A comparative study of analytical representations of potential energy curves for CO in its ground electronic state

In this work, a comparative study of four functional forms used to represent potential energy curves (PECs) is presented. The starting point is the Hulburt-Hirschfelder, followed by the Extended Rydberg potential function, ending with two of the most recent potentials presented in the literature for diatomic systems: the Araújo-Ballester potential and the Improved Extended Lennard-Jones potential. The chosen potentials have in common the fact that all their parameters are algebraically calculated, without any fitting procedure, and all of them have direct dependence on Dunham's parameters. The mathematical behavior of these functions for the short- and long-range regions is discussed. As study case, the diatomic system $\text{CO}$ in its ground electronic state was selected. To quantify the accuracy of the potential energy functions, the least-squares Z-test method, proposed by Murrell and Sorbie, is used. Furthermore, the main spectroscopic constants and vibrational energy levels are calculated and compared for all potentials.