  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.
