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Polyhedral Structures with Three‐, Four‐, and Five Fold Symmetry in Metal‐Centered Ten‐Vertex Germanium Clusters
Author(s) -
King R. Bruce,
SilaghiDumitrescu Ioan,
Uţă MateiMaria
Publication year - 2008
Publication title -
chemistry – a european journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.687
H-Index - 242
eISSN - 1521-3765
pISSN - 0947-6539
DOI - 10.1002/chem.200701582
Subject(s) - square antiprism , crystallography , chemistry , cluster (spacecraft) , germanium , atom (system on chip) , metal , vertex (graph theory) , density functional theory , electron , atomic physics , physics , molecule , computational chemistry , combinatorics , silicon , quantum mechanics , graph , mathematics , organic chemistry , computer science , oxygen atom , embedded system , programming language
Studies using density functional theory (DFT) at the hybrid B3LYP level indicate that the relative energies of structures with three‐fold, four‐fold, and five‐fold symmetry for centered 10‐vertex bare germanium clusters of the general type M@Ge 10 z depend on the central metal atom M and the skeletal electron count. For M@Ge 10 clusters with 20 skeletal electrons the DFT results agree with experimental data on the isoelectronic centered 10‐vertex bare metal clusters. Thus the lowest energy structure for Ni@Ge 10 , isoelectronic with the known Ni@In 10 10− , is a C 3 v polyhedron derived from the tetracapped trigonal prism. However, Zn@Ge 10 2+ is isoelectronic with the known cluster Zn@In 10 8− , which has the lowest energy structure, a D 4 d bicapped square antiprism. For the clusters Ni@Ge 10 2− , Cu@Ge 10 − , and Zn@Ge 10 that have 22 skeletal electrons the lowest energy structures are the D 4 d bicapped square antiprism predicted by the Wade–Mingos rules. For the clusters Ni@Ge 10 4− , Cu@Ge 10 3− , and Zn@Ge 10 2− that have 24 skeletal electrons the lowest energy structures are C 3 v polyhedra with 10 triangular faces and 3 quadrilateral faces derived from a tetracapped trigonal prism by extreme lengthening of the edges of the capped triangular face of the underlying trigonal prism. For the clusters Cu@Ge 10 5− and Zn@Ge 10 4− that have 26 skeletal electrons the lowest energy structures are the D 5 d pentagonal antiprisms predicted by the Wade–Mingos rules and the C 3 v tetracapped trigonal prism as a somewhat higher energy structure. However, for the isoelectronic Ni@Ge 10 6− the relative energies of these two structure types are reversed so that the C 3 v tetracapped trigonal prism becomes the global minimum. The effects of electron count on the geometries of the D 5 d pentagonal prism and D 4 d bicapped square antiprism centered metal cluster structures are consistent with the bonding/antibonding characteristics of the corresponding HOMO and LUMO frontier molecular orbitals.