Centrosymmetric and pseudo-centrosymmetric structures refined as non-centrosymmetric

Abstract

The behaviour of the Flack parameter for centrosymmetric and pseudo-centrosymmetric crystal structures based on crystal structures published as being non-centrosymmetric is presented. It is confirmed for centrosymmetric structures that the value obtained for the Flack parameter is critically dependent on the Friedel coverage of the intensity data, approaching 0.5 for a coverage of 100% and sticking near the starting value for a coverage of 0%. For pseudo-centrosymmetric structures, even those very close to being centrosymmetric, it is found that it is often possible to obtain significant values of the Flack parameter. A theoretical basis for this surprising result is established. It has also been possible to establish an a priori estimate of the standard uncertainty of the Flack parameter based only on the chemical composition of the compound and the wavelength of the radiation. The paper concludes with preliminary presentations of bias in the Flack parameter and of inconsistent chemical and crystallographic data.