Nearly Free Electron Gas in a Silicon Cage

Theoretical investigations of the ground state geometries, electronic structure, spin magnetic moment and the stability of the metal encapsulated MSi$_{12}$ ( M= Sc, Ti, V, Cr, Mn, Fe, Co, Ni) clusters have been carried out within a gradient corrected density functional formalism. The ground state of most MSi$_{12}$ clusters are shown to have the lowest spin multiplicity as opposed to the high spin multiplicity of 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 Si$_{12}$ clusters. Using such rules, CrSi$_{12}$ and FeSi$_{12}$ are found to exhibit the highest binding energy across the neutral while VSi$_{12}^{-}$ has the highest binding energy across the anionic MSi$_{12}^{- }$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.