Discrepancy indices for use in crystal structure analysis. IV. Theoretical expressions for the indices_BR₁(I) and_BR(I) for any incomplete model of a complex structure

Abstract

General expressions for the discrepancy indices BRI (IN) and BR (IN), which are needed to test the correctness of any type of incomplete model of a complex structure containing any number and species of atoms in the unit cell, are derived for the related and unrelated cases. Explicit expressions for these indices for crystals containing all atoms in general positions are also tabulated for the seven categories of space group in the triclinic, monoclinic and orthorhombic systems. Expressions needed for handling crystals containing atoms in both general and special positions and those needed for taking into account random errors of observation in the intensities are also derived.

Discrepancy indices for use in crystal structure analysis. V. A comparative study of the normalized and unnormalized Booth-type indices in the structure completion stage

“…a~/(lg) [see equations (54) and (55) of Parthasarathy (1975)]. The present ideal procedure was adopted to test the efficiency of the results under identical conditions.…”

“…t The papers by Parthasarathy & Parthasarathi (1972), Parthasarathi & Parthasarathy (1975a), Parthasarathy & Parthasarathi (1975) and Parthasarathy (1975) will be referred to as Parts I, II, III and IV respectively.…”