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

Abstract

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge₈^z (z = −6, −4, −2, 0, +2, +4) using nine initial geometries. For Ge₈²⁻ the D_2d 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 T_d tetracapped tetrahedron global minimum predicted to exhibit spherical aromaticity. The hyperelectronic clusters Ge₈⁴⁻ and Ge₈⁶⁻ have nido B₈H₁₂ and square antiprism structures, respectively, as global minima in accord with the Wade–Mingos rules and experimental data on E₈²⁺ (E = Sb, Bi) cations. Hypoelectronic eight-vertex clusters isoelectronic and isolobal with Ge₈, Ge₈²⁺ and Ge₈⁴⁺ 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.