An Introduction To Solid-State NMR
An Introduction to Solid-State NMRB01H-31P CP/MAS NMRA M 54.74 R Workshop - June 24, 2010R.W. SchurkoDepartment of Chemistry & Biochemistry, University of Windsorhttp://www.uwindsor.ca/schurko
Outline1.Solution vs. Solid-State NMR2.Anisotropic NMR InteractionsChemical ShieldingSpin-Spin Coupling: Dipolar vs. J-Coupling3.Averaging Anisotropic NMR InteractionsMagic-Angle Spinning (MAS)Setting the Magic Angle4.Cross-Polarization (CP)
Solution vs. Solid-State NMRSolution 13C NMRLiquids:We observe the average, or isotropic valuesof NMR interactionsSolid State 13C NMRSolids:We observe orientation dependence, oranisotropic features of NMR interactions150100500 ppm
NMR InteractionsSmall perturbative NMR interactions are what makes NMR a useful tool forprobing molecular structure and dynamicsImportant interactions in solution & the solid-state:BlocFB0Chemical Shielding# electronic environment# nature of chemical bonding# bond angles and lengths# coordination numbers# site differentiationJJ-Coupling# through-bond connectivities# bond character# dynamicsAlso important in the solid-state:DDipolar Coupling# through-space connectivities# bond lengths# dynamics# diffusion# primary source of relaxation!
Nuclear Magnetic ShieldingElectrons in molecules cause local magnetic fields to vary on a very small(but noticeable) scale. Magnetic fields experienced by nuclei at differentsites in a molecule are different if the electronic environments are different.The effect is called chemical shielding or nuclear magnetic shielding:CH31H NMR spectrum of CH3CH2OHat 300 MHzProtons of CH3 experiencedifferent internal magnetic fieldsthan CH2 and OH protonsCH2OHEach ppm is 1 millionth of the size of the applied magnetic field. So, for a7.05 T (300 MHz) spectrometer, 1 ppm 300 Hz for protons.
Nuclear Magnetic Shielding, 2If the local magnetic fields produced by electron circulation oppose theapplied magnetic field, B0, the nucleus is said to be shielded; if the localmagnetic fields add to B0, the nucleus is said to be deshielded.Shielding:Usually arises from diamagneticshielding (electron circulation)B0(i)(ii)Deshielding:Arises from paramagneticshielding (mixing of occupied andvirtual orbitals):B0(i)BjindNBjindThe net Larmor frequencydecreases in this casen : 2px*The net Larmor frequencyincreases in this case(ii)
Chemical Shift vs. ShieldingChemical shielding, F (in ppm), is described by: B observed ' B 0 (1 & F)The shielding scale of course is inconvenient as a reference, since wecannot measure the NMR spectrum of a bare nucleus. So, we choose to seta scale to an agreed upon reference:Freference & F*' 10 6 . Freference & F1 & FreferenceHigher FrequencyLess ShieldedDownfield13bare Cnucleusabsolutefrequency: 100.018543F scale:* scale:0.00 ppm185.43 ppmLower FrequencyMore ShieldedUpfieldspecies Areferencecompound(TMS)100.010000100.00000085.41 ppm100.00 ppm185.40 ppm0.00 ppm
Chemical Shielding TensorChemical shielding is an anisotropic property, meaning that it depends onthe orientation of the sample in the field.F33Fxx Fxy FxzF ' Fyx Fyy FyzCS tensor in themolecular frameFzx Fzy FzzF11F22F11 0FPAS '00F22 000F33CS tensor in its ownprincipal axis system(PAS)The three-dimensional nature of chemical shielding can be described by asecond-rank tensor with three principal components# Magnetic interaction: Circulation of electrons induces local fields at nuclei# Magnetically induced mixing of ground and excited state MOs# Tensor is not traceless, does not average to zero# F11 # F22 # F33# Fiso (F11 F22 F33)/3; S F33 - F11,6 3(Fiso - F22)/S# *11 # *22 # *33# *iso (*11 *22 *33)/3; S *11 - *33, 6 3(*22 - *iso)/S
Chemical Shift Anisotropy (CSA)B0F11F22F22F33: Direction ofhighest shieldingF11: Direction oflowest shieldingF33FisoF11F33 These orientations,and the manypossible others, giverise to the solid-stateNMR powder pattern
Chemical Shift Anisotropy (CSA), 2Single-crystal NMR is NMR conducted using a single-crystal goniometer,and acquiring spectra for each orientationtenoncrystal
Chemical Shift Anisotropy (CSA), 3Crystalline powder samples: tensors assume many different orientationsdue to random orientations of crystallitesOverall powder pattern resultsfrom many orientationsB0TIndividual crystallites have thetensors oriented in one positionw.r.t. B0, and give rise to adiscrete frequency
CSA: Structure and SymmetryAside from the fact that the CS tensor is the origin of isotropic chemicalshifts that are observed in solution, there is also a rich connection betweenelectronic structure, symmetry and CSAHC HHHH C C HHHC CHHSpherical symmetry:shielding is similar in alldirections, very smallCSA.Axial symmetry: moleculeis // to B0 maximumshielding; when moleculeis z to B0 maximumdeshieldingNon-axial symmetry:Shielding is different inthree directions
Dipolar Coupling vs. J-CouplingDipolar coupling (direct spin-spin coupling): J-coupling (indirect spin-spin coupling):through space, independent of electronic mediated by the electrons involved instructurebondingHjHjkjCkDDRjkµ0 (j (k h'4B r 3,jk2& HCHHCCRkDepends only upon nuclear characteristics(size of () and internuclear distance.Simple to understand!CrCCH 2CrjkHHDepends upon nature of interveningbonds, distances, angles, substituents,etc. Complex mechanisms!3J isoHH' A % BcosN % C cos 2N
Dipolar Coupling vs. J-Coupling, 2Despite the very different origins of these two-spin mutual couplings, theycan both be described by second-rank tensors which are axially symmetric(i.e., J2 is not the same as Jz; same for RDD)The major difference between these tensors is that the J-tensor is nottraceless; this is what gives rise to the isotropic J-coupling we see insolution NMR spectra. The dipolar tensor is traceless; so, rapid tumblingaverages the effects of the dipolar interaction in solution NMR.B0HClC HClH10-12 sClHCCl10-12 sHH C ClCl10-12 sFluctuating dipolar fields are the major reason for relaxation phenomena inboth solution and solid-state NMR. This reorientation occurs so quickly,that the nuclear spins experience a time average of the angular part of thedipolar interaction 3cos22-1, over all possible orientations 2,N.
Anisotropic Dipolar InteractionsImagine a single crystal in which all of the internuclear vectors are orientedin the same manner:B02 60o2 90o2 0o 2 90E20000"10000 2 60EIf we rotate the crystal with respectto B0, we are able to see theorientation dependence of thedipolar coupling:factor of (1 - 0 200000"2 30E2 0E1000010000"20000-10000 0-100000-20000-10000HzB0-20000 -2RDD10000B0B0"2 54.74E2000020B0HzB0-20000Hz
Anisotropic Dipolar Interactions, 2Just as for CSA, an isolated spin pair in a microcrystalline powder (e.g., two1H in CaSO4C2H2O) gives rise to a powder pattern (called a Pake doublet).2RDD80000400000-40000-80000HzThe pattern arises from the (1 - 3cos22) geometric dependence, and the sizeof the dipolar coupling constant, RDD. It is comprised of two mirror imagepatterns (that resemble CSA patterns) which are superimposed.
Anisotropic Dipolar Interactions, 3Dipolar interactions are typically much largerthan J-couplings, and often dominate solid-stateNMR spectra (in an unhelpful way!!)For instance, a proton in an organic solid willhave strong dipolar couplings to all of thesurrounding protons, and its pattern will beextremely broad, overlapping with similarlybroadened patterns of all of the other protons!HBC-C12"D(s)HBC-C12(s)HBC-C12(lc)Schnell & Spiess, J. Magn. Reson. 2001, 151, 153–227.As a result, 1H NMR in the solid state is notparticularly useful in comparison to solution 1HNMR - though there are some tricks!HBC-C12(soln)
Averaging Anisotropic NMR InteractionsThere are three common ways to average anisotropic NMR interactions, inorder to extract information contained within the higher-resolutionspectra:Magic-angle spinning (MAS):Sample is rapidly spun in order to spatially average the anisotropicinteractions (we will focus on this aspect in this lecture)Specialized pulse sequences:Sample (usually under MAS conditions) is subjected to a series of pulseswith average the anisotropic interactions in “spin space”Two-dimensional NMRHomonuclear (e.g., 1H, 1H) and heteronuclear (e.g., 1H, 13C) correlationexperiments are utilized to improve resolution and develop correlationsamong nuclei at different sites in the system.
Magic-Angle Spinning (MAS): PreparationThe solid-sample is taken (either on the benchtop or in a glovebox) andground into a fine powder, and packed into a rotor.The rotor is inserted intothe stator of the probe,and the probe is insertedinto the magnet, such thatthe angle between therotor axis and B0 is 54.74o(magic angle)B054.74E
MAS: How it worksThe rotor is spun rapidly about its axis at speeds ranging from 1 to 70 kHz(this depends on what probe you are using, and what sort of results you arehoping to achieve with your experiment).B054.74EAll of the NMR interactions (CS, J, DD) yieldfrequencies that are dependent upon theorientation of the interaction tensor in themagnetic field (or the coordinates of B0 in theinteraction frame)The Hamiltonians describing these frequencies canbe made time dependent when the sample isrotated in the magnetic fieldBy choosing the correct angle, it is possible to coherently average theanisotropic NMR interactions (i.e., all that is left is the isotropic average).
A simple caseConsider an NMR interaction tensor R which is axially symmetric. Theunique component, Rzz, which determines the interaction frequency Tint, is:RzzLABR zz' R iso % R 2RyyRxxRxx Ryy3cos2 2 & 12Anisotropic partR2Consider the simplest system:- single transition frequency, Tint- simple Iz operator (single spin)- depends on one angle, 2(like in a single crystal)Then:RzzLAB Iz / Tint IzB02
Static powder patternIf we make a single B/2 pulse on the system, we create the observable I coherence (i.e., magnetization in the xy-plane). Then, the total observablesignal averaged all possible angles 2 is: I %(t), 'Iexp[& iTint(2)t]Probability offinding acrystallite withorientation 2Powder pattern22 0o,2z 90o,2m 54.74o,B0 along unique axis,B0 along unique axis,B0 along unique axis,T Riso R2T Riso - R2/2T Riso [ 2 cos-1(%3/3) ]p(2)d2
Rotating the sampleRotate the sample at a frequency of Tr inclined at some angle w.r.t. B0:(a) Over one rotational cycle, the averagedirection of R2 is along the rotational axis(regardless of original orientation)(b) Now, imagine the fixed frame of therotor. R2 is fixed in this frame witharbitrary angles " and . B0 wouldappear to precess about the z axis of thisframe, fixed at the angle 2m (magicangle), and sweeping a time-dependentazimuthal angle TrtAn instantaneous angle 2(t) between R2and B0 is predicted by the spherical lawof cosines:cos[2(t)] ' cos2m cos % sin2m sin cos(" & Trt)(from 2m- to 2m , and phaseangle from 0 to 2B)
Time-dependent frequenciesSo, if 2 is time dependent, so is Tint(2):3cos2 2 & 1Tint(2) ' R iso % R22' R iso % ½R2 [ 2 sin2 cos(" & Trt)% sin2 cos 2(" & Trt)]This means that 2(t), cos(2) and Tint(2) areall related non-linearly; there is aperiodicity determined by the modulo Tr,and a second one by 2TrA plot of fraction of the rotational cycle,t/Tr, as a function of a dimensionlessfrequency parameter, (T - Riso)/R2, is shownfor a single crystallite of orientation 2In short, the average orientationdependence of the interaction is given by: 3cos22-1, ½(3cos22m-1)(3cos2 -1)
Multiple rotor cyclesSo, the time average for a single cycle is given by:Hint (t,", ) Tint(t,", ) Iz Riso Izfor any ", combinationin other words, the system evolves only under the isotropic HamiltonianWhat if there are multiple cycles (which is always the case)?Imagine now that we have time-dependent frequencies, described by afunction (t): (t) 'T(t ))dt )Then, over multiple rotor periods, we have a function dependent upon theisotropic parameter, Riso, and a time-dependent anisotropic function: (t,", ) 'R22Tr( 2 sin2 [sin" & sin(" & Trt)]% ½sin2 [sin2" & sin2(" & Trt)]) % R iso t
Fast vs. slow spinningThe important portion of the equation is the ratio of the anisotropic termand the rotation frequency, R2/Tr:(i.e., Tr much larger than R2, infinitely fast spinning)If R2/Tr 6 0- We get a single isotropic peak, and the anisotropic term disappears(i.e., Tr much smaller than R2, sample not rotating)If R2/Tr 6 4- We get the “static” powder pattern pictured on the previous page(this is the most common case!)If R2 . Tr- The basic pattern is repeated in each revolution of the rotor I%(t,", ), ' Iexp[&i (t,", )]In other words, the Tint(t,", ) and FID (free induction decay) are affected:rotational echoes appear in the FID (in the time domain).This means that the FT of the FID will yield a frequency pattern:# centred at T Riso (irregardless of spinning speed)# composed of spinning sidebands at multiples of Tr from the centreband# intensities of all peaks depend on R2, Tr, " and
Rotational EchoesRefocusing of the magnetization occurs each time the rotor completes acycle (and the crystallites return to their initial positions). In the FID, thisleads to the formation of rotational echoes. FT first periodFT multiple periods FT echo tops only
Spinning sidebandsConsider these CSA patterns:# The isotropic centreband alwaysremains in the same position, andindicates the same isotropic shift asin solution.# At slower spinning rates, many ssbscan be seen - they are actually useful,in that they may be analyzed toobtain the CSA# At infinite spinning speeds (or whenR2/Tr 6 0), all of the ssbs disappear,and only the isotropic centrebandremainsMost importantly:MAS gives a huge boost in signal-tonoise, since the integrated signalintensity is the same in all of thesespectra
Example of 13C MAS NMR SpectraPictured to the right are 13C(a) static and (b,c) MAS NMR ofzinc acetate, which has CO2- andCH3 resonances.Note that at moderate MASspeeds (i.e., around 5 kHz orhigher) it is possible to attentuatemost SSBs in general 13C NMRspectra.
Example of195Pt MAS NMR SpectrumOn the other hand, heavy metals nuclides like 195Pt have enormous CSAs,and patterns can span hundreds of kHz to several MHz:ClNMR Parameters*iso (ppm)S pm-600kHzCl
Setting the Magic Angle, 1Setting the magic angle in crucial for obtaining high-resolution SSNMRspectra. If improperly set, lines can be broad or split, and you lose bothresolution and signal to noise!Running 79Br NMR of KBr can be useful for setting the magic angle:1. Run a test spectrumIdeally, you would like to position the transmitter frequency dead centre onthe isotropic centreband.
Setting the Magic Angle, 22. Set the transmitter on-resonance, and run it again!The FID on the right covers a time period ofca. 15 ms. Since you are on-resonance, thebeat pattern from being off resonance isabsent, and only a clear decay topped byrotational echoes is observed. In this case,the magic angle is slightly off. FT leads to aspectrum which clearly indicates the misset.3. Adjust the angle and reacquire!The rotational echoes increase in intensity;adjust until the echoes stretch out as far intime as possible (the more intensity, thebetter). FT leads to a nice sharp line!
Bloch DecayThe simplest NMR experiment is the single pulse or Bloch decayexperiment, where a single B/2 pulse is followed by an acquisition ngRelaxtionDelayHTypically, for organic molecules, this experiment is accompanied by highpower proton decoupling in order to resolve sharp 13C resonances, and toeliminate dipolar and J-couplings between 13C and 1H.Disadvantage: the relaxation delay for most spin-1/2 nuclei is quite long!
Cross Polarization (CP)CP is one of the most commonly used techniques in SSNMR, and is oftencoupled with MAS (i.e., CP/MAS). It involves transferring spin polarizationfrom abundant spins (e.g., 1H) to dilute spins (e.g., 13C) which are ntact TimeJCTAdvantages:# Enhancement of signal by a ratio of (H/(X (for 1H/13C, this is ca. 4x)# No B/2 pulse on 13C means the relaxation delay is dependent upon the1H longitudinal relaxation time (T1), which is typically very short!
Hartmann-Hahn MatchingIn order for CP to work, it is necessary to tune the B1 fields for the 1H and 13Cnuclei. The best way to picture this is as two separate rotating frames, eachnutating at distinct frequencies, T1(13C) and T1(1H), that must be matched:T1(13C) ((13C)B1(13C) T1(1H) ((1H)B1(1H)Lab frame: T0H T0C1HExtremely different frequencies (MHz)T0HT0CRf rotating frame: T1H T1C1HT1H13C13CMatched frequencies (kHz)PolarizationT1C
How CP Works1. First, make a B/2(1H) pulse to get things started. Nothing is initially doneon the 13C channel.zz1H2 B/213CyyB1x(1H)xx2. Now, let’s look at the xy-plane in each of the rotating frames. We willapply B1 fields known as spin-locking fields along with -y axis. In addition,we insure that they have the same nutation frequencies (this means thatthe frames rotate at the same frequencies)113HCyy13B1(1H)B1( C)xx
How CP Works, 23. Think about the difference between these frames. The 1H frame has asmall B1 field, but a massive magnetization created by B0 precessing aboutthe y axis. The 13C frame has no magnetization at all along the y axis.113H EEC 0 0""&E / kTN e' &E / kT ' e &(E & E ")/ kTN"e " T' e T0 / kT . 1 % 0kTAccording to the Boltzmann distribution, which tells us about thepopulations of these levels, the spin temperature of 1H along the y axis isvery cold (big population difference, low temperature), and that of 13C isvery hot (no population difference, high temperature)
How CP Works, 34. If the Hartmann-Hahn match is in place, the frames have very similarenergies, but very different temperatures. They are said to be in thermalcontact with one another. Hence, polarization is transferred from theabundant protons to the dilute 13C nuclei as long as the spin locking fieldsare left on. This is known as the contact time (usually milliseconds). 13Cpolarization builds along the -y axis.113HCyB1x(1H)yB1x(13C)xxThe best contact time for achieving optimum transfer of polarization ishighly dependent upon the relaxation characteristics of the 1H and 13Cnuclei; notably, cross relaxation can influence the setting of this timeperiod.In addition: the 1H and 13C nuclei must be dipolar coupled to one anotherfor CP to work; otherwise, thermal contact between these frames cannotbe established.
How CP Works, 45. Finally, the spin locking fields are shut off, and the receiver is opened onthe 13C channel. Normally, one applies high power 1H decoupling to ensurethat the 13C NMR spectrum is sharp and of high S/N!131H (decoupled)Cyxyx6. One must wait for the 1H magnetization to recover to thermal equilibriumbefore starting the sequence again - this is the relaxation delay. Forcommon organic molecules with at least one methyl group, the RD is ca. 4to 6 seconds long.Compare this to some 13C RDs, which may be many seconds to minutes inlength. The situation for heavy metals can be even worse: some have RDson the order of hours or days!
Variable Contact Time ExperimentsDifferent structural motifs for carbon have distinct responses to variation incontact times - which can be very useful for structural assignment, butchallenging for quantitation via CP/MAS.The CO resonance (leftmost) builds up more slowly (wrt CT) than theprotonated carbons; the proximity of protons in the latter case facilitatesefficient polarization transfer compared to the unprotonated CO carbon. p
NMR spectra (in an unhelpful way!!) As a result, 1H NMR in the solid state is not particularly useful in comparison to solution 1H NMR - though there are some tricks! For instance, a proton in an organic solid will have strong dipolar couplings to all of the surrounding protons, and its pa
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