Calculation of the interaction potential energy curve and vibrational levels for the a3Σu+ state of Li27 molecule

•Bound state solutions of the Schrödinger equation with the improved expression of the Manning–Rosen potential energy model are explored.•Interaction potential curve for the a3Σu+ state of Li27 is modeled by employing the improved Manning–Rosen potential model.•Vibrational levels predicted by the improved Manning–Rosen potential are in good agreement with the RKR data and ab initio determinations.

We solve the Schrödinger equation with the improved expression of the Manning–Rosen empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curve for the a3Σu+ state of Li27 molecule is modeled by employing Manning–Rosen potential model. Favorable agreement for the Manning–Rosen potential is found in comparing with ab initio   data. The vibrational energy levels predicted by using the Manning–Rosen potential for the a3Σu+ state of Li27 are in good agreement with the RKR data and ab initio determinations.