Searching over a domain critical function. Recasting the phase problem of X-ray crystallography

X-ray crystallography is the study of crystal structure determination by X-ray diffraction analysis. In order to recover the crystal structure from the diffraction data, one needs to know the values of diffracted X-ray beams in both intensity and phase. However, the phases of the diffracted X-ray beams are lost in the experiments and have to be derived from the observed diffraction intensities. This derivation of correct phases constitutes the phase problem of X-ray crystallography. Recently, a new formulation of the phase problem based on a minimal function has been proposed [2]. It is suggested that the set of values which minimize this minimal function forms the set of correct phases. For this function, it is important to produce a solution that is close, in terms of the input vector in the domain of the function, to the unique optimal solution. In this paper, we present a heuristic minimization search technique which shows promising results on the minimal function. This technique performs local search in the domain space in an effort to determine the global minimum. The local search procedure employs a variant of hill climbing and exploits on implicit chemical constraints. In this paper, a description of the heuristic search algorithm is given, along with a presentation of master/slave MIMD implementations on an intel iPSC/860 Hypercube and a Connection Machine CM-5.