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different gradient strength to prevent any kind of untwisting from occuring. The advantage of this approach is that no spin echoes are required to refocus evolution that happens during the gradients. The disadvantage is that echo-antiecho phase encoding cannot be incorporated because there is no selection of coherence order during the t1 period.

### 11.7.5 Edited HSQC

Editing (modification of the sign of crosspeaks based on the type of carbon—CH3, CH2, or CH) is easily accomplished by allowing a period of1 JCH-coupling evolution of time 1/J while we have 13C SQC. We saw in Chapter 6 (Section 6.8) how the in-phase 13C coherence of a CH or CH3 group reverses sign after a 1/J delay while a CH2 group does not. This is the strategy of the APT experiment. Adding a spin echo that allows only J-coupling evolution at the end of the t1 period will accomplish this without interfering in any other way with the pulse sequence (Fig. 11.43). The fact that we are starting with antiphase rather than in-phase coherence does not change the effect of the 1/J delay. For example, for a CH carbon:

2SV Iz cos(^c t^1—J) — Sx cos(^c t^1—J) — 2SV Iz cos(^c t1) For a CH2 group we have to consider coupling to both protons-H1 and H2:

2Sy Iz

2SVI

V Iz

omitting the cosine multiplier and considering only coherence that transferred from Hi in the first coherence transfer step. For the first delay, the antiphase relationship to H1 refocuses from antiphase to in-phase (2Syli -—- - Sx) and the in-phase relationship to H2 defocuses from in-phase to antiphase (-Sx --— - 2SyI2). During the second delay they reverse roles again: -2SyI2 -— Sx -—- 2Syli. As always, each time we change from antiphase to inphase or vice versa as the phase of the observable operator (13C in this case) advances by 90° in the counterclockwise direction. Finally, for a CH3 group we consider coupling to H1,H2, and H3:

For each delay there is a phase advance of 270° because there are three J couplings that are active: J1, J2, and J3 (all equal). In the first step the 13C coherence refocuses with respect to H1 and defocuses with respect to H2 and H3 as the S operator rotates by 90° three times: Sy — - Sx — - Sy — Sx. The normalization factor of 4 is used because we are multiplying by two Iz operators, each of which carries a factor of 1/2 in the density matrix representation. Overall we see the editing effect:

CH: 2SyIz W) -2SyIz (reversed) CH2 : 2SyI1 — 2SyI1 (unchanged) CH3 : 2SyI1 — 2SyI1 (reversed)

This editing is carried through the rest of the sequence and shows up in the sign of the observed in-phase 1H coherence. In the 2D data processing we phase the CH and CH3 crosspeaks positive, which makes the CH2 crosspeaks negative.

11.7.6 Sensitivity Enchancement by Preservation of Equivalent Pathways

In every 2D experiment we have looked at, the chemical-shift evolution during the t1 delay produces two terms—sine and cosine—and in each case only one of them survives the mixing step to reach the FID as observable magnetization. The HSQC experiment is no exception:

Evolution: 2Sy Iz -—2SyIz cos(^ci1) - 2SxIzsin(^ci1)

90y1H,90x13C .

Mixing: 2Sy Izcos(^ci1) — 2IxSzcos(^ci1) (observable1HSQC)

90„1h,90x13c

-2SxIzsin(^ci1) y — -2IxSxsin(^ci1) (nonobservable ZQC/DQC)

The second (sine) term produced by the evolution delay has all the information we need—it is antiphase 13C coherence labeled with the 13C chemical shift in t1—but it is lost because its phase (Sx) causes it to be unaffected by the 90°x 13C pulse at the end of t1. Effectively we are throwing away half of our signal at this point. A new method was developed to "save" this wasted signal and boost the sensitivity of HSQC and many other experiments. These modified pulse sequences are called "sensitivity enhanced" or "sensitivity improved" (Bruker adds "si" to the pulse sequence name) and the strategy is called "preservation of equivalent pathways" (PEP) because the two terms are equivalent except for their phase.

The strategy is quite simple: after the mixing step, the cosine term is refocused as before with a spin echo of duration 1/(27) whereas the sine term "sits out" the refocusing delay on the sidelines because ZQC and DQC do not undergo /-coupling evolution with respect to the active coupling (1JCH):

2Ix Sz cos(^c t1) ) Iy cos(^c t1) -2IxSxsin(^ct1) ) -2IxSxsin(^ct1)

Then the cosine term is flipped to the z axis where it "sits out" another 1/(2/) refocusing delay while the sine term, converted by the same pulse to antiphase 1H coherence (completing the coherence transfer), is refocused to in-phase 1H coherence:

Finally, a 90° 1H pulse flips the cosine term back to the X-y' plane:

90y 1H

90y 1H

Now we have observable in-phase 1H coherence coming from both terms. This is some pretty fancy footwork in the world of spin choreography: taking one partner for a spin while the other sits out, then reversing the roles. The complete pulse sequence is shown in Figure 11.44. Note that each of the 1/(2/) delays is a spin echo with simultaneous 1H and 13C 180° pulses in the center to prevent any chemical-shift evolution and permit only /-coupling evolution. Some fancy phase-cycling tricks are required to get the desired pure cosine and sine terms with the same phase in t2. This is equivalent to acquiring two FIDs in which one has the opposite sign for the second (sine) term. Adding the two FIDs gives the pure cosine term: 2 Ix cos(^c t1), and subtracting with a 90° shift in receiver phase gives the pure sine term: 2 Ix sin(^c t1). Thus we have the same two FIDs we would get with a States mode experiment acquiring the "real" and "imaginary" FIDs for each t1 value. Because we also acquire noise in the two FIDs we have increased the noise by V2 (because it is random), and the increase in sensitivity (S/N) is 2/V2 = V2 or 1.414. An increase in sensitivity of 41% is worth a little bit of trouble!

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