Bound excitons in time-dependent density-functional-theory: optical and energy-loss spectra

A robust and efficient frequency dependent and non-local exchange-correlation $f_{xc}(r,r^{\mathrm{\prime }};\omega )$ is derived by imposing time-dependent density-functional theory (TDDFT) to reproduce the many-body diagrammatic expansion of the Bethe-Salpeter polarization function. As an illustration, we compute the optical spectra of LiF, \sio and diamond and the finite momentum transfer energy-loss spectrum of LiF. The TDDFT results reproduce extremely well the excitonic effects embodied in the Bethe-Salpeter approach, both for strongly bound and resonant excitons. We provide a working expression for $f_{xc}$ that is fast to evaluate and easy to implement.