Pulse EPR Spectroscopy: ENDOR, ESEEM, DEER
Pulse EPR Spectroscopy:ENDOR, ESEEM, DEER3rd Penn State Bioinorganic Workshop,May/June 2014Stefan StollUniversity of Washington, Seattlestst@uw.eduSome References:BooksA. Schweiger, G. Jeschke, Principles of Pulse Electron Paramagnetic,Resonance, Oxford, 2001M. H. Levitt, Spin Dynamics - Basics of Nuclear Magnetic Resonance, Wiley, 2008ReviewsW. B. Mims, Electron Spin Echoes, in: S. Geschwind (ed.), Electron Paramagnetic Resonance, Plenum, 1972, ch.4, 263-351S. A. Dikanov, Yu. D. Tsvetkov, Electron Spin Echo Envelope Modulation (ESEEM) Spectroscopy, CRC Press, 1992Y. Deligiannakis, M. Louloudi, N. Hajiliadis, ESEEM spectroscopy as a tool to investigate thecoordination environment of metal centers, Coord. Chem. Rev. 204, 1-112 (2000)1
MössbauerXAS/XES14400 eV7000 eV(57Fe)(Fe K-edge)UV/Vis2 eV(600 nm)IR/Raman0.01 eV(800 cm-1)EPR0.00004 eV(10 GHz 40 μeV)ENDOR etc.0.000000004 eV(1 MHz 4 neV)2
Coupled spinsCrystallography view:Structural cartoonMagnetic resonance view:System of coupled H14N1 unpaired electron spin on Fe3 (S 1/2)all magnetic nuclei (1H, 2H, 14N, 15N, 13C, .)nonmagnetic nuclei invisible (12C, 16O, 32S)3
Information from cw EPR and pulse EPRPulse EPR: Set of high-resolution EPR techniques todetermine local structure around a spin center (metal ion, metal cluster, or radical)CW EPR: low resolution- metal center, (ligands)- strongly coupledmagnetic erspin center1H1H1H1HPulse EPR: high resolution- weakly coupled magneticnuclei (1H, 14N, 13C, etc)- ligands in first andsecond ligand sphere- hydrogen bonds- distances to other spincentersmagnetic nuclei within a few Åelectron spins with a few nm4
Hidden details in solid-state CW EPR spectrafrozen solutionCW EPR "powder" spectrumas recordedOrigins of static line broadenings1. anisotropies of g tensor,A tensor, D tensor2. site-to-site structural heterogeneityresulting in g, A, D heterogeneity3. unresolved splittings- hyperfine coupling to magneticnuclei- coupling to other electron spinsintegratedHidden structuresingleorientation(unresolvable with CW EPR)pulse EPR5
1. BasicsCW vs. pulse EPRSample and spectrometerResonators and bandwidthsPulses, excitation widthOrientation selectionFIDs and EchoDeadtime, Relaxation1H1H14N14N14N2. Interactions1HNuclear Zeeman interactionHyperfine interactionCoupling regimesNuclear spectraQuadrupole interaction14N1H14N14N3. ExperimentsField sweepsENDORESEEMHYSCOREDEER13Ce1He6
Comparison CW and pulse EPRCW (continuous-wave) EPR- continuous excitation- low microwave power (μW-mW)- absorption spectroscopy- measures steady-state responseduring excitation- low resolutionPulse EPR- pulse excitation- very high microwave power (W-kW)- emission spectroscopy- measures transient responseafter excitation- high resolutionEPR frequencies and fieldsEPR unit conversions-Energy units:30 GHz 1.00 cm-1 0.124 meV 1.20 J/molField to frequency: 1 mT 28 MHz @ g 2Field units:1 mT (millitesla) 1 G (gauss)7
How to make samples for EPRSample quantity and positioning- know O.D. and I.D. of EPR sample tube- fill no more than fits in the resonatorThings to watch out for:(1) Unwanted dioxygen- oxygen-sensitive samples- dissolved dioxygen enhances relaxation- important for liquid samples- remove by freeze/pump/thaw, or Ar purging(2) Other paramagnetic centers- avoid paramagnetic impurities- run controls on buffers and reagents- use quartz ("fused silica") tubesSample concentrationmagnetically dilutecw EPR: 1 mMpulse EPR: ESEEM/ENDOR: max 5 mMDEER: less than 200 μMToo concentrated?- broadened spectra- enhanced relaxationToo dilute?- Not enough signal.(3) Aggregation- due to slow freezing, solvent crystallization- enhances relaxation, shortens Tm, T1- add glassing agent (glycerol, sucrose), freeze fast(4) Dielectric constant- high r solvents kill mw fields in resonator- sensitivity loss- worst: liquid water (static r 80 at 20 C)- frozen water: ( r 3.15 at 0 C)EPR measurement temperatures (approx)organic radicals30-200 Kmononuclear metal centers5-40 Koligonuclear metal clusters2-10 K8
Frozen solutions; lab and molecular frameMost common form of bioinorganic EPRsamples: frozen aqueous solutions of proteins.B0Frozen solution random uniform distribution of static orientationsof the molecules, like a dilute powder.B1Lab frame- fixed in laboratory- z(lab) along static field B0- x(lab) along oscillatingmicrowave field B1moleculesRelative orientationEuler angles 𝜑, 𝜃, 𝜒Molecular frames- fixed in molecules- most commonly molecularsymmetry frame or g tensorframez(mol)z(lab)y(lab)x(lab)y(mol)x(mol)9
cw sourcespulse or0-60dBmw1PFUphasemw receivermw transmitterPulse EPR spectrometeramplifierslow-noiseprotectionamplifier fierrf1digitizercomputerlow mw powerPFUB0att.sampleresonatorcryostatENDOR transmitterhigh mw powerSNvideo signal10
Pulse EPR spectrometer11
Resonators and bandwidthWhy to use a resonator? concentrates microwave magneticfield (B1) on sample; higher signalintensity separates microwave electric fieldfrom sample; lower sample heating- downside: works only for a verynarrow range of frequenciesΔ𝜈Types of resonators1. dielectric (ring, split-ring)2. cavity (rectangular, cylindrical)3. loop-gap resonatorsResonator Q factor and bandwidth𝜈0𝑄 Δ𝜈resonator frequencybandwidth (undercoupled)Q factor; range: 100 - 10000cw EPR: high sensitivity high Q, critically coupledpulse EPR: large bandwidth high Q overcoupled, orlow Q critically coupled12
Microwave irradiation reorients spinsprecession𝑩0nutationequilibriumrotating frame:follow precession(l running alongwith the merry-goround)non-equilibriumResonance condition:mw frequency precession frequency(Larmor or Zeeman frequency)ℎ𝜈mw 𝑔𝜇B 𝐵Planck constant6.626·10-34 J smagnetic fieldmw frequencyg factorBohr magneton9.274·10-24 J/T71.447732𝜈mw𝐵 𝑔GHzmT1 mT 10 G1 G 2.8 MHz @ g 213
Pulses and excitation bandwidthRectangular pulseπ/2, 90 flip anglepulse amplitudetppulse lengthcarrierfrequencyMicrowave pulses (for electron spins)frequency 9-10 GHz, 34-36 GHz, 95 GHzshort5-20 nsmedium20 ns-200 nslong200 ns-several μsRF pulses (for nuclear spins)frequency 1-200 MHzshort10 μslong100 μsPulse excitation bandwidth- excitation bandwidth approx.distance between zeroes: 2/tp(for pi and pi/2 pulses)- example: 10 ns pulse 200 MHz14
Spin gymnastics and Energy level diagramsEnergy level diagramB0EEClassical description:Quantum description:Bloch equations (limited to a single spin)Liouville-von Neumann equation (general)
Spectral width and pulse excitation bandwidthEPR absorption intensityspectral width: several GHzg 2.00mw pulse at 9.5 GHzpulse hits spins within10-100 MHz of mw frequencyg 2.55g 1.83frequency (GHz) Only a small fraction of spins in the sample are excited.They have resonance frequencies close to the mw frequency.They have specific orientations orientation selection16
Orientation selectionResonance frequency depends onorientation relative to field.Different orientation different resonance frequency17
Free induction decay (FID)90 deadtimeFIDB0fast spinsslow spinsspins in thermalequilibriumpulse rotates spins by90 degreesspins precess withdifferent frequenciesall are in phasedephasing18
Dead timedead timeμWkWkWsignal cannotbe measured!ττμWkWkWττDead time:- time after pulses during which powerlevels are too high to openthe sensitive receiver- due to 1) ringdown in cavity2) reflections in spectrometer3) recovery of receiver protection- typical value: 100 ns at X-bandshorter at higher frequencies- affects all pulse EPR experimentsConsequences- short values of τ cannot be accessed- loss of broad lines- phase distortions in spectrum- spurious features in spectrum1 kW 1 mile1 μW 0.0016 mm19
Two-pulse echoalso called primary echo or Hahn echo90 pulse two-pulse echo( 2x FID)180 pulse FIDB0thermalequilibriumrotated by 90oprecessing anddephasingdephasedrotated by 180oprecessing andrephasingrefocused20
Three-pulse echoalso called stimulated echo90 pulse 90 pulse90 pulseTthree-pulseecho FIDB0complexmotionthermalequilibriumrotated by 90oprecessing anddephasingdephased"stored"along -z,precessing(approximate)precessingand rephasingrefocused21
RelaxationRelaxation constantsT1: longitudinal relaxation (spin-lattice relaxation)T2: transverse relaxation (spin-spin relaxation)Tm: phase memory time (similar to T2)Spectral diffusion- spin center randomly changesfrequency during pulse sequence- leads to dephasing and loss of signal- contributes to Tmcw EPR- choose low mw power that avoids saturation- choose scan rates, modulation amplitudes andfrequencies that avoid passage effectspulse EPR- fast relaxation prevents long pulse experiment- slow relaxation prevents fast repetition22
1. BasicsCW vs. pulse EPRSample and spectrometerResonators and bandwidthsPulses, excitation widthOrientation selectionFIDs and EchoDeadtime, Relaxation1H1H14N14N14N2. Interactions1HNuclear Zeeman interactionHyperfine interactionCoupling regimesNuclear spectraQuadrupole interaction14N1H14N14N3. ExperimentsField sweepsENDORESEEMHYSCOREDEER13Ce1He23
Magnetic nuclei and their interactionsNuclear spin Hamiltonian (for one nuclear spin coupled to one electron spin):ℋnuc 𝑔n 𝜇N 𝑩 𝑰 ℎ 𝑺 𝑨 𝑰 ℎ 𝑰 𝑷 𝑰Nuclear Zeeman interactionMagnetic interaction withexternal applied magnetic field(static or oscillating)Hyperfine interactionMagnetic interaction ofnucleus with field dueto electron spinB magnetic fieldS electron spinI nuclear spinNuclear quadrupole interactionElectric interaction betweennonspherical nucleus andinhomogeneous electric fieldOnly for nonsphericalnuclei (spin 1/2)!Two contributions:1. through-bond(isotropic; "Fermi contact")2. through-space(anisotropic; dipolar)24
Nuclear Zeeman Interactionmagnetic interaction of magnetic nucleus with external applied magnetic field (static, oscillating)ℋ 𝑩0 𝝁nuc 𝑔n 𝜇N 𝑩0 𝑰nuclear Bohr magnetonmagnetic nuclear nuclear 5.0508·10-27 J/Tmagneticfieldg factormomentNuclear precession frequency:𝜈I 𝑔n 𝜇N 𝐵0 /ℎNMR: gyromagnetic ratio 𝛾 𝑔n 𝜇N /25/21/27/23/2%69319.51002.11001.1no spin: 56Fe, 58Ni, 60Ni, etc.gn 1.484 1.588- 0.3147 1.3819 0.1806 1.318- 1/2%99.990.0199.60.41.10.04100gn 5.58569 0.857438 0.403761- 0.566378 1.40482- 0.757516 2.2632 6.5oppositesignno spin: 12C, 16O, 32S, etc.25
Hyperfine coupling: 1. Fermi contact interactionOrigin:Small, but finite, probability of finding an electronat position of nucleus (s orbitals only!)ℋ ℎ 𝐴iso 𝑺 𝑰one (unpaired)electron𝐴iso 2 𝜇0 𝜇B 𝜇N𝑔e 𝑔n 𝛹0 (𝒓n )3ℎscales* with 𝑔nmore general𝐴iso Spin1/211/21/2Aiso(100%)1420 MHz1811 MHz, 1538 MHz-2540 MHz, -2158 MHz3777 MHz, 3109 MHzalternative: compare to quantumchemical estimates(SI units, Aiso in Hz)spin density atposition of nucleus1 𝜇0 𝜇B 𝜇N𝑔e 𝑔n 𝜎𝛼 𝛽 (𝒓n ) 𝑆𝑧3ℎChemist's interpretation:spin population in atom-centered orbitals relativeto 100% orbital occupancy via reference AisoNucleus1H14N15N13C2 1* possible isotopeeffect for 1H/2HReasons for non-zero Aiso(1) ground-state open s shell(2) valence and core polarizationse.g 3d 2s, 3d 1s(3) configurations with open s shellExample:Aiso(1H) 20 MHz 20/1420 1.4%26
Hyperfine coupling: 2. Through-space dipolar couplingB0ℋ ℎ𝑺 𝑻 𝑰magnetic dipolefield of nucleuselectron spinmagnetic dipolefield of electron mn nucleus𝑻 𝑇 meelectronnuclear spinrBnBe, Bhf 𝑇 1 000 1 000 2𝜇0𝑔e 𝑔𝑛𝑇 𝜇 𝜇 4𝜋ℎ B N 𝑟 3- orientation dependence- distance dependence 2𝑇 T dipolar hyperfine matrixeigenvalues: principal valuesThis assumes electron is localized.In delocalized systems, integrate over electron spin density.27
Combining Hyperfine and Zeeman: Local fieldsB0B0Zeeman fieldBtottotal fieldBhfhyperfine fielddue to electronspinnucleuselectronat equilibrium, nuclear spinaligns along total field28
Combining Hyperfine and Zeeman: Local fieldschanged!Btottotal fieldflipped!B0B0Zeeman fieldBhfhyperfine field dueto electron spinnucleuselectron29
Hyperfine Zeeman: Nuclear frequenciesexternal (Zeeman)magneticB0 fieldtotal field actingon the nucleusBtot Ihyperfinefield linecomponent of hyperfine fieldperpendicular to external field(nonsecular)𝐵 𝐴 𝐴 sin𝜃 cos𝜃 3𝑇 sin𝜃 cos𝜃𝑚𝑆 𝐵𝑚𝑆 𝐴Bhfcomponent of hyperfine fieldparallel to external field(secular)𝐴 𝐴 cos 2 𝜃 𝐴 sin2 𝜃 𝐴iso 𝑇 (3cos2 𝜃 1)can be neglected at high fieldfor small hfcNuclear frequencies:𝜈 𝑚𝑆 (𝜈I 𝑚𝑆 𝐴)2 (𝑚𝑆 𝐵)2𝜈I 𝑔n 𝜇N 𝐵0 /ℎ𝑚𝑆 1/230
Hyperfine vs. Zeeman: Three regimesIntermediate coupling𝑩0 𝑩hfWeak coupling𝑩0 𝑩hfStrong coupling𝑩0 𝑩hfmatching fieldsBtot( )Btot( )Btot( )Btot( ) Btot( )Btot( )nucleus angle between twototal field vectors: v u 𝜈I 𝐵2sin 𝜉 𝜈𝛼 𝜈𝛽 2 𝑘k modulation depth parameter(important in ESEEM)31
Nuclear frequencies and powder spectra𝜈 𝑚𝑆 (𝜈I 𝑚𝑆 𝐴)2 (𝑚𝑆 𝐵)2neglecting 𝑚𝑆 𝐵 term(valid for weak and strong coupling only)𝜈 𝑚𝑆 𝜈I 𝑚𝑆 𝐴 Weak coupling regime𝜈I 𝑔n 𝜇B 𝐵0 /ℎ𝜈I 𝑚𝑆 𝐴 centered at νI, split by AStrong coupling regime𝜈I 𝑚𝑆 𝐴 centered at A/2, split by 2νI32
Nuclear Quadrupole Interaction: Basics(1) Some nuclei have electric quadrupole moment- Nuclei with spin 1/2 are nonspherical, described by an electric quadrupole moment Q. Nucleus2H14N33S63Cu17O55Mn Q 0prolate nucleusegg shapedQ 0oblate nucleusburger shapedSpin113/23/25/25/2Quadrupole moment (b) 0.00286 0.020441 b (barn)- 0.0678 100 fm2- 0.22- 0.02558 0.33- Spin is tied to nuclear shape!(2) Inhomogeneous electric fields in molecules: electric field gradient (EFG) at nuclei(3) Quadrupole nuclei haveorientation-dependentenergy electric, notmagnetic interaction! highest energytorquelowest energy33
Nuclear Quadrupole Interaction: MathematicsElectric field gradient (EFG) at nucleusEFG is a 3x3 matrix V𝑉𝑥𝑥 , 𝑉𝑦𝑦 , 𝑉𝑧𝑧Principal values𝑉𝑧𝑧 𝑉𝑦𝑦 𝑉𝑥𝑥𝑉𝑥𝑥 𝑉𝑦𝑦 𝑉𝑧𝑧 0Largest componentRhombicity𝑉𝑧𝑧 𝑒𝑞𝑉𝑥𝑥 𝑉𝑦𝑦𝜂 𝑉𝑧𝑧0 𝜂 1sign of q ambiguousfor 𝜂 1Imidazole ligands: EFG at 14N dependson electron populations of 2px,y,z orbitalsSpin Hamiltonian termInteraction of quadrupole moment with EFGℋ ℎ𝑰 𝑷 𝑰nuclear spin vectorquadrupole tensor00𝑒 2 𝑄𝑞/ℎ (1 𝜂)𝑷 0 (1 𝜂) 04𝐼(2𝐼 1)00 2Experimental parameters:e2Qq/hand EFG asymmetryquadrupolemomentEFG strengthD2O: e2Qq/h 0.213 MHz, η 0.1234
Nuclear Quadrupole Interaction: 14N, 2H, 17O, 33S2H33SI 1 gives 2x3 linesstrong hf couplingsmall nq splittingmCoM reductase, 33S HYSCOREJACS 2005 127 17744 linkLength of H-bonds to semiquinones𝐾 𝑎 17OI 5/2 gives 2x6 lines𝑏3𝑟O DJ. Biol. Chem. 2012 287 4662 link14NEFG depends on electron populationsNx,y,z of 2px,y,z orbitalsvery useful for imidazole ligands!Aconitase, 17O ENDORJ. Biol. Chem. 1986 261 4840 link35
1. BasicsCW vs. pulse EPRSample and spectrometerResonators and bandwidthsPulses, excitation widthOrientation selectionFIDs and EchoDeadtime, Relaxation1H1H14N14N14N2. Interactions1HNuclear Zeeman interactionHyperfine interactionCoupling regimesNuclear spectraQuadrupole interaction14N1H14N14N3. ExperimentsField sweepsENDORESEEMHYSCOREDEER13Ce1He36
EPR spectrum: Field sweep spectraFID-detected field sweep90 deadtimeFIDintegrateFID- works only if FID is longer than dead time- use long microwave pulsetwo-pulse echotau 140 nsEcho-detected field sweep90 echo180 ττtwo-pulse echotau 300 nsAlexey SilakovDistortions due to tau-dependent nuclear modulation of echo amplitude37
Relaxation measurementsT1: Inversion recoverymeasure echo intensity as a function of t180 90 180 invertedechoτtτ𝑉 𝑡𝑉 0 1 2exp( 𝑡/𝑇1 )Other methods for T1: saturation recovery, three-pulse echo decayT2, Tm: Two-pulse echo decay90 echo180 τmeasure echo intensity as a function of τ𝑉 𝑡𝑉 0 exp( 2𝜏/𝑇2 )- approximately exponential decay- phase memory, Tm, rather than T2 is obtained- best with small flip angles (avoids instantaneous diffusion)38
Nuclear spectra: Mims ENDORMims ENDOR: rf pulse frequency is varied90 180 90 echoBasics- use short hard mw pulses- acquire echo intensity asfunction of rf pulse frequencymwτrf180 rf frequencytrfτSpectrum- echo intensity decreaseswhenever rf frequency isresonant with a nucleartransition- upside-down representationBlind spots- intensity is modulatedwith -dependent sawtoothpattern, centered at Larmorfrequency and with period 0.5/ ("Mims holes")- central hole at Larmor frequency!works best for small hyperfinecouplings less than about 1/ (typically 2H, 13C)39
Nuclear spectra: Davies ENDORDavies ENDOR: rf frequency is varied180 90 180 invertedechomwrftp180 rf frequencytrfττBasics- based on inversion recovery- use medium/long mw pulses- acquire echo intensity as functionof rf pulse frequencySpectrum- fully inverted echo is baseline- decrease in echo intensity whenrf frequency is resonant withnuclear transitionBlindspots- no -dependent blindspots- central hole at Larmor frequency- width proportional to 1/tp- suited for larger hf couplings- for small couplings, use long pulses(narrower central hole)40
ENDOR example: Weak coupling 2H, 13CS-adenosyl-methionine (SAM)binding to [4Fe4S] cluster inpyruvate formate-lyase activating enzyme (PFL-AE)Broderick & HoffmanJACS 2002 124 3143 link2HCW EPR13CENDOR𝒈 -SAMENDOR𝒈 SAM𝒈 𝒈 𝒈 𝒈 41
ENDOR example: Strong coupling 55Mn[Mn4Ca] cluster in PSIIS2: Mn(III,III,III,IV)55MnJACS 2000 122 1092642
Nuclear spectra: ESEEMelectron spin echo envelope modulationTwo-pulse ESEEM: is varied90 V2pprimary (Hahn)echo180 modulationdepth/amplitudeV2pτττThree-pulse ESEEM: T is varied90 180 stimulatedecho90 V3pmodulationdepth/amplitudeV3pτTττ T- modulation of echo amplitude as a function of interpulse delay(s)- modulation with nuclear resonance frequencies and their combinations- modulation due to hyperfine coupling of electron spin with surrounding nuclei- modulation depth depends on hyperfine coupling, quadrupole coupling, nuclear Zeeman43
ESEEM: Pictorial model(1) Electron spin flip induces nuclear precessionBtot( )B0B0Btot( )suddenelectronspin flipBhf( )stationarynuclear spinBhf( )nuclear spinprecession!"forbidden" transition!- Electron spin flip inverts hyperfine field at nucleus.- This changes the total local field and the quantization direction of the nucleus.- The change is sudden on the timescale of the nucleus.- The nucleus will precess around the new field direction.44
ESEEM: Pictorial model(2) Nuclear precession modulates electron precessionBtot( )B0B0Bhf( )ΔB(t)precessiontime-dependentprecession frequency!- precessing nucleus causes a time-dependentfield along z felt by the electron- electron precession frequency becomestime dependentL. G. Rowan, E. L. Hahn, W. B. Mims, Phys. Rev. A 137, 61-71, 1965D. Grischkowsky, S. R. Hartmann, Phys. Rev. B 2, 60-74,1970S. A. Dikanov, Yu. D. Tsvetkov, ESEEM Spectroscopy, CRC Press, 199245
ESEEM: Data processing46
Nuclear spectra: ENDOR vs. ESEEMENDORTwo-pulse ESEEMThree-pulse ESEEMk/2k/2k 1 cos β 4𝜈𝛼 𝜈𝛽𝜈𝛼𝜈𝛽𝜈𝛼 𝜈𝛽𝜈𝛼 k / 4equal intensitiesk 1 cos α 4𝜈𝛽𝜈𝛼𝜈𝛽 k / 4Tm decay (fast)sum and difference frequenciesno blind spotsT1 decay (slower)no sum and difference frequenciesblind spots adds to dead time47
Nuclear spectra: ENDOR vs. ESEEMENDOR:- maximum intensity at 90 - mimimum intensity at 0 ESEEM:- no intensity along principal axes- maximum intensity off-axisdifficult to measurebroad lines with ESEEM!only central part visible!Situations for best intensitiesESEEM enhanced by nuclear statemixing; most intense in matchingregime, i.e. low nuclear frequenciesENDOR enhanced by hyperfineenhancement, most intense forhigh nuclear frequencies48
HYSCORE: A two-dimensional ESEEM experimentHYSCORE: t1 and t2 is varied90 180 90 HYSCORE hyperfinesublevel correlationHYSCOREecho90 V(t1,t2)π pulse should beas short as possibleτt12D time domain (TD)t2τ2D frequency domain (FD)2nd quadrant3rd quadrant(identical to 1st)echo intensity as afunction of t1 and t21st quadrant4th quadrant(identical to 2nd)only 1st and 2nd quadrant are shown49
HYSCORE: Data processingTime-domain datat2 baseline correctiont1 baseline correction2D windowing212xtapertowardszero2x3Spectrum42D Fourier transform2D zero filling50
HYSCORE: SpectraQuadrupole splittingsWeak couplingStrong coupling𝜈α𝜈α𝜈β𝜈βsecond quadrantfirst quadrant𝜈β 𝜈α𝜈α𝜈α𝜈β𝜈βPowder spectra 𝜈α 𝜈β51
HYSCORE: Blind spotsConsequences:- peaks are missing- peaks are distorted- danger of wrong assignmentBlind spots:- τ-dependent intensity factor: sin(𝜋𝜈1 𝜏)sin(𝜋𝜈2 𝜏)- intensity drops to zero at frequenciesthat are multiples of 1/𝜏- both dimensions, all quadrantsExample:𝜏 120 ns1/𝜏 8.33 MHz 3/𝜏 2/𝜏 1/𝜏01/𝜏2/𝜏Remedies:- acquire spectra with severaldifferent tau values- use blind-spot free advancedtechniques3/𝜏3/𝜏2/𝜏1/𝜏052
HYSCORE: Example[FeFe] hydrogenase modelAngew. Chem. 2011 50 1PCCP 2009 11 659253
ENDOR/ESEEM at higher fields and frequenciesENDOR/ESEEM frequency ranges for common isotopes:Advantages- separation of isotopes- weak coupling regime forlarge hyperfine couplings- increased sensitivity forlow-gamma nuclei- larger spin polarization- larger orientation selectivityDisadvantages- less signal for stronglyanisotropic systems- less available power- longer pulsesPulse EPR powerX-band 9-10 GHzQ-band 34-36 GHzW-band 95 GHzD-band 130 GHzG-band 263 GHz1000 W10 W0.4 W0.125 W0.020 W54
DEER: Distances between electron spinsDEER double electron-electron resonance(also called PELDOR pulse electron double resonance)mw2AB0mw1B4-pulse DEER: t is varied90 180 Echo modulationDipolar coupling betweentwo electron spins analogousto dipolar hyperfine coupling𝜈ee𝜇0 𝜇B21 𝑔 𝑔4𝜋ℎ 𝐴 𝐵 𝑟 3A probe spin, mw1B pump spin, mw2180 refocusedtwo-pulseechotwo-pulseechomw1τ1τ1180 τ2τ2tmw2pump spin uppump spin down55
DEER: Data analysisDistance distributionEcho modulationcalled formfactor afterbackgroundcorrectionLeast-squares analysis(Gaussian fit orTikhonov regularization)Fouriertransformestimation diagramDipolar spectrum𝜈ee 52 MHz(𝑟/nm)3(gA gB 2.00)56
DEER: ExamplesArrangement ofiron-sulfur clustersComplex 1 (NADH:quinone oxidoreductase)Hirst et al; PNAS 2010 107 1930 linkAnnu.Rev.Biochem. 2013 82 551 linkConformational change upon substrate bindingCytochrome P450camStoll et al; PNAS 2012 109 12888 link57
What you can learn from EPR dataMeasurementsStructural informationEPR spectrum (CW or pulse)type of spin center (metal, radical)g tensorspin quantum numberhyperfinedelocalization of spin onto ligandszero-field splittingcoordination geometryrelaxation timesoxidation state, spin multiplicityNuclear spectra (ESEEM/ENDOR)nuclear Zeeman frequencyisotropic hyperfineanisotropic hyperfinenuclear quadrupoleDipolar spectra (DEER)dipolar couplingtype of ligand nucleiligand protonation stateslocation of protonsoxidation state assignment in clusterscoordination mode of ligandsdistance between spin centers58
Aug 07, 2015 · Energy level diagram E E Spin gymnastics and Energy level diagrams . Two-pulse echo 90 pulse 180 pulse two-pulse echo ( 2x FID) FID thermal o equilibrium rotated by 90 . frequency during pulse sequence - leads to dephasing and loss of signal - contributes to T m
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to the understanding of many biological systems. In addition to those systems in which vanadium naturally occurs, the vanadyl ion has found favor as a spectroscopic probe in place of spectroscopically silent cations, EPR, ESEEM, and ENDOR spectroscopies are the tools of choice for examining these paramagnetic systems.
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