The effect of atomic heterogeneity on the exact probability distribution of structure factors – crystals of space group P[unk]

Abstract

Abstract An attempt has been made to study the effect of atomic heterogeneity of various degrees on the probability distribution of the normalised structure factors. This treatment provides a method of studying separately the effect of two factors affecting heterogeneity, namely p = N H/N L and g = f H/f L where N H and N L are numbers per asymmetric unit of heavy and light atoms, respectively and f H and f L are atomic scattering factors of the heavy and light atoms, respectively. A number of real examples of various p and g values indicating different degrees of heterogeneity have been studied. We have shown that in cases of atomic heterogeneity a modified structure factor E′ may be defined which is Gauss distributed irrespective of whether E is Gauss distributed or not. Depending on the parameters p and g, the agreement between the two distributions P(E′) vs E′ and P(E) vs E vary from being poor to excellent. In cases where the agreement is excellent it should be possible, in principle, to obtain the heavy atom position.