Reactions of Experimentally Known Closo -C 2 B 8 H 10 with Bases. A Computational Study

: On the basis of the direct transformations of closo -1,2-C 2 B 8 H 10 with OH ( − ) and NH 3 to arachno -1,6,9-OC 2 B 8 H 13( − ) and arachno -1,6,9-NC 2 B 8 H 13 , respectively, which were experimentally observed, the DFT computational protocol was used to examine the corresponding reaction pathways. This work is thus a computational attempt to describe the formations of 11-vertex arachno clusters that are formally derived from the hypothetical closo -B 13 H 13(2 − ) . Moreover, such a protocol successfully described the formation of arachno -4,5-C 2 B 6 H 11( − ) as the very ﬁnal product of the ﬁrst reaction. Analogous experimental transformations of closo -1,6-C 2 B 8 H 10 and closo -1,10-C 2 B 8 H 10 , although attempted, were not successful. However, their transformations were explored through computations.


Introduction
Polyhedral borane and heteroborane clusters are known for the presence of delocalized electron-deficient bonding [1,2] and characterized by forming three-center, two-electron (3c-2e) bonds. This bonding is quite different from organic chemistry that is dominated by classical two-center two-electron (2c-2e) bonds. The trigonal faces of boranes and carboranes are assembled to create three-dimensional shapes such as icosahedron and bicapped-square antiprism [2] appearing in closo systems. The preparation and subsequent reactivity of these clusters have been extensively studied by experiments [1,2]. In particular, the 12-vertex icosahedral closo clusters have been one of the main targets. In contrast to well-understood reaction mechanisms in organic chemistry, those in boron cluster chemistry can be very complex because there are very small energy differences between many intermediates and transition states. On that basis, the reaction of boron hydrides may involve many competing pathways [3]. For that reason, relatively little progress has so far been made in the understanding of the reaction mechanisms of boron hydrides and carboranes of various molecular shapes [4][5][6]. To our knowledge, the reaction pathways associated with ten-vertex closo carboranes, for instance closo-1,2-C 2 B 8 H 10 (see Scheme 1), have not yet been explored. Scheme 1. Molecular diagrams of closo-1,2-C2B8H10, arachno-1,6,9-OC2B8H13 (−) (oP1-O), and arachno-1, 6, and the corresponding atomic numberings.
The C2B8H10 molecular shape of a bicapped-square antiprism exists in seven positional isomers, only three of which (1,2-, 1,6-and 1,10-isomers) are known experimentally [2]. The most stable one is the 1,10-isomer and the least stable one is the 2,3-isomer [7]. The 1,6-isomer has recently been examined experimentally [8]. In addition, a new synthetic pathway for the preparation of the 1,2-isomer has also been outlined, including some mechanistic considerations [9]. Mutual isomerizations of all the possible closo-C2B8H10 have been studied computationally [10]. As to the observed reactivity of the 1,2-isomer, its direct closo to arachno transformations have been experimentally observed [11,12], with the resulting arachno structural motif being based on the hypothetical closo-B13H13 (2−) as also seen from the corresponding atomic numberings (see also Scheme 1) [13]. Since no computational work has been reported in the area of the reactions of 10-vertex closo carboranes, we have undertaken a computational study of the experimentally known isomers of closo-C2B8H10 with the Lewis bases OH (−) and NH3. Both bases are hard in terms of the HSAB theory of acids and bases [14] with OH (−) being harder than NH3 on the HSAB scale.

Methods
All of the stationary points in the reactions of closo-1,2-, 1,6-, and 1,10-C2B8H10 with OH (−) were optimized and frequencies were calculated at the SMD(water) [15,16]/B3LYP/6-311+G(2d,p) level, a model chemistry well-established for this class of materials [4][5][6]. The entries in Table 1 for B3LYP/6-311+G(2d,p) are single-point energies at SMD(water)/B3LYP/6-311+G(2d,p)-optimized geometries. The reactions of the same carborane with neutral NH3 were optimized at the B3LYP/6-311+G(2d,p) level without taking solvation effects into account, which is quite reasonable for neutral species. Moreover, unlike the investigation of organic reaction mechanisms where the bonding is 2c-2e and bond-breaking reaction steps can cause the wave function to become unstable with respect to symmetry-breaking, in the investigation of electron deficient reactions, the bonding scheme fluidly changes between different patterns of multi-center bonding. While dynamic electron correlation is important (and described by the B3LYP approach used in this study), non-dynamic (i.e., static) electron correlation (caused by near degeneracy effects) is not important. All of the transition states were relaxed in terms of the application of the intrinsic reaction coordinate (IRC) approach at the SMD(water)/B3LYP/6-31+G(d) level for the reactions with OH (−) and at the B3LYP/6-31G(d) level for the reactions with NH3, and the structures obtained are very similar to those obtained with the 6-311+G(2d,p) basis set. In order to check the possible influence of dispersion corrections, the wB97XD/6-311+G(2d,p), model chemistry was also employed for some stationary points. All the computations were performed using Gaussian09, in which the above model chemistries and basis sets are incorporated [17]. Table 1. Solvation free energies (kcal.mol −1 ), and free energies relative to the appropriate reference. The small "o" refers to ortho (1,2-) C2B8H10. The capital letters "A", "B", "C", etc. and "TS#" are related to individual intermediates and transition states, respectively. If there were two The C 2 B 8 H 10 molecular shape of a bicapped-square antiprism exists in seven positional isomers, only three of which (1,2-, 1,6-and 1,10-isomers) are known experimentally [2]. The most stable one is the 1,10-isomer and the least stable one is the 2,3-isomer [7]. The 1,6-isomer has recently been examined experimentally [8]. In addition, a new synthetic pathway for the preparation of the 1,2-isomer has also been outlined, including some mechanistic considerations [9]. Mutual isomerizations of all the possible closo-C 2 B 8 H 10 have been studied computationally [10]. As to the observed reactivity of the 1,2-isomer, its direct closo to arachno transformations have been experimentally observed [11,12], with the resulting arachno structural motif being based on the hypothetical closo-B 13 H 13 (2−) as also seen from the corresponding atomic numberings (see also Scheme 1) [13]. Since no computational work has been reported in the area of the reactions of 10-vertex closo carboranes, we have undertaken a computational study of the experimentally known isomers of closo-C 2 B 8 H 10 with the Lewis bases OH (−) and NH 3 . Both bases are hard in terms of the HSAB theory of acids and bases [14] with OH (−) being harder than NH 3 on the HSAB scale.

Methods
All of the stationary points in the reactions of closo-1,2-, 1,6-, and 1,10-C 2 B 8 H 10 with OH (−) were optimized and frequencies were calculated at the SMD(water) [15,16]/B3LYP/6-311+G(2d,p) level, a model chemistry well-established for this class of materials [4][5][6]. The entries in Table 1 for B3LYP/6-311+G(2d,p) are single-point energies at SMD(water)/B3LYP/6-311+G(2d,p)-optimized geometries. The reactions of the same carborane with neutral NH 3 were optimized at the B3LYP/6-311+G(2d,p) level without taking solvation effects into account, which is quite reasonable for neutral species. Moreover, unlike the investigation of organic reaction mechanisms where the bonding is 2c-2e and bond-breaking reaction steps can cause the wave function to become unstable with respect to symmetry-breaking, in the investigation of electron deficient reactions, the bonding scheme fluidly changes between different patterns of multi-center bonding. While dynamic electron correlation is important (and described by the B3LYP approach used in this study), non-dynamic (i.e., static) electron correlation (caused by near degeneracy effects) is not important. All of the transition states were relaxed in terms of the application of the intrinsic reaction coordinate (IRC) approach at the SMD(water)/B3LYP/6-31+G(d) level for the reactions with OH (−) and at the B3LYP/6-31G(d) level for the reactions with NH 3 , and the structures obtained are very similar to those obtained with the 6-311+G(2d,p) basis set. In order to check the possible influence of dispersion corrections, the wB97XD/6-311+G(2d,p), model chemistry was also employed for some stationary points. All the computations were performed using Gaussian09, in which the above model chemistries and basis sets are incorporated [17]. Table 1. Solvation free energies (kcal·mol −1 ), and free energies relative to the appropriate reference. The small "o" refers to ortho (1,2-) C 2 B 8 H 10 . The capital letters "A", "B", "C", etc. and "TS#" are related to individual intermediates and transition states, respectively. If there were two conformations possible, two letters are used to differentiate between them (e.g., oG/G -O, oK/K -O and oM/M -O). The capital "-O" and "-N" distinguish between the reactions of OH (−) and NH 3 , respectively. Wherever the intermediate is relatively stable (and already isolated or possibly trappable), "P1", "P2", "P3", etc. are used instead of "A", "B", "C".

The Reaction with Hydroxides
The first part of the reaction of 1,2-C 2 B 8 H 10 with OH (−) is a quite straightforward process. This experimentally verified reaction, with the oP1-O final product, arachno-1,6,9-OC 2 B 8 H 13 (−) (Scheme 1), proceeds through three transition states (TSs) and two intermediates, with the latter still bearing OH (−) (see Figure 1)  Table 1) [18]. Note that the first barrier associated with oTS1-O was also examined with wB97XD/6-311+G(2d,p) and no significant difference from the B3LYP/6-311+G(2d,p) value was found, i.e., 24.9 kcal·mol −1 vs. 27.2 kcal·mol −1 as seen from Table 1. The potential energy surface attributed to the reaction of 1,6-C 2 B 8 H 10 + OH (−) was rather difficult to follow. Since this reaction was not observed experimentally, we moved this computational effort to Supplementary Materials (see Figures S1 and S2). The geometrical shape of the final product mP3-O bears a slight resemblance to the nido-11 vertex geometry, but not with the open pentagonal belt because the OH (−) group migrates through the entire process without any indication of the insertion of oxygen into the cage boron atoms (see Figure S1). The mechanism of the reaction of the 1,10 isomer with OH (−) , also not observed experimentally, is even more complex. Interestingly, the final product (pP1-O, see Figures S3 and S4) of the latter reaction is of the same molecular shape, i.e., with a B-O-B bridge, as in the case of the reaction of 1,2-C 2 B 8 H 10 with OH (−) (oP1-O), but it originates through five TSs instead of three.

The Reaction with Hydroxides
The first part of the reaction of 1,2-C2B8H10 with OH (−) is a quite straightforward process. This experimentally verified reaction, with the oP1-O final product, arachno-1,6,9-OC2B8H13 (−) (Scheme 1), proceeds through three transition states (TSs) and two intermediates, with the latter still bearing OH (−) (see Figure 1) Table 1) [18]. Note that the first barrier associated with oTS1-O was also examined with wB97XD/6-311+G(2d,p) and no significant difference from the B3LYP/6-311+G(2d,p) value was found, i.e., 24.9 kcal.mol −1 vs. 27.2 kcal.mol −1 as seen from Table 1. The potential energy surface attributed to the reaction of 1,6-C2B8H10 + OH (−) was rather difficult to follow. Since this reaction was not observed experimentally, we moved this computational effort to Supplementary Materials (see Figures S1 and S2). The geometrical shape of the final product mP3-O bears a slight resemblance to the nido-11 vertex geometry, but not with the open pentagonal belt because the OH (−) group migrates through the entire process without any indication of the insertion of oxygen into the cage boron atoms (see Figure S1). The mechanism of the reaction of the 1,10 isomer with OH (−) , also not observed experimentally, is even more complex. Interestingly, the final product (pP1-O, see Figures S3 and S4) of the latter reaction is of the same molecular shape, i.e., with a B-O-B bridge, as in the case of the reaction of 1,2-C2B8H10 with OH (−) (oP1-O), but it originates through five TSs instead of three.     Table 1 and Methods for details).

The Reaction with Amines
The reaction of closo-1,2-C2B8H10 with NH3 has been experimentally known to provide arachno-1,6,9-NC2B8H13 (Scheme 1) [11,17]. The initiation of this reaction is based on the attack of NH3 on the most positive boron within the cage, i.e., B(3), which forms a triangle with both C vertices. The highest free energy barrier (50.3 kcal.mol −1 ) is TS2-N, through which the NH3 group becomes NH2 in the 1,6,9 isomer denoted as oP1-N in the reaction pathway (see Figures 3 and 4 and Table 1). However, this experimentally known part of the entire reaction (see above) occurs without any large intervening barriers and, consequently, the oP1-N isomer is obtained through two transition states and one intermediate. The same is apparently true for various amines of the R1R2NH type [19]. This reaction proceeds through a series of intermediate steps to the known 1,8,11-isomer (oP2-N), experimentally available by another procedure [20]. To our knowledge, there is no experimental evidence of the conversion of oP2-N to oP1-N, although this process is computed to be exothermic (∆G = −8.6 kcal.mol −1 ). Note that the experimentally detected arachno-1,6,9-NC2B8H13 originates under less exothermic conditions than its oxygen analog. In analogy with the reaction of 1,2-C2B8H10 with OH (-) , we also examined the first barrier using wB97XD/6-311+G(2d,p) and again no significant difference from the B3LYP/6-311+G(2d,p) value was computed, i.e., 28.3 kcal.mol −1 vs. 32.1 kcal.mol −1  Table 1 and Methods for details).

The Reaction with Amines
The reaction of closo-1,2-C 2 B 8 H 10 with NH 3 has been experimentally known to provide arachno-1,6,9-NC 2 B 8 H 13 (Scheme 1) [11,17]. The initiation of this reaction is based on the attack of NH 3 on the most positive boron within the cage, i.e., B(3), which forms a triangle with both C vertices. The highest free energy barrier (50.3 kcal·mol −1 ) is TS2-N, through which the NH 3 group becomes NH 2 in the 1,6,9 isomer denoted as oP1-N in the reaction pathway (see Figures 3 and 4 and  Table 1). However, this experimentally known part of the entire reaction (see above) occurs without any large intervening barriers and, consequently, the oP1-N isomer is obtained through two transition states and one intermediate. The same is apparently true for various amines of the R 1 R 2 NH type [19]. This reaction proceeds through a series of intermediate steps to the known 1,8,11-isomer (oP2-N), experimentally available by another procedure [20]. To our knowledge, there is no experimental evidence of the conversion of oP2-N to oP1-N, although this process is computed to be exothermic (∆G = −8.6 kcal·mol −1 ). Note that the experimentally detected arachno-1,6,9-NC 2 B 8 H 13 originates under less exothermic conditions than its oxygen analog. In analogy with the reaction of 1,2-C 2 B 8 H 10 with OH (−) , we also examined the first barrier using wB97XD/6-311+G(2d,p) and again no significant difference from the B3LYP/6-311+G(2d,p) value was computed, i.e., 28.3 kcal·mol −1 vs. 32.1 kcal·mol −1 as provided by Table 1. When the 1,6,9-isomer (oP1-N) was examined computationally in terms of searching for another TS, i.e., oTS7-N, it isomerizes to a new isomer, oP3-N, through two TSs and one intermediate, oE-N, with the C-C bond remains intact as judged by a separation of 1.565 Å. When the Crystals 2020, 10, 896 8 of 12 C-C separation was increased, another TS and intermediate, i.e., oTS9-N and oF-N, respectively, were located with much longer C . . . C separations of 2.409 and 2.774 Å, respectively. This significant geometrical change initiates a continuation of the reaction through other four subsequent TSs to the next known isomer, i.e., oP4-N. The reaction of the 1,6-isomers (see Figures S5 and S6) was a result of the simultaneous initial attack of NH 3 on B(3) and C(6); the N atom forms a cap above the B(2)B(3)C(6) triangle in the transition state with a free energy barrier of 34.6 kcal·mol −1 . The second free energy barrier was even higher, 52.0 kcal·mol −1 and might account for the fact that this reaction does not occur experimentally. Interestingly, when the common product of the reactions of closo-1,2-C 2 B 8 H 10 and closo-1,6-C 2 B 8 H 10 with NH 3 , i.e., oP4-N, is reached (see also Figure S5), both reactions proceed in the same way and closo-C 2 B 7 H 9 is obtained, where the two carbon atoms are separated from each other. Basically, there are five isomers of closo-C 2 B 7 H 9 . The isomerization barrier between the most stable C 2v (C . . . C separation) and the third most stable C 1 (C-C bond) forms is quite high (36 kcal·mol −1 ). The high barrier is not unusual as isomerizations involving the C-C bond in carboranes often have rather high barriers. This type of closo/closo isomerization can also be described [21] in a more detailed way in terms of the consecutive double-Diamond-Square-Diamond (DSD) mechanism [10,22]. These two closo isomers have already been discussed by Schleyer [7] favoring the C 2v -symmetrical 4,5-isomer as well.     Table 1 and Methods for details).

Conclusions
The reaction pathways of the experimentally known reactions of closo-1,2-C2B8H10 with both OH (−) and NH3 were computed using the DFT protocol. The final predicted products from the extensive search of the potential energy surfaces correspond to the same products detected experimentally. Both the closo-1,6-C2B8H10 and the closo-1,10-C2B8H10 isomers were allowed to react with the OH (-) and NH3 bases, without any defined products being observed. Finally, this work represents a computational attempt to study the debor reaction, in contrast to the debor principle [23] (the successive elimination of vertices), where boron vertices are removed in the course of the reaction as illustrated by obtaining arachno-C2B6H11 (-) as the very final product from the reaction of closo-1,2-C2B8H10 with OH (−) .

Supplementary Materials:
The following are available online at www.mdpi.com/xxx/s1: Figure S1: Individual stationary points as detected in the reaction pathway of the reaction of closo-1,6-C2B8H10 with OH (−) , Figure S2: Relative free energies (kcal.mol −1 ) of the individual stationary points on the PES of the reaction of closo-1,6-C2B8H10 with OH (−) , Figure S3: Individual stationary points as detected in the reaction pathway of the reaction of closo-1,10-C2B8H10 with OH (−) , Figure S4: Relative free energies (kcal.mol −1 ) of the individual stationary points on the PES of the reaction of closo-1,10-C2B8H10 with OH (−) , Figure S5: Individual stationary points as detected in the reaction pathway of the reaction of closo-1,6-C2B8H10 with NH3, Figure S6: Relative free energies (kcal.mol −1 ) of the individual stationary points on the PES of the reaction of closo-1,6-C2B8H10 with NH3, Figure S7: Individual stationary points as detected in the reaction pathway of the reaction of 1,10-C2B8H10 with  Table 1 and Methods for details).
The reaction of the 1,10 isomer with NH 3 is rather complex and proceeds through a cascade of TSs. The initial attack of NH 3 simultaneously takes place at the boron atoms of both CB 4 hemispheres (pTS1-N) with an initial free energy barrier of more than 60 kcal·mol −1 and closo-C 2 B 7 H 9 originating as the final product in the endothermic reaction, which is entirely the same as above (see Figures S7  and S8). The experimental reaction of neither the 1,6-nor the 1,10-isomer of C 2 B 8 H 10 with NH 3 have been successfully carried out.

Conclusions
The reaction pathways of the experimentally known reactions of closo-1,2-C 2 B 8 H 10 with both OH (−) and NH 3 were computed using the DFT protocol. The final predicted products from the extensive search of the potential energy surfaces correspond to the same products detected experimentally. Both the closo-1,6-C 2 B 8 H 10 and the closo-1,10-C 2 B 8 H 10 isomers were allowed to react with the OH (−) and NH 3 bases, without any defined products being observed. Finally, this work represents a computational attempt to study the debor reaction, in contrast to the debor principle [23] (the successive elimination of vertices), where boron vertices are removed in the course of the reaction as illustrated by obtaining arachno-C 2 B 6 H 11 (−) as the very final product from the reaction of closo-1,2-C 2 B 8 H 10 with OH (−) .