Pervasive approximate periodic symmetry in organic P1 structures

Abstract

The goal of this project was to identify the prevalence of approximate symmetry in organic P1 structures. In the November 2019 version of the Cambridge Structural Database (CSD), there are 2592 organic, P1, R ≤ 0.050 structures; complete, unique entries are available for 1407 Z = Z′ > 1 and 1049 Z = Z′ = 1 structures. All the Z > 1 structures can have approximate symmetry; the Z = 1 structures were scanned to find those composed of molecules or ions that might lie on a special position and those that have two or more large molecules or ions that are very similar. The number of Z = 1 structures so identified was 285, of which 49 were grouped with the Z > 1 structures because Z effective > 1. The packing in each of the 1407 + 285 = 1692 structures was investigated. The 144 that should almost certainly have been described in a smaller or higher-symmetry unit cell were removed from the list; 120 of the 144 are composed of achiral or racemic material. (About half of the Z = 1 and 89% of the Z > 1 structures are composed of enantiopure material.) Approximate periodic symmetry was found in 86% of the 1337 remaining Z > 1 structures and in 72% of the 211 remaining Z = 1 structures. About a third of the enantiomerically pure structures mimic inversion symmetry; 38% have approximate rotational symmetry. For the structures of achiral and racemic material, distorted glide or mirror symmetry is more common than is distorted inversion symmetry. Approximate rotational and glide symmetry was found to be periodic in two dimensions considerably more often than in three. In 4% of the structures, different layer types alternate or layers are related by approximate local rotations, as well as by small translations. In 5% of the structures, different parts of the molecule are segregated into two-dimensional regions that have different approximate symmetries. More than a third of the structures that are a distorted version of a higher-symmetry structure were determined at T ≥ 288 K.

Prevalence and Significance of Approximate Symmetry in Organic Pc Structures

“…Approximate, periodic symmetry is very common in organic structures having more than one independent formula unit ( Z′ >1). This generalization has been documented for Z′ >4 structures [1] and P 1 structures, [2] and is shown here for Pc structures.…”

“…In 72 of the 347 reliable SG #7 structures (21 %), there is one layer type that has good approximate symmetry but that is offset from adjacent layers in a way that precludes approximate 3‐D symmetry. The prevalence of layers having approximate symmetry higher than that of the 3‐D structure has been reported previously [2,13] …”

“…Thirteen structures are composed of layers having different approximate symmetry; an example, LIZLOX, [25] is shown in Figure 6. This type of arrangement has been described previously [1,2,13] . Six of the 13 are salts and/or co‐crystals in which the layers differ chemically.…”

“…The methodology was essentially the same as for the survey of P 1 structures [2] . Version 5.43 of the Cambridge Structural Database [6] was searched along with the March 2022 updates.…”

Learning from approximate periodic symmetry in organic P1 structures

“…The article by Brock (2022) is the result of an ambitious 3+ year long project to study the occurrences of approximate symmetries in the space group P1. Brock selected the November 2019 version of the Cambridge Structural Database (CSD; Groom et al, 2016) where 2592 reports of organic crystal structures (based on Z, Z 0 and an R value 0.05) were found.…”