Derivation of Morse potential

Abstract

The Morse potential is widely used in chemistry, physics, and material science to describe interatomic interactions. We show that the Morse potential can be derived from a simple screened charge model accounting for the shielding of the nuclear charge by electron density. In this model, the parameter governing the width of the potential is related to the average shielding strength and the exponents of the atomic orbitals used in electronic structure calculations. The parameter representing the bond dissociation energy of a diatomic molecule is derived by combining the quantum mechanical covalent and classical electrostatic interactions. Moreover, the revealed connection between the parameters of the Morse potential and Pauling’s bond order and electronegativity provides insight into the relation between the classical and quantum mechanical descriptions of chemical bonds. This derivation of the Morse potential from the atomic quantities is expected to contribute to the development of the new basis sets incorporating Slater-type orbitals for electronic structure calculations and the transferable reactive force fields for molecular dynamics simulations. Furthermore, this interpretation of the Morse potential helps to understand the relationships between widely used chemical concepts, including effective atomic charge, bond dissociation energy, electronegativity, and bond order.