Implementation of Morse potential for approximation of vibrational terms of diatomic molecules

We analysed the problem of approximation of the potential function of a diatomic molecule by a Morse model function with constant anharmonicity $\nu x$ using the Birge–Sponer extrapolation. The analysis of the approximations used in the derivation of the Morse equation shows that the solution of this problem is ambiguous. A scheme for optimizing the selection of initial parameters is proposed, which is illustrated by examples taken from the literature. The advantages of delineation of anharmonicity in the excitation of vibrational levels by deviations of the value $\nu x$ from the constant value according to Morse are demonstrated. An attempt is made to use the dimensionless anharmonicity parameter $x^*$ as a universal characteristic of the shape features of the electronic term of the molecule.