  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 quasi-separate 5d and 6s
electron gasses, each one oscillating with its own frequency at resp. 5.1 eV
and 10.2 eV. We find that the contribution near 2.2 eV comes from 5d to 6s
interband transitions modified by the intraband contribution to the real part
of the dielectric function, which we call a mixed excitation.
