Related Experiment Video
Updated: Sep 28, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
Published on: July 19, 2019
On integrating the techniques of direct methods and SIRAS: the probabilistic theory of doublets and its applications
Hongliang Xu1, Herbert A Hauptman
1Hauptman-Woodward Medical Research Institute and Department of Structural Biology, School of Medicine and Biomedical Sciences, State University of New York at Buffalo, 73 High Street, 14203, USA. xu@hwi.buffalo.edu
Abstract:
The mathematical formalism of direct methods is here applied to the SIRAS (single-isomorphous replacement combined with anomalous scattering) case. Specifically, the joint probability distribution of three structure factors, which plays the central role in the probabilistic theory of the two-phase structure invariants (doublets), is derived. This distribution leads directly to the conditional probability distribution of the two-phase structure invariants, given the values of selected sets of magnitudes. Furthermore, a probabilistic formula for estimating individual phases of the derivative structure is derived, provided that the heavy-atom substructure is assumed to be known. The formulas were tested for experimental SIRAS data and results are reported.
Related Concept Videos
Applications of Integration to Probability Density Functions
Double Resonance Techniques: Overview
Spin decoupling is usually achieved by...
Integration by Parts: Problem Solving
Introduction to Double Integrals
Fundamental Theorem of Calculus I
Real-Life Applications of Multiple Integrals
