Electronic eigenvalues of copper

Abstract

The cellular method as developed by Howarth & Jones (1952) is applied to the face-centred cubic crystal, and, in particular, the eigenvalues and wave functions of the 3d and 4s electrons in metallic copper are obtained for states whose wave vectors lie at the ends of the three- and four-fold axes in the Brillouin zone. The conduction electrons approximate closely to free electrons inside the first Brillouin zone, but the energy gaps at the zone faces are found to be sensitively dependent upon the potential used to represent the copper ion. The eigenvalues of the 3d band agree closely with Fletcher's results for nickel, and show a band with of 3$\cdot $46 eV. An approximate solution of the Hartree equations for the metal shows the top of the d-band to lie 3$\cdot $7 eV below the Fermi level in the conduction band.