By employing the extended Nikiforov–Uvarov (ENU) method, we solved the radial Schrodinger equation with the shifted screened Kratzer potential model. The analytical expression of the energy eigenvalues and numerical results were determined for some selected diatomic molecule systems. Variations of the energy eigenvalues obtained with potential parameters and quantum numbers were discussed graphically. Also, variations of different thermodynamic properties with temperature and maximum vibration quantum numbers were discussed extensively. Our results correspond to the results obtained in the literatures. The shifting parameters contribute a great effect to the energy results obtained. It has also been established that there exists a critical temperature at specific entropy values for the selected diatomic molecule systems.
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