Potentials, band structures, and Fermi surfaces in the noble metals

We have calculated the electronic energy-band structures of the noble metals—Cu, Ag, and Au—by the linear-augmented-plane-wave (LAPW) method. The potentials were constructed using the local approximation to the density-functional formalism and calculated self-consistently by the atomic-sphere approximation to the linear-muffin-tin-orbital (LMTO) method. Relativistic band shifts were included but spin-orbit coupling was neglected. The band structures are analyzed in terms of canonical bands, which describe the dependence on the crystal structure, and potential parameters. The latter are derived from the potential in a single atomic cell and specify the positions and widths of the various bands, and hence the degree of hybridization between them. The effect of the relative band positions on the anisotropy and neck radius of the Fermi surface is discussed. Empirical logarithmic derivatives deduced from de Haas-van Alphen measurements are used to evaluate a number of different potentials, and we find that our potentials account for the Fermi surfaces comparatively satisfactorily. It is emphasized that relativistic band shifts are significant for all three metals, and that the neck radius is not, in itself, a good criterion for evaluating how well a potential reproduces the overall shape of the experimental Fermi surface. Optical measurements of excitation energies are compared with calculated differences in band energies and it is discovered that no existing $a$ priori potential is able to account satisfactorily for all of the experimental evidence. The main discrepancies are due to the difficulty of placing the $d$ bands consistently, and it is suggested that many-body corrections to the excitation energies may be particularly important when $d$ electrons are involved.