Ro-vibrational spectroscopy of molecules represented by a Tietz-Hua oscillator potential

Accurate low and high-lying bound states of Tietz-Hua oscillator potential are presented. The radial Schr"odinger equation is solved efficiently by means of the generalized pseudospectral method that enables optimal spatial discretization. Both $\mathrm{\ell }=0$ and rotational states are considered. Ro-vibrational levels of six diatomic molecules \emph{viz.}, H${}_2$, HF, N${}_2$, NO, O${}_2$, O${}_2^{+}$ are obtained with good accuracy. Most of the states are reported here for the first time. A detailed analysis of variation of eigenvalues with $n,\mathrm{\ell }$ quantum numbers is made. Results are compared with literature data, wherever possible. These are also briefly contrasted with the Morse potential results.