The use of X-ray anomalous scattering for the detection of small deviations from centrosymmetry

Abstract

A quantitative relation is obtained between Bijvoet differences and the deviations from centrosymmetry of a structure. An expression is derived for the root-mean-square value of Δ, where Δ=[I(H)-I(H̅)]/σN²,σN² =Σ^N_j=i f²_J, in terms of <|Δr_j|> and k" where #916;r_j are the deviations in atomic coordinates from ideal centrosymmetry, and k"=Δf"/f'. Curves are given connecting r.m.s. Δ with <|Δr_J|> for a two-dimensional hypothetical model. When <|Δr_J|> is small the r.m.s. is quite sensitive to <|Δr_J|> with a moderate anomalous scatterer present in the structure. The behaviour of the Bijvoet ratio is also studied empirically.