The pair-functional method for direct solution of molecular structures. II. Small-molecule tests

The new pair-functional direct method has been implemented and tested. Like the Patterson function, the pairing force has valuable imaging properties at high resolution. Two simple iterative algorithms were designed to refine on the total pair potential and the normalized intensity correlation coefficient of an atomic model. The first algorithm is a peak-picking method which selects the best-paired high peaks from a density map and then uses the strong reflections to generate a new Fourier filtered map. The second algorithm, the pair-and-square method, uses a tangent formula step instead of the Fourier and is a little more efficient. Computational experiments on a point-atom grid model, with perfect data, reached exact ab initio solutions for up to 600 atoms. Point-atom models were also solved by searching for reduced structures that contained as few as one quarter of the atoms. Seeded searches, guided by a small known fragment, solved up to 30000 atoms on the grid. Realistic tests on actual molecules showed that Sheldrick's [Acta Cryst. (1990), A46, 467-473] test structures of 50-200 atoms can be solved under a variety of conditions.