High-spin face-capped deltahedra in divanadadicarbaboranes are very different from the singlet structures of chromium analogues

Abstract

Using density functional theory (DFT), divanadadicarbaboranes Cp₂V₂C₂B_n−4H_n−2 are found to have very different low-energy structures than the corresponding dichromadicarbaboranes Cp₂Cr₂C₂B_n−4H_n−2. Thus, the low-energy divanadadicarbaborane structures with n vertices have triplet or quintet states rather than singlet spin states, frequently based on an (n − 1)-vertex VC₂B_n−4 deltahedron having a face capped by the second vanadium atom bearing most of the spin density. Such structures are analogous to the low-energy structures of dimanganaboranes Cp₂Mn₂B_n−2H_n−2, even though the vanadium and manganese systems are not isoelectronic with each other. Most of the low-energy 8-vertex Cp₂V₂C₂B₄H₆ structures are based on the hexagonal bipyramid, whereas most of the low-energy 9- and 10-vertex structures are based on the 9-vertex isocloso deltahedron. The bicapped square antiprism capped by a high-spin vanadium vertex is characteristic of the low-energy 11-vertex Cp₂V₂C₂B₇H₉ structures. Similarly, an 11-vertex closo deltahedron capped by a high-spin vanadium vertex is the lowest energy Cp₂V₂C₂B₈H₁₀ structure by a substantial margin of ∼18 kcal mol⁻¹.

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1. Introduction

The preferred structures of deltahedral boranes and isoelectronic carboranes are based on the most spherical closo deltahedra in which all of the faces are triangles and the vertices are as nearly similar as possible (Fig. 1).^1–3 Each of the boron and carbon vertices in such structures uses one valence orbital for bonding to an external atom or group R such as hydrogen, a halogen, or a simple alkyl or aryl group. This leaves the remaining three vertex atom valence orbitals available to participate in skeletal bonding. Much of the early development of this chemistry was based on structures with an external hydrogen atom bonded to each boron or carbon vertex. In the electron bookkeeping for such systems, each BH vertex thus contributes two skeletal electrons and each CH vertex contributes three skeletal electrons. The preferred n-vertex deltahedral species were of the B_nH_n²⁻, CB_n−1H_n⁻, and C₂B_n−2H_n types with 2n + 2 skeletal electrons as discussed by Wade and Mingos^4–6 in early papers and justified by chemical bonding models based on graph theory/topology⁷ and tensor surface harmonics.⁸

Fig. 1 The closo, isocloso, and oblatocloso deltahedra having 8 to 12 vertices. Vertices of degrees 4, 5, 6, and 7 are indicated in red, black, green, and blue, respectively.

The research groups of Hawthorne⁹ and Grimes¹⁰ were the pioneers in synthesizing the first deltahedral boranes having transition metal vertices. Vertices of the CpM type (Cp = η-C₅H₅) were preferred owing to the robust nature of the cyclopentadienyl–metal bond. This allows a variety of chemical transformations to be performed on the metallaborane structure with the CpM vertices remaining intact. Cobalt vertices of the CpCo type were used in the early metallaborane and metallacarbaborane research. For electron bookkeeping purposes, a CpCo vertex is isoelectronic with a BH vertex as a contributor of two skeletal electrons. Thus, among the nine valence orbitals of the sp³d⁵ manifold of the cobalt atom, three are used for external bonding to the Cp⁻ anion and three are occupied by lone pairs. This leaves three orbitals and two electrons available for skeletal bonding, corresponding to the favored 18-electron configuration for the cobalt atom.^11–13 In the early work, Hawthorne's group⁹ focused on metallaboranes obtainable using B₁₀H₁₄ as the boron hydride source, whereas Grimes’ group¹⁰ focused on metallaboranes obtainable from B₅H₉. Because of the U. S. government's interest in the 1960s in the use of boron hydrides as possible rocket fuels, these key binary boron hydride starting materials were much more readily available then than they are now in modern times.

The pioneering work by Hawthorne and Grimes on metallaboranes was followed by work in the laboratory of Kennedy on systems using platinum group metals of the 4d and 5d transition series as vertex atoms. The Kennedy group identified alternative deltahedra known as isocloso¹⁴ or hypercloso^15–17 deltahedra for the 9- and 10-vertex systems, particularly the latter (Fig. 1).^18–21 The isocloso 9- and 10-vertex deltahedra have a single degree 6 vertex, whereas the corresponding 9- and 10-vertex closo deltahedra have exclusively degree 4 and 5 vertices (Fig. 1). The favored skeletal electron count for n-vertex isocloso metallaboranes was 2n, so they were hypoelectronic relative to the 2n + 2 skeletal electron count for the corresponding n-vertex closo metallaboranes. However, O'Neill and Wade²² showed that the 8- and 9-vertex closo deltahedra have non-degenerate molecular orbitals in the frontier regions so that either 2n or 2n + 2 skeletal electrons could be favored for these systems. This is reflected experimentally in the long-known^23,24 deltahedral boron chlorides B_nCl_n (n = 8, 9) as well as the dirhodaboranes Cp*₂Rh₂B_n−2H_n−2 (Cp* = η-Me₅C₅) synthesized by Ghosh and co-workers in recent years_.^25,26

A seminal advance in the chemistry of metallaboranes was the discovery of dirhenaboranes Cp*₂Re₂B_n−2H_n−2 (n = 8, 9, 10, 11, 12) by Ghosh, Fehlner, and their coworkers.²⁷ X-ray crystallography showed that these dirhenaboranes have a non-spherical deltahedral structure approximating an oblate (flattened) ellipsoid in which one of the three primary axes is significantly shorter than the other two (Fig. 1). Because of this characteristic, deltahedra of this type can conveniently be designated as oblatocloso deltahedra.²⁸ The only one of these five oblatocloso deltahedra that is clearly recognizable is the hexagonal bipyramid. In these oblatocloso deltahedra, the rhenium atoms are degree 6 or 7 vertices located at relatively flat points on the deltahedral surface, whereas the boron atoms are degree 4 or 5 vertices located at relatively high curvature points on the deltahedral surface. Electron bookkeeping using the Wade–Mingos assumption that the Cp*Re vertices use three of the rhenium valence orbitals for skeletal bonding classifies them as more severely hypoelectronic systems with 2n − 4 Wadean skeletal electrons. This hypoelectronicity is illusory, however, since a more reasonable chemical bonding scheme considers the rhenium atoms at degree 6 and 7 vertex sites of low local curvature to use five rather than three valence orbitals for skeletal bonding, thereby making them effectively 2n + 4 skeletal electron systems.

Several years ago, we gratifyingly showed by density functional theory (DFT) calculations that these unusual experimentally known oblatocloso Cp*₂Re₂B_n−2H_n−2 (n = 8, 9, 10, 11, 12) structures (Fig. 1) with the rhenium atoms in approximately antipodal positions are the lowest energy isomers.²⁹ However, higher energy Cp*₂Re₂B_n−2H_n−2 isomers were found exhibiting a new structural paradigm, namely that of a closo deltahedron having adjacent rhenium atoms with a short rhenium–rhenium distance suggesting a multiple bond. Upon replacement of the two Cp*Re vertices with a single PnRe₂ unit (Pn = pentalenyl {η^5,5-C₈H₆}), thereby forcing the two rhenium atoms into adjacent vertices of the Re₂B_n−2 deltahedron, such closo deltahedral structures were found by DFT to be the lowest energy structures.³⁰

The synthetic methods used to prepare these dirhenaboranes of considerable structural interest not only involve the rare metal rhenium but also require several steps to prepare the Cp*ReCl₄ starting material from typical rhenium sources such as perrhenate. Therefore, our subsequent theoretical studies were directed to explore the viability of structures similar to the dirhenaboranes but using the more abundant first-row transition metals. Our first work in this area studied dichromadicarbaboranes of the Cp₂Cr₂C₂B_n−4H_n−2 isoelectronic type with Cp*₂Re₂B_n−2H_n−2 systems.³¹ In addition, Stone and co-workers³² reported a species formulated as Cp₂Cr₂C₂B₈H₁₀ shown by X-ray crystallography to have a central Cr₂C₂B₈ icosahedron with adjacent chromium vertices with a short chromium–chromium distance of 2.272 Å. Initially we thought that this short chromium–chromium distance might correspond to the formal quadruple bond required to provide enough skeletal electrons from the chromium atoms to give 26 (=2n + 2 for n = 12) skeletal electrons for a closo icosahedral system. However, our conclusion from this study based on the comparison of predicted chromium–chromium distances for various structures with the experimental chromium–chromium distance determined by X-ray crystallography suggested that the species reported by Stone and co-workers has a Cr≡Cr triple bond bridged by two hydrogen atoms, not revealed in their X-ray crystallographic study dating back to the 1980s. In general, this study revealed low-energy oblatocloso structures Cp₂Cr₂C₂B_n−4H_n−2 similar to those of their isoelectronic rhenium Cp*₂Re₂B_n−2H_n−2 analogues as well as closo and isocloso structures with short chromium–chromium distances, suggesting formal quadruple and triple bonds, respectively.

More recently, we used DFT to study Cp₂Mn₂B_n−2H_n−2 systems that are the direct analogues of Cp₂Re₂B_n−2H_n−2 systems for which the oblatocloso structures are preferred.³³ However, low-energy oblatocloso structures were not found for dimanganese systems. Instead, the energetically preferred structures for the Cp₂Mn₂B_n−2H_n−2 systems were found to be higher spin state triplet and quintet structures, apparently a consequence of the lower ligand field strength in manganese complexes relative to analogous rhenium complexes. In general, the lowest energy Cp₂Mn₂B_n−2H_n−2 structures were typically found to have a central MnB_n−1closo deltahedron with one face capped by the second CpMn unit.

Our studies on the Cp₂Cr₂C₂B_n−4H_n−2 systems found a variety of interesting singlet oblatocloso, isocloso, and closo structures as low-energy structures. We now report a DFT investigation of the corresponding divanadadicarbaboranes Cp₂V₂C₂B_n−4H_n−2. Unexpectedly, we found that the low-energy vanadadicarbaborane structures are of a totally different type from those of the dichromadicarbaboranes. Thus, the low-energy Cp₂V₂C₂B_n−4H_n−2 structures are seen to resemble those of the dimanganaboranes Cp₂Mn₂B_n−2H_n−2 in exhibiting higher spin state triplet and quintet structures with central VC₂B_n−3 deltahedra capped by a high-spin CpV unit, even though the Cp₂V₂C₂B_n−4H_n−2 and Cp₂Mn₂B_n−2H_n−2 systems are not isoelectronic. Our results thus show that the two skeletal electron difference resulting in the substitution of vanadium for chromium in the dimetalladicarbaboranes Cp₂M₂C₂B_n−4H_n−2 has a profound effect on the energetically preferred structure types.

2. Theoretical methods

The initial Cp₂V₂C₂B_n−4H_n−2 structures were constructed by systematic substitution of two boron vertices in B_nH_n²⁻ with two CpV units in various n-vertex polyhedral geometries, followed by further substitution of two of the remaining BH vertices by CH vertices. Thus, 337 structures of the 8-vertex Cp₂V₂C₂B₄H₆ clusters, 347 structures of the 9-vertex Cp₂V₂C₂B₅H₇ clusters, 538 structures of the 10-vertex Cp₂V₂C₂B₆H₈ clusters, 407 structures of the 11-vertex Cp₂V₂C₂B₇H₉ clusters, and 223 structures of the 12-vertex Cp₂V₂C₂B₈H₁₀ clusters were chosen as starting points for the optimizations (see the ESI†).

Full geometry optimizations were carried out on the Cp₂V₂C₂B_n−4H_n−2 systems (n = 8–12) at the B3LYP/6-31G(d) level of theory with all of them optimized, in turn, as neutral singlets, triplets, and quintets. For the singlet structures, the broken symmetry approach was also considered. The lowest-energy structures were then reoptimized at a higher level of theory, namely PBE0/Def2TZVP, and these are the structures presented in the manuscript.³⁴ The nature of the stationary points after the optimization was checked by calculations of harmonic vibrational frequencies. If significant imaginary frequencies were found, the 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 package³⁵ with the default settings for the SCF cycles and geometry optimization. The Wiberg bond indices (WBIs) for the V–V interactions in the optimized Cp₂V₂C₂B_n−4H_n−2 structures were obtained from the NBO analysis automatically provided in the Gaussian output.³⁶ All of the structures reported in this paper have appreciable HOMO–LUMO gaps of 2.59–4.40 eV (see Table S7 in the ESI†).

The Cp₂V₂C₂B_n−4H_n−2 (n = 8 to 12) structures are numbered as B(n−4)C2V2-xY where n is the total number of polyhedral vertices, x is the relative order of the structure on the energy scale (PBE0/Def2TZVP including zero-point corrections) and Y is the spin state designating singlets, triplets, and quintets as S, T and Q. The lowest energy optimized structures discussed in this paper are depicted in Fig. 2 through 6. 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 ESI.†

Fig. 2 The lowest energy 8-vertex Cp₂V₂C₂B₄H₆ structures.

3. Results and discussion

3.1. Eight-vertex Cp₂V₂C₂B₄H₆ clusters

Six 8-vertex Cp₂V₂C₂B₄H₆ structures were found within 11 kcal mol⁻¹ of the lowest energy structure B4C2V2-1T (Fig. 2 and Table 1). The triplet structure B4C2V2-1T has a central VC₂B₄ pentagonal bipyramid in which one face is capped by a CpV moiety with two hydrogen bridges to this vanadium atom from adjacent boron atoms. The spin density on the capping vanadium atom of 3.22 corresponds to the three unpaired electrons of high-spin vanadium(II) in a CpV⁺ moiety. This is analogous to the localization of five unpaired electrons in the capping CpMn⁺ moieties in many of the previously studied dimanganaboranes.³³ The opposing spin density of −1.17 on the other vanadium atom located at one of the apices of the pentagonal bipyramid leads to a net vanadium spin of 2.05, consistent with the triplet spin state of B4C2V2-1T.

Table 1 The lowest energy Cp₂V₂C₂B₄H₆ structures up to 11.5 kcal mol⁻¹. Energies are given in kcal mol⁻¹ and distances are given in Å

Structure (symmetry)		Vanadium vertices				Net V	V⋯V	V⋯V
	ΔE	Degree	Spin	Degree	Spin	Spin	Distance	WBI	Polyhedron
B4C2V2-1T (C1)	0.0	3(2μ-H)	3.22	6	−1.17	2.05	3.24	0.72	Cap pent bipy
B4C2V2-2T (Cs)	0.5	6	2.91	6	−0.85	2.06	2.95	0.53	Hex bipy
B4C2V2-3Q (Cs)	3.1	6	2.45	6	2.42	4.87	3.04	0.25	Hex bipy
B4C2V2-4Q (C2h)	5.1	6	2.33	6	2.33	4.66	3.07	0.22	Hex bipy
B4C2V2-5T (C2v)	8.6	6	2.07	6	0.54	2.61	2.86	0.39	Hex bipy
B4C2V2-6T (Cs)	11.1	6	2.65	6	−0.24	2.41	3.26	0.40	Hex bipy

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The other five low-energy Cp₂V₂C₂B₄H₆ structures are all hexagonal bipyramids having the vanadium atoms in the axial positions with V–V distances of ∼3 Å, suggesting some vanadium–vanadium interaction through the center of the hexagonal bipyramid (Fig. 2 and Table 1). These five structures can thus be considered as 8-vertex oblatocloso structures (Fig. 1). The B4C2V2-2T, B4C2V2-5T, and B4C2V2-6T structures lying 0.5, 8.6, and 11.1 kcal mol⁻¹, respectively, above B4C2V2-1T, are triplet structures with the two carbon atoms located in meta (non-adjacent/non-antipodal), para (antipodal), and ortho (adjacent) positions in the equatorial hexagon, respectively. The quintet Cp₂V₂C₂B₄H₆ structures, B4C2V2-3Q and B4C2V2-4Q, lying 3.1 and 5.1 kcal mol⁻¹, respectively, in energy above B4C2V2-1T, are quite similar to the carbon atoms located in the meta and para positions in the equatorial hexagon, respectively.

3.2. Nine-vertex Cp₂V₂C₂B₅H₇ clusters

The potential energy surface for the 9-vertex Cp₂V₂C₂B₅H₇ is more complicated than that of Cp₂V₂C₂B₄H₆ with 10 structures lying within 11 kcal mol⁻¹ of the lowest energy structure B5C2V2-1Q (Fig. 3 and Table 2). This quintet structure B5C2V2-1Q has a central VC₂B₄ pentagonal bipyramid with the fifth boron atom capping a VB₂ face. The remaining CpV moiety then caps the B₃ face including this capping boron atom with B–H–V bridges from all three boron atoms in the capped face. This degree 3 capping vanadium atom has a spin density of 3.11 corresponding to a high-spin vanadium(II) CpV⁺ similar to that in the Cp₂V₂C₂B₄H₆ structure B4C2V2-1T (Fig. 2 and Table 1).

Fig. 3 The lowest energy 9-vertex Cp₂V₂C₂B₅H₇ structures.

Table 2 The lowest energy Cp₂V₂C₂B₅H₇ structures up to 11 kcal mol⁻¹. Energies are given in kcal mol⁻¹ and distances are given in Å

Structure (symmetry)		Vanadium vertices				Net V	V⋯V	V⋯V
	ΔE	Degree	Spin	Degree	Spin	Spin	Distance	WBI	Polyhedron
B5C2V2-1Q (Cs)	0.0	3(3μ-H)	3.11	6	1.69	4.80	3.99	0.03	Central pent bipy
B5C2V2-2Q (C1)	0.9	6	2.28	5	2.32	4.60	3.69	0.14	9-Vertex isocloso
B5C2V2-3Q (C1)	2.7	3(1μ-H)	3.16	6	1.29	4.45	3.07	0.21	Cap bisdisphen
B5C2V2-4Q (C1)	3.3	4(1μ-H)	2.50	6	2.24	4.74	2.78	0.25	9-Vertex isocloso
B5C2V2-5Q (C1)	6.4	5(1μ-H)	2.37	6	2.29	4.66	3.67	0.12	9-Vertex isocloso
B5C2V2-6Q (Cs)	6.8	4(2μ-H)	2.62	5	2.50	5.12	3.91	0.06	Tricap trig prism
B5C2V2-7T (C1)	7.1	5(1μ-H)	2.37	6	−0.08	2.29	3.50	0.18	9-Vertex isocloso
B5C2V2-8Q (C2)	9.5	5	2.36	5	2.35	4.70	3.84	0.10	Tricap trig prism
B5C2V2-9T (C1)	9.8	5	2.40	6	−0.09	2.31	3.54	0.15	9-Vertex isocloso
B5C2V2-10T (C1)	10.3	5	2.40	6	−0.07	2.33	3.44	0.19	9-Vertex isocloso

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Three of the 10 lowest energy Cp₂V₂C₂B₅H₇ structures, namely the quintets B5C2V2-2Q, B5C2V2-4Q, and B5C2V2-5Q lying 0.9, 3.3, and 6.4 kcal mol⁻¹ above B5C2V2-1Q, have central V₂C₂B₅ 9-vertex isocloso deltahedra (Fig. 3 and Table 2). The somewhat higher energy triplet 9-vertex isocloso deltahedral structures B5C2V2-7T, B5C2V2-9T, and B5C2V2-10T lie at 7.1, 9.8, and 10.3 kcal mol⁻¹, respectively, above B5C2V2-1Q. All six of these Cp₂V₂C₂B₅H₇ structures have one of the vanadium atoms located at the unique degree 6 vertex of the 9-vertex isocloso deltahedron. Except for B5C2V2-4Q, the second vanadium vertex is not adjacent to the degree 6 vertices, leading to long V⋯V distances of ∼3.7 Å with WBIs of ∼0.13 for the quintet structures and ∼3.5 Å with somewhat higher WBIs for the triplet structures. The V–V distance in B5C2V2-4Q with adjacent vanadium atoms at a distance of 2.78 Å corresponds to a significantly higher WBI of 0.25.

The three remaining Cp₂V₂C₂B₅H₇ structures have other central polyhedra (Fig. 3 and Table 2). The quintet structure B5C2V2-3Q, lying 2.7 kcal mol⁻¹ above B5C2V2-1Q, has a central VC₂B₅ bisdisphenoid (the 8-vertex closo deltahedron—Fig. 1) with one of its faces capped by a high-spin CpV⁺ moiety with a spin density of 3.16 and one B–H–V bridge. The quintet structure B5C2V2-6Q, lying 6.8 kcal mol⁻¹ above B5C2V2-1Q, has a tricapped trigonal prismatic structure (the 9-vertex closo deltahedron—Fig. 1) with one vanadium atom at a degree 5 vertex and the other vanadium atom at a degree 4 vertex. The degree 4 vanadium vertex in B5C2V2-6Q forms two V–H–B bridges with adjacent boron atoms. Finally, the V₂C₂B₅ polyhedron in B5C2V2-8Q, lying 9.5 kcal mol⁻¹ above B5C2V2-1Q in energy, is also a tricapped trigonal prism with the two carbon atoms and a boron atom as degree 4 vertices capping the underlying V₂B₄ trigonal prism.

3.3. Ten-vertex Cp₂V₂C₂B₆H₈ clusters

Five 10-vertex Cp₂V₂C₂B₆H₈ structures were found within 13 kcal mol⁻¹ of the lowest energy structure B6C2V2-1T (Fig. 4 and Table 3). The central polyhedron in the triplet structure B6C2V2-1T is a 10-vertex isocloso polyhedron with one of the vanadium atoms at the degree 6 vertex. The short V=V distance of 2.53 Å with a relatively high WBI of 0.56 in B6C2V2-1T suggests some type of multiple bond. The second vanadium atom in B6C2V2-1T is a degree 4 vertex with a high spin density of 3.09 corresponding to a high-spin vanadium(II) CpV⁺ unit similar to that found in a number of the other low-energy Cp₂V₂C₂B_n−4H_n−2 structures.

Fig. 4 The lowest energy 10-vertex Cp₂V₂C₂B₆H₈ structures.

Table 3 The lowest energy Cp₂V₂C₂B₆H₈ structures up to 13 kcal mol⁻¹. Energies are given in kcal mol⁻¹ and distances are given in Å

Structure (symmetry)		Vanadium vertices				Net V	V⋯V	V⋯V
	ΔE	Degree	Spin	Degree	Spin	Spin	Distance	WBI	Polyhedron
B6C2V2-1T (Cs)	0.0	4	3.09	6	–1.23	1.86	2.53	0.56	10v-isocloso
B6C2V2-2Q (C1)	0.8	3(1μ-H)	3.15	7	1.32	4.47	3.31	0.10	Cap 9v isocloso
B6C2V2-3T (Cs)	1.1	3(3μ-H)	3.17	7	–1.25	1.92	3.36	0.11	Cap 9v isocloso
B6C2V2-4Q (Cs)	2.4	3(1μ-H)	3.17	7	1.29	4.46	4.01	0.18	Cap 9v isocloso
B6C2V2-5Q (Cs)	3.3	3(3μ-H)	3.15	6	1.32	4.47	4.64	0.02	Cap 9v isocloso

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The remaining four low-energy Cp₂V₂C₂B₆H₈ structures, namely B6C2V2-2Q, B6C2V2-3T, B6C2V2-4Q, and B6C2V2-5Q, are closely spaced in energy, lying 0.8, 1.1, 2.4, and 3.3 kcal mol⁻¹, respectively, above B6C2V2-1T. All four structures have a central 9-vertex isocloso VC₂B₆ deltahedron (Fig. 1), in which one of the faces is capped by a high-spin vanadium(II) atom in a CpV⁺ unit with a spin density of ∼3.15 (Fig. 4 and Table 3). These four nearly isoenergetic structures differ in their spin state and in which of the faces of the 9-vertex isocloso deltahedron is capped by the second vanadium atom.

3.4. Eleven-vertex Cp₂V₂C₂B₇H₉ clusters

The relevant potential energy surfaces of the 11-vertex Cp₂V₂C₂B₇H₉ system (Fig. 5 and Table 4) and the 12-vertex Cp₂V₂C₂B₈H₁₀ system are simple compared with the systems with fewer vertices discussed above. Thus the 11-vertex Cp₂V₂C₂B₇H₉ system has three structures within 5 kcal mol⁻¹ of the lowest energy structure B7C2V2-1Q. However, any other isomeric structures lie at least 18 kcal mol⁻¹ above B7C2V2-1Q (Fig. 5). All three of these structures have a central VC₂B₇ bicapped square antiprism (the 10-vertex closo deltahedron—Fig. 1), in which one of the faces is capped by a high-spin CpV⁺ unit with a spin density of ∼3.15. The capping vanadium atoms form one to three V–H–B bridges to adjacent boron atoms (Table 4). In all three Cp₂V₂C₂B₇H₉ structures, the capped face includes one of the degree 4 vertices of the underlying deltahedron.

Fig. 5 The lowest energy 11-vertex Cp₂V₂C₂B₇H₉ structures.

Table 4 The lowest energy Cp₂V₂C₂B₇H₉ structures up to 18 kcal mol⁻¹. Energies are given in kcal mol⁻¹ and distances are given in Å

Structure (symmetry)		Vanadium vertices				Net V	V⋯V	V⋯V
	ΔE	Degree	Spin	Degree	Spin	Spin	Distance	WBI	Polyhedron
B7C2V2-1Q (Cs)	0.0	3(2μ-H)	3.15	6	1.55	4.70	4.19	0.02	Cap 10v closo
B7C2V2-2Q (C1)	4.0	3(1μ-H)	3.14	6	1.55	4.69	3.32	0.10	Cap 10v closo
B7C2V2-3T (Cs)	4.6	3(3μ-H)	3.17	6	–1.35	1.82	3.35	0.11	Cap 10v closo

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3.5. Twelve-vertex Cp₂V₂C₂B₈H₁₀ clusters

The potential energy surface of the 12-vertex Cp₂V₂C₂B₈H₁₀ system is even simpler since the lowest energy structure B8C2V2-1Q (Fig. 6) lies ∼18 kcal mol⁻¹ below the next lowest energy structure, which has a similar geometry but with a triplet rather than quintet spin state. Structure B8C2V2-1Q is a capped 11-vertex closo deltahedron with one of the vanadium atoms at a degree 6 vertex. The other vanadium atom is the degree 3 capping atom with a spin density of 3.18 corresponding to a high-spin CpV⁺ unit. This capping vanadium atom forms three V–H–B bridges with adjacent boron atoms.

Fig. 6 The lowest energy Cp₂V₂C₂B₈H₁₀ structure B8C2V2-1Q lying ∼18 kcal mol⁻¹ in energy below the next lowest energy structure.

4. Conclusion

In a previous study,³¹ the low-energy structures of the dichromadicarbaboranes Cp₂Cr₂C₂B_n−4H_n−2 (n = 8 to 12) were found to be singlet spin state structures with flattened oblatocloso Cr₂C₂B_n−4 deltahedra having degree 6 and 7 chromium vertices similar to the lowest energy²⁹ and experimentally known²⁷ structures of the isoelectronic dirhenaboranes Cp₂Re₂B_n−4H_n−2. In addition, singlet spherical closo deltahedral structures having adjacent chromium vertices with surface chromium–chromium triple or quadruple bonds are found for the dichromadicarbaboranes at accessible energies.

Simple substitution of two vanadium atoms for the two chromium atoms in the dichromadicarbaboranes to give the divanadadicarbaboranes Cp₂V₂C₂B_n−4H_n−2 (n = 8 to 12) leads to very different potential energy surfaces with all of the lowest energy structures being higher spin state triplet and quintet structures rather than singlet structures. A conspicuous feature in many of the low-energy structures is a degree 3 high-spin vanadium(II) CpV⁺ moiety capping a face of an (n − 1)-vertex deltahedron with one to three B–H–V bridges to this vanadium atom. In this respect, the divanadadicarbaboranes resemble the dimanganaboranes³³ Cp₂Mn₂B_n−2H_n−2, even though the systems are not isoelectronic. Thus the low-energy dimanganaborane structures are all higher spin triplet and quintet spin state structures with the frequent feature of a similar high-spin CpMn⁺ moiety capping a face of an (n − 1)-vertex deltahedron with one to three B–H–Mn bridges to the capping manganese atom.

Most of the low-energy 8-vertex divanadadicarbaboranes Cp₂V₂C₂B₄H₆ exhibit oblatocloso structures having a V₂C₂B₄ hexagonal bipyramid with the vanadium atoms in antipodal positions at the low-curvature degree 6 vertices. The 9-vertex Cp₂V₂C₂B₅H₇ potential energy surface is rather complicated but the 9-vertex isocloso deltahedron (Fig. 1) is a key feature of many of the low-energy structures. Most of the low-energy structures for the 10-vertex Cp₂V₂C₂B₆H₈ system are also based on a central 9-vertex VC₂B₆ isocloso deltahedron but with one of the faces capped by the second vanadium atom in a high-spin vanadium(II) CpV⁺ moiety with one to three B–H–V hydrogen bridges to this vanadium atom. The three lowest-energy structures of the 11-vertex Cp₂V₂C₂B₇H₉ system by a wide margin all have a central 10-vertex VC₂B₇closo deltahedron, namely the bicapped square antiprism (Fig. 1), in which one of the faces is capped by the second vanadium atom, likewise in a high-spin CpV⁺ moiety bridged by one to three hydrogen atoms to the adjacent boron atoms. The lowest energy Cp₂V₂C₂B₈H₁₀ structure by a substantial margin of ∼18 kcal mol⁻¹ has a central 11-vertex closo deltahedron capped by a high-spin vanadium vertex with three V–H–B bridges.

Conflicts of interest

The authors declare no competing financial interest.

Data availability

The data are available from the authors upon request.

Acknowledgements

The computational facilities were provided by the Babeş-Bolyai University under project POC/398/1/1/124155 – co-financed by the European Regional Development Fund (ERDF) through the Competitiveness Operational Program for Romania 2014–2020.

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Footnote

† Electronic supplementary information (ESI) available: Initial structures, distance and energy ranking tables, orbital energies and HOMO/LUMO gaps, complete Gaussian09 reference (.pdf file), and the concatenated .xyz file containing the optimized structures that can be visualized using free software such as the Mercury program. See DOI: https://doi.org/10.1039/d5dt01520k

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