This article presents an extension of the report made at the 2nd International Symposium "Non-Covalent Interactions" 10/14/22 in Moscow. That report outlined the basic principles of modeling the potential function of diatomic molecules using the Morse potential. Based on the published results of high-level quantum-chemical calculations, as well as the experimental spectroscopic measurements of the vibrational structure of electronic transitions, potential curves for several molecules were constructed and their approximations were carried out using the Morse formula. The possibilities of using the Morse formula as the simplest anharmonic approximation for describing the features of the shape of potential curves and their vibrational structure of a real molecule are evaluated. A perspective is outlined for studying the bond character in van der Waals diatomic molecules according to the shape and features of anharmonicity function.