# 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.

## Key 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.

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Source: https://tomesphere.com/paper/PMC12585501