Insights into the spin dynamics of a large anisotropy spin subjected to long-pulse irradiation under a modified REDOR experiment

Distance measurements between a spin-1/2 and a second spin bearing a large anisotropy are performed using a modified rotational echo double resonance (REDOR) experiment. By applying pairs of rotor-synchronized π pulses on the detected spin and a single long pulse on the coupled spin the dipolar interaction is efficiently recoupled even at the sudden passage limit where both adiabaticity and the hard pulse approximation are not valid. In this manuscript we derive the theoretical basis for analyzing the behavior of single crystallites in order to gain insight into the mechanism of dipolar recoupling, and in order to find conditions for optimizing the experiment. The use of reduced time and frequency variables show that the signal depends on the ratios of the radio frequency strength ν₁ and the anisotropy, either the CSA (ν_σ) or the quadrupolar interaction (ν_Q), with respect to the spinning frequency ν_R. We derive expressions for the contribution of individual crystallites to the signal arising from the different frequencies mν_d (m = 0, 1 ... 2S) associated with the dipolar interaction and show that they result in a non-random distribution of intensities. For a spin-1/2 with a large CSA (up to 1 MHz and more) we show using calculations and simulations that the result is a recoupling signal that takes maximal values ΔS/S₀ of ∼0.6-0.7, beyond the saturation limit of 0.5, defined by equal contribution of all transitions. For a spin-3/2 we show that at certain conditions the non-random scrambling may result in an apparent saturation-like behavior. In all cases large RF amplitudes are not necessarily required for obtaining efficient recoupling. ¹³C-¹¹B LA-REDOR (Low-Alpha/Low-rf-Amplitude REDOR) dipolar recoupling experiments on 4-methoxyphenylboronic acid were performed following optimization of the spinning rates suitable for low amplitude radio-frequency power levels and show that efficient recoupling can be obtained for a spin-3/2, and that distance determination is not very strongly dependent on the actual value of the quadrupolar coupling constant.