Multivariate estimation of substructure amplitudes for a single-wavelength anomalous diffraction experiment

Abstract

To determine a substructure from single-wavelength anomalous diffraction (SAD) data using Patterson or direct methods, the substructure-factor amplitude (|F a|) is first estimated. Currently, the absolute value of the Bijvoet difference is widely used as an estimate of |F a| values for SAD data. Here, an equation is derived from multivariate statistics and tested that takes into account the correlation between the observed positive (F +) and negative (F −) Friedel pairs and F a along with measurement errors in the observed data. The multivariate estimation of |F a| has been implemented in a new program, Afro. Results on over 180 test cases show that Afro provides a higher correlation to the final substructure-factor amplitudes (calculated from the refined, final substructures) than the Bijvoet differences and improves the robustness of direct-methods substructure detection.