# Polyhedral Dicobaltadithiaboranes and Dicobaltdiselenaboranes as Examples of Bimetallic Nido Structures without Bridging Hydrogens

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}Co

_{2}E

_{2}B

_{n}

_{−4}H

_{n}

_{−4}(E = S, Se; n = 8 to 12) have been investigated via the density functional theory. Most of the lowest-energy structures in these systems are generated from the (n + 1)-vertex most spherical closo deltahedra by removal of a single vertex, leading to a tetragonal, pentagonal, or hexagonal face depending on the degree of the vertex removed. In all of these low-energy structures, the chalcogen atoms are located at the vertices of the non-triangular face. Alternatively, the central polyhedron in most of the 12-vertex structures can be derived from a Co

_{2}E

_{2}B

_{8}icosahedron with adjacent chalcogen (E) vertices by breaking the E–E edge and 1 or more E–B edges to create a hexagonal face. Examples of the arachno polyhedra with two tetragonal and/or pentagonal faces derived from the removal of two vertices from isocloso deltahedra were found among the set of lowest-energy Cp

_{2}Co

_{2}E

_{2}B

_{n}

_{−4}H

_{n}

_{−4}(E = S, Se; n = 8 and 12) structures.

## 1. Introduction

_{n}H

_{n}

^{2−}as well as those of the isoelectronic carborane monoanions CB

_{n}

_{−1}H

_{n}

^{−}and neutral dicarbaboranes C

_{2}B

_{n}

_{−2}H

_{n}are based on the most spherical deltahedra, which are known as the closo deltahedra (Figure 1) [1,2]. Except for the 13-vertex systems, the most spherical deltahedra have exclusively triangular faces with vertex degrees as nearly similar as possible. The 11- and 13-vertex systems contain 1 and 2 degree-6 vertices, respectively, whereas the other closo polyhedra have exclusively degree-4 and -5 vertices, for which the degree of a vertex is defined as the number of edges meeting at the vertex in question. The chemical bonding in these polyhedral boranes and carboranes is based on 2n + 2 skeletal electrons for an n-vertex system, with each BH and CH vertex contributing 2 and 3 skeletal electrons, respectively, after providing an electron for the external B–H or C–H bond. This is a key aspect of the Wade–Mingos rules [3,4,5] relating polyhedral geometry to skeletal electron count. A reasonable chemical bonding model for these deltahedra consists of a resonance hybrid of canonical structures containing a single n-center bond composed of orbitals from each of the n-vertex atoms overlapping at the center of the polyhedron supplemented by n two-center, two-electron bonds on the surface of the polyhedron [6]. This structural model accounts for the 2n + 2 skeletal electrons in the stable closo deltahedral borane structures. The delocalization implicit in this bonding model, particularly the presence of the multicenter core bond, is consistent with the interpretation of these species as three-dimensional aromatic systems [7,8].

_{10}H

_{14}) as a precursor, whereas the research of the Grimes group [10] studied metallaboranes obtained from pentaborane (B

_{5}H

_{9}) as a precursor. The chemistry of polyhedral boranes and their transition metal derivatives remains of interest even after approximately half a century following the discovery of the original metallaboranes with the possibilities of applications in medicine [11,12] and catalysis [13].

_{n}H

_{n+}

_{4}(n = 2, 5, 6, 8, 9, 10) exhibiting nido structures, of which B

_{10}H

_{14}is the most stable [19,20], predates that of the more stable closo boranes by going back to the original boron hydride syntheses of Stock. The structures of B

_{5}H

_{9}and B

_{6}H

_{10}are derived by the removal of a degree-4 vertex from an octahedron and a degree-5 vertex from a pentagonal bipyramid, respectively, thereby generating a square and a pentagonal face, respectively (Figure 3). The structures of the larger B

_{n}H

_{n+}

_{4}(n = 8, 9, 10) boranes are derived by removal of the unique degree-6 vertex from the corresponding (n + 1) vertex isocloso deltahedron. The polyhedral frameworks of all of the B

_{n}H

_{n}

_{+4}boranes (n = 5, 6, 8, 9, 10) all have n BH vertices with the four “extra” hydrogen atoms bridging the B–B edges surrounding the non-triangular face. A relatively large non-triangular face such as a hexagonal hole versus a pentagonal or tetragonal face provides more space for the four hydrogen atoms bridging the hole B–B edges.

_{4}B

_{n}

_{−4}H

_{n}provide the required 2n + 4 skeletal electrons. In this connection, species of the type C

_{4}B

_{n}

_{−4}R

_{n}(R = H or alkyl) are known experimentally to have such structures with 6 [21,22], 8 [23,24], 10 [25,26,27,28], 11 [29], and 12 [30,31,32,33,34,35,36] vertices. Furthermore, the structures and energetics of the tetracarbaboranes have been studied by using modern density functional theory methods [37].

_{2}B

_{n}

_{−2}H

_{n}

_{−2}(E = S, Se) structure since bare sulfur or selenium vertices are each donors of four skeletal electrons after diverting 2 of their 6 valence electrons to an external lone pair. In this connection, the 11-vertex nido-B

_{9}H

_{9}E

_{2}(E = S, Se) structures have been synthesized and shown via X-ray crystallography to have a central polyhedron obtained via the removal of one vertex from an icosahedron [38].

_{2}B

_{9}H

_{9}has been synthesized and shown to have a ni-13〈VI〉 structure derived via the removal of a degree-6 vertex from a docosahedron, which is the 13-vertex closo deltahedron [35]. This structure can also be derived from a central CoSe

_{2}B

_{9}icosahedron with a Se–Se edge by breaking the Se–Se edge and an adjacent Se–B edge to generate an SeCoSeBB pentagonal face, leaving a degree-3 selenium vertex. This structure is shown by density functional theory to be 1 of the 3 lowest-energy structures lying within 1 kcal/mol of each other [39].

_{2}Co

_{2}S

_{2}B

_{7}H

_{7}with 2 pentamethylcyclopentadienylcobalt vertices (Cp*Co) have been isolated by Kang and Sneddon [40] from the mixture that was obtained from the reaction between LiCp*, NaS

_{2}B

_{7}H

_{8}, and CoCl

_{2}(Figure 5). Attempts to obtain definitive structural information on these species via X-ray crystallography were prevented by disorder problems. However, the poor X-ray data were sufficient to indicate the relative positions of the cobalt atom and 11-vertex Co

_{2}S

_{2}B

_{7}geometries obtained via removal from a vertex from a central icosahedron. Furthermore, 1 of the 3 structures appears to be an ultimate pyrolysis product at 300 °C. The structures were assigned on the basis of the

^{11}B NMR spectra. In addition, trace quantities of a 10-vertex Cp*

_{2}Co

_{2}S

_{2}B

_{6}H

_{6}structure were obtained, which was suggested to have a decaborane-like structure on the basis of its

^{11}B NMR.

_{2}Co

_{2}E

_{2}B

_{n}

_{−4}H

_{n}

_{−4}(E = S, Se; n = 8, 9, 10, 11, 12) systems with unsubstituted cyclopentadienyl rings. In addition, we have included the Cp*

_{2}Co

_{2}S

_{2}B

_{7}H

_{7}system with pentamethylcyclopentadienyl (Cp*) rings in this study for comparison with the reported experimental data. This theoretical study extends the previous study [36] of the dicobaltadiselenaboranes by introducing a second cobalt atom into the metallaborane polyhedron. This provides an opportunity to assess preferences for a pair of cobalt atoms in these structures to occupy adjacent bonding positions or to be as far removed from each other as possible or something in between. The dicobaltadithiaboranes and dicobaltadiselena boranes are of interest in representing the first examples of nido structures without bridging hydrogen atoms containing two transition metal vertices in the underlying polyhedron.

## 2. Results and Discussion

#### 2.1. The 11-Vertex Systems Cp_{2}Co_{2}E_{2}B_{7}H_{7} (E = S, Se)

_{2}Co

_{2}E

_{2}B

_{7}H

_{7}(E = S, Se) systems within 15 kcal/mol of the lowest-energy structure (Figure 6 and Table 1). The central ni-11〈V〉 polyhedron in all of the eight structures can be derived from an icosahedron via the removal of one vertex, leaving a pentagonal face that is similar to the dicarbollide anion C

_{2}B

_{9}H

_{12}

^{−}that was originally used by Hawthorne and co-workers [9] to synthesize a variety of transition metal complexes having a central MC

_{2}B

_{9}icosahedron. For both Cp

_{2}Co

_{2}E

_{2}B

_{7}H

_{7}(E = S, Se) systems, the lowest-energy structures

**B7Co2E2-1**(E = S, Se) have both cobalt atoms and both chalcogen atoms at the surface of the pentagonal face and, thus, at degree-4 vertices. This is the most prevalent example of generating an n-vertex nido polyhedral borane by the removal of a vertex from an (n + 1)-vertex closo deltahedral borane. Furthermore, in each of the 8 low-energy Cp

_{2}Co

_{2}E

_{2}B

_{7}H

_{7}structures, both chalcogen atoms are located at the degree-4 pentagonal face vertices rather than at interior degree-5 vertices. This is consistent with the preference of chalcogen atoms for lower degree vertices in polyhedral selena- and thiaboranes.

_{2}Co

_{2}S

_{2}B

_{7}H

_{7}complexes have been isolated by Kang and Sneddon in small quantities from the reaction between LiCp*, NaS

_{2}B

_{7}H

_{8}, and CoCl

_{2}which they designated by the Roman numerals III, IV, and V in their paper (Figure 5) [37]. Extensive disorder prevented complete X-ray structure determinations on these molecules beyond location of the cobalt atoms. On the basis of

^{11}B NMR and 2D

^{11}B-

^{11}B COSY NMR, Kang and Sneddon assigned structures analogous to

**B7Co2S-1**,

**B7Co2S-2**, and

**B7Co2S-3**to III, IV, and V, respectively. We found that complete substitution of hydrogen atoms with methyl groups did not affect the relative energy ordering of the 3 lowest-energy structures with the relative energies of the Cp* structures

**B7Co2S-1***,

**B7Co2S-2***, and

**B7Co2S-3***being 0.0, 0.6, and 6.7 kcal/mol, respectively. What is strange is the observation that the Kang/Sneddon isomer III, which has the assigned structure

**B7Co2S2-1***and has both cobalt atoms as well as both sulfur atoms located on pentagonal face vertices, is converted ultimately upon heating to 300 °C to the Kang/Sneddon isomer V (Figure 5), which was assigned the higher-energy structure

**B7Co2S2-3***, as it has both cobalt atoms located at degree-5 interior vertices. This is contrary to expectation because pyrolysis, particularly to a temperature as high as 300 °C, would be expected to give a lower-energy isomer rather than a higher-energy isomer. Our theoretical studies cast some doubt about the structure assignments of III, IV, and V that were given by Kang and Sneddon in their 1988 study [37]. Note that the predicted Co

^{…}Co distances in

**B7Co2S-1**,

**B7Co2S-2**, and

**B7Co2S-3**are all approximately 3.8 to 3.9 Å, so the determination of these distances by an otherwise incomplete X-ray crystallography study on an extensively disordered system would not be sufficient to distinguish between these three structures. The improvements in X-ray crystallography methodology in the 35 years since the Kang/Sneddon report of the 3 Cp*

_{2}Co

_{2}S

_{2}B

_{7}H

_{7}isomers might provide a resolution to this dilemma.

#### 2.2. The 12-Vertex Systems Cp_{2}Co_{2}E_{2}B_{8}H_{8} (E = S, Se)

_{2}Co

_{2}E

_{2}B

_{8}H

_{8}(E = S, Se) systems up to 9 kcal/mol (E = S) and 12 kcal/mol (E = Se) in energy (Figure 7 and Table 2). These structures are of three types. The polyhedra for the lowest-energy Cp

_{2}Co

_{2}S

_{2}B

_{8}H

_{8}structure

**B8Co2S2-1**, as well as those for 4 of the 5 next higher-energy structures

**B8Co2S2-2**,

**B8Co2S2-3**,

**B8Co2S2-5**, and

**B8Co2S2-6**, lying 3.0, 3.1, 3.8, and 5.6 kcal/mol in energy above

**B8Co2S2-1**, respectively, can be derived from a Co

_{2}E

_{2}B

_{8}icosahedron with an S–S edge by breaking the S–S edge and at least one S–B edge to create typically a gaping, bent hexagonal face. These five structures can be divided in two categories. In

**B8Co2S2-1**,

**B8Co2S2-5**, and

**B8Co2S2-6,**the cobalt atoms are located in meta (non-adjacent, non-antipodal) positions of the original octahedron. However, in

**B8Co2S2-2**and

**B8Co2S2-4**, the cobalt atoms are located in para (antipodal) positions in the original icosahedron.

_{2}Co

_{2}Se

_{2}B

_{8}H

_{8}derivatives leads to a different energy ordering of the 9 lowest-energy structures (Table 2). The lowest-energy Cp

_{2}Co

_{2}Se

_{2}B

_{8}H

_{8}structure

**B8Co2Se2-1**and the higher-energy structure

**B8Co2Se2-4**, which lies 4.0 kcal/mol higher in energy, are exceptional among the complete series of Cp

_{2}Co

_{2}E

_{2}B

_{n}

_{−4}H

_{n}

_{−4}(n = 8 to 12) structures in exhibiting ideal C

_{2v}symmetry, whereas all of the remaining structures of this type have the lower-symmetry point groups of C

_{1}, C

_{2}, or C

_{s}. These 2 structures are ni-12〈IV〉 structures derived from the 13-vertex closo deltahedron, namely, the docosahedron (Figure 1), by the removal of the unique degree-4 vertex, thereby creating a tetragonal face with alternating degree-5 and degree-4 vertices. In both

**B8Co2Se2-1**and

**B8Co2Se-4,**the tetragonal face has alternating cobalt and sulfur vertices. The Cp

_{2}Co

_{2}S

_{2}B

_{8}H

_{8}structures corresponding to

**B8Co2Se2-1**and

**B8Co2Se2-4**are

**B8Co2S-9**and

**B8Co2S-8**, respectively, which lie 9.0 and 7.9 kcal/mol in energy above

**B8Co2S-1**.

_{2}Co

_{2}E

_{2}B

_{8}H

_{8}(E = S, Se), structures, namely,

**B8Co2S-3**and

**B8Co2S-7**for E = S, which lie 3.1 and 7.1 kcal/mol, respectively, in energy above

**B8Co2S-1**, and

**B8Co2Se-5**and

**B8Co2Se-9**, respectively, which lie 8.2 and 12.3 kcal/mol, respectively, in energy above

**B8Co2Se2-1**, can be considered to be arachno ar-12〈V,V〉 structures that are obtained by removing 2 vertices from a 14-vertex deltahedron. However, the central 14-vertex deltahedron from which these structures are derived is not the 14-vertex closo deltahedron, namely, the D

_{6d}bicapped hexagonal antiprism with 2 degree-6 vertices in antipodal positions, as well as 12 degree-5 vertices, but instead, it is a less symmetrical 14-vertex deltahedron with 3 degree-6 vertices, 10 degree-5 vertices, and 1 degree-4 vertex (Figure 8). This 14-vertex deltahedron is closely related to the 14-vertex polyhedron in experimentally known Cp*

_{2}Ru

_{2}C

_{2}B

_{10}H

_{12}by lengthening an edge connecting a degree-6 vertex with a degree-5 vertex [41,42].

#### 2.3. The Cp_{2}Co_{2}E_{2}B_{n−4}H_{n−4} (E = S, Se) Systems Having 8 to 10 Vertices

_{2}E

_{2}B

_{4}polyhedra in 7 of the 8 lowest-energy structures of the 8-vertex Cp

_{2}Co

_{2}E

_{2}B

_{4}H

_{4}(E = S, Se) systems (Figure 9 and Table 3) are all derived by the removal of a vertex from the closo 9-vertex deltahedron, namely, the tricapped trigonal prism (Figure 1). Removal of a degree-4 vertex from the tricapped, trigonal prism gives the bicapped trigonal prism, which is found in the lowest-energy structures

**B4Co2E2-1**(E = S, Se), as well as the higher-energy structures

**B4C2S2-2**and

**B4Co2Se2-5**, which lie ~6 kcal/mol in energy above the lowest-energy structures (Table 3). In the lowest-energy structure

**B4Co2E2-1**, the atoms of the open tetragonal face are alternating cobalt and chalcogen atoms with all four boron atoms located at interior vertices. The other bicapped trigonal prismatic Cp

_{2}Co

_{2}E

_{2}B

_{4}H

_{4}(E = S, Se) structures have the two sulfur atoms as well as one of the cobalt atoms at the open tetragonal face, with the other cobalt atom at an interior vertex.

_{2}Co

_{2}Se

_{2}B

_{4}H

_{4,}the 2 low-energy bicapped trigonal prismatic structures

**B4Co2Se-1**and

**B4Co2Se-2**are essentially isoenergetic, as they lie within ~1 kcal/mol of each other (Figure 9 and Table 3). The lowest-energy Cp

_{2}Co

_{2}Se

_{2}B

_{4}H

_{4}ni-8〈V〉 structure

**B4Co2Se2-3**, which is derived from a tricapped trigonal prism by removing a degree-5 rather than a degree-4 vertex, lies 11.1 kcal/mol above

**B4Co2Se-1**. In total, 4 more ni-8〈V〉 Cp

_{2}Co

_{2}Se

_{2}B

_{4}H

_{4}structures, namely,

**B4Co2Se2-4**,

**B4Co2Se2-5**,

**B4Co2Se2-6**, and

**B4Co2Se2-8,**lie in the energy range of 11 to 15 kcal/mol above

**B4Co2Se2-1**. The potential energy surface of the corresponding 8-vertex sulfur system Cp

_{2}Co

_{2}Se

_{2}B

_{4}H

_{4}is significantly different since 3 of the 5 ni-8〈V〉 structures

**B4Co2S2-2**,

**B4Co2S2-3**, and

**B4Co2S2-4**lie within ~2 kcal/mol of the lowest-energy structure

**B4Co2S2-1**and below the higher-energy, bicapped trigonal prism isomer

**B4Co2S2-5**. In all eight lowest-energy Cp

_{2}Co

_{2}E

_{2}B

_{4}H

_{4}(E = S, Se) structures, both sulfur atoms lie on tetragonal or pentagonal face vertices, which is consistent with the preference of sulfur for lower degree vertices in borane polyhedra.

_{2}Co

_{2}E

_{2}B

_{4}H

_{4}(E = S, Se) structures,

**B4Co2S2-8**and

**B4Co2Se2-7**, which lie at 10.3 and 14.9 kcal/mol in energy, respectively, above the corresponding

**B4Co2E2-1**structure, are not derived by removing a vertex from a tricapped trigonal prism (Figure 9 and Table 3). Instead, the central Co

_{2}S

_{2}B

_{4}polyhedron in these structures is generated via the removal of the 2 degree-4 vertices that are bridged by the unique degree-6 vertex from the 10-vertex isocloso deltahedron of ideal C

_{3v}symmetry. This leads to an arachno 8-vertex ar-8〈IV,IV〉 structure with 2 tetragonal faces sharing a cobalt atom and a sulfur atom. The process of removing 2 degree-4 vertices from the 10-vertex isocloso deltahedron to give the 8-vertex Cp

_{2}Co

_{2}E

_{2}B

_{4}H

_{4}structures

**B4Co2S2-8**and

**B4Co2Se2-7**is analogous to the process of removing a degree-4 and a degree-5 vertex from a 14-vertex isocloso 14-vertex deltahedron (Figure 8) to give the 12-vertex ar-14〈IV,V〉 Cp

_{2}Co

_{2}E

_{2}B

_{8}H

_{8}structures

**B8Co2S23**and

**B8Co2S27**(Figure 7) that are discussed above.

_{2}Co

_{2}E

_{2}B

_{5}H

_{5}(E = S, Se) structures (Figure 10 and Table 4) are all derived from the 10-vertex closo deltahedron, namely, the bicapped square antiprism, by removing either a degree-4 vertex or a degree-5 vertex. Whether a degree-4 vertex is removed to give a capped square antiprism or a degree-5 vertex is removed to give a ni-9〈V〉 structure with a pentagonal face makes relatively little difference in energy since the 6 structures lying within 7 kcal/mol of the lowest-energy structures

**B5Co2E2-1**(E = S, Se) include 2 representatives of the former type and 4 representatives of the latter type. Both chalcogen vertices are always located at a non-triangular face in all of the low-energy structures.

_{2}Co

_{2}E

_{2}B

_{6}H

_{6}(E = S, Se) systems are the simplest of all, with only 3 structures lying within 16 kcal/mol (E = S) or 21 kcal/mol (E = Se) of the lowest-energy structures

**B6Co2E2-1**(Figure 11 and Table 5). The central Co

_{2}E

_{2}B

_{6}framework of all three structures is that of the very stable decaborane, B

_{10}H

_{14}, which is obtained via the removal of the unique degree-6 vertex of the closo 11-vertex deltahedron (sometimes called by the confusing name of “edge-coalesced icosahedron”) to create a bent hexagonal face. The structures

**B6Co2E2-1**, in which the hexagonal face has only boron and sulfur atoms with the sulfur atoms in opposite (“para”) positions, is favored energetically over the next lowest-energy structures

**B6Co2E2-1**by significant margins of ~11 kcal/mol (E = S) and ~12 kcal/mol (E = Se).

## 3. Theoretical Methods

_{n}H

_{n}

^{2−}polyhedra, for which a systematic substitution of 2 BH vertices with 2 CpCo units, followed by the substitution of 2 BH vertices with 2 chalcogen atoms (sulfur or selenium) led to the generation of a total of 5389 different starting structures for each of the Cp

_{2}Co

_{2}S

_{2}B

_{n}

_{−4}H

_{n}

_{−4}and Cp

_{2}Co

_{2}Se

_{2}B

_{n}

_{−4}H

_{n}

_{−4}systems (n = 8 to 12) (see the Supporting Information).

_{2}Co

_{2}E

_{2}B

_{n}

_{4}H

_{n}

_{−4}(E = S, Se; n = 8 to 12) are designated as

**B(n−4)Co2E2-x**throughout the text, where

**n**is the total number of polyhedral vertices, and

**x**is the relative ordering of the structure on the energy scale. Only the lowest-energy and, thus, potentially chemically significant structures are considered in detail in this paper. More comprehensive structural information including higher-energy structures, connectivity information not readily seen in the figures, and orbital energies and HOMO-LUMO gaps are provided in the Supporting Information.

## 4. Summary

_{2}E

_{2}B

_{n}

_{−4}polyhedra in the low-energy structures of the n-vertex polyhedral dicobaltadithiaboranes and dicobaltadiselenaboranes Cp

_{2}Co

_{2}E

_{2}B

_{n}

_{−4}H

_{n}

_{−4}(E = S, Se; n = 8 to 12) in general are generated from the (n + 1)-vertex most spherical closo deltahedra via the removal of a single vertex, leading to a tetragonal, pentagonal, or hexagonal face, depending on the degree of the vertex removed. In all of these low-energy structures, both chalcogen atoms are located on the non-triangular face vertices, reflecting the energetic preference of chalcogens for lower degree vertices. For the 8- and 9-vertex systems, the structures obtained via the removal of a degree-4 or degree-5 vertex from the corresponding (n + 1)-vertex closo deltahedra, namely, the tricapped trigonal prism and the bicapped square antiprism, have similar energies. The low-energy structures for the 10-vertex Cp

_{2}Co

_{2}E

_{2}B

_{6}H

_{6}(E = S, Se) systems all have the framework of the most stable B

_{n}H

_{n}

_{+4}borane, namely, B

_{10}H

_{14}with a bent hexagonal face. The lowest-energy of these 10-vertex Cp

_{2}Co

_{2}E

_{2}B

_{6}H

_{6}structures by significant margins exceeding 10 kcal/mol has only boron and both sulfur atoms located at the 6 hexagonal face vertices. The central polyhedra of all of the 11-vertex Cp

_{2}Co

_{2}E

_{2}B

_{7}H

_{7}structures are similar to the polyhedron of the dicarbollide anion C

_{2}B

_{9}H

_{12}

^{−}in being generated by loss of a vertex from a regular icosahedron to generate a pentagonal face.

_{2}Co

_{2}E

_{2}B

_{8}H

_{8}(E = S, Se) structures can be derived via the removal of a vertex from the 13-vertex closo deltahedron, namely, the docosahedron. However, the central polyhedron in most of the 12-vertex structures can also be derived from a Co

_{2}E

_{2}B

_{8}icosahedron with adjacent chalcogen vertices by breaking the E–E edge and 1 or more E–B edges to create a hexagonal hole.

_{2}Co

_{2}E

_{2}B

_{n}

_{−4}H

_{n}

_{−4}(E = S, Se; n = 8 to 12) structures. The central polyhedron of one structure within 15 kcal/mol of the lowest-energy structure in each of the 8-vertex Cp

_{2}Co

_{2}E

_{2}B

_{4}H

_{4}(E = S, Se) systems is an arachno polyhedron with 2 tetragonal faces sharing an edge that is derived from the 10-vertex isocloso deltahedron via the removal of the 2 degree-4 vertices bridged by the unique degree-6 vertex. In addition, 2 of the structures in each of the 12-vertex Cp

_{2}Co

_{2}E

_{2}B

_{8}H

_{8}(E = S, Se) systems are ar12〈IV,V〉 structures that are derived from the 14-vertex isocloso deltahedron that is found in the experimentally known Cp*

_{2}Ru

_{2}C

_{2}B

_{10}H

_{12}by removing the unique degree-4 vertex as well as a degree-5 vertex.

## Supplementary Materials

_{2}Co

_{2}S

_{2}B

_{4}H

_{4}structures. Table S1C: Distance matrices and energy rankings for the lowest energy Cp

_{2}Co

_{2}Se

_{2}gB

_{4}H

_{4}structures. Table S2A: Initial 9-vertex starting structures. Table S2B: Distance matrices and energy rankings for the lowest energy Cp

_{2}Co

_{2}S

_{2}B

_{5}H

_{5}structures. Table S2C: Distance matrices and energy rankings for the lowest energy Cp

_{2}Co

_{2}Se

_{5}B

_{5}H

_{5}structures. Table S3A: Initial 10-vertex starting structures. Table S3B: Distance matrices and energy rankings for the lowest energy Cp

_{2}Co

_{2}S

_{2}B

_{6}H

_{6}structures. Table S3C: Distance matrices and energy rankings for the lowest energy Cp

_{2}Co

_{2}Se

_{2}B

_{6}H

_{6}structures. Table S4A: Initial 11-vertex starting structures. Table S4B: Distance matrices and energy rankings for the lowest energy Cp

_{2}Co

_{2}S

_{2}B

_{7}H

_{7}structures. Table S4C: Distance matrices and energy rankings for the lowest energy Cp

_{2}Co

_{2}Se

_{2}B

_{7}H

_{7}structures. Table S5A: Initial 12-vertex starting structures. Table S5B: Distance matrices and energy rankings for the lowest energy Cp

_{2}Co

_{2}S

_{2}B

_{8}H

_{8}structures. Table S5C: Distance matrices and energy rankings for the lowest energy Cp

_{2}Co

_{2}Se

_{2}B

_{8}H

_{8}structures. Table S6A: Distance matrices and energy rankings for the lowest energy permethylated Cp*

_{2}Co

_{2}S

_{2}B

_{7}H

_{7}structures. Table S6B: Distance matrices and energy rankings for the lowest energy permethylated Cp*

_{2}Co

_{2}Se

_{2}B

_{7}H

_{7}structures. Table S7: Orbital energies and HOMO-LUMO gaps for the lowest Cp

_{2}Co

_{2}S

_{2}B

_{n−4}H

_{n−4}(n = 8 to 12) structures. Table S8: Orbital energies and HOMO-LUMO gaps for the lowest Cp

_{2}Co

_{2}Se

_{2}B

_{n−4}H

_{n−4}(n = 8 to 12) structures. Table S9: Orbital energies and HOMO-LUMO gaps for the lowest permethylated Cp*

_{2}Co

_{2}E

_{2}B

_{7}H

_{7}(E = S, Se) structures

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

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**Figure 1.**The most spherical closo deltahedra having 9 to 13 vertices from which the nido structures discussed in this paper are generated. Vertices of degrees 4, 5, and 6 are indicated in red, black, and green, respectively, in Figures 1, 2, and 8.

**Figure 3.**Generation of the binary B

_{n}H

_{n+}

_{4}borane structures from closo and isocloso deltahedra by the removal of the starred vertices.

**Figure 4.**Alternative ways of generating the central 12-vertex polyhedron of the experimentally known CpCoSe

_{2}B

_{9}H

_{9}from the 12-vertex icosahedron by breaking edges and from the 13-vertex docosahedron by removing the starred degree-5 vertex.

**Figure 5.**The 11-vertex frameworks suggested for the 3 Cp*

_{2}Co

_{2}S

_{2}B

_{7}H

_{7}isomers isolated by Kang and Sneddon from the reaction between LiCp*, NaS

_{2}B

_{7}H

_{9}, and CoCl

_{2}.

**Figure 6.**The eight lowest-energy Cp

_{2}Co

_{2}E

_{2}B

_{7}H

_{7}(E = S, Se) structures oriented to have the open pentagonal face at the bottom.

**Figure 8.**The D

_{6d}bicapped hexagonal antiprism as the 14-vertex closo deltahedron and a 14-vertex isocloso deltahedron derived from it via a diamond-square-diamond process that is the polyhedron found in the experimentally known Cp*

_{2}Ru

_{2}C

_{2}B

_{10}H

_{12}. The 12-vertex arachno Cp

_{2}Co

_{2}E

_{2}B

_{8}H

_{8}(E = S, Se) structures

**B8Co2S2-3**,

**B8Co2S2-7**,

**B8Co2Se2-5**, and

**B8Co2eS2-9**are obtained from this 14-vertex isocloso deltahedron by the removal of a degree-4 vertex and a degree-5 vertex, which are so situated that the resulting tetragonal and pentagonal faces share an edge.

**Figure 11.**The three lowest-energy Cp

_{2}Co

_{2}E

_{2}B

_{6}H

_{6}(E = S, Se) structures are oriented so that the bent hexagonal face is at the top.

**Table 1.**Relative energies (kcal/mol) and geometries of the lowest-energy 11-vertex Cp

_{2}Co

_{2}E

_{2}B

_{7}H

_{7}(E = Se, S) structures. In all 8 structures, the central Co

_{2}E

_{2}B

_{7}polyhedron is derived from an 11-vertex polyhedron that is obtained via the removal of a vertex from the 12-vertex regular icosahedron, leaving a pentagonal face.

Cp_{2}Co_{2}Se_{2}B_{7}H_{7} | Cp_{2}Co_{2}S_{2}B_{7}H_{7} | Vertex Degrees | Co^{…}S | Co^{…}Co (E = Se) | Pentagonal | ||||
---|---|---|---|---|---|---|---|---|---|

Structure (sym) | ∆E | Structure | ∆E | S | Co | Edges | Dist (Å) | WBI | Face Atoms |

B7Co2Se2-1 (C_{1}) | 0.0 | B7Co2S2-1 | 0.0 | 4, 4 | 4, 4 | 3 | 3.91 | 0.10 | SCoSBCo |

B7Co2Se2-2 (C_{1}) | 2.5 | B7Co2S2-2 | 1.8 | 4, 4 | 4, 5 | 3 | 3.81 | 0.10 | SCoSBB |

B7Co2Se2-3 (C_{1}) | 8.1 | B7Co2S2-3 | 6.2 | 4, 4 | 4, 5 | 2 | 3.79 | 0.09 | SCoBSB |

B7Co2Se2-4 (C_{1}) | 9.4 | B7Co2S2-4 | 7.7 | 4, 4 | 4, 5 | 2 | 3.71 | 0.10 | SCoBSB |

B7Co2Se2-5 (C_{s}) | 10.1 | B7Co2S2-5 | 18.2 | 4, 4 | 4, 5 | 2 | 3.68 | 0.09 | SCoSBB |

B7Co2Se2-6 (C_{s}) | 11.8 | B7Co2S2-6 | 19.9 | 4, 4 | 5, 5 | 2 | 3.73 | 0.09 | SBSBB |

B7Co2Se2-7 (C_{1}) | 13.5 | B7Co2S2-7 | 10.7 | 4, 4 | 4, 5 | 1 | 3.67 | 0.08 | SCoBSB |

B4Co2Se2-8 (C_{1}) | 14.7 | B7Co2S2-8 | 12.6 | 4, 4 | 5, 5 | 2 | 3.73 | 0.08 | SBSBB |

**Table 2.**Relative energies (kcal/mol) and geometries of the lowest-energy 12-vertex Cp

_{2}Co

_{2}E

_{2}B

_{8}H

_{8}(E = S, Se) structures.

Cp_{2}Co_{2}Se_{2}B_{8}H_{8} | Cp_{2}Co_{2}S_{2}B_{8}H_{8} | Vertex Degrees | Co^{…}S | Co^{…}Co (E = Se) | |||||
---|---|---|---|---|---|---|---|---|---|

Structure (sym) | ∆E | Structure | ∆E | S | Co | Edges | Dist (Å) | WBI | Polyhedron |

B8Co2Se2-1 (C_{2v}) | 0.0 | B8Co2S2-9 | 9.0 | 5, 5 | 4, 4 | 4 | 3.18 | 0.17 | ni-12〈IV〉 |

B8Co2Se2-2 (C_{1}) | 4.0 | B8Co2S2-1 | 0.0 | 3, 3 | 5, 5 | 2 | 3.85 | 0.12 | meta Co_{2} open icosahedron |

B8Co2Se2-3 (C_{1}) | 4.5 | B8Co2S2-5 | 3.8 | 3, 4 | 4, 5 | 2 | 3.83 | 0.09 | meta Co_{2} open icosahedron |

B8Co2Se2-4 (C_{2v}) | 5.3 | B8Co2S2-8 | 7.9 | 4, 4 | 5, 5 | 4 | 3.48 | 0.15 | ni-12〈IV〉 |

B8Co2Se2-5 (C_{1}) | 8.2 | B8Co2S2-3 | 3.1 | 3, 4 | 5, 5 | 1 | 3.61 | 0.09 | ar-12〈IV,V〉 |

B8Co2Se2-6 (C_{2}) | 8.2 | B8Co2S2-4 | 3.5 | 3, 3 | 5, 5 | 2 | 4.22 | 0.05 | para Co_{2} open icosahedron |

B8Co2Se2-7 (C_{2}) | 9.3 | B8Co2S2-2 | 3.0 | 3, 3 | 5, 5 | 2 | 4.82 | 0.08 | para Co_{2} open icosahedron |

B8Co2Se2-8 (C_{1}) | 11.8 | B8Co2S2-6 | 5.6 | 3, 4 | 5, 5 | 1 | 3.73 | 0.11 | meta Co_{2} open icosahedron |

B8Co2Se2-9 (C_{1}) | 12.3 | B8Co2S2-7 | 7.1 | 3, 4 | 5, 5 | 1 | 3.72 | 0.10 | ar-12〈IV,V〉 |

**Table 3.**Relative energies (kcal/mol) and geometries of the lowest-energy Cp

_{2}Co

_{2}E

_{2}B

_{4}H

_{4}(E = S, Se) structures.

Cp_{2}Co_{2}Se_{2}B_{4}H_{4} | Cp_{2}Co_{2}S_{2}B_{4}H_{4} | Vertex Degrees | Co^{…}S | Co^{…}Co (E = Se) | Non-Triang Face | |||||
---|---|---|---|---|---|---|---|---|---|---|

Structure (sym) | ∆E | Structure | ∆E | S | Co | Edges | Dist (Å) | WBI | Atoms | Polyhedron |

B4Co2Se2-1 (C_{2}) | 0.0 | B4Co2S2-1 | 0.0 | 4, 4 | 4, 4 | 4 | 3.39 | 0.12 | SCoSCo | bicap trig prism |

B4Co2Se2-2 (C_{s}) | 7.1 | B4Co2S2-5 | 5.2 | 4, 4 | 4, 4 | 3 | 3.75 | 0.14 | SCoSB | bicap trig prism |

B4Co2Se2-3 (C_{1}) | 11.1 | B4Co2S2-4 | 1.9 | 3, 3 | 4, 5 | 2 | 2.55 | 0.38 | SCoBBB | ni-8〈V〉 |

B4Co2Se2-4 (C_{1}) | 11.4 | B4Co2S2-3 | 0.7 | 3, 3 | 4, 5 | 2 | 3.44 | 0.10 | SCoBSB | ni-8〈V〉 |

B4Co2Se2-5 (C_{s}) | 12.5 | B4Co2S2-2 | 0.1 | 3, 3 | 5, 5 | 2 | 2.64 | 0.24 | SCoBSB | ni-8〈V〉 |

B4Co2Se2-6 (C_{1}) | 13.5 | B4Co2S2-6 | 6.5 | 3, 3 | 4, 5 | 3 | 2.59 | 0.40 | SCoSBB | ni-8〈V〉 |

B4Co2Se2-7 (C_{1}) | 14.9 | B4Co2S2-8 | 10.3 | 3, 4 | 4, 4 | 2 | 2.65 | 0.44 | 2 × SCoSB | ar-8〈IV,IV〉 |

B4Co2Se2-8 (C_{s}) | 15.3 | B4Co2S2-7 | 8.3 | 3, 3 | 4, 4 | 2 | 2.62 | 0.09 | SCoSBB | ni-8〈V〉 |

**Table 4.**Relative energies (kcal/mol) and geometries of the lowest-energy 9-vertex Cp

_{2}Co

_{2}E

_{2}B

_{5}H

_{5}(E = S, Se) structures.

Cp_{2}Co_{2}Se_{2}B_{5}H_{5} | Cp_{2}Co_{2}S_{2}B_{5}H_{5} | Vertex Degrees | Co^{…}S | Co^{…}Co (E = Se) | Non-Triang Face | |||||
---|---|---|---|---|---|---|---|---|---|---|

Structure (sym) | ∆E | Structure | ∆E | S | Co | Edges | Dist(Å) | WBI | Atoms | Polyhedron |

B5Co2Se2-1 (C_{1}) | 0.0 | B5Co2S2-1 | 0.0 | 3, 4 | 4, 5 | 2 | 3.67 | 0.11 | SCoBSB | ni-9〈V〉 |

B5Co2Se2-2 (C_{1}) | 0.7 | B5Co2S2-4 | 3.9 | 3, 4 | 4, 5 | 3 | 3.82 | 0.07 | SCoBSCo | ni-9〈V〉 |

B5Co2Se2-3 (C_{1}) | 0.9 | B5Co2S2-3 | 3.6 | 4, 4 | 4, 5 | 3 | 3.77 | 0.12 | SCoSB | capped square antiprism |

B5Co2Se2-4 (C_{1}) | 2.7 | B5Co2S2-2 | 2.8 | 3, 4 | 4, 5 | 3 | 3.40 | 0.07 | SCoBSB | ni-9〈V〉 |

B5Co2Se2-5 (C_{s}) | 3.7 | B5Co2S2-5 | 6.0 | 4, 4 | 4, 4 | 2 | 3.65 | 0.11 | SCoSB | capped square antiprism |

B5Co2Se2-6 (C_{1}) | 6.9 | B5Co2S2-6 | 6.2 | 3, 4 | 4, 5 | 2 | 3.72 | 0.12 | SBBSB | ni-9〈V〉 |

**Table 5.**Relative energies (kcal/mol) and geometries of the lowest-energy 10-vertex Cp

_{2}Co

_{2}E

_{2}B

_{6}H

_{6}(E = S, Se) structures. In all 3 structures, the central Co

_{2}E

_{2}B

_{6}polyhedron has the same geometry as the B

_{10}polyhedron in decaborane-14 with a hexagonal face.

Cp_{2}Co_{2}Se_{2}B_{6}H_{6} | Cp_{2}Co_{2}S_{2}B_{6}H_{6} | Vertex Degrees | Co^{…}S | Co^{…}Co (E = Se) | Hexagonal Face | |||||
---|---|---|---|---|---|---|---|---|---|---|

Structure (sym) | ∆E | Structure | ∆E | S | Co | Edges | Dist (Å) | WBI | Atoms | Polyhedron |

B6Co2Se2-1 (C_{2v}) | 0.0 | B6Co2S2-1 | 0.0 | 3, 3 | 5, 5 | 2 | 3.77 | 0.10 | SBBBBS | B_{10}H_{14} framework |

B6Co2Se2-2 (C_{1}) | 10.6 | B6Co2S2-2 | 12.4 | 3, 3 | 4, 5 | 2 | 3.78 | 0.09 | SBBSCoBS | B_{10}H_{14} framework |

B6Co2Se2-3 (C_{1}) | 15.7 | B6Co2S2-3 | 18.1 | 3, 3 | 4, 5 | 2 | 2.49 | 0.41 | SBBSCoBS | B_{10}H_{14} framework |

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**MDPI and ACS Style**

Attia, A.A.A.; Lupan, A.; King, R.B.
Polyhedral Dicobaltadithiaboranes and Dicobaltdiselenaboranes as Examples of Bimetallic *Nido* Structures without Bridging Hydrogens. *Molecules* **2023**, *28*, 2988.
https://doi.org/10.3390/molecules28072988

**AMA Style**

Attia AAA, Lupan A, King RB.
Polyhedral Dicobaltadithiaboranes and Dicobaltdiselenaboranes as Examples of Bimetallic *Nido* Structures without Bridging Hydrogens. *Molecules*. 2023; 28(7):2988.
https://doi.org/10.3390/molecules28072988

**Chicago/Turabian Style**

Attia, Amr A. A., Alexandru Lupan, and Robert Bruce King.
2023. "Polyhedral Dicobaltadithiaboranes and Dicobaltdiselenaboranes as Examples of Bimetallic *Nido* Structures without Bridging Hydrogens" *Molecules* 28, no. 7: 2988.
https://doi.org/10.3390/molecules28072988