The true diatomic potential as a perturbed Morse function

The problem of representing a diatomic (true) Rydberg-Klein-Rees potential U^t by an analytical function U^a is discussed. The perturbed Morse function is in the form U^a = U^M + ∑b_nyⁿ, where the Morse potential is U^M = Dy², y = 1 ?exp(?;a(r ? r_e)). The problem is reduced to determination of the coefficients b_n so U^a(r) = U^t(r). A standard least-squares method is used, where the number N of b_n is given and the average discrepancy ΔU = |(U^t ? U^a)/U^t| is observed over the useful range of r. N is varied until ΔU is stable. A numerical application to the carbon monoxide X¹∑ state is presented and compared to the results of Huffaker¹ using the same function with N = 9. The comparison shows that the accuracy obtained by Huffaker is reached in one model with N = 5 only and that the best ΔU is obtained for N = 7 with a gain in accuracy. Computation of the vibrational energy E_v and the rotational constant B_v, for both potentials, shows that the present method gives values of ΔE and ΔB that are smaller than those found by Huffaker. The dissociation energy obtained here is 2.3% from the experimental value, which is an improvement over Huffaker's results. Applications to other molecules and other states show similar results. © 1995 by John Wiley & Sons, Inc.