Spherical Closo Deltahedra with Surface MetalâMetal Multiple

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Spherical Closo Deltahedra with Surface Metal−Metal Multiple Bonding versus Oblate Deltahedra with Internal Metal−Metal Bonding in Dichromadicarbaborane Structures: The Nature of Stone’s Icosahedral Dichromadicarbaborane Szabolcs Jaḱ o,́ † Alexandru Lupan,*,‡ Attila-Zsolt Kun,*,† and R. Bruce King*,§

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†

Department of Chemistry and Chemical Engineering, Hungarian Line of Study, Faculty of Chemistry and Chemical Engineering, and ‡Department of Chemical Engineering, Faculty of Chemistry and Chemical Engineering, Babeş-Bolyai University, Cluj-Napoca 400084, Romania § Department of Chemistry and Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States S Supporting Information *

ABSTRACT: The dichromadicarbaboranes Cp2Cr2C2Bn−4Hn−2 (n = 8−12) related to the icosahedral structure reported in 1983 by Stone and co-workers and formulated by them as Cp2Cr2C2B8H10 have been investigated using density functional theory. In most cases, the lowest-energy structures are flattened oblatocloso structures with degree 6 and 7 chromium vertices similar to the lowest-energy and experimental structures of the isoelectronic dirhenaboranes Cp2Re2Bn−2Hn−2. However, most isomeric spherical closo deltahedral structures with surface Cr≣Cr quadruple bonds as well as isocloso structures with surface metal−metal CrCr triple bonds lie at accessible energies, typically lower than those in the corresponding dirhenaborane systems. However, for the 11-vertex Cp2Cr2C2B7H9 system, the most spherical closo/isocloso deltahedral structure with a degree 6 metal vertex and degree 4 carbon vertices as well as a surface MM triple bond lies energetically below the lowest-energy oblatocloso structure. Calculations of the Cr−Cr distances in an icosahedral Cp2Cr2C2B8H10 structure and in a dihydrogenated icosahedral Cp2Cr2(μ-H)2C2B8H10 structure suggest the latter structure for “Cp2Cr2C2B8H10” reported by Stone and coworkers.

1. INTRODUCTION The metallaboranes initially synthesized by Callahan and Hawthorne1 include the cobaltadicarbaboranes CpCoC2B9H11 (Cp = η5-cyclopentadienyl) and [Co(C2B9H11)2]− as well as their substitution products. Because Cp− and C2B9H112− are monoanionic and dianionic species, respectively, the central cobalt atom in these diamagnetic metallaboranes exhibit the d6 formal cobalt(III) oxidation state analogous to the cobalt atom in the long-known extensive series of Wernerian cobalt(III) ammines. Alternatively, the cobalt atoms in such cobaltadicarbaboranes can be considered to have the favored 18electron configuration.2−4 The other first-row transition metal known for more than a century to form stable ammines is chromium, also in the 3+ formal oxidation state. However, chromium(III) is a d3 system and is thus paramagnetic with three unpaired electrons. The chemistry of chromaboranes, analogous to the cobaltaboranes mentioned above, is considerably more limited. However, the icosahedral chromadicarbaboranes CpCrC2B9H11 and [Cr(C2B9H11)2]− were synthesized by Hawthorne and coworkers,5,6 and the latter was structurally characterized crystallographically (Figure 1).7 Recent density functional theory (DFT) studies8 on the complete series of chromadi© XXXX American Chemical Society

carbaboranes CpCrC2Bn−3Hn−1 (n = 8−12) show the lowestenergy structures to be the most spherical closo deltahedral structures with three unpaired electrons in accordance with the preferred spin state of the central chromium(III) atom. Dimetallaboranes have also been synthesized with two metal vertices in an icosahedral structure. Originally, a number of isomers of the dicobaltadicarbaboranes Cp2Co2C2B8H10 were synthesized including an isomer with adjacent cobalt atoms.1 In addition, a dichromadicarbaborane was synthesized by Stone and co-workers9 from the direct reaction of chromocene, Cp2Cr, with nido-5,6-C2B8H12. This species was assigned the formula Cp2Cr2C2B8H10 on the basis of an X-ray crystallography study indicating a central Cr2C2B8 icosahedron with adjacent chromium atoms (Figure 1). However, our theoretical study reported in this paper suggests that the species synthesized by Stone and co-workers is actually Cp2Cr2(μH)2C2B8H10 with two “extra” hydrogen atoms bridging the Cr−Cr bond. The nature of the Cr−Cr interaction in a presumed icosahedral structure Cp2Cr2C2B8H10 without any “extra” Received: December 13, 2018

A

DOI: 10.1021/acs.inorgchem.8b03476 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 1. Experimentally known icosahedral chromadicarbaborane species including the structure suggested by Stone and co-workers for their presumed “Cp2Cr2C2B8H10.”.

Table 1. Skeletal Electron Bookkeeping for a 12-Vertex Icosahedral Dichromadicarbaborane Cp2Cr2C2B8H10 without “Extra” Bridging Hydrogen Atoms 2 CpCr vertices 2 CH vertices 8 BH vertices total available skeletal electrons 1 12-center, 2-electron core bond 12 2-center, 2-electron surface bonds 2π + δ components of the Cr≣Cr quadruple bond skeletal electrons required

Source of Skeletal Electrons 2×5= 2×3= 8×2= Use of Skeletal Electrons 1×2= 12 × 2 = 3×2= = (2 × 12) + 8 =

10 electrons 6 electrons 16 electrons 32 electrons 2 electrons 24 electrons 6 electrons 32 electrons

three additional internal orbitals per chromium atom so that each chromium atom in Cp2Cr2C2B8H10 uses all nine orbitals of its sp3d5 manifold for bonding, leaving no external lone pairs. Thus, three of the nine chromium orbitals are used for σ + 2π bonding to the Cp ring, three more orbitals for the skeletal bonding of the Cr2C2B8 icosahedron, and the final three orbitals for the additional 2π + δ components of the Cr≣Cr quadruple bond. For such systems with surface Cr≣Cr quadruple bonds, each CpCr vertex is a donor of five skeletal electrons after one of the six chromium valence electrons was assigned to reduce neutral Cp to the Cp− anion. This leads to the skeletal electron bookkeeping summarized in Table 1 for icosahedral Cp2Cr2C2B8H10 based on the Wade−Mingos rules11−13 and the graph-theory-based model for skeletal bonding in borane deltahedra14 supplemented by the additional electrons required for the 2π + δ components of the Cr≣Cr quadruple bond. A similar electron-bookkeeping scheme can be used to provide dichromadicarbaboranes Cp2Cr2C2Bn−4Hn−2 of other sizes with 2n + 8 skeletal electrons. This corresponds to the 2n + 2 Wadean skeletal electrons for the most spherical closo borane deltahedra (Figure 2) with an additional 6 electrons for the 2π + δ components of the Cr≣Cr quadruple bond. The most spherical closo deltahedra having 6 to 12 vertices except for the 11-vertex system have exclusively degree 4 and 5 vertices. For such an n-vertex system, the 2n + 2 Wadean skeletal electrons include 2 electrons for a multicenter core bond, in addition to 2n electrons for surface bonding.14 For the 9- and 10-vertex systems, alternative metallaborane deltahedra with a degree 6 vertex for a metal atom are also found (Figure 2).15−18 Such deltahedra are called either isocloso19 or hypercloso20−22 deltahedra; the former terminology is used in this paper. Such n-vertex isocloso metallaboranes have only 2n

bridging hydrogen atoms is of interest. In the monometallic icosahedral structure CpCrC2B9H11, the chromium atom is formally chromium(III) with three unpaired electrons and thus a quartet spin state. Introducing two adjacent chromium atoms in a Cp2Cr2C2B8H10 structure provides the opportunity for Cr−Cr multiple bonding through pairing of the unpaired electrons on the individual chromium atoms. Complete pairing of the three unpaired electrons on each chromium atom in an icosahedral Cp2Cr2C2B8H10 structure adds three components to the Cr−Cr surface bonding resulting in a formal Cr≣Cr quadruple bond related to that in the long-known chromium(II) acetate dimer Cr2(O2CMe)4. In this connection, the experimental Cr−Cr distance of 2.272 Å in the species reported as Cp2Cr2C2B8H10 is close to that in anhydrous Cr2(O2CMe)4 of 2.288 Å.10 Also, note that the formal oxidation state of the chromium atoms in a Cp2Cr2C2B8H10 structure without extra bridging hydrogen atoms is 2+, like that in Cr2(O2CMe)4 considering the Cp− and C2B8H102− ligands as monoanions and dianions, respectively, similar to assigning the 3+ oxidation state to the chromium atom in CpCrC2B9H11. Complete pairing of the chromium electrons in a Cp2Cr2C2B8H10 structure without extra bridging hydrogen atoms to give each chromium atom the favored 18-electron configuration makes each CpCr vertex a −1 electron donor (i.e., a single-electron acceptor) in the Wade−Mingos electroncounting scheme11−13 assuming that each vertex atom in a borane cluster uses three orbitals to bind to the polyhedral skeleton. In this sense, Cp2Cr2C2B8H10 is a 20 Wadean skeletal electron system, i.e., 2n − 4 skeletal electrons for a 12-vertex system (n = 12). Such systems are hypoelectronic relative to the n-vertex most spherical deltahedral borane structures with 2n + 2 Wadean skeletal electrons. However, the formation of a surface Cr≣Cr quadruple bond in Cp2Cr2C2B8H10 requires B


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Inorganic Chemistry

Figure 2. Structures of the most spherical closo borane deltahedra, the isocloso metallaborane deltahedra, and the flattened oblatocloso deltahedra for 8 to 12-vertex structures.

Wadean skeletal electrons and thus can exhibit a skeletal bonding topology involving only surface bonding.23 The 11vertex closo deltahedron necessarily has a degree 6 vertex and thus can function either as a closo deltahedron with 2 × 11 + 2 = 24 skeletal electrons or as an isocloso deltahedron with only 2 × 11 = 22 skeletal electrons. A 12-vertex equivalent of an isocloso deltahedron necessarily has two degree 6 vertices (Figure 2). The 8-vertex equivalent of an isocloso deltahedron would be the capped pentagonal bipyramid, but this has a degree 3 vertex. The presence of a degree 3 vertex can be avoided in the hexagonal bipyramid with two degree 6 vertices (Figure 2). Consider an n-vertex dichromadicarborane Cp2Cr2C2Bn−4Hn−2 with an isocloso deltahedral structure. Because only 2n skeletal electrons are required, a formal CrCr triple bond rather than a Cr≣Cr quadruple bond is sufficient to provide the required skeletal electrons. This is illustrated in Table 2, summarizing the skeletal electron bookkeeping for the 12-vertex isocloso Cp2Cr2C2B6H8 structure noting that each CpCr vertex forming a CrCr triple bond with an adjacent chromium atom is a donor of three skeletal electrons leaving an external lone pair. The dichromadicarbaboranes Cp2Cr2C2Bn−4Hn−2 are valence isoelectronic with a series of dirhenaboranes Cp*2Re2Bn−2Hn−2 (Cp* = η5-Me5C5; n = 8−12) synthesized by Fehlner, Ghosh, and co-workers.24 Thus, adding two skeletal electrons upon replacement of two group 6 chromium atoms with two group 7 rhenium atoms is balanced by removing two skeletal electrons

Table 2. Skeletal Electron Bookkeeping for a 12-Vertex Isocloso Deltahedral Dichromadicarbaborane Cp2Cr2C2B8H10 Source of Skeletal Electrons 2 CpCr vertices 2×3= 2 CH vertices 2×3= 8 BH vertices 8×2= total available skeletal electrons Use of Skeletal Electrons 12 3-center, 2-electron surface bonds 12 × 2 = 2π components of the CrCr triple 2×2= bond skeletal electrons required = (2 × 12) + 4 =

6 electrons 6 electrons 16 electrons 28 electrons 24 electrons 4 electrons 28 electrons

upon replacement of two carbon vertices with boron vertices. The experimental structures for the dirhenaboranes Cp*2Re2Bn−2Hn−2 are found by X-ray crystallography to be flattened oblatocloso deltahedra (Figure 2).25−27 Such deltahedra have degree 6 and/or 7 rhenium vertices located at approximately antipodal (quasipolar) points of low curvature on the underlying oblate ellipsoid and degree 4 and 5 boron vertices located at points of relatively high curvature. The flattening of these oblate ellipsoidal deltahedra brings the antipodal rhenium atoms within bonding distance through the center of the deltahedron. Skeletal electron bookkeeping in these dirhenaboranes with a central n-vertex oblatocloso deltahedron suggests canonical structures having n 3-center, C


Article

Inorganic Chemistry Table 3. 17 Optimized Cp2Cr2C2B8H10 Structures within 12 kcal/mol of the Lowest-Energy Structures vertex degrees

Cr−Cr distance

structure

ΔE, kcal/mol

v3

v4

v5

v6

v7

Å

WBI

B8C2Cr2-1* B8C2Cr2-2* B8C2Cr2-3* B8C2Cr2-4* B8C2Cr2-5* B8C2Cr2-6* B8C2Cr2-7 B8C2Cr2-8 B8C2Cr2-9 B8C2Cr2-10 B8C2Cr2-11 B8C2Cr2-12 B8C2Cr2-13 B8C2Cr2-14 B8C2Cr2-15 B8C2Cr2-16 B8C2Cr2-17

0.0 1.8 2.1 3.6 3.9 4.6 5.1 5.6 6.3 6.4 6.5 6.6 9.0 10.4 10.7 11.5 11.8

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 0 3 2 0 0 0 2 3 0 2 2 0 0 0 0 3

8 12 7 8 12 12 12 8 7 12 8 8 12 12 12 12 7

2 0 1 2 0 0 0 2 1 0 2 2 0 0 0 0 1

0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1

2.114 1.884 2.803 2.112 1.892 1.891 1.892 2.103 2.818 1.892 2.099 2.097 1.899 1.894 1.895 1.895 2.781

1.62 2.60 0.55 1.66 2.58 2.58 2.59 1.70 0.69 2.57 1.71 1.70 2.55 2.57 2.58 2.58 0.48

C−C, Å (degrees)a 3.29 2.97 2.79 3.49 3.21 2.75 2.74 3.49 3.65 2.65 2.64 2.77 2.63 2.58 2.58 2.62 2.48

(44) (m) (54) (54) (p) (m) (m) (54) (44) (m) (54) (54) (m) (m) (m) (m) (55)

M−C edges

comments

4 4 3 3 2 3 3 2 3 2 2 3 1 1 1 0 2

2v6 deltahedron icosahedron oblatocloso-7,6 2v6 deltahedron icosahedron icosahedron icosahedron 2v6 deltahedron oblatocloso-7,6 icosahedron 2v6 deltahedron 2v6 deltahedron icosahedron icosahedron icosahedron icosahedron oblatocloso-7,6

a

For the nonicosahedral structures, the degrees of carbon vertices are given in parentheses. For the icosahedral structures, the designations m and p refer to nonadjacent nonantipodal (meta) and antipodal (para) positions, respectively.

isocloso derivatives. However, our theoretical studies reported in this paper focusing on the comparison of calculated Cr−Cr distances with the experimental values suggest that the presumed “Cp2Cr2C2B8H10” is really Cp2Cr2(μ-H)2C2B8H10 with two “extra” hydrogen atoms bridging the Cr−Cr bond, which then becomes a formal triple bond. Thus, experimental data, at least, appear to suggest divergent behavior for the rhenium and chromium systems. In order to explore further this structural dichotomy, we have now used DFT methods to investigate the complete series of dichromadicarbaboranes Cp2Cr2C2Bn−4Hn−2 (n = 8−12). We now report our results in this paper.

2-electron surface bonds and a ReRe double bond through the center of the deltahedron.28 A DFT study on the dirhenaboranes Cp*2Re2Bn−2Hn−2 (n = 8−12) gratifyingly confirmed the experimentally observed oblatocloso structures (Figure 2).29 However, significantly higher-energy isomers with adjacent rhenium vertices in central Re2Bn−2 closo deltahedra (Figure 2) similar to the icosahedral “Cp2Cr2C2B8H10” structure proposed by Stone and co-workers for their Cp2Cr/nido-C2B8H12 reaction product were found. All of these structures have unusually short Re≣Re distances, suggesting formal quadruple bonds similar to the suggested Cr≣Cr quadruple bond in Cp 2Cr2 C 2B 8 H10 . Furthermore, related closo dirhenaborane structures were predicted to be the lowest-energy structures in related pentalene dirhenaboranes PnRe2Bn−2Hn−2 (Pn = η5,η5pentalene; n = 8−12), in which two CpRe units are replaced by a single PnRe2 unit, forcing the rhenium atoms to occupy adjacent polyhedral vertices.30 In summary, there appears to be the following two distinctly different structural motifs for n-vertex dimetallaboranes with 2n − 4 apparent Wadean skeletal electrons for which experimental examples are known: (1) Flattened oblatocloso deltahedral structures with degree 6 and/or 7 antipodal metal vertices at low-curvature points on the underlying oblate ellipsoidal surface such as those found experimentally in the rhenaboranes Cp*2Re2Bn−2Hn−2 (n = 8− 12)25−27 corresponding to the lowest-energy structures predicted theoretically.29 The metal−metal interactions in these structures can be considered to be formal double bonds passing through the deltahedral interior. (2) Most spherical closo deltahedral structures or isocloso deltahedral structures with adjacent metal vertices and unusually short metal−metal bonds. Such a structure was originally proposed for the experimentally9 known dichromadicarbaborane formulated as “Cp2Cr2C2B8H10” on the basis of X-ray crystallography showing a central Cr2C2B8 icosahedron with adjacent chromium atoms and a short Cr−Cr distance. Metal−metal bonds in deltahedral structures can be formal quadruple bonds for the closo derivatives or triple bonds for the

2. THEORETICAL METHODS The initial Cp2Cr2C2Bn−4Hn−2 structures were constructed by the systematic substitution of two boron vertices in BnHn2− with chromium atoms in various n-vertex polyhedral geometries, followed by the further substitution of two of the remaining BH vertices by CH vertices. Thus, 484 structures of the 8-vertex clusters Cp2Cr2C2B4H6, 467 structures of the 9-vertex clusters Cp2Cr2C2B5H7, 1112 structures of the 10-vertex clusters Cp2Cr2C2B6H8, 1142 structures of the 11vertex clusters Cp2Cr2C2B7H9, and 438 structures of the 12-vertex Cp 2 Cr2 C 2 B 5 H 7 clusters were chosen as starting points for optimizations (see the Supporting Information). Full geometry optimizations were carried out on the Cp2Cr2C2Bn−4Hn−2 systems (n = 8−12) at the B3LYP/6-31G(d) level of theory. The lowest-energy structures were then reoptimized at a higher level of theory, namely, PBE0/6-311G(d,p), and these are the structures presented in the manuscript.31 The nature of the stationary points after optimization was checked by calculations of the harmonic vibrational frequencies. If significant imaginary frequencies were found, optimization was continued by following the normal modes corresponding to the imaginary frequencies to ensure that genuine minima were obtained. All calculations were performed using the Gaussian 09 package32 with default settings for the self-consistent-field cycles and geometry optimization. The Wiberg bond indices (WBIs) for the Cr−Cr interactions in the optimized Cp2Cr2C2Bn−4Hn−2 structures were obtained from natural bond order analysis automatically provided in the Gaussian output.33 All of the structures reported in this paper have appreciable highest occupied molecular orbital (HOMO)− D


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Inorganic Chemistry

Figure 3. Six lowest-energy Cp2Cr2C2B8H10 structures. (starred in Table 3). lowest unoccupied molecular orbital (LUMO) gaps of 3.0−4.2 eV (see Table S6). The Cp2Cr2C2Bn−4Hn−2(n = 8−12) structures are numbered as B(n−4)C2Cr2-x, where n is the total number of polyhedral vertices and x is the relative order of the structure on the energy scale [PBE0/ 6-311G(d,p) including zero-point corrections]. The lowest-energy optimized structures discussed in this paper are depicted in Figures 3−8. Only the lowest-energy and thus potentially chemically significant structures are considered in detail in this paper. More comprehensive lists of structures, including higher-energy structures, are given in the Supporting Information.

structures (Table 2). Finally, the oblatocloso structures B8C2Cr2-3 and B8C2Cr2-9 with nonadjacent surface chromium atoms have CrCr distances of ∼2.8 Å through the interior of the deltahedron, with significantly lower WBIs of ∼0.6. These can be interpreted as formal double bonds similar to the ReRe double bonds suggested for the skeletal bonding topology in the likewise oblatocloso dirhenaboranes Cp2Re2B10H10.28 The three lowest-energy Cp 2 Cr 2 C2 B 8 H 10 structures, B8C2Cr2-1, B8C2Cr2-2, and B8C2Cr2-3, lying within ∼2 kcal/mol (Figure 3), represent these three different 12-vertex deltahedra, suggesting that there is no inherent energy preference between the closo icosahedron, the isocloso 12vertex deltahedron, and the oblatocloso 12-vertex deltahedron. Structures with the two carbon atoms at nonadjacent degree 4 vertices appear to be energetically preferred. The experimental “Cp2Cr2C2B8H10” structure determined by X-ray crystallography9 has a central Cr2C2B8 icosahedron with a Cr≣Cr distance of 2.272 Å similar to the experimental Cr≣Cr quadruple bond length of 2.288 Å in anhydrous chromium(II) acetate, Cr2(O2CMe)4.10 Before the theoretical studies reported in this paper, it therefore seemed reasonable to regard the Cr≣Cr interaction in Cp2Cr2C2B8H10 as a formal quadruple bond, consistent with the electron-bookkeeping scheme in Table 1. The Cp2Cr2C2B8H10 structure B8C2Cr2-2, lying only 1.8 kcal/mol above the lowest-energy structure B8C2Cr2-1 (Figure 3 and Table 1), has the same arrangement of chromium, carbon, and boron atoms in the central Cr2C2B8 icosahedron as the experimental structure. However, the predicted Cr≣Cr distance of 1.884 Å in B8C2Cr2-2 is very different from the experimental 2.272 Å distance by a large discrepancy of ∼0.4 Å. Furthermore, the experimental distance of 2.272 Å in the reported Cp2Cr2C2B8H10 structure is much closer to the calculated CrCr distance of ∼2.11 Å calculated for the isocloso Cp2Cr2C2B8H10 structures, including the

3. RESULTS AND DISCUSSION 3.1. 12-Vertex Cp2Cr2C2B8H10 Structures. The potential energy surface of the Cp2Cr2C2B8H10 system is relatively complicated, having 17 structures within 12 kcal/mol of the global minimum B8C2Cr2-1 (Table 3 and Figure 3). This complexity arises from three different types of vertex atoms, each appearing at least twice in the underlying deltahedra. Representative closo, isocloso, and oblatocloso structures are included among the six lowest-energy structures falling within 5 kcal/mol (Figure 3). These three structure types have distinctly different Cr−Cr formal bond orders, reflecting the electron-bookkeeping schemes in Tables 1 and 2. Thus, the icosahedral derivatives such as B8C2Cr2-2, B8C2Cr2-5, B8C2Cr2-6, B8C2Cr2-7, and B8C2Cr2-11 exhibit Cr≣Cr distances of 1.89 Å corresponding to a WBI of ∼2.6. These may be interpreted as formal quadruple bonds in accordance with the skeletal bonding topology summarized in Table 1. The global minimum B8C2Cr2-1 and the higher-energy structures B8C2Cr2-4, B8C2Cr2-8, B8C2Cr2-11, and B8C2Cr2-12 have 2v6 deltahedral structures with two degree 6 vertices corresponding to the 12-vertex isocloso deltahedral topology (Figure 2). The CrCr distances of ∼2.11 Å coupled with WBIs of ∼1.7 correspond to the formal triple bonds required by the skeletal bonding topology for isocloso E


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Inorganic Chemistry

Figure 4. Comparison of the optimized structure of the dihydride Cp2Cr2(μ-H)2C2B8H10 with the experimental Cp*2Cr2(CO)4 structure.

Figure 5. Six lowest-energy Cp2Cr2C2B4H6 structures.

Table 4. Six Optimized Cp2Cr2C2B4H6 Structures within 28 kcal/mol of the Lowest-Energy Structures vertex degrees

Cr−Cr distance

structure

ΔE, kcal/mol

v3

v4

v5

v6

Å

WBI

B4C2Cr2-1 B4C2Cr2-2 B4C2Cr2-3 B4C2Cr2-4 B4C2Cr2-5 B4C2Cr2-6

0.0 2.1 6.9 23.5 25.6 28.1

0 0 0 2 2 0

6 6 6 2 2 4

0 0 0 2 2 4

2 2 2 2 2 0

2.532 2.500 2.529 2.401 2.366 2.015

0.86 0.80 0.75 0.68 0.65 1.84

C−C, Å (degrees) 2.60 3.11 1.45 2.78 2.80 2.71

(44) (44) (44) (43) (33) (44)

comments hexagonal bipyramid hexagonal bipyramid hexagonal bipyramid bicapped octahedron bicapped octahedron bisdisphenoid

Furthermore, the nido-C2B8H12 reagent used to synthesize the reported Cp2Cr2C2B8H10 by reaction with Cp2Cr provides a possible source of “extra” hydrogen atoms to hydrogenate the Cr≣Cr quadruple bond in an icosahedral structure. In view of these considerations, we used similar DFT methods to optimize an icosahedral Cp2Cr2(μ-H)2C2B8H10 structure with a central Cr2C2B8 icosahedron similar to the experimental structure (Figure 4). The CrCr distance was

lowest-energy structure B8C2Cr2-1. Because of this discrepancy, we considered an alternative Cp2Cr2(μ-H)2C2B8H10 structure in which the Cr≣Cr quadruple bond in the icosahedral structure B8C2Cr2-2 has been hydrogenated to a formal triple bond, thereby creating a central Cr2(μ-H)2 unit. Two extra hydrogen atoms in the experimental structure could have easily been missed considering the X-ray crystallography state of the art in 1983 when “Cp2Cr2C2B8H10” was reported.9 F


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Inorganic Chemistry

Figure 6. Eight lowest-energy Cp2Cr2C2B5H7 structures.

with a ΔH value of −4.1 kcal/mol and a ΔG value of 4.4 kcal/ mol. 3.2. Cp2Cr2C2Bn−4Hn−2 Structures Having Fewer Than 12 Vertices. The three lowest-energy structures of the 8vertex system Cp2Cr2C2B4H6 have a central Cr2C2B4 hexagonal bipyramid with the chromium atoms at the axial (polar) degree 6 vertices and CrCr distances of ∼2.5 Å with WBIs of ∼0.8 (Figure 5 and Table 4). These structures can be considered as oblatocloso structures with CrCr double bonds passing through the center of the hexagonal bipyramid. The lowest energy of these hexagonal-bipyramidal Cp2Cr2C2B4H6 structures, namely, B4C2Cr2-1, has the two carbon vertices located in the meta (nonadjacent nonantipodal) positions of the equatorial hexagon. Structure B4C2Cr2-2, lying 2.1 kcal/mol

found to be 2.219 Å in this structure, which is reasonably close to the experimental CrCr distance of 2.272 Å in the species reported as Cp2Cr2C2B8H10. On the basis of these calculations, we believe that the species reported by Stone and co-workers9 as “Cp2Cr2C2B8H10” actually has two “extra” hydrogen atoms bridging the Cr−Cr bond, leading instead to a Cp2Cr2(μH)2C2B8H10 structure. We also note that the experimental CrCr distance in Stone’s “Cp2Cr2C2B8H10” of 2.272 Å is very close to the 2.280 Å CrCr distance in Cp*2Cr2(CO)4 (Figure 4).34 We predict hydrogenation of the icosahedral structure B8C2Cr2-2 with the same arrangement of vertex atoms as the experimental structure to give the Cp2Cr2(μH)2C2B8H10 structure in Figure 4 to be close to thermoneutral G


Article

Inorganic Chemistry Table 5. Eight Optimized Cp2Cr2C2B5H7 Structures within 17 kcal/mol of the Lowest-Energy Structures vertex degrees

Cr−Cr distance

structure

ΔE, kcal/mol

v3

v4

v5

v6

Å

WBI

B5C2Cr2-1 B5C2Cr2-2 B5C2Cr2-3 B5C2Cr2-4 B5C2Cr2-5 B5C2Cr2-6 B5C2Cr2-7 B5C2Cr2-8

0.0 3.5 6.8 6.9 10.3 10.6 10.7 15.6

0 0 0 0 0 0 0 0

5 5 5 5 5 5 3 3

2 2 2 2 2 2 6 6

2 2 2 2 2 2 0 0

2.654 2.619 2.659 2.682 2.662 2.635 1.973 1.993

0.64 0.56 0.65 0.77 0.72 0.56 2.16 2.04

C−C, Å (degrees) 2.79 1.54 2.99 2.61 2.73 1.54 2.52 2.67

(44) (44) (54) (44) (54) (54) (44) (44)

comments oblatocloso-6,6 oblatocloso-6,6 oblatocloso-6,6 oblatocloso-6,6 oblatocloso-6,6 oblatocloso-6,6 tricapped trigonal prism tricapped trigonal prism

Figure 7. Eight lowest-energy Cp2Cr2C2B6H8 structures.

in energy above B4C2Cr2-1, has its two carbon vertices located in the para (antipodal) positions of the equatorial hexagon, whereas the higher-energy hexagonal bipyramidal structure B4C2Cr2-3, lying 6.9 kcal/mol in energy above

B4C2Cr2-1, has its two carbon vertices located in the ortho (adjacent) positions of the equatorial hexagon. The C−C edge length in B4C2Cr2-3 of 1.452 Å is close to that expected for a formal single bond. H


Article

Inorganic Chemistry Table 6. Eight Optimized Cp2Cr2C2B6H8 Structures within 17 kcal/mol of the Lowest-Energy Structures vertex degrees

Cr−Cr distance

structure

ΔE, kcal/mol

v4

v5

v6

v7

Å

WBI

B6C2Cr2-1 B6C2Cr2-2 B6C2Cr2-3 B6C2Cr2-4 B6C2Cr2-5 B6C2Cr2-6 B6C2Cr2-7 B6C2Cr2-8

0.0 8.7 9.0 9.5 11.3 14.0 14.7 15.0

4 4 5 2 3 5 4 4

4 4 3 8 6 3 4 4

2 2 1 0 1 1 2 2

0 0 1 0 0 1 0 0

2.767 2.771 2.617 1.935 2.149 2.627 2.789 2.802

0.54 0.55 0.49 2.41 1.39 0.58 0.68 0.64

C−C, Å (degrees) 2.58 2.73 2.47 3.34 2.71 3.50 3.30 2.79

(44) (54) (54) (44) (44) (44) (44) (44)

comments oblatocloso-6,6 oblatocloso-6,6 oblatocloso-7,6 bicappped tetragonal antiprism 10 vertex isocloso oblatocloso-7,6 oblatocloso-6,6 oblatocloso-6,6

likewise tricapped trigonal prism Cp2Cr2C2B5H7 structure B5C2Cr2-8, lying 15.6 kcal/mol in energy above B5C2Cr2-1, both carbon atoms are located at two of the degree 4 caps of the underlying Cr2B4 trigonal prism. The chromium atoms form a Cr≣Cr bond corresponding to an edge shared by a rectangular and a triangular face of the underlying trigonal prism. The Cr≣Cr distances of ∼1.94 Å coupled with WBIs of ∼2.1 suggest the formal quadruple bond required by a bonding topology for the closo 9-vertex deltahedron analogous to that in Table 1 for the icosahedron. Seven of the eight lowest-energy structures of the 10-vertex Cp2Cr2C2B6H8 system have a central oblatocloso Cr2C2B6 framework (Figure 7 and Table 6). However, two types of 10-vertex oblatocloso deltahedra are found. In the lowest-energy Cp2Cr2C2B6H8 structure B6C2Cr2-1, as well as the higherenergy structures B6C2Cr2-2, B6C2Cr2-7, and B6C2Cr2-8, lying 8.7, 14.7, and 15.0 kcal/mol in energy above B6C2Cr2-1, the central oblatocloso deltahedron, designated as oblatocloso6,6 in Table 6, has two degree 6 vertices for the chromium atoms as well as four degree 4 and four degree 5 vertices for the boron and carbon atoms. However, in the Cp2Cr2C2B6H8 structures B6C2Cr2-3 and B6C2Cr2-6, lying 9.0 and 14.0 kcal/mol in energy above B6C2Cr2-1, the central oblatocloso deltahedron, designated as oblatecloso-7,6 in Table 6, has one chromium atom located at the degree 7 vertex and the other chromium atom located at the degree 6 vertex with five degree 4 vertices and three degree 5 vertices for the boron and carbon atoms. For comparison, the experimental Cp*2Re2B8H8 structure is of the oblatocloso-6,6 type.25−27 The CrCr distance of ∼2.78 Å in the four oblatocloso-6,6 Cp2Cr2C2B6H8 structures is significantly longer than the CrCr distance of ∼2.62 Å in the oblatocloso-7,6 Cp2Cr2C2B6H8 structures. However, the CrCr WBIs are fairly similar in both types of oblatocloso Cp2Cr2C2B6H8 structures, ranging from 0.49 to 0.68, with no clear separation between the oblatocloso-6,6 and oblatocloso-7,6 structures. Examples of both closo and isocloso structures are also found among the eight lowest-energy Cp2Cr2C2B6H8 structures. The structure B6C2Cr2-4, lying 9.5 kcal/mol in energy above B6C2Cr2-1, has a central bicapped tetragonal antiprism, the 10-vertex closo deltahedron (Figure 7 and Table 6). The carbon atoms in B6C2Cr2-4 are located at the two degree 4 vertices. The short Cr≣Cr distance of 1.935 Å coupled with a WBI of 2.41 is consistent with the formal quadruple bond required by a skeletal bonding topology analogous to that in Table 1 for Cp2Cr2C2B8H10. The structure B6C2Cr2-5, lying 11.3 kcal/mol in energy above B6C2Cr2-1, has a central 10vertex isocloso deltahedron (Figure 2). The carbon atoms in B6C2Cr2-5 are located at two of the three degree 4 vertices, and the chromium atoms are located at the unique degree 6

Hexagonal-bipyramidal structures for the 8-vertex system Cp2Cr2C2B4H6 are obviously very favorable because the lowest-energy structure with a different central Cr2C2B4 polyhedron is the bicapped octahedral structure B4C2Cr2-4, lying 23.5 kcal/mol in energy above B4C2Cr2-1 (Figure 5 and Table 4). Structure B4C2Cr2-5, lying only slightly higher in energy than B4C2Cr2-4 at 25.6 kcal/mol above B4C2Cr2-1, also has a central Cr2C2B4 bicapped octahedron. Both of these bicapped octahedral Cp2Cr2C2B4H6 structures have adjacent chromium atoms located at degree 5 vertices on one of the capped faces with a CrCr distance of ∼2.4 Å corresponding to a WBI of ∼0.7 and interpreted as a formal double bond. Considering the BH, CH, and CpCr vertices as donors of 2, 1, and −1 skeletal electrons, respectively, and allowing for an extra 2 skeletal electrons from the CrCr surface double bond provide 14 skeletal electrons for these bicapped octahedral Cp2Cr2C2B4H6 systems. This corresponds to the 2n + 2 = 14 (for n = 6) skeletal electrons for the central octahedron in B4C2Cr2-4 and B4C2Cr2-5. Structure B4C2Cr2-4 has a carbon atom at one of the degree 3 capping vertices and the other carbon atom at a nonadjacent degree 4 vertex adjacent to one of the chromium atoms. In B4C2Cr2-5, both degree 3 capping vertices are occupied by the carbon atoms. The 8-vertex closo deltahedron is the bisdisphenoid with four degree 5 and four degree 4 vertices (Figure 2). The lowestenergy bisdisphenoidal structure B4C2Cr2-6 lies 28.1 kcal/ mol in energy above B4C2Cr2-1 with the carbon atoms at nonadjacent degree 4 vertices and the chromium atoms at a pair of degree 5 vertices. The short Cr≣Cr distance of 2.015 Å with a WBI of 1.84 can be interpreted as a formal quadruple bond. This leads to an electron-bookkeeping scheme for this bisdisphenoidal structure similar to that for the icosahedral Cp2Cr2C2B8H10 system given in Table 1. The six lowest-energy 9-vertex Cp2Cr2C2B5H7 structures have a central oblatocloso Cr2C2B5 deltahedron with the chromium atoms located at the two degree 6 vertices (Figure 6 and Table 5). The CrCr distances ranging from 2.62 to 2.68 Å, with WBIs ranging from 0.56 to 0.77, can be interpreted as formal double bonds through the deltahedron similar to other oblatocloso structures. The two lowest-energy structures, namely, B5C2Cr2-1 and B5C2Cr2-2, and the higher-energy structure B5C2Cr2-4 have the carbon atoms located at degree 4 vertices. Among these three structures, the carbon atoms in B5C2Cr2-2 are located at adjacent vertices, with a 1.54 Å C− C distance suggesting a single bond. The 9-vertex closo deltahedron is the tricapped trigonal prism (Figure 2). The lowest-energy Cp2Cr2C2B5H7 structure with a central Cr2C2B5 tricapped trigonal prism is B5C2Cr2-7, lying 10.7 kcal/mol in energy above B5C2Cr2-1 (Figure 6 and Table 5). In B5C2Cr2-7 as well as the somewhat higher I


Article

Inorganic Chemistry Table 7. 23 Optimized Cp2Cr2C2B7H9 Structures within 17 kcal/mol of the Lowest-Energy Structures vertex degrees

Cr−Cr distance

structure

ΔE, kcal/mol

v3

v4

v5

v6

v7

Å

WBI

B7C2Cr2-1* B7C2Cr2-2* B7C2Cr2-3* B7C2Cr2-4* B7C2Cr2-5* B7C2Cr2-6* B7C2Cr2-7* B7C2Cr2-8* B7C2Cr2-9 B7C2Cr2-10 B7C2Cr2-11 B7C2Cr2-12 B7C2Cr2-13 B7C2Cr2-14 B7C2Cr2-15 B7C2Cr2-16 B7C2Cr2-17 B7C2Cr2-18 B7C2Cr2-19 B7C2Cr2-20 B7C2Cr2-21 B7C2Cr2-22 B7C2Cr2-23

0.0 1.2 4.3 6.5 6.5 6.8 6.9 7.4 7.7 7.8 8.5 9.4 9.5 9.7 10.6 10.7 10.9 11.1 11.5 11.9 13.6 14.1 14.2

0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

2 3 4 2 4 2 2 2 4 2 1 5 2 2 2 2 2 2 3 2 2 2 2

8 6 4 8 5 8 6 5 5 8 8 4 8 8 8 8 8 8 5 8 8 8 8

1 2 3 1 1 1 1 3 1 1 1 0 1 1 1 1 1 1 3 1 1 1 1

0 0 0 0 1 0 1 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0

2.106 2.909 2.817 2.098 2.742 3.659 2.530 2.141 2.751 2.108 2.926 2.618 2.136 2.116 2.112 3.754 3.637 2.118 2.089 2.114 3.657 2.123 2.148

1.61 0.57 0.46 1.69 0.64 0.23 0.70 1.57 0.60 1.56 0.52 0.61 1.54 1.56 1.68 0.17 0.15 1.57 1.65 1.64 0.24 1.57 1.54

C−C, Å (degrees) 3.44 3.62 2.55 3.35 3.53 3.33 2.70 3.39 3.50 2.85 2.66 3.56 2.80 3.12 2.58 3.27 3.25 3.49 3.50 2.60 3.27 2.65 2.73

(44) (44) (44) (54) (44) (44) (44) (44) (54) (54) (54) (44) (44) (54) (54) (44) (54) (54) (44) (54) (44) (54) (54)

comments closo/isocloso 2v6 deltahedron oblatocloso-6,6 closo/isocloso oblatocloso-7,6 closo/isocloso, 2 μ3-H capped 10-vertex isocloso capped 10-vertex closo, μ-H oblatocloso-7,6 closo/isocloso closo/isocloso oblatocloso-7,7 closo/isocloso closo/isocloso closo/isocloso closo/isocloso, 2 μ-H closo/isocloso, 2 μ-H closo/isocloso capped 10-vertex isocloso closo/isocloso closo/isocloso, μ-H closo/isocloso closo/isocloso

chromium atoms with a CrCr distance of ∼2.1 Å corresponding to WBIs in the 1.54−1.69 range (Table 7). This corresponds to the expected values for the CrCr triple bond in the isocloso bonding topology of Table 2 rather than the Cr≣Cr quadruple bond in the closo bonding topology of Table 1. This suggests that the 11-vertex most spherical deltahedron, which necessarily has a degree 6 vertex and thus can have either closo bonding topology (Table 1) or isocloso bonding topology (Table 2), prefers the isocloso bonding topology, which requires only a CrCr triple bond. The presence of bridging external hydrogen atoms in the most spherical 11-vertex deltahedral Cp2Cr2C2B7H9 structure has the net effect of bridging otherwise external chromium lone pairs into the skeletal bonding. Such hydrogen bridges present an alternative to surface Cr−Cr multiple bonding in the otherwise hypelectronic Cp2Cr2C2B7H9 system. Because Cr− Cr multiple bonding is not required in these hydrogen-bridged systems, the two chromium atoms occupy nonadjacent vertices in the 11-vertex most spherical deltahedron, leading to a Cr··· Cr distance of ∼3.7 Å with a WBI of ∼0.2. The significant nonzero value of the Cr···Cr WBIs in these hydrogen-bridged structures can arise from indirect Cr···Cr interactions through the multicenter core bonding in the closo deltahedral bonding topology (Table 1). Five of the remaining 11-vertex Cp2Cr2C2B7H9 structures are oblatocloso structures representing three different topologies. The structure B7C2Cr2-3, lying 4.3 kcal/mol in energy above B7C2Cr2-1, is an oblatocloso-6,6 structure, with the chromium atoms located at the degree 6 vertices (Figure 8 and Table 7). The structures B7C2Cr2-5 and B7C2Cr2-9, lying 6.5 and 7.7 kcal/mol, respectively, in energy above B7C2Cr2-1, are oblatocloso-7,6 structures, with one chromium atom located at the degree 7 vertex and the other chromium atom located at the degree 6 vertex. A structure of this type is the lowest-energy structure for the oblatocloso dirhenaborane

vertex and an adjacent degree 5 vertex. The CrCr distance of 2.09 Å in B6C2Cr2-5 coupled with a WBI of 1.39 is consistent with the formal triple bond required for a skeletal bonding topology analogous to that in Table 2 for the 12-vertex 2v6 deltahedron. The potential energy surface of the 11-vertex Cp2Cr2C2B7H9 is unusually complicated, with 23 structures lying within 17 kcal/mol of the lowest-energy structure B7C2Cr2−1 (Table 7). Three general types of deltahedra are found in this cornucopia of structures, namely, the most spherical 11-vertex deltahedron and a closely related deltahedron with two degree 6 vertices (Figure 1), oblatocloso deltahedra of three types, and capped 10-vertex closo and isocloso deltahedra with a single degree 3 capping vertex. All of these types of 11-vertex deltahedra are represented in the eight lowest-energy Cp2Cr2C2B7H9 structures (Figure 8). The lowest-energy Cp2Cr2C2B7H9 structure B7C2Cr2-1 and 13 of the higher-energy structures have a central most spherical 11-vertex deltahedron with a single degree 6 vertex (Table 7). One of these higher-energy structures, namely, B7C2Cr2-6 lying 6.8 kcal/mol in energy above B7C2Cr2-1, has two of its external hydrogen atoms bridging CrB2 faces sharing a chromium atom (Figure 8). Two other Cp2 Cr2C2B7H9 structures, namely, B7C2Cr2-16 and B7C2Cr2-17 at ∼11 kcal/mol in energy above B7C2Cr2-1, have two of their external hydrogen atoms bridging Cr−B edges sharing the same cobalt atom. The Cp2Cr2C2B7H9 structure B7C2Cr2-21, lying 13.6 kcal/mol above B7C2Cr2-1, has a single Cr−B edge bridged by one of the external hydrogen atoms. The possibility of edge- and face-bridging external hydrogen atoms, coupled with the relatively low symmetry of the most spherical 11vertex deltahedron, contributes to the multiplicity of energetically closely spaced Cp2Cr2C2B7H9 structures. The most spherical 11-vertex deltahedral Cp2Cr2C2B7H9 structures without bridging hydrogen atoms all have adjacent J


Article

Inorganic Chemistry

Figure 8. Eight lowest-energy Cp2Cr2C2B7H9 structures (starred in Table 7).

Cp*2Re2B9H9 found experimentally.25−27 Finally, the oblatocloso-7,7 structure B7C2Cr2-12, lying 9.4 kcal/mol in energy above B7C2Cr2-1, has the chromium atoms located at the two degree 7 vertices. The CrCr distances decrease as the degrees of the chromium vertices increase in these oblatocloso structures. Thus, the CrCr distances for the oblatocloso-6,6, oblatocloso-7,6, and oblatocloso-7,7 structures are ∼2.82, ∼2.75, and ∼2.62 Å, respectively. The CrCr WBIs ranging from 0.46 to 0.61 are consistent with the formal intrapolyhedral double bonds of the oblatocloso skeletal bonding topology. The 11-vertex most spherical and oblatocloso structures account for 21 or 23 lowest-energy Cp2Cr2C2B7H9 structures, leaving two structures derived from 10-vertex deltahedra by capping a triangular face. This necessarily leads to a single degree 3 vertex. The structure B7C2Cr2-7, lying 6.9 kcal/mol in energy above B7C2Cr2-1, has a central 10-vertex isocloso deltahedron with a Cr2B face capped by a boron atom. This

leads to a degree 7 vertex for one chromium atom and a degree 6 vertex for the other chromium atom. The CrCr distance of 2.530 Å in B7C2Cr2-7 with a WBI of 0.70 can be interpreted as a formal double bond. Considering the CH, BH, and CpCr vertices as 3, 2, and −1 electron donors and the extra two electrons from the surface CrCr double bond leads to 20 skeletal electrons for the capped 10-vertex isocloso deltahedron of B9C2Cr2-7 corresponding to the 2n skeletal electrons for an isocloso deltahedron. Similarly, the Cp2Cr2C2B7H9 structure B9C2Cr2-8, lying 7.4 kcal/mol in energy above B7C2Cr2-1, has a central 10-vertex bicapped square antiprism (the 10vertex closo deltahedron in Figure 1) with a Cr2B face capped by a boron atom. In B9C2Cr2-8, both chromium atoms are located at degree 6 vertices. The CrCr distance of 2.141 Å with a WBI of 1.57 corresponds to a formal triple bond. The extra four skeletal electrons arising indirectly from this CrCr triple bond combined with those from the CH, BH, and CpCr K


Article

Inorganic Chemistry

for several of the isocloso Cp2Cr2C2Bn−4Hn−2 structures found in this work. These considerations suggested the possibility of a CrCr triple bond in the experimental “Cp2Cr2C2B8H10” structure. Such a CrCr triply bonded structure could arise from hydrogenation of the original Cr≣Cr quadruple bond in an original Cp2Cr2C2B8H10 structure, B8C2Cr2-2, to give a dihydride. This is not unreasonable because the reported “Cp2Cr2C2B8H10” is obtained from Cp2Cr and C2B8H12 in rather good yield (70%) under relatively mild conditions. In order to explore this possibility, we optimized a hydrogen-rich Cp2Cr2(H)2C2B8H10 structure. This led to the doubly bridged structure Cp2Cr2(μ-H)2C2B8H10 with the two “extra” hydrogen atoms bridging a CrCr bond of length 2.219 Å, which is much closer to the experimental value of 2.272 Å for the species reported as “Cp2Cr2C2B8H10” (Figure 4). This suggests that the reported “Cp2Cr2C2B8H10” is really the dihydride Cp2Cr2(μ-H)2C2B8H10. The CrCr interaction can be regarded as a diprotonated triple bond. The availability in relatively good yield from Cp2Cr and C2B8H12 of what we now believe to be Cp2Cr2(μ-H)2C2B8H10 containing a novel diprotonated CrCr triple bond suggests some interesting new areas of chemistry of metal−metal multiple-bonded derivatives. Thus, Cp2Cr2(μ-H)2C2B8H10 is a potential source of a likewise triply bonded [Cp2Cr2C2B8H10]2− dianion by double deprotonation with a suitable base or a source of the genuine neutral Cp2Cr2C2B8H10 by mild oxidation/dehydrogenation. A point of interest in view of the theoretical studies reported here is whether dehydrogenation of Cp2Cr2(μ-H)2C2B8H10 to give Cp2Cr2C2B8H10 will result in rearrangement of the central Cr2C2B8 icosahedron into a deltahedron, with two degree 6 vertices for the chromium atoms corresponding to the lowestenergy Cp2Cr2C2B8H10 structure B8C2Cr2-1 (Figure 3 and Table 3).

vertices make B9C2Cr2-8 a 22-skeletal electron system. This corresponds to the 2n + 2 skeletal electrons required by the central 10-vertex closo bicapped square antiprism in B9C2Cr28.

4. CONCLUSION Our previous studies29 indicate oblatocloso structures to be the lowest-energy structures for the dirhenaboranes Cp2Re2Bn−2Hn−2 relative to deltahedral isomers with surface metal−metal multiple bonds (Table 8). With the exception of Table 8. Energy Differences (kcal/mol) between the Lowest-Energy Oblatocloso Dimetallaborane Structure and Lowest-Energy-Indicated Deltahedral Isomer with the Indicated M−M Bond Order no. of vertices 8 8 9 10 10 11 12

deltahedron bicapped octahedron bisdisphenoid tricapped trigonal prism isocloso bicapped tetragonal antiprism closo/isocloso icosahedron

M−M bond order

Cp2Cr2C2Bn−4Hn−2 system

Cp2Re2Bn−2Hn−2 system

2

23.5

8.4

4 4

28.1 10.7

23.3 25.0

3 4

11.3 9.5

16.4 23.3

3 4

−4.3 1.8

5.8 8.0

the 11-vertex system, we now find the same to be true for the dichromadicarbaboranes Cp2Cr2C2Bn−4Hn−2 that are isoelectronic with the dirhenaboranes. However, the 11-vertex Cp2Cr2C2B7H9 system is exceptional because the lowestenergy closo/isocloso deltahedral structure B7C2Cr2-1 lies 4.3 kcal/mol below the lowest-energy oblatocloso isomer B7C2Cr2-3 (Table 7). For the 9 to 12-vertex systems, the energy differences between the lowest-energy oblatocloso structure and the indicated structures with surface metal− metal multiple bonding are less for the Cp2Cr2C2Bn−4Hn−2 derivatives than for the isoelectronic Cp2Re2Bn−2Hn−2 derivatives (Table 8). This may relate to the fact that the generally higher degree metal vertices found in the oblatocloso structures relative to the lower degree metal vertices in the more nearly spherical deltahedral structures with metal−metal multiple bonds are more favorable for the third-row transition-metal rhenium than for the first-row transition-metal chromium. In view of the calculated relative energies in Table 8, it is not surprising that all of the experimental Cp*2Re2Bn−2Hn−2 dirhenaborane structures are oblatocloso structures.25−27 However, X-ray crystallography clearly indicates that the product synthesized from Cp2Cr and C2B8H12, initially assumed to be Cp2Cr2C2B8H10, is an icosahedral structure with the vertex positions of the chromium, carbon, and boron atoms similar to B8C2Cr2-2 lying only 1.8 kcal/mol above the global minimum B8C2Cr2-1 (Table 3).9 Despite this apparent similarity in the molecular topology, we do not think that the reported “Cp2Cr2C2B8H10” is really B8C2Cr2-2 because of the large discrepancy between the predicted Cr−Cr distance of 1.884 Å in B8C2Cr2-2 and the experimental Cr−Cr distance of 2.272 Å. This experimental distance of 2.272 Å is even longer than the ∼2.1 Å CrCr triple bond distance predicted

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b03476. Initial structures, distance and energy ranking tables, orbital energies and HOMO−LUMO gaps, and the complete Gaussian09 reference (PDF) Concatenated .xyz file containing the optimized structures, which can be visualized with free software such as the Mercury program (XYZ)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (A.L.). *E-mail: [email protected] (A.-Z.K.). *E-mail: [email protected] (R.B.K.). ORCID

R. Bruce King: 0000-0001-9177-5220 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding from the Romanian Ministry of Education and Research (Grant PN-III-P4-ID-PCE-2016-0089) is gratefully L


Article

Inorganic Chemistry

cluster-geometry patterns. J. Chem. Soc., Dalton Trans. 1994, 229− 236. (19) Kennedy, J. D. Structure and bonding in recently isolated metallaboranes. Inorg. Chem. 1986, 25, 111−112. (20) Baker, R. T. Hyper-closo metallaboranes. Inorg. Chem. 1986, 25, 109−111. (21) Johnston, R. L.; Mingos, D. M. P. Molecular orbital calculations relevant to the hypercloso vs. iso-closo controversy in metallaboranes. Inorg. Chem. 1986, 25, 3321−3323. (22) Johnston, R. L.; Mingos, D. M. P.; Sherwood, P. Bonding and electron counting in hyper closo metalloboranes and metallocarboranes. New J. Chem. 1991, 15, 831−841. (23) King, R. B. Topological aspects of the skeletal bonding in “isocloso” metallaboranes containing “anomalous” numbers of skeletal electrons. Inorg. Chem. 1999, 38, 5151−5153. (24) For a review of much of the relevant chemistry from Fehlner’s group, see: Fehlner, T. P. In Group 13 Chemistry: From Fundamentals to Applications; Shapiro, P. J., Atwood, D. A., Eds.; American Chemical Society: Washington, DC, 2002; pp 49−67. (25) Ghosh, S.; Shang, M.; Li, Y.; Fehlner, T. P. Synthesis of [(Cp*Re)2BnHn] (n = 8−10). Metal boride particles that stretch the cluster structure paradigms. Angew. Chem., Int. Ed. 2001, 40, 1125− 1127. (26) Wadepohl, H. Hypoelectronic dimetallaboranes. Angew. Chem., Int. Ed. 2002, 41, 4220−4223. (27) Le Guennic, B.; Jiao, H.; Kahlal, S.; Saillard, J.-Y.; Halet, J.-F.; Ghosh, S.; Shang, M.; Beatty, A. M.; Rheingold, A. L.; Fehlner, T. P. Synthesis and characterization of hypoelectronic rhenaboranes. Analysis of the geometric and electronic structurtes of species following neither borane nor metal cluster electron-counting paradigms. J. Am. Chem. Soc. 2004, 126, 3203−3217. (28) King, R. B. The oblate deltahedra in dimetallaboranes: geometry and chemical bonding. Inorg. Chem. 2006, 45, 8211−8216. (29) Lupan, A.; King, R. B. Hypoelectronic dirhenaboranes having eight to twelve vertices: internal versus surface rhenium-rhenium bonding. Inorg. Chem. 2012, 51, 7609−7616. (30) Lupan, A.; King, R. B. Dimetallaboranes with polyhedral surface metal-metal multiple bonds: deltahedral dirhenaboranes with pentalenedirhenium vertices. Organometallics 2013, 32, 4002−4008. (31) Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999, 110, 6158−6170. (32) Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. The complete reference is given in the Supporting Information. (33) Weinhold, F.; Landis, C. R. Valency and Bonding: A Natural Bond Order Donor−Acceptor Perspective; Cambridge University Press: Cambridge, U.K., 2005; pp 32−36. (34) Potenza, J.; Giordano, P.; Mastropaolo, D.; Efraty, A. Crystallographic study of dicarbonylpentamethylcyclopentadienylchromium dimer, a complex with a Cr≡Cr bond. Inorg. Chem. 1974, 13, 2540−2544.

acknowledged. S.J. acknowledges the scientific performance scholarship awarded by Babeş-Bolyai University. Additional computational resources were provided by the high-performance computational facility MADECIP, POSCCE, COD SMIS 48801/1862, cofinanced by the European Regional Development Fund of the European Union.

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