A continuous symmetry breaking measure for finite clusters using Jensen-Shannon divergence

TL;DR

This paper introduces a quantitative, statistical measure based on Jensen-Shannon divergence to assess symmetry breaking in finite clusters, enabling detailed analysis of structural distortions and defects.

Contribution

The paper presents a novel symmetry breaking measure using Jensen-Shannon divergence, with software implementation and applications to various finite cluster cases.

Findings

Effective in quantifying surface-induced symmetry breaking in crystallites.

Able to detect atomic displacements from high symmetry positions.

Useful for analyzing collective atomic motions and distortions.

Abstract

A quantitative measure of symmetry breaking is introduced that allows the quantification of which symmetries are most strongly broken due to the introduction of some kind of defect in a perfect structure. The method uses a statistical approach based on the Jensen-Shannon divergence. The measure is calculated by comparing the transformed atomic density function with its original. Software code is presented that carries the calculations out numerically using Monte Carlo methods. The behavior of this symmetry breaking measure is tested for various cases including finite size crystallites (where the surfaces break the crystallographic symmetry), atomic displacements from high symmetry positions, and collective motions of atoms due to rotations of rigid octahedra. The approach provides a powerful tool for assessing local symmetry breaking and offers new insights that can help researchers understand how different structural distortions affect different symmetry operations.