Issue 3, 2007

Density functional theory study of twelve-atom germanium clusters: conflict between the Wade–Mingos rules and optimum vertex degrees

Abstract

Density functional theory (DFT) at the hybrid B3LYP level has been applied to Ge12z bare germanium clusters (z = −6, −4, −2, 0, +2, +4, +6) starting from 11 initial configurations. The Wade–Mingos rules are seen to have limited value in rationalizing the results since they frequently require vertex degrees higher than the optimum vertex degree of 4 for germanium. Thus the expected Ih regular icosahedron is no longer the global minimum for Ge122− although it remains a low energy structure for Ge122− lying only 5.6 kcal mol−1 above a bicapped arachno structure conforming to the Wade–Mingos rules. The three lowest energy structures for Ge124− within 11 kcal mol−1 are a prolate (elongated) polyhedron with six quadrilateral faces and eight triangular faces, the dual of the bisdisphenoid with four trapezoidal and four pentagonal faces, and a polyhedron with two quadrilateral and 16 triangular faces related but not identical to the polyhedron found in the known tetracarbon carboranes R4C4B8H8. The lowest energy structures for the neutral Ge12 are seen to be distorted versions of the icosahedron and the bicapped 10-vertex arachno lowest energy structures for Ge122−. The low energy structures for the even more hypoelectronic Ge122+ and Ge124+ are even more unusual including a hexacapped octahedron, a tetracapped square antiprism, and a double cube for Ge122+ and a C2v structure with a central unique degree 6 vertex for Ge124+.

Graphical abstract: Density functional theory study of twelve-atom germanium clusters: conflict between the Wade–Mingos rules and optimum vertex degrees

Supplementary files

Article information

Article type
Paper
Submitted
19 Oct 2006
Accepted
13 Nov 2006
First published
08 Dec 2006

Dalton Trans., 2007, 364-372

Density functional theory study of twelve-atom germanium clusters: conflict between the Wade–Mingos rules and optimum vertex degrees

R. B. King, I. Silaghi-Dumitrescu and M. M. Uţă, Dalton Trans., 2007, 364 DOI: 10.1039/B615225B

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