The Aromatic 8-Electron Cubic Silicon Clusters Be@Si8, B@Si8+ and C@Si82+

The geometrical and electronic structures of the Si-8(2-) dianion and isovalent silicon clusters doped by main second-row elements including Li@Si-8(-), Be@Si-8, B@Si-8(+), C@Si-8(2+), N@Si-8(3+), and O@Si-8(4+), are investigated using quantum chemical methods. The analyses of phenomenological shell model (PSM) combined with partial electron localizability indicators (pELI-D) rationalize the existence of cubic silicon clusters. A cubic cluster can be formed, in the cases of Be@Si-8, B@Si-8(+), and C@Si-8(2+), when three conditions are satisfied, namely, a full occupancy of electronic shells (34 electrons), a presence of positive charge at the center, and a type of spherical aromaticity. A chemical bonding picture for the cubic cage of the doped silicon clusters is illustrated. Each Si atom has four lobes of sp(3) hybridization in which three lobes make three covalent a bonds with other Si atoms, and the fourth lobe makes a chemical bond with the dopant. The eight delocalized electrons distributed on the fourth lobes describing the bonding between dopant and Si cage follow the Hirsch rule. We demonstrate that a way of applying electron counting rule is to take into account delocalized electrons on the shell orbitals with N > 1 (2S and 2P shell orbitals).