We present a detailed investigation of the dynamic structure factor S(Q,$\omega${}) as well as of the dielectric function $\epsilon${}M(Q,$\omega${}) of the prototypical semiconductor silicon for finite momentum transfer, combining inelastic x-ray scattering measurements and ab initio calculations. We show that, in contrast to optical spectra, for finite momentum transfer, time-dependent density-functional theory in adiabatic local-density approximation (TDLDA) together with the inclusion of lifetime effects in a modified independent-particle polarizability $\chi${}0,LT describes the physics of valence excitations with high precision. This applies to the dynamic structure factor as well as to the dielectric function, which demonstrates that TDLDA contains the short-range many-body effects that are crucial for a correct description of $\epsilon${}M(Q,$\omega${}) in silicon at finite momentum transfer. The form of a nonlocal and energy-dependent exchange-correlation kernel is presented which provides the inclusion of the lifetime effects using the true independent-particle polarizability $\chi${}0. The description of the silicon L2,3 absorption edge has been possible by including the outer core electrons 2s and 2p in the valence electrons of the pseudopotential. The energy of the edge is underestimated but a scissor shift of the respective states by the self-energy correction for these states yields good agreement with experiment. Short-range crystal local-field effects and exchange-correlation effects become important with increasing momentum transfer. The inclusion of crystal local-field effects in the random-phase approximation is able to describe the anisotropy of the response well. Our results demonstrate the quantitative predictive power of the first-principles description.

We present both theoretical ab-initio results within the Hedin's GW approximation and experimental angle-resolved photoemission and scanning tunneling spectroscopy measurements on TiSe2. With respect to the density-functional Kohn-Sham metallic picture, the many-body GW self-energy leads to a $\approx${}0.2-eV band-gap insulator consistent with our STS spectra at 5 K. The highest valence and the lowest conduction bands are strongly renormalized, with a loss of k2 parabolic dispersion toward a k4 shape. In particular, GW moves the top of valence moved toward a circle of points away from $\Gamma${}, arising in a Mexican hat shape commonly associated with an excitonic insulator. Our calculations are in good agreement with experiment.

We present a detailed study of the dynamical electronic response in bulk sodium and aluminum within time-dependent density-functional theory (TDDFT). The poor results of the random-phase approximation (RPA) and the time-dependent local-density approximation (TDLDA) in sodium are greatly improved by the approximate inclusion of the finite lifetimes of electrons and holes via a modified independent-particle polarizability, which brings the calculated spectra into good agreement with experiment. For aluminum the changes are less visible, but at some values of momentum-transfer lifetime effects are necessary to obtain qualitatively correct spectra. The double-peak structure in aluminum, induced by band-structure effects, is partially washed out by the inclusion of the finite lifetimes. The latter do not, however, create a double peak by themselves as they do in the case of the homogeneous electron gas. Studying the performance of different time-dependent and nonlocal TDDFT kernels, we conclude that the Gross-Kohn, Corradini et al., and the Hubbard local-field factors improve the spectra compared to the RPA results. However, the results agree less well with experiment than those obtained using TDLDA with added lifetime effects. These results apply to both the loss spectra and the plasmon dispersion.

We introduce a method, based on the linearization of the band dispersion, to include intraband contributions in ab initio calculations of the optical spectra of metals. We illustrate its application to cubic iron and hexagonal magnesium, by analyzing the contributions of interband and intraband transitions to the dielectric function and the optical conductivity. These calculations demonstrate a way to compute the conductivity anisotropy of noncubic metals without the need to resort to phenomenological parametrizations. In particular, we introduce a method to recover the correct asymptotic trend of the response functions in the $\omega${}$\rightarrow${}0 limit and hence compare directly with the experimental static conductivity.