Determination of Electron Energy Bands by Phase-Shift Parametrization: Application to Silver

Abstract

We discuss a band parametrization scheme (within the framework of the Green's-function method, i.e., the Korringa-Kohn-Rostoker-type theory) specifying the phase shifts ${\eta }_0$, ${\eta }_1$, and ${\eta }_2$ as functions of energy. This approach is particularly useful for the noble and transition metals, where both $d$-band and free-electron-like effects are important. The ${\eta }_l\mathrm{}\left(E\right)\mathrm{}$ for a family of elements are expected to have characteristic energy dependences, with each ${\eta }_l\mathrm{}\left(E\right)\mathrm{}$ being specified over a substantial energy range by a few parameters. Such a parametrization scheme serves to present the information contained in an electron energy-band structure in a form in which one can conveniently blend empirical information with the results of first-principles calculations. First, we show the existence and form of the characteristic energy dependence of the $tan{\eta }_l$'s for the noble metals. We then use our phase-shift parametrization scheme in a semiempirical way to find the band structure of Ag. To do this, we use a first-priciples calculation as a guide, and adjust the parameters specifying the $tan{\eta }_l$'s to fit some available Fermi-surface, optical, and photoemission data. The realistic phase shifts so obtained correspond to a modified crystal potential. Thus the semiempirical phase-shift parametrization scheme offers a practical and conceptually clear way of effectively incorporating experimental information about the solid state into the potential.