On integrating the techniques of direct methods with anomalous dispersion. IV. A simplified perturbation treatment...

Results from probabilistic theory for the single-wavelength anomalous-scattering (SAS) Friedel pair, two-phase structure invariants, psi H = phi H + phi-H, are used to show that the SAS three-phase structure invariants, psi HK = phi H + phi K + phi-H-K, tend to positive values that are easily estimated. Appropriate averages of the estimates provide SAS perturbation corrections in the form of positive origin shifts for the probability distribution of psi HK values and for the tangent formula. The theoretical probabilistic results are verified by empirical statistical analyses of model-calculated phases and experimentally measured structure-factor magnitudes for a small-molecule and a protein crystal structure.