Exchange-correlation energy functional constructed from orbital-dependent coupling-constant-averaged pair correlation functions

An exchange-correlation energy functional $E_{\mathrm xc}$ and the resultant exchange-correlation potential $v_{\mathrm xc}({\bf r})$ in density-functional theory are proposed using orbital-dependent coupling-constant-averaged pair correlation functions, ${\bar{g}}^{\sigma \sigma'}({\bf r, r'})$ for electronic structure calculations of atoms, molecules, and solids. These orbital-dependent ${\bar{g}}^{\sigma \sigma'}({\bf r, r'})$ fulfill the symmetric property, the Pauli principle and the sum rules. In the limit of uniform density ${\bar{g}}^{\sigma \sigma'}({\bf r, r'})$ are reduced to the very accurate analogues of the electron liquid that are obtained from an interpolation between long- and short-range correlations involving the exchange corrections. The major contribution of $v_{\mathrm xc}({\bf r})$ is given in the form of the Coulomb interaction with the exchange-Coulomb hole around an electron. The present theory not only guarantees local charge neutrality, but also reproduces the exact asymptotic form of the exchange potential, $v_{\mathrm x}({\bf r}) = - e^2 / r$ for finite systems. The present method of dealing with correlations, if properly applied to finite systems, can give even the asymptotic form of the correlation potential $v_{\mathrm c}({\bf r})$ of order $r^{-4}$ as well as the van der Waals potential of order $r^{-6}$ for large r.