  Motivated by recent terahertz (THz) spectroscopy measurements in
$\alpha$-RuCl$_3$, we develop a theory for magnetoelectric (ME) effects in Mott
insulators of $d^5$ transition metal ions in an octahedral crystal field. For
$4d$ and $5d$ compounds, the relatively wide-spread orbitals favor charge
fluctuations of localized electrons to neighboring ions and a significant ME
effect from electronic mechanisms is expected. From a three-orbital Hubbard
model with strong spin-orbit coupling, we derive the mechanisms for the
electric polarization originating from virtual hopping of the localized holes
carrying the spins. We consider the electric polarization generated by pairs of
spin operators on nearest neighbor bonds with either an edge-sharing geometry
(i.e., two ligands are shared) or a corner-sharing geometry (i.e., one ligand
is shared). The allowed couplings are first derived using a symmetry approach.
Then, we explicitly calculate the coupling constants and evaluate the effective
polarization operator in the ground state manifold using perturbation theory
and exact diagonalization. The results are relevant when considering the THz
optical conductivity of magnetic systems such as some perovskite iridates or
Kitaev materials. In particular, they help explain the recent THz optical
measurements of $\alpha$-RuCl$_{3}$ for which the electric-dipole-induced
contribution has been shown to be strong.
