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

Abstract An exchange-correlation energy functional E xc and the resultant exchange-correlation potential v xc (r) in density-functional theory are proposed us-ing orbital-dependent coupling-constant-averaged pair correlation functions,¯g σσ ′ (r,r ′ ) for electronic structure calculations of atoms, molecules, and solids.These orbital-dependent ¯g σσ ′ (r,r ′ ) fulfill the symmetric property, the Pauliprinciple and the sum rules. In the limit of uniform density ¯g σσ ′ (r,r ′ ) are re-duced to the very accurate analogues of the electron liquid that are obtainedfrom an interpolation between long- and short-range correlations involving theexchange corrections. The major contribution of v xc (r) is given in the form ofthe Coulomb interaction with the exchange-Coulomb hole around an electron.The present theory not only guarantees local charge neutrality, but also repro-duces the exact asymptotic form of the exchange potential, v x (r) = −e 2 /r forfinite systems. The present method of dealing with correlations, if properlyapplied to finite systems, can give even the asymptotic form of the correlationpotential v