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: