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

The 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‐ f n ( x )] 2 with f n ( x ) = Σ   m = 1 na m x m . The problem of the determination of the disposable parameters a 1 … a n [in order that U(r) fits the given RKR potential] is reduced to that of a set of linear equations in a m 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 XO g —I 2 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 X ΣLi 2 , 0.0005% for X ΣHCl, 0.06% for XO g I 2 , and 0.05% for BO u I 2 (as examples). This approach shows the same success for deep and shallow potentials. The comparison of the computed E v (vibrational energy) and B v (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.