DFT Studies on Structures, Stabilities, and Electron Affinities of closo

Article pubs.acs.org/Organometallics

DFT Studies on Structures, Stabilities, and Electron Affinities of closo-Supercarboranes C2Bn−2Hn (n = 13−20) Jiji Zhang,† Zhenyang Lin,*,‡ and Zuowei Xie*,† †

Department of Chemistry and State Key Laboratory of Synthetic Chemistry, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China ‡ Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China S Supporting Information *

ABSTRACT: Structures, stabilities, and electron affinities of closo-supercarboranes C2Bn−2Hn (n = 13−20) were studied with the aid of DFT calculations. The results regarding the relative stability of positional isomers for each clososupercarborane can be well understood with the qualitative rules established on the basis of early studies on 5- to 12-vertex carboranes C2Bn−2Hn (n = 5−12). The calculated cumulative BH addition energies for the most stable CAd (CAd = carbonatoms-adjacent) and CAp (CAp = carbon-atoms-apart) positional isomers (using the equation 1,2-C2B10H12 + (n − 12) BHinc → C2Bn−2Hn (n = 13−20), where BHinc is set as the energy difference between B6H10 and B5H9) suggest that the thermodynamic stability should not be the reason for nonobservation of 15-vertex CAp closo-carborane and other larger closo-supercarboranes C2Bn−2Hn (n = 16−20), and effort toward their synthesis is worth spending. The calculated HOMO−LUMO energy gaps show the relatively low chemical stability of 15-vertex closo-carboranes, explaining the difficulty of their experimental synthesis. Among these closo-supercarboranes studied, the 17-vertex carborane is predicted to be the most stable one, thus the most plausible target for experimental synthesis.

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INTRODUCTION Boron, an electron-deficient element with more valence orbitals than valence electrons, forms a large family of stable, in some cases exceedingly stable, cluster structures via multicenter bonding.1−3 Among the members of this family, carboranes are polyhedral boron hydride clusters each having one or more of its B(H) vertices replaced by C(H) units. Since the discovery and characterization of the icosahedral o-carborane (1,2-C2B10H12) in 1963,4 carboranes have attracted considerable interest over the last half-century.5 They show extraordinary thermal stability and unusual chemical reactivities. Thus, these cluster compounds are finding a broad range of applications encompassing organic synthesis, drug design, polymers, cancer therapy, catalysis, metal−organic frameworks, electronic devices, and more.5 closo-Carboranes C2Bn−2Hn with the number of vertices less than or equal to 12 have been exhaustively investigated both experimentally and theoretically. Various positional isomers for C2B10H12,4,6 C2B9H11,7−9 C2B8H10,7a,b,10 C2B7H9,7a,11 C2B6H8,7a,b,11a,12 C2B5H7,7a,11d,13−15 C2B4H6,7a,11d,13,16,17 and C2B3H57a,11d,13,17,18 were experimentally synthesized and structurally characterized. Theoretically, the relative stability of all possible positional isomers for each carborane C2Bn−2Hn (n = 5−12) has been extensively investigated. The stability trend of carboranes C2Bn−2Hn (n = 5−12) with increasing size has also been studied by Schleyer and co-workers using ab initio calculations.19 © 2015 American Chemical Society

In contrast, supercarboranes C2Bn−2Hn with the number of vertices larger than 1220 are much less studied. Only a handful of 13- and 14-vertex carboranes are experimentally known (Chart 1).21,22 Their chemistry has been studied, showing some unique properties of their own that are significantly different from the 12-vertex ones, such as one-electron reduction to form a stable carborane radical anion with [2n + 3] framework electrons21e and reactions with various nucleophiles to afford the cage carbon and/or boron extrusion products.21c,f−n However, the synthesis of supercarboranes C2Bn−2Hn with n > 14 has not been achieved yet. To gain some insight into the thermodynamic stability of supercarboranes for facilitating the selection of synthetic targets, we conducted DFT calculations on supercarboranes C2Bn−2Hn (n = 13−20). The structures, stability of positional isomers for each supercarborane, their stability trend, and the electronic properties of supercarboranes C2Bn−2Hn (n = 13−20) have been studied. These results are reported in this article.

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COMPUTATIONAL DETAILS

All calculations were conducted using the Gaussian 09 program.23 Structures and relative energies of isomeric supercarboranes C2Bn−2Hn Received: September 16, 2015 Published: November 30, 2015 5576

DOI: 10.1021/acs.organomet.5b00796 Organometallics 2015, 34, 5576−5588

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Organometallics Chart 1. Experimentally Known closo-Supercarboranes

The parent structures for BnHn2− (n = 13−20) used in our discussion are presented/summarized in Scheme 1. Positional Isomers of closo-Supercarboranes C2Bn−2Hn (n = 13−20). C2B11H13. The 13-vertex closo-borane dianion B13H132− has a C2v symmetry (Scheme 1). This structure can be viewed as derived from formal addition of a neutral BH unit to an edge of the B12H122− icosahedron. B13H132− has six different kinds of positions (see the numbering scheme shown in Scheme 1). Position 1 is unique and five-connected (the B−H bond is included), positions 2 (= 3), 6 (= 7, 8, 9), 10 (= 11), and 12 (= 13) are six-connected, and positions 4 (= 5) are sevenconnected. On the basis of the structure of the parent closo-borane dianion B13H132− (C2v, Scheme 1), a total of 12 positional isomers for C2B11H13 were located (optimized) from 28 starting geometries with all possible locations of the two carbon atoms being considered. Experimentally, three of these isomers, 1,2-C2B11H13, 1,6-C2B11H13, and 1,12-C2B11H13, have been synthesized,21a−d and the predicted/calculated structures match well with the corresponding single-crystal X-ray structures. It is noteworthy that the most stable positional isomer for 1,2-C2B11H13 has a very different geometry from that of the parent closo-borane dianion B13H132−. The two carbon atoms in the most stable positional isomer are equivalent (both being five-connected), and there is a trapezoidal C2B2 open face composed of the two carbon atoms and two of their neighboring boron atoms, which is in an excellent agreement with the experimental results.21a−d Our calculations show that the seven-connected positions 4 (= 5) are least favorable for replacement by a carbon atom. Optimizations of the starting geometries with one carbon atom occupying a seven-connected position always lead to other lower energy isomers having the carbon atom(s) being five- or six-connected. Despite this, we were able to locate the positional isomer when both carbon atoms occupy the two seven-connected positions. This isomer, 4,5-C2B11H13 (27.8 kcal/mol), is higher in energy than any other positional isomers we have located. In contrast, the five-connected position 1 is the most favorable for replacement by a carbon atom. For example, the CAd (CAd = carbon-atoms-adjacent) isomer 1,2-C2B11H13 is more stable than

(n = 13−20) were optimized without symmetry restriction at the B3LYP/6-311+G(d,p) level of theory.24 Frequency calculations at the same level of theory were performed to determine the nature of a stationary point (a minimum or saddle point) and to afford the zeropoint energies (ZPE). In our discussion, enthalpy changes were adopted for stability comparison. The vertical one-electron affinities of clososupercarboranes were calculated at the same level of theory. The HOMO/LUMO energies were calculated at the B3LYP/6-31G(d) level. NPA charge analysis was also carried out using the NBO program implemented in the Gaussian 09 package.25 All graphical structures are presented using the XYZviewer software developed by de Marothy.26

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RESULTS AND DISCUSSION In our study, all plausible positional isomers for clososupercarboranes C2Bn−2Hn (n = 13−20) were located, by systematically substituting two boron atoms of the corresponding closo-borane dianions BnHn2− (n = 13−20) with two carbon atoms. The structures of closo-borane dianions BnHn2− (n = 13− 20) were taken from the previous studies of Lipscomb,27 Schleyer, and their co-workers.28a Lipscomb and co-workers have hypothetically proposed the structures of 13−24-vertex closo-borane dianions27a and calculated their energies using the PRDDO (partial retention of diatomic differential overlap) method.27b They found that 13−17-vertex closo-borane dianions favor high-symmetry point groups, e.g., B14H142− (D6d), B15H152− (D3h), and B17H172− (D5h). Further study by Schleyer and coworkers using DFT calculations (B3LYP/6-311+G(d,p)) confirmed the earlier conclusions, except for B16H162−, which was found to adopt a D4d (instead of Td) symmetry.28 Here, B16H162− is considered as having a closo geometry in spite of the presence of square faces. For larger closo-borane dianions BnHn2− (n = 18−20), Lipscomb and co-workers reported that B18H182− favors a D3d symmetry, while B19H192− and B20H202− adopt Cs and D3h symmetries, respectively.27 We reoptimized all these structures using DFT calculations (B3LYP/6-311+G(d,p)). The results show that B18H182− favors a D3 symmetry, and the D3d structure is a saddle point lying higher in energy by 23.9 kcal/mol. The structures of B19H192− and B20H202− reported by Lipscomb and co-workers were confirmed to be the most stable ones. 5577


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Organometallics Scheme 1. closo-Borane Dianions, BnHn2− (n = 13−20) with NPA Charges of Each Vertex

for B13H132− (Scheme 1). The results show that the five-connected position 1 carries the most negative charge (NPA charge: −0.27), while the seven-connected position 4 (= 5) carries the least negative charge (NPA charge: −0.01). The correlation between the charge distribution of B13H132− and the position preference of a carbon atom in C2B11H13 agrees well with Gimarc’s topological charge stabilization rule31 saying that more electronegative carbons prefer the positions with higher negative charges. However, neither Williams’s empirical rule nor Jemmis and Schleyer’s ring-cap matching rule can predict the position preference of carbons among the positions that have the same connectivity. In the structure of B13H132−, there are 10 positions that are six-connected. NPA charge analysis shows that there is no significant difference in the charges among these positions (NPA charges: −0.16 to −0.18, shown in Scheme 1). Our energetic calculation results reveal that among the 10 six-connected positions, position 2 (= 3) is the most favorable for replacement by a carbon atom, position 6 (= 7, 8, 9) is the second most favorable, and position 10 (= 11) or 12 (= 13) is the least favorable. As shown in Figure 1, the CAd isomer 2,8-C2B11H13 (8.9 kcal/mol) is much more stable than 6,7-C2B11H13 (19.0 kcal/mol), while 6,7-C2B11H13 is even more stable than 10,12-C2B11H13 and 12,13-C2B11H13 (22.1 and 21.2 kcal/mol, respectively). Similarly, the CAp isomer 2,3-C2B11H13 shows much higher stability than 6,9-C2B11H13 and 10,11-C2B11H13 (−16.9 vs 1.9 and 8.9 kcal/mol). Here, a plausible explanation for the high

the other CAd isomers, such as 2,8-, 6,7-, 10,11-, and 12,13C2B11H13, in which the two carbon atoms occupy six-connected positions (Figure 1). The preference for a cage carbon to occupy position 1 is also reflected in the higher stability of the CAp (CAp = carbon-atoms-apart) isomer 1,10-C2B11H13 versus 10,11-C2B11H13 (−13.5 vs 8.9 kcal/mol) and the higher stability of 1,6-C2B11H13 versus 6,9-C2B11H13 (−15.8 vs 1.9 kcal/mol). The calculation results also show that the two carbon atoms prefer to be as far apart as possible. As shown in Figure 1, 1,12-C2B11H13 has the two carbon atoms furthest apart and is the most stable isomer located. The CAp isomers 1,6-C2B11H13 and 1,10-C2B11H13 are more stable than the most stable CAd isomer 1,2-C2B11H13, which is in very good agreement with the experimental data.20e All these results indicate that CAd isomers are in general less favorable. The relative stability observed and discussed above for the 13-vertex carboranes is well consistent with Williams’s empirical valence rule summarized for carboranes C2Bn−2Hn (n = 5−12).29 The rule states that the two cage carbons prefer locations of low connectivity and to be as far apart as possible. The high preference of a carbon atom for a five-connected position and low preference for a seven-connected position also agree with Jemmis and Schleyer’s ring-cap matching rule:30 the orbital overlap of a CH cap with borocycles decreases in the order of ring size as 4 > 3 > 5 ≫ 6. To rationalize the position preference of carbon atoms in the supercarborane structures, we carried out NPA charge analysis 5578


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Figure 1. Structures of all the isomeric 13-vertex carboranes C2B11H13 with relative energies in kcal/mol.

carbon atom(s). In addition, we again found that the two carbon atoms, when both occupy six-connected positions, prefer to be farther apart. As shown in Figure 2, among the isomers that have two carbon atoms occupying six-connected positions, the CAp isomers 2,5-C2B12H14 and 2,10-C2B12H14 are more stable than 2,4-C2B12H14 and 2,9-C2B12H14, and all these CAp isomers are more stable than the CAd isomers (2,3-C2B12H14 and 2,8-C2B12H14). In comparison with those isomers that have two carbon atoms occupying six-connected positions, the isomers 1,2-, 1,9-, and 1,14-C2B12H14 that have one or two carbon atoms occupying seven-connected position(s) are much less stable. C2B13H15. The 15-vertex closo-borane dianion B15H152− has a D3h symmetry (Scheme 1). B15H152− has only three different types of positions. Positions 7−9 on the σh mirror plane are sevenconnected. Positions 1−3 and 13−15 (labeled as positions I) on the two antipodal triangles are six-connected. The remaining positions 4−6 and 10−12 (labeled as positions II) are also six-connected. On the basis of the structure of the parent closo-borane dianion B15H152−, a total of 13 positional isomers for the 15-vertex carborane C2B13H15 were located/optimized from 14 starting geometries. Experimentally, none of these isomers has been reported yet. The charge distribution for the boron atoms in B15H152− suggests that positions II (4−6, 10−12) are slightly more favorable than positions I (1−3, 13−15) for replacement by an

preference of carbon atoms to occupy positions 2 and 3 is given as follows. In the structure of 2,3-C2B11H13 (Figure 1), the two carbons do not maintain the connectivity as those in the parent structure of B13H132− (Scheme 1). Clearly, carbon has less diffused valence orbitals and cannot effectively interact with two adjacent seven-connected borons (B4 and B5) if a structural reorganization does not occur upon carbon replacement, and as a result, the connectivity of the carbon in position 2 or 3 is decreased by breaking one C−B bond, making the carbon occupy a low-connectivity position and stabilizing the structure. C2B12H14. The 14-vertex closo-borane dianion B14H142− adopts a bicapped hexagonal antiprism with a D6d symmetry (Scheme 1). B14H142− has only two different types of positions. Positions 1 and 14 are seven-connected, and the remaining 12 equivalent positions are six-connected. Based on the structure of the parent closo-borane dianion B14H142−, a total of 9 positional isomers for the 14-vertex carborane C2B12H14 have been located (Figure 2), and among them four positional isomers, 2,3-, 2,8-, 2,4-, and 2,9-C2B12H14, have been experimentally synthesized.22 Similar to what we have observed in the 13-vertex carborane structures, we found that in the 14-vertex carborane structures the six-connected positions 2−13 are more electron-rich than the seven-connected positions (NPA charge: −0.16 vs −0.01), and thus more favorable for replacement by the more electronegative 5579


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in B16H162−, positions 1−4 and 13−16 (labeled as position III), at the two rhombus faces and the remaining positions 5−12 (labeled as position IV). On the basis of the structure of the parent closo-borane dianion B16H162−, a total of 13 positional isomers were located for the 16-vertex carborane C2B14H16. Although both positions III and IV are six-connected, positions IV are more electron-rich than positions III (NPA charge: −0.20 vs −0.04), thus more favorable for replacement by the more electronegative carbon. Among the CAd isomers, 5,9-C2B14H16 is more stable than 1,2-, 1,5-, and 1,12-C2B14H16 (Figure 4). For the CAp isomers, those isomers having the two carbon atoms located at positions IV are more stable than the isomers having only one carbon atom located at one of the positions IV and are also more stable than those isomers that have both carbon atoms located at positions III. For instance, the CAp isomers 5,6-, 5,10-, and 5,7-C2B14H16 (both carbons occupy positions IV) are more stable than 1,9-, 1,6-, and 1,10-C2B14H16 (one carbon occupies one of the positions IV and the other occupies one of the positions III). The CAp isomers 1,3-, 1,15-, and 1,13-C2B14H16, which have both carbon atoms occupying the positions III, are less stable than other CAp isomers. When both cage carbon atoms locate at the positions IV, the stabilities increase with the increase of the separating distance of the two cage carbon atoms, which follows the stability order 5,6C2B14H16 < 5,10-C2B14H16 < 5,7-C2B14H16. Similarly, the isomers with only one cage carbon located at a position IV follow the stability order 1,9-C2B14H16 < 1,6-C2B14H16 < 1,10-C2B14H16, and the isomers with both cage carbon atoms located at the positions III follow the stability order 1,15-C2B14H16 < 1,13C2B14H16 ≈ 1,3-C2B14H16. C2B15H17. The 17-vertex closo-borane dianion B17H172− has a D5h symmetry (Scheme 1). B17H172− has three different types of positions. Positions 7−11 on the σh mirror plane are sevenconnected. The two farthest apart positions, 1 and 17 (labeled as positions V), are six-connected; so are the remaining 10 equivalent positions, 2−6 and 12−16 (labeled as positions VI). On the basis of the structure of the parent homoatomic dianion cluster B17H172−, a total of 14 positional isomers were located for the 17-vertex carborane C2B15H17. The charge distribution in B17H172− suggests that positions VI (NPA charge: −0.17) are slightly more favorable than positions V (NPA charge: −0.14) for replacement by the more electronegative carbon, and the five seven-connected positions are least favorable (NPA charge: −0.01). However, our calculations show that positions VI are not necessarily more favorable than positions V. The CAd isomer 2,3-C2B15H17, which has both carbon atoms occupying positions VI, turns out to be slightly less stable than 1,2-C2B15H17, which has one carbon atom occupying one of the positions V. For the CAp isomers, 1,17-C2B15H17, which has the two carbon atoms occupying the two farthest apart positions (V), is the most stable isomer located, and 1,12-C2B15H17, which has the two carbon atoms being farther apart, is more stable than the isomers that have both carbon atoms occupying positions VI, such as 2,12-, 2,13-, and 2,16-C2B15H17. Similar to what we found in 15-vertex carboranes, 17-vertex carborane isomers that have one or two carbon atom(s) located at the seven-connected position(s) also undergo structural reorganization to reduce the connectivity of the cage carbon atom(s), which stabilizes these isomers to some extent. Despite that the structural reorganization gains extra stability, these isomers are still much less stable when compared with other isomers that have the two carbon atoms occupying six-connected


electronegative carbon (NPA charge: −0.17 vs −0.15), and the three seven-connected positions are least favorable (NPA charge: −0.01). Our calculations show that in spite of the electronic preference of positions II over positions I, the isomers with both the carbon atoms occupying positions II are not necessarily more stable (Figure 3). For example, the CAd isomer 4,12-C2B13H15 is less stable than 1,4-C2B13H15. Similarly, the CAp isomers 4,5C2B13H15 and 4,10-C2B13H15 are less stable than 1,5-C2B13H15. For the remaining CAp isomers with the two carbon atoms occupying position(s) I and/or position(s) II, those with the two cage carbons being farther apart are generally more stable. For example, 1,13-C2B13H15 and 1,14-C2B13H15 are more stable than 1,10-C2B13H15 and 1,11-C2B13H15. It is noted that the isomer 7,8-C2B13H15, with both the carbon atoms occupying the least favored seven-connected positions, does not correspond to a local minimum on the potential energy surface. Further optimization of this structure leads to the isomer 4,10-C2B13H15, which has both the carbon atoms being six-connected. For those having only one carbon atom occupying a seven-connected position, such as 1,7-C2B13H15, 1,9-C2B13H15, and 4,8-C2B13H15, optimization of these isomers leads to structural distortion/rearrangement in which the connectivity of the carbon atom changes from seven to six. These rearranged structures are not necessarily highly unstable. For instance, 1,7-C2B13H15 and 1,9-C2B13H15 show comparable stability with that of 1,5-C2B13H15, although 4,8-C2B13H15 is still much less stable. C2B14H16. The 16-vertex closo-borane dianion B16H162− has a D4d symmetry (Scheme 1). There are only two types of positions 5580


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the basis of the structure of B18H182−, a total of 27 positional isomers were located for the 18-vertex carborane C2B16H18 from 30 starting geometries. The structures of selected low-energy isomers are shown in Figure 6 (structures of all positional isomers are given in Figure S1 in the Supporting Information). Similar to what we have seen in the 16-vertex carborane C2B14H16, the two cage carbon atoms of the 18-vertex carborane C2B16H18 also prefer the positions at the triangles (positions VII) over those at the four-membered open faces (positions VIII, IX). As shown in Figure 6, 1,2-C2B16H18 is the most stable CAd isomer, which is 3.8 kcal/mol lower in energy than 1,9-C2B16H18, which has one carbon atom located at one parallelogram face position IX. For the CAp isomers, 1,16-, 1,17-, and 1,18C2B16H18, which have both cage carbon atoms located at

position(s) V and/or position(s) VI. For instance, the CAp isomers 1,7-, 2,8-, and 2,9-C2B15H17, which have one carbon atom located at one seven-connected position, are much less stable than the CAp isomers 1,12-, 1,17-, 2,4-, 2,16-, 2,12-, and 2,13-C2B15H17, which have both carbon atoms located at sixconnected positions. The CAp isomers 7,8- and 7,9-C2B15H17, which have both carbon atoms located at two seven-connected positions, are even less stable. C2B16H18. The 18-vertex closo-borane dianion B18H182− has a D3 symmetry (Scheme 1). There are three different kinds of positions in B18H182−, positions 1−3 and 16−18 (labeled as positions VII) at the two antipodal triangles, positions 4−6 and 13−15 (labeled as positions VIII), and positions 7−12 (labeled as positions IX) at the three parallelogram faces. On 5581


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with respect to the remaining six-connected positions 1, 3, 5, 10, 18, and 19 (NPA charges: −0.17−0.00 vs −0.24 to −0.18) and thus less favored for replacement by carbon atoms. The calculated results show that all the low-energy positional isomers have the two carbon atoms located at the more electron-rich sixconnected positions 1, 3, 5, 10, 18, and 19, such as the most stable CAd isomer 1,3-C2B17H19 and the low-energy CAp isomers 1,19C2B17H19, 1,18-C2B17H19, 3,18-C2B17H19, and 10,18-C2B17H19. C2B18H20. The 20-vertex closo-borane dianion B20H202− has a D3h symmetry (Scheme 1). There are four different types of positions in B20H202−. Positions 1 and 20 are sevenconnected, positions 2, 4, 6, 15, 17, 19, and 8−13 on the three four-membered-ring open faces are six-connected, and the remaining six equivalent positions 3, 5, 7, 14, 16, and 18 (labeled as positions X) are also six-connected. On the basis of the structure of B20H202−, a total of 14 positional isomers have been located for the 20-vertex carborane C2B18H20 from 27 starting geometries. The structures of selected low-energy positional isomers are shown in Figure 8 (structures of all positional isomers are given in Figure S3 of the Supporting Information). The charge distribution of B20H202− suggests that positions X are the most favorable for replacement by electronegative carbon

positions VII, are more stable than all the other isomers. The next most stable isomer is 1,10-C2B16H18, which has one cage carbon atom located at a position VII, while the other cage carbon is located at a position IX, which is the farthest away from the first one. C2B17H19. The 19-vertex closo-borane dianion B19H192− has a Cs symmetry (Scheme 1). There are 12 different types of positions in B19H192−. Position 5 is seven-connected, positions (2, 6, 7, 13), (8, 9, 14, 15), and (11, 12, 16, 17) on the three fourmembered-ring open faces are six-connected, and the remaining six positions (1, 3, 5, 10, 18, 19) are also six-connected. On the basis of the structure of B19H192−, a total of 27 positional isomers for the 19-vertex carborane C2B17H19 were located from 94 starting geometries. The structures of selected low-energy positional isomers are shown in Figure 7 (structures of all positional isomers are given in Figure S2 of the Supporting Information). Similar to what we have seen in the 13−18-vertex carboranes, the two carbon atoms in the 19-vertex carborane C2B17H19 also do not favor the seven-connected and the six-connected positions on the four-membered-ring open faces. NPA charge analysis of B19H192− shows that these positions are electron-poor 5582


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(NPA charge: −0.23 of positions X vs 0.00 to −0.08 of other positions). This prediction is similar to what we have seen in the 13−19-vertex carboranes, that the seven-connected positions and the six-connected positions on the four-membered-ring open faces are not favored by carbon atoms. Indeed, our calculations show that 2,3-C2B18H20, which have one carbon atom located at the position X, is the most stable CAd isomer (Figure 8), and 3,16-C2B18H20, which have two carbon atoms located at two farther apart positions X, is the most stable CAp isomer.

We found that the position preference is not significant among different CAp positional isomers. For example, the energy difference between the most stable CAp isomer 3,16-C2B18H20 and the most unfavorable CAp isomer 8,10-C2B18H20 (shown in the Supporting Information) is only 5.4 kcal/mol. The reason can be ascribed to the flexibility of the 20-vertex carborane cage, in which a slight rearrangement in the structures would make vertices similar in their connectivity. Stability Trend of closo-Supercarboranes C2Bn−2Hn (n = 13−20). A number of studies have been carried out to investigate 5583


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Figure 6. Structures of selected low-energy positional isomers of 18-vertex carboranes C2B16H18 with relative energies in kcal/mol.

Figure 7. Structures of selected low-energy isomers of 19-vertex carboranes C2B17H19 with relative energies in kcal/mol.

the stability trend of the boron clusters BnHn2− (n = 5−24), CBn−1Hn− (n = 5−12), and C2Bn−2Hn (n = 5−12) with increasing size, by calculating the average BH energies E(BnHn2−)/n,27a,28,32 cumulative BH addition energies (ΔHadd),28,33 and/or deviations of the cumulative BH addition energies from a reference line (ΔHdev).19 Employing the cumulative BH addition energies (ΔHadd), we studied the stability trend of supercarboranes by considering their most stable CAd and CAp positional isomers C2Bn−2Hn (n = 13−20) discussed in the previous sections. Equation 1

defines the chemical reactions for calculations of the cumulative BH addition energies (ΔHadd) with 12-vertex CAd carborane 1,2-C2B10H12 being taken as the reference, where the energy for the BH increment (BHinc) is set as the energy difference between B6H10 and B5H9. Table 1 lists the cumulative BH addition energies (ΔHadd) calculated based on the most stable positional isomers of the CAd and CAp supercarboranes C2Bn−2Hn (n = 13−20) discussed in the previous sections. 1,2‐C2B10H12 + (n − 12)BH inc → C2Bn − 2Hn 5584

(n = 13−20)

(1)


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Figure 8. Structures of selected low-energy isomers of 20-vertex carboranes C2B18H20 with relative energies in kcal/mol.

Table 1. Cumulative BH Addition Energies, Disproportionation Energies, HOMO−LUMO Gap (eV), and Vertical One-Electron Affinities (kcal/mol) Calculated for the Most Stable CAd and CAp Carborane Positional Isomers C2Bn−2Hn (n = 12−20) CAd-isomers 1,2-C2B10H12 1,2-C2B11H13 2,3-C2B12H14 1,4-C2B13H15 1,2-C2B13H15 5,9-C2B14H16 1,2-C2B15H17 1,2-C2B16H18 1,3-C2B17H19 2,3-C2B18H20 CAp-isomers 1,12-C2B10H12 1,12-C2B11H13 2,10-C2B12H14 1,13-C2B13H15 5,7-C2B14H16 1,17-C2B15H17 1,18-C2B16H18 1,19-C2B17H19 3,16-C2B18H20 a

ΔHadda

ΔHdisb

H−L gap

vertical EA 0 → −1

0.0 28.9 22.9 30.8 32.5 23.6 19.7 25.7 25.3 22.9

−35.0 14.0 −15.2 −18.5 3.3 9.9 −6.4 −2.0

8.35 5.11 5.92 4.57 4.82 6.21 6.46 5.77 5.57 5.22

3.7 −34.2 −13.3 −38.3 −34.5 −12.5 −5.0 −20.6 −25.4 −36.3

−18.6 10.6 3.1 8.4 1.7 −6.3 2.4 −0.1 −0.7

−36.6 12.8 −12.0 −1.2 16.6 −11.1 1.9

8.62 5.54 6.15 5.27 6.22 6.56 6.24 6.22 6.27

14.6 −18.9 −9.1 −29.0 −12.3 −1.7 −15.0 −15.6 −19.5

Figure 9. Plot of the cumulative BH addition energies (defined in eq 1) against the number of vertices n. 1,2-C2B10H12 is taken as the reference.

(2) The 14-vertex carborane 2,3-C2B12H14, 16-vertex carborane 5,9-C2B14H16, and 20-vertex carborane 2,3-C2B18H20 have very similar stabilities, while the 18-vertex carborane 1,2-C2B16H18 and 19-vertex carborane 1,4-C2B17H19 are slightly less stable. (3) The 17-vertex carborane 1,2-C2B15H17 is predicted to be the most stable one among all the CAd-supercarboranes studied, which can be considered as a feasible synthetic target. For the CAp carboranes, the stability trend predicted is similar to that predicted for the CAd carboranes. The 13-vertex carborane 1,12-C2B11H13 is much less stable and the 17-vertex carborane 1,17-C2B15H17 is more stable than the other CAp supercarboranes studied. A slight difference is that the 15-vertex carborane 1,13-C2B13H15 is more stable than the 13-vertex carborane 1,12-C2B11H13. On the basis of the results shown in Figure 9, we may conclude that the thermodynamic stability should not be the reason for the nonobservation of CApsupercarboranes with a size larger than 14. Disproportionation energies (ΔHdis, eq 2),28 another indicator used for predicting carborane stabilities, were also calculated to evaluate the relative stabilities of supercarboranes with respect to their neighboring members (carboranes with one vertex larger and one vertex smaller). From the plot of the disproportionation

Cumulative BH addition energies. bDisproportionation energies.

We plotted ΔHadd against the number of vertices shown in Figure 9. It is clear that all the CAd- and CAp-supercarboranes C2Bn−2Hn (n = 13−20) considered here are less stable than the corresponding 12-vertex analogues. The results from the cumulative BH addition energies calculated for the CAd carboranes give the following observations. (1) The 13-vertex carborane 1,2-C2B11H13 and the 15-vertex carborane 1,4C2B13H15 are significantly less stable than the others. Between these two unstable closo-supercarboranes, the latter is even less stable than the former. The stability trend found here is different from that found for borane dianions, in which B15H152− was predicted to be more stable than B13H132−. 5585


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Of all the supercarboranes studied here, the 17-vertex carborane has the greatest HOMO−LUMO gap, suggesting its high stability. The stability trend predicted from the HOMO−LUMO gaps is also consistent with that predicted above and further indicates that the 17-vertex carborane is a viable synthetic target. In sharp contrast, both the 13- and 15-vertex carboranes have much smaller HOMO−LUMO gaps, indicating their low stabilities. The calculated vertical one-electron affinities (Figure 12) for the most stable CAd and CAp positional isomers show a stability

Figure 10. Plot of disproportionation energy (defined in eq 2) against the number of vertices.

energy against the number of vertices n (Figure 10), it is clear that the 13-, 15-, and 18-vertex carboranes have a very high tendency to disproportionate to form a smaller and a larger size carborane, while the 14- and 17-vertex carboranes are relatively stable against disproportionation. The stability trend predicted using the disproportionation energies is consistent with that predicted using the cumulative BH addition energies, in which the 13-vertex carborane is less stable and the 17-vertex carborane is the most stable one. 2C2Bn − 2Hn → C2Bn − 3Hn − 1 + C2Bn − 1Hn + 1

Figure 12. Plot of vertical one-electron affinity (kcal/mol) against number of vertices.

(n = 13−20) (2)

trend very similar to that derived from the HOMO−LUMO energy gaps. The 13- and 15-vertex carboranes have relatively more negative one-electron affinities than the others, while the 12- and 17-vertex carboranes have less negative one-electron affinities. Since the 13- and 15-vertex carboranes show very similar electronic properties, we predict that the 15-vertex CAdcarborane might easily undergo one-electron reduction to afford a carborane radical anion with an electron count of [2n + 3], like what has been observed for the 13-vertex CAd-carboranes.21

HOMO−LUMO Gaps and Vertical Electron Affinities. The chemical stability of these closo-supercarboranes C2Bn−2Hn (n = 13−20) was also studied by calculating their HOMO−LUMO energy gaps (Figure 11). The plot of the

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CONCLUSIONS We have studied the structures, stabilities, and electron affinities of closo-supercarboranes C2Bn−2Hn (n = 13−20) with the aid of DFT calculations. On the basis of DFT results, we make the following major conclusions. (1) The two cage carbons in each closo-supercarborane prefer to occupy positions of low connectivity and to be as far apart as possible, a result consistent with the qualitative rules established for 5- to 12-vertex closocarboranes C2Bn−2Hn (n = 5−12). (2) In case of several available positions of the same connectivity, such as the six-connected positions, the cage carbon atoms prefer to occupy the positions on triangle faces rather than those on trapezoidal faces. (3) The experimentally unobserved 15-vertex CAd closo-carborane indeed is less stable than other closo-supercarboranes examined in this article, explaining the difficulty in its experimental synthesis. (4) The 15-vertex CAp closo-carborane and other larger clososupercarboranes C2Bn−2Hn (n = 15−20) are thermodynamically stable, and efforts toward their synthesis are worthwhile. (5) Among the closo-supercarboranes studied, the 17-vertex carborane is the most stable one, thus the most plausible target for experimental synthesis. To meet these challenges, future effort should be put on the development of new synthetic methods for these targets.

Figure 11. Plot of HOMO−LUMO gap (eV) against number of vertices.

HOMO−LUMO gap against the number of vertices n shows the maxima (which indicates enhanced stability) at n = 12, 14, and 17. The HOMO−LUMO gap of the 12-vertex carborane is extraordinarily higher than those of other supercarboranes, which is consistent with the experimental observation that 12-vertex carborane is relatively inert when compared with supercarboranes.20 5586


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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.organomet.5b00796. Figures giving structures and relative energies of all positional isomers for the 18-, 19-, and 20-vertex carboranes (PDF) Text file of all computed molecule Cartesian coordinates in a format for convenient visualization (XYZ)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail (Z. Lin): [email protected]. *E-mail (Z. Xie): [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administration Region (Project No. CUHK7/CRF/12G).

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REFERENCES

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DFT Studies on Structures, Stabilities, and Electron Affinities of closo

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