On the structural landscape in endohedral silicon and germanium clusters, M@Si12 and M@Ge12.

Amongst the endohedral clusters of the tetrel elements, M@En, the 12-vertex species are unique in that three completely different geometries, the icosahedron (Ih, [Ni@Pb12](2-)), the hexagonal prism (HP, Cr@Si12) and the bicapped pentagonal prism (BPP, [Ru@Ge12](3-)) have been identified in stable molecules. We explore here the origins of this structural diversity by comparing stability patterns across isovalent and isoelectronic series, M@Si12, M@Ge12 and [M@Ge12](3-). The BPP structure dominates the structural landscape for high valence electron counts (57-60) while the HP has a rather narrower window of stability around the 54-56 count. Moreover the preference for an HP structure is unique to silicon: in no case is a rigorously D6h-symmetric structure the global minimum for M@Ge12. Distortions from the high-symmetry limits, where present, can be traced to degeneracies or near-degeneracies in the frontier orbital domains. In all cases the structure adopted is that which maximizes the delocalization of electron density between the metal and the cluster cage, such that both components attain stable electronic configurations.