On Integrating the Techniques of Direct Methods with Anomalous Dispersion. IV. A Simplified Perturbation Treatment for SAS Phasing

• Published in: Acta crystallographica. Section A, Foundations of crystallography Vol. 53; no. 1; pp. 74 - 83
• Main Authors: Guo, D. Y., Blessing, R. H., Langs, D. A., Hauptman, H. A.
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01.01.1997; Blackwell
• Subjects: Chemistry, Physical - methods; Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; Mathematical Computing; Physics; Probability; Proteins - chemistry; Scattering, Radiation; Single-crystal and powder diffraction; Structure of solids and liquids; crystallography; X-ray diffraction and scattering; X-Rays; Direct method; Perturbation theory; Anomalous scattering; Tangent formula; Structure resolution; Structural invariant; Theoretical study; Amplitude phase; XRD; Crystal structure
• ISSN: 0108-7673; 1600-5724
• DOI: 10.1107/S0108767396011993

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.