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Metallic clusters on a model surface: quantum versus geometric effects

We determine the structure and melting behavior of supported metallic clusters using an ab initio density-functional-based treatment of intracluster interactions and an approximate treatment of the surface as an idealized smooth plane yielding an effective Lennard-Jones interaction with the ions of the cluster. We apply this model to determine the structure of sodium clusters containing from 4 to 22 atoms, treating the cluster-surface interaction strength as a variable parameter. For a strong cluster-surface interaction, the clusters form two-dimensional (2D) monolayer structures; comparisons with calculations of structure and dissociation energy performed with a classical Gupta interatomic potential show clearly the role of quantum shell effects in the metallic binding in this case, and evidence is presented that these shell effects correspond to those for a confined 2D electron gas. The thermodynamics and melting behavior of a supported Na_20 cluster is considered in detail using the model for several cluster-surface interaction strengths. We find quantitative differences in the melting temperatures and caloric curve from density-functional and Gupta treatments of the valence electrons. A clear dimensional effect on the melting behavior is also demonstrated, with 2D structures showing melting temperatures above those of the bulk or (at very strong cluster-surface interactions) no clear meltinglike transition.