On prediction of the fractional vibrational energies for diatomic molecules with the improved Tietz potential

Abstract

ABSTRACT New solutions to the -dimensional Schrödinger equation (SE) have been found using the improved Tietz potential (ITP) in the framework of the generalised fractional derivative (GFD). By employing the generalised fractional Nikiforov-Uvarov (GFNU) technique, the analytical formulas of the energy spectra and wave functions have been expressed in terms of the fractional parameters in -dimensions. Furthermore, the derived solutions have been employed for various diatomic molecules (DMs) that have wide applications in chemical and molecular physics. With the aid of molecular constants, the potential energy curves for the chosen DMs have been generated using the ITP. To verify the efficacy of the method used in this study, the vibrational energy levels for various DMs have been predicted in both the classical and fractional forms. It has been demonstrated that the predicted values for the vibrational energy spectra agree with the observed data far better than in the previous studies. Moreover, it is discovered that the vibrational energies of different DMs calculated in the existence of fractional parameters are better in fitting the experimental Rydberg-Klein-Rees (RKR) data than those calculated in the classical case. In light of this, it can be concluded that fractional order has a considerable impact on the vibrational energy spectrum of DMs. As goodness of fit indices, the average absolute deviation (AAD) and mean absolute percentage deviation (MAPD) have been estimated. Based on the estimated AAD and MAAD results, the ITP is an excellent model for fitting the RKR data for all of the selected DMs.