Hartree-Fock study of the ground-state energy and band structure of metallic copper

Abstract

An approximate solution of the Hartree-Fock (HF) problem in metallic copper has been obtained using the spherical cellular method to solve the one-electron equations. The largest part of the total energy is due to the interactions inside the central Wigner-Seitz cell. This energy contribution "in the cell" is calculated in the HF approximation using the wave functions of the cellular method, and self-consistency is achieved. The remaining part of the total energy, or "external" exchange contribution, which is much smaller, is approximately calculated and found to agree with the semiempirically predicted value. The band structure obtained by this method is very different from those resulting of other calculations using local exchange: the $d$ band lies considerably lower and the $s$ band is broader. The comparison between the HF and experimental transition ${\epsilon }_F-X_5$ shows that the correlation contribution to such a transition is of the order of 0.30 Ry.