Theoretical study of metal-encapsulating Si cage clusters: Revealing the nature of their peculiar geometries

We present a density-functional (DF) study of structures of Si cage clusters that encapsulate metal atoms. As a prototypical example, the case of WSi$_{n}$ clusters is shown. To obtain the low-energy clusters in efficient and unbiased ways, genetic-like geometry updates have been performed for generating inputs for subsequent local optimizations within DF calculations. Well-defined cages occur for a certain range of $n$. Such cages are modelled as simple 3-polytopes where the numbers of their inner diagonals close to the metal atom are maximized.