EPR Spectroscopy:Fundamentals andMethods

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EPR Spectroscopy:Fundamentals andMethodsEditors

Daniella GoldfarbWeizmann Institute of Science, Rehovot, Israel

Stefan StollUniversity of Washington, Seattle, WA, USA

This edition first published 2018© 2018 John Wiley & Sons Ltd

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Cover Design: WileyCover Images: (Background) © kWaiGon/Gettyimages; (Top, left to right) Pulse shapeimage, courtesy of Stefan Stoll; HYSCORE, courtesy of Sabine Van Doorslaer; EnergyLevel Diagram, courtesy of Jeffrey Harmer; Tyrosyl Radical, courtesy of Franke Neese;(Bottom, left to right) DEER, courtesy of Gunnar Jeschke; Spectra, courtesy of EnricaBordignon

Set in 9.5/11.5 pt TimesLTStd by SPi Global, Chennai, India

10 9 8 7 6 5 4 3 2 1

eMagResEditorial Board

Editors-in-ChiefRoderick E. WasylishenUniversity of AlbertaEdmonton, AlbertaCanada

From 1st January 2018

Sharon AshbrookUniversity of St AndrewsSt AndrewsUK

Section EditorsSOLID-STATE NMR & PHYSICS

Marina CarravettaUniversity of SouthamptonSouthamptonUK

SOLUTION-STATE NMR & CHEMISTRY

George A. GrayApplications Scientist (formerly

Varian Inc. & Agilent)Portola Valley, CAUSA

BIOCHEMICAL NMR

Tatyana PolenovaUniversity of DelawareNewark, DEUSA

ENVIRONMENTAL & ECOLOGICAL NMR

André J. SimpsonUniversity of TorontoOntarioCanada

Myrna J. SimpsonUniversity of TorontoOntarioCanada

vi eMagRes

MRI & MRS

John R. GriffithsCancer Research UKCambridge Research InstituteCambridgeUK

Ian R. YoungImperial CollegeLondonUK

HISTORICAL PERSPECTIVES

Edwin D. BeckerNational Institutes of HealthBethesda, MDUSA

eMagRes vii

International Advisory Board

Robin K. Harris(Chairman)University of DurhamDurhamUK

David M. Grant(Past Chairman)(deceased)University of UtahSalt Lake City, UTUSA

Isao AndoTokyo Institute

of TechnologyTokyoJapan

Adriaan BaxNational Institutes of HealthBethesda, MDUSA

Chris BoeschUniversity of BernBernSwitzerland

Paul A. BottomleyJohns Hopkins UniversityBaltimore, MDUSA

William G. BradleyUCSD Medical CenterSan Diego, CAUSA

Graeme M. BydderUCSD Medical CenterSan Diego, CAUSA

Paul T. Callaghan(deceased)Victoria University

of WellingtonWellingtonNew Zealand

Melinda J. DuerUniversity of CambridgeCambridgeUK

James W. EmsleyUniversity of SouthamptonSouthamptonUK

Richard R. ErnstEidgenössische Technische

Hochschule (ETH)ZürichSwitzerland

Ray FreemanUniversity of CambridgeCambridgeUK

Lucio FrydmanWeizmann Institute

of ScienceRehovotIsrael

Bernard C. GersteinAmes, IAUSA

Maurice GoldmanVillebon sur YvetteFrance

Harald GüntherUniversität SiegenSiegenGermany

Herbert Y. KresselHarvard Medical SchoolBoston, MAUSA

Ann E. McDermottColumbia UniversityNew York, NYUSA

Gareth A. MorrisUniversity of ManchesterManchesterUK

C. Leon PartainVanderbilt University Medical

CenterNashville, TNUSA

Alexander PinesUniversity of California

at BerkeleyBerkeley, CAUSA

viii eMagRes

George K. RaddaUniversity of OxfordOxfordUK

Hans Wolfgang SpiessMax-Planck Institute

of Polymer ResearchMainzGermany

Charles P. SlichterUniversity of Illinois

at Urbana-ChampaignUrbana, ILUSA

John S. Waugh (deceased)Massachusetts Institute

of Technology (MIT)Cambridge, MAUSA

Bernd Wrackmeyer(deceased)Universität BayreuthBayreuthGermany

Kurt WüthrichThe Scripps Research

InstituteLa Jolla, CAUSA

and

ETH ZürichZürichSwitzerland

Contents

Contributors xi

Series Preface xv

Preface xvii

Part A: Fundamental Theory 1

1 Continuous-Wave EPRArt van der Est 3

2 EPR Interactions – g-AnisotropyPeter Gast and Edgar J.J. Groenen 17

3 EPR Interactions – Zero-field SplittingsJoshua Telser 29

4 EPR Interactions – Coupled SpinsEric J.L. McInnes and David Collison 63

5 EPR Interactions – Hyperfine CouplingsMarina Bennati 81

6 EPR Interactions – Nuclear Quadrupole CouplingsStefan Stoll and Daniella Goldfarb 95

7 Quantum Chemistry and EPR ParametersFrank Neese 115

8 Spin DynamicsAkiva Feintuch and Shimon Vega 143

9 Relaxation MechanismsSandra S. Eaton and Gareth R. Eaton 175

Part B: Basic Techniques and Instrumentation 193

10 Transient EPRStefan Weber 195

11 Pulse EPRStefan Stoll 215

12 EPR InstrumentationEdward Reijerse and Anton Savitsky 235

13 EPR ImagingBoris Epel and Howard J. Halpern 261

x Contents

14 EPR Spectroscopy of Nitroxide Spin ProbesEnrica Bordignon 277

Part C: High-Resolution Pulse Techniques 303

15 FT-EPRMichael K. Bowman, Hanjiao Chen, and Alexander G. Maryasov 305

16 Hyperfine Spectroscopy – ENDORJeffrey R. Harmer 331

17 Hyperfine Spectroscopy – ELDOR-detected NMRDaniella Goldfarb 359

18 Hyperfine Spectroscopy – ESEEMSabine Van Doorslaer 377

19 Dipolar Spectroscopy – Double-resonance MethodsGunnar Jeschke 401

20 Dipolar Spectroscopy – Single-resonance MethodsPeter P. Borbat and Jack H. Freed 425

21 Shaped Pulses in EPRPhilipp E. Spindler, Philipp Schöps, Alice M. Bowen, Burkhard Endeward, and Thomas F. Prisner 463

Part D: Special Techniques 483

22 Pulse Techniques for Quantum Information ProcessingGary Wolfowicz and John J.L. Morton 485

23 Rapid-scan EPRGareth R. Eaton and Sandra S. Eaton 503

24 EPR MicroscopyAharon Blank 521

25 Optically Detected Magnetic Resonance (ODMR)Etienne Goovaerts 537

26 Electrically Detected Magnetic Resonance (EDMR) SpectroscopyChristoph Boehme and Hans Malissa 559

27 Very-high-frequency EPRAlexander Schnegg 581

Index 603

Contributors

Marina Bennati Max Planck Institute for Biophysical Chemistry and University ofGöttingen, Göttingen, GermanyChapter 5: EPR Interactions – Hyperfine Couplings

Aharon Blank Schulich Faculty of Chemistry, Technion, Haifa, IsraelChapter 24: EPR Microscopy

Christoph Boehme University of Utah, Salt Lake City, UT, USAChapter 26: Electrically Detected Magnetic Resonance (EDMR)Spectroscopy

Peter P. Borbat Cornell University, Ithaca, NY, USAChapter 20: Dipolar Spectroscopy – Single-resonance Methods

Enrica Bordignon Ruhr-Universität Bochum, Bochum, GermanyChapter 14: EPR Spectroscopy of Nitroxide Spin Probes

Alice M. Bowen Goethe University Frankfurt, Frankfurt am Main, GermanyChapter 21: Shaped Pulses in EPR

Michael K. Bowman The University of Alabama, Tuscaloosa, AL, USAChapter 15: FT-EPR

Hanjiao Chen The University of Alabama, Tuscaloosa, AL, USAChapter 15: FT-EPR

David Collison The University of Manchester, Manchester, UKChapter 4: EPR Interactions – Coupled Spins

Gareth R. Eaton University of Denver, Denver, CO, USAChapter 9: Relaxation MechanismsChapter 23: Rapid-scan EPR

Sandra S. Eaton University of Denver, Denver, CO, USAChapter 9: Relaxation MechanismsChapter 23: Rapid-scan EPR

Burkhard Endeward Goethe University Frankfurt, Frankfurt am Main, GermanyChapter 21: Shaped Pulses in EPR

xii Contributors

Boris Epel University of Chicago, Chicago, IL, USAChapter 13: EPR Imaging

Akiva Feintuch Weizmann Institute of Science, Rehovot, IsraelChapter 8: Spin Dynamics

Jack H. Freed Cornell University, Ithaca, NY, USAChapter 20: Dipolar Spectroscopy – Single-resonance Methods

Peter Gast Leiden University, Leiden, The NetherlandsChapter 2: EPR Interactions – g-Anisotropy

Daniella Goldfarb Weizmann Institute of Science, Rehovot, IsraelChapter 6: EPR Interactions – Nuclear Quadrupole CouplingsChapter 17: Hyperfine Spectroscopy – ELDOR-detected NMR

Etienne Goovaerts University of Antwerp, Antwerp, BelgiumChapter 25: Optically Detected Magnetic Resonance (ODMR)

Edgar J.J. Groenen Leiden University, Leiden, The NetherlandsChapter 2: EPR Interactions – g-Anisotropy

Howard J. Halpern University of Chicago, Chicago, IL, USAChapter 13: EPR Imaging

Jeffrey R. Harmer University of Queensland, St Lucia, Queensland, AustraliaChapter 16: Hyperfine Spectroscopy – ENDOR

Gunnar Jeschke ETH Zürich, Zürich, SwitzerlandChapter 19: Dipolar Spectroscopy – Double-resonance Methods

Hans Malissa University of Utah, Salt Lake City, UT, USAChapter 26: Electrically Detected Magnetic Resonance (EDMR)Spectroscopy

Alexander G. Maryasov V. V. Voevodsky Institute of Chemical Kinetics and Combustion, Novosi-birsk, RussiaChapter 15: FT-EPR

Eric J.L. McInnes The University of Manchester, Manchester, UKChapter 4: EPR Interactions – Coupled Spins

John J.L. Morton University College London, London, UKChapter 22: Pulse Techniques for Quantum Information Processing

Frank Neese Max Planck Institute for Chemical Energy Conversion, Mülheim an derRuhr, GermanyChapter 7: Quantum Chemistry and EPR Parameters

Thomas F. Prisner Goethe University Frankfurt, Frankfurt am Main, GermanyChapter 21: Shaped Pulses in EPR

Contributors xiii

Edward Reijerse Max Planck Institute for Chemical Energy Conversion, Mülheim an derRuhr, GermanyChapter 12: EPR Instrumentation

Anton Savitsky Max Planck Institute for Chemical Energy Conversion, Mülheim an derRuhr, GermanyChapter 12: EPR Instrumentation

Philipp Schöps Goethe University Frankfurt, Frankfurt am Main, GermanyChapter 21: Shaped Pulses in EPR

Alexander Schnegg Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin,GermanyChapter 27: Very-high-frequency EPR

Philipp E. Spindler Goethe University Frankfurt, Frankfurt am Main, GermanyChapter 21: Shaped Pulses in EPR

Stefan Stoll University of Washington, Seattle, WA, USAChapter 6: EPR Interactions – Nuclear Quadrupole CouplingsChapter 11: Pulse EPR

Joshua Telser Roosevelt University, Chicago, IL, USAChapter 3: EPR Interactions – Zero-field Splittings

Art van der Est Brock University, Ontario, CanadaChapter 1: Continuous-Wave EPR

Sabine Van Doorslaer University of Antwerp, Antwerp, BelgiumChapter 18: Hyperfine Spectroscopy – ESEEM

Shimon Vega Weizmann Institute of Science, Rehovot, IsraelChapter 8: Spin Dynamics

Stefan Weber Albert-Ludwigs-Universität Freiburg, Freiburg, GermanyChapter 10: Transient EPR

Gary Wolfowicz University of Chicago, Chicago, IL, USAChapter 22: Pulse Techniques for Quantum Information Processing

Series Preface

The Encyclopedia of Nuclear Magnetic Resonancewas originally published in eight volumes in 1996,in part to celebrate the fiftieth anniversary of the firstpublications describing the discovery of NMR (nu-clear magnetic resonance) in January 1946. Volume1 contained a historical overview and 200 articles byprominent NMR practitioners, whilst the remainingseven volumes consisted of 500 articles on a widevariety of topics in NMR, including MRI (magneticresonance imaging). A ninth volume was brought outin 2000 and two ‘spin-off’ volumes incorporating thearticles on MRI and MRS (together with some newones) were published in 2002. In 2006, the decisionwas taken to publish all the articles electronicallywith the resulting Encyclopedia becoming availableonline in 2007. Since then, new articles have beenpublished online every 3 months and many of theoriginal articles have been updated. To recognize thefact that the Encyclopedia of Magnetic Resonance isa true online resource, the website was redesignedand new functionalities added, with a relaunch in Jan-uary 2013 in a new Volume and Issue format, underthe new name eMagRes. In December 2012, a newprint edition of the Encyclopedia of Nuclear Mag-netic Resonance was published in 10 volumes (6200pages). This much needed update of the 1996 edi-tion of the Encyclopedia encompassed the entire fieldof NMR.

As part of the development of eMagRes, a seriesof printed handbooks on specific areas of magneticresonance have been introduced. The handbooks areplanned in advance by specially selected editors, andnew articles written to give appropriate complete cov-erage of the subject area. The handbooks are intendedto be of value and interest to research students, post-doctoral fellows, and other researchers learning aboutthe topic in question and undertaking relevant experi-ments, whether in academia or industry. All of the pre-vious handboooks have dealt with topics that fall underthe general area of NMR. Under the broader headingof ‘Magnetic Resonance’, we now include ‘ElectronParamagnetic Resonance’. This new handbook is thefirst that deals with electron paramagnetic resonance(EPR) and will, of course, be of interest to scientistsworking in this area but also to those across the NMRcommunity. With the exciting developments in dy-namic nuclear polarization NMR, understanding thefundamentals of EPR is essential and this new hand-book will be a welcome addition to the community.

Roderick E. Wasylishen

November 2017

Consult the eMagRes website at (www.wileyonlinelibrary.com/ref/eMagRes) for details ofall our eMagRes handbooks.

Preface

This is a multi-author graduate-level textbook onmodern EPR (electron paramagnetic resonance) spec-troscopy. In the last two decades, EPR spectroscopyhas witnessed tremendous progress, in terms of bothnew methods and new applications. These develop-ments are of course captured in the primary scientificliterature, but are scattered across many articles invery diverse journals. For a researcher entering thefield, such as a beginning graduate student or postdoc,this scatter makes it quite difficult to quickly obtain acoherent overview of the field. In particular, the widevariety of methods, encompassing continuous-waveEPR, pulse EPR, high-field methods, as well as opti-cal and electrical detection, can be bewildering to anovice. In addition, the physical principles underlyingEPR are non-trivial and are not easy material forresearchers without a substantial physics background.There is no textbook that one could hand a beginningnon-expert researcher with the words ‘Read this tolearn about EPR!’

This book is intended to at least partially fill this gap.It provides an introductory, but fairly comprehensiveoverview of the current field of EPR. The 27 chaptersof the book cover the theoretical principles, the com-mon experimental techniques, and several importantapplication areas of modern EPR spectroscopy. Thebook is not intended as a review or monograph, butrather as a graduate-level textbook. It is not a replace-ment for more advanced and comprehensive texts suchas the 2001 monograph on pulse EPR by Schweigerand Jeschke, though it does cover new developmentsnot covered in that book. Rather, it is intended as apreparatory text that will prepare – and hopefullyentice – readers to study more advanced treatmentsand the original literature.

When we started to approach leaders in the fieldabout contributing to a textbook on modern EPR, wereceived an overwhelmingly positive response. Thisdemonstrated that the need for such a book is stronglyperceived across the entire EPR research community.Many of the authors have been active in EPR educa-tion, particularly as lecturers at several EPR SummerSchools, organized by the European Federation of EPRGroups (EFEPR), and held every 2–3 years in differentplaces across Europe. Since its first edition in Caorle,Italy, in 1999, this Summer School has helped train andinspire new generations of EPR spectroscopists. Thisbook draws substantially from the experience of lec-turers at the Summer Schools.

This book would not have been possible without theimpressive commitment and tireless effort of all thecontributing authors. They not only spent significanttime and effort in putting together accessible intro-ductions to specific topics, but also put up with us aseditors. We are grateful that all contributors were ex-traordinarily patient with us as they diligently and gra-ciously accommodated our multiple rounds of revisionrequests, which ranged from complete rearrangementsto tedious notational and typographical adjustments.

Another big Thank You goes to the reviewers. Allchapters have been reviewed by at least one outsideexpert, typically the author of another chapter, in addi-tion to us. These reviewers added substantial value bypointing out misunderstandings, omissions, and oppor-tunities for pedagogical improvements. Of course, anyremaining issues are solely our fault.

It was one of our goals to create a set of chaptersthat is maximally coherent and consistent in notationand terminology, so as to minimize the potentialfor confusion for the intended audience. It turned

xviii Preface

out that it is an almost impossible feat to achievecomplete consistency. There are remaining differ-ences among chapters. For example, some utilize spinHamiltonians in energy units, whereas others preferangular-frequency units. These choices reflect the re-ality of different practices in various subfields of EPR.

We hope that this book will help beginning graduatestudents and postdocs get a grasp of the theoretical andexperimental principles of modern EPR. Of course,‘modern’ is a relative term and needs to be understoodas of the year 2017. We have no illusion at all that many

parts of this book will be rendered outdated in the nearfuture by the continuing rapid progress in experimentaltechniques and applications of EPR. Until then, wehope it is useful.

Stefan StollUniversity of Washington, Seattle, WA, USA

Daniella GoldfarbWeizmann Institute of Science, Rehovot, Israel

December 2017

Abbreviations and Acronyms

1D one-dimensionalAA Aharonov–AnandanADMR absorption-detected magnetic resonanceADP adenosine diphosphateAFC automatic frequency controlAFM atomic force microscopyAFP adiabatic fast passageAILFT ab initio ligand-field theoryAO atomic orbitalAOM angular overlap modelARS Advanced Research SystemsATP adenosine triphosphateAWG arbitrary waveform generatorBDPA 𝛼,𝛽-bisphenylene-𝛽-phenylallyl-benzolateBEBOP broadband excitation by optimized pulsesBIR4 B1 insensitive rotationBO Born–OppenheimerBP Breit–PauliBPP Bloembergen, Purcell, PoundBW bandwidthBWO backward-wave oscillatorC-NOT controlled-NOTC-PHASE controlled-phaseCAP constant adiabaticity pulseCASPT2 complete active space second-order

perturbation theoryCASSCF complete active space self-consistent fieldCC coupled clusterCESR conduction electron-spin resonanceCFT crystal field theoryCIDEP chemically induced dynamic electron

polarizationCIDME chirp-induced dipolar modulation

enhancementCLR cross-loop resonatorCP combination-peakCPMG Carr–Purcell–Meiboom–GillCPT coherence pathway transferCSR coherent synchrotron radiationCT clock transitionsCT coherence transferCW continuous waveDAC digital-to-analog converterDC direct currentDD dynamical decouplingDDBSQ 2,5-dichloro-3,6-dihydroxy-1,4-

benzosemiquinoneDDS direct digital synthesizerDEER double electron–electron resonanceDEER ESE double electron–electron resonance in

electron spin-echoDEFENCE deadtime-free ESEEM by nuclear

coherence-transfer echoesDFDMR delayed fluorescence detection of magnetic

resonanceDFG Deutsche ForschungsgemeinschaftDFT density functional theory

DKH Douglas–Kroll–HessDNP dynamic nuclear polarizationDONUT double nuclear coherence transferDPPH 2,2-diphenyl-1-picrylhydrazylDQ double-quantumDQC double-quantum coherenceDQF DQ filteringDQM double-quantum modulationDSV diameter spherical volumeEC electron coherenceED-EPR echo-detected EPREDDEER electrically detected double

electron–electron resonanceEDMR electrically detected magnetic resonanceEFG electric field gradientEIK extended interaction klystronEIO extended interaction oscillatorELDOR electron-electron double resonanceELDOR-detected

NMRelectron-electron doubleresonance-detected NMR

ENDOR electon-nuclear double resonanceEP electron polarizationEPR electron paramagnetic resonanceEPRI EPR imagingEPRM EPR microscopyESE electron spin echoESEEM electron spin echo envelope modulationET electron transferEZ electron Zeemanf.w.h.h. full width at half heightFAD flavin adenine dinucleotideFBP filtered backprojectionFD-EPR frequency-domain EPRFD-FT THz-EPR frequency-domain Fourier-transform

THz-EPRFDMR fluorescence detection of magnetic

resonanceFDMR frequency-domain magnetic resonanceFEL free-electron laserFFT fast Fourier transformationFID free induction decayFJ field-jumpFMR ferromagnetic resonanceFPGA field-programmable gate arrayFR Faraday rotatorFRET fluorescence resonance energy transferFT Fourier transformFT Fourier transformationFWHM full width at half maximumGGA generalized gradient approximationGIAOs gauge-including atomic orbitalsGM Gifford–McMahonHAS hindered amine stabilizersHF Hartree–FockHF high magnetic fieldHF hyperfineHFCs hyperfine couplings

HFEPR high-frequency and high-field EPRHFHF high-field high-frequencyHFI hyperfine interactionHFML High Field Magnet LaboratoryHOMO highest occupied molecular orbitalHS high-spinHTA high-turning-angleHWHH half width at half heighthwhm half-width at half maximumHYSCORE hyperfine sublevel correlationID instantaneous diffusionIF intermediate frequencyINS inelastic neutron scatteringIQ in-phase quadratureIRESE inversion recovery electron spin-echoISC intersystem crossingISHE inverse spin Hall effectJB Jeener–BroekaertKS Kohn–ShamKSM Kaplan, Solomon, and MottLAC level anticrossingLAN local area networkLCP left circular polarizationLDA “local density” approximationLF-DFT ligand-field density functional theoryLFT ligand-field theoryLGR loop-gap resonatorLHS left-hand sideLiPc lithium phthalocyanineLMO localized molecular orbitalLNA low-noise amplifierLO local oscillatorLP lone-pairLUMO lowest unoccupied molecular orbitalLWHH linewidth at half heightMCD magnetic circular dichroismMCDA magnetic circular dichroism in absorptionMCP magnetic circular polarizationMCPE magnetic circular polarization in emissionMEH-PPV polymer poly[2-methoxy-5-(2-

ethylhexyloxy)-1,4-phenylenevinylene]MFG modulated field gradientMHF-EPR multi-high-frequency EPRMO molecular orbitalMR magnetic resonanceMTSL methanethiosulfonato spin labelMVNA mm-wave network vector analyzerMW microwaveNARS nonadiabatic rapid scanNC nuclear coherenceNCO numerically controlled oscillatorNEP noise equivalent powerNEVPT2 second-order N-electron valence

perturbation theoryNHMFL National High Magnetic Field LaboratoryNMR nuclear magnetic resonanceNP nuclear polarizationNPA natural population analysisNQ nuclear quadrupoleNQI nuclear quadrupole interactionNQR nuclear quadrupole frequencies

NV nitrogen vacancyOCT optimum control theoryODENDOR optically detected ENDORODMR optically detected magnetic resonanceODMRI optically detected magnetic resonance

imagingODNP Overhauser dynamic nuclear polarizationOLED organic light-emitting diodeOPO optical parametric oscillatorP3HT poly(3-hexylthiophene)PAS principal axis systemPC paramagnetic centerPCET proton-coupled electron transferPDB protein data bankPDMR phosphorescence detection of magnetic

resonancePDS pulse dipolar EPR spectroscopyPE primary echopEDMR pulse electrically detected magnetic

resonancePEDOT:PSS poly(3,4-ethylenedioxythiophene)PELDOR pulse electron–electron double resonancepEPR pulse EPRPET polyethylene terephthalatePFU pulse-forming unitPID proportional–integral–derivativePMMA polymethyl methacrylatePNT perinaphthenyl radicalPO product operatorPP point-to-pointPP polaron pairPR projection reconstructionQCISD quadratic configuration interactionQDPT quasi-degenerate perturbation theoryQE quantum efficiencyQIP quantum information processingQPT quantum process tomographyRCP right circular polarizationRE refocused echoRF radio frequencyRHS right-hand sideRIDME relaxation-induced dipolar modulation

enhancementRNR ribonucleotide reductaseROCIS restricted open-shell configuration

interaction method with single excitationsROHF restricted open-shell Hartree–FockROS reactive oxygen speciesRS rapid scanRSE refocused stimulated echoRVE refocused virtual echoRWA rotating wave approximationRYDMR reaction-yield detected magnetic resonanceSC semiconductorSCRP spin-correlated radical pairSDSL site-directed spin labelingSE singlet excitonSE stimulated echoSEDOR spin echo double-resonanceSH spin HamiltonianSHF-EPR single-high-frequency EPR

SIFTER single-frequency technique for refocusingSLE stochastic Liouville equationSMART single pulse matched resonance transferSNR signal-to-noise ratioSOC spin-orbit couplingSOMF spin-orbit mean-fieldSOMO singly occupied molecular orbitalSOO spin-other-orbitSORF second-order rotating frameSOS sum over statesSPAM state preparation and measurementSPF spin projection factorSPI single-point imagingSPU signal processing unitSQ single-quantumSQC single-quantum coherenceSRSL slowly relaxing local structureSSC spin–spin couplingSSO spin-same-orbitSTE self-trapped excitonSTH self-trapped holeT4L T4 lysozymeTCSQ tetrachloro-1,4-benzosemiquinoneTD Townes–DaileyTE triplet excitonTEM transmission electron microscopeTEMPO 2,2,6,6-tetra-methyl-piperidine-1-oxyl

TEs triplet excitonsTHYCOS triple resonance hyperfine sublevel

correlation spectroscopyTHz-TDS THz time-domain spectroscopyTMBSQ 2,3,5,6-tetramethoxy-1,4-benzosemiquinoneTMI transition-metal-iontrEPR transient EPRTTA triplet–triplet annihilationTTET triplet–triplet energy transferTWT traveling wave tubeTWTA traveling wave tube amplifiersUC upconversionUHF unrestricted Hartree–FockUR universal rotationUV ultravioletUWB ultra-widebandVHF very high frequencyVHF-EPR very-high-frequency EPRVTI variable temperature insertVTVH variable-temperature and variable-fieldWAHUHA Waugh–Huber–Haeberlen sequenceWURST wideband, uniform rate, smooth truncationXC exchange-correlationZEFOZ zero first-order Zeeman shiftZF zero magnetic fieldZFS zero-field splittingZORA 0th-order regular approximation

PART AFundamental Theory

Chapter 1Continuous-Wave EPR

Art van der EstBrock University, Ontario, Canada

1.1 Introduction 31.2 Basic Design and Operation of a CW-EPR

Spectrometer 41.3 Solution Spectra 101.4 The Effect of Motion on CW-EPR

Spectra 121.5 Spectra of Solids 121.6 Concluding Remarks 15

Acknowledgment 16Further Reading 16References 16

1.1 INTRODUCTION

The vast majority of EPR data in the literature are CWfield-swept spectra collected using field-modulationdetection. Despite the many advances in pulse tech-niques, it is not feasible to collect the frequency spec-trum as the Fourier transform of the time-dependentresponse to a pulse in all but a few special cases.Hence, EPR spectra are usually measured using con-tinuous microwave irradiation at a fixed frequency,while the magnetic field is varied over a region of inter-est. The difficulty in measuring the frequency spectrumis the extremely broad spectral widths encountered in

EPR Spectroscopy: Fundamentals and Methods.Edited by Daniella Goldfarb and Stefan Stoll© 2018 John Wiley & Sons, Ltd. ISBN: 978-1-119-16299-5Also published in eMagRes (online edition)DOI: 10.1002/9780470034590.emrstm1508

EPR, which arise because electrons are not spatiallylocalized. The delocalization means that the orbitalangular momentum contributes to the total magneticmoment of the electron and that spin–orbit couplingis important. In some instances, the zero-field split-ting (ZFS) arising from spin–orbit coupling is thedominant interaction in the Hamiltonian. Moreover,the dipolar coupling between unpaired electrons canbe very strong if they are colocalized in close prox-imity on the same atom(s). A further challenge isthat the energies associated with EPR transitions aretypically much less than thermal energy (kBT), and asa result the population differences are very small andthe absorbance is weak. To overcome the problem ofweak absorbance, the signal is usually detected using aresonator, although at very high frequency direct mea-surement of the absorbance is possible. The gain insensitivity obtained using a resonator is paid for witha narrow bandwidth, which only allows the frequencyspectrum to be collected over a narrow range. Hence,the spectrum is measured by keeping the frequencyfixed at the resonance frequency of the resonator andby sweeping the magnetic field. Further sensitivityenhancement is gained by modulating the field andusing lock-in detection. This combination of sweep-ing the field and using field-modulation detection givesEPR spectra some unusual properties not encounteredin other forms of spectroscopy. In this chapter, a briefintroduction to CW-EPR spectroscopy will be given,with emphasis on important experimental features.

4 Fundamental Theory

1.2 BASIC DESIGN AND OPERATIONOF A CW-EPR SPECTROMETER

1.2.1 Field/Frequency Combinations

The microwave components needed for EPR spec-trometers are available only at specific narrowfrequency bands designated by letters. These let-ter codes were introduced during the development ofradar technology and do not carry any specific mean-ing. X-band (9–10 GHz, 0.32–0.36 T for g= 2) EPRspectrometers are by far the most common becausethe field can be easily generated with an electromag-net and microwave components are inexpensive atthis frequency. Q-band (33–35 GHz, 1.2–1.3 T forg= 2) instruments are also widespread and are thehighest frequency spectrometers that use electro-magnets. At W-band (95 GHz, 3.4 T for g= 2), theneed for a superconducting magnet adds substan-tially to the cost. Nonetheless, such spectrometershave become more common in recent years. EPRspectrometers that operate at frequencies above95 GHz are only found in a handful of laborato-ries. Low-frequency spectrometers, for example, atS-band (2–4 GHz, 0.07–0.42 T for g= 2), are alsocommercially available but not as widely used asX- and Q-band instruments. The choice of theappropriate field/frequency for a CW-EPR experimentis dictated primarily by the properties of the speciesunder investigation. Solution spectra of free radicalsare dominated by hyperfine interactions and thus highfield/frequency does not provide better resolution, butmeasurements at several frequencies can be helpful forcharacterizing the motional dynamics of the radicals.For solids or frozen solutions, the g-tensor compo-nents of spin-1/2 metal centers are often well resolvedat X- or Q-band. For most organic radicals, 95 GHzor higher is required to resolve the g-anisotropy. Forsystems with S>1/2, high field/frequency can beadvantageous for determining the ZFS parameters.

1.2.2 The Microwave Bridge

Figure 1.1 shows a schematic diagram of a simpleCW-EPR spectrometer. The microwave source is typ-ically a Gunn diode oscillator, or a klystron in olderinstruments. The emitted microwaves from the sourceare divided into signal and reference arms of themicrowave bridge to allow phase-sensitive detection.A small amount of power is also usually diverted to

a frequency counter to monitor the microwave fre-quency. The microwave power in the reference arm iscontrolled by the bias attenuator, and the relative phasebetween the signal and reference arms is controlledby the phase shifter. In the signal arm, the microwavesare passed through a circulator to the resonator and anattenuator allows the amount of power reaching thesample to be regulated. The circulator ensures that onlyreflected power returning from the resonator reachesthe detector. For tuning, the main source, or a separatevoltage-controlled oscillator source, is swept rapidlyover a narrow frequency range around the resonancefrequency of the resonator and the reflected microwavepower is monitored as a function of the frequency asillustrated in Figure 1.2. The resonator is coupled tothe bridge using an adjustable tuning element such asan iris, which allows the amount of power enteringthe resonator to be controlled. When the couplingelement is adjusted so that no power is reflected at theresonance frequency of the resonator, the resonator iscritically coupled (Figure 1.2b). The microwave sourceis then locked to the resonance frequency of the res-onator using the automatic frequency control (AFC).The spectrum is measured by sweeping the field overa region of interest and when an EPR transition comesinto resonance, microwave absorption by the sampleoccurs, the critical coupling is disturbed, and power isreflected. Thus, the reflected power reports indirectlyon the power absorbed by the sample, and because theamount of reflected power is greater than would beabsorbed by simply passing the microwaves throughthe sample, amplification of the signal is achieved.

The detector is usually a Schottky diode, whichrectifies the microwave signal to give a DC voltage.In the so-called square-law region, the voltage pro-duced by the diode is proportional to the microwavepower. However, this relationship breaks down atvery low microwave power. Because the resonator iscritically coupled and no power reaches the detectorexcept when EPR absorption occurs, the detectormust be biased to bring it into the square-law region.Thus, the reference arm not only serves to providephase-sensitive detection but also acts as a bias for thedetector.

1.2.3 The Resonator

The most common resonators used in CW-EPRare rectangular and cylindrical cavities. Split-ringand dielectric ring resonators are also sometimes

Continuous-Wave EPR 5

Detector

Phase

shifter

Bias

attenuator

Signal arm

attenuator

Circulator Preamplifier

Microwave bridge

Microwave

source

Automatic

frequency

control

Resonator

Magnet

ComputerLock−in

amplifier

100 kHz

Modulation

Frequency

counter

Figure 1.1. Schematic diagram of a simple CW-EPR spectrometer. (Reproduced from Molecular Biophysics for the LifeSciences, Electron Paramagnetic Resonance Spectroscopy, 2015, 175-213, J. H. Golbeck; A. van der Est © With permissionof Springer)

Microwave frequency

Re

fle

cte

d m

icro

wa

ve

po

we

r

(a) (b) (c)

Figure 1.2. Tuning mode patterns for different coupling regimes: (a) undercoupled; (b) critically coupled; and (c) overcou-pled

6 Fundamental Theory

used, particularly for measuring aqueous samplesat room temperature, but they are better suited fortime-resolved and pulsed EPR experiments. Somehigh-field/frequency instruments (95 GHz and higher)employ Fabry–Perot resonators.1 In all cases, theresonance mode of the resonator is chosen such thatthe magnetic lines of force are concentrated in thecenter of the cavity where the sample is placed.Figure 1.3 shows the magnetic (B1) and electric (E1)components of the microwave field in a rectangularTE102 resonator, which is widely used in X-band spec-trometers. For a given mode TElmn of a rectangularresonator, the dimensions a, b, and d of the resonatorare related to the wavelength, 𝜆, and frequency, 𝜈, ofthe microwaves by

𝜈

c= 1𝜆= 1

2

( la2

+ mb2

+ nd2

)1∕2

(1.1)

For the TE102 mode shown in Figure 1.3, dimen-sions of approximately 2 and 4 cm for a and d,respectively, correspond to 𝜆≈ 3.3 cm and 𝜈 ≈ 9 GHz.In Figure 1.3(a), the magnetic and electric lines offorce at the center of the resonator and the positionof the sample tube are shown. In Figure 1.3(b), thesquares of the amplitudes of the electric and magneticcomponents of the microwave are plotted. Figure 1.3

shows that in the center of the cavity, there is a maxi-mum in the B1 field, while the E1 field has a node. Thisdistribution of the field components is particularlyimportant when solvents with high dielectric constantssuch as liquid water are used. Such solvents absorbmicrowaves strongly through the interaction with theE1 field. To avoid this unwanted absorption, the sam-ple must be placed in a region of the cavity in whichthe E1 field is minimal and the B1 field is maximal. Forthe TE102 mode of a rectangular resonator, this can beachieved using a flat cell, which restricts the sample toa thin plane at the center of the resonator. Placing thesample in a thin capillary or bundle of capillaries alsolimits the unwanted interaction with the E1 field, espe-cially if a cylindrical resonator is used. As can be seenin equation (1.1), the dimensions of the resonator scalewith the wavelength of the microwaves or inverselywith the spectrometer frequency. Thus, as the spec-trometer frequency increases, it becomes increasinglydifficult to measure high dielectric samples owing tothe decreasing size of the resonator.

The sensitivity of the resonator is governed by thequality factor and the filling factor. The quality factoris given by Q=𝜔 /Δ𝜔, where 𝜔 is the resonator fre-quency and Δ𝜔 the width of the resonance. The fillingfactor, 𝜂, is the fraction of the total magnetic energystored by the microwave in the resonator cavity that

b

a

Sample tube

(a)

(b) a

d

dd

a

B1

B1 E1

E1

22

Figure 1.3. Magnetic and electric field intensity distribution in a TE102 rectangular resonator

Continuous-Wave EPR 7

interacts with the sample and is given by

𝜂 =∫sample B2

1dV

∫resonator B21dV

(1.2)

For a microwave field that is uniform throughoutthe resonator (a situation that is difficult to achieve inpractice), 𝜂 is the ratio of the sample volume to thevolume of the resonator. Both the filling factor andthe quality factor should be as large as possible, butoptimizing one of them often leads to a decrease inthe other. For example, increasing the sample size sothat it interacts with a greater fraction of the B1 fieldgives a larger value of 𝜂 but it also leads to dampingof the resonator and an increase in width of the reso-nance and a drop in Q. In the case of the rectangularresonator in the TE102 mode, the value of Q is highbut this is offset by a poor filling factor, particularly ifit is necessary to use a flat cell.

1.2.4 The Magnet and Lock-in Detection

As the magnetic field must be swept, it is simplest touse an electromagnet. With a gap of a few centimetersbetween the pole faces, fields up to about 1.5–2.0 Tcan be achieved with relative ease. For higher fieldstrengths, superconducting magnets fitted with sweepcoils that allow the field to be varied over a range of200–600 mT are used. In addition to the main field, asmall modulation field is applied using a further set ofcoils that are usually mounted on or in the resonator.During a measurement, the main field is swept slowlyacross the region of interest and the modulation fieldis applied, typically with a frequency of 100 kHz orlower. As a result of the field modulation, the observedEPR signal oscillates at the modulation frequency asillustrated in Figure 1.4(a). The signal also containscomponents at zero frequency and at multiples of themodulation frequency, but these are discarded whenit is amplified. In general, the signal is the sum ofcomponents that can be written2 as

s(t) ∝ ΔI cos(𝜔st + 𝜙) (1.3)

where 𝜙 is the phase difference between the signalfrom the detector and the field modulation. The ampli-tude ΔI of the oscillating signal is proportional to themagnitude of the change in amplitude of the absorptionline, between B0 −Bmod and B0 +Bmod. In the lock-inamplifier (Figure 1.1), the signal from the microwave

EP

R s

ignal am

plit

ude

B0

B0

ΔI(B0)

ΔI(

B0)

cosϕ

Bmod

(a)

(b)

Figure 1.4. Field modulation of an EPR absorption line.(a) A Gaussian absorption line and the modulated signal atseveral positions in the line. (b) The resulting derivative-likeline shape produced by the lock-in amplifier

detector is mixed with a reference signal with the samefrequency and phase as the field modulation:

r(t) ∝ cos(𝜔rt) (1.4)

The output of the mixer is

Sout(t) ∝ ΔI[cos((𝜔s−𝜔r)t + 𝜙) + cos((𝜔s +𝜔r)t+𝜙)](1.5)

The DC component of the mixer output signal,resulting from the first term in equation (1.5) with𝜔s = 𝜔r, is proportional to ΔI cos𝜙. As can be seenin Figure 1.4, the phase difference, 𝜙, is zero on therising flank of the peak, whereas it is 180∘ on fallingflank. As a result, the derivative-like line shape shownin Figure 1.4(b) is obtained. The advantage of thismethod of detection is that the DC signal can beseparated from the noise using a low-pass filter, whichgives a large increase in the signal-to-noise ratio.The first-derivative-like line shape also emphasizesshoulders in the absorption spectrum making par-tially resolved splitting easier to detect and quantify.