Methods are described for obtaining the orientation dependence of individual motional spectral densities, J1(omega0) and J2(2omega0), from deuterium spin relaxation experiments on polycrystalline materials. Spectral density measurements provide detailed information in a motional regime too fast to be studied by the two-dimensional (2D) exchange method. Their potential as a source of detailed kinetic and geometric information is illustrated for hexamethylbenzene-d18 (HMB). The relaxation behavior of HMB cannot be explained exclusively by six-site jumps around the C6upsilon axis. Agreement between the experimentally determined spectral densities and simulations is improved if the methyl rotation is explicitly included. At ambient temperature the experimental data are best fitted with the simultaneous jump rates, k6=3.85 X 10(8) s-1 and k3=5.0 X 10(11) s-1. This is significantly different from the rate determined using a simple six-site jump model, k6=3.9 X 10(9) s-1. Geometric distortions of the methyl rotation axes can account for the observed motionally averaged electric field gradient tensor. When these distortions are included in analysis of the spectral density data, there is a small, but significant, improvement in the fit. k3 is unchanged and the best fit k6 is reduced to 2.2 X 10(8) S-1, with distortions out of plane by delta=2.5-degrees and in plane epsilon=epsilon’=1.202.