The real structure of the ${\mathrm{Si}}_6$ cluster

Contrary to well-established recent theoretical results based on second-order Moller-Plesset perturbation theory, it is illustrated here that the distorted octahedron of $D_{4h}$ symmetry cannot be the ground state of the “magic” ${\mathrm{Si}}_6$ cluster, but a transition state, connecting two almost isoenergetic structures of lower symmetry, which can coexist. This conclusion, the consequences of which could be far reaching for other magic clusters, is based on higher-order perturbation theory, accurate coupled-cluster CCSD(T) calculations and density-functional theory at the hybrid B3LYP level. The discrepancy is due to the poor convergence of the perturbation expansion, related to the flatness of the energy hypersurface near the minimum. As a result, the structural and electronic properties of ${\mathrm{Si}}_6$ are still not well understood, although several suggestions are put forward here.