The Reaction of Hydrogen Halides with Tetrahydroborate Anion and Hexahydro-closo-hexaborate Dianion

The mechanism of the consecutive halogenation of the tetrahydroborate anion [BH4]− by hydrogen halides (HX, X = F, Cl, Br) and hexahydro-closo-hexaborate dianion [B6H6]2− by HCl via electrophile-induced nucleophilic substitution (EINS) was established by ab initio DFT calculations [M06/6-311++G(d,p) and wB97XD/6-311++G(d,p)] in acetonitrile (MeCN), taking into account non-specific solvent effects (SMD model). Successive substitution of H− by X− resulted in increased electron deficiency of borohydrides and changes in the character of boron atoms from nucleophilic to highly electrophilic. This, in turn, increased the tendency of the B–H bond to transfer a proton rather than a hydride ion. Thus, the regularities established suggested that it should be possible to carry out halogenation more selectively with the targeted synthesis of halogen derivatives with a low degree of substitution, by stabilization of H2 complex, or by carrying out a nucleophilic substitution of B–H bonds activated by interaction with Lewis acids (BL3).

Di-and tri-substituted halogenated derivatives of BH 4 − (BH 2 X 2 − and BHX 3 − ) can be obtained through MBH 4 -MBX 4 (X = F, Cl) exchange [12][13][14]. However, this reaction always leads to a mixture of products (due to disproportionation and low selectivity of the process), as well as to the formation of by-products as a result of the interaction of substitution products with the initial reagents [12]. Another possible approach to the synthesis of halogenated derivatives is direct halogenation; however, the reported halogenation of BH 4 − by the reaction with HF has resulted in the formation of a mixture of substitution products [14]. However, as exemplified in [15], the use of 1 H NMR monitoring during the bubbling of tBuNH 2 ·BH 3 with anhydrous hydrogen halides HX (X = F, Cl, Br) allows for the reaction to be stopped when the desired halogenation product is formed.
The halogenated derivatives of [B 6 H 6 ] 2− are typically obtained by the reaction in highly alkaline aqueous solutions in the presence of free halogens X 2 (X = Cl, Br, I) [16,17]. However, this approach always results in mixtures of several components. Moreover, due to the fast rate of halogenation, the mono-and dihalogen derivatives are available as minor products, while tri-and penta-substituted derivatives are major products. Therefore, the use of preparative scale ion exchange column chromatography is essential for the isolation of pure compounds. However, for geometrical isomers with the same degree of halogenation, the difference in phase mobility is small (5-15%); thus, their separation could be achieved only by repeated ion exchange column chromatography [18].

Interaction Tetrahydroborate-Anion with Hydrogen Halides
In our previous work [20], we showed (by DFT investigation of stepwise alcoholysis of tetrahydroborate-anion BH 4 − ) that first proton-hydride transfer is the rate-limiting stage of the reaction, and that the energy profile takes the form of a cascade, since the energy of each next transition state is lower than the one previous. That, in turn, is associated with a decrease in Lewis acidity of the corresponding neutral borane (RO) x BH (3−x) and a weakening of B-H bond in [(RO) x BH (4−x) ] − (x = 0−3) anion entailed by the successive substitution of H − by RO − at the boron atom. Thus, the B-H bond activation of BH 4 − and its ability to hydride transfer appeared to be crucial to this process.
It is known that alkaline tetrahydroborates react violently with concentrated mineral acids (such as H 2 SO 4 , HF, etc.) [14,32], yielding the substituted products and diborane, which is formed as a result of interaction between the reaction products. However, as we demonstrated in [30], an introduction of EWG (X − , X = F, Cl, Br) to boron atoms increases the Lewis acidity of the parent borane BH (3−x) X x and reduces the ability of B-H bonds in [BH (4−x) X x ] − (x = 0−3) to hydride transfer. In this regard, it was interesting to investigate, in the current work, the reaction of BH 4 − with strong mineral acids such as hydrogen halides. For these purposes, we investigated this stepwise process of halogenation of BH 4 − with HX (where X = F, Cl, Br) in acetonitrile (MeCN) at M06/6-311++G(d,p) and wB97XD/6-311++G(d,p) levels of theory.
The dihydrogen-bonded (DHB) complexes are active intermediates of the BH 4 − reaction with HX [33] and HOR [20,21,34,35]. DHB complexes with hydrogen halides HX (X = F, Cl, Br) found in this work (Table S1) were monodentate (except for H 3 BH − ···HF) with H···H distances of 1.425-1.850 Å and angles ∠X-H···H = 159-178 • . Their structures were similar to those found in BH 4 − alcoholysis [20,21], with the geometric parameters typical of DHB complexes [36][37][38]. It should be noted, that for [H 2 XBH] − and [HX 2 BH] − (X = F, Cl, Br) molecules, two coordination modes were found, where halogen atom X was located in transand cis-position to the dihydrogen-bonded HX molecules. The formation energies of DHB complexes with a halogen atom in trans-position are slightly less favorable than those of DHB complexes with X in cis-position; the difference in the Gibbs free energy of these two complexes, ∆∆G f  Table S1) and other parameters characterizing the H···H interactions strength (E H···H and E 2 are given in Table S1, and Wiberg bond indices (WBI) and QTAIM delocalization indices (DI)-in Table S3) decreased, in agreement with the HX acidity and hydrogen bond donor strength [39].
Substitution of one H − by X − (X = F, Cl, Br) in BH 4 − led to an increase of s-character of the B-H bond hybrid orbital in the resulting [BH 3 X] − , from 25.0% up to 31.9% (from sp 3 to sp 2 , Table S3). In general, an increase of s-character of a B-H bond, as in the case of BH 4 − alcoholysis [20], is associated with strengthening of B-H bonds (according to QTAIM delocalization index, DI, Table S4) and weakening of DHB bonds. However, in the case of the BH 4 − reaction with HF for the H 2 FBH − ···HF and HF 2 BH − ···HF complexes (Figure 1), there was an increase of DHB interaction strength (E 2 = 19.2 kcal/mol and 18.6 kcal/mol, respectively, Table S1). In fluoroborohydrides, the strong electron-withdrawing inductive σeffect-due to the large difference in boron and fluorine electronegativity (∆χ A-R = 2.1) [40]led to the large positive charge on the boron atom (1.53 for BF 3 ) [41]. On the other hand, this effect was compensated by the strong back donation from nonbonding 2p π electron pairs of F to vacant 2p π (B) orbital of the same symmetry [42,43]. For BCl 3 and BBr 3 , due to a larger size of 2p π orbitals, their effective overlap with vacant boron 2p π orbital decreased; therefore, back-donation for BF 3 was stronger than for BCl 3 and BBr 3 , and Lewis acidity decreased in the row BF 3 > BH 3 > BCl 3 > BBr 3 (as can be seen from their hydride affinity values, HA 298K , Table S3).
The reaction of BH 4 − with HX (where X = F, Cl, Br) in acetonitrile (MeCN) occurs as a successive proton-hydride transfer and H 2 elimination, yielding [BH (4− Figures S1 and S2). In the case of weak acids like HF (pK a MeCN (estim) = 25.2 [44]) only one product-like concerted transition state (TS) of proton-hydride transfer and H 2 elimination was found (TS1 CONC HF , Figure 3). In the case of stronger acids HCl (pK a MeCN = 10.3 [45]) or HBr (pK a MeCN = 5.4 [45]), two TS's were observed: a reagent-like transition state of proton transfer (TS1 PT HCl ) and a product-like transition state of H 2 elimination (TS1 ELIM HCl ). Both concerted TS of proton-hydride transfer/H 2 elimination TSn CONC HX and TS of H 2 elimination TSn ELIM HX (preceded by proton transfer step TSn PT HX ) exhibited a similar triangle-shaped form of front-side nucleophilic substitution of H 2 by halide-ion X − . The B···H 2 and H···H distances (Tables S5 and S6) in TSn ELIM HX could be considered indirect indicators of activation barrier height. With the increase of the activation energy, the B···H 2 distances decreased for the borohydrides with EWG substituents, while at the same time, H···H distances shortened for weak proton donors (such as HF, ROH, Table S7). Similar transition states were described previously in a theoretical study of BH 4 − alcoholysis by weak (MeOH, CF 3 CH 2 OH) and strong (CF 3 OH) proton donors [21].  Figures S1 and S2). In the case of weak acids like HF (pKa MeCN (estim) = 25.2 [44]) only one product-like concerted transition state (TS) of protonhydride transfer and H2 elimination was found (TS1 CONC HF, Figure 3). In the case of stronger acids HCl (pKa MeCN = 10.3 [45]) or HBr (pKa MeCN = 5.4 [45]), two TS's were observed: a reagent-like transition state of proton transfer (TS1 PT HCl) and a product-like transition state of H2 elimination (TS1 ELIM HCl). Both concerted TS of proton-hydride transfer/H2 elimination TSn CONC HX and TS of H2 elimination TSn ELIM HX (preceded by proton transfer step TSn PT HX) exhibited a similar triangle-shaped form of front-side nucleophilic substitution of H2 by halide-ion X − . The B•••H2 and H•••H distances (Tables S5 and S6) in TSn ELIM HX could be considered indirect indicators of activation barrier height. With the increase of the activation energy, the B•••H2 distances decreased for the borohydrides with EWG substituents, while at the same time, H•••H distances shortened for weak proton donors (such as HF, ROH, Table S7). Similar transition states were described previously in a theoretical study of BH4 − alcoholysis by weak (MeOH, CF3CH2OH) and strong (CF3OH) proton donors [21].   In the case of strong acids (like HCl, HBr), the formation of a metastable H2 intermediate X − (η 2 -H2)BH3 (INTn H2 ) was observed ( Figure 3). This resembled the intermediates of transition metal hydrides' protonation [46], which have also been proposed for the protonation of main group element hydrides [21,[47][48][49][50][51]. It should be noted that INTn H2 was formed only at the first and second reaction step for HCl, and at the first step for HBr. This was due to an increase in electron deficiency of BH2Cl, BH2Br, and BHCl2 fragments, strengthening of B-H and X•••H(H) (X = Cl, Br) bonds, and a decrease of the donation from σ(B-R) (where R = H, Cl, Br) to σ*(H-H-B), which ultimately destabilized the H2 intermediate (Table S2). It should be noted that σ(B-R) to σ*(H-H-B) donation from R group in trans position to H2 complex was the greatest (E 2 1 = 8.8-13.3 kcal/mol) and had a key effect on the stabilization of (η 2 -H2) complex. This is also in line with the less energy-demanding  In the case of strong acids (like HCl, HBr), the formation of a metastable H 2 intermediate X − (η 2 -H 2 )BH 3 (INTn H2 ) was observed ( Figure 3). This resembled the intermediates of transition metal hydrides' protonation [46], which have also been proposed for the protonation of main group element hydrides [21,[47][48][49][50][51]. It should be noted that INTn H2 was formed only at the first and second reaction step for HCl, and at the first step for HBr. This was due to an increase in electron deficiency of BH 2 Cl, BH 2 Br, and BHCl 2 fragments, strengthening of B-H and X···H(H) (X = Cl, Br) bonds, and a decrease of the donation from σ(B-R) (where R = H, Cl, Br) to σ*(H-H-B), which ultimately destabilized the H 2 intermediate (Table S2). It should be noted that σ(B-R) to σ*(H-H-B) donation from R group in trans position to H 2 complex was the greatest (E 2 1 = 8.8-13.3 kcal/mol) and had a key effect on the stabilization of (η 2 -H 2 ) complex. This is also in line with the less energy-demanding attack of HX in the case of [H 2 XBH] − and [HX 2 BH] − bearing X in trans-position to HX, in comparison to complexes with X in cis-position.
Thus, for the appearance of the transition state of proton transfer, which is absent in the case of weak acids and leads to the (η 2 -H 2 ) complex formation, two conditions must apparently be satisfied. First, the pK a of the acid should be greater than the pK a of H 3 B(η 2 -H 2 ) and, second, R 3 B borane should be a good Lewis acid; at that, σ(B-R) orbital (such as R = H, SiH 3 , SiF 3 [51]) should donate to σ*(B-H-H) orbital and R should not be able to π-back-donate to a vacant 2p π (B) orbital.
In addition, a strong acid can significantly lower the activation energy of the 2nd reaction stage-that is, the H 2 elimination. However, the process of H 2 elimination will still be rate-limiting and will always have the highest value of the activation barrier, because of the relatively high B-H bond strength and its hydride transfer ability. In this regard, the reactivity of substituted borohydrides in reactions involving hydride transfer can be evaluated via their hydride donor ability (HDA MeCN , Table S3). In the case of BH 4 − reaction with HF ( Figures S1 and S2 Table S3). As a result, the activation energy decreased by 7.6 and 2.4 kcal/mol for the reaction with the 2nd and 3rd molecule of HF. However, it increased by 6.3 kcal/mol at the last stage (Table 1). Thus, the reaction of BH 4 − with HF followed a trend similar to that of THF·BH 3 and Me 2 NH·BH 3 alcoholysis by (CF 3 ) 2 CHOH [20,52]. In the case of HCl ( Figure 2, Figure S3) and HBr ( Figures S4 and S5), the reaction featured two distinct TS's, i.e., for proton transfer (TSn PT ) and H 2 elimination (TSn ELIM ). The activation barriers of TSn PT were small (0.5-4.1 kcal/mol in the case of M06/6-311++G(d,p) and 3.2-7.1 kcal/mol in the case of wB97XD/6-311++G(d,p), see Figures S3 and S5), comparable to the first step of the gas phase reaction between BH 4 − and CF 3 OH (4.2 kcal/mol) [21]. The case of HCl demonstrates how the energy of the complex with molecular hydrogen Cl − [(η 2 -H 2 )BH (3−x) Cl x ] (x = 0−3) changes during the reaction (Figure 2). At the first step (n = 1, Figure 2), η 2 -H 2 complex was a local minimum with ∆G • MeCN = 3.8 kcal/mol. Then, at the second step (n = 2, Figure 2), the energy rose, and it became a quasi-stationary intermediate at 11.7 kcal/mol. Over the next two steps, it disappeared, and the transition state became concerted. These changes were not surprising; during the reaction, as H − was replaced by X − (X = Cl, Br), the electron deficiency of the boron atom increased and, on the other hand, π-back-donation from occupied 2p π (X) orbital to vacant 2p π (B) orbital decreased. This led to an increase in the HDA MeCN of B-H bond in substitution products, and hence to a decrease of the B-H bond's capability to hydride transfer. As a result, the hydrohalogenation process became concerted, and the activation barriers (∆G Thus, the value of the activation energy was influenced by two factors: the strength of the acid, which significantly lowered the activation barrier by increasing the polarization of the B-H bond in DHB complexes, and the ability of the occupied 2p π (X) orbital to effectively back-donate to vacant 2p π (B). In view of both of these factors, hydrogen chloride was the golden reactant, and the observed activation energy values the reaction of BH 4 − with HCl were the lowest (Table 1). Taking into account these findings, the DFT investigation of the reactivity of [B 6 H 6 ] 2− in electrophile-induced nucleophilic substitution (EINS) was carried out only on an example of the interaction with HCl in acetonitrile (MeCN).

Interaction of Hexahydro-Closo-Hexaborate Dianion with Hydrogen Chloride
Polyhedral closo-boranes are characterized by rather high values of hydride donor ability (e.g., HDA MeCN = 71.9 kcal/mol for [B 6 H 6 ] 2− and 79.6 kcal/mol for [B 12 H 12 ] 2− ), which indicates the weak ability of the nonactivated B-H bond in closo-boranes to hydride transfer [29]. It is not surprising, therefore, that the most common method of functionalization of polyhedral boron hydrides follows the mechanism of electrophile-induced nucleophilic substitution (EINS) (Scheme 1). At the first stage, an electrophile promoter E + is attached to the boron skeleton of a closo-borane. Then, the hydride bound to the electrophile is eliminated, with the formation of a quasi-borinium cation [53]. Finally, at the last stage, the nucleophile attachment occurs. At that point, if E + = H + , the protonated closoborane intermediate should convert into a η 2 -H 2 complex-which is generally unstable and readily loses H 2 , making the addition of the nucleophile easier. substitution (EINS) (Scheme 1). At the first stage, an electrophile promoter E + is attached to the boron skeleton of a closo-borane. Then, the hydride bound to the electrophile is eliminated, with the formation of a quasi-borinium cation [53]. Finally, at the last stage, the nucleophile attachment occurs. At that point, if E + = H + , the protonated closo-borane intermediate should convert into a η 2 -H2 complex-which is generally unstable and readily loses H2, making the addition of the nucleophile easier. However, the main problems of functionalization of polyhedral boron hydrides through this mechanism are low specificity of nucleophilic substitution and difficulties in controlling the degree of substitution [54]. The reactivity of the remaining BH groups in nucleophilic substitution products can be estimated using the hydride donor ability (HDAMeCN). Thus, as discussed in this section, applying this approach, we explored the EINS successive mechanism on the example of the reaction of [B6H6] 2− with HCl in acetonitrile.
The [B6H6] 2− is the smallest stable closo-borane dianion [29,55,56], where the bulk of electron density is located on the boron atoms of the octahedral skeleton. The high nucleophilicity of boron atoms [57] in [B6H6] 2− leads to its easy protonation. However, an attempt to isolate protonated species from Cs2[B6H6] in acidic aqueous solutions was unsuccessful due to irreversible hydrolysis of [B6H6] 2− to borates and boric acid under these conditions [58]. Nevertheless, [ fac HB6H6] − (pKa H 2 O = 7.00) [18,59], in the form of Bu4N + and Ph4P + salts, was isolated from weakly acidic (pH = 4.5) H2O-HCl solutions and characterized by X-ray diffraction [58,60]. It was found that the fac H + proton was located above the B3 triangle facets of the octahedron and coordinated through the 4c--3e bond [18,58,60]. The tendency of [B6H6] 2− to hydrolyze in an acidic environment can be explained by the instability of the hypothetical doubly-protonated B6H8 closo-borane [18,61,62]. However, [B6H6] 2− could be stable in acidic solutions if the protonation were stopped at the stage of [ fac HB6H6] − formation [61]. However, the main problems of functionalization of polyhedral boron hydrides through this mechanism are low specificity of nucleophilic substitution and difficulties in controlling the degree of substitution [54]. The reactivity of the remaining BH groups in nucleophilic substitution products can be estimated using the hydride donor ability (HDA MeCN ). Thus, as discussed in this section, applying this approach, we explored the EINS successive mechanism on the example of the reaction of [B 6 H 6 ] 2− with HCl in acetonitrile.
The [B 6 H 6 ] 2− is the smallest stable closo-borane dianion [29,55,56], where the bulk of electron density is located on the boron atoms of the octahedral skeleton. The high nucleophilicity of boron atoms [57] in [B 6 H 6 ] 2− leads to its easy protonation. However, an attempt to isolate protonated species from Cs 2 [B 6 H 6 ] in acidic aqueous solutions was unsuccessful due to irreversible hydrolysis of [B 6 H 6 ] 2− to borates and boric acid under these conditions [58]. Nevertheless, [ fac HB 6 H 6 ] − (pK a H2O = 7.00) [18,59], in the form of Bu 4 N + and Ph 4 P + salts, was isolated from weakly acidic (pH = 4.5) H 2 O-HCl solutions and characterized by X-ray diffraction [58,60]. It was found that the fac H + proton was located above the B 3 triangle facets of the octahedron and coordinated through the 4c-3e bond [18,58,60]. The tendency of [B 6 H 6 ] 2− to hydrolyze in an acidic environment can be explained by the instability of the hypothetical doubly-protonated B 6 H 8 closo-borane [18,61,62]. However, [B 6 H 6 ] 2− could be stable in acidic solutions if the protonation were stopped at the stage of [ fac HB 6 H 6 ] − formation [61].
It should be noted that the mechanisms of [B 6 H 6 ] 2− consecutive halogenation remain practically unexplored. Only the addition of the second halogen to [B 6 H 5 X] 2− in the presence of X 2 and H 2 O (X = Cl, Br) has been explored by DFT, which proceeds with the partial opening of the boron cluster [17].
Thus, herein, we focused on the investigation of the EINS successive mechanism, simulated on the example of a model reaction in acetonitrile (MeCN) at DFT/M06/6-311++G(d,p) ( Figure 4) and wB97XD/6-311++G(d,p) ( Figure S7, Table S12) (Figure 4), the H 2 elimination was the rate-limiting stage and, therefore, the activation barrier of this stage and the selectivity of this process should be determined by the metastable η 2 -H 2 reaction intermediate.
of the proton donor used should be higher than the pKa of Cl − •[ fac HB6H(6−x)Clx] − (x = 0−5). After protonation, the reaction turned into a classical one-isomerization of Cl − •[ fac HB6H(6−x)Clx] − to Cl − •[(η 2 -H2)B6H(5−x)Clx] − (x = 0-5) (TSn ISO fac-apx ) and H2 elimination (TSn ELIM ) in the presence of a nucleophile (Cl − ). As can be seen from the reaction profile (Figure 4), the H2 elimination was the rate-limiting stage and, therefore, the activation barrier of this stage and the selectivity of this process should be determined by the metastable η 2 -H2 reaction intermediate.   [66,67]. Upon the successive replacement of H − with Cl − in the closo-borane structure, gradual increases in the electron deficiency of the skeleton of closo-borane and the electrophilicity of boron atoms were observed. As the result, the values of hydride donor ability (HDAMeCN , Table S8) increase, whereas the values of proton donor ability (PDAMeCN) decrease (Table S8) [63]. It should be noted that the electron density of hydride atoms in [B 6 [66,67]. Upon the successive replacement of H − with Cl − in the closo-borane structure, gradual increases in the electron deficiency of the skeleton of closo-borane and the electrophilicity of boron atoms were observed. As the result, the values of hydride donor ability (HDA MeCN , Table S8) increase, whereas the values of proton donor ability (PDA MeCN ) decrease (Table S8). This indicates a change in the character of boron atoms in closo-borane from nucleophilic to highly electrophilic and an increase of the Lewis acidity of the corresponding quasi-borinium cations [B 6 [42,43]. The study of the electronic structure of polyhedral closo-borane dianions [B 6 H (6−x) Cl x ] 2− (x = 1−5) utilizing the NBO method showed that, as the substitution proceeded, the polarization of the hydrogen atom occurred. which It became less hydridic (the charge of the hydrogen atom varied from −0.027 to 0.002). These changes were manifested in a weakening of the hydrogen bond (decrease of E H···B(B2) and E 2 , Table S8), an elongation of H···B 3 distances (Table S9), and a decrease in the enthalpy of H···B 3 (INTn HB3 ) complexes' formation (Table S9).
The energy barrier of the proton transfer reaction was very low (2.5-7.5 kcal/mol); thus, in the presence of acids, the protonated reaction intermediates Cl − [ fac HB 6 H (6−x) Cl x ] − (x= 0−5) (INTn PT ) were immediately formed ( Figure S3). At the early stages of the reaction, these were characterized by significant energy formation (∆G f  Table S10) was less than 3.8 kcal/mol. All this indicated that it was possible to stop the protonation reaction at the stage of the monoprotonated product, in the presence of equimolar amounts of the proton donor.
isomerization process (TSn ISO fac-fac* , Table S9 ), which corresponded to fac H/H term exchange. As is known, [B6H6] 2− can be completely deuterated in D2O solution-and activation energy of the deuteration (18.0 kcal/mol) [18,59] was close to the calculated activation energy of 17.3 kcal/mol for the TSn ISO fac-fac* isomerization of [ fac HB6H6] − . Thus, the exchange between fac H and H term ligands (TSn ISO fac-fac* , Scheme 2 ) featuring a lower barrier than TSn ELIM did not result in H2 elimination-which requires η 2 -H2 complex formation.  As the halogenation of [B 6 H 6 ] 2− progressed, the formation energy of the H 2 intermediate decreased, and B-H and Cl···H bonds became stronger while H···H interaction weakened. This coincided with a trend toward an increase in the electrophilicity of the B-H bond and an increase in its acidity. Thus, the established regularities allowed for the use of the stabilization of H 2 complex to control the process of nucleophilic substitution and lower the activation energy of this process.
The same trend was observed for the rate-limiting stage of H 2 elimination, for which the energy barrier increased from 19.6 to 42.3 kcal/mol (∆G • MeCN ‡ (TSn PT ), shown in Table 2, and from 24.6 to 44.6 kcal/mol for wB97XD/6-311++G(d,p), shown in Table S12. It should be noted that nucleophilic substitution by Cl − and solvation contributed greatly to the stabilization of the transition state-which was noticeable, as the activation energies obtained were compared with gas-phase activation energies for H 2 elimination from [ fac HB 6 H 6 ] − (∆E = 45.9 kcal/mol) [69].
In the reaction of [B 6 H 6 ] 2− with HCl there were three branch points at the second, third, and fourth steps (Scheme 3) of halogenation when several geometries of halogenated derivatives were possible (Table 2). However, the optimal reaction pathway (with the lowest activation energy of TSn ELIM at 2nd and 3rd steps) was [B 6 Table 2, the smallest activation barrier corresponded to nucleophilic substitution at the boron atom, the bond of which was characterized by the smallest HDA MeCN value.
be noted that nucleophilic substitution by Cl − and solvation contributed greatly to the stabilization of the transition state-which was noticeable, as the activation energies obtained were compared with gas-phase activation energies for H2 elimination from [ fac HB6H6] − (∆E = 45.9 kcal/mol) [69].
In the reaction of [B6H6] 2− with HCl there were three branch points at the second, third, and fourth steps (Scheme 3) of halogenation when several geometries of halogenated derivatives were possible (  Table 2, the smallest activation barrier corresponded to nucleophilic substitution at the boron atom, the bond of which was characterized by the smallest HDAMeCN value. It should be noted that under real conditions of halogenation of [B6H6] 2− by X2 (X = Cl, Br) in strong alkaline solutions, the reaction is nonspecific. In the second, third, and fourth steps of halogenation, the geometric isomers are formed in different ratios [18]. In this case, for X = I pure geometric isomers, 1,6-[B6H4I2] (trans), 1,6,2-[B6H3I3] (mer) and 1,6,2,4- It should be noted that under real conditions of halogenation of [B 6 H 6 ] 2− by X 2 (X = Cl, Br) in strong alkaline solutions, the reaction is nonspecific. In the second, third, and fourth steps of halogenation, the geometric isomers are formed in different ratios [18]. In this case, for X = I pure geometric isomers, 1,6-[B 6 H 4 I 2 ] (trans), 1,6,2-[B 6 H 3 I 3 ] (mer) and 1,6,2,4-[B 6 H 2 I 4 ] (trans) were observed [70,71]. This was due to the less effective backdonation of larger-sized 2p π iodine orbitals to vacant 2p π (B). That, in turn, led to the favorable formation of the protonated complex [ fac HB 6 H 5 X] − , where fac H + was located in antipodal-sphere of the [B 6 H 6 ] 2− octahedron [18,72]. Our calculations showed that, for [ fac HB 6 H 5 Cl] − , the formation energy of the complex with fac H + in the ipso-sphere of the [B 6 H 6 ] 2− octahedron was higher than that of the complex with fac H + in the antipodal-sphere (∆∆G f

Computational Details
In the present manuscript, the calculations were performed at the DFT/M06/6-311++G(d,p) level for comparison to the hydride donor ability (HDA) values of boron hydrides and other main group hydrides, as previously calculated by the same method [28,30,73]. Additionally, the values obtained can be used as a reference for assessing the effectiveness of the B-H bond activation by transition metals. In this regard, M06 is a more versatile method than M06-2X (generally recommended for thermochemistry calculations of main group elements) and can be used in cases where multi-reference systems are or might be involved, since it has been parametrized for both main group elements and transition metals [74]. The continuum solute model based on density (SMD) was used for nonspecific solvation, since this model was parametrized to work with the Minnesota functionals family (such as M06, M06-2X, etc.) and has proven to be effective for use in both charged and uncharged systems [75]. The nature of the stationary points on potential energy surfaces was proved by reoptimization of M06 geometries at wB97XD/6-311++G(d,p) level of theory.
All calculations were performed without symmetry constraints using the M06 hybrid functional [74] and wB97XD dispersion-corrected, range-separated hybrid functional [76] implemented in the Gaussian09 (Revision D.01) [77] software package, using 6-311++G(d,p) [78] basis set. Vibrational frequencies were calculated for all optimized complexes at the same level of theory to confirm a character of local minima on the potential energy surface. Visualization-optimized geometries were realized using the Chemcraft 1.8 graphical visualization program [79].
The inclusion of nonspecific solvent effects in the calculations was performed using the SMD method [75]. Acetonitrile (MeCN, ε = 35.7) was chosen as a solvent for optimization because of significant data, specific to MeCN, already existed on reduction potentials, pKa values, and experimental values of hydride donor ability (HDA) of transition metal hydrides [24,25].
Calculations were carried out with an ultrafine integration grid and a very tight SCF option to improve the accuracy of the optimization procedure.
Hydride donor ability (HDA MeCN ) and proton donor ability (PDA MeCN ) of E-H bond in MeCN were calculated as Gibbs free energy of hydride or proton transfer: The value of G • MeCN (H − ) = −413.9 kcal/mol was calculated by M06/6-311++G(d,p) for the H − in MeCN. The values of G • MeCN (H + ) = −260.2 kcal/mol were taken from [80]. From data obtained during the geometry optimization for each molecule, the most stable configuration was chosen. To find the most stable configuration of cationic boranes, the terminal hydrogen atoms (B-H term ) were torn off as H − or as H + from each vertex in optimized molecules. In the case of polyhedral closo-boranes, due to the rigid frame of the boron cluster [49,50], several quasi-borinium cations were observed, localized on vertices from which hydride was torn off.
The Wiberg bond indices [81] (WBI)-as a measure of electron distribution between two atoms [82]-and natural atomic charges were calculated using the natural-bond orbital (NBO) analysis [83] implemented in GAUSSIAN09 (Revision D.01) [77]. Topological analysis of the electron-density distribution function ρ(r) was performed using the AIMALL [84] program package based on the wave function obtained by M06 calculations. The delocalization index (DI) [85][86][87], a measure of electrons that are shared or exchanged between two atoms or basins obtained from the integration of the Fermi hole density, was directly related to the bond order [87,88]. The X-Y bond ellipticity, ε X-Y , was defined as ε = (λ 1 /λ 2 − 1), where λ 1 and λ 2 are the negative eigen values of the Hessian of the electron density at the bond critical point, ordered such that λ 1 < λ 2 < 0 [89][90][91]. The energies of H···H or H···B 3 interactions were calculated as E H···H = 0.5·V(r), according to [92,93].

Conclusions
The mechanism of the sequential halogenation of tetrahydroborate anions [BH 4 ] − by hydrogen halides (HX, X = F, Cl, Br) and halogenation of hexahydro-closo-hexaborate dianions [B 6 H 6 ] 2− was established by ab initio DFT calculations (M06/6-311++G(d,p) and wB97XD/6-311++G(d,p)) in acetonitrile (MeCN), taking into account nonspecific solvent ef-fects (SMD model). The active intermediates of the reaction-XH···HB dihydrogen-bonded (DHB) complexes for [BH 4 ] − and ClH···B 3 complexes for [B 6 H 6 ] 2− -were identified, and their geometric parameters, energetic characteristics, and electron structures were deduced. In the case of [B 6 H 6 ] 2− , an electrophile-induced nucleophilic substitution (EINS) mechanism of halogenation was established. The obtained values of activation energies of H 2 elimination were relatively high. Nonetheless, the identified pattern in the changes of electronic characteristics, the reactivity of B-H bonds (such as thermodynamic hydridicity and acidity of halogenated products) and the structures of H 2 complexes suggests that it should be possible to control the degree of halogenation and carry out the targeted synthesis of products with a low degree of substitution using a wide range of synthetic approaches.   Figure S1. M06-calculated energy profile (∆G • MeCN in kcal/mol) of the reaction of BH 4 − with HF in MeCN. Figure S2. wB97XD-calculated energy profile (∆G • MeCN in kcal/mol) of the reaction of BH 4 − with HF in MeCN. Figure