Quantum chemical insights into hexaboride electronic structures: correlations within the boron $p$-orbital subsystem

The notion of strong electronic correlations arose in the context of $d$-metal oxides such as NiO but can be exemplified on systems as simple as the H$_2$ molecule. Here we shed light on correlation effects on B$_6^{2-}$ clusters as found in $M$B$_6$ hexaborides and show that the B 2$p$ valence electrons are fairly correlated. B$_6$-octahedron excitation energies computed for CaB$_6$ and YbB$_6$ agree with peak positions found by resonant inelastic x-ray scattering, providing a compelling picture for the latter. Our findings characterize these materials as very peculiar $p$-electron correlated systems and call for more involved many-body investigations within the whole hexaboride family, both alkaline- and rare-earth compounds, not only for $N$- but also ($N\pm1$)-states defining e. g. band gaps.