Nuclear spin-lattice relaxation from hindered rotations in dipolar solids

A semiclassical theory is developed for the nuclear spin-lattice relaxation in dipolar solids resulting from hindered rotations of a general class of molecules in which the separations of the resonant nuclei in a molecule are equal. Within the weak-collision framework of nuclear spin-lattice relaxation the nuclear-spin coordinates are treated quantum mechanically while the spatial rotations are treated classically as simultaneous, independent Poisson processes constituting a Markov chain. Threefold rotations of C${\mathrm{H}}_3$ and multiple hindered rotations of N${\mathrm{H}}_4^{+}$ and P${\mathrm{F}}_6^{-}$ ions are used as illustrations of the theory.