Theoretical Design of Stable Pentacoordinate Boron Compounds

Through theoretical computations, we found that boron can form thermodynamically stable pentacoordinate compounds. Pentacoordinate boron (penta-B) is just hypercoordinate but not hypervalent because it forms only four covalent bonds, of which at least one is a multicenter bond. Being electron deficient, to be pentacoordinate, at least two of its bonding atoms should have low electronegativity. Penta-B can be formed in HkB(CH3)m(XH3)n (X = Si, Ge, Sn, and n ≥ 2) and BR5 (R = BH2NH3, AsH2, and BeH). Based on a systematic investigation of these model compounds, we designed three thermodynamically stable penta-B compounds that can potentially be synthesized by hydrogenating their tricoordinate counterparts under mild reaction conditions.


■ INTRODUCTION
Hypercoordination is the property of the main-group elements in a molecule having a larger than normal coordination number, typically greater than four. 1 Hypercoordination is common for the elements in period 3 and beyond. 2 However, it is difficult to form hypercoordinate compounds for the elements in period 2. 3 Over the past few decades, several research studies on hypercoordination in period 2 elements with more than three valence electrons such as carbon and nitrogen have been reported. 2d,4 However, for electrondeficient elements such as boron, there is still debate over whether they can form hypercoordinate compounds and what their bonding nature is if they exist.
The attempts on synthesizing hypercoordinate single-boroncenter compounds were unsuccessful from our point of view. Since 1984, a series of the so-called pentacoordinate boron (penta-B) compounds has been synthesized, by forcing a tricoordinate boron center to form two additional bonds with Lewis-base ligands. 5,6 However, the two additional B−X (X = O, N, or Cl) bonds in these compounds (B−O: ∼2.4 Å; B−N: ∼2.5 Å; and B−Cl: ∼2.7 Å) are much longer than normal. In addition, Wiberg bond indexes (WBI) 7 of the B−X bonds are all below 0.15. Thus, they can hardly be regarded as real penta-B compounds because there are no covalent bonds formed between B and the other two additional ligands. So far, only one theoretical study mentioned five hypothetical silylboranes whose boron centers look like real pentacoordinate. 8 However, no electronic structure analyses and thermodynamic properties were provided, and it is unknown what their bonding nature is and whether they are thermodynamically stable. Because normal tricoordinate silylboranes can be synthesized and have many interesting properties, 9 we wonder if it is possible to synthesize penta-B compounds from normal tricoordinate silylboranes. Hence, in this work, we first studied the electronic and geometric properties of a hierarchy of model penta-B compounds to reveal their bonding nature. Then, we try to design several thermodynamically stable silylboranes with a penta-B center that may be synthesized by experiments under mild reaction conditions.
The low WBIs of the B−Si/B−H bonds of the eight molecules suggest that they are not normal single covalent bonds. Meanwhile, the sum of the WBIs of five B−X (X = H, Si, or C) bonds for the eight molecules is no more than 8, implying that no more than four covalent bonds are formed. These results suggest that B must have formed multicenter bonds with its five bonding atoms. Adaptive natural density partitioning (AdNDP) analyses 11 show that there are four, three, and two multicenter bonds around the B center in 1c, 2c, and 3a ( Figure 2; Figure S1 for the other five molecules), respectively. These results suggest that boron is not hypervalent, 1 and the Lewis octet rule is not violated. Boron accommodates five bonding atoms by forming multicenter bonds with some of them.
For formation of multicenter bonds, at least two of the bonds between boron and its ligands should not be too strong. It is critical for boron to be hypercoordinate. In addition, because boron is electron deficient, forming covalent bonds requires its bonding atoms to give electrons to boron. Therefore, at least two bonding atoms must have similar electronegativity to boron. Other than silicon, beryllium, germanium, tin, and arsenic also meet such criteria. Replacing the Si atoms by Ge/Sn in H k B(CH 3 ) m (SiH 3 ) n (n ≥ 2), 16 penta-B compounds ( Figure 3) could be optimized. Similarly, 3 penta-B compounds, BR 5 (R = BH 2 NH 3 , AsH 2 , and BeH), could be optimized.
Hypercoordination usually means instability. Table 2 tabulates the Gibbs free-energy changes (Δ r G) and barriers (ΔG ‡ ) of five decomposition reactions of 2b (Table S5 for the other seven) at 298.15 K. The results indeed show that these hypothetical compounds are unstable. Among them, releasing SiH 4 is the easiest one with a ΔG ‡ of just 2.9 kcal/mol. Releasing disilane is the second-easiest one, with a 13.8 kcal/ mol ΔG ‡ and a negative Δ r G. However, the positive Δ r G of the pathway to release H 2 and its low ΔG ‡ imply that it is possible to synthesize pentacoordinate silylboranes by hydrogenating their tricoordinate counterparts with at least two silyl groups. To obtain pentacoordinate silylboranes stable at room temperature (RT), we need to increase ΔG ‡ of the lowestenergy decomposition pathway so that they are kinetically stable at RT or increase Δ r G to be positive if ΔG ‡ must be low so that they are thermochemically stable.
The first attempt we tried is to replace the SiH 3 groups in H k B(CH 3 ) m (SiH 3 ) n by more realistic SiR 3 (R = methyl (Me) or phenyl (Ph)) groups. A total of five such compounds ("A" series) were designed (A1 to A5, Figure S2). Among them, A5 (pentacoordinate H 2 B(SiPh 3 ) 3 ) is a potential candidate of   thermodynamically stable penta-B compounds. To design it, we make use of the π−π stack interaction to stabilize A5 and to increase Δ r G and ΔG ‡ of the decomposition pathways. In addition to the π−π stack effect, another effect could be the electron-withdrawing effect of the phenyl group, which makes Si more electron deficient for forming such hypercoordinate bonding. However, a potential disadvantage of synthesizing A5 is that H 2 B(SiPh 3 ) 3 has two low-energy conformers in fast equilibrium ( Figure 4). Except BLYP and B3LYP, other seven functionals (PBE, ωB97XD, M06-L, MN15-L, M06, M06-2X, and MN15) all give similar results that A5 is 1.6∼3.6 kcal/mol lower in free energy than η 2 -H 2 B(SiPh 3 ) 3 at 298.15 K (Table  S9). Although an ∼2 kcal/mol free-energy lowering cannot guarantee that the experiment can surely obtain A5 other than η 2 -H 2 B(SiPh 3 ) 3 due to uncertainties in theoretical computa-tions, our results indicate that the chance to observe A5 by hydrogenating B(SiPh 3 ) 3 is high and it is worth a try because B(SiPh 3 ) 3 had been synthesized in 1984 with a relatively easy method. 9a Other than the "A" series, we have designed other 17 penta-B compounds ( Figure S2): the "B" series (B1 to B7) containing two silyl groups, and the "C" series (C1 to C7) containing three silyl groups. Backbones were used to constrain the silyl groups and hinder the release of HSiR 3 and (SiR 3 ) 2 . Their stability and tricoordinate counterparts (removing two bonding H atoms on B) have been studied by searching all possible decomposition and deformation pathways ( Figure S3) based on knowledge of chemical bonding and reactions. The Δ r G and ΔG ‡ values of the lowest-energy pathway are named as Δ r G Min or ΔG Min ‡ , respectively. Promising penta-B candidates should have (1) negative Δ r G H 2 and low ΔG H 2 ‡ , i.e., they are easy to be synthesized from hydrogenating their tricoordinate counterparts (Table  S10), and (2) positive Δ r G Min or high ΔG Min ‡ , i.e. both the pentacoordinate silylborane and its tricoordinate counterpart are stable at RT (Table S11). For ΔG ‡ , we set the criteria for ΔG H 2 ‡ to be better below 25 kcal/mol and ΔG Min ‡ to be better above 25 kcal/mol, based on an estimation of the half-life of reaction from classical transition state theory. The calculations show that the half-life of a unimolecular reaction is about 66 h and the half-life of a bimolecular reaction is about 94 h at 298.15 K with a ΔG ‡ of 25 kcal/mol. The geometries of two promising compounds, B3_Me from the "B" series and C5 from the "C" series that meet such criteria, are presented in Figure 5. Between them, we would recommend the synthesis of B3_Me first because it has fewer backbones and consequently can be synthesized more easily.
Once these pentacoordinate silylboranes are synthesized, they can be verified by NMR spectroscopy. Table 4 tabulates the NPA charges and the 11 B NMR chemical shifts (δ(B)) of simple and recommended silylboranes. Penta-B draws electrons from silyl groups and are negatively charged. Consequently, it is much more shielded than tricoordinate boron and has very negative δ(B) values. Indeed, for penta-B silylborane compounds, δ(B) has a linear relationship with the NPA charge of the boron atom ( Figure S4). On the other hand, neutral tricoordinate silylboranes have very positive δ(B) values. In addition, η 2 -complex and pentacoordinate conformers can be well differentiated by NMR spectroscopy because δ(B) of the pentacoordinate conformer is more

■ CONCLUSIONS
In summary, boron can be pentacoordinate by forming multicenter covalent bonds with elements, e.g., Be, B, Si, Ge, Sn, and As, having similar electronegativities to boron. We showed that penta-B is not hypervalent and does not violate the Lewis octet rule. Although hypercoordination usually implies instability, we designed three thermodynamically stable pentacoordinate silylboranes, A5, B3_Me, and C5, that may potentially be synthesized by hydrogenating their tricoordinate counterparts under mild reaction conditions. Potential usage of pentacoordinate silylboranes recommended in this study is hydrogenation catalysts or reductants.

■ COMPUTATIONAL METHODS
Validation of Computational Methods. First, we took pentacoordinate silylborane H 3 B(SiH 3 ) 2 ( Figure 6) as an example to test the effect of basis set and method on the geometry. Eight methods including MP2, M06-2X, 10a MN15, 13a ωB97XD, 13b PBE0, 13c TPSSH, 13d DSD-PBE-P86, 13e,f and PBE0DH 13g were tested. Two basis sets were tested: (a) a large basis set in which the aug-cc-pVTZ (AVTZ) basis set 10b−d was used for all the atoms; (b) a smaller basis set (SBS) in which the 6-31+G(d,p) basis set 14a,b was used for B and its five bonding atoms, whereas the 6-31G(d,p) basis set 14c−g was used for the other atoms. Selected bond lengths of H 3 B(SiH 3 ) 2 are listed in Table 5. From the results in Table 5, it can be concluded that the method and basis set both have small effect on the geometry of H 3 B(SiH 3 ) 2 : The standard deviation of all 16 combinations of methods and basis sets is below 0.01 Å for each B−X (X = H or Si) bond; the mean absolute deviation between the two basis sets for the eight methods is also below 0.01 Å for each B−X bond.
Second, we tested the performance of density functional theory (DFT) methods on computing relative energies. We used the M06-2X/AVTZ method to optimize the geometries of eight pent-B silylboranes, H k B(CH 3 ) m (SiH 3 ) n (k = 1∼5, m = 0∼2, n = 2∼5, and k + m + n = 5). A total of 23 decomposition reactions (Table S2) for them were studied. The geometry optimizations and harmonic vibrational frequency analyses of the reactants, transition states, and products were all performed with the M06-2X/AVTZ method. The G4 method 15 was used to perform single-point energy calculations on these optimized geometries. The errors of the M06-2X method using two basis sets, AVTZ and SBS, on the energetics of the 23 reactions are summarized in Table 6. The results in Table 6 indicate that the smaller basis set (SBS) systematically underestimates the reaction energies and energy barriers by about 1 kcal/mol. On the other hand, using a larger basis set, AVTZ, there is almost no systematic error because the mean error is close to 0. In addition, using AVTZ, both reaction energies and energy barriers are improved and the overall root mean square error (RMSE) over 46 relative energies is just 1.2 kcal/mol. Therefore, these results indicate that geometry optimization can be performed using an SBS, whereas a larger basis set is better to be used to further refine the energetic   results. In the present study, for small systems, we used the M06-2X/AVTZ method to optimize geometry and used the G4 method to perform single-point energy calculations. For large systems where G4 calculations are prohibitively expensive, we used M06-2X/SBS to optimize geometry and a larger basis set to perform single-point energy calculations. The basis set used for single-point energy calculations is also a combined basis set: the AVTZ basis set was used for B and its five bonding atoms, and the aug-cc-pVDZ (AVDZ) basis set was used for the other atoms. This combination basis set was abbreviated as LBS. LBS is a compromise between accuracy and efficiency because for those key atoms involved in bond making and broken processes, the large AVTZ basis set was used, whereas for other "observing" atoms, a smaller AVDZ basis set was used. Although G4 is very accurate, it is prohibitively expensive for large systems. We should find a cheaper method as accurate as possible. In the present study, we tested a total of 11 DFT functional methods: two GGA functionals, BLYP and PBE; two hybrid GGA functionals, B3LYP and ωB97XD; two meta-GGA functionals, M06-L and MN15-L; three hybrid meta-GGA functionals, M06, M06-2X, and MN15; and two double hybrid GGA functionals, PBE0DH and DSD-PBEP86. All energetic results were obtained by performing single-point energy calculations on geometries optimized with the M06-2X/AVTZ method. The errors of these functionals using G4 as the standard are summarized in Table 7. The results in Table 7 indicate that M06-2X is the best method, which has the smallest error on both reaction energy changes and energy barriers. Therefore, for the calculations of large systems, we will use the M06-2X/SBS method to perform both geometry optimizations and vibrational frequency analyses. Then, we will use the M06-2X/LBS method to perform single-point energy calculations.
Computational Details. All quantum calculations were performed with the Gaussian 16 program package. 16 Wiberg bond indices, 7 NPA atomic charges, and AdNDP orbitals 11 were performed with the NBO 17 and Multiwfn programs. 18 In all the DFT calculation, a pruned (99,590) grid (using keyword "int. = ultrafine" in Gaussian 16) was used. Solvation effect was considered using the polarizable continuum solvation model 19a with radii and nonelectrostatic terms for Truhlar and co-workers' SMD solvation model. 19b Except H 2 , for which it is a gas under standard state, Gibbs free energy of a compound in the solution (G T ) is computed by the following equation: where E e is the electronic energy computed with solvation effect considered, ZPE and ΔG 0 → T are the zero-point vibrational correction and thermal correction to Gibbs free energy in the gas phase computed by the M06-2X/SBS method, and 1.9 kcal/mol is the correction from the gas-phase standard state of 1 bar to the solution standard state of 1 mol/ L. The geometry used for the single-point calculation in the solution was optimized in the gas phase. 11 B NMR chemical shifts were computed by a well validated method. 12 In this method, NMR calculations were computed with the mPW1PW91/6-311+G(2d,p) method in THF solution under the SMD solvation model. The 11 B NMR chemical shift (δ(B), in ppm) was computed using the following scaling equation:  The G4 results were computed at the G4//M06-2X/AVTZ level. b SBS: 6-31+G(d,p) for B and its five bonding atoms and 6-31G(d,p) for other atoms. Geometries were fully optimized using this basis set. c AVTZ: aug-cc-pVTZ. Geometries were fully optimized using this basis set.

■ ACKNOWLEDGMENTS
Financial support from the National Natural Science Foundation of China (NSCF) (21873019 and 22173021) is gratefully acknowledged.