Comparison of empirical closed-form functions for fitting diatomic interaction potentials of ground state first- and second-row diatomics

Twenty-one empirical potentials, having simple functional forms and varying numbers of adjustable parameters, were fitted to experimental RKR data for the ground states of 14 first- and second-row diatomics. The goodness-of-fit was evaluated in each case using the statistical least-squares Z-test of Murrell and Sorbie, and functions with more parameters generally produced better fits (lower Z values), as expected. The dependence of the goodness-of-fit varied in a complicated way with the number of adjustable parameters; for a given number of parameters, some functions outperformed others, indicating that certain functional forms give rise to inherently better empirical potentials, at least for the limited set of diatomics selected here.