Implementation of the Modified jaffe's expression to nsσg H2+

We have recently presented a generalized and modified form of Jaffe's expression for studying two-centered nuclei systems. We reported that the newly modified expression removes all the problematic energy dependences of Jaffe's expression across the ionization threshold. This enables us to get high-lying Rydberg series of hydrogen molecular ions, which are previously difficult to calculate, since the wave functions near threshold energies diverge even at small distance. The energy levels and wave functions of the nsσg series are calculated up to n=15 for hydrogen molecular ions in a prolate spheroidal coordinates. Among them, the lowest three energy levels are compared with the previous calculations. The fixed nuclei potentials for various internuclear distances are presented in tables and Born-Oppenheimer potential curves are also plotted. All the potential curves of nsσg series are confirmed to be repulsive except 1sσg, which can accommodate vibrational states