Acta Crystallographica Section A

Foundations of Crystallography

Volume 58, Part 1 (January 2002)

research papers

Acta Cryst. (2002). A58, 21-26 [ doi:10.1107/S0108767301014714 ]

A new interpretation and practical aspects of the direct-methods modulus sum function. VIII

J. Rius, X. Torrelles, C. Miravitlles, J. M. Amigó and M. M. Reventós

Abstract: Since the first publication of the direct-methods modulus sum function [Rius (1993). Acta Cryst. A49, 406-409], the application of this function to a variety of situations has been shown in a series of seven subsequent papers. In this way, much experience about this function and its practical use has been gained. It is thought by the authors that it is now the right moment to publish a more complete study of this function which also considers most of this practical knowledge. The first part of the study relates, thanks to a new interpretation, this function to other existing phase-refinement functions, while the second shows, with the help of test calculations on a selection of crystal structures, the behaviour of the function for two different control parameters. In this study, the principal interest is focused on the function itself and not on the optimization procedure which is based on a conventional sequential tangent formula refinement. The results obtained are quite satisfactory and seem to indicate that, when combined with more sophisticated optimization algorithms, the application field of this function could be extended to larger structures than those used for the test calculations.

Keywords: direct methods; modulus sum function; phase refinement.