Long-range contribution to the exchange-correlation kernel of time-dependent density functional theory

Abstract

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