Central-transition double-quantum sideband NMR spectroscopy of half-integer quadrupolar nuclei: estimating internuclear distances and probing clusters within multi-spin networks

We introduce a strategy to estimate the size of clusters of recoupled homonuclear half-integer quadrupolar nuclei under magic-angle spinning (MAS) conditions, by combining double-quantum (2Q) sideband NMR experiments with an approximate numerical analysis based on the summation of all spin-pairs present over a given radius of the structure. The experiment relies solely on the evolution of homonuclear 2Q coherences (2QC) among the central-transitions (CT) of half-integer spins and is suitable for probing clusters in network structures, such as those encountered in large groups of oxide-based materials. Experimental B-11, Na-23 and Al-27 NMR results are presented on bis(catecholato)diboron, Na2SO4 and Al2O3, respectively; in each case, the growth of the spin-cluster size was monitored from a series of experiments that employed progressively lengthened 2QC excitation intervals. Our new approach is the first option for probing larger constellations of half-integer spins; it provides similar information as the "multiple-quantum spin counting" experiment, which is well-established for spin-1/2 applications but has hitherto not been demonstrated for half-integer spins undergoing MAS. We also discuss various options for determining the internuclear distance within a (nearly) isolated pair of half-integer spins by comparing the experimental 2Q sideband NMR spectra with results from numerical simulations involving various degrees of approximation.