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

journal contribution

posted on 16.05.2005, 00:00 by R. B. King, I. Silaghi-Dumitrescu, A. LupanDensity 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}*to*_{h}*C*_{2}*symmetry. However, the much more spherical edge-coalesced icosahedron, also of*_{v}*C*_{2}*symmetry, expected by the Wade-Mingos rules for a 2*_{v}*n*+ 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}*pentacapped trigonal prisms are the global minima for the electron-rich structures Ge*_{h}_{11}^{4-}and Ge_{11}^{6-}. For Ge_{11}^{4-}the*C*_{5}*5-capped pentagonal antiprism analogous to the dicarbollide ligand C*_{v}_{2}B_{9}H_{11}^{2-}is of significantly higher energy (∼28 kcal/mol) than the*D*_{3}*global minimum. The*_{h}*C*_{2}*edge-coalesced icosahedron is also the global minimum for the electron-poor Ge*_{v}_{11}similar to its occurrence in experimentally known 11-vertex “isocloso” metallaboranes of the type (η^{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*_{5}*centered pentagonal prismatic structure for Ge*_{h}_{11}^{2+}and isoelectronic metal clusters.## Read the peer-reviewed publication

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Cluster Geometry DensityD 5 hisoelectronic carboranes2 nenergy polyhedral structuresisoelectronic metal clustersD 3 hTl 9D 3 h pentacappedelectron systemDFT studiesgermanium clusters Ge 11 zpentagonal antiprismB 3LYP levelDensity Functional Theory StudyElectron CountC 2 v symmetrypentagonal prismatic structure

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## Read the peer-reviewed publication

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## Keywords

Cluster Geometry DensityD 5 hisoelectronic carboranes2 nenergy polyhedral structuresisoelectronic metal clustersD 3 hTl 9D 3 h pentacappedelectron systemDFT studiesgermanium clusters Ge 11 zpentagonal antiprismB 3LYP levelDensity Functional Theory StudyElectron CountC 2 v symmetrypentagonal prismatic structure