  We present arguments demonstrating that the application of the
Nikiforov-Uvarov polynomial method to solve the Schr\"odinger equation with the
Tietz-Hua potential is valid only when $e^{-b_{h}r_{e}}\leq c_{h}<1$ and
$r_{0}<r<+\infty $. In particular, it is pointed out that the numerical results
with $c_{h}\neq 0$ for the diatomic molecules $\mathrm{HF}$, $\mathrm{N}_{2}$,
$\mathrm{I}_{2}$, $\mathrm{H}_{2}$, $\mathrm{O}_{2}$ and $\mathrm{O}_{2}^{+}$
given in Tables 3-5 by Hamzavi and co-workers are wrong. When $-1\leq c_{h}<0$
or $0<c_{h}<e^{-b_{h}r_{e}}$, this approach is not suitable. In both cases, it
is shown that the solutions of the Schr\"odinger equation are expressed in
terms of the generalized hypergeometric functions $_{2}F_{1}\left(
a,b,c;z\right) $. The determination of the energy levels requires the solution
of transcendantal equations involving the hypergeometric function by means of
the numerical procedure.
