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We present arguments demonstrating that the application of theNikiforov-Uvarov polynomial method to solve the Schr\"odinger equation with theTietz-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 resultswith $c_{h}\neq 0$ 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, itis shown that the solutions of the Schr\"odinger equation are expressed interms of the generalized hypergeometric functions $_{2}F_{1}\left(a,b,c;z\right) $. The determination of the energy levels requires the solutionof transcendantal equations involving the hypergeometric function by means ofthe numerical procedure.

Comment on “the rotation–vibration spectrum of diatomic molecules with the T ietz– H ua rotating oscillator”