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

To determine a substructure from single-wavelength anomalous diffraction (SAD) data using Patterson or direct methods, the substructure-factor amplitude (|F|) is first estimated. Currently, the absolute value of the Bijvoet difference is widely used as an estimate of |F| 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 along with measurement errors in the observed data. The multivariate estimation of |F| 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.