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Abstract:
Traceless symmetric second-rank tensors such as quadrupole coupling (QC) tensors can be determined from data (line splittings in the case of QC tensors of spin-1 nuclei) collected from rotating crystals about two axes provided these are neither parallel nor orthogonal. We give a simple argument for the latter condition. Rotating a monoclinic crystal about a single axis provides, in general, data for two axes and is sufficient for determining all five independent components of QC tensors. The accuracy of the results of this so-called single-rotation method, however, depends sensitively on the choice of the rotation axis. Here we give an error analysis of this method, focusing attention on the errors introduced by the uncertainty in the direction of the rotations axis. We apply the single-rotation method for measuring the 10 independent deuteron QC tensors in bullvalene, of which only one 50% deuteron-enriched single crystal was available. The challenge lies in the need to disentangle the dependence of 40 resonances on the rotation angle while in no spectrum could more than 36 peaks be resolved. The measured QC tensors are discussed in terms of the local symmetry of the deuteron sites and the approximate C3v, symmetry of the bullvalene molecule in its crystal environment. They provide a reliable basis for studying the complex dynamics of bullvalene in the solid state by deuteron NMR lineshape analysis and 2D exchange spectroscopy.