Each /-coupling evolution from antiphase to in-phase involves a 90° rotation in the X-y' plane. We can view the refocusing as two steps, first /-coupling evolution with respect to H1 and then /-coupling evolution with respect to H2:

2[2SxI1]I2sin©cos© —(2/)H> 2[S-]I2sin©cos©

2SyI2sin©cos© 1 /—2 J — H2> —Sx sin ©cos©

Because we could do the same thing starting with I2 and get sin© cos© again, we have a final spin state of — Sx [2sin©cos©], and we can say that the CH2 group 13C resonance is edited by a factor of 2sin©cos©, which works out to 1 for DEPT-45, zero for DEPT-90, and —1 for DEPT-135.

Now for a real challenge, let's look at the CH3 group. Again, we start with the z magnetization of one proton, I1, and at the end we will multiply by 3 to account for the coherence transfer from all three attached protons. Everything is the same until the second delay, where we have multiple-quantum coherence (ZQC/DQC) between 13C and H1, which during the delay undergoes / coupling evolution with respect to both of the passive couplings: 13C-1H2 and 13C-1H3. As before, we can consider /-coupling evolution with respect to H2 first and then as a second step consider the /-coupling evolution with respect to H3: -2lX[Sy] ————i -2IX[-2Sxl2] = 4IXSXI2

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