The problem of representing a diatomic (true) Rydberg-Klein-Rees potential U ' by an analytical function U" is discussed. The perturbed Morse function is in the form U" = U M + Cb, y", where the Morse potential is U M = Dy2, y = 1 -exp( -a(r -re)). The problem is reduced to determination of the coefficients b, so UYr) = U ' ( r ) . A standard least-squares method is used, where the number N of b, is given and the average discrepancy n = I(U' -U a ) / U ' I is observed over the useful range of r. N is varied until n is stable. A numerical application to the carbon monoxide X 'C state is presented and compared to the results of Huffaker' 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 is obtained for N = 7 with a gain in accuracy. Computation of the vibrational energy E, and the rotational constant B,, for both potentials, shows that the present method gives values of and a 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. 0 1995 by John Wiley & Sons, Inc.In the early decades of quantum mechanics, the rotationless potential U ( r ) was given by an analytical function. The functions of Durham3