Electron-Phonon Coupling and Pseudopotentials: The Mass Enhancements of the Noble Metals

Abstract

The first-principles form factors of Harrison and Moriarty (HM) and the empirical form factors of Fong and Cohen (FC) are investigated as a starting point for calculations of electron-phonon (EP) coupling in noble metals. A compact representation of Harrison's pseudopotential method for transition metals is presented. A theorem by Sham on the use of orthogonalized-plane-wave-based pseudopotentials for EP matrix elements is expressed in operator language and generalized to include a wide class of pseudopotentials, including Harrison's. With the underlying principles justified, single-plane-wave calculations of the EP mass enhancement and resistivity are presented. The FC form factors give results that are more nearly consistent with experimental knowledge than the HM form factors. The discrepancy is traced to the sign and magnitude of the $d$-wave interaction.