Symmetry loss as a criterion for cluster melting, with application to (D2)13

Continuous symmetry measures are proposed as mathematical tools to quantify the extent of cluster symmetry as a function of temperature. In particular, the continuous variation of symmetry as a function of temperature is suggested as a structural criterion for the follow-up of melting in computational studies of clusters. Numerical tests are presented for the (ortho-D2)13 cluster. A thermal distribution of configurations for this cluster was obtained using the path integral Monte Carlo technique. The continuous symmetry measure selected to follow the structural changes of these nearly icosahedral structures was the degree of centrosymmetricity. It is found to have some conceptual advantages and better numerical properties in comparison with the standard root mean square fluctuations in the intermolecular distance, commonly applied as a criterion of cluster melting.