A Computational Study of Rare Gas Clusters: Stepping Stones to the Solid State

Abstract

An upper-level undergraduate or beginning graduate project is described in which students obtain the Lennard–Jones 6-12 potential parameters for Ne2 and Ar2 from ab initio calculations and use the results to express pairwise interactions between the atoms in clusters containing up to N = 60 atoms. The students use simulated annealing, or the genetic algorithm, to find the globally optimized binding energies and structures of the Ne and Ar clusters. They employ the liquid drop model to extrapolate the cluster binding energies to the solid state and compare the result with the experimental cohesive energy of the rare gas solid. A Windows-based application is provided that allows students to explore the energetic and structural properties of the rare gas clusters. Students encounter the “magic numbers”, for example, N = 13, 55, and others, associated with clusters that have higher-than-expected binding energies arising from enhanced nearest-neighbor interactions. They also estimate the solid density of each element from the size of the model cubic cluster (N = 14) that represents the face-centered unit cell.