The interplay of structure and dynamics in the melting of small clusters

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Abstract
Extensive classical simulations of the melting–freezing transition of small clusters (N=7–33) of rare gas atoms have been performed in which quenching by steepest descent has been coupled to isoergic molecular dynamics. A mechanistic description of the phase change is given in terms of the local potential minima accessed in the transition region and the isomerization pathways for and the frequencies of interwell passages. All of the small clusters, at energies low in the transition range of energy, exhibit some separation (by factors of approximately 5 to 60) of the short time scale for motions about the various potential minima and the longer time scale separating interwell passages. The onset of diffusion is marked by passages over saddles linking the minima. Fully liquid-like behavior is observed for all the clusters when the time scale separation for the motions no longer exists. The coexistence and magic number phenomena observed in previous simulations are explained in terms of the kinds of potential minima on the surface and the accessibility of one from another. The existence of a potential energy minimum very low relative to the nearest accessible, high-lying minima as well as time scale separation are necessary conditions for the observation of the kind of coexistence of liquid-like and solid-like forms over a well-defined energy or temperature range predicted by a quantum statistical model and observed, e.g., in isoergic and isothermal simulations of the Ar13 cluster. Such conditions are met in some but not all clusters. Structures with underlying pentagonal, and especially icosahedral, symmetry are important for clusters in the size range N=7–33, not only in previously recognized cases; defective icosahedral structures occur among the lower-energy minima even for some clusters for which they had not been considered.

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