Approximate Symmetry in Low-Symmetry Space Groups: P2 and C2

Abstract

This project determined the frequency of approximate periodic symmetry in well-determined (R ≤ 0.050) organic crystal structures refined in space groups (SGs) #3 (P2) and #5 (C2, A2, I2). The survey considered structures with Z′ > 1 (Z′ is the number of crystallographically independent molecules) and Z′ = 1 = 2(¹/₂) (two molecules, each on a 2-fold axis). The reasons that group #3 occurs rarely (20 structures) have been analyzed. Of the 570 SG #5 structures examined, 13 (2%) should have been refined in a higher symmetry group, leaving 557 reliable structures. The frequency of approximate symmetry in SG #5 is high (73%) but is somewhat lower than that in SG #1 (P1; 86%) and in SG #7 (Pc, Pn, Pa; 83%). As was found for SG #1, many of the enantiopure substances (95 of 471) mimic centrosymmetric packing; in another 17, the achiral parts of the molecule are segregated in layers described by non-Sohncke symmetry. Molecular layers well described by a layer group occur considerably less frequently than in SGs #1 and 7, but in SG #5, there are more structures in which symmetric layers are related by a good 2_x axis perpendicular to the layer normal but with x not close to either 0 or 1. A guide to identifying and documenting approximate periodic symmetry has been deposited.