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Density Functional Theory Study of 11-Atom Germanium Clusters:  Effect of Electron Count on Cluster Geometry

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journal contribution
posted on 16.05.2005, 00:00 by R. B. King, I. Silaghi-Dumitrescu, A. Lupan
Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge11z (z = −6, −4, −2, 0, +2, +4, +6) starting from eight different initial configurations. The global minimum within the Ge112- set is an elongated pentacapped trigonal prism distorted from D3h to C2v symmetry. However, the much more spherical edge-coalesced icosahedron, also of C2v symmetry, expected by the Wade-Mingos rules for a 2n + 2 skeletal electron system and found experimentally in B11H112- and isoelectronic carboranes, is of only slightly higher energy (+5.2 kcal/mol). Even more elongated D3h pentacapped trigonal prisms are the global minima for the electron-rich structures Ge114- and Ge116-. For Ge114- the C5v 5-capped pentagonal antiprism analogous to the dicarbollide ligand C2B9H112- is of significantly higher energy (∼28 kcal/mol) than the D3h global minimum. The C2v edge-coalesced icosahedron is also the global minimum for the electron-poor Ge11 similar to its occurrence in experimentally known 11-vertex “isocloso” metallaboranes of the type (η6−arene)RuB10H10. The lowest energy polyhedral structures computed for the more hypoelectronic Ge114+ and Ge116+ clusters are very similar to those found experimentally for the isoelectronic ions E117- (E = Ga, In, Tl) and Tl9Au29- in intermetallics in the case of Ge114+ and Ge116+, respectively. These DFT studies predict an interesting D5h centered pentagonal prismatic structure for Ge112+ and isoelectronic metal clusters.