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

✍ Scribed by M. Dagher; H. Kobeissi; M. Kobressi; J. D'Incan; C. Effantin

• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 490 KB
• Volume: 14
• Category: Article
• ISSN: 0192-8651
• DOI: 10.1002/jcc.540141108

✦ Synopsis

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(lexp( -fn(x)I2 withf,(x) = Ck=, a,P. The problem of the determination of the disposable parameters al, . . . a,, [in order that U(r) fits the given RKR potential] is reduced to that of a set of linear equations in a, 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 X0,-12 bounded by 109 vibrational levels, for which the RKR potential is defiied by the coordinates of 219 points. It is shown that the percentage deviation IU(r)RKR -U(r)l throughout the range of r values is about 0.04% for XX-Li2, 0.0005% for XS--HC1,0.06% for XO,-I,, and 0.05% for B0,-12 (as examples). This approach shows the same success for deep and shallow potentials. The comparison of the computed E, (vibrational energy) and B,, (rotational constant) with their corresponding experimental values shows that a good agreement is reached even for high vibrational levels close to the dissociation.