Exchange-Charge-Model Calculation of the Born—Mayer Repulsive Potential in Ionic Gases and Crystals

Abstract

By considering the deformation of the free ions and within the framework of the exchange charge model (ECM) of Dick and Overhauser and the technique of symmetrical orthoganalization of Löwdin, we have calculated the radial dependence of the repulsive potential for ionic gases and solids. The repulsive potential is considered to be a summation of the electrostatic energy between effective nuclear charges and the exchange charges, and it very closely fits the form of the Born—Mayer repulsive potential, B exp(—r/ρ). We have shown that the ECM values of the potential for the gases do not depend on the size of the effective nuclear charge and the values of ρ agree to within 10% with the experimental data. The crystalline values of ρ agree with the data reasonably well, but deviations are noted. The calculation of ρ depends only on the Hartree—Fock free-ion functions whereas calculations of dissociation energies, molecular force constants, vibrational frequencies, cohesive energies, compressibilities, and Debye temperatures depend also on the equilibrium spacing. The alkali hydride and hydride—hydride overlap integrals and their radial dependence are tabulated.