Product Operator Analysis Of The Dept Experiment

The DEPT pulse sequence is more difficult to understand than refocused INEPT, but it accomplishes the same thing. Coherence is transferred from to 13C via the one-bond /CH coupling, and the 13C signal is edited according to the number of hydrogens attached. We saw in the refocused INEPT that the refocusing period A can be used to modify the editing: A = 1/(4J) gives all positive peaks, A = 1/(2 J) gives only the CH peak, and A = 3/(4J) gives CH and CH3 carbons positive and CH2 carbons negative. This is due to the effect of refocusing time on the in-phase signal intensity: sin(^JA) for CH, 2sin(nJA)cos(nJA) for CH2, and 3sin(n/A)cos(n/A)cos(n/A) for CH3. DEPT accomplishes the same control over spectral editing by maintaining the refocusing period constant at 1/(2J) and varying the pulse width of the final 1H pulse, 0. The in-phase intensity of the 13C signal in the FID is sin© for CH, 2sin(©)cos(©) for CH2, and 3sin(©)cos(©)cos(©) for CH3. Thus, for a 45° pulse ("DEPT-45": sin© = cos© = 0.707), we get positive peaks for CH, CH2, and CH3 (CH:CH2:CH3 = 0.707:1:1.060), for a 90° pulse ("DEPT-90": sin© = 1; cos© = 0) we see only the CH peaks (CH:CH2:CH3 = 1:0:0), and for a 135° pulse ("DEPT-135": sin© = 0.707; cos© = -0.707) we see positive peaks for CH and CH3 and negative peaks for CH2 (CH:CH2:CH3 = 0.707:-1:1.060).

To understand the pulse sequence, we will try to get an overview of what is happening and then look at some simplified product operator analysis. Consider first the CH case in the DEPT-90 experiment. Ignoring the 180° pulses, the DEPT-90 sequence can be viewed as an INEPT sequence in which the coherence transfer is split up into two steps (Fig. 7.41): the two 90° pulses are no longer simultaneous and between them we have an intermediate state in coherence transfer: multiple-quantum coherence (ZQC and DQC).

The 90 °x 1H pulse puts the 1H magnetization on the — y' axis, and /-coupling evolution for a period of exactly 1/(2/) allows this in-phase magnetization to evolve into antiphase. For simplicity, we assume that the 13 C and 1H are on-resonance so we can ignore chemical shift evolution during the delays. The 13C 90° pulse then converts this to a mixture of ZQ and

DQ (—2IXSy = ZQy - DQy). Both operators in the product are in the X-/ plane, so this can be thought of as an intermediate state in coherence transfer.

During the second 1/(27) delay, we have no /-coupling evolution because ZQC and DQC do not undergo evolution of the active (1H-13C) coupling of the MQC. Because both 1H and 13C are on-resonance, we can ignore chemical shift evolution as well. The next pulse, the second 90o pulse on 1H, completes the coherence transfer by moving the 1H operator from the X-y' plane to the z axis, resulting in antiphase 13C coherence (2SyIz). The final 1/(2/) delay is for refocusing: the antiphase 13C coherence undergoes /-coupling evolution back to the in-phase state and we can observe the FID with 1H decoupling. The result is exactly the same as a refocused INEPT with refocusing delay set for observing the CH 13 C signal. All we have done is pull apart the simultaneous 1H and 13C 90o pulses and insert a delay of 1/(2/) between them.

The next step in understanding the DEPT-90 sequence is to insert the 180o pulses and look at their effect on chemical shift evolution for "real" 1H and 13 C peaks that are not on-resonance. For this it is best to consider what kind of evolution is going on at each stage of the pulse sequence. In the first delay, we have 1H coherence that is undergoing /-coupling evolution (in-phase to antiphase) as well as 1H chemical shift evolution, so we can write "/" and "vH" in this space. The 180o 1H pulse at the end of this delay reverses the 1H chemical shift evolution so that after this we have "—vH." But now we have ZQC and DQC, so the chemical shift evolution that occurs in this second delay is "—vH — vC" for DQC and "—vH + vC" for ZQC. For simplicity let's consider just the DQC part: "—vH — vC." Notice that the 1H chemical shift evolution that occurred in the first 1/(2/) delay is now refocused by the opposite 1H chemical shift evolution in the second delay. We can think of the first two 1/(2/) delays as a 1H spin echo, with the 1H 180o pulse in the center (Fig. 7.42). There is no /-coupling evolution during this second delay because ZQC and DQC are not affected by the active / coupling. At the end of this delay, the 1H 90o pulse

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