Kohn-Sham calculations with self-interaction-corrected local-spin-density exchange-correlation energy functional for atomic systems

We have investigated the accuracy of the local-spin-density approximation with orbital-density-dependent self-interaction correction (LSDSIC) as proposed by Perdew and Zunger within a Kohn-Sham approach in which electrons with a given spin projection all move in a single optimized effective potential (OEP). We have also studied the accuracy of the Krieger-Li-Iafrate (KLI) approximation to the OEP for the same energy functional in order to assess its applicability to systems in which the integral equation for the OEP cannot be reduced to a one-dimensional problem, e.g., molecules. Self-consistent Kohn-Sham LSDSIC calculations have been performed for atoms with atomic number Z=1–20 in the exchange-only case for the total energy, the highest-occupied orbital energy ${\mathrm{\epsilon }}_{\mathit{m}}$, and the expectation value of ${\mathit{r}}^2$. In addition, the structure of the resulting exchange potential is examined and compared with the exact exchange-only density-functional theory (OEP method with Hartree-Fock exchange-energy functional) results. Furthermore, we display ${\mathrm{\epsilon }}_{\mathit{m}}$, the ionization potential I, and the electron affinity A when both exchange and correlation energy effects are included. Finally, we also consider the results of evaluating the LSDSIC energy functional by employing the exact (in the central-field approximation) single particle orbitals as proposed by Harrison. We find that the LSDSIC energy functional generally leads to calculated values that are superior to those provided by the LSD approximation and that the KLI approximation yields results in excellent agreement with the corresponding exact OEP results for this energy functional. In particular, quantities strongly related to the behavior of the valence electrons are nearly identical in both the OEP and KLI calculations, i.e., the difference between the 〈${\mathit{r}}^2$〉 and ${\mathrm{\epsilon }}_{\mathit{m}}$ is less than 0.2% on average, while the difference between the calculated I is less than 0.2 millihartree on average with the corresponding difference of only 0.1 millihartree for A. © 1996 The American Physical Society.