Advances and some recent applications of the origin-free modulus sum function

Abstract

Abstract Since its discovery, the direct methods origin-free modulus sum function [Rius, J., Acta Cryst A49 (1993) 406—409] has been responsible for the solution of a number of difficult crystal structures of minerals and other inorganic compounds from powder diffraction data. This is principally due to the efficiency, robustness and simplicity of implementation of this phase refinement function. The first part of the contribution describes some recent examples on the application of the origin-free modulus sum function to complex structures. In the second part, a powerful variant of this function is introduced which discriminates even better the correct solutions from the wrong ones. This is illustrated with its application to single-crystal data of three selected organic structures. One of these test structures contains 317-atom molecules and is regarded as one of the most difficult structures to be solved with reciprocal space direct methods. This variant could also be useful for those phase refinement strategies based on alternating reciprocal- and real-space procedures, provided that the weak reflections are known.