Electron energy loss spectroscopy of bulk gold with ultrasoft pseudopotentials and the Liouville-Lanczos method

The implementation of ultrasoft pseudopotentials into time-dependent density-functional perturbation theory is detailed for both the Sternheimer approach and the Liouville-Lanczos (LL) method, and equations are presented in the scalar relativistic approximation for periodic solids with finite momentum transfer q. The LL method is applied to calculations of the electron energy loss (EEL) spectrum of face-centered cubic bulk Au both at vanishing and finite q. Our study reveals the richness of the physics underlying the various contributions to the density fluctuation in gold. In particular, our calculations suggest the existence in gold of two quasiseparate 5d and 6s electron gasses, each one oscillating with its own frequency at, respectively, 5.1 eV and 10.2 eV. We find that the contribution near 2.2 eV comes from 5d→6s interband transitions modified by the intraband contribution to the real part of the dielectric function, which we call a mixed excitation.