Abstract
Currently there is considerable interest in analyzing solid-state NMR lineshapes (powder patterns) to obtain information about molecular motion in samples ranging from small molecules to biological macromolecules (Z-5). In the fast motion limit, data analysis normally consists of finding a physically reasonable model for the orientational distribution function of the molecule that yields a calculated powder pattern in agreement with experiment. The purpose of this note is to establish the model-independent information on the orientational distribution function that is contained in a fast-limit powder pattern. Powder lineshapes result from orientation-dependent interactions such as chemicalshift anisotropy (CS) for a spin Z = i nucleus, electric quadrupole coupling (Q) for a spin Z = 1 nucleus, and magnetic dipole-dipole coupling between two spin Z = i nuclei. These distinct physical interactions can all be represented as second-rank tensors p’, h = CS, Q, D, and consequently the position (frequency) of the NMR signal has the same orientation dependence for all three interactions (6-9):
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