REPULSION, A Novel Approach to Efficient Powder Averaging in Solid-State NMR

A novel approach to efficient powder averaging in magnetic resonance is presented. The method relies on a simple numerical procedure which based on a random set of crystallite orientations through simulation of fictive intercrystallite repulsive forces iteratively determines a set of orientations uniformly distributed over the unit sphere. The so-called REPULSION partition scheme is compared to earlier methods with respect to the distribution of crystallite orientations, solid angles, and powder averaging efficiency. It is demonstrated that powder averaging using REPULSION converges faster than previous methods with respect to the number of crystallite orientations involved in the averaging. This feature renders REPULSION particularly attractive for calculation of magic-angle-spinning solid-state NMR spectra using a minimum of crystallite orientations. For numerical simulation of powder spectra, the reduced number of required crystallite orientations translates into shorter computation times and simulations less prone to systematic errors induced by finite sets of nonuniformly distributed crystallite orientations.