A Proposal of an Orbital-Dependent Correlation Energy Functional for Energy-Band Calculations

Abstract

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. There is a strong possibility that the present orbital-dependent correlation energy functional, if applied to the so-called strongly correlated electron systems, will produce the energy-band structure significantly different from that calculated only with the orbital-dependent exchange energy functional particularly in the neighborhood of the Fermi level or the energy gap. A detailed discussion, accompanied by an accurate calculation of the quasiparticle energy dispersion of the electron liquid, is given about the relationship between Kohn–Sham equations and Dyson equations in order to justify the application of Kohn–Sham equations to the band theory.