Dynamical study of metallic clusters using the statistical method of time series clustering

Abstract We perform common neighbor analysis on the long-time series data generated by isothermal Brownian-type molecular dynamics simulations to study the thermal and dynamical properties of metallic clusters. In our common neighbor analysis, we introduce the common neighbor label (CNL) which is a group of atoms of a smaller size (than the cluster) designated by four numeric digits. The CNL thus describes topologically smaller size atomic configurations and is associated an abundance value which is the number of “degenerate” four digits all of which characterize the same CNL. When the cluster is in its lowest energy state, it has a fixed number of CNLs and hence abundances. At nonzero temperatures, the cluster undergoes different kinds of atomic activities such as vibrations, migrational relocation, permutational and topological isomer transitions, etc. depending on its lowest energy structure. As a result, the abundances of CNLs at zero temperature will change and new CNLs with their respective new abundances are created. To understand the temperature dependence of the CNL dynamics, and hence shed light on the cluster dynamics itself, we employ a novel method of statistical time series analysis. In this method, we perform statistical clustering at two time scales. First, we examine, at given temperature, the signs of abundance changes at a short-time scale, and assign CNLs to two short-time clusters. Quasi-periodic features can be seen in the time evolution of these short-time clusters, based on which we choose a long-time scale to compute the long-time correlations between CNL pairs. We then exploit the separation of correlation levels seen in these long-time correlations to extract strongly-correlated collections of CNLs, which we will identify as effective variables for the long-time cluster dynamics. It is found that certain effective variables show subtleties in their temperature dependences and these thermal traits bear a delicate relation to prepeaks and main peaks seen in clusters Ag 14 , Cu 14 and Cu 13 Au 1 . We therefore infer from the temperature changes of effective variables and locate the temperatures at which these prepeaks and principal peaks appear, and they are evaluated by comparing with those deduced from the specific heat data.