A general method is presented for obtaining a model potential for calculation of Rydberg states and ionized states of an electron in a diatomic (or more complex) molecule. The potential is derived from a known wavefunction for the ionic molecule core by expanding the charge distribution, including the fixed-position nuclei, in spherical harmonics. Exchange effects are included in the form of an effective local ρ1/3 potential. The method is applied to the Rdberg states of H2 to examine the various contributions to the level splittings and the dependence of these on internuclear distance R. It is also applied to the determination of phase shifts in e–H2+ scattering and to the dependence of these phase shifts on R. The particular utility of the method is the ease and efficiency with which one can explore the behavior of electronic contributions to a wide variety of matrix elements, as functions of all the parameters n(or E), l, m, and R.