  The optical conductivity of LaFeAsO, BaFe$_2$As$_2$, SrFe$_2$As$_2$, and
EuFe$_2$As$_2$ in the spin-density wave (SDW) state is investigated within
density functional theory (DFT) in the framework of spin-polarized generalized
gradient approximation (GGA) and GGA+U. We find a strong dependence of the
optical features on the Fe magnetic moments. In order to recover the small Fe
magnetic moments observed experimentally, GGA+$U_{\rm eff}$ with a suitable
choice of negative on-site interaction $U_{\rm eff}=U-J$ was considered. Such
an approach may be justified in terms of an overscreening which induces a
relatively small U compared to the Hund's rule coupling J, as well as a strong
Holstein-like electron-phonon interaction. Moreover, reminiscent of the fact
that GGA+$U_{\rm eff}$ with a positive $U_{\rm eff}$ is a simple approximation
for reproducing a gap with correct amplitude in correlated insulators, a
negative $U_{\rm eff}$ can also be understood as a way to suppress magnetism
and mimic the effects of quantum fluctuations ignored in DFT calculations. With
these considerations, the resulting optical spectra reproduce the SDW gap and a
number of experimentally observed features related to the antiferromagnetic
order. We find electronic contributions to excitations that so far have been
attributed to purely phononic modes. Also, an orbital resolved analysis of the
optical conductivity reveals significant contributions from all Fe 3d orbitals.
Finally, we observe that there is an important renormalization of kinetic
energy in these SDW metals, implying that the effects of correlations cannot be
neglected.
