Fast synthesis and refinement of the atomic pair distribution function

A fast method for calculating the atomic pair distribution function is described in the context of performing refinements of structural models. Central to the speed of synthesis is the approximation of Gaussian functions of varying full widths at half-maximum using a narrower Gaussian with a fixed full width at half-maximum. The initial Gaussians are first laid down as delta functions which are then convoluted with the narrower Gaussian to form the final pattern. The net result is an algorithm, which has been included in the Rietveld refinement computer program TOPAS, that synthesizes and refines structural parameters a factor of 300-1000 times faster than alternative algorithms/programs, with speed advantages increasing as the number of atomic pairs increases.