Structure Determination Algorithms in Computational X-Ray Crystallography.

This dissertation focuses on the development and implementation of practical algorithms for solving the phase problem of X-ray crystallography. We based our strategies on the Shake-and-Bake method of structure determination which alternates phase refinement in reciprocal space with density modification in real space. The strategies we consider include variants of Shake-and-Bake which incorporate optimization techniques based on parameter shift, genetic algorithms, tangent formula, and one based on special properties of space group P1. These four approaches have been implemented on a variety of parallel and sequential machines, including a Thinking Machine Corporation CM-5, an Intel iPSC/860, and a network of SGI Indigo workstations. Experimental results show that the tangent formula approach is the most cost-effective means for solving structures of small size, while the parameter shift variant is better for medium -size or larger structures. The P1 approach appears to be promising for structures in certain space groups. We show that the tangent formula approach can be successfully applied to the CRAMBIN structure, which contains approximately 400 atoms in the asymmetric unit cell. This represents the first successful application of a tangent formula-based approach to solve the CRAMBIN structure.