In this study, we propose the exponential Kratzer–Feus potential and study the effect of the screening parameter on the diatomic molecules of CH, H2α=0, 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 H2α=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.