Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms

Using accurate correlated wave functions calculated earlier by Bunge and by Larsson, we have constructed the Hohenberg-Kohn-Sham density functionals and exchange-correlation (ground-state) potentials and have obtained orbital energy eigenvalues for a number of light atoms by in principle exact numerical algorithms. While the uppermost occupied density-functional eigenvalue always gives an exact excitation energy as has been shown earlier, we find that eigenvalues for deeper shells lie above the corresponding excitation energy. We have compared our essentially exact density-functional (DF) results with those obtained in the local-density (LD) approximation. We find that the LD theory approximates the exchange-correlation energy rather well, but that it gives larger errors in the exchange-correlation potential and in the DF orbital eigenvalues. In all cases we have found that the LD error in the orbital eigenvalue is larger than the difference between the true DF eigenvalue and the corresponding exact excitation energy. Possible implications of these results for solid-state work are briefly discussed.