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

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.