The invariant character of two-body binding potentials

Abstract

The universality of one-dimensional two-body potential energy surface of real systems with chemical bonds is the shape of the potential energy, which is an inherent invariant character for any systems with a single energy minimum regardless of its analytical presentations. A simple mathematical description of the invariant character is presented. Based upon the invariance, equivalences among various analytical potential models of the same system can be determined and therefore, inter-used. A concept of potential energy well width, 2 δ, together with the potential energy well depth, V min and its position r e, is introduced to fully describe the potential energy of system. As these characteristic parameters of a potential energy curve can be determined from only two points on the potential energy-separation relation, a two-point technique to accurately determine analytical energy potential models for a real chemical bonding system is, therefore, introduced and fitting discrete points for the potential energy functions becomes unnecessary.