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 (ℓ = 0) and rotational (ℓ ≠ 0) states for low and high quantum numbers are calculated for four representative diatomic molecules, namely H2, LiH, HCl and CO. First nine states belonging to a maximum of n, ℓ = 2 are computed with good accuracy, along with nine other high-lying states for each of these molecules. Present results surpass the accuracy of 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, ℓ shows 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.