, 68, 72, 78–81Double quantum coherence-ESR (DQC-ESR),

52, 80Douglas-Kroll-Hess (DKH) Hamiltonian, 325,

371DQC-ESR. See Double quantum coherence-

ESR (DQC-ESR)D tensors, 224, 364–367, 369, 371, 375,

378–380, 382–385Dynamical electron correlation effects, 370,

371Dynamic effects, 103–162, 314, 324, 333,

352Dynamic J-T effect, 199, 202Dynamics of radicals in zeolites, 33–34Dynamic structure, 32, 172, 191, 201–211

EEasyspin, 14, 18, 38, 39, 52Echo-detected, 69, 76Echo-detected EPR (ED-EPR), 56, 65–76, 112,

114, 116, 118, 152, 155–162EchoEPR, 52, 71, 74–78

spectral profiles, 74ED-EPR. See Echo-detected EPR (ED-EPR)Effective charge of nucleus, 369Effective fields, 6, 7, 54Eigenfield, 244–246, 250, 253, 255, 364, 378Eigenfield perturbation, 244–246, 255Eigenvalues, 10, 14, 36, 41, 74, 245, 247, 248,

250, 253Eigenvectors, 14, 74, 245, 250, 253Electron correlation, 286, 287, 290–293, 304,

310, 324, 328, 329, 332, 334, 340, 370,371, 382–384

Electron–electron interactions, 72, 76–77, 84

406 Index

Electronic g-tensors, 323–352Electron nuclear double resonance (ENDOR)

frequencies, 8–10, 12, 13, 21, 82–84, 86frequencies due to 1H, 12intensities, 20–23from nuclei with I �1, 8–10, 22, 25

Electron spin echo (ESE), 52–56, 60–63,65–76, 78, 79, 85, 87, 88, 92, 105, 135,148, 149, 151, 153–154, 160, 161

Electron spin echo envelope modulation(ESEEM), 25, 52, 61, 63, 73, 80,82–88, 90–92, 105, 114, 122, 135, 148,150–152, 161, 226, 227, 236, 349

modulation, 63Electron spin polarization, 62Electron Zeeman, 5, 128, 224, 225, 230, 233,

267, 268, 270–271, 274E-lines, 115, 174, 176El-Sayed’s rule, 374ENDOR. See Electron nuclear double

resonance (ENDOR)Energy level, 22, 53, 104, 182, 236, 244, 264,

270, 274–275, 376Energy level diagrams, 9, 131, 227, 230, 236,

251, 264–265Environmental effects, 287, 294–295, 300,

304, 312, 333, 334, 338, 351, 384EPR and ENDOR simulation software,

25–26EPR intensity in disordered systems, 19–20Equatorial (“e”) site, 189, 192, 193ESE. See Electron spin echo (ESE)ESEEM. See Electron spin echo envelope

modulation (ESEEM)ESR spectroscopy, 286, 289, 364Euler angles, 4, 112, 234, 279Evolution (mixing), 53Ex. See Exchange functional (Ex)Exact methods (calculation), 18, 19, 25Exchange-correlation energy functional (EXC),

291, 292Exchange-correlation functional, 291, 292,

329, 345, 371, 377Exchange functional (Ex), 291, 292Exchange of electrons, 107Exchange of protons, 106, 107, 146Exchange symmetry, 113, 130, 134Excitation bandwidth, 55Excited triplet states, 365, 366, 368, 378,

380–382Exothermic process, 181, 186

FFast limit of exchange, 120Fe(III), 70, 76, 91, 233, 251, 252, 263–266,

270, 271, 273, 275octaethylporphyrin, 70

[FeFe]-hydrogenase, 90Fermion, 134, 146, 176, 185[2Fe-2S]C cluster, 89[Fe3S4]C clusters, 70FID. See Free induction decay (FID)Field modulation, 28, 29Field segmentation, 229, 237, 244–246Fine-structure constant, 326, 367Fine-structure parameters, 177, 365, 371, 372First order analysis of hfc-and nqc-tensors, 13Flip-flop(s), 64, 69, 72, 75, 93, 128, 154, 161Fluorocarbon anion radicals, 19Forbidden �mI D 1 transitions, 6Forbidden transitions, 7, 84, 151, 174, 271Fourier transform (FT), 55, 79, 86, 87, 127,

148, 151, 152, 230, 257, 260Four pulses version in PELDOR, 79Free diffusion, 105, 113, 149Free induction decay (FID), 53–56, 62, 63, 67,

105, 236Free radical kinetics in solids, 37–38Free rotation, 33, 105, 135, 142, 145, 185Frontier MOs, 376Frozen, 15–17, 20, 26, 32, 68, 70, 76, 89, 91,

92, 135, 136, 156, 233, 276, 312, 314,344–346

FT. See Fourier transform (FT)FT-EPR, 55, 152Fullerene, 68, 69, 92, 366Fused silica, 114, 140

GGAMESS, 372g-anisotropy, 5, 9, 15–17, 20–22, 25, 39, 79,

80, 338, 350, 351g-A strain, 255, 276Gauss function, 26Gd(III), 80, 81

-nitroxide, 81Generalized gradient approximations (GGA),

397Generalized unrestricted Møller-Plesset

approach, 371Geometry relaxation, 380, 381GF. See Goodness of fit (GF)

Index 407

1/g factor for field-swept EPR, 20g-factor resolution, 15GGA. See Generalized gradient

approximations (GGA)GGA-corrected exchange functionals, 291Glasses, 17, 26, 74, 76, 91–92, 112, 114,

139–145, 156–157, 233, 276Glassy phases, 68–69Glycyl, 27, 30, 339, 350Goodness of fit (GF), 256–260Graphical user interface, 227–229, 231, 232,

234, 235, 237, 238, 261, 279Group-16 triplet diatomics, 372–374g-tensor, 3–5, 15, 19, 37, 80, 88, 111, 121,

128, 133, 138, 140, 146, 199, 286, 317,323–353

HH6

C (radical cation), 172, 184–187Hahn echo, 55, 56, 62, 71, 151, 152

decay, 62, 71H-and D-atoms, 108, 172, 180, 181, 189, 190,

200Harmonic oscillation, 108Harmonic oscillator, 111, 113Hartree-Fock (HF), 289–292, 328, 329,

332–335, 397H-atom(s) abstraction, 173, 212, 215H-atom methyl radical pair, 177H-atoms exchange, 190H���CH3. See Hydrogen atom methyl radical

pair (H : : :CH3)H���CHD2, 177H2

C-core H6C (H4D2

C), 186H���D2, 182[H2(H2)D2]C, 185, 186H4D2

C, 185, 186H5DC, 185H���D2 complex, 182Heinzer

method, 33, 34model, 33

Hellmann-Feynman theorem, 14HF. See Hartree-Fock (HF)HFCCs. See Hyperfine coupling constants

(HFCCs)hfc. See Hyperfine coupling (hfc or HFC)[H2(HD)H2]C, 186H���H2 complex, 181–182H���HD, 182[H2(H2)HD], 186

1H hfc tensor, 7, 20H���H, H���D and D���D, 179[H2(H2)H2]C ion, 184Higher order and exact analysis, 13–14High-field approximation, 4, 14, 122High field EPR, 2, 15, 16, 25, 111, 120, 151High field measurements, 15–17High resolution EPR, 109, 142, 172–179,

182–188, 227Hindered methyl rotor, 132, 136Hindered oscillation, 138Hindered rotation, 3, 75, 107, 113, 135–137,

150Hindered rotors, 105H���NH2 and D���ND2, 178Homogeneous and inhomogeneous broadening,

26Homogeneous broadening, 105, 124, 127Hooke and Jeeves, 230, 257–260HSA. See Human serum albumin (HSA)Human serum albumin (HSA), 80, 398Hybrid CASSCF/MRMP2 approach, 370Hybrid eigenfield method, 364Hybrid functionals, 291, 318, 333, 338, 371Hybrid quantum mechanic/molecular

mechanic (QM/MM) methods, 310, 311Hydrazinium ions, 75Hydrogenated amorphous silicon (a-Si:H), 70,

397Hydrogen atom hydrogen molecule complex,

179–182Hydrogen atom methyl radical pair

(H : : :CH3), 172, 174, 178Hydroxyproline, 295, 296, 298–300, 303

derived radicals, 298Hyperfine (HF, hf), 2, 52, 106, 180, 224,

285, 323, 363 coupling, 3–7, 15–22, 25,30, 34, 39, 40, 60, 67, 69, 81, 89, 111,137, 139, 141, 161, 225, 226, 268, 276,285–305, 310–319, 323, 395, 396, 402

coupling anisotropy, 20–21coupling constants (HFCCs), 286, 288,

289, 292–305, 310–318coupling (hfc) tensor, 4–7, 10, 12, 13,

16–20, 23, 25, 37, 39, 40, 139, 141,285–305, 310–319, 323

enhancement, 8, 20, 21, 23, 26interaction, 2, 13, 16, 21, 60, 81–88, 90–92,

108, 110–111, 120, 130, 138, 151, 153,183, 224, 234, 270–271, 288, 323

splittings, 16, 139, 180–181, 199, 208, 287,302

408 Index

Hydroxyproline (cont.)sublevel correlation (HYSCORE), 52, 82,

85–87, 90, 91, 114, 148, 236, 238–241,262, 276, 277, 396

HYSCORE. See Hyperfine sublevel correlation(HYSCORE)

IImidogen (NH), 308, 374, 375Inert gas matrices, 105, 130, 133, 173Inertial (effects), 105, 110, 123, 130–147Inhomogeneous broadening, 26, 30, 105, 112,

128, 153Inhomogeneous line, 26, 55, 81, 105Inhomogeneously broadened, 27, 153, 156Inorganic, 2, 6, 16, 19, 20, 26, 70, 71, 74, 76,

90–92, 173, 177, 235, 327, 364, 367,369, 372

Inorganic radicals, 6, 19, 20, 327Instantaneous diffusion, 52, 72–78, 92, 105,

154–156, 159, 160Interaction tensor, 224, 231, 378–380Interstitial, 108, 141, 178–180, 182Interstitial octahedral site, 178–180Intra-molecular dynamics, 195, 201Intramolecular exchange process, 209Intramolecular hydrogen-bonding, 298Intramolecular motions, 32, 67, 72, 75Intrinsic broadening, 119Inversion recovery, 65, 67–70Isochromats, 54Isomerization, 107Isotropic exchange, 119, 225, 230, 236, 268,

273Isotropic hyperfine coupling constant (HFCC),

288, 292–294, 296–298, 300–302, 304,311, 312, 314, 315, 317, 318

JJahn-Teller (J-T), 107, 172, 173, 188–195,

199–203, 206, 208, 397distorted structures, 201–202distortion, 188effects, 173, 193, 194, 199, 202

J-T. See Jahn-Teller (J-T)Jump exchange, 111

KKivelson’s linewidth model, 255

LL-alanine, 23, 69, 148Lattice-temperature, 124Libration, 34, 72, 75, 76, 106–112, 114,

116–119, 151, 155–162Lifetime broadening, 119, 128, 149Limit, 26, 35, 66, 75, 87, 88, 92, 105, 112–114,

120, 123, 125–127, 149, 156, 203, 205,258, 290, 291, 305, 328, 329

Linear regression, 13, 336Line broadening, 16, 55, 142Lineshape, 11, 17, 22, 26, 28–33, 38, 39, 55,

71, 74, 86, 92, 104, 108–111, 113–123,130, 133–139, 142, 144, 145, 147, 148,150, 155–158, 161, 175, 187, 193, 204,211, 228, 233, 241, 242, 249, 250, 260,271, 279

Linewidth, 15, 26, 27, 30, 33, 35, 38, 71, 72,78, 81, 82, 118, 120, 121, 125, 128,129, 138–141, 148, 174, 175, 183, 184,229, 230, 233, 243, 247–250, 253–256,260, 261, 271, 272, 276, 279

Liouville-von Neumann equation, 59Liquid helium (He) temperatures, 105, 107,

123, 135, 144Localized MO analysis, 379Local spin density approximation (LSDA),

291–293, 336Longitudinal relaxation, 54, 55, 73, 124, 125,

150rate, 150

Looping transitions, 265, 266, 270, 274–275Lorentz (Lorentzian) function, 26–28, 55, 126,

148, 241

MMagnetic-dipole interactions, 289Magnetic interactions between different

paramagnetic species, 67Magnetic moment, 3, 172, 184, 288, 395Magnetic properties, 104, 172, 310, 311, 400Malonic acid radical, 7, 113Matrix isolation, 106, 133, 172, 187, 334, 364

techniques, 364MCSCF. See Multiconfiguration self-consistent

field (MCSCF)Mean-field approximation, 368, 372, 375, 378Mean total hf splitting, 197Mean total 1H hf splitting, 198, 2041,1-Me2-cC6. See 1,1-Dimethylcyclohexane

(1,1-Me2-cC6)

Index 409

1,1-Me2-cC6C , 201, 206Me-cC6C, 201, 2061-Me-cSiC5-2,2-d2

C, 206, 208Metallo-centers, 90Metalloproteins, 21, 90–91, 231, 233, 271, 275Methane radical cations, 173, 189–191Methanol cation (CH3OHC), 200Methylcyclohexane (Me-cC6), 2014-Methyl-2,6-di-t-butyl phenol, 75Methylene, 33, 34, 64, 123, 135, 150, 317, 368,

374, 375Methylfluoride cations, 199–200Methyl group conformation, 173, 195Methyl-group rotation, 33, 69, 72Methyl-like quantum rotors, 136Methyl quartet, 130, 133Methyl radicals, 104, 115, 133, 137–142, 144,

145, 172–179, 211–215Methyl (-type) rotor, 105, 113, 130–136Methylsilane (CH3SiH3), 173, 211–215Microcrystalline, 114Microcrystallite, 114, 248Microwave frequency, 4, 14–16, 69, 79, 82,

143, 236, 239, 241, 245, 253, 262, 268,270, 271, 274, 394

Microwave power, 26–31, 72, 77, 82, 152, 177,262, 395

Microwave power effects on EPR spectralshape, 30–31

Microwave saturation, 26, 28–31Mims ENDOR, 88–89, 91Mixed state, 58Mn(II), 91, 231, 233, 235Modulation depth, 82–84Molecular crystals, 69Molecular dynamics, 139, 146, 172, 195, 201,

310, 311, 313–316, 319simulation, 313, 316, 319, 333, 349, 351,

384Molecular hydrogen, 136, 137Molecular Sophe (Mosophe), 223–278Moment of inertia, 130, 146Monofluoromethane (CFH3), 173, 195Monte Carlo, 259Mosaic misorientation, 229, 230, 247–250MoSophe. See Molecular Sophe (Mosophe)Motion, 3, 31–36, 38, 54, 66–67, 71–73, 75,

76, 92, 104–107, 109–113, 116–120,122, 124–130, 132, 134–136, 138, 139,141, 146–151, 155–162, 187, 290, 294,312, 313, 333, 338, 345, 349

Motional dynamics, 104, 114, 116, 118, 121,136, 172, 187

MRCI. See Multireference CI (MRCI)Multiconfiguration self-consistent field

(MCSCF), 329, 338, 340–342, 368,370, 371, 397

Multifrequency, 16, 91, 223, 230, 256, 257,261, 270, 272, 279

EPR, 16, 256, 257, 261Multireference CI (MRCI), 286, 291, 293, 304,

328, 329, 334–338, 368, 371, 372, 397

NNarGHI. See Nitrate reductase A (NarGHI)N@C60, 70N07D basis set, 311, 318Neon matrix, 189Neopentane radical cation C(CH3)4

C, 18814N hfc and nqc tensor, 13, 17, 3714N hyperfine coupling, 34Nitrate reductase A (NarGHI), 90, 91Nitrogen-centred free radicals, 17Nitroxide(s), 35, 39, 63, 68, 74–76, 80, 81,

104–107, 109–112, 116–119, 135, 151,155–160, 162, 274, 311–315, 318, 324,333, 339, 343, 350, 352, 385

biradicals, 385labels, 151probe, 112, 116, 117radicals, 68, 75, 106spectra, 160spin labels, 68, 80, 158, 160, 333, 339, 352

14N ���14N, 14N���15N, and 15N���15N, 179NO2, 17, 36, 172, 187–188, 335, 336

adsorbed on zeolites, 36NO in Na-A and Na-ZSM-5 zeolites, 37Nonbonding  -MO, 193Non-interacting approximation, 368, 375, 377,

378Non-linear least squares, 4, 9, 13–14, 29, 261Nonlinear refinement, 13Non selective pulse, 55, 93nqc. See Nuclear quadrupole couplings (nqc)Nuclear flip-flop transitions, 72, 75Nuclear frequency, 10, 394Nuclear g-factors, 6, 17, 189, 400–402Nuclear quadrupole couplings (nqc), 2, 4, 19,

25, 395, 396tensors, 2, 5, 9, 10, 13

Nuclear quadrupole interactions, 2, 20, 22Nuclear spin flips, 60, 154Nuclear spin-rotation coupling, 172, 174, 176Nuclear Zeeman (term), 3–5, 7, 8, 17–19, 21,

39, 225, 230, 267, 268

410 Index

O17O, 92o-D2. See Ortho-D2 (o-D2)OEC. See Oxygen evolving complex (OEC)o-H2. See Ortho-hydrogen (o-H2)Oligonitrenes, 378, 379One-electron spin–orbit, 369ONIOM, 312, 314, 384

like approach, 314Optimisation, 228–230, 256, 257, 260Orbach-Aminov process, 66Orbital interactions, 376ORCA, 317, 332, 371Order parameter, 116, 118–119Organic free radicals, 20, 318, 319Organic radical cations, 173Organic spin multiplets, 363–385Orientation selectivity, 16Ortho-D2 (o-D2), 182, 185, 186Ortho-hydrogen (o-H2), 136, 182, 183Out-of-phase ESEEM, 80Oxygen evolving complex (OEC), 91

PPake distribution, 79Para-D2 (p-D2), 182Para-H2 matrix, 172, 182–188Para-hydrogen (p-H2), 182–188Parallelization, 256Paramagnetic, 2, 15, 25, 26, 36, 51–93,

104–107, 123, 124, 128, 129, 136, 140,154, 160, 223–227, 231, 233, 235, 241,254, 263, 268, 276, 279, 288, 310, 326,329, 352

Partially deuterated methyl radicals, 175Partial orientation, 172, 187–188Pauli principle, 146, 172, 174, 176PCM. See Polarizable continuum model

(PCM)p-D2. See Para-D2 (p-D2)Pederson–Khanna (PK), 371, 372PELDOR. See Pulsed electron double

resonance (PELDOR)PELDOR (DEER), 68, 78–80Perdeuterated methyl radical CD3, 175Peroxyl radicals, 287Perturbation, 4, 13, 18, 19, 21, 41, 155, 159,

182, 227, 231, 241, 244–247, 255, 268,325–330, 333, 338–340, 342, 352, 366,367, 369, 376, 384

2p-ESE, 56, 60–63, 71–75, 78, 79, 83–85, 88decay, 71, 73, 74

3p-ESE, 60–63, 68, 83–853p-ESEEM, 83–85p-H2. See Para-hydrogen (p-H2)Phase memory, 56, 71, 75, 77, 148–150, 155,

156, 161time (TM), 52, 56, 65–77, 92, 93, 149, 150,

155, 156, 161Phenomena, 104, 105, 121, 254, 364, 365Phenomenological decay function Vd(t), 63Phenoxyl (radical), 15, 287, 323, 339–343m-Phenylenebis(phenylcarbene), 378Phenylene-1,3-dinitrene, 378Photosynthetic reaction centers of rhodobacter

sphaeroides, 76 -spin polarization mechanism, 378Planar-rotor, 133Point-dipole approximation, 87, 378, 382, 383Polarizable continuum model (PCM), 294,

295, 313–319, 333, 334, 384Polarization functions, 290, 295, 339Polycrystalline, 3, 15, 18, 24, 28, 69, 74, 106,

114, 115, 141Polycrystals, 3, 15, 18, 24, 28, 69, 74, 92, 106,

114, 115, 138, 141, 156–157Pople diagram, 291Populations, 38, 59, 60, 67, 68, 85, 121, 122,

133, 206, 236, 269, 287, 297, 298Powder ENDOR spectra, 20–22Powder line shape, 22Powder spectrum (spectra), 3, 11, 15–26, 32,

39, 114, 158, 248, 263Power dependence, 27, 77Preferential orientation, 187Preparation, 38, 53, 59, 65, 67, 87, 271, 346,

347Principal components, 36, 268, 279, 288, 342Principal directions, 5, 6, 12, 18, 39, 84, 188,

264Principal g-values, 4, 5, 15Principal values, 5–12, 16, 18, 23, 39–41, 92,

137, 366Product operator, 64–65Propagation of errors, 41Protein-based radicals, 316Protons exchanged, 105Pseudo J-T distortion, 172, 201Puckering motion, 17, 32Pulse-based electron spin transient nutation

(ESTN) spectroscopy, 364Pulsed electron double resonance (PELDOR),

52, 68, 69, 78–81Pulsed EPR, 3, 16, 25, 30, 91, 92, 103–162,

223–279

Index 411

Pulse ENDOR, 52, 82–88, 90–92, 148,223–278

at W-band, 88Pure state, 58Pyrazine, 380, 381Pyridazine, 380Pyrimidine, 381

QQM/MM methods. See Quantum

mechanic/molecular mechanic(QM/MM) methods

QRO. See Quasi-restricted orbital (QRO)Quadratic, 127, 176, 230, 253, 257, 258, 260,

293, 308, 312, 330Quadratic configuration interaction (QCI), 213,

286, 293, 3604Quadrupole, 2, 4, 14, 18–22, 225, 230, 233,

274Quantitative EPR, 1, 3, 26Quantum bits, 364Quantum computing, 364Quantum effects, 105, 113, 124, 130, 133–136,

145, 171–215Quantum entanglement, 386Quantum information processing, 70, 364, 386Quantum mechanical master equation, 63Quantum mechanic/molecular mechanic

(QM/MM) methods, 310, 311, 315,319, 334, 343, 351, 384

Quantum rotors, 107, 113, 130, 132, 134–136,172, 174

Quantum solid, 136, 172, 182Quantum tunnelling, 172Quartet, 104, 113, 130, 132, 133, 137, 139Quasi-restricted orbital (QRO), 371, 372Qubits, 364, 385Quinone radicals, 287Quinonoidal electronic structure, 382

RRadical cations, 3, 32–34, 172, 173, 184, 186,

188–203, 206–210, 217Radical pair, 37, 80, 84, 172, 174, 176–179Raman process, 66, 68, 123, 124Rare-(noble) gas (matrix), 45, 133RASSCF, 368Redfield-Freed theory, 72Redfield limit, 92Redfield relaxation limit, 112, 125–127Redfield-relaxation theory, 125

Relaxationinduced by the spin-orbit coupling, 66mechanisms, 63, 64, 67, 69, 71–73, 75, 77,

93, 107, 123, 124, 138, 153, 154, 161superoperator, 63times, 3, 26, 28, 30, 51, 66, 68–71, 76, 88,

123–126Reorientation, 33, 55, 74, 106–108, 111, 112,

115–120, 138, 145, 147–150, 348Resonance frequency, 55, 60, 93, 115, 149,

156, 160, 289Resonance structures, 312, 383Resonant field, 242, 244–248, 250, 253, 254,

268Restricted motion, 106, 117, 148Restricted open-shell HF (ROHF), 290, 293,

328, 329, 334, 340Restricted oscillations, 138Restricted reorientations, 106, 108, 112, 115,

117, 119, 150Restricted rotational motion, 122Ribonucleotide reductase enzyme, 80Ring puckering, 3, 32, 109RNA, 80, 90ROHF. See Restricted open-shell HF (ROHF)Rotational constants, 130, 135, 184Rotational diffusion, 36, 187

of NO2, 36, 187Rotational frequencies, 134Rotational quantum number, 132, 135, 183Rotational states, 130, 135, 142, 146, 176, 182,

185Rotation barrier, 138Rotation states, 134, 142, 144, 176Rotation symmetry, 146Ru(II), 81

SSAC-CI. See Symmetry-adapted cluster-

configuration interaction (SAC-CI)Saturation curves, 3, 26–29, 31, 141Saturation factor, 30Saturation properties, 26–31Saturation recovery, 65, 67, 69–71Scalar parameters D and E, 365Schonland ambiguity, 7, 8, 10–13, 23

in ENDOR, 12–13Schonland method, 4, 6, 10–13, 39, 40SECI. See Single excitation configuration

interaction (SECI)Second-order J-T theory (pseudo J-T effect),

208

412 Index

Second-order multireference Møller-Plesset(MRMP2) method, 370

Second quantization, 367Selectively alkyl-substituted cyclohexanes, 201Self-consistent reaction field (SCRF), 294Semiconductors, 92Semiquinone, 323, 339, 343–349Septet, 134, 136, 145, 146, 193, 204, 378–380SH2 reactions, 212–215 See also Bimolecular

homolytic substitution (SH2) reactionsSi(CH3)2(CD3)2

C (TMS-d6C), 191

Si(CH3)4C (TMSC), 191

Si(CH3)3CD3C (TMS-d3

C), 191SiD3CH3, 213, 214Signal analysis, 87SiH4. See Silane (SiH4)Silacyclohexane (cSiC5), 173, 201, 206, 208,

210(radical) cation(s), 206–211

Silane (SiH4), 215Silica gel

samples, 139surfaces, 130, 138–140, 145

Silica glass, 114Silver nanoparticles, 70Simplex, 230, 257–260Simulated annealing, 230, 257, 259–260Simulation of ENDOR spectra, 22–25Single crystals, 2, 4, 6, 7, 13–16, 18, 19, 21–23,

25, 30, 31, 39–41, 63, 64, 70, 75, 78, 86,111, 112, 123, 137, 138, 140, 148–150,177, 224, 226–231, 237, 241, 275, 278,295, 296, 303, 323, 330, 339, 351, 364,378

Single excitation configuration interaction(SECI), 368

Singlet diradicaloid, 382Singlet triplet energy gaps, 374Site-directed spin labelling, 80Sites(s), 11, 15, 20, 25, 32–35, 80, 86, 90,

91, 107, 111, 113, 118–122, 149, 150,178–182, 189, 190, 192, 193, 198, 200,203, 204, 233, 234, 255, 271, 323,346–349, 351, 378–380

Site exchange, 35, 120, 149, 150, 204Site jump model, 33, 113Skew plane, 11Slow exchange, 119–121, 149Slow-motional effects, 39Slow-motion EPR theory, 36Slow passage condition, 29, 30Slow tumbling, 121, 124Small organic radicals, 172, 173, 183–184SO-CI. See Spin-orbit CI (SO-CI)

Softwarefor EPR analysis of motional effects, 38–39for microwave saturation analysis, 31for single crystal analysis, 14

Solidargon, 141, 172–176, 179–182gases, 107, 136, 141H2 (molecular hydrogen), 137, 172,

182–184, 187p-H2, 183–187

Solvation structure, 25Sophe, 223–279

interpolation, 229, 230, 244, 246–250partition scheme, 242, 243

SOS. See Sum-over-states (SOS)SO-SI. See Spin-orbit state interaction (SO-SI)Spectral and spin diffusion, 68Spectral density, 126, 127, 148, 149Spectral diffusion, 62, 65–69, 84, 93, 105, 149,

152, 154, 159Spin contamination, 290, 292, 377Spin density, 60, 92, 182, 191, 199, 200, 208,

227, 286, 288, 289, 291–293, 304, 317,323, 341–343, 368, 372, 375–377,382–384

matrix, 60, 289, 368, 382Spin dephasing, 71–73, 154, 156Spin-diffusion, 105, 106, 114Spin dynamics, 58, 64, 72, 104, 112, 124,

128–129, 148Spin flips, 30, 60, 72, 77, 83, 93, 127, 129,

152–155, 160, 373, 376, 379excitations, 373, 376lines, 30

Spin Hamiltonian, 4, 14, 18, 21, 58–60, 76,89, 127, 153, 224–231, 233, 235, 238,241, 243, 248, 250, 256, 257, 260, 261,272–274, 276, 278, 279, 324, 325, 363,365

parameters, 363Spin labels, 17, 35, 39, 68, 76, 80, 81, 90, 155,

157–161, 333, 339, 352Spin-lattice, 26, 28, 62, 65–70, 72, 84,

123–126, 128, 141, 146, 153, 154, 161Spin-lattice relaxation, 62, 65–70, 72, 84, 123,

124, 128, 141, 153, 154processes, 66–67times, 68, 124, 141

Spin-orbit CI (SO-CI), 370, 371Spin-orbit coupling(s) constant, 66, 68, 331,

364, 367, 369, 370, 372–374, 379, 380Spin-orbit state interaction (SO-SI), 371Spin-other-orbit (SOO), 326, 327, 330–332,

337

Index 413

Spin packet, 28, 29, 55, 56, 61, 62, 65, 71–74,87, 88, 93, 114, 128, 153, 160

Spin polarization, 62, 87, 293, 295, 297, 298,308, 310, 318, 328, 330, 336, 338, 377,378

model, 293Spin populations, 60, 121, 289, 297, 298Spin probes, 3, 36, 75, 78, 80, 81, 90, 136, 146,

187, 344Spin-rotation coupling, 107, 130, 133, 136,

172, 174, 176Spin-same-orbit, 369Spins B, 72, 73, 79, 153Spin-spin contact term, 369Spin-spin dipolar coupling, 366, 367Spin-spin relaxation rate, 114Spin-spin relaxation times, 26Spin temperature, 114Spintronics, 70, 364State mixing, 238, 270, 274–275Stimulated echo, 62, 63, 68, 84, 88, 93, 151,

152Stimulated or 3p-ESE, 68Stopped, 110, 113, 132, 134, 135Stopped classical rotor, 132Stopped methyl-rotor, 113, 134Stopped quantum rotors, 132, 135Stopped rotor, 113Stretched exponentials, 66, 70, 72, 73, 92, 112,

154, 161Substitutional (site), 64, 108, 178–181, 187Sum-over orbital pair equations, 371Sum-over-states (SOS), 369, 372Superhyperfine (Super-hf ), 55, 90, 108, 224,

225, 231, 235, 276interaction, 90, 108, 224, 231, 235Splitting, 180

Supermolecular model, 294, 295Surface complex structures, 25Symmetric-top, 130, 131Symmetry-adapted cluster-configuration

interaction (SAC-CI), 377, 380

TT1, 28, 29, 52, 55, 65–76, 123–126, 128, 129,

150, 154, 161, 381T2, 28, 29, 52, 54, 55, 63, 65–76, 124–128,

149, 150, 154, 161T2*, 55, 67Td symmetry, 188, 191Temperature-dependent EPR spectra, 195,

204–206, 209, 210

Temperature-dependent 1H hf splittings, 195,197–199

Temperature effects, 111, 139, 294Tempone radical, 16, 17, 75Tetramethylsilane radical cation (TMSC), 173,

191–1931,1,2,2-Tetramethyltrimethylenemethane, 195Theoretical modelling (modeling), 22, 25, 113,

161, 179, 364, 372Theory, 3, 52, 112, 173, 227, 286, 306, 325,

365Thermal

activation, 123, 182contact, 105, 135energy, 105, 185, 186excitation, 135fluctuations, 153isolation, 104motion, 124, 130, 134reservoir, 135

Thermally activated, 105, 110, 124, 126Thermally excited triplet state, 382Three-site jump model, 33TM. See Phase memory time (TM)TMMC. See Trimethylenemethane radical

cation (TMMC)Tooth enamel, 76Torsional oscillations, 107, 135Transition metals complexes, 70Transition roadmaps, 227, 229, 230, 236, 264,

265, 278Transition surfaces, 229, 230, 239, 250,

252–254, 264–266, 278Translational diffusion, 36, 112Transversal relaxation, 125, 150

rate, 150Transverse relaxation, 54, 63, 71–76, 84, 87Trifluoromethyl radical, CF3, 18Trimethylenemethane (TMM), 189, 193–195

radical cation (TMMC), 189, 193–195Triplet arylnitrenes, 374–378Triplet states, 69, 70, 76, 91, 174, 177, 179,

189, 329, 365, 366, 368, 373, 374, 378,380–383

Tryptophan radicals, 315–317, 351Tumbling, 39, 68, 107, 112, 121, 124, 138,

140, 141Tunnelling, 67, 75, 132, 134, 136, 151–152,

172, 173, 179, 181–182, 200, 215frequency, 151–152quantum rotor, 132reaction, 179, 181–182rotor, 136sidebands, 152

414 Index

Twist angle, 110Twisted-crossover conformations, 106Two-particle spin density matrix, 368, 382Two-site, 34, 111, 120, 149

exchange, 111, 120, 149model, 34

UUbisemiquinone (USQ), 90, 344, 345, 349Unrestricted Hartree-Fock (UHF), 290

VValence space, 293Variable temperature, 230, 236, 237, 273,

274Vector model, 53, 56, 61, 64Vibrational averaging, 108, 294, 301Vibrational degrees of freedom, 135Vibrational levels, 108Vibration amplitudes, 107Vibration(s), 54, 68, 70, 107, 108, 123, 124,

129, 135, 139, 171–173, 182, 190, 191,195, 197, 203, 204, 294, 301, 338

states, 139Vibronic coupling, 294Vm and Vd nuclear modulation and decay

functions, 74VO2C, 90, 91

Voigt function, 28Voigt line, 31Vycor (glass), 17, 139

WWell-balanced basis set, 293

XX-ray irradiation, 178X-ray radiolysis, 142, 174, 180, 181

ZZeeman interaction, 4, 8, 18, 21, 76, 114, 128,

224, 225, 230, 244, 267, 268, 274, 324,325

Zeolite(s), 3, 25, 32–37, 90, 104, 140, 323matrices, 34

Zero-field splitting (ZFS), 177, 325, 363–385tensors, 363–385

Zero-level oscillations, 135Zero-level vibrations, 124Zero-point vibrational energy (ZPVE), 171,

172, 190, 203of C-H stretching vibration, 173, 191, 195

Zwitterionic amino acid radicals, 302, 304Zwitterionic forms, 295, 300, 303, 304, 312