The present work deals with the solutions to the radial Schrodinger equation for harmonic plus screened Kratzer potential (HSKP) within the framework of the Nikiforov–Uvarov functional analysis method. The Greene–Aldrich approximation is used to handle the inverse square terms of the HSKP. Reducing the HSKP into Kratzer and screened Kratzer potentials, the energy spectra of selected diatomic molecules, i.e. LiH, HCl, and are computed. Further, the equations for expectation values of several parameters, including inverse of position (), square of inverse of position (), kinetic energy (T) and the square of momentum () are obtained invoking the Hellmann–Feynman theorem. Results of this study are consistent with other similar previous studies. The analytical expressions for partition function and other thermodynamic properties of the diatomic molecules are determined.

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