Cyclopentadienylcobalt azaboranes violating the Wade–Mingos rules: a degree 3 vertex for the nitrogen atom

Abstract

The experimentally realized chemistry of polyhedral azaboranes includes the very stable cobalt derivative CpCoNHB₉H₉, which has been synthesized and structurally characterized by X-ray crystallography. The structures and energetics of the complete series of cobaltaazaboranes CpCoNHB_n−2H_n−2 have now been studied by density functional theory. Low-energy structures are found for the 8- and 9-vertex systems based on non-spherical deltahedra providing a degree 3 vertex for the nitrogen atom and thus violating expectations from the Wade–Mingos rules. Thus the lowest energy CpCoNHB₆H₆ structure is an antipodally bicapped octahedron with the nitrogen atom at a degree 3 vertex rather than the most spherical bisdisphenoid. For the 9-vertex CpCoNHB₇H₇ system the lowest energy structures are based on the most spherical tricapped trigonal prism. However, isomeric CpCoNHB₇H₇ structures at ∼13 kcal mol⁻¹ in energy above these structures are found with a central capped bisdisphenoid having the nitrogen atom at the degree 3 capping vertex. In contrast to the 8- and 9-vertex systems, the low-energy CpCoNHB_n−2H_n−2 structures for the 10 to 12 vertex systems are based on the most spherical deltahedra. For the 10- and 11-vertex systems all of the low-energy structures have the nitrogen atom at a degree 4 vertex. The predicted Co–N and Co–B distances in the lowest energy CpCoNHB₉H₉ structure are very close to the experimental values.

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1. Introduction

The chemistry of polyhedral azaboranes originated with the synthesis by Muetterties and co-workers¹ of the arachno azadecaborane derivative B₉H₁₃NH (Fig. 1) from decaborane in low yield as its monoanion B₉H₁₂NH⁻. Subsequently Heřmánek, Schaeffer, and their coworkers used the nitrosation of decaborane followed by acidification to obtain the arachno azanonaborane B₈H₁₂NH.² Todd and co-workers³ showed that careful control of the nitrosation of decaborane gave the nido azadecaborane derivative B₉H₁₁NH, having a structure closely related to that of decaborane (Fig. 1). The 11-vertex closo cobaltaazaborane derivative CpCoNHB₉H₉ (Cp = η⁵-C₅H₅) was synthesized from B₉H₁₁NH by reaction with NaCp/CoCl₂.

Fig. 1 Some experimentally known azaborane derivatives. In Fig. 1 and 2 unlabeled vertex atoms are boron atoms and terminal hydrogen atoms are omitted for clarity.

The NH vertices found in the azaboranes are donors of four skeletal electrons in accord with the Wade–Mingos rules.^4,5,6 The initial azaborane syntheses often lead to electron-rich nido and arachno structures as exemplified by the metal-free structures in Fig. 1. Nevertheless, the 10-vertex and 12-vertex closo structures B₉H₉NH and B₁₁H₁₁NH have been synthesized and structurally characterized by X-ray crystallography (Fig. 2).⁷ The 10-vertex azaborane B₉H₉NH has the nitrogen atom at a degree 4 rather than a degree 5 vertex of the bicapped square antiprismatic B₉N cage. The NH vertices in the azaboranes can be deprotonated with bases and the resulting anions alkylated to give NR vertices without disturbing the azaborane cage structure. In addition, azaborane cages can be expanded by thermal reactions with borane adducts BH₃·L (L = Me₂S, THF, etc.).^8,9 This method was used to synthesize the closo icosahedral azadodecaborane, B₁₁H₁₁NH.

Fig. 2 The two known closo azaboranes. Hydrogen atoms are omitted for clarity.

The synthesis of the 11-vertex CpCoNHB₉H₉ raises the question whether other cobaltaazaboranes CpCoNHB_n−2H_n−2 with different numbers of vertices can be synthesized. As noted above, metal-free polyhedral azaboranes are available for the syntheses of such species. According to the Wade–Mingos rules^4–6 such n-vertex cobaltaazaboranes CpCoNHB_n−2H_n−2 have the 2n + 2 skeletal electrons required for the most spherical deltahedra (Fig. 3 and 4). We now report density functional theory studies on such cobaltaazaboranes having from eight to twelve vertices. This work has led to the discovery of low-energy structures violating the Wade–Mingos rules by having central CoNB_n−2 polyhedra that are not the most spherical deltahedra. This can be related to the preference of the nitrogen atom for vertices of lower degrees. The most extreme example occurs in the 8-vertex system where the lowest energy CpCoNHB₆H₆ structure is not the most spherical 8-vertex deltahedron, namely the bisdisphenoid, but instead the D_3d antipodally bicapped octahedron with two degree 3 vertices and six degree 5 vertices (Fig. 4). The nitrogen atom in this CpCoNHB₆H₆ structure is located at one of the degree 3 vertices.

Fig. 3 The most spherical closo deltahedra having from 9 to 12 vertices found in n-vertex metallaboranes having 2n + 2 Wadean skeletal electrons. In Fig. 3 and 4, vertices of degrees 3, 4, 5, and 6 are purple, red, black, and green, respectively.

Fig. 4 Comparison of the bisdisphenoid and the antipodally bicapped octahedron, both of which are 8-vertex deltahedra.

2. Theoretical methods

Full geometry optimizations were carried out on the CpCoNB_n−2H_n−1 systems (n = 8 to 12) at the B3LYP/6-31G(d) level of theory.^10–13 The lowest energy structures were then reoptimized at a higher level, i.e., M06L/6-311G(d,p), and these are the structures presented in the manuscript.¹⁴ The initial structures were chosen by systematic substitution of one BH vertex by a CpCo vertex in various polyhedral frameworks, followed by all possible substitutions of a boron atom in the resulting cobaltaborane by a nitrogen atom. The large number of different starting structures for the optimizations included 101 structures of the 8-vertex clusters CpCoNB₆H₇, 68 structures of the 9-vertex clusters CpCoNB₇H₈, 97 structures of the 10-vertex clusters CpCoNB₈H₉, 140 structures of the 11-vertex clusters CpCoNB₉H₁₀, and 35 structures of the 12-vertex clusters CpCoNB₁₀H₁₁ (see the ESI†). The natures of the stationary points after optimization were checked by calculations of the harmonic vibrational frequencies. If significant imaginary frequencies were found, the optimizations were continued by following the normal modes corresponding to imaginary frequencies to insure that genuine minima were obtained.

All calculations were performed using the Gaussian 09 package¹⁵ with the default settings for the SCF cycles and geometry optimization, namely the fine grid (75 302) for numerically evaluating the integrals, 10⁻⁸ hartree for the self-consistent field convergence, maximum force of 0.000450 hartree/bohr, RMS force of 0.000300 hartree/bohr, maximum displacement of 0.001800 bohr, and RMS displacement of 0.001200 bohr.

The CpCoNHB_n−2H_n−2 (n = 8 to 12) structures are numbered as B(n − 2)NCo-x where n is the total number of polyhedral vertices, and x is the relative order of the structure on the energy scale (M06L/6-311G(d,p) including zero-point corrections). The lowest energy optimized structures discussed in this paper are depicted in Fig. 5 to 9. Only the lowest energy and thus potentially chemically significant structures are considered in detail in this paper. All of the low-energy structures reported in this paper are closed-shell structures with substantial HOMO–LUMO gaps ranging from 1.5 to 3.3 eV (Tables S1B to S5B of the ESI†). More comprehensive lists of structures, including higher energy structures, are given in the ESI.†

Fig. 5 The four optimized CpCoNHB₆H₆ structures within 15 kcal mol⁻¹ of the global minimum.

3. Results

Four CpCoNHB₆H₆ structures of the 8-vertex CpCoNHB₆H₆ system were found within 15 kcal mol⁻¹ of the global minimum (Fig. 5 and Table 1). The central CoNB₆ polyhedron in the lowest energy such structure B6NCo-1 is not the most spherical 8-vertex deltahedron expected by the Wade–Mingos rules^4–6 but instead an antipodally bicapped octahedron with two degree 3 vertices capping opposite faces (Fig. 4). This allows the nitrogen atom in B6NCo-1 to occupy one of the degree 3 vertices so that the local tetrahedral environment of the nitrogen atom is similar to that of an ammonium ion. The formal positive charge on such a nitrogen atom can be balanced by a formal negative charge on the antipodally situated tetrahedral borate ion with a local environment similar to BH₄⁻.

Table 1 Details of the four 8-vertex CpCoNHB₆H₆ structures within 15 kcal mol⁻¹ of the global minimum. Adjacent Co–N distances corresponding to polyhedral edges are indicated in italics

Structure (symmetry)	ΔE kcal mol^−1	Vertex degrees		Co–N distance	HOMO–LUMO gap, eV	Polyhedron
		Co	N
B6NCo-1 (Cs)	0.0	5	3	2.678 Å	2.90	Bicap. octahed.
B6NCo-2 (C1)	1.9	5	4	1.957 Å	2.31	Bisdisphenoid
B6NCo-3 (Cs)	7.4	5	4	2.724 Å	2.27	Bisdisphenoid
B6NCo-4 (C1)	10.5	4	4	3.028 Å	2.27	Bisdisphenoid

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The remaining low-energy CpCoNHB₆H₆ structures have a central CoNB₆ bisdisphenoid as expected by the Wade–Mingos rules (Fig. 4 and 5; Table 1).^4–6 The two lowest energy such structures, namely B6NCo-2 and B6NCo-3 lying 3.8 and 7.4 kcal mol⁻¹, respectively, in energy above B6NCo-1, have the cobalt and nitrogen atoms at degree 5 and 4 vertices, respectively. This is in accord with the expected preferences of cobalt for high degree vertices and nitrogen for low degree vertices. Structure B6NCo-2 has a Co–N polyhedral edge of length 1.957 Å whereas in B6NCo-3 the cobalt and nitrogen atoms do not occupy adjacent vertices. The higher energy CpCoNHB₆H₆ structure B6NCo-4, lying 10.5 kcal mol⁻¹ in energy above B6NCo-1, has the cobalt and nitrogen atoms at non-adjacent degree 4 vertices.

The three lowest energy structures of the 9-vertex CpCoNHB₇H₇ system are all based on the most spherical deltahedron, namely the tricapped trigonal prism (Fig. 6 and Table 2). The lowest energy such structure, namely B7NCo-1, is the unique tricapped trigonal prism structure with the cobalt atom at a degree 5 vertex and the nitrogen atom at a non-adjacent degree 4 vertex. The next CpCoNHB₇H₇ structure in energy, namely B7NCo-2 at 3.8 kcal mol⁻¹ above B7NCo-1, also has the cobalt and nitrogen atoms at degree 5 and degree 4 vertices, respectively. However, in B7NCo-2 the cobalt and nitrogen atoms are adjacent forming a deltahedral edge of length 1.915 Å. The third CpCoNHB₇H₇ structure B7NCo-3, lying 13.0 kcal mol⁻¹ in energy above B7NCo-1, is the unique tricapped trigonal prismatic structure with both the cobalt and nitrogen atoms at degree 4 vertices. These degree 4 vertices in the tricapped trigonal prism are necessarily non-adjacent. The low HOMO–LUMO gap of 1.53 eV for B7NCo-3 relative to the HOMO–LUMO gaps greater than 2 eV for the isomeric CpCoNHB₇H₇ structures (Table 2) may relate to the presence of the cobalt atom at a degree 4 rather than a degree 5 vertex in the CoNB₇ tricapped trigonal prism.

Fig. 6 The five optimized CpCoNHB₇H₇ structures within 17 kcal mol⁻¹ of the global minimum.

Table 2 Details of the five CpCoNHB₇H₇ structures within 17 kcal mol⁻¹ of the global minimum. Adjacent Co–N distances corresponding to polyhedral edges are indicated in italics

Structure (symmetry)	ΔE kcal mol^−1	Vertex degrees		Co–N distance	HOMO–LUMO gap, eV	Polyhedron
		Co	N
B7NCo-1 (Cs)	0.0	5	4	2.905 Å	2.35	Tricap trig prism
B7NCo-2 (C1)	3.8	5	4	1.915 Å	2.08	Tricap trig prism
B7NCo-3 (Cs)	13.0	4	4	2.984 Å	1.53	Tricap trig prism
B7NCo-4 (C1)	13.2	5	3	2.682 Å	2.15	Cap bisdisphenoid
B7NCo-5 (Cs)	15.3	5	3	2.659 Å	3.23	Cap bisdisphenoid

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The next two 9-vertex CpCoNHB₇H₇ structures in terms of energy, namely B7NCo-4 and B7NCo-5 at 13.2 and 15.3 kcal mol⁻¹, respectively, above B7NCo-1, violate the Wade–Mingos rules^4–6 by having central CoNB₇ capped bisdisphenoids rather than the most spherical tricapped trigonal prism. Such capped bisdisphenoids have a single degree 3 vertex for the nitrogen atom as well as two degree 4 vertices, five degree 5 vertices, and one degree 6 vertex. Interestingly, the cobalt atom in both B7NCo-4 and B7NCo-5 occupies a degree 5 vertex not adjacent to the nitrogen atom at the degree 3 vertex rather than the degree 6 vertex, which necessarily is adjacent to the degree 3 vertex. In B7NCo-4 the cobalt atom is located at a degree 5 vertex adjacent to the unique degree 6 vertex. However, in B7NCo-5 the cobalt atom is located at a degree 5 vertex not adjacent to the degree 6 vertex.

Unlike the CpCoNHB_nH_n structures with 8 and 9 vertices, the low-energy CpCoNHB_nH_n structures with 10, 11, and 12 vertices are all based on the most spherical deltahedra (Fig. 3). For the 10-vertex CpCoNHB₈H₈ system the lowest energy structure B8NCo-1 is the unique bicapped square antiprismatic structure with the cobalt and nitrogen atoms at non-adjacent degree 5 and 4 vertices, respectively (Fig. 7). The unique CpCoNHB₈H₈ structure B8NCo-2 with the cobalt and nitrogen atoms at adjacent degree 5 and 4 vertices, respectively, lies 7.5 kcal mol⁻¹ in energy above B8NCo-1. The unique structure B8NCo-3 with both the cobalt and nitrogen atoms at degree 4 vertices is a much higher energy structure, lying 19.0 kcal mol⁻¹ above B8NCo-1. The next CpCoNHB₈H₈ structure in energy, namely B8NCo-4 at 28.5 kcal mol⁻¹ above B8NCo-1, has the cobalt and nitrogen atoms at adjacent degree 5 vertices. The potential energy surface of the 10-vertex system CpCoNHB₈H₈ is obviously much simpler than that of the 8- and 9-vertex CpCoNHB_n−2H_n−2 (n = 8, 9) systems since only two CpCoNHB₈H₈ structures lie within the 17 kcal mol⁻¹ energy cutoff point used for the 8- and 9-vertex structures (Tables 1 and 2).

Fig. 7 The four optimized CpCoNHB₈H₈ structures within 36 kcal mol⁻¹ of the global minimum.

The lowest energy 11-vertex CpCoNHB₉H₉ structure B9NCo-1 is the unique structure with the cobalt and nitrogen atoms located at the degree 6 vertex and one of the degree 4 vertices of the most spherical 11-vertex deltahedron (Fig. 8). The cobalt and nitrogen atoms in B9NCo-1 are necessarily in adjacent positions forming a deltahedral edge of length 1.946 Å. The next three CpCoNHB₉H₉ structures in terms of energy, namely B9NCo-2, B9NCo-3, and B9NCo-4 lying 5.8, 11.7, and 15.2 kcal mol⁻¹ above B9NCo-1, are the three possible structures with the nitrogen atom at a degree 4 vertex and the cobalt atom at a non-adjacent degree 5 vertex.

Fig. 8 The four optimized CpCoNHB₉H₉ structures within 17 kcal mol⁻¹ of the global minimum.

The cobaltaazaborane CpCoNHB₉H₉ has been synthesized and shown by X-ray crystallography to have the lowest energy structure B9NCo-1 in accord with our theoretical predictions.³ The predicted Co–N distance in B9NCo-1 of 1.946 Å is essentially identical with the experimental Co–N distance of 1.942(7) Å. In addition the predicted five Co–B deltahedral edges in sequence around the base of the CoNB₅ hexagonal subpyramid in B9NCo-1 of 2.030, 2.305, 2.197, 2.197, and 2.305 Å are very close to the experimental values of 2.040, 2.309, 2.263, 2.252, and 2.314 Å.

Three structures are possible for the 12-vertex CpCoNHB₁₀H₁₀ system in which the central CoNB₁₀ unit is a “regular” icosahedron with all degree 5 vertices. These are the only low-energy CpCoNHB₁₀H₁₀ structures, lying within 3.5 kcal mol⁻¹ of each other (Fig. 9). The lowest energy such CpCoNHB₁₀H₁₀ structure B10NCo-1 has the cobalt and nitrogen atoms in adjacent positions forming a 2.027 Å icosahedral edge and is thus the ortho isomer. The highest energy icosahedral CpCoNHB₁₀H₁₀ structure B10NCo-3 is the para isomer with the cobalt and nitrogen atoms in antipodal positions. The lowest energy non-icosahedral CpCoNHB₁₀H₁₀ lies a gigantic 43.3 kcal mol⁻¹ above B10NCo-1 and thus is probably not chemically relevant. This C_s structure has the cobalt atom at a unique degree 6 vertex, the nitrogen atom at a unique degree 3 vertex, three degree 4 vertices, seven degree 5 vertices, and two equivalent quadrilateral faces.

Fig. 9 The three possible optimized CpCoNHB₁₀H₁₀ structures with a central CoNB₁₀ icosahedron having all degree 5 vertices.

4. Discussion

In metallaboranes containing heteroatoms the transition metals typically prefer higher degree vertices whereas carbon and nitrogen prefer lower degree vertices. This difference in the preferred vertex degrees of various vertex atoms can lead to deviations from sphericity. As a result, low-energy polyhedra different from the most spherical deltahedra (Fig. 3) found in the deltahedral borane dianions B_nH_n²⁻ (n = 6 to 12) having 2n + 2 Wadean skeletal electrons^4–6 might be found in isoelectronic polyhedral metallaboranes in which some of the boron vertices are replaced by heteroatom vertices. For the cobaltadicarbaboranes CpCoC₂B_n−3H_n−1, also with 2n + 2 Wadean skeletal electrons, the lowest energy structures are the same deltahedra found in the B_nH_n²⁻ anions.¹⁶ However, for the isoelectronic ferratricarbaboranes CpFeC₃B_n−4H_n−1, 8-vertex CpFeC₃B₄H₇ structures based on the less spherical hexagonal bipyramid are found to be of comparable energy to the most spherical bisdisphenoidal isomers.¹⁷ This can be related to the possibility of the three carbon atoms occupying three non-adjacent degree 4 vertices in the hexagonal bipyramid but not in the bisdisphenoid. In addition, low energy 10-vertex CpFeC₃B₆H₉ structures based on the isocloso 10-vertex deltahedron with three non-adjacent degree 4 vertices for the carbon atoms are comparable in energy with isomeric structures based on the most spherical bicapped square antiprism.

The preference of the nitrogen atom in the polyhedral cobaltaazaboranes CpCoNHB_n−2H_n−2 for lower degree vertices can lead to deviations from the most spherical deltahedra in the lowest energy structures. Such deviations from the most spherical deltahedra can even provide degree 3 vertices for the nitrogen atoms, which then have a local environment similar to the ammonium ion. Thus in the 8-vertex system the lowest energy CpCoNHB₆H₆ structure B6NCo-1 has a central CoNB₆ antipodally bicapped octahedron rather than a bisdisphenoid. This provides two degree 3 vertices, one of which is occupied by the nitrogen atom. However, only slightly higher energy isomeric CpCoNHB₆H₆ structures are based on the most spherical bisdisphenoid. For the 9-vertex CpCoNHB₇H₇ system the three lowest energy structures are the three possible structures based on the most spherical tricapped trigonal prism with the nitrogen atom at a degree 4 vertex. However, the central CoNB₇ polyhedron in the next two CpCoNHB₇H₇ structures in terms of relative energy is a most spherical 8-vertex bisdisphenoid with one of the triangular faces capped by the ninth vertex. This capping vertex provides a degree 3 vertex for the nitrogen atom. The lowest energy CpCoNHB₆H₆ structure B6NCo-1 (Fig. 5) and the CpCoNHB₇H₇ structures B7NCo-4 and B7NCo-5 (Fig. 6) represent unprecedented examples of metallaborane structures having a degree 3 vertex in a deltahedron with at least 8 vertices.

All of the central polyhedra in the 10- to 12-vertex CpCoNHB_n−2H_n−2 systems (n = 10, 11, 12) are the most spherical deltahedra (Fig. 2). These deltahedra for the 10- and 11-vertex systems have two degree 4 vertices. One of these degree 4 vertices is occupied by the nitrogen atom in all of the low-energy structures. The unique 10-vertex CpCoNHB₈H₈ structure with the cobalt atom at a degree 5 vertex and the nitrogen atom at a non-adjacent degree 4 vertex is the lowest energy structure by a significant margin of 7.5 kcal mol⁻¹ (Fig. 7). Similarly the unique 11-vertex CpCoNHB₉H₉ structure with the cobalt atom at the unique degree 6 vertex and the nitrogen atom at a degree 4 vertex is the lowest energy structure by 5.8 kcal mol⁻¹.

Three structures of the 12-vertex system CpCoNHB₁₀H₁₀ are possible with a central CoNB₁₀ “regular” icosahedron with all degree 5 vertices. All three such structures have similar energies within 3.5 kcal mol⁻¹ and lie more than 43 kcal mol⁻¹ in energy below the lowest energy structure not based on a “regular” icosahedron.

Acknowledgements

Funding from the Romanian Ministry of Education and Research, (Grant PN-II-ID-PCE-2012-4-0488) and the US National Science Foundation (Grant CHE-1057466) is gratefully acknowledged.

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Footnote

† Electronic supplementary information (ESI) available: Table S1A: initial CpCoNHB₆H₆ structures; Table S1B: distance table for the lowest-lying CpCoNHB₆H₆ structures; Table S1C: energy ranking for all the CpCoNHB₆H₆ structures; Table S2A: initial CpCoNHB₇H₇ structures; Table S2B: distance table for the lowest-lying CpCoNHB₇H₇ structures; Table S2C: energy ranking for all the CpCoNHB₇H₇ structures; Table S3A: initial CpCoNHB₈H₈ structures; Table S3B: distance table for the lowest-lying CpCoNHB₈H₈ structures; Table S3C: energy ranking for all the CpCoNHB₈H₈ structures; Table S4A: initial CpCoNHB₉H₉ structures; Table S4B: distance table for the lowest-lying CpCoNHB₉H₉ structures; Table S4C: energy ranking for all the CpCoNHB₉H₉ structures; Table S5A: initial CpCoNHB₁₀H₁₀ structures; Table S5B: distance table for the lowest-lying CpCoNHB₁₀H₁₀ structures; Table S5C. Energy ranking for all the CpCoNHB₁₀H₁₀ structures; complete Gaussian 09 reference (ref. 15). See DOI: 10.1039/c5ra09849a

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