Quantifying Pseudosymmetry in Molecular Crystals

TL;DR

This paper introduces a new way to measure and quantify approximate symmetry in molecular crystals using a continuous symmetry measure.

Contribution

The novel contribution is applying the continuous symmetry measure (CSM) to quantify pseudosymmetry in crystals.

Findings

The CSM approach reveals hidden insights about approximate symmetry in crystal structures.

The method enables a continuous, quantitative analysis of symmetry in crystals.

Results show how crystals can be classified along a gradient of symmetry rather than as strictly symmetric or asymmetric.

Abstract

Crystal structures that exhibit approximate higher-order symmetry compared with their assigned space group are commonly termed pseudosymmetric. Unlike errors in space group assignments, which are corrected and well-documented in crystallographic databases, information about approximate symmetry is not always readily accessible, and generally lack clear quantification. Here we propose a shift in perspective on crystal pseudosymmetry, introducing quantification through the continuous symmetry measure (CSM) approach. This method, which has proven effective in numerous studies on individual molecules is applied to address crystals in which symmetry arises from the spatial arrangement of molecular sets, irrespective of the symmetry of the individual molecules. The method enables the analysis of extensive crystallographic datasets, uncovering hidden insights associated with approximate symmetry. This approach revises the binary classification of symmetric and asymmetric crystals, introducing a continuous, quantitative, and informative gradient of symmetry. Results of CSM analysis for a variety of crystals will be discussed.