A relationship between the 2-body energy of Kaxiras-Pandey and Pearson-Takai-Halicioglu-Tiller Potential Functions

Abstract

A parametric relationship between the Pearson-Takai-Halicioglu-Tiller (PTHT) and the Kaxiras-Pandey (KP) empirical potential energy functions is developed for the case of 2-body interaction. The need for such relationship arises when preferred parametric data and adopted software correspond to different potential functions. The analytical relationship was obtained by equating the potential functions derivatives at zeroth, first and second order with respect to the interatomic distance at the equilibrium bond length, followed by comparison of coefficients in the repulsive and attractive terms. Plots of non-dimensional 2-body energy versus the non-dimensional interatomic distance verified the analytical relationships developed herein. The discrepancy revealed in theoretical plots suggests that the 2-body PTHT and KP potentials are more suitable for curve-fitting "softer" and "harder" bonds respectively.