Spherical Deltahedra Research Articles

Rule breaker boron clusters: a new class of hypoelectronic osmaborane clusters [(Cp*Os)2BnHn] (n = 6-10).

Since the pioneering electron counting rule for borane clusters was proposed by Wade, the structures and bonding of boron clusters and their derivatives have been elegantly rationalised. However, this rule and its modified versions faced problems explaining the electronic structures of less spherical deltahedra, unlike the core geometries of borate dianions [BnHn]2- (n = 6-12). Herein, we report the isolation of a series of osmaborane clusters [(Cp*Os)2BnHn], 1-5, (n = 6-10) by the thermolysis of an in situ generated intermediate, obtained from the rapid condensation of [Cp*OsBr2]2 and [LiBH4·THF], with [BH3·THF] or [BH3·SMe2]. Interestingly, all these clusters show unusual less spherical deltahedral shapes that can be generated from canonical [BnHn]2- (n = 8-12) shapes by doing diamond-square-diamond (DSD) rearrangements. The DSD rearrangements led to the generation of higher degree vertices, which are occupied by Os atoms and also generated Os-Os bonds in these clusters. Theoretical calculations revealed that these Cp*Os⋯OsCp* interactions in clusters 1-5 played a crucial role in their structural shape and electron count. These less spherical deltahedral clusters are rare, and most significantly, clusters 1-5 with (n-1) skeleton electron pairs (SEPs) do not follow Wade-Mingos electron counting rules and can be classified as hypoelectronic closo clusters.

Phosphorus as a heteroatom in metallaborane structures: Cyclopentadienylcobalt diphosphaboranes

The icosahedral cobaltadiphosphaborane CpCoP2B9H9 and its indenyl analog were recently synthesized by Welch and coworkers and characterized structurally by X-ray crystallography. The complete series of related cobaltadiphosphaboranes CpCoP2Bn−3Hn−3 (n=8–12) have now been studied by density functional theory. A significantly larger number of low-energy CpCoP2Bn−3Hn−3 structures relative to the global minima were found than for the carbon analogs CpCoC2Bn−3Hn−1 suggesting more complicated energy surfaces and possible fluxional systems. In all of the lowest energy CpCoP2Bn−3Hn−3 structures the central CoP2Bn−3 polyhedra are found to be the most spherical deltahedra similar to those found in the corresponding BnHn2− dianions. The lowest energy CpCoP2Bn−3Hn−3 structures typically but not always have the cobalt atom at a degree 5 or 6 vertex and the phosphorus atoms at degree 4 vertices. For the icosahedral CpCoP2B9H9 system the four structures with adjacent phosphorus vertices all lie at higher energies relative to all five structures with non-adjacent phosphorus vertices.

Metal–metal interactions in deltahedral dirhoda- and diiridadicarbaboranes

The lowest energy Cp2M2C2Bn−4Hn−2 (M=Rh, Ir; n=9, 10, and 12) structures are found by density functional theory to be the most spherical deltahedra having the metal atoms at degree 5 vertices and the carbon atoms preferably at degree 4 vertices. Structures with direct surface M–M bonds appear to be energetically more favorable than for the corresponding cobalt derivatives. For the 11-vertex systems Cp2M2C2B7H9 one of the three lowest energy structures is based on the 11-vertex most spherical deltahedron with one of the metal atoms at the unique degree 6 vertex. The 11-vertex polyhedron in one of the other low-energy Cp2M2C2B7H9 structures has a quadrilateral face thereby avoiding the presence of a degree 6 vertex. The Wiberg bond indices (WBIs) for the M–M interactions along deltahedral edges range from 0.36 to 0.40 and can be considered to be formal single bonds. The WBIs for non-adjacent M⋯M interactions are much lower at 0.07–0.12 suggesting weak metal–metal interactions through the center of the deltahedron.

From closo to isocloso Structures and Beyond in Cobaltaboranes with 9 to 12 Vertices

Density functional theory (DFT) studies predict the dianions CpCoB(n-1)H(n-1)(2-) (n = 9, 10, 11, 12; Cp = eta(5)-C(5)H(5)) to have structures based on the most spherical deltahedra found in the isoelectronic boranes B(n)H(n)(2-). In the CpCoB(8)H(8)(2-) dianion the non-equivalent structures with the cobalt atom at a degree 4 vertex and at a degree 5 vertex are essentially degenerate in terms of energy (within approximately 1 kcal/mol). For the CpCoB(n-1)H(n-1)(2-) dianions (n = 10, 11, 12) the cobalt atom prefers energetically the vertices of the lowest possible degree (four for n = 10 and 11, five for n = 12). Structures for the neutral species CpCoB(n-1)H(n-1) (n = 10, 11, 12) based on isocloso deltahedra with the cobalt atom at a degree 6 vertex are preferred energetically by 9, 19, and 53 kcal/mol, respectively, over alternative structures. However, for CpCoB(8)H(8) the closo tricapped trigonal prismatic structure with the cobalt atom at a degree 5 vertex is energetically preferred by approximately 9 kcal/mol over the isocloso deltahedral structure with the cobalt atom at a degree 6 vertex. The lowest energy structures predicted for the dications CpCoB(8)H(8)(2+) and CpCoB(9)H(9)(2+) are highly oblate (flattened) deltahedra with the cobalt atom at a degree 7 vertex. A complicated potential energy surface was found for CpCoB(10)H(10)(2+) including non-deltahedral structures with a single quadrilateral or pentagonal face. The predicted lowest energy structures for both CpCoB(11)H(11) and CpCoB(11)H(11)(2+) are based on the same 12-vertex deltahedron with three degree 6, six degree 5, and three degree 4 vertices, and thus topologically different from the regular icosahedron normally found in boron chemistry.

Geometry and chemical bonding in polyhedral boranes, metallaboranes, and dimetallaboranes: From closo to isocloso to oblatocloso polyhedra

Abstract The geometry and chemical bonding in the closo metal-free boranes B n H n 2 - and the isoelectronic carboranes CB n - 1 H n - and C2Bn−2Hn with 2n + 2 skeletal electrons are based on the most spherical deltahedra with a preference for degree 5 vertices, particularly for the boron atoms. Such deltahedral boranes can be considered to be three-dimensional aromatic systems, as indicated by strongly diatropic nucleus independent chemical shift values for B n H n 2 - (n = 6, 8, 9, 12). Metallaborane structures, particularly those with 9–11 vertices and only 2n rather than 2n + 2 apparent skeletal electrons, are often based on isocloso deltahedra with the metal atom at a degree 6 vertex. Dimetallaborane structures, particularly the rhenium derivatives Cp2Re2Bn−2Hn−2 (8 ⩽ n ⩽ 12), are based on highly non-spherical and very oblate deltahedra with the metal atoms typically at degree 6 or 7 vertices, which are the lowest curvature sites of the deltahedra. A viable model for the skeletal bonding in such dimetallaboranes can be developed if each of the two metal vertices is assumed to contribute five internal orbitals to the skeletal bonding. This leads to 2n + 4 skeletal electrons, which are partitioned into n surface bonds and a formal metal–metal double bond inside the oblate deltahedron.

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 BnHnz (n = 8 and 11, z = −2, −4, and −6) for comparison with isoelectronic germanium clusters Genz. 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 B8H82- and B11H112-, the lowest energy computed structures are the corresponding experimentally observed most spherical deltahedra predicted by the Wade−Mingos rules, namely the D2d bisdisphenoid and the C2v edge-coalesced icosahedron, respectively. Only in the case of B8H82- is there a second structure close (+2.6 kcal/mol) to the D2d bisdisphenoid global minimum, namely the C2v 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 B8H82-. Stable borane structures with 3-fold symmetr...

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.

Energy–architectural patterns among the five‐ to twelve‐vertex closo‐carboranes

AbstractIn 1969 the order of stabilities of all possible neutral two‐carbon closo‐carboranes, i.e. from closo‐C2B3H5 to closo‐C2B10H12, was forecast. It was wistfully anticipated that all 52 skeletal structures would be based solely upon the most spherical deltahedra (polyhedra consisting exclusively of triangular faces, closo‐n〈III〉; n = 5 to 12) and that the order of stabilities would be based upon the presumed preference of the two carbon atoms to occupy (a) low‐coordinated and (b) nonadjacent sites.The 52 potential isomers reduce to 42 isomers upon optimization (using the DFT B3LYP/6‐311G* level of theory and the Gaussian 94 program), as seven isomers rearrange spontaneously into more stable isomers and three isomers rearrange spontaneously into two structures incorporating four‐membered open faces within which are accommodated both carbon atoms, in adjacent 4k‐edge sites. The order of stability of the ‘surviving’ 42 closo‐carborane configurations comports nicely with the 1969 projections with the exception of three intimately related closo‐11 vertex isomers. An explanation for the marginally increased stability of these three intimately related closo‐11 vertex isomers is offered. For the remaining 39 isomers, the differences, between the calculated and estimated stability values, seldom exceed 6 kcal mol−1. Copyright © 2003 John Wiley & Sons, Ltd.