On Intermolecular Forces and the Crystal Structures of the Rare Gases

Abstract

The relation between the intermolecular potential field and the stability of crystal structures of the rare gases is investigated for a face-centered cubic lattice and a structure of hexagonal closest packing. Two models of the potential field are used: a Lennard-Jones (s,6) potential and a ``modified'' Buckingham potential (α,6). The effect of zero-point energy is taken into account on the basis of Corner's method. It is found that for an addititive Lennard Jones (s,6) potential (s between 7 and 16) the hexagonal structure is the stable one. For an additive Buckingham potential (α,6), with α varying from 10 to 16, the hexagonal lattice is again more stable than the cubic structure. For both forms of the potential field considered in the analysis, the differences in energy between the two structures is of the order of one ten-thousandth of the cohesive energies of the crystals. These results agree with the conclusions reached by Kihara and Koba, who neglected the influence of zero-point energy. It is known from experiments that neon, argon, krypton, and xenon crystallize in the face-centered cubic lattice. Therefore, if additivity of intermolecular forces is assumed, the results indicate that neither the Lennard Jones nor a modified Buckingham potential can explain the crystal structures of the rare gases except helium. The possible importance of many-body interactions is discussed.