  An explicitly orbital-dependent correlation energy functional is proposed,
which is to be used in combination with the orbital-dependent exchange energy
functional in energy-band calculations. It bears a close resemblance to the
second-order direct and exchange perturbation terms calculated with Kohn-Sham
orbitals and Kohn-Sham energies except that one of the two Coulomb interactions
entering each term is replaced by an effective interaction which contains
information about long-, intermediate-, and short-range correlations beyond
second-order perturbation theory. Such an effective interaction can rigorously
be defined for the correlation energy of the uniform electron liquid and is
evaluated with high accuracy in order to apply to the orbital-dependent
correlation energy functional. The coupling-constant-averaged spin-parallel and
spin-antiparallel pair correlation functions are also evaluated with high
accuracy for the electron liquid. The present orbital-dependent correlation
energy functional with the effective interaction borrowed from the electron
liquid is valid for tightly-binding electrons as well as for nearly-free
electrons in marked contrast with the conventional local density approximation.
