Self-consistent band theory of the Fermi-surface, optical, and photoemission properties of copper

A two-parameter self-consistent theory of the electronic structure of copper is presented. The first parameter, the exchange coefficient $\ensuremath{\alpha}$ appearing in Slater's $X\ensuremath{\alpha}$ theory, is adjusted so that the ground-state energy bands generate the measured Fermi surface. The second parameter, the electron-electron contribution to the effective electron mass ${m}^{*}$ appearing in the Sham-Kohn local-density theory of excitations, is adjusted to optical-absorption data. The theory treats all electrons identically and provides a more accurate unified interpretation of Fermi-surface, optical-absorption, and photoemission data than previously obtained. We show that the transition probabilities (momentum matrix elements), while their inclusion is necessary for a convincing description of ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$, can for the most part be assumed constant in the calculation of photoemission spectra. Comparison with the Chodorow potential shows that it gives excellent results for the $d$ bands, but leads to excited-state energies which are approximately 7% too low. A detailed description is given of our computational procedures, including the generation of momentum matrix elements, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ extrapolation, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$-space integration procedures and convergence tests, as well as our procedure for constructing photoemission energy distributions.