Bound Excitons in Time-Dependent Density-Functional Theory: Optical and Energy-Loss Spectra

A robust and efficient frequency dependent and nonlocal exchange correlation f_xc(r,r';ω) 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, SiO₂, 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.