Empty versus filled polyhedra: 11 vertex bare germanium clusters.

The structures and energetics of centered 10-vertex Ge@Ge₁₀(z) (z = -4, -2, 0, +2, +4) clusters have been investigated by density functional theory (DFT) for comparison with the previously studied isomeric empty 11-vertex Ge₁₁(z) clusters. For the cationic species (z = +2, +4) such centered Ge@Ge₁₀(z) structures are shown to be energetically competitive (within ∼1 kcal mol⁻¹) to the lowest energy isomeric empty Ge₁₁(z) structures. These Ge@Ge₁₀(z) structures can be derived from the lowest energy empty 10-vertex Ge₁₀(z-4) structures by inserting a Ge⁴⁺ ion in the center.

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

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.