Excitonic effects in solids described by time-dependent density-functional theory

A time-dependent density functional theory (TDDFT) equation from the Bethe-Salpeter equation which should be particularly suitable for practical applications to the absorption spectra of solids was derived. It was demonstrated that the static exchange-correlation kernel has a long-range contribution stemming from the electron-hole interaction. It was explained why this long-range contribution is particularly important for the absorption spectra of solids. At the example of bulk silicon, it was shown how a very simple approximation for the kernel can yield excellent agreement between the calculated TDDFT absorption spectrum and experiment.