for stable covalent bonding are only partially fulfilled. The numbers of occupied states are indicated by the \# symbol. The Fermi levels are indicated by red vertical lines. Light-blue areas indicate unoccupied states, and the numbers of unoccupied states is given in brackets. (Lower panel) Similar plot for impurity-containing ${\rm B_{50}C_{2}}$ and ${\rm B_{50}N_{2}}$. ${\rm B_{50}N_{2}}$ can properly fulfill the the conditions for stable covalent bonding, i.e. all valence bands are occupied and no in-gap states are created.[]{data-label="fig:POSfilling"}](Figs/dos_B50_4c "fig:"){width="8"}\
![(Upper panel) Valence filling for B$_{50+n}$ as the number $n$ of $4c$-site B atoms increases. Only B$_{52}$ can completely fill up the valence bands, but 12 in-gap states remain. This indicates that the conditions for stable covalent bonding are only partially fulfilled. The numbers of occupied states are indicated by the \# symbol. The Fermi levels are indicated by red vertical lines. Light-blue areas indicate unoccupied states, and the numbers of unoccupied states is given in brackets. (Lower panel) Similar plot for impurity-containing ${\rm B_{50}C_{2}}$ and ${\rm B_{50}N_{2}}$. ${\rm B_{50}N_{2}}$ can properly fulfill the the conditions for stable covalent bonding, i.e. all valence bands are occupied and no in-gap states are created.[]{data-label="fig:POSfilling"}](Figs/dos_B50C2_B50N2 "fig:"){width="8"}

This valence filling scheme becomes clearer, when examining 