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

Abstract

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,,

Modified Morse Potential for Diatomic Molecules

“…[4] to the vibrational data of a diatomic molecule will be to manipulate the potential parameters and adjust the resulting eigenenergy spectrum until this latter is consistent with the measured transition spectrum to within some predetermined limit. In such a procedure, for the sake of economy and practical convenience, we shall not target for fitting every level of the eigenspectrum that the experimental transitions specify relative to some ground state E 0 .…”

“…To make the potential function U(r) of Eq. [4] explicit for computational purposes, it is convenient to define the standard ramp function S(a, b; r) as…”

“…D e r Ն r c [4] which is piecewise analytic and, as will be demonstrated, can accurately fit experimental data with only a small number of ramp segments.…”