An orbital-dependent correlation energy functional in density-functional theory for the study of strongly-correlated electronic systems

An orbital-dependent correlation energy functional E_c to be accompanied by the exact exchange energy functional E_x is proposed for applications of density-functional theory (DFT). The present E_c comprises spin-antiparallel and spin-parallel contributions, E_c ^σ-σ and E_c^σσ. E _c^σ-σ is a modification of the spin-antiparallel component of the Hartree energy functional with a factor of ḡ_c^σ-σ(r, r′) - 1 and E _c^σσ a modification of the spin-parallel component of the same energy functional with ḡ_c ^σσ(r, r′) where ḡ_c ^σσ(r, r′) (or ḡ_c ^σ-σ(r, r′)) is the spin-antiparallel(or the correlational part of the spin-parallel) coupling-constant-averaged pair correlation function. The present orbital-dependent ḡ ^σ-σ(r, r′) and ḡ_c ^σσ(r, r′) 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 E_c 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 v_c(r). The present scheme for E _c, if applied to finite systems after making a suitable change in the treatment of long-range correlation, can give the correct asymptotic form of v_c(r) of order r^-4 for large r as well as the van der Waals potential.