A systematic study of the ground state geometries, electronic structure, and stability of the metal (M) encapsulated $M{\mathrm{Si}}_{12}$ ($M=\mathrm{Sc}$, $\mathrm{Ti}$, $\mathrm{V}$, $\mathrm{Cr}$, $\mathrm{Mn}$, $\mathrm{Fe}$, $\mathrm{Co}$, $\mathrm{Ni}$) clusters has been carried out within a gradient-corrected density functional formalism. It is shown that the ground state of most $M{\mathrm{Si}}_{12}$ clusters has the lowest spin multiplicity as opposed to the high spin multiplicity in free transition metal atoms. Consequently, a proper inclusion of the spin conservation rules is needed to understand the variation of the binding energy of $M$ to ${\mathrm{Si}}_{12}$ clusters. Using such rules, ${\mathrm{CrSi}}_{12}$ and ${\mathrm{FeSi}}_{12}$ are found to exhibit the highest binding energy across the neutral while ${\mathrm{VSi}}_{12}^{-}$ has the highest binding energy across the anionic $M{\mathrm{Si}}_{12}^{-}$ series. It is shown that the variations in binding energy, electron affinity, and ionization potential can be rationalized within an 18-electron sum rule commonly used to understand the stability of chemical complexes and shell filling in a confined free-electron gas.

• Received 20 April 2005

DOI:https://doi.org/10.1103/PhysRevB.72.165413