Relationship and Discrepancies Among Typical Interatomic Potential Functions

We develop a simultaneous relationship among parameters of the generalized version of the Lennard-Jones, Morse, Rydberg and Buckingham pair potentials, and the two-body portion of the Kaxiras--Pandey potential function by introducing a set of scaling factors. These potential functions are selected according to their frequent adoption in condensed matter and molecular computation. In addition to verifying the parametric relations, theoretical plots of these potential curves show that each of these potential functions is unique in terms of their characteristic shape. However, gaps between these potential functions are narrowed for interatomic interactions possessing lower separation energy and longer interatomic equilibrium distance. Finally, comparison with the \it ab initio results shows that the extended-Rydberg potential energy curve gives the best agreement among the five empirical potential functions, for the specific case of hydrogen
molecule.