55thExperimental Nuclear Magnetic Resonance ConferenceBoston, 2014The Basic Building Blocksof NMR Pulse SequencesJames KeelerUniversity of CambridgeDepartment of Chemistry1Introduction and outlinemost pulse sequences are built up from simpler elements orbuilding blocks of which there are not that manyrecognising these elements can help in understanding how apulse sequence works, and will usually simplify a detailedanalysisnew pulse sequences are often designed by joining togetherthese building blocksa PDF of this presentation is available to download atwww-keeler.ch.cam.ac.ukIntroduction and outline2Introduction and outlinewe will restrict ourselves to building blocks used in liquid-stateNMR for scalar coupled spins systemseverything will be illustrated for two coupled spins one-halfwe will start with a brief reminder of the product operatormethod, as this will be used to describe each building blockand then go on to cover as many buildings blocks as timepermitsfor more detail: James Keeler, Understanding NMRSpectroscopy, 2nd edit., Wiley 2010Introduction and outline3Building blocks to be covered1. Product operators2. Decoupling3. Spin echoes4. Heteronuclear coherence transfer using INEPT5. Heteronuclear coherence transfer using HMQC6. Generation and detection of multiple-quantum coherence7. Constant time sequences8. Isotropic mixing (TOCSY)9. z-lters10. Gradient echoes11. Spin lockingIntroduction and outline4Product operatorsProduct operators 5Product operators: one spinthe state of the spin system can be expressed in terms thenuclear-spin angular momentum operators Ix, Iy, and Iz Ix, Iy, and Iz represent the x-, y- and z-components of themagnetizationcan just read off the expected magnetizationequilibrium magnetization only along z: IzProduct operators 6Evolutionevolution depends on the relevant Hamiltonianfree precession:Hfree= Iz is the offset in the rotating framehard pulse about x-axis:Hx,hard pulse= 1Ix1 is the RF eld strengthhard pulse about y-axis:Hy,hard pulse= 1IyProduct operators 7Arrow notationwrite Hamiltonian time over the arrowinitial stateHamiltonian time nal statefor example, pulse of duration tp about x to equilibrium (z-)magnetizationIz1tpIxnal statebut 1tp is the ip angle IzIxnal statefor example, free evolution of x-magnetization for time tIxtIznal stateProduct operators 8Diagrammatic representation of rotationsin general the rotation of an operatorA gives two terms:1.A multiplied by the cosine of an angle2. a new operator,B, multiplied by the sine of the same anglecos original operator + sin new operatorcan work out what the new operator is by looking at thediagramIxIzIy Product operators 9Diagrammatic representation of rotationszy-z-y xz-x-zx yxy-x-y z(a) (b) (c)rotation about x rotation about y rotation about zcan be used to determine the effect of any rotationcos original operator + sin new operator90 or 180 rotations particularly simple: just move one or twosteps around the clockProduct operators 10Operators for two spinsdescription operator(s)z-magnetization on spin 1I1zin-phase x- and y-magnetization on spin 1I1x, I1yz-magnetization on spin 2I2zin-phase x- and y-magnetization on spin 2I2x, I2yanti-phase x- and y-magnetization on spin 1 2I1xI2z, 2I1yI2zanti-phase x- and y-magnetization on spin 2 2I1zI2x, 2I1zI2ymultiple-quantum coherence 2I1xI2x, 2I1xI2y, 2I1yI2x, 2I1yI2ynon-equilibrium population 2I1zI2zProduct operators 11Generation of anti-phase terms by evolution of couplingHamiltonian for coupling: 2J12I1zI2zevolution of I1x under coupling from time I1x2J12I1zI2z cos (J12)I1x + sin (J12) 2I1yI2zevolution of in-phase (along x) to anti-phase (along y)magnetizationcomplete conversion to anti-phase when = 1/(2J12)Product operators 12Anti-phase terms evolve back into in-phase termsevolution of 2I1yI2z under coupling from time 2I1yI2z2J12I1zI2z cos (J12) 2I1yI2z sin (J12)I1xcomplete conversion to in-phase when = 1/(2J12)note anti-phase along y goes to in-phase along xProduct operators 13Diagrammatic representation: evolution of couplingx-yz-xyz zzyxz-y-xz zz(a) (b)angle = Jt2I1yI2z2J12tI1zI2z cos (J12t) 2I1yI2z sin (J12t)I1xnote that the angle is JtProduct operators 14Coherence transferan absolutely key concept in multiple-pulse NMRachieved by applying 90 pulse to anti-phase term2I1yI2z

on spin 1(/2)I1x 2I1zI2z(/2)I2x 2I1zI2y

on spin 2only anti-phase terms are transferredanti-phase terms arise due to the evolution of couplingProduct operators 15DecouplingDecoupling16Heteronuclear broadband decouplinga broad-band decoupling sequence applied to the I spinseffectively sets all heteronuclear couplings to the S-spins tozerothe following are likely to be dephased:1. I-spin coherences (including heteronuclear multiple quantum)2. anti-phase terms on I (e.g. 2IzSx)3. z-magnetization on I unless decoupling only applied for a short periodbroad-band sequences gives decoupling over wide range ofI-spin shifts with minimum of power, but there are practicallimits to the range that can be coveredDecoupling17Semi-selective decouplingby deliberately reducing the RF power level it is possible torestrict the decoupling effect to a narrower range of shiftse.g. decoupling of only the carbonyl carbons, or the -carbonsonly likely to be successful for a group of resonances which iswell-separated from othersDecoupling18Spin echoesSpin echoes 19Spin echo for one spin or 180start with IxIxIz cos ()Ix + sin ()Iy180 pulse about x does not affect Ix, and inverts Iycos ()Ix + sin ()IyIx cos ()Ix sin ()Iysecond delaycos ()Ix sin ()IyIzcos () cos ()Ix + sin () cos ()Iy cos () sin ()Iy + sin () sin ()Ix IxSpin echoes 20Spin echo for one spin or 180evolution between the dashed lines isIx Ixthe offset is said to be refocused between the dashed linesi.e. it is as if the offset (or the delay) is zeroworks just as well with other initial statesin fact Spin echoes 21Spin echo for (homonuclear) coupled spins or 180start with I1x and assume that offset is refocusedthe 180 pulse affects both spins . . .. . . nal result iscos (2J12)I1x + sin (2J12)2I1yI2zcoupling is not refocused, but continues to evolve for theentire period 2Spin echoes 22Spin echo for (homonuclear) coupled spinsa spin echo is equivalent to1. evolution of the coupling for time 22. followed by a 180 pulse (here about x).this is a very useful short cut in calculationskey thing about a spin echo is that it enables us to interconvertin-phase and anti-phase magnetization in a way which isindependent of the offset i.e. works for all spinsSpin echoes 23Spin echoes in heteronuclear spin systemscan choose which spins to apply 180 pulses to ISISIS (a)(b)(c)(a) offsets refocused, coupling notrefocused (as homonuclear)(b) only I-spin offset refocused,coupling refocused(c) only S-spin offset refocused,coupling refocusedgives considerable exibilitySpin echoes 24Spin echoes: summaryin homonuclear systems spin echoes allow the coupling toevolve while effectively suppressing the evolution due to theoffset (shift)means that we can interconvert in-phase and anti-phaseterms in a way which is independent of the offsetin heteronuclear systems spin echoes can effectivelysuppress the evolution of heteronuclear couplings, which isequivalent to decoupling, independent of offsetSpin echoes 25Heteronuclear coherencetransfer using INEPTHeteronuclear coherence transfer using INEPT26INEPT transfer1122A CBISstart with in-phase magnetization on I e.g. Ixanti-phase generated during spin echo A (independent ofoffset)coherence transfer from I to S during pulses Btransferred anti-phase goes in-phase during spin echo C(independent of offset)overall result is transfer of in-phase on I to in-phase on SHeteronuclear coherence transfer using INEPT27INEPT transfer1122A CBISstarting with Ix, rst echo gives11cos (2JIS1)Ix +sin (2JIS1) 2IySzonly the anti-phase term is transferred by the pulsessin (2JIS1) 2IySz(/2)Ix(/2)Sx sin (2JIS1) 2IzSyanti-phase term goes in-phase during second spin echo22sin (2JIS2) sin (2JIS1) SxHeteronuclear coherence transfer using INEPT28INEPT transfer1122A CBISoverall result isIxINEPTsin (2JIS2) sin (2JIS1) Sxmaximum transfer when 1= 1/(4JIS) and 2= 1/(4JIS)if anti-phase term present at start of A, can omit rst spinechophase of 90 pulse to I affects which term is transferredi.e. 2IySz or 2IxSzHeteronuclear coherence transfer using INEPT29Double INEPT transfertransfer from I to S; evolution; transfer back from S to I ISevolution on SIxdouble INEPT mod. from period on S spin sin (2JIS)4 Ixcan omit middle two spin echoes if evolution of an anti-phaseterm is acceptable ISevolution on SIxdouble INEPT mod. from period on S spin sin (2JIS)2 IxHeteronuclear coherence transfer using INEPT30Heteronuclear coherencetransfer using HMQCHeteronuclear coherence transfer using HMQC31Coherence transfer using heteronuclear multiple quantumAE CFB DISrather like double INEPTI-spin offset refocused over whole of period F (spin echo dueto central 180 pulse)start with Ix: goes anti-phase during to give sin (JIS) 2IySzS-spin 90 pulse transfers this to heteronuclearmultiple-quantum coherence (HMQC)sin (JIS) 2IySz(/2)Sx sin (JIS) 2IySyHeteronuclear coherence transfer using HMQC32Coherence transfer using HMQCAE CFB DISHMQC does not evolve under JIS; I-spin offset also refocusedevolution under just S-spin offset for period Ccos (St) sin (JIS) 2IySy + sin (St) sin (JIS) 2IySx90 pulse to S transfers only the rst term to givecos (St) sin (JIS) 2IySzthis goes in-phase during the nal delay to givecos (St) sin (JIS) sin (JIS)IxHeteronuclear coherence transfer using HMQC33Coherence transfer using HMQCAE CFB DISnet result isIxHMQC transfer mod. from S-spin sin2(JIS)Ixoptimum delay is 1/(2JIS)similar to double INEPTHeteronuclear coherence transfer using HMQC34Generation and detection ofmultiple-quantum coherenceGeneration and detection of multiple-quantum coherence35Generation of multiple quantum coherence (MQC)simply:2I1xI2z

anti-phase on spin 1(/2)(I1x+I2x) 2I1xI2y

MQConly anti-phase terms are converted to MQCMQC not directly observable, but can be transferred back toanti-phase with a further pulse2I1xI2yevolution of offsetmixture of terms: 2I1xI2y, 2I1yI2y, 2I1xI2x, 2I1yI2xonly 2I1xI2y and 2I1yI2x transferred back to observableanti-phase by 90(x) pulseGeneration and detection of multiple-quantum coherence36Typical MQC sequenceevolution A CBanti-phase generated during spin echo AMQC generated by pulse Bevolutionanti-phase regenerated by pulse C; could add a further spinecho to re-phaseGeneration and detection of multiple-quantum coherence37Constant time sequencesConstant time sequences 38Constant time (CT) pulse sequence elementt1(T - t1) (T - t1)A B(T - t1)Ta way of suppressing the splittings in an indirect dimensiondue to homonuclear couplingthe time T is xed, but the position of the 180 pulse changeswith t1coupling evolves for the entire time T which, as it is constant,means that the signal is not modulated by the couplingoffset refocused over period A, but evolves over period B( t1), so signal is modulated by offsetConstant time sequences 39CT pulse sequence element - in actiont1t1t1t1T180 pulse moves backwards as t1 increasesproblems:1. relative amounts of in-phase and anti-phase at end ofsequence depend on the size of the couplings and the time T2. it may be difcult to nd a value of T which gives reasonableamounts of the required terms3. the maximum value of t1 is limited by T4. signal relaxes for entire time T, even when t1= 0: loss ofintensityConstant time sequences 40CT pulse sequence element: heteronuclear caset1(T - t1) (T - t1)A BTISI-spin 180 pulse refocuses heteronuclear coupling overperiod AS-spin 180 pulse refocuses heteronuclear coupling overperiod B (t1)can re-introduce modulation due to heteronuclear coupling bydisplacing the S-spin pulse from the centre of period BConstant time sequences 41Isotropic mixing (TOCSY)Isotropic mixing (TOCSY) 42Isotropic mixinga specially designed pulse sequence (e.g. DIPSI) can, over arange of offsets, generate the effective HamiltonianHiso=

all pairs i,j2Jij Ii .Ijthis is the full version of the Hamiltonian for coupling (nottruncated for weak coupling) Hiso is invariant to rotations hence described as isotropicDIPSI involves a continuous train of pulses with variable ipangles and phases; issue over power depositionIsotropic mixing (TOCSY) 43Isotropic mixingthe effect ofHiso is to transfer magnetization (along x, y or z)from one spin to any other spin connected by an unbrokenchain of couplingsrate of transfer depends on the size of the coupling constants;for a two-spin system transfer goes as sin2(J12)transfer also results in generation of anti-phase terms from I1xor I1y, and zero-quantum coherence from I1zneed to clean up the transfer e.g. using a z-lterIsotropic mixing (TOCSY) 44z-ltersz-lters 45Aim of z lterx -xzA B C Dsuppose that at point A we have a mixture of terms, but wishto select just one in-phase term such as I1y90(x) rotates I1y to I1z; other terms rotated in various waysuse phase cycling or gradient pulses to select justz-magnetization at point C90(x) pulse rotates I1z to I1y at point Deffectively selects I1y at A by passing through z-magnetizationz-lters 46Problem with z lterx -xzA B C Dsome anti-phase terms at A are transferred to zero-quantumcoherence (ZQC) at point BZQC is not distinguishable from z-magnetization by phasecycling or gradient pulses: it is not suppressed, thereforeZQC at C becomes anti-phase magnetization at D, makingz-lter ineffectivez-lters 47Problem with z lter: possible solutionx -xzA B C DZQC evolves for time z, thus acquiring a phaseco-addition of the results of experiments with different zvalues will result in partial cancellation of contributions arisingfrom ZQC z needs to range up to a value comparable with1/(2 zero-quantum frequency); difcult to arrange for acomplex spin systemrepetition with different z values is time consumingz-lters 48z lter with swept gradientGzGsweepswept180GGzRFx -xzA B C Duse gradient Gz to dephase all but z-magnetization and ZQCuse weak gradient in combination with swept-frequency 180pulse to suppress ZQC (see Chapter 11, Section 11.15.2)one-shot z-lter: no phase cycling or repetition neededz-lters 49TOCSY with double z ltert2t1mixgradientisotropic mixing embedded in z-lterselection of z-magnetization before and after mixingensures that only y-magnetization present before second 90pulse and after third 90 pulse contributes to spectrumgives in-phase multiplets with absorption-mode lineshapesz-lters 50Gradient echoesGradient echoes 51Field gradient pulsesnormally we try to make the B0 eld as homogeneous aspossible . . . but it can be advantageous to introducecontrolled inhomogeneitya small coil, in the probe, generates a small eld which varieslinearly along z: a eld gradientcan control the size of the gradient by varying the current, andthe sign by altering the direction in which the current owscan also control the duration of the gradientGradient echoes 52Defocusing and refocusingRFG1G1G22p1p2during rst gradient pulse coherence (e.g. transversemagnetization) is dephasedextent of dephasing depends on the coherence order p, theduration of the gradient and its strength Gafter RF pulse, the coherence can be re-phased by applying asecond gradient; refocusing condition:G11G22= p2p1p1 p2 pathway refocused; (hopefully) others remaindephased and so are not observedGradient echoes 53Refocusing pulses+p-pRFGGGan ideal 180 pulse causes p pselected, for all p, by a pair of equal gradientsif pulse is imperfect, gradient pair cleans up any unwantedtransfersthis gradient echo is simple and convenientGradient echoes 54Cleaning up 180 pulses in heteronuclear experimentsGG-GISt1coherence on S but not on I: role of 180 pulse is to invert Izif pulse is imperfect may also generate transversemagnetization: second gradient dephases thiscoherence on S dephased by rst gradient and rephased bysecondGradient echoes 55Selective excitation with the aid of gradients180(a)GRFG1G1180(b)GRFG1G1180 pulse is selectiveonly the magn. from those spins which experience theselective pulse as a refocusing pulse will be refocused bysecond gradienteverything else remains defocused: very clean excitationcan add extra 90 pulse to ip magnetization onto z:gives selective inversionGradient echoes 56Double pulsed eld gradient spin echo180 180(c)GRFG1G1G2G2double pulsed eld gradient spin echo (DPFGSE)only the magn. from those spins which experience bothselective pulses as refocusing pulses will be excitedadvantage over single spin echo is that the phase is constantover the excited bandwidthtwo gradient pairs must be independentGradient echoes 57Spin lockingSpin locking58Typical spin locking sequenceSLyxnon-selective pulse puts magnetization along xthen apply a strong RF eld along xif the RF eld strength is greater than typical offsets thenevolution due to offsets is suppressed and the magnetizationremains locked along xSpin locking59Features of spin lockingSLxmagnetization not along the spin-lock axis likely to bedephased due to inhomogeneity of RF eldresult is a selection of just the x-magnetizationif RF eld is not large compared to the offset, then thespin-lock axis tilts up in the xz-plane (aligned with the effectiveeld)heating of the sample and/or damage to the probe limits theRF power that can be usedSpin locking60Applications: ROESYt2t1xROESY: detection of cross relaxation between transversemagnetization on different spins i.e. transverse NOEuseful in cases where conventional NOE is zerocan also probe relaxation dispersion and chemical exchangeby measuring decay of spin-locked magnetization as functionof the spin-locking eld strengthSpin locking61Applications: cross-polarization in solidsSLy1H13CxHartmannHahn cross polarization in solids via dipolarcouplingtransfer of magnetization from abundant 1H to low-abundance13C: need to match eld strengths according to I1,I= S1,Sused for: (a) sensitivity enhancement; (b) transfer ofmagnetization in multiple-pulse experimentsSpin locking6255thExperimental Nuclear Magnetic Resonance ConferenceBoston, 2014The Basic Building Blocksof NMR Pulse SequencesThe EndWant more on the basic theory of NMR?Search for ANZMAG on YouTubeThe end63