We discuss the effects of a static long-range contribution Ϫ␣/q 2 to the exchange-correlation kernel f xc (q) of time-dependent density functional theory. We show that the optical absorption spectrum of solids exhibiting a strong continuum excitonic effect is considerably improved with respect to calculations where the adiabatic local-density approximation is used. We discuss the limitations of this simple approach, and in particular that the same improvement cannot be found for the whole spectral range including the valence plasmons and bound excitons. On the other hand, we also show that within the range of validity of the method, the parameter ␣ depends linearly on the inverse of the dielectric constant, and we demonstrate that this fact can be used to predict continuum excitonic effects in semiconductors. Results are shown for the real and imaginary part of the dielectric function of Si, GaAs, AlAs, diamond, MgO, SiC and Ge, and for the loss function of Si.

Absorption spectra of very small metal clusters exhibit individual peaks that reflect the discreteness of their localized electronic states. With increasing size, these states develop into bands and the discrete absorption peaks give way to smooth spectra with, at most, a broad localized surface-plasmon resonance band. The widely accepted view over the last decades has been that clusters of more than a few dozen atoms are large enough to have necessarily smooth spectra. Here we show through theory and experiment that for the ubiquitous thiolate cluster compound Au 144 (SR) 60 this view has to be revised: clearly visible individual peaks pervade the full near-IR, VIS and near-UV ranges of low-temperature spectra, conveying information on quantum states in the cluster. The peaks develop well reproducibly with decreasing temperature, thereby highlighting the importance of temperature effects. Calculations using time-dependent density-functional theory indicate the contributions of different parts of the cluster-ligand compound to the spectra.

The physical properties of metals change when their dimensions are reduced to the nano-scale and new phenomena like the Localized Surface-Plasmon Resonance (LSPR) appear. This collective electronic excitation can be tuned over a large spectral range by adapting the material, size and shape. The existing literature is as rich as controversial as e.g. size-dependent spectral shifts of the LSPR in small metal nanoparticles, induced by quantum effects, are reported to the red, to the blue or entirely absent. Here we report how complementary experiments on mass-selected small silver nanoparticles embedded in silica can yield inconsistent results on the same system: while optical absorption shows no size-effect in the range between only a few atoms and ~10 nm, a clear spectral shift is observed in single-particle electron spectroscopy. Our quantitative interpretation, based on a mixed classical/quantum model, resolves the apparent contradictions, not only within our experimental data, but also in the literature. Our comprehensive model describes how the local environment is the crucial parameter controlling the manifestation or absence of size effects.