Nuclear magnetic spin relaxation in molecules undergoing anisotropic rotational brownian motion and internal rotation involving inequivalent sites

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Abstract
The nuclear magnetic dipole-dipole relaxation rate has been calculated for a two-spin system undergoing anisotropic rotational brownian motion associated with an internal rotation. The model for the internal rotation is jumps among three inequivalent sites, two of which are equivalent. Calculations have been carried out for unlike spin-pairs having, as a result of the internal rotation, a time-dependent internuclear distance. The resulting equation can be shown to reduce, under appropriate conditions, to other equations already in the literature, with the exception of that due to Woessner involving internal rotation about an axis at a fixed angle to the symmetry axis of an axial ellipsoid. The reason for this lack of agreement is shown to be Woessner's inconsistent use of time averaging.