Energy levels and potential energy curves for H2, N2, and O2 with an independent particle model

Energy levels for valence and Rydberg states are calculated for H2, N2, and O2. An independent particle model (IPM) with an effective one-electron potential whose nuclear charge depends on the electron position is utilized to approximate the Coulomb and exchange interactions. An analytical generalization of the potential parameters to reflect a change in internuclear separation yields accurate average molecular potential energy curves E(R) when experimental ion energies E+(R) are added to IPM molecular orbital energies ε(R), viz., E(R)=E+(R)+ε(R). A convergence formula for incrementing the energy in the numerical integration procedure is presented.