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