Direct Methods are commonly used by crystallographers to determine relatively small crystal structures. However, traditional approaches do not appear to be extensible to larger structures. The combination of a new formulation of the phase problem of x-ray crystallography based on Hauptman's minimal principle, and advances in massively parallel computing, have led to the development of our Shake-and-Bake solution strategy. This approach to crystal structure determination consists of a cyclical process which alternates phase refinement in reciprocal space with the imposition of phase constraints through an atomic interpretation of the electron density in real space in an effort to determine the set of phases that minimize the minimal function.
Our computer program SnB, which is based on Shake-and-Bake, has been developed over the past three years, and has been used successfully to solve more than three dozen structures over a variety of space groups. Highlights of SnB include i) solving two previously complex and important unknown 100-atom structures (Ternatin_E and Ternatin_D), which had escaped solution for over a decade, in about an hour, ii) solving numerous other previously unknown structures, some of which could not be solved by traditional direct methods, iii) dramatically improving the success rates over traditional direct methods, and iv) re-solving Crambin, a 400-atom structure, in a matter of several hours. The original solution to Crambin relied on special properties of the Crambin molecule and the measurement of additional x-ray data. Further, previous attempts to solve this structure by direct methods in other laboratories had failed. These attempts were significant in that more than 500,000 ambiguities were considered without success, while we obtained a success rate of approximately 4%.
A number of phase refinement techniques have been considered within the Shake-and-Bake framework, including the tangent formula, where the minimal function is used only as a passive figure-of-merit. Experimentation has shown that the tangent formula can be a cost-effective alternative to traditional phase refinement approaches. For this reason, the tangent formula has been incorporated as an optional phase refinement technique into SnB.
Recently, traditional optimization strategies have been successfully revisited, including genetic algorithms and simulated annealing, for exploiting the minimal function to solve the phase problem within the framework of Shake-and-Bake. Previous attempts at using traditional optimization strategies with the minimal function, but without the alternation between real and reciprocal space, had failed.
SnB has been shown to be more robust than traditional methods in terms of solving structures based on partial structure information. In addition, SnB can be successfully applied to difficult electron diffraction data sets.
Initially, experimentation was performed on an Intel iPSC/2, Intel iPSC/860, and Thinking Machines Corporation CM-2. The current version of SnB was developed on a Thinking Machines Corporation CM-5, and is available on the CM-5, Unix workstations, the Cray C90, and the new massively parallel Cray T3D. The package is available commercially from both Molecular Structures Corporation and MacScience, and is also available on machines at the Pittsburgh Supercomputing Center.