Beyond the Icosahedron: A Density Functional Theory Study of 14‐Atom Germanium Clusters

Abstract

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge14z (z = –8, –6, –4, –2, 0, +2, +4) starting from seven different initial configurations. An Oh omnicapped cube structure is the most stable for Ge142– followed by a hexagonal antiprism structure with a relative energy of 42.7 kcal/mol. The lowest‐energy structure for neutral Ge14 is a triplet omnicapped cube with full Oh symmetry followed by a singlet omnicapped cube compressed to D4h symmetry through Jahn–Teller distortion. The lowest energy Ge142+ structure is also an Oh structure derived from the omnicapped cube through elongation of the 12 edges of the underlying cube to give a rhomboidal dodecahedron with 12 rhombus faces. The lowest‐energy Ge124+ structure is a bicapped icosahedron. Some D6h hexagonal wheel structures at higher energies are also found for the hypoelectronic systems Ge14, Ge142+, and Ge144+. The lowest‐energy structures for the hyperelectronic Ge144–, Ge146–, and Ge148– are relatively unsymmetrical not readily recognizable open structures typically with some pentagonal or hexagonal faces. The D6d bicapped hexagonal antiprism found in 14‐vertex C2B12 carborane and M2C2B10 dimetallacarborane structures is not the lowest‐energy structure for any of the Ge14z clusters.(© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008)

The structural landscape in 14-vertex clusters of silicon, M@Si14: when two bonding paradigms collide

“…22 Here we focus on the question of the role of the d electrons on the metal: are they integral to stability in the same way as they are isomer B? A significant clue comes from the work of King and co-workers 32 The fact that the structure of isomer C is adapted to accommodate precisely two electrons from the metal accounts for its relative stability both at the start of the period and at the end, where low oxidation states dominate the chemistry. Early in the series this is simply because there are few electrons in the d orbitals, while at the end it is because the d orbitals have descended into the core and are therefore less available.…”

Metallacarboranes and their interactions: theoretical insights and their applicability

“…King et al 32 An early DFT study on a 14-vertex bimetallic closo-ruthenacarborane was done by Bühl et al 23 The position of the C atoms in the carborane framework can be established from geometry optimizations of the most probable isomers and NMR experimental data. By comparing bond distances between theoretical and experimental structures it is difficult to determine unambiguously the structural isomer, but it can be used to discard the carbon adjacent isomer.…”

“…1g). 32 The most studied 13-vertex metallacarboranes adopted the docosahedron geometry in their ground state but the henicosahedron geometry can be found as intermediates or transition states. It was calculated by DFT 33 that the docosahedron is preferred over the henicosahedron for [B 13 H 13 ] 2À (0.9 kcal mol À1 ) but for 1,2-C 2 B 11 H 13 , the reverse trend was shown (1.8 kcal mol À1 ).…”

“…14 vertex cluster ligands. King et al 32 calculated relative energy stabilities of 14-vertex clusters using the Ge atom as vertex instead of B-H, C-H or metals. Wade-Mingos rules suggest the bicapped hexagonal antiprism for Ge 14 2À similar to that found experimentally in metallacarboranes.…”

A theoretical study on the stability difference of the borane BnHn2− and carborane C2Bn−2Hn(5 ≤ n ≤ 7) clusters

“…There are also some compounds that isoelectronic and isostructure with boranes, which are called borane analogs. Borane analogs began to attract the attention of chemists in recent years, such as the alanes, the gallanes, the silicium clusters, and the Germanium Clusters …”