Density functional theory study of eight-atom germanium clusters: effect of electron count on cluster geometry

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge8z(z=-6, -4, -2, 0, +2, +4) using nine initial geometries. For Ge8(2-) the D2d bisdisphenoid structure predicted by the Wade-Mingos rules is not computed to be the global minimum but instead lies 3.9 kcal mol-1 above the Td tetracapped tetrahedron global minimum predicted to exhibit spherical aromaticity. The hyperelectronic clusters Ge(8)4- and Ge8(6-) have nido B8H12 and square antiprism structures, respectively, as global minima in accord with the Wade-Mingos rules and experimental data on E(8)2+(E=Sb, Bi) cations. Hypoelectronic eight-vertex clusters isoelectronic and isolobal with Ge8, Ge8(2+) and Ge(8)4+ are not known experimentally. Their computed structures include smaller polyhedra having one or more capped triangular faces as well as more open non-polyhedral structures.