Electronic counting rules for the stability of metal-silicon clusters

First principles electronic structure calculations have been carried out to examine the stability of cationic, neutral, and anionic MSi15, MSi16, and MSi17 (M=Sc, Ti, and V) clusters. ScSi16-, TiSi16, and VSi16+ are found to be particularly stable in agreement with recent experiments. It is shown that the enhanced stability can be reconciled within a model where each Si atom coordinated to the metal contributes one electron to the valence pool. Clusters where the total number of valence electrons obtained by summing one electron from each Si site coordinated to metal atom and the valence electrons of the metal attain 20 are found to be particularly stable. Combined with the earlier reported stability at 18 electrons, it is proposed that such valence pools might be looked upon as a nearly free electron gas inside a silicon cage.