Multi-rank nuclear magnetic resonance studies of half-integer quadrupolar nuclei in solids by three-dimensional dynamic-angle correlation spectroscopy

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Abstract
The present work introduces a new three-dimensional nuclear magnetic resonance (3D NMR) experiment for the analysis of half-integer quadrupolar nuclei in solids. The method is based on the multi-rank expansion of the high-field NMR Hamiltonian governing the central transition of these spins in terms of irreducible spherical tensor elements. This approach leads to a temporal spin evolution given by an isotropic term characteristic of each chemical site, as well as by second- and fourth-rank anisotropies depending on the principal values and relative orientations of the shielding and quadrupolar interactions. A method for extracting the 3D spectral distribution correlating these three frequency components is presented, based on the acquisition of dynamic-angle spinning NMR signals collected as a function of different initial and final spinning axes. Computational and instrumental details involved in the acquisition of these 3D dynamic-angle correlation spectroscopy (DACSY) data are discussed, and applications of the DACSY methodology to the analysis of different rubidium salts are illustrated. The new type of chemical information that this experiment can provide and its relation to other NMR techniques that have been recently developed for the analysis of quadrupolar nuclei in solids are also discussed.