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.

We solve the Schrödinger equation with the modified Rosen−Morse empirical potential model to obtain rotation-vibrational energy spectra and unnormalized radial wave functions. The vibrational energy levels calculated with the modified Rosen−Morse potential model for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential model.

We solve the Schrödinger equation with the improved Tietz empirical potential energy model. The rotationvibrational energy spectra and the unnormalized radial wave functions have been obtained. The vibrational energy levels predicted by using the improved Tietz potential model for the 5 1 ⌬ g state and C 1 ⌸ u state of the Na 2 molecule are in good agreement with the experimental Rydberg−Klein−Rees data.