This study investigates the thermochemical functions of selected diatomic molecular systems under the shifted Newing function framework. By employing the Nikiforov-Uvarov functional analysis method, the radial Schrodinger equation is solved with the help of a Pekeris approximation scheme to check the centrifugal barrier term. vibrational energy solutions obtained are varied with arbitrary vibration quantum numbers. Vibrational energy eigenvalues are seen to increase positively and further degenerate, as the quantum numbers are enhanced. The vibrational energies are also used to study some thermochemical functions with temperature variation. Our results can model the experimental data of the thermochemical functions in literature for the selected diatomic molecules. Negligible deviations computed are within acceptable range and their graphically consideration are presented to support our results.