The exact summation of asymptotic ion-pair potentials in simple metallic structures

Abstract

A new approach to the problem of developing a tractable and physical effective ion-ion potential in simple metals for use in computer simulation is suggested. Essentially the procedure involves separating the interaction into its asymptotic (large ionic separation) form, together with a short-range correction potential. It is shown that the asymptotic form can be summed exactly over any periodic structure, and expressions are developed which allow calculation of the contribution of the asymptotic form to lattice energy, elastic constants and phonon dispersion curves. Tables of the numerical values of the sums for body centred cubic, face centred cubic and hexagonal close packed lattices are included. Extension of the technique to the case of disordered or imperfect structures with periodic boundary conditions is discussed.