GENERALIZED MORSE ANALYTIC-FUNCTION FOR THE TRUE DIATOMIC POTENTIAL OF THE RKR TYPE

The problem of the representation of the RKR (or IPA) diatomic potenti al by a simple analytic function is considered. This old problem has f or a fairly good solution the Coxon-Hajigeorgiou function U(x) = D[1 - exp(-f(n)(x)]2 with f(n)(x) = SIGMA(m=1)n a(m)x(m). The problem of th e determination of the disposable parameters a1, ... a(n) [in order th at U(r) fits the given RKR potential] is reduced to that of a set of l inear equations in a(m) where a standard least-squares technique is us ed. The application to several states (ground or excited) of several m olecules shows that a fairly ''good'' fit is obtained for n is similar to 10, even for the state XO(g)-I2 bounded by 109 vibrational levels, for which the RKR potential is defined by the coordinates of 219 poin ts. It is shown that the percentage deviation \U(r)RKR - U(r)\ through out the range of r values is about 0.04% for XSIGMA-Li2, 0.0005% for X SIGMA-HCl, 0.06% for XO(g)-I2, and 0.05% for BO(u)-I2 (as examples). T his approach shows the same success for deep and shallow potentials. T he comparison of the computed E(v) (vibrational energy) and B(v) (rota tional constant) with their corresponding experimental values shows th at a good agreement is reached even for high vibrational levels close to the dissociation. (C) 1993 by John Wiley & Sons, Inc.