Towards a Kohn-Sham potential via the optimized effective-potential method

The optimized effective-potential (OEP) method is applied to a self-interaction-corrected local-spin-density (SIC-LSD) energy functional. The local potential which results has the useful properties of being both self-interaction free and orbital independent, and it can thus be regarded as a good approximation to the exact Kohn-Sham potential. A number of atomic systems are examined in the exchange-only and in the Ceperley-Alder exchange-correlation approximations. The resulting total energies are very close to those obtained by previous applications of the LSD-SIC functional. The resultant potentials are structurally similar to those derived by applying the OEP method to a Hartree-Fock Hamiltonian: showing much improved behavior over the local-spin-density approximation in both large- and small-r regions as well as the characteristic intershell cusplike structure. The eigenvalues have less formal significance than the more standard approaches, especially those for unoccupied orbitals which seem to have no significance whatsoever. Nonetheless, the highest occupied eigenvalue agrees closely with the conventional LSD-SIC value. However, for the deeper levels, each eigenvalue lies higher than the comparable eigenvalue of the conventional SIC, although lower than the eigenvalue of the LSD potential---the deeper the level, the larger the difference. This property follows from the nonvariational character of the eigenvalues, and it is shown that one can obtain realistic excitation spectra from this formalism by utilizing the appropriate variational quantity. The results obtained illustrate some of the less understood issues in the application of the Kohn-Sham procedure within density-functional theory. Based on observations made here using atomic calculations, we can offer a plausible explanation of the underestimation by LSD calculations of the experimental band gaps in insulators.