Solving the crystal structures of zeolites using electron diffraction data. I. The use of potential-density histograms

The maximum-entropy and likelihood method for solving zeolite crystal structures from electron diffraction data is modified to use potential-map-density histograms as an additional figure of merit. The experimental histogram is compared to an idealized one (based on known zeolite structures) using Pearson and Spearman correlation coefficients. These supplement the use of log-likelihood estimates as figures of merit to select the optimal solution from a collection of phase sets. The method has been applied with success to seven zeolite and one inorganic crystal structures that have varying associated data quality. The technique works easily even with two-dimensional data sets of less than 50 unique diffraction data and a resolution of less than 2 A. The method is very fast, and the computer time needed on a modest PC was never more than a few minutes.