Comment on "The Rotation-Vibration Spectrum of Diatomic Molecules with the Tietz-Hua Rotating Oscillator"

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 $e^{-b_h{r}_e}\le c_h<1$ and $r_0<r<+\mathrm{\infty }$. In particular, it is pointed out that the numerical results with $c_h\mathrm{\ne }0$ for the diatomic molecules $\mathrm{H}\mathrm{F}$, ${\mathrm{N}}_2$, ${\mathrm{I}}_2$, ${\mathrm{H}}_2$, ${\mathrm{O}}_2$ and ${\mathrm{O}}_2^{+}$ given in Tables 3-5 by Hamzavi and co-workers are wrong. When $-1\le c_h<0$ 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.