Spectroscopic properties of the H2+ molecular ion in the 8kπ, 9kσ, 9lπ, 9lσ and 10oσ electronic states

► We fitted the potential energy curves of the H2+ excited states. ► We calculated the rovibrational energies and spectroscopic constants. ► The largest fitting error did not exceed 2.18 × 10−5 Eh. ► The two methods employed (Dunham's and DVR) yielded similar results for the constants.