Accurate orbital-independent density-functional potential including self-interaction correction

A new method of constructing approximate Kohn-Sham exchange-correlation potentials, $v_{\mathrm{xc}}$, from the orbital-dependent potentials ${\mathit{v}}_{\mathrm{xc}}^{\left(\mathit{i}\right)}$=δ${\mathit{E}}_{\mathrm{xc}}$[{${\mathit{n}}_{\mathit{i}}$}]/δ${\mathit{n}}_{\mathit{i}}$ is proposed in which $v_{\mathrm{xc}}$ is obtained from integrating the weighted average of electric (WAE) field produced by the $v_{\mathrm{xc}{}^{\left(i\right)}}$. Application of the WAE method to atoms with closed subshells employing exchange-only local-spin-density self-interaction correction and gradient-expansion-approximation self-interaction correction energy functionals yields $v_x$ and n(r) which closely approximate the OPM potentials and Hartree-Fock electron densities, respectively.