  In a recent publication Larson \textit{et al.} reported remarkably clear
$d$-$d$ excitations for NiO and CoO measured with x-ray energies well below the
transition metal $K$ edge. In this letter we demonstrate that we can obtain an
accurate quantitative description based on a local many body approach. We find
that the magnitude of $\vec{q}$ can be tuned for maximum sensitivity for
dipole, quadrupole, etc. excitations. We also find that the direction of
$\vec{q}$ with respect to the crystal axes can be used as an equivalent to
polarization similar to electron energy loss spectroscopy, allowing for a
determination of the local symmetry of the initial and final state based on
selection rules. This method is more generally applicable and combined with the
high resolution available, could be a powerful tool for the study of local
distortions and symmetries in transition metal compounds including also buried
interfaces.

Strongly Correlated Electrons