rotates the XH magnetization to the z axis and the 13 C 180° pulse reverses the 13 C chemical shift evolution that occurred during the central 1/(27) delay. So during the final 1/(2/) delay, we have "+vC" for chemical shift evolution and "/" for /-coupling evolution (from 13C antiphase to 13C in-phase coherence). We see that the last two 1/(2/) delays form a 13C spin echo with a 13C 180° pulse in the center. Thus, all chemical shift evolution, 1H and 13 C, is refocused in this sequence and we have only the necessary /-coupling evolution to move 1H from in-phase to antiphase before the coherence transfer and to refocus 13C from antiphase to in-phase after the coherence transfer.

Next, we need to make the pulse width of the final 1H pulse variable, with a rotation angle of © (© = 45°, 90°, or 135°). For the CH case, we have already discussed the full coherence transfer, so in the final pulse we have:

Note that the 180°), pulse on the 13 C channel has no effect on Sy .The cosine term is just the product operator we started with, unaffected by the1H pulse, and the sine term is the operator we would get with a full 90° 1H pulse. Note that rotation of the Ix magnetization vector by a 1H B1 field on the ) axis goes from x to —z to — x to +z as © is incremented from 0° to 90° to 180° to 270° in the trigonometric expression. The first term is DQC/ZQC, which will not be observable in the FID—there are no more pulses in the sequence to convert it to observable magnetization. Only the second term represents full coherence transfer to antiphase 13C coherence, which will refocus during the final 1/(2/) delay into in-phase 13C coherence:

Thus, the intensity of the in-phase coherence varies as sin© with the pulse width © of the final 1H pulse for a CH group. This gives intensities of 0.707, 1, and 0.707 for the DEPT-45, DEPT-90, and DEPT-135 experiments, respectively.

Now we can understand all aspects of DEPT clearly, at least for a CH group. The final step is to understand the spectral editing aspect of the DEPT experiment, and here we will have to look at the complexities of CH2 and CH3 groups. For the CH2 group, we can start with I1 and work our way through the pulse sequence. Although starting with I2 would give the same result (coherence transfer to the same 13 C), we can just multiply by 2 when we are finished to reflect the fact that coherence is transferred to the 13 C from each of the two attached protons. Things get more complicated after the 13C 90° pulse. The DQC/ZQC term —2IJS represents a multiple-quantum "dance" between the 13 C nucleus and one of the attached protons (H1), and the other proton (H2) is not involved. While it is true that / coupling is not involved in the evolution of ZQC/DQC, this is true only for the active coupling, in this case the 13C-1H1 coupling. The other coupling, 13C-1H2, is a passive coupling not involved in the MQC and we will see /-coupling evolution with respect to this proton during the second 1/(2/) delay. Because of the spin-echo effects of the two 180° pulses, we can continue to ignore chemical shift evolution but we have to consider the /-coupling evolution due to these passive couplings during the second delay:

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