Ro-vibrational studies of diatomic molecules in a shifted Deng-Fan oscillator potential

Bound-state spectra of shifted Deng-Fan oscillator potential are studied by means of a generalized pseudospectral method. Very accurate results are obtained for \emph{both low as well as high} states by a non-uniform optimal discretization of the radial Schr\"odinger equation. Excellent agreement with literature data is observed in \emph{both $s$-wave and rotational} states. Detailed variation of energies with respect to potential parameters is discussed. Application is made to the ro-vibrational levels of four representative diatomic molecules (H$_2$, LiH, HCl, CO). Nine states having $\{n,\ell\} =0,1,2$ are calculated with good accuracy along with 15 other higher states for each of these molecules. Variation of energies with respect to state indices $n$, $\ell$ show \emph{behavior} similar to that in the Morse potential. Many new states are reported here for the first time. In short, a simple, accurate and efficient method is presented for this and other similar potentials in molecular physics.