A robust and efficient frequency dependent and nonlocal exchange correlation $f_{xc}(\mathbf{r},{\mathbf{r}}^{\prime };\omega )$ 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, ${\mathrm{S}\mathrm{i}\mathrm{O}}_2$, 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.

• Received 17 July 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.256402