Calculation of even moments of the trigonometric structure factor. Methods and results

Two algorithms for the evaluation of even moments of the trigonometric structrure factor are described. The first algorithm is based on conventional structure-factor algebra in the complex notation and is applicable to any space group with multiplicity of general positions not exceeding 24. The second algorithm, capable of dealing with all space groups, involves an interpretation of trigonometrical expressions input in a symbolic form and a programmed execution of algebraic and analytic operations. The results obtained in this study include the fourth and sixth moments of the trigonometric structure factor for all 230 space groups. It is assumed that all the atoms occupy general positions. All the subsets of hkl indices giving rise to different forms of the trigonometric structure factor (except those for zones and rows) are considered.