Polyhedral structures with three-, four-, and five fold symmetry in metal-centered ten-vertex germanium clusters

摘要

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, 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, 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.