Does the 18-Electron Rule Apply to CrSi$_{12}$?

Understanding the bonding between silicon and transition metals is valuable for devising strategies for incorporating magnetic species into silicon. CrSi$_{12}$ is the standard example of a cluster whose apparent high stability has been explained by the 18-electron rule. We critically examine the bonding and nature of stability of CrSi$_{12}$ and show that its electronic structure does not conform to the 18-electron rule. Through theoretical studies we find that CrSi$_{12}$ has 16 effective valence electrons assigned to the Cr atom and an unoccupied 3d$_{\mathrm{z}}^{2}$ orbital. We demonstrate that the cluster's apparent stability is rooted in a crystal field-like splitting of the 3d orbitals analogous to that of square planar complexes. CrSi$_{14}$ is shown to follow the 18-electron rule and exhibits all the conventional markers characteristic of a magic cluster. We will also present results on the stability and electronic structure of FeSi$_{\mathrm{n}}$ clusters and in particular examine the valence configuration of FeSi$_{12}$ since Fe has two additional valence electrons compared to Cr.