Analytical representation of potential energy surfaces for diatomic systems: a centenary historical review and new perspectives

Abstract

Interatomic potentials laid at the heart of the molecular physics. They are a bridge between spectroscopic and structural properties of a molecular systems. In this work, a century-old review, from 1920 to 2020, of functional forms used to analytically represent potential energy as a function of interatomic distance for diatomic systems is presented. With such a purpose fifty functions were selected. For all of them motivation and main mathematical features are discussed. Our goal is to provide a chronological pathway showing how to calculate each parameter that composes the interatomic potentials, as well as the methods to obtain spectroscopic constants from them. A comparative evaluation for the N2, CO and HeH+ systems in their ground electronic states is also presented. Some results of a work presented at the Quitel Congress in 2018, are also presented. Moreover, a methodology from a mathematical point of view to obtain correct potential energy functions for diatomic systems is introduced. Finally, a new and flexible function to represent the potential energy interactions of diatomic systems for the whole domain of internuclear separations is proposed. This function is a member of a family of functions containing a product of an exponential and a polynomial. A method for generating the parameters of the new potential as a function of Dunham’s parameters is described. Coefficients for 22 selected diatomic systems with elements from the first to the sixth rows, including some ground and excited electronic states, are presented. To quantify the accuracy of the so constructed potential energy functions, the least-squares Z-test method, proposed by Murrell and Sorbie, is used. Furthermore, main spectroscopic parameters are calculated and compared with available data