Thermal Responses and the Energy Spectral of Diatomic Molecules Using Nikiforov–Uvarov Methodology

Abstract

The parametric Nikiforov–Uvarov approach and the Greene–Aldrich approximation scheme were used to achieve approximate analytical solutions to the Schrödinger equation, involving an interaction of the modified deformed Hylleraas potential mixed linearly with the improved Frost–Musulin diatomic molecular potential. For each ℓ-state, the energy spectra and normalized wave functions were generated from the hypergeometric function in the closed form. The thermal properties of such a system, including the vibrational partition function, vibrational mean energy, vibrational mean free energy, vibrational specific heat capacity, and vibrational entropy, were then calculated for the selected diatomic molecules using their experimental spectroscopic parameters. Furthermore, the peculiar conditions of this potential were evaluated, and their energy eigenvalues were calculated for the purpose of comparison. The acquired results were found to be in reasonable agreement with those reported in the literature.

The calculation of ro-vibrational energies, franck-condon factors and r-centroids for Yttrium/Scandium oxides in D-dimension

“…The equation (30) is known in the literature as the Deng-Fan potential function [32]. By using Lambert function as z = w(z)e w( z) [33], the screening parameter α is expressed in the following form: When the literature is scanned, it is seen that ro-vibrational energies are calculated for many diatomic molecules by using different potential functions [34][35][36][37][38][39][40][41][42][43]. In this study, taking = a q e r e and the screening parameter as in equation ( 32), Deng-fan potential given by equation (30) will be considered in D-Dimensional (D 3).…”