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NMR of Paramagnetic MoleculesKara L. BrenUniversity of Rochester

Outline Resources Examples of effects on spectra What we can learn (why bother?) NMR fundamentals (review) Relaxation mechanisms in NMR Effects of unpaired electrons on relaxation Effects of unpaired electrons on chemical shifts2016PSUBioinorganicWorkshop,Bren2

Resources Bertini & Luchinat, “NMR of Paramagnetic Molecules inBiological Systems,” 1986, Benjamin/Cummings: MenloPark. ISBN: 0-8053-0780-X Bertini & Luchinat, “NMR of Paramagnetic Substances,”Coord. Chem. Rev. 1996, 150, 1-296. Banci, “Nuclear and Electron Relaxation. The MagneticNucleus-unpaired Electron Coupling in Solution,” 1991, VCH:Weinheim. ISBN: 3-5272-8306-4 Bren, “NMR Analysis of Spin States and Spin Densities,” inSpin States in Biochemistry and Inorganic Chemistry:Influence on Structure and Reactivity, (Eds: Swart & Costas),2016, Wiley: Chichester. DOI: hop,Bren3

Outline Resources Examples of effects on spectra What we can learn (why bother?) NMR fundamentals (review) Relaxation mechanisms in NMR Effects of unpaired electrons on relaxation Effects of unpaired electrons on chemical shifts2016PSUBioinorganicWorkshop,Bren4

Effects of Unpaired ElectronsHorse ferricytochrome c2016PSUBioinorganicWorkshop,BrenS 1/25

Effects of Unpaired ElectronsHorse ferricytochrome cS 1/2Heme methyls2016PSUBioinorganicWorkshop,Bren6

Effects of Unpaired ElectronsCN-Fe(III) cytochrome c, D2O* heme methyls**S hromec,c,DD2O2OH 2O***FeN*NHHis2520151050-5-10 -15δ, ppmJACS 1995, 80672016PSUBioinorganicWorkshop,Bren7

Effects of Unpaired ElectronsH. thermophilus Fe(III)M61A cyt cS 1/2, 5/25 COH215 CFe25 CNNH35 CHisa,b,c,d heme methyls45 CBren group2016PSUBioinorganicWorkshop,Bren8

Effects of Unpaired ElectronsP. aeruginosa Cu(II) azurinS 1/2HisH 2CMetSNCysSCuNHHisH 2CNO6050403020100NHδ, ppmJACS 2000, 37012016PSUBioinorganicWorkshop,Bren9

Effects of Unpaired ElectronsS 1Ni(II) azurinBiochemistry 1996, 18102016PSUBioinorganicWorkshop,Bren10

Effects of Unpaired ElectronsT. thermophilus CuA domainCu(I)Cu(II) S 1/2pH 8.0, H2OpH 4.5, H2OHNHisCysNHSJACS 1996, tOSNNH11

Outline Resources Examples of effects on spectra What we can learn (why bother?) NMR fundamentals (review) Relaxation mechanisms in NMR Effects of unpaired electrons on relaxation Effects of unpaired electrons on chemical shifts2016PSUBioinorganicWorkshop,Bren12

What Can We Learn? Metal oxidation state and spin state Electron spin relaxation time (estimate) Presence of low-lying excited states Pattern and amount of electron spin delocalizationonto ligands; hyperfine coupling constants Presence of hydrogen bonds Magnetic anisotropy, magnetic axes Structural refinement is possible (In addition, 3D structure, exchange phenomena,dynamics, etc.)2016PSUBioinorganicWorkshop,Bren13

Outline Resources Examples of effects on spectra What we can learn (why bother?) NMR fundamentals (review) Relaxation mechanisms in NMR Effects of unpaired electrons on relaxation Effects of unpaired electrons on chemical shifts2016PSUBioinorganicWorkshop,Bren14

NMR FundamentalsSome nuclei have spin angular momentum and anassociated magnetic moment, µI.µIµI gN (e/2mp) IgN (1H) 5.5856947 µI (h/2π) I[I(I 1)]1/2Need nucleus with non-zero spin (I 0)Examples:1H, 13C, 15N, 19F, 31P2H, 14N,(I 1/2)(I 1)Herein we will base examples in nuclei with I 1/22016PSUBioinorganicWorkshop,Bren15

NMR FundamentalsA nucleus with spin I has states with associated MIvalues where MI -I, I 1, IWhen I 1/2, MI 1/2In the absence of a magneticfield, states with different MI aredegenerate and their magneticmoments µ orient randomly2016PSUBioinorganicWorkshop,Bren16

NMR FundamentalsApplying a magnetic field lifts this degeneracy. 1H with MI -1/2 have a higher energy and 1H with MI 1/2 have alower energy.The nuclear spins align with (MI 1/2) or opposed to (MI -1/2) theapplied magnetic field:B0The z component of themagnetic moment is shown andis MIh/2π2016PSUBioinorganicWorkshop,Bren17

NMR FundamentalsThe energies of the nuclei in the magnetic field are:E -MIµ Β0/ITransitions may be induced between MI states.The selection rule is ΔMI 1MI -1/2E0ΔΕ µB0/I hνMI 1/2B02016PSUBioinorganicWorkshop,Bren18

NMR FundamentalsThe energies of the nuclei in the magnetic field are:E -MIµ Β0/IΔΕ µB0/I hνTraditionally, the magnetogyricratio γ (T-1 s-1) is used in NMR:γ µ 2π/hI, soB0ΔE γB0/2π hν2016PSUBioinorganicWorkshop,Bren19

NMR FundamentalsΔΕ γB0/2πA transition between MI statescorresponds to a “spin flip.”At equilibrium there is a smallexcess of spins aligned with thefield:N(-1/2)N( 1/2)B0 exp [–(E-1/2 – E 1/2)/kBT]2016PSUBioinorganicWorkshop,Bren20

NMR FundamentalsWe can consider a net magnetization vector for thesample. Exciting the sample decreases the different in upand down spins, tipping this vector, after which it returns toequilibrium:MzB0MzPulse (By)zzRelaxation (T1, T2)yyxzxyxPulse width is time of pulse; adjust time to change tip angle (i.e. 90 pulse)2016PSUBioinorganicWorkshop,Bren21

NMR FundamentalsMz is undergoing precession throughout this process –think of a cone rather than just the Mz vector tipping –precession frequency is the Larmor frequency:ω0 γB0 (rad) or ν0 γB0/2π (Hz)(Larmor equation)MzB0Pulse (By)zzyyx2016PSUBioinorganicWorkshop,Brenx22

NMR FundamentalsThe observable signal is recorded in the xy plane duringrelaxation. T1 relaxation along z axis; T2 relaxation inxy plane. Precession frequency is observed.Record FID: signalin xy planezB0MzRelaxation(T1, T2)yxzyxtime2016PSUBioinorganicWorkshop,Bren23

NMR FundamentalsThe observable signal is recorded in the xy plane duringrelaxation. T1 relaxation along z axis; T2 relaxation inxy plane. Precession frequency is observed.Line widthΔν 1/(πT2)FID: time-domainsignal in xy planeFourier op,Bren24

NMR FundamentalsThe chemical shift results from small deviations from ν0Chemical shift:δ (ppm) 106 [ν(obs) - ν(ref)]/ν(ref)The chemical environment of nuclei (especiallycirculation of electrons) leads to deviations of ν(obs)giving different chemical shifts.Unpaired electrons can have very large effects onchemical shifts through different mechanisms.2016PSUBioinorganicWorkshop,Bren25

Electrons vs. NucleiQuantitySpinMagnetic momentGyromagnetic ratioTransition energy infield B0ElectronS 1/2µeγe µB ge/hhν ge µB B0I 1/2µIγI µI gI/hhν h γI B0/2πTransition betweenstatesMS 1/2MI 1/22016PSUBioinorganicWorkshop,Bren1H26

Electrons vs. NucleiTwo major differences: Electrons have a larger magnetic moment µB 658 µI(1H) Larger resonance frequency More efficient relaxation Electrons are in orbitals Delocalization Spin-orbit coupling2016PSUBioinorganicWorkshop,Bren27

Outline Resources Examples of effects on spectra What we can learn (why bother?) NMR fundamentals (review) Relaxation mechanisms in NMR Effects of unpaired electrons on relaxation Effects of unpaired electrons on chemical shifts2016PSUBioinorganicWorkshop,Bren28

Relaxation in NMRThe observable signal is recorded in the xy plane duringrelaxation. T1 relaxation along z axis; T2 relaxation inxy plane.Line widthΔν 1/(πT2)FID: time-domainsignal in xy planeFourier op,Bren29

Relaxation in NMRThe observable signal is recorded in the xy plane duringrelaxation. T1 relaxation along z axis; T2 relaxation inxy plane.Assumption here: T1 T2 (simplest case – fast motion)Relaxation must be induced by exchange of energy at theresonance frequency νEnergy provided by fluctuating magnetic field – here we’llconsider unpaired electrons as a source2016PSUBioinorganicWorkshop,Bren30

Relaxation Mechanisms Dipole-dipole Most important Through-space interaction betweenmagnetic moments and fluctuating magneticfield Modulated by molecular tumbling Quadrupolar (I 1/2), scalar Spin rotation Chemical shift anisotropy Others 2016PSUBioinorganicWorkshop,Bren31

Dipole-dipole Relaxation The relaxation of one spin (dipole) by through-spaceinteractions with other dipoles A fluctuating field is needed, and this is generated bymolecular motion Relaxation rate depends on µ12µ22, r-6, τcτc: correlation timeτc 4πa3η/3kT2016PSUBioinorganicWorkshop,Bren32

Outline Resources Examples of effects on spectra What we can learn (why bother?) NMR fundamentals (review) Relaxation mechanisms in NMR Effects of unpaired electrons on relaxation Effects of unpaired electrons on chemical shifts2016PSUBioinorganicWorkshop,Bren33

Dipole-dipole Relaxation Depends on µ12µ22, r-6, τc An unpaired electron’s µ is 658x greater than µ for 1H. Unpaired electron has a large impact on 1H relaxationFor dipole-dipole nuclear relaxationby unpaired electron:1Heµ0 2 γΙ2 ge2 µe2 S(S 1)ττscT1,2-1 R1,2 4/364πrNote dependence on S, γI, r-6, τcBut there is more to τc 2016PSUBioinorganicWorkshop,Bren34

Correlation TimeThe correlation time τc actually contains threecontributions:1. molecular tumbling time (τr), 2. electron spinrelaxation time (τs), 3. chemical exchange (τM).The overall correlation τc time is:τc-1 τr-1 τs-1 τM-1Assuming no chemical exchange:τc-1 τr-1 τs-1In a diamagnetic system, no chemical exchange:τc-1 τr-12016PSUBioinorganicWorkshop,Bren35

Correlation TimeIn a paramagnetic molecule, especially if it is not toolarge (large means long τr), τs usually dominates τcτr ranges from 10-9 s (small protein) to 10-7 s (large for NMR)τs ranges from 10-13 s to 10-8 s; but values 10-13 to 10-10 mostfeasible for high-resolution NMR.Thus τr-1 τs-1 and τs dominates τc for metalloproteins.Example: Fe(III)cytochrome c (MW 12 kDa):τc-1 τr-1 τs-1 (10-9 s)-1 (10-13 s)-1τc 10-13 s τs2016PSUBioinorganicWorkshop,Bren36

Correlation TimeIn a paramagnetic molecule, especially if it is not toolarge (large means long τr), τs usually dominates τcNote for small molecules, especially with long τs, insteadyou may have τc τrSmall Cu(II) complex, τs (10-8 s), τr (10-12 s)In this case, τs-1 τr-1 and τc τr.2016PSUBioinorganicWorkshop,Bren37

Dipole-dipole Relaxation – e-/nucleusµ0 2 γΙ2 ge2 µe2 S(S 1)R1,2 4/3τsτc64πrτc τs1HeFor NMR of metalloproteins,variations in τs are the mostimportant factor determining linewidths. It also can be importantfor small molecules.Long τs large R1,2 smallT1,2 large Δν (broad line)2016PSUBioinorganicWorkshop,Bren38

Electron Spin Relaxation Times τsµ0 2 γΙ2 ge2 µe2 S(S 1)R1,2 4/3ττss4πr6MetalOx stateSC.N.Linebroadening(Hz)*Fe 31/25,610-12 - 10-13Fe 35/24,5,610-9 - 10-11Fe 22410-11Fe 225,610-12 - 10-135-20Cu 21/2any(1-5) x 10-91000-5000Mn 25/24,5,610-8Mn 324,5,610-10 - 10-11τs(s)Coord. Chem. Rev. 1996, 150, p. 50100000150-1500*for 1H 5 Å from metal39

Paramagnetic Relaxation Enhancementµ0 2 γΙ2 ge2 µe2 S(S 1)R1,2 4/3ττss4πr6 Measure distances (r) and/or refine structures by measuringeffects of a paramagnetic probe on line widths andrelaxation times (R1,2) Need to be in regime where dipolar relaxation dominates Other effects on relaxation: Contact, applicable mostly for small molecules (rapidtumbling) with large τs (slow electron relaxation) Curie, most relevant for very large molecules with high S Effects of quadrupolar nuclei2016PSUBioinorganicWorkshop,Bren40

Contact RelaxationContact:(in absence of exchangephenomena)Dipolar:(when τs-1 τr-1)R1,2 2/3 S(S 1) (A/h)2 ττsµ0 2 γΙ2 ge2 µe2 S(S 1)R1,2 4/3ττss4πr6 Depends on S, A2, and τs Never depends on τr (why not)? May be in effect when hyperfine coupling is strong over anumber of bonds (so not extremely small r) Will be in effect when τs/τr is relatively large May be in effect for very large A values.2016PSUBioinorganicWorkshop,Bren41

What can I do with these broad peaks? Try some cool tricks, and learn what you can! Change metal or metal oxidation state (although youmay want to study the native metal in a particularoxidation state, of course). Take advantage of the situation! Fast relaxation timesmeans you can use a short acquisition time and recycletime, and get many scans in a short period of timewhile enhancing intensity of broad peaks Increase the temperature – faster tumbling (shorter τr)and faster electron relaxation (shorter τs) (and fasterexchange if present) can help significantly. Detect nuclei other than 1H – especially 13C, 15N, or 2H.Relaxation enhancement and line widths depend on γ2.2016PSUBioinorganicWorkshop,Bren42

Finding Hidden PeaksS 1/2τs 10-9 sP. aeruginosa Cu(II) azurinHisH 2CMetC/DSJ (Hα)NCysSNHACuH 2CNO60504030δ, ppmJACS 2000, 3EHis

Finding Hidden PeaksSaturation transfer experimentAz Cu(I)* Az Cu(II)intensityAz Cu(II)* Az Cu(I)Saturate Cys 1H in diamagneticCu(I), observe change in intensity inspectrum of Cu(II)ppmJACS 2000, 37012016PSUBioinorganicWorkshop,Bren44

What can I do with these broad peaks?Why does this have a 120,000Hz line width?1. It is very close to Cu(II)2. But line width can’t beexplained by dipolarrelaxation3. Contribution from contactrelaxation because of large A4. Observation consistent withefficient spin delocalizationonto Cys residueJACS 2000, 3701S 1/2τs 10-8 sHisH 2CMetC/DSJ (Hα)NCysSNHACuH 2CNOBNHC/DE800, 850 ppm120,000 Hz(!)2016PSUBioinorganicWorkshop,Bren45EHis

What can I do with these broad peaks? Try some cool tricks, and learn what you can! Change metal or metal oxidation state (although youmay want to study the native metal in a particularoxidation state, of course). Take advantage of the situation! Fast relaxation timesmeans you can use a short acquisition time and recycletime, and get many scans in a short period of timewhile enhancing intensity of broad peaks Increase the temperature – faster tumbling (shorter τr)and faster electron relaxation (shorter τs) (and fasterexchange if present) can help significantly. Detect nuclei other than 1H – especially 13C, 15N, or 2H.Relaxation enhancement and line widths depend on γ2.2016PSUBioinorganicWorkshop,Bren46

Metal SubstitutionS 1, τs 10-12 sNi(II) azurinBiochemistry 1996, 18102016PSUBioinorganicWorkshop,Bren47

What can I do with these broad peaks? Try some cool tricks, and learn what you can! Change metal or metal oxidation state (although youmay want to study the native metal in a particularoxidation state, of course). Take advantage of the situation! Fast relaxation timesmeans you can use a short acquisition time and recycletime, and get many scans in a short period of timewhile enhancing intensity of broad peaks Increase the temperature – faster tumbling (shorter τr)and faster electron relaxation (shorter τs) (and fasterexchange if present) can help significantly. Detect nuclei other than 1H – especially 13C, 15N, or 2H.Relaxation enhancement and line widths depend on γ2.2016PSUBioinorganicWorkshop,Bren48

Finding Hidden Peaks1H-15NHSQC spectra of 1 mM Hydrogenobacter thermophilus [U-15N]ferricytochrome c552 showing the effect of a decreased INEPT delay onintensity of the peak correlating the heme axial His δHN nuclei.From Encyclopedia of Inorganic Chemistry DOI: p,Bren49

What can I do with these broad peaks? Try some cool tricks, and learn what you can! Change metal or metal oxidation state (although youmay want to study the native metal in a particularoxidation state, of course). Take advantage of the situation! Fast relaxation timesmeans you can use a short acquisition time and recycletime, and get many scans in a short period of timewhile enhancing intensity of broad peaks Increase the temperature – faster tumbling (shorter τr)and faster electron relaxation (shorter τs) (and fasterexchange if present) can help significantly. Detect nuclei other than 1H – especially 13C, 15N, or 2H.Relaxation enhancement and line widths depend on γ2.2016PSUBioinorganicWorkshop,Bren50

Effect of Temperature1H26 Cresonances of heme methylgroups of Hydrogenobacterthermophilus ferricytochrome c55211 C1 C-6 CFrom Encyclopedia of Inorganic Chemistry DOI: p,Bren51

What can I do with these broad peaks? Try some cool tricks, and learn what you can! Change metal or metal oxidation state (although youmay want to study the native metal in a particularoxidation state, of course). Take advantage of the situation! Fast relaxation timesmeans you can use a short acquisition time and recycletime, and get many scans in a short period of timewhile enhancing intensity of broad peaks Increase the temperature – faster tumbling (shorter τr)and faster electron relaxation (shorter τs) (and fasterexchange if present) can help significantly. Detect nuclei other than 1H – especially 13C, 15N, or 2H.Relaxation enhancement and line widths depend on γ2.2016PSUBioinorganicWorkshop,Bren52

Detection of 13C2-D in-phase-anti-phasespectrum correlatingbackbone 13C and 15N nuclei,with detection of 13C (CONIPAP experiment). Data wereacquired on a 1.5 mM sampleof 13C,15N labeled reducedmonomeric superoxidedismutase (see ID779-) with a14.1 T Bruker Avancespectrometer equipped with acryogenically cooledprobehead optimized for 13Cdetection at 298 KProg. Nucl. Magn. Reson. Spectrosc. 2006, 48, 25.2016PSUBioinorganicWorkshop,Bren53

Detection of 13Cµ0 2 γΙ2 ge2 µe2 S(S 1)R1,2 4/3τs64πrProg. Nucl. Magn. Reson. Spectrosc. 2006, 48, 25.2016PSUBioinorganicWorkshop,Bren54

Detection of 13Cµ0 2 γΙ2 ge2 µe2 S(S 1)R1,2 4/3τs64πrProg. Nucl. Magn. Reson. Spectrosc. 2006, 48, 25.2016PSUBioinorganicWorkshop,Bren55

Relaxation Summary Properties of metal site have a profound effect onrelaxation and thus line widths, with τs being mostimportant A number of systems show minimal line broadening –especially LS Fe(III), 4-coordinate HS Ni(II), 5- and 6coordinate HS Co(II), 5- and 6-coordinate HS Fe(II). Also –most Ln(III), (not Gd(III)), Ru(III), and many bi- andmultinuclear sites Line broadening is diminished for low γ nuclei (by γ2 factor) Relaxation enhancement provides information onmolecular and electronic structure We have ways to deal with it!2016PSUBioinorganicWorkshop,Bren56

Outline Resources Examples of effects on spectra What we can learn (why bother?) NMR fundamentals (review) Relaxation mechanisms in NMR Effects of unpaired electrons on relaxation Effects of unpaired electrons on chemical shifts2016PSUBioinorganicWorkshop,Bren57

Paramagnetic Chemical Shifts Values are not necessarily related to amount of linebroadening Can be higher or lower than diamagnetic (positive ornegative; to high frequency or low frequency) Are caused by two primary mechanisms: contact(through-bond) and dipolar (through-space) Unlike with relaxation, both contact and dipolar oftenplay a role Contain information on electronic structure, molecularstructure, spin delocalization, magnetic anisotropy2016PSUBioinorganicWorkshop,Bren58

Paramagnetic Chemical Shiftsδobs δpara δdiaδpara δcon δpcδdiais shift in isostructural diamagnetic moleculeδconis contact shift – through-bond electronnucleus interactionδpcis pseudocontact (also called dipolar) shift –through-space electron-nucleus interaction2016PSUBioinorganicWorkshop,Bren59

Contact Shiftδcon [(2πA/h)ge βe S (S 1)]/[3 kBT γI]Note dependence on: Hyperfine coupling constant (A) Spin (S (S 1)) Temperature (1/T) Value γI in denominator cancels with part of A2016PSUBioinorganicWorkshop,Bren60

Contact Shiftδcon [(2πA/

ranges from 10-9 s (small protein) to 10-7 s (large for NMR) τ s ranges from 10-13 s to 10-8 s; but values 10-13 to 10-10 most

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