Spin–spin relaxation of nuclear quadrupole resonance coherences and the important role of degenerate energy levels

Abstract

We present an extension of a Redfield approach for calculating spin–spin relaxation rates of zero-field nuclear quadrupole resonance (NQR) coherences, which was published in [Kruk et al., PCCP, 2018, 20, 23414–23426]. The oversimplification of the secular approximation made in the recent paper makes the calculation invalid for zero-field NQR and has led to partially large deviations between predicted and experimental data from Bi-containing molecular crystals. Furthermore, these deviations led to speculations about an additional dipole–dipole relaxation mechanism besides the main electric field gradient (EFG) fluctuations. Here, we demonstrate how a complete application of the Redfield relaxation expression eliminates the deviation from experimental data without the need for additional assumptions. In particular, we point out the important role of off-diagonal elements in the Redfield relaxation matrix within the 3/2–1/2 block appearing due to degenerate energy levels. The resulting coupling between single and double coherence spin density elements leads to a faster coherence decay than for all other transitions. The pseudo rotational model for EFG fluctuations, as proposed in the earlier publication and usually applied for isotropic liquids, is extended in a second analysis by introducing a vibrational mode to account for the case of crystalline solids.