Compact and accurate models for the diatomic potential energy

Two compact analytical models for the diatomic potential energy are presented and tested. The first (6-parameter) model represents a significant improvement on the extended Lennard-Jones (ELJ) function proposed by Hajigeorgiou [J. Mol. Spectrosc. 263, 101 (2010)], and the second (7-parameter) model is a modified Hulburt-Hirschfelder function. The adjustable parameters of the two functions can be determined either by an algebraic scheme that employs semiclassical expressions in terms of vibrational-rotational molecular constants, or by direct nonlinear least-squares fits to available numerical potential functions. Accuracy tests are carried out for a set of ground electronic states of 30 diatomic molecules. The two potential energy functions give accurate representations of the available numerical potential energy curves with average deviations over the 30 molecules of approximately 0.06% of De, or 1 meV (∼ 8 cm−1). The best cases give average absolute deviations of 0.0002% of De, or 0.007 meV (∼ 0.06 cm−1). Quantum-mechanical vibrational eigenvalues of the new potential representations are shown for selected molecules to agree very well with the experimental vibrational energies, with average absolute deviations of much less than 1 cm−1.