We solve the Schrödinger equation with the improved Rosen−Morse empirical potential energy model. The rotationvibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curves for the 3 3 ⌺ g + state of the Cs 2 molecule and the 5 1 ⌬ g state of the Na 2 molecule are modeled by employing the improved Rosen−Morse potential and the Morse potential. Favourable agreement for the improved Rosen−Morse potential is found in comparing with the Rydberg−Klein−Rees potential. The vibrational energy levels predicted by using the improved Rosen−Morse potential for the 3 3 ⌺ g + state of Cs 2 and the 5 1 ⌬ g state of Na 2 are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential.