Alexandru Lupan

Hypoelectronic dirhenaboranes having eight to twelve vertices: internal versus surface rhenium-rhenium bonding.

Fehlner, Ghosh, and their co-workers have synthesized a series of dirhenaboranes Cp(2)Re(2)B(n-2)H(n-2) (n = 8, 9, 10, 11, 12) exhibiting unprecedented oblate (flattened) deltahedral structures. These structures have degree 6 and/or 7 rhenium vertices at the flattest regions on opposite sides of an axially compressed deltahedron thereby leading to Re═Re distances in the range 2.69 to 2.94 Å suggesting internal formal double bonds. These experimental oblate (flattened) deltahedral structures are shown by density functional theory to be the lowest energy structures for these dirhenaboranes. In some cases the energy differences between such oblate deltahedral structures and the next higher energy structures are quite considerable, that is, up to 25 kcal/mol for the nine-vertex Cp(2)Re(2)B(7)H(7) structures. The higher energy Cp(2)Re(2)B(n-2)H(n-2) structures are of the two types: (1) Most spherical (closo) deltahedra having unusually short 2.28 to 2.39 Å Re-Re edges with unusually high Wiberg bond indices suggesting formal multiple bonds on the deltahedral surface; (2) Deltahedra having one or two degree 3 vertices and 2.6 to 2.9 Å Re-Re edges. The latter deltahedra are derived from smaller deltahedra by capping Re(2)B faces with the degree 3 vertices.

Nonspherical Deltahedra in Low-Energy Dicarbalane Structures Testing the Wade–Mingos Rules: The Regular Icosahedron Is Not Favored for the 12-Vertex Dicarbalane

Theoretical studies on the dicarbalanes C2Al(n-2)Men (n = 7-14; Me = methyl) predict both carbon atoms to be located at degree 4 vertices of a central C2Al(n-2) deltahedron in the lowest energy structures. As a consequence, deltahedra having two degree 4 vertices, two degree 6 vertices, and eight degree 5 vertices rather than the regular icosahedron having exclusively degree 5 vertices are found for the 12-vertex dicarbalane C2Al10Me12. However, the lowest energy C2Al(n-2)Men (n = 7-11) structures are based on the same most spherical (closo) deltahedra as the corresponding deltahedral boranes. The lowest energy structures for the 13- and 14-vertex systems C2Al(n-2)Men (n = 13 and 14) are also deltahedra having exactly two degree 4 vertices for the carbon atoms. The six-vertex C2Al4Me6 system is exceptional since bicapped tetrahedral and capped square pyramidal structures with degree 3 vertices for the carbon atoms are energetically preferred over the octahedral structure suggested by the Wade-Mingos rules.

Novel non-spherical deltahedra in trirhenaborane structures

The geometries and energetics of the trirhenaboranes Cp3Re3Bn−3Hn−3 (Cp = η5-C5H5; n = 5 to 12) have been investigated using density functional theory for comparison with the experimentally known oblatocloso dirhenaboranes Cp*2Re2Bn−2Hn−2 (Cp* = η5-Me5C5; n = 8 to 12). The low-energy Cp3Re3Bn−3Hn−3 (7 ≤ n ≤ 12) structures are found to be Re3Bn−3 deltahedra with internally bonded Re3 triangles. The rhenium atoms are generally located at degree 6 to 8 vertices representing sites of low local curvature and the boron atoms at degree 3 to 5 vertices representing sites of high local curvature. The Re–Re bonds in the Re3 triangles of such clusters typically range from 2.6 to 2.7 A if they are located on or near the deltahedral surface and from 2.8 to 3.0 A if they go through the interior of the deltahedron away from the surface. Such highly non-spherical structures, typically having little symmetry, are related to the oblatocloso structures of the dirhenaboranes. A low-energy, more nearly spherical 12-vertex Cp3Re3B9H9 structure, essentially degenerate with the global minimum, has an Re–Re–Re chain embedded in a deltahedron having degree 5 and 6 rhenium vertices and degree 4 and 5 boron vertices. Low-energy structures for the 5-vertex Cp3Re3B2H2 system are derived from a trigonal bipyramid. Similarly, low-energy 6-vertex Cp3Re3B3H3 structures have central Re3B3 bicapped tetrahedra.

Hypoelectronic diruthenaboranes and diosmaboranes having eight to twelve vertices: capped isocloso and bicapped closo structures

The oblate deltahedral structures for the experimentally known 2n − 4 Wadean skeletal electron systems Cp2Re2Bn−2Hn−2 (Cp = η5-R5C5 ligand; R = H, CH3; n = 8 to 12) differ radically from the more nearly spherical 2n skeletal electron isocloso deltahedra such as the known Cp2Fe2C2Bn−4Hn−2 and 2n + 2 skeletal electron closo systems such as the extensive series of known Cp2Co2C2Bn−4Hn−2 derivatives. Density functional theory has now been used to investigate the intermediate “missing” systems, namely the 2n − 2 Wadean skeletal electron systems Cp2M2Bn−2Hn−2 (M = Ru, Os). The lowest energy such structures are predicted to have central deltahedra with n − 1 or n − 2 vertices capped by the remaining BH vertices. This generates larger deltahedra having one or two degree 3 vertices leading to tetrahedral cavities. In all of the lowest energy Cp2M2Bn−2Hn−2 structures the metal atoms are located at the highest degree vertices, most frequently degree 6 vertices. These metal vertices share a deltahedral edge with M–M distances ranging from 2.7 to 2.9 A and Wiberg bond indices of ∼0.3 to ∼0.4. The structural pattern changes drastically for the 12-vertex systems Cp2M2B10H10 (M = Ru, Os) where the lowest energy structures are “isoisocloso” deltahedra having two adjacent degree 6 vertices for the metal atoms as well as eight degree 5 and two degree 4 vertices. Higher energy Cp2M2B10H10 structures are based on a regular icosahedron with all degree 5 vertices having unusually short MM edges of ∼2.2 to ∼2.3 A with corresponding high Wiberg bond indices of ∼1.3 to ∼1.5 suggesting formal metal–metal triple bonds.

Cyclopentadienylironphosphacarboranes: fragility of polyhedral edges in the 11-vertex system

The lowest energy CpFeCHP(CH3)Bn−3Hn−3 (n = 8 to 12) structures, including the experimentally known CpFeCHP(CH3)B8H8, have been investigated by density functional theory. The central FeCPBn−3 polyhedra in all of the lowest energy such structures are the most spherical closo deltahedra. The heteroatoms are so located to have adjacent iron and phosphorus atoms and non-adjacent phosphorus and carbon atoms. One of the Fe–B bonds from the degree 6 iron vertex in the 11-vertex CpFeCHP(CH3)B8H8 structure appears to be fragile, readily elongating to ∼3.1 A in one of the low-energy structures, consistent with experimental observation on this system.

Metal–metal bonding in deltahedral dimetallaboranes and trimetallaboranes: a density functional theory study

Abstract The skeletal bonding topology as well as the Re=Re distances and Wiberg bond indices in the experimentally known oblatocloso dirhenaboranes Cp*2Re2Bn−2Hn−2 (Cp*=η5Me5C5, n=8–12) suggest formal Re=Re double bonds through the center of a flattened Re2Bn−2 deltahedron. Removal of a boron vertex from these oblatocloso structures leads to oblatonido structures such as Cp2W2B5H9 and Cp2W2B6H10. Similar removal of two boron vertices from the Cp2Re2Bn−2Hn−2 (n=8–12) structures generates oblatoarachno structures such as Cp2Re2B4H8 and Cp2Re2B7H11. Higher energy Cp2Re2Bn−2Hn−2 (Cp=η5-C5H5, n=8–12) structures exhibit closo deltahedral structures similar to the deltahedral borane dianions BnHn2−. The rhenium atoms in these structures are located at adjacent vertices with ultrashort Re≣Re distances similar to the formal quadruple bond found in Re2Cl82− by X-ray crystallography. Such surface Re≣Re quadruple bonds are found in the lowest energy PnRe2Bn−2Hn−2 structures (Pn=η5,η5-pentalene) in which the pentalene ligand forces the rhenium atoms to occupy adjacent deltahedral vertices. The low-energy structures of the tritungstaboranes Cp3W3(H)Bn−3Hn−3 (n=5–12), related to the experimentally known Cp*3W3(H)B8H8, have central W3Bn−3 deltahedra with imbedded bonded W3 triangles. Similar structures are found for the isoelectronic trirhenaboranes Cp3Re3Bn−3Hn−3. The metal atoms are located at degree 6 and 7 vertices in regions of relatively low surface curvature whereas the boron atoms are located at degree 3–5 vertices in regions of relatively high surface curvature. The five lowest-energy structures for the 11-vertex tritungstaborane Cp3W3(H)B8H8 all have the same central W3B8 deltahedron and differ only by the location of the “extra” hydrogen atom. The isosceles W3 triangles in these structures have two long ~3.0 Å W–W edges through the inside of the deltahedron with the third shorter W–W edge of ~2.7 to ~2.8 Å corresponding to a surface deltahedral edge.

Paramagnetism in Metallacarboranes: The Polyhedral Chromadicarbaborane Systems

The chromadicarbaboranes CpCrC2Bn-3Hn-1 (8 ≤ n ≤ 12) are of interest in providing stable paramagnetic deltahedral metallaboranes among which the 12-vertex CpCrC2B9H11 has been synthesized by Hawthorne and co-workers. Density functional theory shows that the lowest-energy such structures are quartet spin-state Cr(III) structures in which the central CrC2Bn-3 units exhibit most spherical closo deltahedral geometries similar to those found in the borane dianions BnHn2-. Higher-energy doublet CpCrC2Bn-3Hn-1 (8 ≤ n ≤ 11) structures are found exhibiting central CrC2Bn-3 isocloso deltahedral geometries, thereby providing a degree 6 vertex for the chromium atom. The lowest-energy CpCrC2Bn-3Hn-1 (8 ≤ n ≤ 11) structures all have both carbon atoms at degree 4 vertices. However, the lowest-energy CpCrC2B9H11 structures all have central CrC2B9 icosahedra and thus lack degree 4 vertices for the carbon atoms. For all of the CpCrC2Bn-3Hn-1 (8 ≤ n ≤ 12) systems the lowest-energy isomers are those with the maximum number of Cr-C edges in contrast to the related CpCoC2Bn-3Hn-1 systems.

Hydrogen migration in hypoelectronic biicosahedral metallaborane structures

The biicosahedral metallaboranes CpMB20H17 (M = Pd, Pt; Ru, Os; Mo, W) and CpM′CB19H17 (M′ = Rh, Ir; Re; Ta) have been investigated by density functional theory to supplement the earlier work on the first-row transition metal derivatives CpMB20H17 (M = Ni, Fe) and CpCoCB19H17. The CpMB20H17 (M = Ni, Pd, Pt) and CpMCB19H17 (M = Co, Rh, Ir) systems have the ideal 46 skeletal electrons by the Jemmis rules. Their lowest energy structures have the metal atom in the meta position of the biicosahedron. Hydrogen migration occurs in the low-energy structures of the hypoelectronic systems CpMB20H17 (M = Fe, Ru, Os; Mo, W) to give one or two M–B biicosahedral edges bridged by hydrogen atoms. In CpReCB19H17 and one of the CpTaCB19H17 structures more extensive hydrogen migration occurs to give low-energy structures having terminal M–H bonds and metal vertices of a degree of at least 6. The CpTaCB19H17 system also has a low-energy structure in which the TaCB19 biicosahedron becomes distorted enough to provide a degree 8 vertex for the tantalum atom.

Tetracarbaboranes: nido structures without bridging hydrogens

The structures and energetics of the tetracarbaboranes C4Bn-4Hn (n = 6 to 13) have been investigated by density functional theory and coupled cluster calculations. In general, the lowest energy structures of the tetracarbaboranes C4Bn-4Hn minimize the number of C-C polyhedral edges as well as the degrees of the carbon vertices. For the C4B2H6 and C4B3H7 systems the lowest energy structures are pyramidal structures having all four carbon atoms located on the base of the pyramid. The lowest energy structure for the 9-vertex C4B5H9 system is a capped square antiprism. The frameworks of the lowest energy C4B4H8 and C4B6H10 structures resemble those of the isoelectronic experimentally known B8H12 and B10H14 structures. However, an experimentally known S4 adamantane-like 10-vertex structure found in Me4C4B6Et6 based on a tetracapped octahedron lies only ∼7 kcal mol-1 in energy above the lowest energy structure. The lowest energy structures for the 11- to 13-vertex C4Bn-4Hn (n = 11, 12, 13) systems can be derived from an (n + 1)-vertex closo deltahedron by removing a high-degree vertex. At least three of the four carbon atoms are located on edges of the resulting pentagonal or hexagonal open face in the low-energy structures. However, the structures of the experimentally known R4C4B8H8 (R = Me, Et) obtained from the dimerization of R2C2B4H42- differ from these low-energy structures. The Me4C4B8H8 polyhedron has a C4 chain and two tetragonal faces whereas the Et4C4B8H8 polyhedron has a hexagonal face with two C2 units. These structures lie within 2 kcal mol-1 of each other thereby accounting for the fluxional properties of these systems observed by NMR spectroscopy.