Total Energy of Copper, Silver, and Gold

The pseudopotential theory of d-band metals discussed by the author in a previous paper is used to consider the total energy of the noble metals. The theoretical total-energy calculation is completed by adding to the total electronic energy the direct electrostatic repulsion between ions and subtracting from it an energy equal to the electron-electron interaction. The result is expressed as a sum of four quantities: a free-electron energy, a band-structure energy, an electrostatic (or Ewald) energy, and an overlap energy. The first three are directly analogous to the usual quantities found in the simple-metal total energy. The fourth contribution enters as a result of overlapping atomic d states and is most conveniently expressed in terms of a repulsive pair potential. Energy-wave-number characteristics are evaluated for copper, silver, and gold by the numerical procedures previously used to calculate the form factors of these metals. Two improvements relating to exchange approximations are introduced, however. The most important of these involves a modification of the Kohn-Sham conduction-core, d exchange potential in a manner suggested by Lindgren. This removes the spurious behavior otherwise obtained at long wavelengths in both the form factor and the energy-wave-number characteristic. The overlap potential for each metal is evaluated as a function of the separation between two ions in the metal and then fitted to a simple analytic form. Applications to the calculation of the binding energies, the low-temperature stable phases, and the phonon spectra of the noble metals are described. All three metals are calculated to be most stable in an hcp structure, rather than in the observed fcc structure. Reasonable phonon spectra are obtained, although large Kohn anomalies, which have not been reported experimentally, are seen in copper.