Generalized morse analytic function for the “true” diatomic potential of the RKR type

Abstract

AbstractThe problem of the representation of the RKR (or IPA) diatomic potential by a simple analytic function is considered. This old problem has for a fairly good solution the Coxon‐Hajigeorgiou function U(x) = D[1 ‐ exp‐fn(x)]2 with fn(x) = Σ amxm. The problem of the determination of the disposable parameters a1 … an [in order that U(r) fits the given RKR potential] is reduced to that of a set of linear equations in am where a standard least‐squares technique is used. The application to several states (ground or excited) of several molecules shows that a fairly “good” fit is obtained for n ∼ 10, even for the state XOg—I2 bounded by 109 vibrational levels, for which the RKR potential is defined by the coordinates of 219 points. It is shown that the percentage deviation |U(r)RKR ‐ U(r)| throughout the range of r values is about 0.04% for XΣLi2, 0.0005% for XΣHCl, 0.06% for XOgI2, and 0.05% for BOuI2 (as examples). This approach shows the same success for deep and shallow potentials. The comparison of the computed Ev (vibrational energy) and Bv (rotational constant) with their corresponding experimental values shows that a good agreement is reached even for high vibrational levels close to the dissociation. © John Wiley & Sons, Inc.