Understanding The Hmqc Pulse Sequence

The HMQC experiment gives exactly the same result as the HSQC, and the data is processed in the same way. There are some differences in sensitivity and peak shape that depend on the size and complexity of the molecule, and the pros and cons of the two experiments are the subject of some debate in the literature. Because it relies on double-quantum and zero-quantum coherences (DQC and ZQC) during the evolution (t1) period, the HMQC is more difficult to explain and understand than HSQC, which uses only the familiar singlequantum transitions that can be diagramed and analyzed using vectors. We discuss it here because it forms the basis of the HMBC (multiple-bond) experiment.

The sequence is similar to the HSQC sequence, but much simpler—there are only four pulses (Fig. 11.45). The preparation period is the same, except that we do not bother to refocus chemical-shift evolution—this ends up being corrected by the final (refocusing) delay. Neglecting chemical-shift evolution, we have 1H magnetization at the end of the first 1/(27) delay which is antiphase with respect to the directly bound 13C. Instead of subjecting this to simultaneous 90o pulses on both 1H and 13C channels, which would cause INEPT transfer of magnetization to antiphase 13 C single-quantum coherence, we have a single 90o pulse on 13 C only. We saw before that this leads to an intermediate state in coherence transfer, a combination ZQC and DQC:

Now we have both the 13 C and the 1H magnetization in the xX-y' plane, not as independent magnetization vectors but tied up together in a product of operators. This is a combination of ZQC and DQC called collectively multiple-quantum coherence (MQC). In the HMQC experiment, the 1H-13C DQC and ZQC precess in the xX-y' plane at rates of vh + vc and vh — vc, respectively, during the evolution (t1) delay (Fig. 11.46). Note that this coherence cannot be called "1H" or "13C" coherence—it involves the entanglement of both nuclei in a mutual dance. The effect of the 180o 1H pulse in the center is to convert DQC into ZQC and vice versa:

180X XH

2Iy Sx

180X XH

DQC/ZQC

Figure 11.46

because only the Iy operator is affected by the 180°x !H pulse. Thus, for the second half of the t1 period, the ZQC that was evolving at a rate of vC — vH is now evolving at a rate of vC + vH, for a total evolution of (vC — vH) x (t1/2) + (vC + vH) x (t1/2) = vC x t1. The net evolution depends only on t1 and vC, so the t1 delay serves the same purpose as the t1 delay in HSQC: to indirectly measure the 13C chemical shift and encode this information as a modulation of intensity of the 1H SQC that is detected in the FID. Even though we only go "halfway" in the process of coherence transfer from 1H SQC to 13C SQC, we still accomplish the goal of labeling the final 1H SQC with the chemical shift of the 13C.

The second 90° 13C pulse converts the ZQC and DQC back into antiphase 1H SQC, which is refocused by the final 1/(27) delay just as it is in the HSQC experiment. This is an important theme that occurs in many of the more sophisticated NMR experiments: multiple-quantum coherences (DQC and ZQC) cannot be directly observed, but they can be created from SQC, allowed to precess, and converted back to measurable SQC. The multiple-quantum coherences can be detected then, but only indirectly. Multiple quantum coherence is essential to the DQF-COSY and DEPT experiments as well, so even though it is difficult to understand it is very important in modern NMR and cannot be ignored.

The spherical operator description of the HMQC experiment is shown in Figure 11.47, along with a diagram of the coherence order. As always, we observe negative coherence order during t2 and positive coherence order during t1 (echo pathway). Because only the 13C chemical-shift evolution is observed during t1, we choose S+ in the DQC/ZQC product operators. Working backward from I-, we have I-S° (antiphase 1H coherence) at the start

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