On the crystal structure problem for heavy rare-gas solids: A three-atom exchange perturbation analysis

The observed higher stability of a face-centered cubic (fcc) arrangement of atoms in heavy rare-gas solids, relative to that of a hexagonal close-packed (hcp) structure, is ascribed to the effect of three-atom short-range (exchange) interactions on the static lattice energy, evaluated in first- and second-order exchange perturbation theory. The summations are limited to 66 isosceles triangles with two atoms nearest neighbors of a central atom in the solid. Highly accurate results are reported, in part supplementing those of early work. An approach is taken in which the electrons of each atom are replaced by one electron on a Gaussian orbital with characteristic parameter beta chosen such as to reproduce the attractive part of a Lennard-Jones (6, 12) pair potential, thus implicitly including intra- and inter-atomic electronic correlations. The results, for a wide range of values for the dimensionless parameter beta R (R is the nearest-neighbor distance in the solid at ambient pressure), invariably favor the fee lattice, with a difference between fee and hcp amounting to 0.4% of the total pair cohesive energy for solid argon, krypton and xenon (solid neon is a border case in this analysis). Recent papers on the crystal stability of rare-gas solids are critically examined.