Density functional theory predicts significant differences in the preferred structures of endohedral M@Ge10z (M = Ni, Pd, Pt; z = 0, 2-, 4-) clusters upon a change of the central metal atom in otherwise isoelectronic systems. For the neutral clusters M@Ge10 the global minima are singlet bicapped square antiprisms. However, triplet regular pentagonal prismatic structures become increasingly energetically competitive in the series Ni --> Pd -> Pt. The pentagonal prismatic dianions M@Ge10(2-) (M = Ni, Pd, Pt) appear to have closed shell structures and are the global minima for palladium and platinum. However, the global minimum for Ni@Ge102- is the capped square antiprism suggested by the Wade-Mingos rules. A number of singlet low-energy unsymmetrical structures are found for the tetraanions M@Ge10(4-). However, for the palladium and platinum tetraanions triplet pentagonal prismatic structures are energetically competitive with the unsymmetrical structures.

Density functional theory (DFT) at the hybrid B3LYP level has been applied to Ge10z germanium clusters (z = -6, -4, -2, 0, +2, +4, +6) starting from 12 different initial configurations. The D4d 4,4-bicapped square antiprism found experimentally in B10H102- and other 10-vertex clusters with 22 skeletal electrons is calculated for the isoelectronic Ge102- to be the global minimum by more than 15 kcal/mol. The global minima found for electron-rich clusters Ge104- and Ge106- are not those known experimentally. However, experimentally known structures for nido-B10H14 and the pentagonal antiprism of arachno-Pd@Bi104+ are found at higher but potentially accessible energies for Ge104- and Ge106-. The global minimum for Ge10 is the C3v 3,4,4,4-tetracapped trigonal prism predicted by the Wade-Mingos rules and found experimentally in isoelectronic Ni@Ga1010-. However, only slightly above this global minimum for Ge10 (+3.3 kcal/mol) is the likewise C3v isocloso 10-vertex deltahedron found in metallaboranes such as (eta6-arene)RuB9H9 derivatives. Structures found for more electron-poor clusters Ge102+ and Ge104+ include various capped octahedra and pentagonal bipyramids. This study predicts a number of 10-vertex cluster structures that have not yet been realized experimentally but would be interesting targets for future synthetic 10-vertex cluster chemistry using vertex units isolobal with the germanium vertices used in this work.

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.