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Article

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

by
Igor E. Golub
1,*,
Oleg A. Filippov
1,
Vasilisa A. Kulikova
1,2,
Natalia V. Belkova
1,
Lina M. Epstein
1 and
Elena S. Shubina
1,*
1
A. N. Nesmeyanov Institute of Organoelement Compounds and Russian Academy of Sciences (INEOS RAS), 28 Vavilova St, 119991 Moscow, Russia
2
Faculty of Chemistry, M.V. Lomonosov Moscow State University, 1/3 Leninskiye Gory, 119991 Moscow, Russia
*
Authors to whom correspondence should be addressed.
†
Dedicated to Professor Bohumil Štibr (1940-2020), who unfortunately passed away before he could reach the age of 80, in the recognition of his outstanding contributions to boron chemistry.
Molecules 2020, 25(12), 2920; https://0-doi-org.brum.beds.ac.uk/10.3390/molecules25122920
Submission received: 6 June 2020 / Revised: 21 June 2020 / Accepted: 23 June 2020 / Published: 25 June 2020
(This article belongs to the Special Issue Boron Chemistry and Its Development in the 21st Century: In Memory of Professor Bohumil Štíbr (1940-2020))
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Abstract

:
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.

Graphical Abstract

1. Introduction

Boron-based chemistry is vast, diverse, and fascinating due to the ability of boron to form electron-deficient structures of various shapes (such as cages, clusters, etc.) with delocalized electrons and multicenter bonding. Boron hydrides, i.e., boranes (e.g., BH4−, [B3H8]−, [BnHn]2− n = 6–12), are of great interest because of their use as ligands in inorganic chemistry [1,2,3,4,5], as building blocks in material chemistry [3,6,7,8], and as materials for the energetic purposes—components of batteries [9,10], rocket fuels [11,12,13] and systems of hydrogen storage [14,15,16,17]. Polyhedral boranes are widely used as sources of boron (10B) in boron neutron capture cancer therapy [18,19,20,21,22,23], in the creation of luminescent materials [24,25,26], thermally stable polymers [5], liquid crystals and nonlinear optical materials [27,28], as well as precursors of nanostructured materials [29,30].
Thermodynamic hydricity, i.e., hydride donating ability (HDA), determined as Gibbs free energy (ΔG°[H]−) for the reaction of hydride ion, H−, detachment, is a very important characteristic of transition metal hydrides [31] and main group hydrides [32,33,34] that describes their reactivity and is used for the rational design of catalytic reactions. In our recent work, we have demonstrated the existence of an inversely proportional dependence of the hydride-transfer ability of Li[L3B–H] on Lewis acidity of L3B [34]. High values of HDA indicate high Lewis acidity of parent borane L3B, whereas low HDA values indicate high hydride transfer ability of Li[L3B–H]. For that reason, the hydride donating ability (HDA) of boranes can be used as a measure of the Lewis acidity of parent neutral borane or boron cations.
However, there are significant problems in the experimental determination of the thermodynamic hydricity for hydrides of main group elements (E–H, where E = Si, C, B, Al) because of their instability in polar solvents (MeCN, H2O), which are typically used for that [32,35]. Besides, the E–H bond of main group hydrides is characterized by low polarizability compared to transition metal hydrides and, therefore, in many cases, the detachment of the hydride ion (H−) is challenging even in the presence of a large excess of strong Lewis acid. Due to these problems, there is a huge gap in our knowledge about the reactivity of boranes towards hydride transfer [32,35,36].
In our previous paper [34], we focused on the DFT investigation of thermodynamic hydricity of tetracoordinate borohydrides Li[L3B–H]. However, despite the attempts to evaluate the electron-donating properties in polyhedral boranes by 1H NMR [37], there is a lack of knowledge of the reactivity of B–H bond in small borane clusters and polyhedral boron hydrides [36]. Thus, in this paper, we report on the results of the DFT analysis of thermodynamic hydricity in MeCN (HDAMeCN) for both well-known, structurally characterized boranes and prospective reaction intermediates, some of which were previously known from theoretical works.

2. Results and Discussion

Borane clusters (such as B2H6, [B2H7]−, [B3H8]−, [B12H12]2−, [B10H10]2−, etc.) were discovered as intermediate products of borohydrides thermal decomposition [38,39,40,41,42,43,44,45,46,47,48,49,50]. These compounds are widely used in direct synthesis of other boranes [51,52], organoboron compounds [53], and new materials [5]. For example, hydride ion abstraction from borane anions (such as BH4−, [B3H8]−, [B4H9]−, etc.) by Lewis acids BX3 (X = F, Cl, Br) is the most convenient route for the preparation of higher boranes [54,55]. Many small borane clusters are highly reactive and unstable species, so their reactivity is hard to assess experimentally. Others, like polyhedral boron hydrides, require the presence of an excess of Lewis or Brønsted acids for generation of boron-centered quasi-borinium cations [36]. Thus, the reactivity of such compounds can be characterized in terms of their ability to hydride transfer as thermodynamic hydricity (HDA) through DFT calculations [32,34].
In this paper, we performed the DFT calculations of the thermodynamic hydricity in MeCN of small borane clusters (containing up to 5 boron atoms) and polyhedral boron hydrides [BnHn]2− (n = 5–17). For anionic species we use their lithium salts to offset the effect of ionic species and to make a correct comparison with the HDAMeCN values for neutral boranes.

2.1. Thermodynamic Hydricity of Small Borane Clusters

Recently, the decomposition pathways of [LiBH4]n, n = 2–12 clusters were investigated by DFT calculations [48]. In the case of dimeric [LiBH4]2 clusters, the release of up to 4 equivalents of H2 was found, as well as [LiBHm]2 (m = 6, 4, 2) reaction intermediates, during the decomposition. Our calculations show that during the decomposition of [LiBH4]2 the first H2 release leads to the decrease of HDAMeCN by 15.9 kcal/mol (Scheme 1). Further H2 release leads to an increase of HDAMeCN due to formation unsaturated diboranes with double and triple bonds.

2.1.1. General Pattern in Thermodynamic Hydricity of Borane Clusters

To gain insight into an effect of borane (BH3) aggregation in small clusters, we used the monomers LiBH4, Li2BH3, LiBH2, and Li2BH along with neutral BH3 and BH species to construct a homologous series of boron clusters (containing up to 5 boron atoms) by consequent addition of BH3 (Table 1, Schemes S1 and S2). Another two homologous series were constructed based on Li[B2H3] and B2H2. In each series there are the most stable boranes (namely BH4−, B2H6, [B2H6]2−, [B3H8]−, B4H10, [B3H7]2−, [B4H9]−, and B5H11), which are generally observed during thermal decomposition of metal borohydrides [38,39,40,41,42,43,44,45,46,47,48,49,50].
According to computed heats of formation [50], neural boranes (such as B2H6, B4H10, and B5H11) are less stable than anionic ones (BH4−, [B3H8]− and [B4H9]−); however, the former may be derived from the latter as a result of hydride abstraction by Lewis acids BX3 (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 (R3B) can be estimated by the analysis of thermodynamic hydricity of their product of hydride addition [R3BH]−. Higher HDAMeCN values of [R3BH]− correspond to higher Lewis acidity of R3B.
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. Previously [57], the formal division of the thermodynamic hydricity scale into weak (above 80 kcal/mol), medium (between 80 and 50 kcal/mol) and strong hydride donors (less 50 kcal/mol) was suggested.
Our study and literature analysis show that borane clusters with HDAMeCN below 41 kcal/mol are strong hydride donors capable of reducing CO2 (HDAMeCN = 44 kcal/mol for HCO2− [31]); however, 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 [58], B4H10, B5H11, etc. [59]). Moreover, in higher boranes, the deprotonation of B–H–B bridges leads to B–B bond formation, in which boron is nucleophilic and susceptible to the attack of electrophiles [59]. Thus, higher borane anions could be generated by the insertion of such electrophile molecules as BH3, B2H2 or BH.
Based on the data obtained for the homologous series (Table 1, Schemes S1 and S2), an evolution of thermodynamic hydricity can be traced on the example of B3 clusters transformations (Scheme 2). Thus, neutral boranes B3H9, B3H7, and B3H5 feature the highest Lewis acidity (highest HDAMeCN values). Monoanionic boranes Li[B3H10] etc. have lower Lewis acidity than parent neutral boranes. The two-electron reduction of the neutral boranes leads to a significant decrease of HDAMeCN values (by 41.1 kcal/mol for Li2[B3H9] and by 20.0 kcal/mol for Li2[B3H7]).
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 HDAMeCN values are not directly connected with the size of borane cluster (Figure S1). However, if we plot computed HDAMeCN values for all series of boranes (n = 1–5; Figure 1), it appears that minimum HDAMeCN values (nucleophilic boron) are typical for the dianionic species and maximum HDAMeCN (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.
An increasing size of borane cluster in neutral BnH3n, BnH3n−2, and BnH3n−4 and dianionic Li2[BnH3n] and Li2[BnH3n−2] series results in a drop of HDAMeCN values. This leads to a smoothing of the extrema in the graph of HDAMeCN for larger borane clusters as B4 and B5. Moreover, in the B3 clusters due to triangle form an effective charge distribution occurs, which leads to the systematically lower values of HDAMeCN.
It is worth noting that a decrease of saturation of the borane cluster results in an increase of HDAMeCN that is especially pronounced for neutral diboranes.

2.1.2. 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 HDAMeCN decrease by 16.4 kcal/mol, while the subsequent BH3 addition leads to a gradual HDAMeCN increase due to the delocalization of electrons between a greater number of atoms.
Tetrahydroborate anions BH4− [4,60,61,62,63,64,65,66,67,68] and [B2H7]− [69,70] are used as ligands in the synthesis of transition metal complexes. Structures of other borohydride anions were accessed by DFT calculations [58,71], but only branched isomers of Li[B4H13] and Li[B5H16] 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 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 HDAMeCN at each step (from 108.4 to 55.1 kcal/mol). Borane BH3 has high HDAMeCN value (HDAMeCN = 108.4 kcal/mol) and cannot be isolated due to its high Lewis acidity; however, it can be stabilized by dimerization into diborane B2H6 molecule (HDAMeCN = 82.1 kcal/mol) or by interaction with Lewis bases (Scheme 5). The Lewis acid–base complexes of BH3 are characterized by reduced HDAMeCN and some of them, especially amine and phosphine boranes, are able to form σ-complexes with transition metals [72,73,74,75,76,77].
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).
The Li2[BnH3n] series is formed by the consecutive addition of BH3 to Li2[BH3] (Scheme S3). Both [BH3]2− [81] and [B2H6]2− [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 two-electron 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 (HDAMeCN = 40.9 kcal/mol for Li2[B2H6]) results in full substitution of terminal BH hydrides in (Cp*M)2(κ2-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 HDAMeCN (Table 1); however, according to our DFT calculations, the structures of [B3H9]2−, [B4H12]2− and [B5H15]2− are based on [B2H6]2− geometry (Scheme S3, Table S4).
The Li[BnH3n−1] series is formed via the consecutive addition of BH3 to LiBH2 (Scheme S4). Along this series, HDAMeCN decreases from 64.4 kcal/mol for LiBH2 to 44.5–45.1 kcal/mol for Li[B4H11] and Li[B5H14]. The most stable structure in this series is Li[B3H8], and this anion is used as a ligand in transition metal complexes [70,90,91,92,93,94]. In the case of Li[B4H11] and Li[B5H14], the isomers, the structures of which are based on [B3H8]−, are found by 19.2 and 24.0 kcal/mol lower in ∆G°MeCN scale than the isomers having a cyclic structure (Scheme S4, Table S5).
According to the literature, there are several possibilities for synthesizing [B3H8]− (Scheme 6) [52,58,95]. Formation of the octahydrotriborate anion [B3H8]− in the reaction of BH4− with B2H6 or with B2H4 can be explained by the electrophilic nature of neutral boranes (evidenced by higher HDAMeCN, Table 1 and Scheme S1) [58,95].
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 HDAMeCN 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, HDAMeCN 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 (HDAMeCN = 105.4 for B2H4 is comparable to HDAMeCN = 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 non-oxidizing 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 HDAMeCN value.
In the Li2[BnH3n−2] series formed by the consecutive addition of BH3 to Li2BH (Scheme S6), the HDAMeCN values decrease by 20–52 kcal/mol relative to the corresponding neutral boranes B3H3n−2 (Table 1 and Scheme 2). Both [B2H4]2− [99,102,104,111] and [B3H7]2− [82,112,113,114] are used as ligands in transition metal complexes. The most stable structures, [B4H12]2− and [B5H15]2−, are based on the geometry of [B3H7]2−, whereas cyclic structures are energetically less favorable by 7.4 and 16.8 kcal/mol (∆G°MeCN), respectively (Table S7).
The Li[BnH3n−3] series is formed by the addition of BH3 to B− (Scheme S7, Table S8). The change in the thermodynamic hydricity in this series is uneven. The first BH3 addition leads to a significant drop in HDAMeCN 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 HDAMeCN by 11.3 kcal/mol. The first two members of this series, [B2H3]− [115,116] and [B3H6]− [80], are observed in the gas phase during collision-induced dissociation [117], and their structures were predicted by DFT calculations. [B4H9]− can be synthesized in quantitative yield by deprotonation of B4H10, whereas the addition of B2H6 to [B4H9]− yields [B5H12]− [51,118]. [B4H9]− is used as a ligand in transition metal complexes [70,119,120,121,122], and it is the most stable structure in this series (HDAMeCN = 60.2 kcal/mol).
Finally, the BnH3n−4 series is formed via the consecutive addition of BH3 to B2H2 (Scheme S8, Table S9). Upon the BH3 addition, HDAMeCN gradually decreases from an extremely high value of 168.6 kcal/mol for B2H2 to 85.5 kcal/mol for B5H11. B2H2 [100,123], B3H5 [100] and B4H8 [124,125] are obtained as a result of higher borane cleavage (e.g., B5H9) and need to be stabilized by the interaction with Lewis bases (Me3P, Me3N, Me2S) due to their high Lewis acidity. Their Lewis acid–base adducts (such as (Me3P)2∙B2H2) have used as ligands in transition metal complexes [104,126,127].

2.2. Thermodynamic Hydricity of Polyhedral Closo-Boranes

During thermal decomposition of metal tetrahydroborates, the formation of stable metal dodecaborane [B12H12]2− with an admixture of [B10H10]2− via intermediate boron clusters such as [B2H7]− and [B3H8]− was observed [42,45,46,47,50]. In octahedral [B6H6]2− and icosahedral [B12H12]2− closo-borane dianions, all terminal BH groups are equivalent. However, in their lithium salts Li2[BnHn], cation–anion interaction causes asymmetry in the bond lengths of terminal BH groups interacting with Li atoms. Therefore, thermodynamic hydricity of polyhedral closo-boranes was assessed for both [BnHn]2− dianions and their lithium salts Li2[BnHn] (n = 5–17).
Theoretical calculations show that the thermodynamic stability of polyhedral closo-boranes increases with an increase in the number of boron atoms participating in the cluster formation from [B5H5]2− to [B12H12]2− [50]. According to thermodynamic stabilities, closo-borane dianions such as [B17H17]2− and [B16H16]2− should be even more stable than [B12H12]2− [128]. Indeed, DFT calculations predict that the formation of large clusters (such as [B42H42]2−, [B60H60]2−, [B92H92]2−) is possible [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 HDAMeCN of small dianionic boranes [BnHn]2− and their lithium salts Li2[BnHn] (n = 2–4) (Figure 2), which can be formally viewed as building blocks or prototypes of polyhedral closo-boranes.
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 Å for [B2H2]2−; rBHterm = 1.209 Å for [B3H3]2− and rBHterm = 1.206 Å for [B4H4]2−). The decrease of HDAMeCN values in this series (Scheme 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].
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 HDAMeCN 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 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 B3H3 triangle, forming a belt of the polyhedron (for further description of structural features of polyhedral closo-boranes, see in SI).
Boron atoms in the belt and caps of the polyhedron have different coordination numbers (CN)—4 and 5, respectively. That in turn leads to a difference in B–H bonds’ lengths (rBHap = 1.194 Å and rBHeq = 1.202 Å, Figure 3) and anisotropy in the charge distribution across the polyhedron (Figure S2). According to natural bond population analysis (NPA) of [B5H5]2− the capping boron atoms are more negatively charged (qMeCN = −0.437) than the equatorial ones (qMeCN = −0.331÷ −0.332). Thus, in the case of [B5H5]2−, the apical BH groups (82.0 kcal/mol) have higher HDAMeCN values than equatorial ones (60.0 kcal/mol) (Figure S2). This HDAMeCN(BHap)/HDAMeCN(BHeq) ratio is conserved when going to larger dianions [B10H10]2−, [B15H15]2− and [B17H17]2−.
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 rBHterm and HDAMeCN (Figure S4).
Thermodynamic hydricity was assessed for both [BnHn]2− dianions (Figure 4, Table S10) and their lithium salts Li2[BnHn] (n = 5–17) (Figure S3, Table S11). In lithium salts, the cation–anion interaction causes asymmetry in BH bond length and leads to different HDAMeCN values for the same vertex types, which pushes us to use HDAMeCN for dianions to make a correct comparison inside the [BnHn]2− series. HDAMeCN 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). HDAMeCN 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 HDAMeCN. Deviation from this rule is observed only for [B11H11]2−, [B13H13]2− and [B14H14]2−, where the boron atoms with the highest CN have the largest HDAMeCN 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., [B11H11]2− (1.773–1.802 Å), [B13H13]2− (1.739–1.826 Å) and [B14H14]2− (1.732–1.904 Å), in comparison to longer bonds at boron atoms with higher CN (r(B-B) is 1.738–1.971 Å for [B11H11]2−, 1.842–1.904 Å for [B13H13]2− and 1.904 Å for [B14H14]2−).
In most cases, except for [B7H7]2− and [B16H16]2−, the equatorial BH groups have the lowest HDAMeCN values. The trend in the ability to hydride transfer (Scheme 8, for Li2[BnHn] see Scheme S10) correlates with the calculated Gibbs free energy per unit (G°/n) for both Li2[BnHn] and [BnHn]2− (n = 5–17) (Figures S5 and S6) and with previously reported energy per unit by PRDDO calculations [136]. The data obtained indicate that the most stable closo-boranes [B12H12]2−, [B10H10]2− and [B6H6]2− are least prone to the reaction of hydride transfer. At the same time, closo-boranes which differ from [B6H6]2− and [B12H12]2− by one BH group (B5/B7 and B11/B13, respectively) and [B8H8]2− are the most reactive in hydride-transfer reactions. The high reactivity of [B13H13]2−, which HDAMeCN (39.7 kcal/mol) is comparable to that of “superhydride” Li[Et3BH] (HDAMeCN = 37.3 kcal/mol) [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 1H NMR, which revealed the electron-donating ability decrease in the row [2-B10H9]2− > [B12H12]2− > [1-B10H9]2− [37]. According to our calculations, the HDAMeCN value for [B12H12]2− (79.6 kcal/mol) is higher than HDAMeCN for equatorial BH groups in [B10H10]2− (75.6 kcal/mol), but lower than for apical BH terminal groups in [B10H10]2− (89.0 kcal/mol).

3. Materials and Methods

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].
All calculations were performed without symmetry constraints using the M06 hybrid functional [138] and MP2 implemented in the Gaussian09 (Revision D.01) (Wallingford, CT, USA) [139] software package, using the 6-311++G(d,p) basis set [140].
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 (HDAMeCN) was calculated as Gibbs free energy of hydride transfer [HDAMeCN ≡ ΔG°[H]−Solv = G°Solv (E+) + G°Solv (H−) − G°Solv (E–H)].
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–Hterm) were torn off from each vertex in optimized molecules. As is widely known, bridge hydrogen atoms (B–Hbr–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.

4. Conclusions

Our DFT study of thermodynamic hydricity (HDAMeCN) revealed that for small borane clusters (up to 5 boron atoms), the hydride detachment occurs only from the ending terminal BHn (n = 1–3) group having the largest number of hydrogen atoms. The experimental data and the HDAMeCN pattern obtained suggest that stable borane clusters have HDAMeCN between 48 and 82 kcal/mol. Hydrides with lower HDAMeCN would be hydrolytically unstable, and those with higher HDAMeCN tend to aggregation in larger clusters. Neutral boranes with high Lewis acidity such as B2H2 (168.6 kcal/mol), B3H5 (109.9 kcal/mol), BH3 (108.4 kcal/mol), B2H4 (105.4 kcal/mol) and B4H8 (89.2 kcal/mol) could be stabilized in the form a Lewis acid–base complex (L∙BxHy, where L = R3N, R3P, THF, etc.), the formation of which increases the BH group’s hydricity (lowers HDAMeCN). These HDAMeCN border lines are exemplified by diborane B2H6 (HDAMeCN = 82.1 kcal/mol) and its dianion [B2H6]2− (HDAMeCN = 40.9 kcal/mol for Li2[B2H6]). Borane clusters with HDAMeCN less than 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 could even serve as proton donors (e.g., B2H6, B4H10, B5H11 etc.).
In closo-boranes, HDAMeCN depends on the coordination number (CN) of the boron atom from which hydride detachment and stabilization of quasi-borinium cation takes place. Thus, HDAMeCN for equatorial boron vertices (75.6 kcal/mol, CN = 6) in [B10H10]2− is lower than those for apical boron vertices (89.0 kcal/mol, CN = 5). That could explain the observed experimental reactivity row [2-B10H9]2− > [B12H12]2− > [1-B10H9]2− [37].

Supplementary Materials

The following are available online. Scheme S1. Scheme of homologous series of neutral and monoanionic boranes clusters. Scheme S2. Homologous series of neutral and dianionic boranes clusters, Figure S1. Plots of HDAMeCN against the number of boron atoms in borane clusters derived from different starting species. Table S1. Computed [M06/6-311++G(d,p)] B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔG°[H]−MeCN in kcal/mol) for Li[BnH3n+1] series. Table S2. Computed [M06/6-311++G(d,p)] B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔG°[H]−MeCN in kcal/mol) for BnH3n series. Table S3. Difference in Gibbs energy (∆G°MeCN in kcal/mol) relative to the most stable isomer of B3H9 in MeCN (∆G°MeCN in kcal/mol), B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔG°[H]−MeCN in kcal/mol). Scheme S3. Li2[BnH3n] series. Table S4. Computed [M06/6-311++G(d,p)] B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔG°[H]−MeCN in kcal/mol) for Li2[BnH3n] series; Scheme S4. Li[BnH3n−1] series. Table S5. Computed [M06/6-311++G(d,p)] B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔG°[H]−MeCN in kcal/mol) for Li[BnH3n−1] series. Scheme S5. BnH3n−2 series. Table S6. Computed [M06/6-311++G(d,p)] B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔG°[H]−MeCN in kcal/mol) for BnH3n−2 series. Scheme S6. Li2[BnH3n−] series. Table S7. Computed [M06/6-311++G(d,p)] B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔG°[H]−MeCN in kcal/mol) for Li2[BnH3n−2] series. Scheme S7. Li[BnH3n−3] series. Table S8. Computed [M06/6-311++G(d,p)] B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔG°[H]−MeCN in kcal/mol) for Li[BnH3n−3] series. Scheme S8. BnH3n−4 series. Table S9. Computed [M06/6-311++G(d,p)] B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔG°[H]−MeCN in kcal/mol) for BnH3n−4 series. Structural features of polyhedral closo−boranes. Figure S2. NPA charge distribution (showed in blue-green-red scale from −0.40 to 0.05), calculated for M06-optimized geometries of dianions [BnHn]2− (n = 5–17) of polyhedral closo-boranes in MeCN. Table S10. Coordination numbers (CN) of boron atom in polyhedral closo-boranes. Computed [M06/6-311++G(d,p)] B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔH°[H]−MeCN in kcal/mol). Table S11. Computed [M06/6-311++G(d,p)] B-H terminal bond length (in Å), hydride donating ability (HDAMeCN alias ΔG°[H]−MeCN in kcal/mol) and enthalpy of hydride detaching reaction (ΔG°[H]−MeCN in kcal/mol). Figure S3. HDAMeCN of polyhedral closo-boranes Li2[BnHn] (n = 5–17). Scheme S9. General trend of HDAMeCN for Li2[BnHn] (n = 2–4). Scheme S10. General trend of HDAMeCN for polyhedral closo-boranes Li2[BnHn] (n = 5–17). Figure S4. Plot HDAMeCN vs bond length of terminal B-H bond for Li salts polyhedral closo-boranes. Figure S5. Free Gibbs energy per BH unit calculated for dianions [BnHn]2− (n = 5–17) of polyhedral closo-boranes and their Li-salts Li2[BnHn] in (n = 5–17) MeCN vs number boron atoms. Figure S6. Graph of normalized lowest HDAMeCN of and free Gibbs energy per BH unit for dianions [BnHn]2− (n = 5–17) of polyhedral closo-boranes vs number boron atoms. Table S12. DFT-optimized geometries (Cartesian coordinates) and electronic energies.

Author Contributions

Funding acquisition, I.E.G.; Investigation, I.E.G.; Resources, O.A.F.; Supervision, L.M.E. and E.S.S.; Visualization, V.A.K.; Writing—original draft, I.E.G.; Writing—review & editing, O.A.F. and N.V.B. All authors have read and agreed to the published version of the manuscript.

Funding

This work was financially supported by the Russian Science Foundation (grant number 19-73-00309).

Conflicts of Interest

The authors declare no conflict of interest.

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Sample Availability: Samples of the compounds are not available from the authors.
Molecules 25 02920 sch001 550
Scheme 1. HDAMeCN (in kcal/mol) for (LiBH4)2 decomposition intermediates [48] and their monomers.
Scheme 1. HDAMeCN (in kcal/mol) for (LiBH4)2 decomposition intermediates [48] and their monomers.
Molecules 25 02920 sch001
Molecules 25 02920 sch002 550
Scheme 2. Interconversion scheme for Li[B3H10]. Lithium atoms are omitted for clarity.
Scheme 2. Interconversion scheme for Li[B3H10]. Lithium atoms are omitted for clarity.
Molecules 25 02920 sch002
Molecules 25 02920 g001 550
Figure 1. Plot of HDAMeCN for borane clusters of different size.
Figure 1. Plot of HDAMeCN for borane clusters of different size.
Molecules 25 02920 g001
Molecules 25 02920 sch003 550
Scheme 3. Formation of Li[BnH3n+1] series. Black numbers denote HDAMeCN values for B–H groups marked by blue color (in kcal/mol), red numbers in square brackets are the Gibbs free energies (∆G°MeCN, in kcal/mol) of branched isomers relative to the most stable linear isomer for Li[B4H13] or Li[B5H16]. Lithium atoms are omitted for clarity.
Scheme 3. Formation of Li[BnH3n+1] series. Black numbers denote HDAMeCN values for B–H groups marked by blue color (in kcal/mol), red numbers in square brackets are the Gibbs free energies (∆G°MeCN, in kcal/mol) of branched isomers relative to the most stable linear isomer for Li[B4H13] or Li[B5H16]. Lithium atoms are omitted for clarity.
Molecules 25 02920 sch003
Molecules 25 02920 sch004 550
Scheme 4. BnH3n series. Black numbers denote HDAMeCN values for B–H groups marked by blue color (in kcal/mol), red numbers in square brackets are the Gibbs free energies (∆G°MeCN in kcal/mol) relative to the corresponding most stable isomer.
Scheme 4. BnH3n series. Black numbers denote HDAMeCN values for B–H groups marked by blue color (in kcal/mol), red numbers in square brackets are the Gibbs free energies (∆G°MeCN in kcal/mol) relative to the corresponding most stable isomer.
Molecules 25 02920 sch004
Molecules 25 02920 sch005 550
Scheme 5. The trend of HDAMeCN (in kcal/mol) for borane Lewis acid–base complexes. The HDAMeCN values are taken from ref. [34].
Scheme 5. The trend of HDAMeCN (in kcal/mol) for borane Lewis acid–base complexes. The HDAMeCN values are taken from ref. [34].
Molecules 25 02920 sch005
Molecules 25 02920 sch006 550
Scheme 6. Reactions of tetrahydroborate anion with neutral boranes leading to [B3H8]−. HDAMeCN values (in kcal/mol) are also given.
Scheme 6. Reactions of tetrahydroborate anion with neutral boranes leading to [B3H8]−. HDAMeCN values (in kcal/mol) are also given.
Molecules 25 02920 sch006
Molecules 25 02920 g002 550
Figure 2. M06-optimized geometries of Li2[BnHn] (n = 2–4). Lithium atoms are omitted for clarity.
Figure 2. M06-optimized geometries of Li2[BnHn] (n = 2–4). Lithium atoms are omitted for clarity.
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Molecules 25 02920 sch007 550
Scheme 7. Order of HDAMeCN (in kcal/mol) for borane dianions [BnHn]2− (n = 2–4).
Scheme 7. Order of HDAMeCN (in kcal/mol) for borane dianions [BnHn]2− (n = 2–4).
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Molecules 25 02920 g003 550
Figure 3. M06-optimized geometries of [BnHn]2− (n = 5–17) dianions of polyhedral closo-boranes. Boron atoms given in violet, green or yellow color represent structural fragments with different coordination numbers of boron atom. Black numbers are B–H bond length in Å. Dotted lines represent the connection between capes and belts of a polyhedron.
Figure 3. M06-optimized geometries of [BnHn]2− (n = 5–17) dianions of polyhedral closo-boranes. Boron atoms given in violet, green or yellow color represent structural fragments with different coordination numbers of boron atom. Black numbers are B–H bond length in Å. Dotted lines represent the connection between capes and belts of a polyhedron.
Molecules 25 02920 g003
Molecules 25 02920 g004 550
Figure 4. HDAMeCN of polyhedral closo-borane dianions [BnHn]2− (n = 5–17). Blue columns represent the lowest HDAMeCN values, and red columns represent the highest in the given anion; green columns show HDAMeCN for symmetric [B6H6]2− and [B12H12]2− dianions.
Figure 4. HDAMeCN of polyhedral closo-borane dianions [BnHn]2− (n = 5–17). Blue columns represent the lowest HDAMeCN values, and red columns represent the highest in the given anion; green columns show HDAMeCN for symmetric [B6H6]2− and [B12H12]2− dianions.
Molecules 25 02920 g004
Molecules 25 02920 sch008 550
Scheme 8. The trend of HDAMeCN for dianions of polyhedral closo-borane [BnHn] (n = 5–17) taking the lowest value in the given anion.
Scheme 8. The trend of HDAMeCN for dianions of polyhedral closo-borane [BnHn] (n = 5–17) taking the lowest value in the given anion.
Molecules 25 02920 sch008
Table
Table 1. Calculated hydride donating ability in MeCN (HDAMeCN in kcal/mol) for homologous series of neutral and anionic boranes clusters.
Table 1. Calculated hydride donating ability in MeCN (HDAMeCN in kcal/mol) for homologous series of neutral and anionic boranes clusters.
nLi[BnH3n+1]BnH3nLi2[BnH3n]Li[BnH3n−1]BnH3n−2Li2[BnH3n−2]Li[BnH3n−3]BnH3n−4
1LiBH4BH3Li2BH3LiBH2BHLi2BH--
64.9108.443.864.490.942.7
2Li[B2H7]B2H6Li2[B2H6]Li[B2H5]B2H4Li2[B2H4]Li[B2H3]B2H2
48.482.140.963.9105.455.688.9168.6
3Li[B3H10]B3H9Li2[B3H9]Li[B3H8]B3H7Li2[B3H7]Li[B3H6]B3H5
49.269.328.266.974.554.647.0109.8
4Li[B4H13]B4H12Li2[B4H12]Li[B4H11]B4H10Li2[B4H10]Li[B4H9]B4H8
55.260.135.844.578.225.860.289.2
5Li[B5H16]B5H15Li2[B5H15]Li[B5H14]B5H13Li2[B5H13]Li[B5H12]B5H11
57.055.138.645.176.438.454.985.5
The HDAMeCN values are given for the most energetically favorable isomer. The most stable boranes in the series according to calculated heats of formation [50,56] are shown by the violet shading of the cells.

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Golub, I.E.; Filippov, O.A.; Kulikova, V.A.; Belkova, N.V.; Epstein, L.M.; Shubina, E.S. Thermodynamic Hydricity of Small Borane Clusters and Polyhedral closo-Boranes. Molecules 2020, 25, 2920. https://0-doi-org.brum.beds.ac.uk/10.3390/molecules25122920

AMA Style

Golub IE, Filippov OA, Kulikova VA, Belkova NV, Epstein LM, Shubina ES. Thermodynamic Hydricity of Small Borane Clusters and Polyhedral closo-Boranes. Molecules. 2020; 25(12):2920. https://0-doi-org.brum.beds.ac.uk/10.3390/molecules25122920

Chicago/Turabian Style

Golub, Igor E., Oleg A. Filippov, Vasilisa A. Kulikova, Natalia V. Belkova, Lina M. Epstein, and Elena S. Shubina. 2020. "Thermodynamic Hydricity of Small Borane Clusters and Polyhedral closo-Boranes" Molecules 25, no. 12: 2920. https://0-doi-org.brum.beds.ac.uk/10.3390/molecules25122920

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