Lattice Dynamics of Noble Metals—Application to Copper

A model band structure with noninteracting $s$ and $d$ bands for copper is used to calculate the static dielectric function and the phonon frequencies. A local empirical pseudopotential is used to describe the electron-ion matrix element for both the $s$ and $d$ electrons. The exchange and the correlation effects are completely neglected. The calculated phonon frequencies are found in fair agreement with the experimental measurements for the longitudinal branches, while the agreement is poor for the transverse branches. It is inferred that the itinerant nature of the $d$ electrons should not be overlooked in a calculation of phonon frequencies of noble metals.