Effect of the Screening Parameter on Shannon Entropy and Thermal Properties for Exponential Kratzer–Feus Potential

In this study, we propose the exponential Kratzer–Feus potential and study the effect of the screening parameter on the diatomic molecules of CH, \(H_2\) $H_2$ , NO, HCL, and LiH. We first solve the Schrödinger equation using the Nikiforov–Uvarov functional analysis method to obtain the energy eigenvalue. Interestingly, the proposed exponential Kratzer–Feus potential exhibits a repulsive interaction for diatomic molecules. We also compute the energy spectra for diatomic molecules for different values of the screening parameter \(\alpha = 0\) $\alpha =0$ , 0.2, 0.4, 0.8, and 1.0. For a more complete study, we analyse the thermodynamic properties of the model. Furthermore, the quantum information measurements are calculated and used to study particle locations.