The true diatomic potential as a perturbed Morse function

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Abstract
The problem of representing a diatomic (true) Rydberg‐Klein‐Rees potential Ut by an analytical function Ua is discussed. The perturbed Morse function is in the form Ua = UM + ∑bnyn, where the Morse potential is UM = Dy2, y = 1 −exp(−;a(r − re)). The problem is reduced to determination of the coefficients bn so Ua(r) = Ut(r). A standard least‐squares method is used, where the number N of bn is given and the average discrepancy ΔU = |(Ut − Ua)/Ut| 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 Ev and the rotational constant Bv, 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.