Accurate ro-vibrational spectroscopy of diatomic molecules in a Morse oscillator potential

This work presents the bound-state spectra of Morse oscillator, which remains one of the oldest important model potentials for molecules. Accurate ro-vibrational energies are obtained by means of a generalized pseudospectral method that offers an optimal, non-uniform discretization of the radial grid. Both s-wave ($\mathrm{\ell }=0$) and rotational ($\mathrm{\ell }\mathrm{\ne }0$) states for low and high quantum numbers are calculated for four representative diatomic molecules, namely H${}_2$, LiH, HCl and CO. First nine states belonging to a maximum of $n, \ell =2$ are computed with good accuracy, along with nine other high-lying states for each of these molecules. Present results \emph{surpass} the accuracy of \emph{all} hitherto published calculations found so far, except the tridiagonal J-matrix method, which produces similar accuracy as ours. Detailed variation of energies with respect to state indices $n,\mathrm{\ell }$ show interesting behavior. A host of new states including the higher ones are reported as well. This offers a simple general efficient scheme for calculating these and other similar potentials in molecular physics.