The effect of lattice vibrations on the NMR second moment. II. Intermolecular contribution

Abstract

The intermolecular contribution to the second moment of a dipolar broadened NMR absorption line of a crystalline solid is corrected for molecular vibrations by expressing it in terms of anisotropic vibration tensors of the atoms and libration tensors of the molecules involved. The expressions derived are based on an expansion of the spatial factor in Van Vleck's equation, (3 cos 2θ − 1)/ r 3, in a power series of atomic displacements up to and including its quadratic term. These expressions are valid approximately for any molecule of which the average motion can be described in terms of the crystallographic rigid body motion formalism and are subject to the assumption of uncorrelated molecular motion. The latter assumption is examined by an application of a model of fully correlated motion. Isotropic and anisotropic vibrations in single-crystal and polycrystalline specimens are accounted for by the theoretical results derived. A comparison is presented with experimental second moments of some polycrystalline samples. This is the first treatment of the effect of anisotropic molecular vibrations on the NMR second moment.