We discuss the effects of a static long-range contribution $-\alpha {/q}^2$ to the exchange-correlation kernel $f_{\mathrm{xc}}\left(\mathbf{q}\right)$ 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 $\alpha$ 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 Au₁₄₄(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.

It is known that the surface-plasmon resonance (SPR) in small spherical Au nanoparticles of about 2 nm is strongly damped. We demonstrate that small Au nanorods with a high aspect ratio develop a strong longitudinal SPR, with intensity comparable to that in Ag rods, as soon as the resonance energy drops below the onset of the interband transitions due to the geometry. We present ab initio calculations of time-dependent density-functional theory of rods with lengths of up to 7 nm. By changing the length and width, not only the energy but also the character of the resonance in Au rods can be tuned. Moreover, the aspect ratio alone is not sufficient to predict the character of the spectrum; the absolute size matters.