Analytical development to determine vibrational energy levels and dissociation energy of diatomic molecules

This study presents the development of an analytical method for calculating vibrational energy levels and dissociation energy of diatomic molecules by solving the Schrödinger equation (SE) via the Floquet theorem and the resonating averages method (RAM) in the presence of a cubic together with a quartic anharmonic perturbation. Our technique reposes on the identifying coefficients of the Taylor expansion series of Morse potential in terms of polynomial anharmonic perturbation parameters. The accuracy of our results is illustrated through numerical calculations for different examples of diatomic molecules: H₂, HF, HCl, LiH, CO, and NO, taken from the literature. Furthermore, we present comparisons of the calculated values obtained using the Morse potential parameters of the above-mentioned molecules, with those of authors existing in the literature.