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

Introduction

Imbedding transition metal vertices into a borane polyhedron leads to an interesting variety of metallaborane structures first studied by Hawthorne [1], Grimes [2], and their coworkers approximately a half-century ago. Using external cyclopentadienyl (Cp=η⁵-C₅H₅) or pentamethylcyclopentadienyl (Cp*=η⁵-Me₅C₅) groups bonded to the transition metal vertices provides robust Cp–M or Cp*–M bonds to complete the coordination sphere of the transition metal vertices. This leads to dimetallaboranes of the types Cp₂M₂B_n−2H_n−2 and Cp*₂M₂B_n−2H_n−2 exhibiting considerable thermodynamic and kinetic stability.

The basic building blocks of the borane anions B_nH_n²⁻ and isoelectronic carboranes CB_n−1H_n⁻ and C₂B_n−2H_n as well as their substitution products are the most spherical closo deltahedra in which all faces are triangles and the vertices are as nearly equal as possible (Fig. 1) [3], [4] For structures typically encountered experimentally having from 6 to 12 vertices such deltahedra have only degree 4 and 5 vertices except for the 11-vertex closo deltahedron, which is required by topology to have a single degree 6 vertex [5].

Fig. 1:

The most spherical closo deltahedra found in boranes and carboranes showing the vertex degrees with degree 4, 5, and 6 vertices in red, black, and green, respectively.

The electron bookkeeping in polyhedral borane derivatives follows the Wade–Mingos rules [6], [7], [8] which assume that each vertex atom contributes three orbitals to the skeletal bonding. Using this approach a B–H vertex contributes two electrons to the skeletal bonding and a C–H vertex contributes three electrons to the skeletal bonding. Skeletal electron counts obtained by this procedure are conveniently called Wadean skeletal electrons. The most spherical closo deltahedra (Fig. 1) are favored for n-vertex structures containing 2n+2 Wadean skeletal electrons.

The early work on metallaboranes frequently resulted in structures containing CpCo vertices, which are donors of two Wadean skeletal electrons similar to B-H vertices. However, in other cases introduction of transition metal vertices into borane polyhedra, especially those of early transition metals with fewer valence electrons, can lead to deviations from the sphericity of the closo deltahedra. This arises from the preference of transition metals for vertices of larger degrees than carbon and boron vertices. For example isocloso deltahedra [9] providing a degree 6 vertex for the transition metal atom (Fig. 2) are found in metallaboranes having only 2n Wadean skeletal electrons [10], [11], [12], [13].

Fig. 2:

The isocloso deltahedra providing a degree 6 vertex for a transition metal atom. Since the 11-vertex closo deltahedron already has a degree 6 vertex, the closo and isocloso 11-vertex deltahedra are the same.

In order to explore the extent of metallaborane chemistry, particularly metallaboranes containing two or more transition metal vertices, we have undertaken an extensive theoretical study on possible such structures. Our protocol involves the initial screening of a large number of possible isomers using a relatively rapid density functional theory method with the B3LYP functional, a 6-31g(d) double zeta basis set for light atoms, and an SDD basis set for heavy atoms [14], [15], [16], [17]. In many cases we are able to examine hundreds of possible isomers for a given metallaborane stoichiometry to find a relatively small number of low-energy structures. We then refine the relative energies and geometries for this relatively small number of lowest energy isomers using the M06-L function with a larger 6-311G(d,p) triple zeta basis set for light atoms and the same SDD basis set for heavy atoms [18]. In some critical cases we also use the more computationally intensive single point coupled cluster DLPNO-CCSD(T) method [19].

Dimetallaboranes

The first dimetallaboranes prepared by Hawthorne and co-workers [1] included species such as Cp₂Co₂C₂B₆H₈ with the correct 2n+2 skeletal electrons (=22 for n=10) for the 10-vertex closo deltahedron, namely the bicapped square antiprism (Fig. 1) [20]. In the early studies the Hawthorne group also synthesized the iron derivative Cp₂Fe₂C₂B₆H₈ having only 2n skeletal electrons shown by X-ray crystallography to have a central Fe₂C₂B₆ deltahedron later interpreted as the 10-vertex isocloso deltahedron (Fig. 2) with a degree 6 vertex for the iron atom [21].

The experimentally known dirhenaboranes of the type Cp₂Re₂B_n−2H_n−2 are even more hypoelectronic, having only 2n 4 apparent Wadean skeletal electrons [22], [23], [24], [25]. The central Re₂B_n−2 deltahedra (Fig. 3) deviate strongly from sphericity with relatively low curvature at the two approximately polar degree 6 and/or 7 rhenium vertices and relatively high curvature at the remaining n 2 equatorial degree 4 and 5 boron vertices. They thus resemble oblate (flattened) ellipsoids rather than spheres and, for this reason, have been called oblatocloso deltahedra [26].

Fig. 3:

The oblatocloso deltahedra found in the dirhenaboranes Cp₂Re₂B_n−2H_n−2.

The dirhenaboranes Cp₂Re₂B_n−2H_n−2 have been the subject of theoretical studies owing to their unusual structures [27], [28]. Such studies gratifyingly show the experimentally known oblatocloso dirhenaborane structures to be the lowest energy structures (Fig. 4). However, higher energy isomers were found having central Re₂B_n2closo deltahedra with adjacent rhenium atoms and short Re–Re distances suggesting formal multiple bonds. Such structures become the lowest energy structures in related pentalenedirhenaboranes PnRe₂B_n−2H_n−2 (Pn=η⁵,η⁵-pentalene) in which the pentalene ligand uses each of its five-membered rings to bond to a rhenium atom so that the two rhenium atoms are forced to stay in adjacent positions (Fig. 5) [29].

Fig. 4:

Structures of the dirhenaboranes Cp₂Re₂B_n−2H_n−2 and PnRe₂B_n−2H_n−2.

Fig. 5:

Comparison of the bonding of a cyclopentadienyl (Cp) ligand to one rhenium atom with that of a pentalene (Pn) ligand to two rhenium atoms.

The lowest energy PnRe₂B_n−2H_n−2 structures are seen to have central Re₂B_n−2closo deltahedra with short Re≣Re distances of 2.24–2.26 Å very similar to that of the formal Re≣Re quadruple bond length of 2.24 Å in K₂Re₂Cl₈ [30]. Such metal–metal multiple bonds provide a way of drawing otherwise non-bonding metal electrons into the skeletal bonding. This can be clarified by considering the skeletal bonding topology in polyhedral boranes and metallaboranes (Table 1).

Consider first closo boranes having n vertices. Two of the three internal (skeletal) orbitals of each vertex atom are used for the surface bonding leading to n two-center two-electron (2e–2c) bonds distributed on the polyhedral surface as a canonical structure. The actual surface bonding, requiring 2n skeletal electrons for these 2c–2e bonds, can then be considered as a resonance hybrid of all such canonical structures. The remaining internal orbitals on each vertex atom overlap in the center of the deltahedron to form a n-center two-electron bond. This bonding scheme accounts for the 2n+2 Wadean skeletal electrons in closo deltahedral boranes [31], [32], [33].

A related bonding topology for isocloso metallaboranes uses all three internal orbitals from each vertex atom to form n three-center two-electron surface bonds in a canonical structure [34]. Again the actual surface bonding, requiring 2n skeletal electrons for these 3c–2e bonds, can be considered as a resonance hybrid of all such canonical structures. This bonding scheme leaves no orbitals for any type of core bonding so that the isocloso metallaboranes have only 2n Wadean skeletal electrons.

A reasonable bonding topology for the oblatocloso dirhenaboranes deviates from the Wade–Mingos scheme [6], [7], [8] by assuming that the CpRe vertices use five rather than three orbitals for the skeletal bonding (Table 1) [27]. This is reasonable owing to the relatively low surface curvature at the rhenium vertices. Providing five skeletal orbitals makes each CpRe vertex a source of four skeletal electrons rather than the zero skeletal electrons that it would provide if using only three orbitals for skeletal bonding in the Wade–Mingos scheme [6], [7], [8]. Although the n-vertex oblatocloso dirhenaboranes appear to be highly hypoelectronic with only 2n−4 Wadean skeletal electrons, they are best interpreted as 2n+4 actual skeletal electron systems. Forming n surface 3c–2e bonds in the oblatocloso dirhenaboranes similar to those in the isocloso metallaboranes discussed above leaves four “extra” skeletal electrons for an internal Re=Re double bond. The two “extra” orbitals on each rhenium atom beyond the three required for the surface bonding are exactly the orbitals needed for such a Re=Re double bond.

The CpM (and Cp*M) vertices found in many metallaboranes use three metal orbitals for bonding to the Cp ring and another three orbitals for a Wadean skeletal electron bonding scheme [5], [6], [7]. Assuming that the metal atom has the favored 18-electron configuration, this leaves three of the nine orbitals in the sp³d⁵ metal valence orbital manifold with non-bonding lone pairs. Some of these lone pair electrons can be drawn into the skeletal bonding if the valence metal atoms form multiple bonds. Thus increasing the formal bond order of a surface metal–metal single bond to a quadruple bond draws six additional electrons into the skeletal bonding. In this way, Cp₂Re₂B_n−2B_n−2 and PnRe₂B_n−2B_n−2 systems with 2n−4 Wadean skeletal electrons and a surface Re≣Re quadruple bond can have the actual 2n+2 skeletal electrons required for a closo deltahedral structure.

At the time that we published our work on dimetallaboranes with metal–metal multiple bonds we were not aware of any experimental examples of such species. However, we subsequently found that we (as well as the reviewers of our papers) had overlooked the paper by Stone and coworkers in 1983 on the synthesis of an icosahedral dichromadicarbaborane Cp₂Cr₂C₂B₈H₁₀ by the reaction of chromocene with C₂B₉H₁₂ (Fig. 6). [35]. X-ray crystallography of Cp₂Cr₂C₂B₈H₁₀ shows an ultrashort Cr≣Cr distance of 2.272 Å very close to the Cr≣Cr distance of 2.288 Å for the chromium–chromium quadruple bond in anhydrous chromium(II) acetate dimer, Cr₂(OAc)₄ [36]. Note that Cp₂Cr₂C₂B₈H₁₀ is valence isoelectronic with Cp₂Re₂B₁₀H₁₀ exhibiting an albeit high-energy structure with a formal Re≣Re quadruple bond.

Fig. 6:

The experimentally known dichromadicarbaborane suggested to have a formal Cr≣Cr quadruple bond.

Removal of a high-degree vertex from a closo or isocloso deltahedron leads to a so-called nido structure with a pentagonal or hexagonal open face [3], [4]. The binary boranes of the type B_nH_n+4 (n=5, 6, 8, 9 10) exhibit such structures (Fig. 7). Removal of a boron vertex from an oblatocloso dirhenaborane deltahedron can lead analogously to an oblatonido dimetallaborane deltahedron. Such oblatonido deltahedra are found in ditungstaboranes of the general type Cp*₂M₂B_n−2H_n+2 (M=W; n=7, 8: Fig. 8) [37], [38], [39], [40], [41], [42]. The internal formal Re=Re double bond in the oblatocloso dirhenaborane structures Cp₂Re₂B_n−2H_n−2 becomes an external W=W double bond in these ditungstaboranes. This W=W bond has been the subject of a topological study using diverse methods [43]. Removal of two adjacent boron vertices from the hexagonal bipyramidal oblatocloso Cp*₂Re₂B₆H₄Cl₂ structure leads to the oblatoarachno structure Cp*₂Re₂B₄H₈ (Fig. 9) [44].

Fig. 7:

Generation of structures for the binary nido boranes B_nH_n+4 by vertex removal from closo and isocloso deltahedra.

Fig. 8:

Formation of the oblatonido ditungstaboranes Cp*₂W₂B_n−2H_n+2 (n=7, 8) structures by removal of a boron vertex from the oblatocloso dirhenaboranes Cp₂Re₂B_n2H_n−2.

Fig. 9:

Formation of the oblatoarachno dirhenaborane Cp*₂Re₂B_n−2H_n+2 (n=6, 9) structures by removal of two adjacent boron vertices from oblatocloso dirhenaboranes.

Trimetallaboranes

In 1998 Fehlner and co-workers [45] reported the synthesis of the unusual tritungstaborane Cp*₃W₃(μ-H)B₈H₈ by the pyrolysis of Cp*WB₄H₁₁. The central 11-vertex W₃B₈ deltahedron in Cp*₃W₃(μ-H)B₈H₈ deviates considerably from sphericity in having degree 6 and 7 vertices for the tungsten atoms and degree 4 and 5 vertices for the boron atoms (Fig. 10). This structure can be considered as a bonded W₃ triangle imbedded into the 11-vertex W₃B₈ deltahedron. One of the W–W bonds in this W₃ triangle lies on the deltahedral surface whereas the remaining two W–W bonds are located inside the deltahedron. This W₃B₈ deltahedron is very different from the most spherical 11-vertex closo deltahedron (Fig. 1). Much later the molybdenum analog Cp*₃Mo₃(H)B₈H₈ was synthesized by Ghosh and coworkers [46].

Fig. 10:

Comparison of the W₃B₈ deltahedron in Cp*₃W₃(μ-H)B₈H₈ with the most spherical 11-vertex closo deltahedron found in B₁₁H₁₁²⁻.

A complication in the theoretical study of the Cp*₃W₃(μ-H)B₈H₈ and related Cp₃W₃B_n−3H_n−2 systems is the location of the “extra” hydrogen atom. Therefore we first studied the related trirhenaborane Cp₃Re₃B₈H₈ without the extra hydrogen atom [47]. The Cp₃W₃(μ-H)B₈H₈ and Cp₃Re₃B₈H₈ systems are isoelectronic (Table 2) since addition of the extra hydrogen atom as a deltahedral edge bridge brings an additional three electrons into the skeletal bonding. One of these three electrons is provided by the hydrogen atom. The remaining two electrons arise when an otherwise non-bonding metal lone pair is drawn into the skeletal bonding by the hydrogen bridge.

Figure 11 shows the four lowest-energy structures for the trirhenaborane Cp₃Re₃B₈H₈ [47]. The lowest energy structure is seen to have the same M₃B₈ deltahedron as the experimental Cp*₃W₃(μH)B₈H₈ deltahedron consistent with the isoelectronicity of the two structures. The lowest energy structures for the Cp₃Re₃B_n−3H_n−3 systems of other sizes (n=9, 10, 12) are shown in Fig. 12. These structures can all be considered to contain an Re₃ triangle imbedded into an Re₃B_n−3 deltahedron. The interior Re–Re bonds in these Re₃ triangles range from 2.8 to 3.0 Å. The surface Re–Re bonds are significantly shorter at 2.6–2.7 Å because of their partial double bond character combining with the overall delocalized surface bonding of the deltahedron (Table 1).

Fig. 11:

The four lowest-energy Cp₃Re₃B₈H₈ structures.

Fig. 12:

The lowest energy Cp₃Re₃B_n−3H_n−3 (n=9, 10, 12) structures.

The lowest energy structures for the Cp₃W₃(μ-H)B_n−3H_n−3 (n=9–12) were determined using the same density functional theory methods [48]. All of the five lowest energy structures for the experimentally known 11-vertex Cp₃W₃(μH)B₈H₈ system were found to have the same 11-vertex central W₃B₈ deltahedron as the experimental Cp*₃W₃(μH)B₈H₈ structure (Fig. 13). They differ only in the location of the “extra” bridging hydrogen atom. The lengths of the interior W–W bonds were found to be ~3.0 Å, whereas those of the surface bonds were found to be significantly shorter at ~2.7 to ~2.8 Å. This is consistent with the observations on the Cp₃Re₃B_n−3H_n−3 systems as noted above.

Fig. 13:

The five lowest energy Cp₃W₃(H)B₈H₈ structures.

Conclusions

The lowest energy structures for the dirhenaboranes Cp₂Re₂B_n−2H_n−2 correspond to the oblatocloso structures found experimentally by Fehlner, Ghosh, and their coworkers. Such structures have Re=Re distances ranging from 2.69 to 2.94 Å suggested by their skeletal bonding topology and Re=Re Wiberg bond indices to be formal double bonds. Higher energy structures for the dirhenaboranes Cp₂Re₂B_n−2H_n−2 have the same closo deltahedra as found in the corresponding B_nH_n²⁻ anions. In these structures the rhenium atoms are located at adjacent vertices with ultrashort Re≣Re distances of 2.28–2.39 Å similar to the experimental Re≣Re distance of 2.24 Å for the formal quadruple bond in K₂Re₂Cl₈. A formal Cr≣Cr quadruple bond of length 2.272 Å is found experimentally in the icosahedral Cp₂Cr₂C₂B₁₀H₁₀ isoelectronic with Cp₂Re₂B₁₀H₁₀. Replacement of the Cp₂Re₂ unit with a PnRe₂ (Pn=η⁵,η⁵-pentalene) unit forces the rhenium atoms to remain in adjacent positions so that the closo deltahedral structures with surface Re≣Re quadruple bonds become the lowest energy structures.

The lowest energy structures for the trimetallaboranes Cp₃Re₃B_n−3H_n−3 and Cp₃W₃(μ-H)B_n−3H_n−3 related to the experimentally known Cp₃W₃(μ-H)B₈H₈ have a central M₃B_n−3 deltahedron typically containing a bonded M₃ triangle. This central M₃B_n3 deltahedron is not the most spherical closo deltahedron since the metal atoms prefer degree 6 and 7 vertices whereas the boron atoms prefer degree 4 and degree 5 vertices. The metal–metal bonds in the central M₃ triangle are ~3.0 Å if they go through the center of the M₃B_n−3 deltahedron but shorter at ~2.7 to ~2.8 Å if they lie on the surface of the M₃B_n−3 deltahedron.