On the screened Kratzer potential and its variants

We argue that several potentials proposed recently for the analysis of the vibrational-rotational spectra of diatomic molecules and their thermodynamic properties exhibit a flaw. One can easily show that the parameters $D_e$ and $r_e$ in those potentials are not the dissociation energy and equilibrium bond length, respectively, as the proposers believe. We show how to overcome the mistake in a simple and quite general way.