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g  ðr; r 0 Þ fulfill the symmetric property, the Pauli principle and the sum rules. In the limit of uniform density the two correlation functions are reduced to the very accurate analogues of the electron liquid that involve long-, intermediate-, and short-range correlations as well as their exchange counterparts. It is stressed that the correlation energy functional Ec in DFT should by its very nature be defined as a functional only of occupied Kohn-Sham orbitals and occupied Kohn-Sham energies for the purpose of employing the optimized potential method (OPM) to evaluate the correlation potential vcðrÞ. The present scheme for Ec, if applied to finite systems after making a suitable change in the treatment of long-range correlation, can give the correct asymptotic form of vcðrÞ of order r  4 for large r as well as the van der Waals potential.

An Orbital-dependent Correlation Energy Functional in Density-functional Theory for the Study of Strongly-correlated Electronic Systems