Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si\u3csub\u3e39\u3c/sub\u3e, Si\u3csub\u3e40\u3c/sub\u3e, Si\u3csub\u3e50\u3c/sub\u3e, Si\u3csub\u3e60\u3c/sub\u3e, Si\u3csub\u3e70\u3c/sub\u3e, and Si\u3csub\u3e80\u3c/sub\u3e

摘要

We performed a constrained search, combined with density-functional theory optimization, of low-energy geometric structures of silicon clusters Si39, Si40, Si50, Si60, Si70, and Si80. We used fullerene cages as structural motifs to construct initial configurations of endohedral fullerene structures. For Si39, we examined six endohedral fullerene structures using all six homolog C34 fullerene isomers as cage motifs. We found that the Si39 constructed based on the C34(Cs:2) cage motif results in a new leading candidate for the lowest-energy structure whose energy is appreciably lower than that of the previously reported leading candidate obtained based on unbiased searches (combined with tight-binding optimization). The C34(Cs:2)cage motif also leads to a new candidate for the lowest-energy structure of Si40 whose energy is notably lower than that of the previously reported leading candidate with outer cage homolog to the C34(C1:1). Low-lying structures of larger silicon clusters Si50 and Si60 are also obtained on the basis of preconstructed endohedral fullerene structures. For Si50, Si60, and Si80, the obtained low-energy structures are all notably lower in energy than the lowest-energy silicon structures obtained based on an unbiased search with the empirical Stillinger–Weber potential of silicon. Additionally, we found that the binding energy per atom (or cohesive energy) increases typically \u3e10 meV with addition of every ten Si atoms. This result may be used as an empirical criterion (or the minimal requirement) to identify low-lying silicon clusters with size larger than Si50.