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 n y n , where the Morse potential is U M = Dy 2 , 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 Δ U = |( U t − U a )/ U t | is observed over the useful range of r . N is varied until Δ U is stable. A numerical application to the carbon monoxide X 1 ∑ state is presented and compared to the results of Huffaker 1 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 Δ U 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 Δ E and Δ B 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.