Continuous symmetry measures: From point groups to space groups

TL;DR

This paper discusses the development of algorithms to measure molecular symmetry and their potential extension to crystal symmetry analysis.

Contribution

The paper introduces new algorithms for symmetry analysis and explores their application to crystals.

Findings

Exact and approximate algorithms for calculating molecular symmetry have been developed.

Efforts are underway to extend these methods to crystal symmetry analysis.

Abstract

The CSM (Continuous Symmetry Measure) was developed in the 1990s by Avnir, Peleg and Zabrodsky as a measure for the symmetry level of molecules ([1]).

For a given molecular structure, the calculation of the CSM is a nontrivial task. Over the past 8 years, we have developed exact and approximate algorithms for the calculation of the CSM in various conditions, depending on the size and type of the molecules ([2]-[5]).

It is natural to try to extend these methods to the symmetry analysis of crystals, where we could have a continuous scale on which the fit of a given crystal to a given space symmetry group will be measured.

In this talk I will describe the algorithms we developed for molecules, and our work in progress towards extending these methods to the symmetry analysis of crystals.

Joint work with Inbal Tuvi-Arad.