Generic representation and evaluation of properties as a function of position in reciprocal space

• Published in: Journal of applied crystallography Vol. 35; no. 6; pp. 655 - 663
• Main Author: Cowtan, Kevin
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England Munksgaard International Publishers 01.12.2002; Blackwell
• Subjects: Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; generic evaluator; Physics; reciprocal space; resolution function; Single-crystal and powder diffraction; Structure of solids and liquids; crystallography; Wilson plot; X-ray diffraction and scattering; Statistical analysis; Atomic position; Structure factors; Structure resolution; Reciprocal lattice; Theoretical study; XRD; Crystal structure
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S0021889802013420

A generalized approach is described for evaluating arbitrary functions of position in reciprocal space. This is a generalization which subsumes a whole range of calculations that form a part of almost every crystallographic software application. Examples include scaling of structure factors, the calculation of structure‐factor statistics, and some simple likelihood calculations for a single parameter. The generalized approach has a number of advantages: all these calculations may now be performed by a single software routine which need only be debugged and optimized once; the existing approach of dividing reciprocal space into resolution shells with discontinuities at the boundaries is no longer necessary; the implementation provided makes employing the new functionality extremely simple and concise. The calculation is split into three standard components, for which a number of implementations are provided for different tasks. A `basis function' describes some function of position in reciprocal space, the shape of which is determined by a small number of parameters. A `target function' describes the property for which a functional representation is required, for example . An `evaluator' takes a basis and target function and optimizes the parameters of the basis function to fit the target function. Ideally the components should be usable in any combination.