Extended accuracy for analytic model potentials for diatomic molecules

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Abstract
Formulas have recently been published which permit the determination of very accurate perturbed‐Morse‐oscillator (PMO) potentials from spectroscopic data. Many of the formulas were presented without a mathematically rigorous derivation. The present work contains such derivations, based on the use of Lagrange series techniques. The derivations are also modified to provide equivalent formulas for two other analytic model potentials, the Dunham and Simons–Parr–Finlan potentials. In addition, general relationships between parameters of the three models are presented, in terms of which one can directly obtain parameters of one model from those of another; the formulas are applied to determine parameters for n?20 for the other two models from published PMO parameters for CO. The suitability and appropriateness of the various models are discussed, especially in relation to problems of convergence and errors due to truncation and roundoff.