Nonadditive Triple-Overlap Interactions among Rare-Gas Atoms in the Thomas—Fermi—Dirac Approximation

Abstract

Formulas for the nonadditive overlap energy of interaction among three atoms, based on the Thomas—Fermi—Dirac (TFD) approximation and the assumption of superimposed, unperturbed densities appropriate to the isolated atoms, have been developed for linear and isosceles arrays. Computations based on these formulas and employing March's variational, modified TF density have been performed for three Kr atoms in symmetric linear and equilateral triangular arrays, and also for three He atoms in symmetric linear arrays. For the case of Kr atoms in equilateral configurations, the ratio of the nonadditive energy to the sum of the repulsive pair energies (obtained in the TF approximation) is found to be −2.5% for an internuclear distance of 1 a.u. and to decrease rapidly with increasing separation. Smaller results are found for the symmetric linear arrays. Cancellation between the kinetic-energy and the exchange-energy contributions is partly responsible for the rapid falloff of the nonadditivity effect. The nonadditive overlap energy, as treated here, is appreciable only if the atoms are close enough to produce appreciable triple overlap of their charge distributions. Such close approach is ordinarily prevented by the repulsive part of the pair potential. The range of the nonadditive overlap interaction is enough shorter than the slow-collision diameter that the nonadditivity effects are negligible at physically significant distances—in agreement with results found previously for He arrays by Rosen and Shostak. We find, in both He and Kr, that the triple-overlap nonadditive interaction is smaller than the triple-dipole nonadditive interaction (Axilrod—Teller—Muto) at internuclear separations corresponding to the minimum of the van der Waals potential and the nearest-neighbor distance in the solid. The nonadditive overlap interaction appears too small to account for the anomalous crystallization of Kr into an fcc lattice or to produce a substantial correction to the third virial coefficient of the gas.