Density functional study of 8- and 11-vertex polyhedral borane structures: comparison with bare germanium clusters.

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the polyhedral boranes B(n)H(n)(z) (n = 8 and 11, z = -2, -4, and -6) for comparison with isoelectronic germanium clusters Ge(n)(z). The energy differences between the global minima and other higher energy borane structures are much larger relative to the case of the corresponding bare germanium clusters. Furthermore, for both B(8)H(8)(2-) and B(11)H(11)(2-), the lowest energy computed structures are the corresponding experimentally observed most spherical deltahedra predicted by the Wade-Mingos rules, namely the D(2)(d) bisdisphenoid and the C(2)(v) edge-coalesced icosahedron, respectively. Only in the case of B(8)H(8)(2-) is there a second structure close (+2.6 kcal/mol) to the D(2)(d) bisdisphenoid global minimum, namely the C(2)(v) bicapped trigonal prism corresponding to the "square" intermediate in a single diamond-square-diamond process that can lead to the experimentally observed room temperature fluxionality of B(8)H(8)(2-). Stable borane structures with 3-fold symmetry (e.g., D(3)(h), C(3)(v), etc.) are not found for boranes with 8- and 11-vertices, in contrast to the corresponding germanium clusters where stable structures derived from the D(3)(d) bicapped octahedron and D(3)(h) pentacapped trigonal prism are found for the 8- and 11-vertex systems, respectively. The lowest energy structures found for the electron-rich boranes B(8)H(8)(4-) and B(11)H(11)(4-) are nido polyhedra derived from a closo deltahedron by removal of a relatively high degree vertex, as predicted by the Wade-Mingos rules. They relate to isoelectronic species found experimentally, e.g., B(8)H(12) and R(4)C(4)B(4)H(4) for B(8)H(8)(4-) and C(2)B(9)H(11)(2-) for B(11)H(11)(4-). Three structures were found for B(11)H(11)(6-) with arachno type geometry having two open faces in accord with the Wade-Mingos rules.

Density functional theory study of eight-atom germanium clusters: effect of electron count on cluster geometry.

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge8z(z=-6, -4, -2, 0, +2, +4) using nine initial geometries. For Ge8(2-) the D2d bisdisphenoid structure predicted by the Wade-Mingos rules is not computed to be the global minimum but instead lies 3.9 kcal mol-1 above the Td tetracapped tetrahedron global minimum predicted to exhibit spherical aromaticity. The hyperelectronic clusters Ge(8)4- and Ge8(6-) have nido B8H12 and square antiprism structures, respectively, as global minima in accord with the Wade-Mingos rules and experimental data on E(8)2+(E=Sb, Bi) cations. Hypoelectronic eight-vertex clusters isoelectronic and isolobal with Ge8, Ge8(2+) and Ge(8)4+ are not known experimentally. Their computed structures include smaller polyhedra having one or more capped triangular faces as well as more open non-polyhedral structures.

Density functional theory study of 11-atom germanium clusters: effect of electron count on cluster geometry.

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge(11)(z) (z = -6, -4, -2, 0, +2, +4, +6) starting from eight different initial configurations. The global minimum within the Ge(11)(2-) set is an elongated pentacapped trigonal prism distorted from D(3)(h) to C(2v) symmetry. However, the much more spherical edge-coalesced icosahedron, also of C(2v) symmetry, expected by the Wade-Mingos rules for a 2n + 2 skeletal electron system and found experimentally in B(11)H(11)(2-) and isoelectronic carboranes, is of only slightly higher energy (+5.2 kcal/mol). Even more elongated D(3)(h) pentacapped trigonal prisms are the global minima for the electron-rich structures Ge(11)(4-) and Ge(11)(6-). For Ge(11)(4-) the C(5v) 5-capped pentagonal antiprism analogous to the dicarbollide ligand C(2)B(9)H(11)(2-) is of significantly higher energy (approximately 28 kcal/mol) than the D(3h) global minimum. The C(2v) edge-coalesced icosahedron is also the global minimum for the electron-poor Ge(11) similar to its occurrence in experimentally known 11-vertex "isocloso" metallaboranes of the type (eta(6)-arene)RuB(10)H(10). The lowest energy polyhedral structures computed for the more hypoelectronic Ge(11)(4+) and Ge(11)(6+) clusters are very similar to those found experimentally for the isoelectronic ions E(11)(7-) (E = Ga, In, Tl) and Tl(9)Au(2)(9-) in intermetallics in the case of Ge(11)(4+) and Ge(11)(6+), respectively. These DFT studies predict an interesting D(5h) centered pentagonal prismatic structure for Ge(11)(2+) and isoelectronic metal clusters.