A Metropolis-like algorithm to improve phases: some preliminary results

Abstract

A procedure to improve phases by a Metropolis-like algorithm (MLA) in reciprocal space is presented. It uses a density modification method (DMM) in a MLA to evaluate progress and to suggest changes to phase angles. First, in the neighborhood of the trial values derived from a DMM, new options for the phase angles are generated. Then, a DMM is used to evaluate and improve compliance with the rule of nonnegativity of direct methods. The procedure of DMM~ phase change~ DMM-~ phase change is iterated several times. For a centrosymmetric case in which phases may not be changed by a DMM, compliance with the non-negativity rule is judged by the ratio of observed to calculated structure-factor amplitudes, and new options for the phase angles are generated by adding 180 °. For a non-centrosymmetric case both the amplitude and the phase values of the structure factors before and after a DMM may differ. However, only the phase values are used to judge the compliance with the non-negativity rule, and to decide phase shifts in a subsequent phase change step. This procedure is shown to improve the phases determined ab initio by the consistent electron density approach [Bhat (1984). Acta Cryst. A40, C15; (1985). Am. Crystallogr. Assoc. Annu. Meet., Stanford, California. Abstr. HI]. The mean phase errors for the phases obtained by the procedure proposed here ranged from 55 to 25 ° in different tests, significantly better than those obtained from a DMM under similar conditions.