Excitonic Effects in Solids Described by Time-Dependent Density-Functional Theory

Starting from the many-body Bethe-Salpeter equation we derive an exchange-correlation kernel [Formula presented] that reproduces excitonic effects in bulk materials within time-dependent density functional theory. The resulting [Formula presented] accounts for both self-energy corrections and the electron-hole interaction. It is static, nonlocal, and has a long-range Coulomb tail. Taking the example of bulk silicon, we show that the [Formula presented] divergency is crucial and can, in the case of continuum excitons, even be sufficient for reproducing the excitonic effects and yielding excellent agreement between the calculated and the experimental absorption spectrum.