Correlated tensor interactions and rotational-echo double resonance of spin clusters

Abstract

Rotational-echo double resonance (REDOR) is an important tool in solid-state NMR for providing heteronuclear distances via the measurement of through-space dipolar couplings. For isolated IS spin pairs, the REDOR dephasing curve reports on a single distance, while in ISN spin clusters the I-spin dipolar dephasing reflects a nonlinear combination of multiple dipolar tensors and their relative orientations. The interpretation of multispin dephasing in REDOR experiments typically requires numerical simulations, offering little insight into the relationship between the spin dynamics and the underlying tensor interactions. Here a novel paradigm for describing correlated-tensor spin dynamics is presented for the REDOR experiment. Significantly, the I-spin dipolar dephasing curve for an ISN spin cluster is found to be reducible to a sum of 2N-1 generalized dephasing curves, corresponding to spatial tensors for single I-spin transitions in the dipolar spectrum. Both simulations and experiments are presented that illustrate the power of this formalism for describing REDOR dephasing in clusters as large as IS12 and for extracting structural parameters. This approach can be extended to other solid state NMR “recoupling” experiments, underscoring the general applicability of correlated-tensor decomposition in NMR.