King R B, Silaghi-Dumitrescu I, Lupan A
Department of Chemistry, University of Georgia, Athens, 30602, USA.
Inorg Chem. 2005 May 16;44(10):3579-88. doi: 10.1021/ic040110x.
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.
在混合B3LYP水平下的密度泛函理论（DFT）已应用于锗簇Ge(11)(z)（z = -6, -4, -2, 0, +2, +4, +6），起始构型有八种。Ge(11)(2-)组内的全局最小值是一个拉长的五角帽三棱柱，从D(3)(h)对称性扭曲为C(2v)对称性。然而，根据Wade-Mingos规则，对于2n + 2骨架电子体系预期的且在实验中在B(11)H(11)(2-)和等电子碳硼烷中发现的对称性同样为C(2v)的更为球形的边缘合并二十面体，其能量仅略高（+5.2千卡/摩尔）。更为拉长的D(3)(h)五角帽三棱柱是富电子结构Ge(11)(4-)和Ge(11)(6-)的全局最小值。对于Ge(11)(4-)，类似于二碳硼烷配体C(2)B(9)H(11)(2-)的C(5v) 5帽五角反棱柱的能量比D(3h)全局最小值高得多（约28千卡/摩尔）。C(2v)边缘合并二十面体也是贫电子Ge(11)的全局最小值，这与其在实验已知的类型为(η(6)-芳烃)RuB(10)H(10)的11顶点“等闭式”金属硼烷中的情况类似。对于电子更少的Ge(11)(4+)和Ge(11)(6+)簇计算出的最低能量多面体结构，分别与在金属间化合物中实验发现的等电子离子E(11)(7-)（E = Ga、In、Tl）和Tl(9)Au(2)(9-)的结构非常相似。这些DFT研究预测了Ge(11)(2+)和等电子金属簇有趣的以D(5h)为中心的五角棱柱结构。
