Density functional theory study of 11-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 Ge(11)(z) (z = -6, -4, -2, 0, +2, +4, +6) starting from eight different initial configurations. The global minimum within the Ge(11)(2-) set is an elongated pentacapped trigonal prism distorted from D(3)(h) to C(2v) symmetry. However, the much more spherical edge-coalesced icosahedron, also of C(2v) symmetry, expected by the Wade-Mingos rules for a 2n + 2 skeletal electron system and found experimentally in B(11)H(11)(2-) and isoelectronic carboranes, is of only slightly higher energy (+5.2 kcal/mol). Even more elongated D(3)(h) pentacapped trigonal prisms are the global minima for the electron-rich structures Ge(11)(4-) and Ge(11)(6-). For Ge(11)(4-) the C(5v) 5-capped pentagonal antiprism analogous to the dicarbollide ligand C(2)B(9)H(11)(2-) is of significantly higher energy (approximately 28 kcal/mol) than the D(3h) global minimum. The C(2v) edge-coalesced icosahedron is also the global minimum for the electron-poor Ge(11) similar to its occurrence in experimentally known 11-vertex "isocloso" metallaboranes of the type (eta(6)-arene)RuB(10)H(10). The lowest energy polyhedral structures computed for the more hypoelectronic Ge(11)(4+) and Ge(11)(6+) clusters are very similar to those found experimentally for the isoelectronic ions E(11)(7-) (E = Ga, In, Tl) and Tl(9)Au(2)(9-) in intermetallics in the case of Ge(11)(4+) and Ge(11)(6+), respectively. These DFT studies predict an interesting D(5h) centered pentagonal prismatic structure for Ge(11)(2+) and isoelectronic metal clusters.