5 Heteronuclear Correlation Spectroscopy H.C-COSY We will generally discuss heteronuclear correlation spectroscopy for x =C(in natura abundance!), since this is by far the most widely used application. However, all this can also be applied to other heteronuclear spins, like 3P, 5N, 1%F,etc In the heteronuclear case, there are some important differences that allow to introduce additional features into the NMR spectra all heteronuclear coupling constants J(H-3C)are very similar, ranging from ca. 125 Hz (methyl groups)up to ca. 160 Hz(aromatic groups)in contrast to the homonuclear couplings 2J CH H)and 3J(H, H), which can differ by more than an order of magnitude(ca. 1 Hz-16 Hz This feature allows to adjust delays for coupling evolution to pretty much their optimum length for all signals r.f. pulses on ' H andC can(and actually must! )be applied separately, due to the very different resonance frequencies for different isotopes. Thus, H andC spins can, e.g., be flipped separately, resulting in refocussing of the heteronuclear coupling. For the same reason, heteronuclear decoupling can also be applied during the acquisition time The basic COSY sequence can be readily extended to the heteronuclear case Again, during tI proton chemical shift $2I evolves, as well as heteronuclear coupling Jis will evolve (following the quite illogical convention, we will use /-insensitive - for the proton spins and s sensitive- for the heteronucleus, i.e.,C)
61 5 Heteronuclear Correlation Spectroscopy H,C-COSY We will generally discuss heteronuclear correlation spectroscopy for X = 13C (in natural abundance!), since this is by far the most widely used application. However, all this can also be applied to other heteronuclear spins, like 31P, 15N, 19F, etc.. In the heteronuclear case, there are some important differences that allow to introduce additional features into the NMR spectra: - all heteronuclear coupling constants 1J(1H-13C) are very similar, ranging from ca. 125 Hz (methyl groups) up to ca. 160 Hz (aromatic groups) in contrast to the homonuclear couplings 2J ( 1H, 1H) and 3J(1H, 1H), which can differ by more than an order of magnitude (ca. 1 Hz - 16 Hz). This feature allows to adjust delays for coupling evolution to pretty much their optimum length for all signals. - r.f. pulses on 1H and 13C can (and actually must!) be applied separately, due to the very different resonance frequencies for different isotopes. Thus, 1H and 13C spins can, e.g., be flipped separately, resulting in refocussing of the heteronuclear coupling. For the same reason, heteronuclear decoupling can also be applied during the acquisition time. The basic COSY sequence can be readily extended to the heteronuclear case. Again, during t1 proton chemical shift WI evolves, as well as heteronuclear coupling JIS will evolve (following the quite illogical convention, we will use I – insensitive – for the proton spins and S – sensitive – for the heteronucleus, i.e., 13C)
For the simplest case, an I-S two-spin system, we get the following evolution(only shown for the elevant term that will undergo coherence transfer during the 90 pulse pair after tI, i.e., 2 Iv s,) 90°y()t fly (_2t1)sin(πJst1) 90°x(D),90°(S) t2 →>2L2 S,cos(91t)sin(πJst1) The transfer function is the same as for the H, H-COsY. We will get modulation in F1(from the ti FT) with the proton chemical shift Q2I and the heteronuclear coupling JIS, and the coupling is ntiphase. Also, in F2 (from the data acquisition during the t2 period) we will get the carbon chemical shift( since we do now have a carbon coherence, 2Iz Sy), and it is also antiphase with respect to JIS. We will therefore get a signal which is an antiphase duble in both the h and C dimensions, split with the JHC coupling However, in the heteronuclear case, we can greatly improve the experiment by decoupling Depending on the presence or absence of 180 pulses, we can choose to refocus or evolve chemical shift and/or heteronuclear coupling: chemical shift evolution is refocussed, whenever a 180 pulse is centered in a delay. For the refocussing of heteronuclear coupling, the" relative orientation""of the two coupling partners must change, i.e., a 180 pulse be performed on one of them(cf table) All these results can be verified by product operator calculations -a good exercise! By inserting a 180 pulse on C in the middle of our tI period, we can decouple the protons from C, so we wont get JIS evolution during tI, won't get a sin(IJIs ty) modulation and hence no antiphase splitting in FI after FT, but instead just a singulett at the proton chemical shift frequency
62 For the simplest case, an I–S two-spin system, we get the following evolution (only shown for the relevant term that will undergo coherence transfer during the 90° pulse pair after t1 , i.e., 2 Iy Sz ): 90°y (I) t1 Iz ¾¾¾® Ix ¾® 2 Iy Sz cos (WI t1 ) sin (p JIS t1 ) 90°x (I), 90°y (S) t2 ¾¾¾¾¾¾¾® 2 Iz Sx cos (WI t1 ) sin (p JIS t1 ) ¾® … The transfer function is the same as for the 1H,1H-COSY. We will get modulation in F1 (from the t1- FT) with the proton chemical shift WI and the heteronuclear coupling JIS, and the coupling is antiphase. Also, in F2 (from the data acquisition during the t2 period) we will get the carbon chemical shift (since we do now have a carbon coherence, 2 Iz Sy ), and it is also antiphase with respect to JIS. We will therefore get a signal which is an antiphase dublet in both the 1H and 13C dimensions, split with the 1JHC coupling. However, in the heteronuclear case, we can greatly improve the experiment by decoupling. Depending on the presence or absence of 180° pulses, we can choose to refocus or evolve chemical shift and/or heteronuclear coupling: chemical shift evolution is refocussed, whenever a 180° pulse is centered in a delay. For the refocussing of heteronuclear coupling, the “relative orientation” of the two coupling partners must change, i.e., a 180° pulse be performed on one of them (cf. table). All these results can be verified by product operator calculations – a good exercise! By inserting a 180° pulse on 13C in the middle of our t1 period, we can decouple the protons from 13C, so we won’t get JIS evolution during t1 , won’t get a sin (p JIS t1 ) modulation and hence no antiphase splitting in F1 after FT, but instead just a singulett at the proton chemical shift frequency
δ(H) evolves 8(C)evolves JHc evolves H) is refocussed 8(C)evolves JHC is refocussed 8(H)evolves 8(C)is refocussed JHC is refocussed 8(H)is refocussed(C)is refocussed JHC evolves /2 (of course, chemical shift evolution of 'H or 3C occurs only when this spin is in a coherent Heteronuclear decoupling can also be performed during the direct acquisition time. This is done by constantly transmitting a Bi field at the H frequency. This causes transitions between the a and B spinstates of H (or, rotations from z to-z and back, about the axis of the B field). If the rate of these H spin flips is faster than JIS, then heteronuclear coupling will be refocussed before it can develop significantly, and no JIs coupling will be observed. In praxi, heteronuclear decoupling is performed by using-instead of a continuous irradiation- composite pulse sequences optimized for decoupling behaviour, which allow to effectively flip the H spins ov spins over a wide range of chemical shifts with minimum transmitter power, similar to the spinlock sequences used for TOCSY. Some opular decoupling sequences are, e.g., WALTZ or GARP The use of decoupling sequences"freezes"spin states with respect to the heteronuclear coupling. e, in-phase terms like Sx will stay in-phase and induce a signal in the receiver coil corresponding to a singulet(after FT). Antiphase terms like 2lSr will stay antiphase, won't refocus to in-phase terms and will not be detectable at all
63 d( 1H) evolves d( 13C) evolves JHC evolves d( 1H) is refocussed d( 13C) evolves JHC is refocussed d( 1H) evolves d( 13C) is refocussed JHC is refocussed d( 1H) is refocussed d( 13C) is refocussed JHC evolves (of course, chemical shift evolution of 1H or 13C occurs only when this spin is in a coherent state) Heteronuclear decoupling can also be performed during the direct acquisition time. This is done by constantly transmitting a B1 field at the 1H frequency. This causes transitions between the a and b spinstates of 1H (or, rotations from z to -z and back, about the axis of the B1 field). If the rate of these 1H spin flips is faster than JIS , then heteronuclear coupling will be refocussed before it can develop significantly, and no JIS coupling will be observed. In praxi, heteronuclear decoupling is performed by using – instead of a continuous irradiation – composite pulse sequences optimized for decoupling behaviour, which allow to effectively flip the 1H spins over a wide range of chemical shifts with minimum transmitter power, similar to the spinlock sequences used for TOCSY. Some popular decoupling sequences are, e.g., WALTZ or GARP. The use of decoupling sequences “freezes” spin states with respect to the heteronuclear coupling, i.e., in-phase terms like Sx will stay in-phase and induce a signal in the receiver coil corresponding to a singulet (after FT). Antiphase terms like 2 Iz Sx will stay antiphase, won’t refocus to in-phase terms and will not be detectable at all!
With this knowledge, we can remove the heteronuclear coupling from both the Fl and F2 dimension of the H, C-COSY experiment, by decoupling during t, and t2 △ t2 Since heteronuclear coupling cannot evolve during tI, but we do need a heteronuclear antiphase term for the coherence transfer, we have to insert an additional delay A, before the 90 pulse pair. Also we need to refocus the carbon antiphase term(after the coherence transfer) to in-phase coherence before acquiring data under h decoupling, which is done during A This pulse sequence will give a singulet cross-peak in both dimensions. However, we will also have chemical shift evolution during the two coupling evolution delays A(H chemical shift) and A2(C chemical shift), which will scramble our signal phases in both dimensions, so that we have to process this spectrum in absolute value mode We can avoid this be introducing a pair of 180 pulses in the two coupling evolution delays. As shown before, this will not interfere with the JIs evolution, but refocus chemical shift evolution t1 t △ In this version, the evolution of h chemical shift(during ti) andC chemical shift(during t2)are completely separated from the evolution and refocussing of the heteronuclear coupling(during the delays△land△2) 90(1)t Ix-)2 Iy S, cos(g2t1)—)2 Iy s cos(s1t1)sin(πJs△1) 90°x(1),90°(S 212S×cos(gat)sin(xJs△)- Sy cos(2nt1)sn(rJs△n)
64 With this knowledge, we can remove the heteronuclear coupling from both the F1 and F2 dimension of the H,C-COSY experiment, by decoupling during t1 and t2 : Since heteronuclear coupling cannot evolve during t1 , but we do need a heteronuclear antiphase term for the coherence transfer, we have to insert an additional delay D1 before the 90° pulse pair. Also, we need to refocus the carbon antiphase term (after the coherence transfer) to in-phase coherence before acquiring data under 1H decoupling, which is done during D2 . This pulse sequence will give a singulet cross-peak in both dimensions. However, we will also have chemical shift evolution during the two coupling evolution delays D1 (1H chemical shift) and D2 (13C chemical shift), which will scramble our signal phases in both dimensions, so that we have to process this spectrum in absolute value mode. We can avoid this be introducing a pair of 180° pulses in the two coupling evolution delays. As shown before, this will not interfere with the JIS evolution, but refocus chemical shift evolution: In this version, the evolution of 1H chemical shift (during t1) and 13C chemical shift (during t2) are completely separated from the evolution and refocussing of the heteronuclear coupling (during the delays D1 and D2 ): 90°y (I) t1 D1 Iz ¾¾¾® Ix ¾® 2 Iy Sz cos (WI t1 ) ¾® 2 Iy Sz cos (WI t1 ) sin (p JIS D1 ) 90°x (I), 90°y (S) D2 ¾¾¾¾¾¾¾® 2 Iz Sx cos (WI t1 ) sin (p JIS D1 ) ¾® Sy cos (WI t1 ) sin (p JIS D1 )
After FT, we get a 2D H, C correlation spectrum ith each cross-peak consisting of a single line, with uniform phase. The factor sin(TJIS Ay does not contain a ti modulation(which would lead to a duble in F1),but merely a constant, which can be maximized by setting A1=712J F2 Actually, the sequence can be written more elegantly by combining the two C 180 pulses into a single pulse. Instead of first refocussing the evolution during tI, and then during A1, one can accomplish the same result with a single 180 pulse in the center of(t1 A1) v2|lz△z2|LA2 t2+△2 t,2+△2 This saves us one 180 pulse! No big deal?-well, no pulse is perfect, and this is not only due to sloppy pulse calibration, but even inherent in the pulse: with limited power from the transmitter, our bulse has a finite length(usually >20 excitation bandwidth is also limited(cf. the FoURIer pairs), and that the effective flip angle for a 180 pulse"(on resonance) will drop significantly at the edges of the spectral window! This causes not only a decrease of sensitivity, but also an increase of artifacts Example: for a 20 us 180 on-resonance pulse (i.e, 25 kHz B1 field), one gets at +10,000 Hz offset(80 ppm for C at a 500 MHz spectrometer) an effective flip angle of ca. 1350-which means that instead of going from to-2(clean inversion), one gets equal amounts of -z and x,y magnetizatIo The best pulse sequence for a H, c-COsY spectrum is therefore the following
65 After FT, we get a 2D 1H,13C correlation spectrum with each cross-peak consisting of a single line, with uniform phase. The factor sin (p JIS D1 ) does not contain a t1 modulation (which would lead to a dublet in F1), but merely a constant, which can be maximized by setting D1= 1 /2J . Actually, the sequence can be written more elegantly, by combining the two 13C 180° pulses into a single pulse. Instead of first refocussing the evolution during t1 , and then during D1 , one can accomplish the same result with a single 180° pulse in the center of (t1 + D1 ): This saves us one 180° pulse! No big deal? - well, no pulse is perfect, and this is not only due to sloppy pulse calibration, but even inherent in the pulse: with limited power from the transmitter, our pulse has a finite length (usually ³ 20 ms for a 13C 180° pulse). This means, however, that its excitation bandwidth is also limited (cf. the FOURIER pairs), and that the effective flip angle for a “180° pulse” (on resonance) will drop significantly at the edges of the spectral window! This causes not only a decrease of sensitivity, but also an increase of artifacts. Example: for a 20 ms 180° on-resonance pulse (i.e., 25 kHz B1 field), one gets at ±10,000 Hz offset (= 80 ppm for 13C at a 500 MHz spectrometer) an effective flip angle of ca. 135° – which means that instead of going from z to -z (clean inversion), one gets equal amounts of -z and x,y magnetization The best pulse sequence for a H,C-COSY spectrum is therefore the following:
t/2△2 An analysis of the rather complicate delays can be quickly done: after the first 90 pulse, ' H chemical shift will evolve during (A/2+t/2 ti/2)(the 1800 carbon pulse does not affect H chemical shift evolution! ) However, the following 180 proton pulse"reverses"the chemical shift evolution then, and it runs backwards"during the last part, so that H chemical shift evolution occurs during(△12+t/2+t2-△1/2)=t1.△1 Evolution of the heteronuclear coupling will also start immediately after the creation of ' H coherence and continue during (A1/2+t/2-t/2+A1/2)=A(coupling evolution is"reversed by each 180 pulse, on either one of the two coupling spins So, again the chemical shift will only evolve during tr (and turn up as chemical shift frequency after FT), not during A1, and we can easily optimize the delay A1=12J, since JIs evolves only during this delay, not during tr So far we have limited ourselves to simple r's two-spin systems. In reality, however, more than one roton can be directly bound to a carbon nucleus: CH /CH2/CH3. As long as we"are on proto (.e, we have a ' H coherence), this doesnt make a difference: each proton is always coupled to just a single carbon (C). However, after the coherence transfer onto C, the carbon couples simultaneously to 1-3 protons(with the same J coupling constant) Let's look at the refocussed INEPT INEPT (Insensitive Nuclei Enhancement Polarization Transfer) sequence, which is the ID equivalent of our H, C-COSY sequence(i.e, without tI period ) it starts with the creation of H coherence, the Jis evolves during AI (H chemical shift is refocussed), and the resulting antiphase term undergoes a coherence transfer onto C with the 90 pulse pair H⊥∏L画
66 An analysis of the rather complicate delays can be quickly done: after the first 90° pulse, 1H chemical shift will evolve during (D1 /2 + t1/2 + t1/2) (the 180° carbon pulse does not affect 1H chemical shift evolution!). However, the following 180° proton pulse “reverses” the chemical shift evolution then, and it “runs backwards” during the last part, so that 1H chemical shift evolution occurs during (D1 /2 + t1/2 + t1/2 - D1 /2) = t1 . D1 Evolution of the heteronuclear coupling will also start immediately after the creation of 1H coherence and continue during (D1 /2 + t1/2 - t1/2 + D1 /2) = D1 (coupling evolution is “reversed” by each 180° pulse, on either one of the two coupling spins!). So, again the chemical shift will only evolve during t1 (and turn up as chemical shift frequency after FT), not during D1 , and we can easily optimize the delay D1 = 1 /2J , since JIS evolves only during this delay, not during t1 . So far we have limited ourselves to simple IS two-spin systems. In reality, however, more than one proton can be directly bound to a carbon nucleus: CH / CH2 / CH3 . As long as we “are on proton” (i.e., we have a 1H coherence), this doesn’t make a difference: each proton is always coupled to just a single carbon (13C). However, after the coherence transfer onto 13C, the carbon couples simultaneously to 1-3 protons (with the same 1J coupling constant). Let’s look at the refocussed INEPT INEPT (Insensitive Nuclei Enhancement Polarization Transfer) sequence, which is the 1D equivalent of our H,C-COSY sequence (i.e., without t1 period): it starts with the creation of 1H coherence, the JIS evolves during D1 ( 1H chemical shift is refocussed), and the resulting antiphase term undergoes a coherence transfer onto 13C with the 90° pulse pair
67 90°() 90°x(1),90y(S) →1→)2 yAsin(Js△) →2 I s, sin(πJs△1) We can easily optimize Al by setting it to 2JIs, so that the sine factor will be 1 for all>C-bound protons. However, once we do have a carbon antiphase coherence and try to refocus it, we have to deal with all protons directly bound to the same carbon 2LzSx->212 Scos(πJs△2)+ Sy sin(πJs△2) (shown in bold face is the detectable in-phase term, antiphase terms cannot be observed under ' H decoupling during the acquisition period t2 for a CH2 group we now have two(equal)couplings, JIs and JIs, to the two H spins I and I' 2Lz Sx Lz Sx cos(πJs△2)cos(πJIs42)+ Sy sin(πJs42)cos(πJs△2) +212 Sy cos(πJs2)sin(πJs△2)+2 SiNsin(πJsA2)sn(rJis2) In order to end up with detectable in-phase terms, we have to refocus the antiphase coupling JIs and not evolve the other coupling JIS for a CH, group similar to the CH2 case, we can only get in-phase C magnetization, if we refocus the antiphase coupling to the first proton I and not evolve the two other couplings ]'Is and JIs to the other two methyl protons, 2L2Sx→>… Sy sin(πJs△2)cos(πJls42)cos(πJIs42)… All other combinations will be either single, double or even triple antiphase terms
67 90°y (I) D1 90°x (I), 90°y (S) Iz ¾¾¾® Ix ¾® 2 Iy Sz sin (p JIS D1 ) ¾¾¾¾¾¾¾® 2 Iz Sx sin (p JIS D1 ) We can easily optimize D1 by setting it to 1 /2JIS , so that the sine factor will be 1 for all 13C-bound protons. However, once we do have a carbon antiphase coherence and try to refocus it, we have to deal with all protons directly bound to the same carbon: - for a CH group: D2 2 Iz Sx ¾® 2 Iz Sx cos (p JIS D2 ) + Sy sin (p JIS D2 ) (shown in bold face is the detectable in-phase term, antiphase terms cannot be observed under 1H decoupling during the acquisition period t2) - for a CH2 group: we now have two (equal) couplings, JIS and J’IS , to the two 1H spins I and I’: D2 2 Iz Sx ¾® 2 Iz Sx cos (p JIS D2 ) cos (p J’IS D2 ) + Sy sin (p JIS D2 ) cos (p J’IS D2 ) + 2 Iz Sy I’z cos (p JIS D2 ) sin (p J’IS D2 ) + 2 Sx I’z sin (p JIS D2 ) sin (p J’IS D2 ) In order to end up with detectable in-phase terms, we have to refocus the antiphase coupling JIS and not evolve the other coupling JIS ! - for a CH3 group: similar to the CH2 case, we can only get in-phase 13C magnetization, if we refocus the antiphase coupling to the first proton I and not evolve the two other couplings J’IS and J”IS to the other two methyl protons, D2 2 Iz Sx ¾® … Sy sin (p JIS D2 ) cos (p J’IS D2 ) cos (p J”IS D2 ) … All other combinations will be either single, double or even triple antiphase terms
Generally, we get-for the observable term Sy-a factor sin(t Jis 4y)cosm-(T /s 4y) for a Chn group, and we have to choose our delay A wisely to get a signal from all groups 10 0.8 -CH2 0.6 04 0.2 delta2 [1/J 0.0 00204060.8 1.214\ 18 -0.2 -0.4 -0.6 -0.8 -1.0 We can now choose different values for A2 and thus select only certain proton multiplicities Relative signal intensities in INEPT spectra as a function of A2 △,=1 4 △2 △2=34 CH 1 2 CH
68 Generally, we get – for the observable term Sy – a factor sin(p JIS D2 ) cos(n-1)(p JIS D2 ) for a CHn group, and we have to choose our delay D2 wisely to get a signal from all groups! -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 delta2 [1/J] CH CH2 CH3 We can now choose different values for D2 and thus select only certain proton multiplicities: Relative signal intensities in INEPT spectra as a function of D2 D2 = 1/4J D2 = 1 /2J D2 = 3/4J CH 1 2 1 1 2 CH2 1 2 0 - 1 2 CH3 1 2 2 0 1 2 2
By adding and subtracting two INEPT spectra acquired with different A2 settings, one can also select exclusively CH or CH3 groups for CH only:(△ for CH2 only: (4=14) -(A=l4) (CH and CH3 are symmetric about A2=723, but not CH2) for CH3only:(Δ=4)+(△=3/4)-2(△=2) removes cha removes ch The multiplicity selection of the INEPT editing scheme is quite sensitive to misset A2 values However, since the JHC values vary ca. +10 from the average 140 Hz, it is impossible to set A2 exactly to its theoretical values for all carbon resonances simultaneously. As a result, suppression of the unwanted multiplicities in an INEPT editing experiment is far from perfect As an improvement for multiplicity editing, the DEPT (Distortionless Enhancement via Polarization Transfer) experiment has been developed (and is still the most widely used technique for that purpose) X Δ△ decoupl AQ The analysis of the DEPT sequence shows how even rather confusing techniques can be understood or at least described in a quantitative way. After a first glance at the DEPT sequence, we see that we can safely skip any chemical shift evolution for H or C, since both will be refocussed during the times where they are in a coherent state(between the first 90 pulse and the 0 pulse for H; between the first C 90 pulse and acquisition for C). All three delays A are set to 1/2J, so that cos(兀J4=0 and sin(兀J4=0 90°(1) 90°(S) 2I、S
69 By adding and subtracting two INEPT spectra acquired with different D2 settings, one can also select exclusively CH or CH3 groups: for CH only: (D = 1 /2J) for CH2 only: (D = 1 /4J) - (D = 3 /4J ) (CH and CH3 are symmetric about D2= 1 /2J , but not CH2 ) for CH3 only: (D = 1 /4J) + (D = 3 /4J) - 2 (D = 1 /2J) removes CH2 removes CH The multiplicity selection of the INEPT editing scheme is quite sensitive to misset D2 values. However, since the 1JHC values vary ca. ±10 % from the average 140 Hz, it is impossible to set D2 exactly to its theoretical values for all carbon resonances simultaneously. As a result, suppression of the unwanted multiplicities in an INEPT editing experiment is far from perfect. As an improvement for multiplicity editing, the DEPT (Distortionless Enhancement via Polarization Transfer) experiment has been developed (and is still the most widely used technique for that purpose). The analysis of the DEPT sequence shows how even rather confusing techniques can be understood or at least described in a quantitative way. After a first glance at the DEPT sequence, we see that we can safely skip any chemical shift evolution for 1H or 13C, since both will be refocussed during the times where they are in a coherent state (between the first 90° pulse and the q pulse for 1H; between the first 13C 90° pulse and acquisition for 13C). All three delays D are set to 1/2J , so that cos (pJD)=0 and sin (pJD)=0 . 90° (I) D 90° (S) Iz ¾¾® Ix ¾® 2 Iy Sz ¾¾® 2 Iy Sx
For a Ch group, this heteronuclear multi-quantum coherence is not affected by coupling evolution, since the H andC spin are "synchronized"in a common coherence and do not couple to each other in this state. Other coupling partners are not available, so that this terms just stays there during the delay△ 6x(I) 2 ySx 2y e 2lySx cos e +2lsx sin 0 sin 0 During the following acquisition time, only the in-phase C coherence term will be detected For a CH2 group, however, there will be a coupling partner available during the second A delay: the second proton, I'. The JIs coupling will cause the C part of the MQC (Sx) to evolve into antiphase with respect to l A 6x(I),180°x(S) 4lS√T ,-4lySy Iz cos e cose-4LzSy Iz sin e cos e +4ly Sy Iy cos e sin 8+ 4z Sy ly sin e sin e ( the 180x(S)pulse reverses the sign of all terms, Sy>Sy) From these terms, only one is a( double antiphase)C single-quantum coherence that can refocus to detectableC in-phase magnetization during the last delay 4. Both couplings(to I and I')refocus simultaneousl 4 L, syIz sin 0 cos0—){2 SxI,sin e cos 6→} S, sin e cos e For a CH3 group, there are two additional protons(I and r )coupling to the carbon 2L S 8IySxIzrz The 0 pulse can only convert this double antiphase MQC term intoC SQC (which will then refocus during a) pulse in a single 8lySxIzIz--8lzSxrzIz sin e cos e cose- Sy sin e cos e cos 8
70 For a CH group, this heteronuclear multi-quantum coherence is not affected by coupling evolution, since the 1H and 13C spin are “synchronized” in a common coherence and do not couple to each other in this state. Other coupling partners are not available, so that this terms just stays there during the delay D: D qx (I) D 2 Iy Sx ¾® 2 Iy Sx ¾¾® 2 Iy Sx cos q ¾® 2 Iy Sx cos q + 2 Iz Sx sin q + Sy sin q During the following acquisition time, only the in-phase 13C coherence term will be detected. For a CH2 group, however, there will be a coupling partner available during the second D delay: the second proton, I’. The JIS coupling will cause the 13C part of the MQC (Sx ) to evolve into antiphase with respect to I’: D qx (I), 180°x (S) 2 Iy Sx ¾® 4 Iy Sy I’z ¾¾¾¾¾® – 4 Iy Sy I’z cos q cos q – 4 Iz Sy I’z sin q cos q + 4 Iy Sy I’y cos q sin q + 4 Iz Sy I’y sin q sin q (the 180°x (S) pulse reverses the sign of all terms, Sy ® Sy ) From these terms, only one is a (double antiphase) 13C single-quantum coherence that can refocus to detectable 13C in-phase magnetization during the last delay D . Both couplings (to I and I’) refocus simultaneously: D 4 Iz Sy I’z sin q cos q ¾® {2 Sx I’z sin q cos q ® } Sy sin q cos q For a CH3 group, there are two additional protons (I’ and I”) coupling to the carbon: D 2 Iy Sx ¾® – 8 Iy Sx I’z I”z The q pulse can only convert this double antiphase MQC term into 13C SQC (which will then refocus during D) pulse in a single way: qx (I) D 8 Iy Sx I’z I”z ¾¾® – 8 Iz Sx I’z I”z sin q cos q cos q ¾® Sy sin q cos q cos q