Ab initio determination of incommensurately modulated structures by charge flipping in superspace

The charge flipping algorithm proposed by Oszlányi & Süto [Acta Cryst. (2004), A60, 134-141 ] for ab initio reconstruction of crystal structures is generalized towards superspace. Its efficiency is demonstrated by successful reconstruction of eight known incommensurately modulated structures from experimental data. The output of the charge flipping algorithm is an electron density with symmetry P1. The symmetry of the structure is recovered by locating the positions of symmetry operators and averaging the density over the symmetry-related pixels. The reconstruction of a modulated structure by the charge flipping algorithm and the accuracy of the result is demonstrated in detail on the modulated structure of tetraphenylphosphonium hexabromotellurate(IV) bis{dibromoselenate(I)}.