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of the refocusing period and I S+ just before the second 90o 13C pulse. Because there is only a pulse on 13 C, the 1H coherence order cannot change. In the center of the evolution period, the 1H 180o pulse converts I+ S+ (DQC, p = 5) to I-S+ (ZQC, p = -3). The first 90o 13 C pulse converts I+So (antiphase 1H coherence) to I+ S+ (DQC). Again, because there is no 1H pulse at this point the I+ operator does not change. During the first 1/(27) delay, I+ undergoes J-coupling evolution to the antiphase product I+ So. The coherence order at each stage can be easily determined by adding the coherence order contribution of each operator in the product, with +4 for I+, —4 for I-, +1 for S+, —1 for S-, and so on. For example, I-S+ has coherence order -3: -4 (I-) +1 (S+). The chemical-shift evolution can also be easily predicted from the operators: I+ S+ will evolve at the rate vH + vC and I-S+ will evolve at the rate - vH + vC (Fig. 11.46, top).

Once we have diagramed the desired coherence order pathway, it is easy to add gradients to select that pathway. One simple solution is to use the 3,4,5 relationship of a right triangle: 3 x 3 + 4 x 4 = 5 x 5. Put a gradient in the first half of t1 of relative amplitude G1 = 5, another in the second half with amplitude G2 = 3, and a third in the refocusing delay with amplitude G3 = 4. As the coherence order p is 5, -3, and -4, respectively, during these three periods, we have a total twist of:

X piGi = 5 x 5 + (-3) x 3 + (-4) x 4 = 25 - 9 - 16 = 0

The pulse sequence is shown in Figure 11.48. The net twist will be zero only for the desired pathway: DQC ^ ZQC ^ 1H SQC. Of course, we have created a new problem: the minimum t1 delay is now twice the time required for a gradient and its recovery. This will lead to a very large phase twist in F1, so we can either present the data in magnitude mode, where phase is not an issue, or insert the appropriate spin echoes to refocus the chemical-shift evolution that occurs during the gradients.

11.9 UNDERSTANDING THE HETERONUCLEAR MULTIPLE-BOND CORRELATION (HMBC) PULSE SEQUENCE

The HMBC experiment is just an HMQC experiment with the 1/(2J) delay set for a J value of about 10 Hz (typical for two- and three-bond JCH) rather than 150 Hz (typical for one-bond 7CH). This corresponds to a much longer 1/(27) delay of 50 ms for remote (multiple-bond) couplings compared to the 3.33 ms used for HMQC and HSQC (direct or one-bond couplings). The protons we are interested in observing are two or three bonds away from a 13 C, and the carbon they are directly bonded to is very likely (99%) to be a 12C. The pulse sequence differs from the HMQC sequence in two ways:

1. Because of the signal loss due to T2 relaxation during the long 1/(27) defocusing delay, the 1/(27) refocusing delay is omitted and we observe antiphase coherence in the FID just as we do in the COSY and DQF-COSY experiments. One consequence of this is that we cannot use 13 C decoupling during the acquisition of the FID because the antiphase lines in the F2 spectrum would cancel and there would be no signal.

2. To suppress the one-bond (HMQC) cross peaks, which would lead to wide doublets in F2 centered on the position of the crosspeaks in the (13C-decoupled) HMQC or HSQC spectrum, a simple trick is applied. After the first 1H 90o pulse a delay of 1/(2 1 7ch) (or -3.33 ms) is followed by a 90o pulse on 13 C. This is identical to the start of the HMQC sequence, right down to the length of the 1/(27) delay. This converts the 1H magnetization from the proton directly attached to the 13C into ZQC and DQC, but the 90o 13C pulse is phase-alternated (+x, +x, —x, -x) whereas the receiver is not (individual FIDs from the first two scans are added to, not subtracted from, the FIDs from the second two scans). This means that any observable 1H magnetization that shows up in the FID due to this pathway will be canceled out by the phase cycle. The 1H magnetization from protons that are two or three bonds away from the 13C, however, is separating into antiphase much more slowly (1/(2 2'3 7ch) - 50 ms) so that after 3.33 ms, it is essentially still in-phase 1H magnetization and is not affected by the 90o 13C pulse (cos(n7r) = 0.995, so only 0.5% of the signal is lost). What follows is a much longer (50 ms) delay to allow these protons that are two or three bonds away from the 13 C to evolve into antiphase with respect to the 13 C. Then a 90o 13 C pulse converts this 1H magnetization into ZQC and DQC that continues through the pulse sequence as it does for the HMQC. This second 90o 13C pulse is phase cycled with the receiver so that the coherences it generates are ultimately added together and appear in the final FID. The pulse sequence is diagramed in Figure 11.49.

The refocusing delay just before acquisition has been eliminated, so the peaks in F2 will be antiphase doublets separated by the long-range 7CH (2-15 Hz). This splitting is in addition to any 1H-1H splitting pattern already present in the 1D proton spectrum (Fig. 11.11). The second 13 C 90o pulse is phase cycled as before to make sure that only 1H magnetization

2,3 j || JCH

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