  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.
