On integrating the techniques of direct methods with anomalous dispersion. II. Statistical properties of the...

Results of a statistical study of probabilistic estimates of two-phase structure invariants (TPSI) for Friedel pairs in the case of single-wavelength anomalous scattering are reported. Numerical analysis of the TPSI sign, magnitude and error distributions shows that the concise formula for TPSI by probability theory [Hauptman (1982). Acta Cryst. A38, 632-641; Giacovazzo (1983). Acta Cryst. A39, 585-592] has desirable statistical properties. Computational results for the known structures of cocaine methiodide (N-methylcocaine iodide) and of cytochrome c550 and its PtCl2-4 derivative show that when [E[ values are large most of the signs of the TPSI are correctly determined - for [E[ greater than 1.0, 90% or more of the TPSI signs are positive as predicted - and the errors in the estimated TPSI magnitudes do not exceed approximately 10% for [E[ greater than 1.0 in the small-molecule case or approximately 50% for [E[ greater than 1.5 in the macromolecular case. These results suggest that the theory will be useful for estimating the TPSI for unknown structures.