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.

Anharmonic properties: Ionic model of the effects of compression and coordination change

“…Although there is still qualitative agreement between the data and the ionic model, the discrepancies are such that the exponential form used for the repulsive potential appears to become too hard (too large a second derivative, resulting in too high an average frequency) upon compression when compared with the observed properties. It is conceivable that slightly improved values could be found for the parameters in the crystal-independent potential models based on such a comparison [e.g., Sirdeshmukh and Rao, 1975]; however, the more fundamental assumption concerning the validity of an exponential repulsive (and in general, central forces) term, separable from the Coulomb term in the ionic potential, needs also to be addressed [see Hafemeister and Flygare, 1965;Hafemeister and Zahrt, 1967;Gilbert, 1968;Carlson, 1973;Davies, 1981].…”

van der Waals Function for Molecular Mechanics

“…The Thomas–Fermi–Dirac statistical and self-consistent-field theories give reliable results that the vdW repulsion energy ( V rep ) can be very well fitted by a simple exponential Born–Mayer term, , V rep ( R ) = A exp­(− bR ), where A and b are constants. Starting from the Schrodinger equation and taking H 2 as a model system, we rededuce the expression of the ground state energy of H 2 at a larger distance.…”

“…As R decreases, the exponential term is increasingly important; ignoring the other terms makes R –2 n –2 dominant, leading to the potential diverging to negative infinity. According to eq , when R is large enough, the dispersion can be approximately with asymptotic multipole expansion, but when simply add the expansion with the Born–Mayer term, , it will cause the potential to dive toward negative infinity like Exp-6 potential . One way to deal with this problem is introducing in damping function as Tang and Toennies et al did. − However, the form of the damping function such as Tang and Toennies is too complicate to be used in a molecular mechanic force field.…”

Evaluation of the Fourth‐Order Elastic Constants of NaCl‐Structure Alkali Halide Crystals

“…Values of ionic radii and coefficients Pij have been taken from Pauling[29]. repulsive hardness parameters p have been used as those derived from overlap integrals[30]. The repulsive strength parameter b and the van der Waals constant Cdd are calculated from the crystal equilibrium condition and the expression for the SOE constant Cll given by Garg et al[9].…”