Polyhedral Structures with Three‐, Four‐, and Five Fold Symmetry in Metal‐Centered Ten‐Vertex Germanium Clusters

Abstract

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(3v) 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(4d) 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(4d) 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(3v) 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(5d) pentagonal antiprisms predicted by the Wade-Mingos rules and the C(3v) 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(3v) tetracapped trigonal prism becomes the global minimum. The effects of electron count on the geometries of the D(5d) pentagonal prism and D(4d) bicapped square antiprism centered metal cluster structures are consistent with the bonding/antibonding characteristics of the corresponding HOMO and LUMO frontier molecular orbitals.

Zintl‐Ionen, Käfigverbindungen und intermetalloide Cluster der Elemente der 14. und 15. Gruppe

“…Das zentrierte D 4 d ‐symmetrische zweifach überdachte quadratische Antiprisma wurde als Grundzustand für [Ni@E 10 ] 2− mit E=Ge, Sn, Pb, wie auch für [Pd@Sn 10 ] 2− , [Pd@Pb 10 ] 2− und [Pt@Pb 10 ] 2− identifiziert 306. Die Strukturen von [M@Ge 10 ] 2− (M=Ni,250, 326, 327 Pd,327 Pt327) wurden besonders ausgiebig untersucht. Dabei wurde das zentrierte D 4 d ‐symmetrische zweifach überdachte quadratische Antiprisma als energetisch günstigste Struktur für [Ni@Ge 10 ] 2− und als lokales Minimum für [Pb@Ge 10 ] 2− gefunden.…”

“…Auch MgPb 10 trat in Gasphasen‐Experimenten auf 324. Für diese Cluster ([Al@E 10 ] + , E=Ge,306 Sn,306 Pb;306 [Mg@Pb 10 ]319), wie auch für [Zn@Si 10 ],325 [Zn@Ge 10 ]326 und [Cu@Ge 10 ] − 326 wurde das zentrierte D 4 d ‐symmetrische zweifach überdachte quadratische Antiprisma als globales Minimum identifiziert. SrPb 10 und BaPb 10 319 bevorzugen nicht‐endohedrale Strukturen.…”

Endohedral Nickel, Palladium, and Platinum Atoms in 10-Vertex Germanium Clusters: Competition between Bicapped Square Antiprismatic and Pentagonal Prismatic Structures

“…19 That work used a polarized (valence) double-6-31G(d) basis set for all of the atoms. Owing to the presence of the heavier transition metals palladium and platinum in this work, the effective core potential † University of Georgia.…”

[Co@Ge10]3−: An Intermetalloid Cluster with Archimedean Pentagonal Prismatic Structure

“…A natural charge of −1.05 calculated for Co supports the assumption of a d 10 configuration. Interestingly, according to recently reported quantum chemical calculations for the isoelectronic species [Ni@Ge 10 ] 2− , [Cu@Ge 10 ] − , and [Zn@Ge 10 ]41 as well as for the empty cluster [Ge 10 ] 2− ,42 the D 4 d symmetric bicapped square antiprism is predicted to be the lowest‐energy structure (B3LYP/6‐31G(d) gas‐phase calculations) 43. With SCI‐PCM/B3LYP/cc‐pVTZ(‐NR) we found that the optimization of a D 4 d bicapped square antiprism led to a stationary state 13.3 kcal mol −1 above the D 5 h minimum for the [Co@Ge 10 ] 3− ion, but this stationary state shows two imaginary frequencies (43.0 i cm −1 ) and does not represent a ground or a transition state.…”