Dipolar recoupling

Dipolar recoupling uses controlled spin rotations to restore sensitivity to NMR dipolar coupling that would otherwise be averaged away, commonly during magic angle spinning. Spinning can narrow spectra by averaging an orientation-dependent interaction; recoupling deliberately preserves a selected part of that interaction so it can reveal spatial information.

REDOR illustrates the experimental purpose. Rotor-synchronized pulses on a second nuclear species change how the coupling contributes during the rotation cycle. A matched reference echo and a dephased echo then supply a coupling-sensitive comparison. Early carbon-13–nitrogen-15 measurements on labeled alanine used isolated-pair calculations and a powder average to choose pulse placement.^[ref]

An original commuting toy model shows how a zero average can become nonzero. Let the interaction bewith dimensionless spin operators and angular-frequency scale $d$. Without control, the integrated coupling over one period vanishes. Ideal instantaneous $\pi$ rotations of the second spin at $T_r/4$ and $3T_r/4$ reverse the sign of $S_z$ between those times. The effective sign $y(t)$ then matches the sign of $\cos ({\omega }_{r}t)$, soHere $\chi$ is the coefficient multiplying $I_z{S}_z$ in the exponent of the interaction propagator $\exp (-i\chi I_z{S}_z)$. It is not automatically the phase of every detected coherence. The model demonstrates controlled sign reversal; it is not a reconstruction of the full REDOR pulse sequence or of all the angular terms in a spinning sample.

Restored sensitivity is not the same as a unique distance measurement. NMR dipolar coupling scales as the inverse cube of separation, but motion, additional spins and the pulse sequence affect the measured echo. NMR pulse errors can also change that echo, which is why reference matching and phase compensation such as XY8 matter.^[ref]