A comparative study of analytic representations of potential energy curves for O2, N2, and SO in their ground electronic states.

In this work, a review of six functional forms used to represent potential energy curves (PECs) is presented. The starting point is the Rydberg potential, followed by functions by Hulburt-Hirschfelder, Murrell-Sorbie, Thakkar, Hua and finalizing with the potential for diatomic systems by Aguado and Paniagua. The mathematical behavior of these functions for the short- and long-range regions is discussed. A comparison highlighting the positive and negative aspects of each representation is also presented. As study cases, three diatomic systems O2, N2 and SO in their respective ground electronic states were selected. To obtain spectroscopic parameters, ab initio energies were first calculated at multi-reference configuration interaction (MRCI) with the Davidson modification (MRCI+Q) level of theory, using aug-cc-pVXZ (X = T,Q,5,6) Dunning basis sets. Such energies were then fitted to respective functional forms. The so-obtained spectroscopic constants are compared also with available literature data.