Dynamical response function in sodium and aluminum from time-dependent density-functional theory

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, 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.