The electronic energies of several molecular ions in different states have been recently determined by applying Hylleraas’ method along with Wind-Jaffe’s series to the Hamilton–Jacobi equation. In this paper, a continuation of three previous studies is presented: we have fitted to fourth-degree Rydberg generalized functions the potential energy curves for the 8kπ, 9kσ, 9lπ, 9lσ and 10oσ electronic states of the H2+ molecular ion. The correspondent rovibrational energies and spectroscopic constants were then derived by both the Discrete Variable Representation and Dunham’s method. The theoretical results – the first reported in the literature – are expected to provide a reliable comparison source to future works.