  In the description of the interaction between electrons beyond the classical
Hartree picture, bare exchange often yields a leading contribution. Here we
discuss its effect on optical spectra of solids, comparing three different
frameworks: time-dependent Hartree-Fock, a recently introduced combined
density-functional and Green's functions approach applied to the bare exchange
self-energy, and time-dependent exact-exchange within time-dependent
density-functional theory (TD-EXX). We show that these three approximations
give rise to identical excitonic effects in solids; these effects are
drastically overestimated for semiconductors. They are partially compensated by
the usual overestimation of the quasiparticle band gap within Hartree-Fock. The
physics that lacks in these approaches can be formulated as screening. We show
that the introduction of screening in TD-EXX indeed leads to a formulation that
is equivalent to previously proposed functionals derived from Many-Body
Perturbation Theory. It can be simulated by reducing the long-range part of the
Coulomb interaction: this produces absorption spectra of semiconductors in good
agreement with experiment.
