Thermodynamic Hydricity of Small Borane Clusters and Polyhedral closo-Boranes †

Thermodynamic hydricity (HDAMeCN) determined as Gibbs free energy (ΔG°[H]−) of the H− detachment reaction in acetonitrile (MeCN) was assessed for 144 small borane clusters (up to 5 boron atoms), polyhedral closo-boranes dianions [BnHn]2−, and their lithium salts Li2[BnHn] (n = 5–17) by DFT method [M06/6-311++G(d,p)] taking into account non-specific solvent effect (SMD model). Thermodynamic hydricity values of diborane B2H6 (HDAMeCN = 82.1 kcal/mol) and its dianion [B2H6]2− (HDAMeCN = 40.9 kcal/mol for Li2[B2H6]) can be selected as border points for the range of borane clusters’ reactivity. Borane clusters with HDAMeCN below 41 kcal/mol are strong hydride donors capable of reducing CO2 (HDAMeCN = 44 kcal/mol for HCO2−), whereas those with HDAMeCN over 82 kcal/mol, predominately neutral boranes, are weak hydride donors and less prone to hydride transfer than to proton transfer (e.g., B2H6, B4H10, B5H11, etc.). The HDAMeCN values of closo-boranes are found to directly depend on the coordination number of the boron atom from which hydride detachment and stabilization of quasi-borinium cation takes place. In general, the larger the coordination number (CN) of a boron atom, the lower the value of HDAMeCN.

According to computed heats of formation [50], neural boranes (such as B 2 H 6 , B 4 H 10 , and B 5 H 11 ) are less stable than anionic ones (BH 4 − , [B 3 H 8 ] − and [B 4 H 9 ] − ); however, the former may be derived from the latter as a result of hydride abstraction by Lewis acids BX 3 (X = F, Cl, Br) [55]. This lower stability of neutral boranes compared to anionic boranes can be explained by higher Lewis acidity. In our previous research, we demonstrated that Lewis acidity of parent borane (R 3 B) can be estimated by the analysis of thermodynamic hydricity of their product of hydride addition [R 3  Although it is generally acknowledged that, in clusters, borane anions' hydridic hydrogen becomes less reactive due to increasing charge distribution across the cluster [8], our calculations show that HDA MeCN values are not directly connected with the size of borane cluster ( Figure S1). However, if we plot computed HDA MeCN values for all series of boranes (n = 1-5; Figure 1), it appears that minimum HDA MeCN values (nucleophilic boron) are typical for the dianionic species and maximum HDA MeCN (electrophilic boron) for the neutral boranes, whereas borane monoanions are in the intermediate position. Since neutral transition metal hydrides are better hydride donors than cationic ones [31], it is obvious that anionic boranes should be much more better hydride donors than neutral boranes. It is worth noting that a decrease of saturation of the borane cluster results in an increase of HDA MeCN that is especially pronounced for neutral diboranes.

Features of Thermodynamic Hydricity in Homologous Series
The Li[BnH3n+1] series is formed by consecutive BH3 addition to tetrahydroborate-anion BH4 − (Scheme 3). The first addition of BH3 yields [B2H7] − and leads to the HDA MeCN decrease by 16.4 kcal/mol, while the subsequent BH3 addition leads to a gradual HDA MeCN increase due to the delocalization of electrons between a greater number of atoms.   [71]. However, we found that their linear isomers were energetically more favorable (see ∆G°MeCN, Scheme 3, Table S1). It is important to note that regardless of the structure of the isomer, the hydride detachment only occurs from the terminal BH3 groups, due to their increased hydricity.
The BnH3n series represents neutral boranes formed by consecutive BH3 aggregation (Scheme 4), which causes a gradual decrease of HDA MeCN at each step (from 108 H 16 ] have been reported [71]. However, we found that their linear isomers were energetically more favorable (see ∆G • MeCN , Scheme 3, Table S1). It is important to note that regardless of the structure of the isomer, the hydride detachment only occurs from the terminal BH 3 groups, due to their increased hydricity.
The B n H 3n series represents neutral boranes formed by consecutive BH 3 aggregation (Scheme 4), which causes a gradual decrease of HDA MeCN at each step (from 108.4 to 55.1 kcal/mol). Borane BH 3 has high HDA MeCN value (HDA MeCN = 108.4 kcal/mol) and cannot be isolated due to its high Lewis acidity; however, it can be stabilized by dimerization into diborane B 2 H 6 molecule (HDA MeCN = 82.1 kcal/mol) or by interaction with Lewis bases (Scheme 5). The Lewis acid-base complexes of BH 3 are characterized by reduced HDA MeCN and some of them, especially amine and phosphine boranes, are able to form σ-complexes with transition metals [72][73][74][75][76][77].
Molecules 2020, 25 [82][83][84][85][86][87][88], which could be obtained by the reduction of B2H6 [89], are used as ligands in transition metal complexes. Boranes of this series formally could be obtained by twoelectron reduction from their neutral analogues BnH3n, leading to a significant decrease in their thermodynamic hydricity by 24 The diborane-based structures B2H5(µ-H)[(BH2)(µ-H)]mBH3 (m = 1-3) were found to be the most stable isomers for higher borane clusters (Scheme 4, Table S2). In previous theoretical works, cyclic structures of B3H9 and B4H12 have been reported to be the most stable isomers in the gas phase [78][79][80]. However, according to our optimization, [M06/ and MP2/6-311++G(d,p) theory levels in MeCN using SMD] is the most stable configuration for B3H9 is B2H5(µ-H)BH3, whereas butterfly-like and cyclic structures are slightly less favorable in terms of Gibbs free energy scale (∆G°MeCN = 0.5 kcal/mol and 2.3 kcal/mol for M06 and 0.7 kcal/mol and 1.3 kcal/mol for MP2, respectively, Table S3 [82][83][84][85][86][87][88], which could be obtained by the reduction of B2H6 [89], are used as ligands in transition metal complexes. Boranes of this series formally could be obtained by twoelectron reduction from their neutral analogues BnH3n, leading to a significant decrease in their thermodynamic hydricity by 24-65 kcal/mol. High reactivity of [B2H6] 2− towards hydride transfer (HDA MeCN = 40.9 kcal/mol for Li2[B2H6]) results in full substitution of terminal BH hydrides in (Cp*M)2(κ 2 -B2H6) (M = V, Nb, Ta) in chlorinated solvents (CH2Cl2 and CHCl3) [86,88]. Higher boranes were not isolated, which is apparently related to their low HDA MeCN (Table 1); however, according to The diborane-based structures B 2 H 5 were found to be the most stable isomers for higher borane clusters (Scheme 4, Table S2). In previous theoretical works, cyclic structures of B 3 H 9 and B 4 H 12 have been reported to be the most stable isomers in the gas phase [78][79][80]. However, according to our optimization, [M06/ and MP2/6-311++G(d,p) theory levels in MeCN using SMD] is the most stable configuration for B 3  The BnH3n−2 series is formed via the consecutive addition of BH3 to BH (Scheme S5). In this series, except for the B5H13, all compounds were obtained experimentally. The first BH3 addition leads to an increase in HDA MeCN by 14.5 kcal/mol, the second addition causes its reduction by 30.9 kcal/mol, whereas for the next members in the series, B3H7, B4H10, and B5H13, HDA MeCN varies in a narrow range of 74.5-78.2 kcal/mol.
Boron monohydride radical is known to be generated in the gas phase by photodissociation of BH3CO [96,97]. B2H4 can be obtained by the reaction of B2H6 with F radicals in the gas phase [98]. Due to its high electrophilicity (HDA MeCN = 105.4 for B2H4 is comparable to HDA MeCN = 108.4 for BH3), there is a lack of transition metal complexes with B2H4 [99]; however, it can be stabilized in the form of a Lewis acid-base complex (Me3P)2B2H4 [100][101][102][103][104]. In turn, (Me3P)2B2H4 can act as a bidentate ligand in transition metal complexes [102][103][104][105]. B3H7 can be easily obtained from B3H8 − by reaction with a nonoxidizing acid (Scheme 6) in ether solvents (e.g., THF) or in the presence of other Lewis bases (L = R3N, R3P) [52,106,107] with the formation of L•B3H7 adduct [108]. The most stable borane in this series, B4H10, was characterized rather a long time ago, and its structure was determined in the gas phase by gas-phase electron diffraction [109,110]. B4H10 geometry is preserved in the structure of B5H13 (Scheme S5, Table S6), which is characterized by a slightly lower HDA MeCN value.
In  Table S8). The change in the thermodynamic hydricity in this series is uneven. The first BH3 addition leads to a significant drop in HDA MeCN by 41.9 kcal/mol, the second addition causes its reduction by 13.3 kcal/mol, and the The B n H 3n−2 series is formed via the consecutive addition of BH 3 to BH (Scheme S5). In this series, except for the B 5 H 13 , all compounds were obtained experimentally. The first BH 3 addition leads to an increase in HDA MeCN by 14.5 kcal/mol, the second addition causes its reduction by 30.9 kcal/mol, whereas for the next members in the series, B 3 Table S8). The change in the thermodynamic hydricity in this series is uneven. The first BH 3 addition leads to a significant drop in HDA MeCN by 41.9 kcal/mol, the second addition causes its reduction by 13.3 kcal/mol, and the third addition leads to an increase of HDA MeCN by 11.3 [124,125] are obtained as a result of higher borane cleavage (e.g., B 5 H 9 ) and need to be stabilized by the interaction with Lewis bases (Me 3 P, Me 3 N, Me 2 S) due to their high Lewis acidity. Their Lewis acid-base adducts (such as (Me 3 P) 2 ·B 2 H 2 ) have used as ligands in transition metal complexes [104,126,127].

Thermodynamic Hydricity of Polyhedral Closo-Boranes
During thermal decomposition of metal tetrahydroborates, the formation of stable metal dodecaborane [B 12 H 12 [129][130][131][132]. However, one should keep in mind that the more B-H bonds present in a polyhedral closo-borane, the higher its stability, since more energy is stored in these chemical bonds [50].
To gain insight in thermodynamic hydricity of polyhedral closo-boranes, we calculated at first stage HDA MeCN of small dianionic boranes [B n H n ] 2− and their lithium salts Li 2 [B n H n ] (n = 2-4) (Figure 2), which can be formally viewed as building blocks or prototypes of polyhedral closo-boranes.   [129][130][131][132]. However, one should keep in mind that the more B-H bonds present in a polyhedral closoborane, the higher its stability, since more energy is stored in these chemical bonds [50].

Thermodynamic Hydricity of Polyhedral Closo-Boranes
To gain insight in thermodynamic hydricity of polyhedral closo-boranes, we calculated at first stage HDA MeCN 4 H 4 ] 2− has been described as having an "intermediate configuration between planar and tetragonal geometry" [133], which is actually disphenoid. In each structure, all B-H term bonds are equivalent (r BHterm = 1.191 7) is apparently associated with a better delocalization of electron density and with an increase in the number of possible resonance structures as the cluster size grows. In [B 2 H 2 ] 2− featuring a triple B≡B bond, there are two 2c-2ē π-bonds, whereas in [B 3 H 3 ] 2− and [B 4 H 4 ] 2− featuring π-aromatic systems, there is one 3c-2ē and one 4c-2ē delocalized π-bond, respectively [133]. Whereas [B2H2] 2− is linear, and [B3H3] 2− is planar, [B4H4] 2− has been described as having an "intermediate configuration between planar and tetragonal geometry" [133], which is actually disphenoid. In each structure, all B-Hterm bonds are equivalent (rBHterm = 1.191 7) is apparently associated with a better delocalization of electron density and with an increase in the number of possible resonance structures as the cluster size grows. In [B2H2] 2− featuring a triple B≡B bond, there are two 2c-2ē π-bonds, whereas in [B3H3] 2− and [B4H4] 2− featuring π-aromatic systems, there is one 3c-2ē and one 4c-2ē delocalized π-bond, respectively [133].  [50], and has never been synthesized [128,133]. The structure of [B 5 H 5 ] 2− is typical for the polyhedral closo-boranes-there are two types of boron atoms-two B atoms form caps, and a group of three other B atoms has the geometry of a B 3  To gain insight into the thermodynamic hydricity of polyhedral closo-boranes, it is highly important to consider the difference in geometry along with the charge distribution in their dianions ( Figure S2, Table S10). These parameters suggest different reactivity of boron atoms forming the polyhedron's caps and belt (Figure 3). Although different bond lengths of terminal B-H already indicate different properties of these centers, it is not possible to estimate their thermodynamic hydricity, since there is no general relationship between r BHterm and HDA MeCN ( Figure S4).

Whereas [B 2 H 2 ] 2− is linear, and [B 3 H 3 ] 2− is planar, [B
Thermodynamic hydricity was assessed for both [B n H n ] 2− dianions ( Figure 4, Table S10) and their lithium salts Li 2 [B n H n ] (n = 5-17) ( Figure S3, Table S11). In lithium salts, the cation-anion interaction causes asymmetry in BH bond length and leads to different HDA MeCN values for the same vertex types, which pushes us to use HDA MeCN for dianions to make a correct comparison inside the [B n H n ] 2− series. HDA MeCN values for lithium salts (typically higher by 10.2-22.3 kcal/mol than those for dianions) are provided for the comparison with the neutral and monoanionic hydrides (Table S11). HDA MeCN of closo-boranes directly depends on the coordination number (Table S10) of the boron atom, for which the hydride abstraction and stabilization of quasi-borinium cation take place. In general, the larger the coordination number (CN) of a boron atom, the lower the value of HDA MeCN . Deviation from this rule is observed only for [B 11 H 11 ] 2− , [B 13 H 13 ] 2− and [B 14 H 14 ] 2− , where the boron atoms with the highest CN have the largest HDA MeCN values. The probable explanation is that despite that the boron atoms forming the polyhedron belt have a lower CN than the boron atoms of the cape, the interaction between them and the surrounding atoms is stronger. This is suggested by shorter r (B-B) for borons with lower CN, as in, e.g., [B 11 H 11  Further increase of borane cluster size results in the formation of polyhedral closo-boranes structures Li2[BnHn] (n = 5-17) (Figure 3), which are formed following the Wade's rules [134,135]. Due to the 3D aromaticity, closo-boranes are characterized by higher HDA MeCN values (Figure 4, Figure S2) than small [BnHn] 2− clusters (n = 2-4). Formal addition of BH to [B4H4] 2− yields [B5H5] 2− , which is the least stable member of the polyhedral closo-boranes [BnHn] 2− according to formation enthalpy [50], and has never been synthesized [128,133]. The structure of [B5H5] 2− is typical for the polyhedral closoboranes-there are two types of boron atoms-two B atoms form caps, and a group of three other B atoms has the geometry of a B3H3 triangle, forming a belt of the polyhedron (for further description of structural features of polyhedral closo-boranes, see in SI). To gain insight into the thermodynamic hydricity of polyhedral closo-boranes, it is highly important to consider the difference in geometry along with the charge distribution in their dianions   [34], which apparently explains the challenge of jumping over the so-called "icosahedral barrier" in the synthesis of higher closo-borane clusters. The higher propensity of some closo-boranes for hydride transfer could be used for the directed generation of quasi-borinium cations, which are postulated as intermediates of the electrophile-induced nucleophilic substitution [36,137].
with the highest CN have the largest HDA MeCN values. The probable explanation is that despite that the boron atoms forming the polyhedron belt have a lower CN than the boron atoms of the cape, the interaction between them and the surrounding atoms is stronger. This is suggested by shorter r(B-B) for borons with lower CN, as in, e.g.,    [34], which apparently explains the challenge of jumping over the so-called "icosahedral barrier" in the synthesis of higher closo-borane clusters. The higher propensity of some closo-boranes for hydride transfer could be used for the directed generation of quasi-borinium cations, which are postulated as intermediates of the electrophile-induced nucleophilic substitution [36,137]. Previously, electron-donating properties of polyhedral boranes were assessed by 1

Computational Details
In the present manuscript, DFT/M06 was used to allow a comparison to hydride donating ability of tetracoordinated boron hydrides previously calculated by the same method [34]. Additionally, the values obtained can be used as a reference for assessing the effectiveness of the activation of B-H bonds by transition metals. In this regard, M06 is a more versatile method than M06-2X (generally recommended for calculation thermochemistry of main group elements) and can be used in the cases where multi-reference systems are or might be involved since it has been parametrized for both main group elements and transition metals [138].
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 of the optimized geometries was realized using the Chemcraft 1.8 graphical visualization program [141]. Previously, electron-donating properties of polyhedral boranes were assessed by 1

Computational Details
In the present manuscript, DFT/M06 was used to allow a comparison to hydride donating ability of tetracoordinated boron hydrides previously calculated by the same method [34]. Additionally, the values obtained can be used as a reference for assessing the effectiveness of the activation of B-H bonds by transition metals. In this regard, M06 is a more versatile method than M06-2X (generally recommended for calculation thermochemistry of main group elements) and can be used in the cases where multi-reference systems are or might be involved since it has been parametrized for both main group elements and transition metals [138].
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 of the optimized geometries was realized using the Chemcraft 1.8 graphical visualization program [141].
The inclusion of nonspecific solvent effects in the calculations was performed by using the SMD method [142]. Acetonitrile (MeCN, ε = 35.7) was chosen as a solvent for the geometry optimization because a large amount of data on reduction potentials, pKa values, and experimental hydride donating ability (HDA) of transition metal hydride complexes were determined in MeCN [31,143].
The calculations were carried out with an ultrafine integration grid and a very tight SCF option to improve the accuracy of the optimization procedure and thermochemical calculations.
Hydride donating ability in MeCN (HDA MeCN ) was calculated as Gibbs free energy of hydride transfer [HDA MeCN . From the data obtained during the geometry optimization, for each molecule, the most stable configuration of each of its conformers was chosen. To find the most stable configuration of cationic boranes, the terminal hydrogen atoms (B-H term ) were torn off from each vertex in optimized molecules. As is widely known, bridge hydrogen atoms (B-H br -B) have an increased acidity [5,58,[144][145][146][147]; therefore, their participation in the hydride transfer was not considered herein. For most of the small borane clusters, due to the structural rearrangements during the geometry optimization only one stable configuration of cationic boranes was found.
In the case of polyhedral closo-boranes due to the rigid frame of the boron cluster [133,148], several quasi-borinium cations were observed, localized on vertices from which hydride was torn off.

Conclusions
Our DFT study of thermodynamic hydricity (HDA MeCN ) revealed that for small borane clusters (up to 5 boron atoms), the hydride detachment occurs only from the ending terminal BH n (n = 1-3) group having the largest number of hydrogen atoms. The experimental data and the HDA MeCN pattern obtained suggest that stable borane clusters have HDA MeCN between 48 and 82 kcal/mol. Hydrides with lower HDA MeCN would be hydrolytically unstable, and those with higher HDA MeCN tend to aggregation in larger clusters. Neutral boranes with high Lewis acidity such as B 2 H 2 (168.6 kcal/mol), B 3