A Computational Characterization of Boron-Oxygen Multiple Bonding in HN=CH−CH=CH−NH−BO

Abstract

Structures, relative energies, and bonding characteristics for various conformers of 3-imino-N-(oxoboryl)prop-1-en-1-amine, HN=CH−CH=CH−NH−BO, and the corresponding borocycle (−HN=CH−CH=CH−NH−B−)O are discussed using results from second-order Møller-Plesset (MP2) perturbation theory with the Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ basis sets. These MP2 results are compared to those from computationally-efficient density functional theory (DFT) calculations using the LDA, PBE, TPSS, BLYP, B3LYP, BVP86, OLYP, O3LYP, and PBE1PBE functionals in conjunction with the economical Pople-type 6−311++G(d,p) basis set, to evaluate the suitability of these DFT/6−311++G(d,p) levels for use with larger boron-containing systems. The effects of an aqueous environment were incorporated into the calculations using COSMO methodology. The calculated boron-oxygen bond lengths, orbital compositions, and bond orders in all the (acyclic) HN=CH−CH=CH−NH−BO conformers were consistent with the presence of a boron-oxygen triple bond, similar to that found in H−B≡O and H₂N−B≡O. The (−HN=CH−CH=CH−NH−B−)O borocycle is predicted to be planar (C_2v symmetry) and it is ~30 kcal/mol lower in energy than any of the (acyclic) HN=CH−CH=CH−NH−BO conformers; the boron-oxygen bond in this borocycle has significant double bond character, a bonding scheme for which there has been only one experimental structure reported in the literature

INTRODUCTION

The chemistry of borates rivals those of the silicates and phosphates in terms of variation and complexity¹. Indeed, the importance of boron derivatives in chemistry^2,3, biochemistry^4,5, medicinal chemistry^6–10, and material science^11–15, is increasing rapidly and advancing the understanding of boron bonding continues to be an important topic among chemists^16,17. The boron-oxygen single bond in tri-coordinated boronic acids (1.35–1.38 Å) and esters (1.31–1.35 Å)³ is quite strong, ~120 kcal/mol₃; not surprisingly, single-bond lengths in tetra-coordinated species are significantly longer (1.43–1.47 Å) and there is an associated loss in bond strength (by as much as 12 kcal/mol)³. Compounds containing boron-oxygen double bonds, i.e. oxoboranes (R−B=O), have been invoked as reactive intermediates for some time¹⁸, but they have defied most attempts at isolation and characterization^18–23; the oxophilicity of boron makes the formation of a B−O−B linkage more facile than formation of a boron-oxygen multiple bond^16–17. Recently, however, Vidovic et al.²⁴ reported the synthesis of a novel borocycle, LBO→AlCl₃ (where L is a chelating β-diketiminate; {HC(CMe)₂(NC₆F₅)₂}⁻), in which the boron-oxygen bond was stabilized with a Lewis acid (AlCl₃). LBO→AlCl₃ had significant double bond character, e.g. single-crystal X-ray diffraction data collected at 153K showed that the boron-oxygen bond length in this borocycle was 1.304(2) Å compared to 1.354(5) to 1.365(4) Å^25,26 in singly-bonded N₂B−O fragments (diaza- and triaza-boroles). Furthermore, calculations in vacuo performed by the same authors at the B3LYP/6−311+G(d) computational level on a (−N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−B−)O borocycle (in the absence or in the presence of a AlCl₃ moiety) indicated that the boron-oxygen functionality in this structure was also predominantly doubled-bonded. However, ongoing computational studies of boron compounds have raised concerns regarding the extent to which the popular B3LYP functional using split-valence Pople-type basis sets adequately describes some aspects of boron bonding^27–30, suggesting that more rigorous calculations are required to confirm the Vidovic et al. ²⁴ results.

Our particular interest in oxoboranes stems from the results of our recent computational investigation²⁹ of several (neutral) reaction mechanisms for the protodeboronation (hydrolysis) of BoroGlycine, H₂N−CH₂−B(OH)₂:

$${\mathrm{H}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{N}-\mathrm{C}{\mathrm{H}}_2-\mathrm{B}{(\mathrm{O}\mathrm{H})}_2\to \mathrm{B}{(\mathrm{O}\mathrm{H})}_3+{\mathrm{H}}_2\mathrm{N}-\mathrm{C}{\mathrm{H}}_3,$$

and for the 1,2-carbon-to-nitrogen shift of the −B(OH)₂ moiety,

$${\mathrm{H}}_2\mathrm{N}-\mathrm{C}{\mathrm{H}}_2-\mathrm{B}{(\mathrm{O}\mathrm{H})}_2\to {\mathrm{H}}_3\mathrm{C}-\mathrm{N}\mathrm{H}-\mathrm{B}{(\mathrm{O}\mathrm{H})}_2.$$

Surprisingly, a species of the form H₃C−NH₂−B(OH)(=O), in which the boron-oxygen double bond was stabilized by a water molecule, proved to be an intermediate in the 1,2-rearrangement mechanism, leading to this study of boron-oxygen multiple bonding.

In this article we report results from a computational investigation of the structures, relative energies, and boron bonding in various acyclic conformers of 3-imino-N-(oxoboryl)prop-1-en-1-amine, HN=CH−CH=CH−NH−BO, and the related borocycle (−HN=CH−CH=CH−NH−B−)O, which has the same cyclic backbone as the structure synthesized by Vidovic et al.²⁴. Conformers of HN=CH−CH=CH−NH−BO are expected to involve a boron-oxygen triple bond^22,31–38, see Scheme 1A. Such oxoborons (R−B≡O) have been known experimentally for more than 30 years^{19,22,31,37–42}; they are intermediates in the oxidation of solid borons, boranes, and other boron-based materials and release large amounts of energy when used in the synthesis of boron compounds, making them favorable candidates to be employed as propellants in air- breathing combusters and as rocket fuels³³.⁴³. Although life-times of these species are only ~100 ms³⁵, several small oxoboranes have been prepared and their bonding characterized in the gas phase and in the solid state; experimental and computational boron–oxygen distances in such structures are relatively short^34,41,42,44, e.g. ~1.2 Å for H−B≡O^34,42,45.

Scheme 1.

On the other hand, the experimental and computational results reported by Vidovic et al.²⁴, suggest that the (−NH=CH−CH=CH−NH−B−)O borocycle is more likely to involve a boron-oxygen double bond, see Scheme 1B. Thus, a rigorous computational investigation of the model compounds HN=CH−CH=CH−NH−BO and (−NH=CH−CH=CH−NH−B−)O provides an opportunity to characterize various aspects of boron-oxygen multiple bonding within a consistent molecular framework^5,46,47.

COMPUTATIONAL METHODS

Equilibrium geometries for the structures described in this article were obtained using second-order Møller-Plesset (MP2) perturbation theory⁴⁸ with the frozen core (FC) option, which neglects core-electron correlation; the Dunning-Woon correlation-consistent (cc) basis sets, cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ, were employed for the majority of the computations^49–52. Frequency analyses were performed analytically to confirm that the optimized structures were local minima on the PES and to correct reaction enthalpies and free energies to 298K. The gas-phase calculations were carried out using the GAUSSIAN 03 suite of programs⁵³. Bonding was analyzed with the aid of natural bond orbitals (NBOs)^54–57.

Calculations using MP2 methodology with cc basis sets are not currently practical for investigations of the larger boron derivatives of primary chemical interest. Density functional theory (DFT) with Pople-style basis sets^58,59 provide an economical alternative, but the reliability of specific functional/basis set combinations for describing the incredibly diverse range¹ of boron chemistry has yet to be fully established^27–30. Thus, our MP2/cc results were compared to those from several more computationally-efficient DFT/6−311++G(d,p) levels using the following functionals: LDA(SVWN5)⁶⁰; BLYP and B3LYP, which incorporate the dynamical functional of Lee, Yang, and Parr (LYP)⁶¹, coupled with Becke's pure DFT exchange functional (B)⁶²; BVP86 which uses Perdew's 1986 functional^63,64 with local correlation replaced by that suggested by Vosko et al. (VWN)⁶⁰; OLYP⁶⁵ and O3LYP⁶⁶, which were constructed from the novel OPTX exchange functional; PBE1PBE⁶⁷.⁶⁸, which makes use of the one-parameter generalized-gradient approximation (GGA) PBE functional⁶⁹ with a 25% exchange and 75% correlation weighting; and TPSS, the non-empirical meta-generalized gradient approximation (MGGA) functional recently developed by Staroverov, Scuseria, Tao, and Perdew⁷⁰.

Results from continuum solvation models were employed to assess the effects of a bulk aqueous environment on the gas-phase results⁷¹; such continuum models only provide a description of long-range interactions and have significant limitations in describing protic solvents^72,73. Thus, in some cases, explicit water molecules were used to provide a description of the short-range/site-specific effects of an aqueous environment. The conductor-like screening model (COSMO), pioneered by Klamt and coworkers^74–77, was employed for the continuum calculations in an aqueous medium using the PQS Ab Initio Program Package 3.2 on a PQS Quantum Cube⁷⁸; we employed the default settings in the COSMO module of this software which were specifically tailored to COSMO theory^76,77 and optimized for the BVP86 functional, i.e. the BP86 functional^63,64 in which local correlation was replaced by VWN⁶⁰, using the svp- and tzvp (Ahlrichs) basis sets^79,80. These COSMO results were also compared to the corresponding gas-phase results using natural resonance theory (NRT)^54–57.

RESULTS AND DISCUSSION

Since no experimental data are currently available for any conformers of HN=CH−CH=CH−NH−BO or for (−NH=CH−CH=CH−NH−B−)O, we initially considered H−BO (C_∞h) and H₂N−BO (C_s) at a variety of computational levels to establish “baseline” structural and bonding parameters.

A.1 H−BOAND H₂N−BO

A significant amount of experimental^{22,31–38,42} and computational data^{33,45,81–87} have been reported in the literature for hydroboron monoxide, H−BO, an intermediate/by-product of a variety of reactions involving boron compounds⁸⁸. Calculated bond lengths of H−BO at the MP2(FC)/cc-pVDZ, MP2(FC)/aug-cc-pVDZ, and MP2(FC)/cc-pVTZ levels are shown in Figure 1, and vibrational frequencies at the MP2(FC)/aug-cc-pVDZ level are listed in Table 1S of the Supplementary Materials. Structural parameters at a variety of more-rigorous computational levels are given in Table 2S (including selected results that incorporate core-electron correlation (FULL)^53,89,90, which has virtually no effect on the calculated geometrical parameters); the analogous structural parameters at several DFT/6−311++G(d,p) levels are shown in Table 3S. The calculated boron-oxygen bond lengths, 1.218, 1.222, and 1.214 Å at the MP2(FC)/cc-pVDZ, MP2(FC)/aug-cc-pVDZ, and MP2(FC)/cc-pVTZ levels respectively, all overestimate this length compared to that obtained from microwave spectroscopy, 1.2007 ± 0.0001 Å^34,41,42,44; indeed, as shown by DeYonker et al.⁴⁵, quite sophisticated computational methodology and large basis sets are required to systematically approach the microwave result. NBOs^54–57 for H−BO at the MP2/cc-pVDZ, MP2/aug-cc-pVDZ, and MP2/cc-pVTZ levels consistently showed the presence of one σ- and two π-boron–oxygen bonding orbitals. NRT^54–57 calculations with the BVP86 functional using the tzvp(svp) basis sets^{60,63,64,79,80} found the boron-oxygen bond order to be ~3.00 in H−BO, consistent with the presence of a B≡O bond;the NRT-derived covalent/ionic contributions to the total bond order were 1.24/1.76 at the BVP86/tzvp level; the Löwdin bond order^91–93 for the boron-oxygen bond in H−BO was also calculated and found to be slightly lower, 2.80(2.86), at the BVP86/tzvp(svp) levels, see Table 4S. We also list in Table 4S selected covalent bond orders derived from the atomic overlap matrix (AOM) using the Bader⁹⁴ atoms-in-molecules (AIM) approach to the analysis of electron density^95–97.

Figure 1.

Optimized structures of HBO, H₂NBO and H₂NB(OH)₂. (Distances are in Å).

One measure of the energy content stored in the boron-oxygen triple bond of R−B≡O monomers can be obtained from the thermochemical parameters for its trimerization to the heteroaromatic ring (R₃B₃O₃) boroxine structure^35,98–100. The calculated values of ΔH⁰₂₉₈for the conversion of hydroboron monoxide to H₃B₃O₃ (D_3h) are extremely exothermic, −91.1 and −93.2 kcal/mol in vacuo at the MP2(FC)/cc-pVDZ and MP2(FC)/aug-cc-pVDZ levels respectively. The calculated boron-oxygen bond lengths in this boroxine are all the same, e.g. 1.388 Å at the MP2(FC)/cc-pVDZ level and 1.394 Å at the MP2(FC)/aug-cc-pVDZ level, nearly 0.2 Å longer than the corresponding values in H−B≡O. The calculated NRT BVP86/svp boron-oxygen bond order in H₃B₃O₃ was 1.46 (0.45/1.01), only about 50% of the corresponding value in H−B≡O, suggestive of significant electron delocalization^91,98; the Löwdin bond order was 1.45 at this level, in good agreement with the NRT value, see Table 4S.

In COSMO aqueous media^76,77 at the BVP86/tzvp level the boron-oxygen bond length of H−B≡O increased from the corresponding gas-phase value, but only by ~0.005 Å; the boron-oxygen bond order, 3.00 (1.16/1.84), remained essentially the same. Thus, there appears to be relatively little difference in the geometrical structure or in the bonding of H−B≡O as a result of any long-range effects of bulk solvation. The calculated values of ΔH⁰₂₉₈ for the conversion of hydroboron monoxide to boroxine in COSMO aqueous media at the BVP86/tzvp level was −92.0 kcal/mol compared to −99.3 kcal/mol in vacuo at this level. To assess short-range/site-specific effects of an aqueous environment, we microsolvated the optimized MP2(FC)/cc-pVDZ gas-phase structure of H−B≡O with a few explicit water molecules initially positioned in the vicinity of the B≡O moiety. Although an exhaustive search of all possible conformers of these complexes was not practical at this level, several distinct stable structures were located for 2- and 3-water cases. The lowest-energy forms we found in these hydrated complexes involved an oxygen atom of one of the water molecules effectively bound to the boron atom in H−BO; the calculated B−O_w distance was 1.68(1.67) Å, the B−O distance was 1.26(1.27) Å, and the HBO angle was 140.4°(138.5°) for the 2(3)-water complexes, see Figure 1S in the Supplementary Materials; thus, there is a significant change from the linear gas-phase geometry of H−B≡O on microsolvation. As would be expected, the calculated values of ΔH⁰₂₉₈ for the formation of the lowest-energy 2(3)-water H−BO complexes were substantially exothermic, −18.8(−31.6) kcal/mol.

Since the borocycle described by Vidovic et al.²⁴, and the model (acyclic) HN=CH−CH=CH−NH−BO and (cyclic) (−NH=CH−CH=CH−NH−B−)O structures, all involve boron–nitrogen bonds, in addition to boron-oxygen bonds, we also geometry optimized aminoboron monoxide, H₂N−BO⁵, to assess the effect of a proximal boron-nitrogen bond on the boron-oxygen structural and bonding parameters. To the authors’ knowledge, no experimental synthesis, isolation, or characterization of H₂N−BO, nor any rigorous computational studies of this small molecule, have been reported. The calculated boron-oxygen separation in H₂N−BO was ~0.01 Å longer than it was in H−B≡O at the MP2(FC)/(cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ) computational levels, see Figure 1; selected structural parameters for H₂N−BO at a variety of DFT/6−311++G(d,p) computational levels are listed in Table 3S and show similar increases for the boron-oxygen distance relative to the corresponding values for H−B≡O. The NBOs of H₂N−BO still involve one σ- and two π-bonds at all the MP2(FC)/cc levels included in this investigation. The NRT boron-oxygen bond order in H₂N−BO, 2.90 (1.19/1.71) at the BVP86/tzvp level, was only ~3% lower than the corresponding value in H−B≡O; the corresponding Löwdin bond order, 2.61, was ~7% lower than that in H−B≡O. Furthermore, the weighting of the resonance structure of the form H₂N=B=O, associated with the interaction of the nitrogen lone pair orbital and an antibonding boron-oxygen orbital, was only ~9.2% at this level. Thus, in the gas-phase, the boron-oxygen bond in H₂N−BO appears to be best described as a triple bond.

We also calculated thermodynamic parameters for the trimerization of aminoboron monoxide to the boroxine structure (H₂N)₃B₃O₃ (D_3h)³⁵; the calculated values of ΔH⁰₂₉₈ in the gas phase were −134.7, −130.2 and −125.3 kcal/mol at the MP2(FC)/cc-pVDZ, MP2(FC)/aug-cc-pVDZ, and BVP86/tzvp computational levels respectively, significantly more exothermic than that for the analogous trimerization of hydroboron monoxide. The boron-oxygen bond lengths in the product boroxine structure were all the same, 1.396 Å at the MP2(FC)/cc-pVDZ level and 1.400 Å at the MP2(FC)/aug-cc-pVDZ level, slightly longer than the corresponding values in H₃B₃O₃, but indicative of significant electron delocalization^98–103; the corresponding boron-nitrogen bond lengths were 1.409 and 1.413 Å, respectively.

As might be expected, in the COSMO aqueous media model^76,77, the calculated boron-oxygen bond length in H₂N−BO increased, but only by ~0.01 Å at the BVP86/tzvp level compared to the analogous value in vacuo; the resulting NRT boron-oxygen bond order, 2.55 (0.98/1.57), however, suggests that in this aqueous model the boron–oxygen bonding in H₂N−BO is best described as intermediate between a double and triple bond; indeed, the NRT weighting of the H₂N=B=O bonded resonance structure, 41.7%, was more than 4-times greater than the corresponding weighting in vacuo. Micosolvation of the gas-phase structure of H₂N−BO with a few water molecules positioned at various points around the boron-oxygen functional group, followed by re-optimization of the complex, often resulted in the corresponding amino boronic acid, H₂N−B(OH)₂, hydrogen-bonded to the remaining water molecules. The hydration reaction:

$${\mathrm{H}}_2\mathrm{N}-\mathrm{B}\equiv \mathrm{O}+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{H}}_2\mathrm{N}-\mathrm{B}{(\mathrm{O}\mathrm{H})}_2,$$

is highly exothermic in vacuo, e.g. ΔH⁰₂₉₈ is −44.2, −41.7, −46.3, and −43.0 kcal/mol at the MP2(FC)/cc-pVDZ, MP2(FC)/aug-cc-pVDZ, MP2(FC)/cc-pVTZ, and BVP86/tzvp levels respectively; in COSMO aqueous media at the BVP86/tzvp level, ΔH⁰₂₉₈ is −34.7 kcal/mol, ~8 kcal/mol less negative than the corresponding value in vacuo. We also located the 4-membered cyclic transition state for this hydrolysis reaction in vacuo, and the value of ΔH^‡ was only +4.8 kcal/mol relative to the separated reactants at the MP2(FC)/cc-pVDZ level. The corresponding value of ΔH^‡ at the BVP86/tzvp level was predicted to be slightly lower, +2.2 kcal/mol, whereas in COSMO aqueous media ΔH^‡ was found to be slightly higher, +5.5 kcal/mol. The calculated values of ΔH⁰₂₉₈ for the trimerization of H₂N−B≡O to the corresponding boroxine structure in this COSMO aqueous medium model was −103.0 kcal/mol compared to −125.3 kcal/mol in vacuo.

The boron-nitrogen bond length in H₂N−BO was calculated to be 1.41, 1.40, and 1.39 Å in vacuo at the MP2/cc-pVDZ, MP2/aug-cc-pVDZ, and MP2/cc-pVTZ levels respectively, see Figure 1; the NRT bond order at the BVP86/tzvp level was 1.10 (0.53/0.59), generally consistent with the presence of a boron-nitrogen single bond with ~10% double-bond character. The calculated B−N distance decreased in COSMO aqueous medium by ~0.05 Å at the BVP86/tzvp level and the NRT bond order increased to 1.45 (0.61/0.84). These findings suggest that the boron-nitrogen bond in this model media is most appropriately described as intermediate between a single and double bond.

A.2 (Acyclic) HN=CH−CH=CH−NH−BO Conformers

With the above reference data on H−BO and NH₂−BO in hand, an extensive conformational search of the (acyclic) NH=CH−CH=CH−NH−BO potential energy surface (PES) at the MP2/cc-pVDZ level was performed. A variety of conformers with different cis/trans arrangements about the heavy-atom backbone were located; these conformers typically differed in energy among each other by less than ~5 kcal/mol. Two of these conformers, 1a and 1b, are shown in Figure 2: 1a (TTT) (C_s) is the lowest-energy acyclic structure we found, whereas conformer 1b (CCT) (_Cs), which is ~3 kcal/mol higher in energy than 1a, see Table 1, has a more “cyclic-like” structure but the terminal nitrogen atom was intentionally oriented to eliminate any possibility of an intramolecular boron-nitrogen dative bonding interaction. Infrared vibrational frequencies of 1a and 1b at the MP2(FC)/aug-cc-pVDZ level are listed in Table 1S of the Supplementary Materials. Calculated xyz-coordinates for a variety of HN=CH−CH=CH−NH−BO conformers are given in Table 5S of the Supplementary Materials.

Figure 2.

Optimized structures of the acyclic conformers 1a and 1b of NH=CH−CH=CH−NH−BO and the borocycle 1c (−NH=CH−CH=CH−NH−B−)O. (Distances are in Å). (AIM calculations using the MP2/cc-pVDZ density find the expected molecular graph for 1c (12 attractors, 12 critical points on attractor interaction lines, and 1 ring point.)

Table 1.

Relative Energies, E(kcal/mol) (Values Thermally Corrected to 298 K° Are Given in Parentheses) for the Acyclic conformers 1a (TTT) and 1b (CCT) of NH=CH−CH=CH−NH−BO and the cyclic conformer 1c (CCC) of (−NH=CH−CH=CH−NH−B−)O at the MP2(FC)/cc-pVDZ, MP2(FC)/aug-cc-pVDZ, and MP2(FC)/cc-pVTZ Computational Levels.

Level	E(kcal/mol)	E(kcal/mol)	E(kcal/mol)
	1c (CCC)	1a (TTT)	1b (CCT)
MP2(FC)/cc-pVDZ	0.0(0.0)	+31.4(+29.8)	+34.8(+33.3)
MP2(FC)/aug-cc-pVDZ	0.0(0.0)	+32.6(+31.1)	+35.3(+33.8)
MP2(FC)/cc-pVTZ	0.0 (0.0)	+33.9(+32.3)	+36.9(+35.4)

The calculated boron-oxygen distances for 1a in vacuo, 1.226, 1.231, and 1.223 Å at the MP2(FC)/cc-pVDZ, MP2(FC)/aug-cc-pVDZ, and MP2(FC)/cc-pVTZ levels respectively, see Figure 2, are nearly the same as those in H₂N−B≡O at the corresponding computational levels, see Figure 1. An examination of the NBOs in 1a at the MP2(FC)/cc-pVDZ and MP2(FC)/aug-cc-pVDZ levels confirmed the existence of a boron-oxygen σ-bonding orbital and predicted a pair of π-bonding orbitals, similar to what was found in both H−B≡O and H₂N−B≡O. The NRT (BVP86/tzvp) bond order for 1a, 2.91 (1.21/1.70), was almost identical to that for H₂N−B≡O, 2.90 (1.19/1.71) and the corresponding Löwdin bond order, 2.63, was nearly the same as in H₂N−B≡O, 2.61, see Table 4S. Furthermore, the weighting of the B≡O bonded resonance structure was ~62.5% compared to only ~8.4% for the B=O bonded structure at the BVP86/tzvp level. Thus, the boron-oxygen bond in 1a is best described as a triple bond in vacuo.

Thermodynamic parameters for the conversion of 1a to the corresponding (NH=CH−CH=CH−NH)₃B₃O₃ boroxine structure⁴² were also computed; the calculated value of ΔH⁰₂₉₈ was −141.1 kcal/mol at the MP2(FC)/cc-pVDZ computational level compared to - 134.7 kcal/mol for the analogous conversion of NH₂−BO.

In the context of the COSMO BPV86/tzvp aqueous medium model, the characteristics of the boron–oxygen bonding in all the (acyclic) HN=CH−CH=CH−NH−BO derivatives that we investigated were similar to those we observed for H₂N−BO, e.g. the boron–oxygen distance in 1a increased slightly, by ~0.007 Å compared to its value in vacuo, and the NRT bond order, 2.63 (1.03/1.60), was lower than its value in vacuo, 2.91 (1.21/1.70), as was the corresponding Löwdin bond order, 2.55 compared to 2.63. Thus, the boron-oxygen bonding of NH=CH−CH=CH−NH−BO (1a) in a COSMO aqueous media model appears to be intermediate between a double and triple bond.

Short-range/site-specific effects of an aqueous environment on the structure of NH=CH−CH=CH−NH−BO (1a) were also investigated using a few explicit water molecules initially positioned in the vicinity of the boron-oxygen moiety of the optimized gas-phase MP2(FC)/cc-pVDZ structure. An exhaustive search of all possible conformers of these complexes was obviously not possible, but a variety of different initial arrangements of the water molecules were considered; of course, this does not ensure that we obtained the global minimum on the appropriate PES. As was noted above for H₂N−B≡O, in some instances these hydrated adducts of NH=CH−CH=CH−NH−BO (1a) (in vacuo, as well as in COSMO aqueous media) converted to the corresponding boronic acid during the re-optimization; in other adducts the NH=CH−CH=CH−NH−BO structure remained intact, although in these conformers the boron-oxygen bond length was relatively long, ~1.28 Å. Indeed, the hydration reaction,

$$\mathrm{H}\mathrm{N}=\mathrm{C}\mathrm{H}-\mathrm{C}\mathrm{H}=\mathrm{C}\mathrm{H}-\mathrm{N}\mathrm{H}-\mathrm{B}\mathrm{O}(\mathbf{1}\mathbf{a})+{\mathrm{H}}_2\mathrm{O}\to \mathrm{H}\mathrm{N}=\mathrm{C}\mathrm{H}-\mathrm{C}\mathrm{H}=\mathrm{C}\mathrm{H}-\mathrm{N}\mathrm{H}-\mathrm{B}{(\mathrm{O}\mathrm{H})}_2,$$

was calculated to be highly exothermic, e.g. ΔH₀²⁹⁸ was −49.4 and −46.4 kcal/mol at the MP2(FC)/cc-pVDZ and MP2(FC)/aug-cc-pVDZ levels respectively, some 5 kcal/mol more exothermic than the analogous reaction for H₂N−B≡O. We also located the transition state for this hydration reaction in vacuo; the value of ΔH^‡ for the formation of the resulting four-membered ring structure was only +1.8 kcal/mol above the separated reactants compared to +4.8 kcal/mol for H₂N−B≡O.

The boron-nitrogen bonding in 1a is also similar to that in H₂N−BO: the compositions of the boron-nitrogen NBOs for NH=CH−CH=CH−NH−BO (1a) and H₂N−BO were nearly the same at the computational levels we employed, and the calculated BVP86/tzvp NRT bond order in 1a, 1.09 (0.49/0.60) was almost identical to that in H₂N−BO, 1.10 (0.51/0.59). The boron-nitrogen bond order for NH=CH−CH=CH−NH−BO (1a) in a COSMO BPV86/tzvp aqueous medium was 1.34 (0.55/0.79), attesting to the increased importance of a N=B=O resonance structure in such an environment.

A.3 (−NH=CH−CH=CH−NH−B−)O Borocycle

The (−NH=CH−CH=CH−NH−B−)O borocycle, 1c, see Figure 2, was ~30 kcal/mol lower in energy than any of the acyclic conformers of HN=CH−CH=CH−NH−BO we found at the MP2/cc-pVDZ, MP2/aug-cc-pVDZ, and MP2/cc-pVT levels, see Table 1; infrared frequencies of 1c, calculated at the MP2/aug-cc-pVDZ level, are listed in Table 1S of the Supplementary Materials. The transition state that connects the borocycle 1c and the acyclic conformer 1b of HN=CH−CH=CH−NH−BO was also located, see Figure 2S of the Supplementary Materials; it was 40.5 and 41.0 kcal/mol higher in energy than 1c at the MP2/cc-pVDZ and MP2/aug-cc-pVDZ levels respectively. The calculated boron-oxygen separation in the borocycle 1c, 1.266, 1.277, and 1.265 Å at the MP2(FC)/ccpVDZ, MP2(FC)/aug-cc-pVDZ, and MP2(FC)/cc-pVTZ levels respectively, is ~0.04 Å longer than it is in the acyclic HN=CH−CH=CH−NH−BO derivatives at these levels. An examination of the NBOs in 1c at the MP2(FC)/cc-pVDZ and MP2(FC)/aug-cc-pVDZ levels confirms the existence of a boron-oxygen σ-bonding orbital and one π-bonding orbital. The NRT boron-oxygen bond order for 1c at the BVP86/tzvp level, 2.28 (0.95/1.33), is significantly lower than the corresponding value for the acyclic conformer, 1a, 2.91 (1.21/1.70) at this level; the Löwdin bond order for 1c is 2.32, compared to 2.63 for 1a and 2.61 in H₂N−B≡O. Thus, in vacuo, it appears reasonable that the boron-oxygen bond in 1c can be regarded as predominately a double bond.

In the COSMO BPV86/tzvp aqueous medium model, the length of the boron-oxygen bond in 1c increased by ~0.03 Å to 1.297 Å compared to its value in vacuo; the corresponding bond order decreased by ~0.3 to 1.95 (0.72/1.23); the Löwdin bond order was only 1.50. We also optimized 1c in the presence of two and three explicit water molecules, initially positioned in the vicinity of the BO moiety; although our computer resources only allowed a limited exploration of these PESs, the resulting B−O_B distances in the re-optimized complexes tended to be relatively long, e.g. ~1.30 Å at the MP2(FC)/cc-pVDZ level. Thus, the short-range/site-specific effects of explicit water molecules on this borocycle appear to be less dramatic than those we observed in the acyclic derivatives. Nevertheless, these findings suggest that the boron-oxygen bond in 1c has a significant degree of double bond character in an aqueous environment.

The calculated value of ΔH⁰₂₉₈ for the hydration reaction,

$$(-\mathrm{N}\mathrm{H}=\mathrm{C}\mathrm{H}-\mathrm{C}\mathrm{H}=\mathrm{C}\mathrm{H}-\mathrm{N}\mathrm{H}-\mathrm{B}-)\mathrm{O}(\mathbf{1}\mathbf{c})+{\mathrm{H}}_2\mathrm{O}\to (-\mathrm{N}\mathrm{H}=\mathrm{C}\mathrm{H}-\mathrm{C}\mathrm{H}=\mathrm{C}\mathrm{H}-\mathrm{N}\mathrm{H}-\mathrm{B}-){(\mathrm{O}\mathrm{H})}_2,$$

was −32.6 kcal/mol at the MP2(FC)/cc-pVDZ level, much less exothermic than for the hydrolysis of the acyclic structure HN=CH−CH=CH−NH−BO (1a) or for H₂N−B≡O, which is a reflection of the stability of the borocycle 1c compared to that of 1a. We located the transition state for this hydrolysis; the value of ΔH^‡ was +7.6 kcal/mol at the MP2(FC)/cc-pVDZ level, slightly higher than the corresponding values for H₂N−B≡O (+4.8 kcal/mol) and HN=CH−CH=CH−NH−BO (1a) (+1.8 kcal/mol).

The two B−N bonds in this novel borocycle 1c have the same length, i.e. there is no structural distinction between the “formal” N−B single bond and the N:B dative bond, a reflection of the extent of electron delocalization in this conformer. The boron-nitrogen distances in 1c, 1.539, 1.534, 1.529, and 1.538 Å at the MP2(FC)/cc-pVDZ, MP2(FC)/aug-cc-pVDZ, MP2(FC)/cc-pVTZ and BPV86/tzvp levels respectively, are ~0.13 Å longer than the corresponding boron-nitrogen separation in 1a and 1b.

For a more direct comparison with the experimental results of Vidovic et al.²⁴, we also geometry-optimized one conformer of the (−N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−B−)O borocycle at the MP2/cc-pVDZ level in vacuo, see Figure 3; the computed boron-oxygen bond length, 1.264 Å, was marginally shorter than the corresponding distance in NH=CH−CH=CH−NH−BO(1c) at this computational level, but significantly shorter than the calculated value at the B3LYP/6−311+G(d) level, 1.292 Å, and even shorter than the experimental X-ray distance in the crystal structure of (−N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−B−)O→AlCl₃, 1.304(2) Ų⁴. The corresponding boron-oxygen bond length for an acyclic conformer of N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−BO that is analogous to conformer 1a of HN=CH−CH=CH−NH−BO was 1.226 Å at the MP2/cc-pVDZ level, slightly longer than the corresponding length in NH=CH−CH=CH−NH−BO(1a), but ~0.04 Å shorter than this length in (−N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−B−)O; this (acyclic) N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−BO conformer was 34.4 kcal/mol higher in energy than that for the analogous borocycle. The NBOs of (−N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−B−)O indicate the presence of one σ- and only one π-boron–oxygen bonding orbital suggesting the presence of a double bond, corroborating the interpretation of Vidovic et al.²⁴.

Figure 3.

Optimized structures of the borocycle (−N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−B−)O and the acyclic conformer N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−BO at the MP2/cc-pVDZ computational level.

A.4 A Comparison of MP2(FC)/(aug)cc-pVxZ (x = D,T) and DFT/6−311++G(d,p) Results for HN=CH−CH=CH−NH−BO and (−NH=CH−CH=CH−NH−B−)O

Calculated boron-oxygen and boron-hydrogen(nitrogen) bond lengths in H−B≡O, H₂N−B≡O, H₂N−B(OH)₂, HN=CH−CH=CH−NH−B≡O(1a–b), and (−NH=CH−CH=CH−NH−B−)O(1c) are listed in Table 3S at a variety of DFT/6−311++G(d,p) levels; the Pople-style 6−311++G(d,p) basis set is at the “upper-end” of basis sets that are likely to be employed in studies of larger boron containing compounds in the near future. In this investigation we have performed a limited comparison between the more rigorous MP2(FC) methodology using the (aug)cc-pV(D,T)Z, basis sets and the more economical DFT methodology with the LDA, PBE, TPSS, BLYP, B3LYP, BVP86, OLYP, O3LYP, and PBE1PBE functionals using the 6−311++G(d,p) basis set.

Comparing the calculated MP2/(cc-pVDZ, aug-cc-pVDZ, cc-pVTZ) boron-oxygen bond distances, see Figure 1 and Figure 2, and the corresponding DFT/6−311++G(d,p) distances given in Table 3S, it is evident that there is reasonable agreement among these various methods/basis-sets to within ~0.02Å. The calculated boron-oxygen bond length in H−B≡O at both the B3LYP/6−311++G(d,p) and the PBE1PBE/6−311++G(d,p) levels was in particularly good agreement with the microwave data, see Table 3S. Furthermore, this finding does not appear to be highly basis-set dependent - the boron-oxygen bond lengths calculated using the B3LYP functional with the cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ basis sets were 1.203, 1.205, and 1.200 Å respectively, and the corresponding PBE1PBE distances were 1.202, 1.204 and 1.199 Å.

Values for a variety of DFT/6−311++G(d,p) energy differences among the acyclic conformers 1a and 1b of HN=CH−CH=CH−NH−BO and of the borocycle (−NH=CH−CH=CH−NH−B−)O 1c are listed in Table 6S of the Supplementary Materials. A comparison of Table 1 and Table 6S shows that there is good agreement between the relative energies of 1a and 1b at the various DFT/6−311++G(d,p) and the MP2(FC)/cc levels, i.e. conformer 1b is consistently ~3–4 kcal/mol higher in energy than 1a. As might be expected, the variation of energy values (corrected to 298K) between the borocycle 1c and the acyclic conformer 1a is significantly greater, ranging from 27.8 kcal/mol (B3LYP) to 42.5 kcal/mol (LDA); however, ignoring the LDA value, which includes only local terms in the correlation functional, the variation is significantly less, the highest value is 35.3 kcal/mol (PBE1PBE); the corresponding MP2(FC)/(aug)-cc-pVD(T)Z values range from 29.8 to 32.3 kcal/mol, see Table 1. Thus, to a large extent, these DFT/6−311++G(d,p) energy differences are in quite good agreement with the available MP2(FC)/cc results; unfortunately, no experimental data are currently available for comparison. In view of our previous results involving dative bonding interactions^27–30 it appears that the PBE1PBE/6−311++G(d,p) computational level is a reasonable, economical alternative to the more-costly MP2(FC)/cc levels for exploring various aspects of boron chemistry.

It is of interest to assess geometrical and energetic results associated with climbing the DFT ladder (“Jacob’s ladder”): LDA→PBE→TPSS¹⁰⁴, using the modest 6−311++G(d,p) basis set. The calculated LDA/6−311++G(d,p) boron-oxygen bond length in H–B≡O, 1.202 Å is in excellent agreement with the experimental microwave value 1.201 Å, as well as with the corresponding B3LYP and PBE1PBE values. The initial LDA→PBE step on the ladder at this computational level results in a boron-oxygen bond length that is ~0.01 Å longer, and nearly the same as the MP2(FC)/6−311++(d,p) length, 1.212 Å. The second step on the DFT ladder is PBE→TPSS; at this step the boron-oxygen bond length changes minimally, see Table 3S. The energy difference between the borocycle 1c and the acyclic derivative 1b improves dramatically in going from LDA to PBE compared to the various MP2(FC)/cc differences and most of the DFT/6−311++G(d,p) differences, see Table 1 and Table 6S; the energy change in going from PBE to TPSS is minimal.

CONCLUDING REMARKS

The importance of boron chemistry is increasing rapidly in a variety of fields, and unveiling the intricacies of boron bonding remain an active area of research^{3,17,19,24,26,29,81,82}. In this article we report results from a computational investigation of the boron-oxygen bonding in H−BO and H₂N−BO, as well as in the acyclic conformers of HN=CH−CH=CH−NH−BO (1a, 1b) and in the corresponding borocycle (−NH=CH−CH=CH−NH−B−)O (1c); MP2 methodology with the correlation-consistent cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ basis sets and DFT methodology with the 6−311++G(d,p) basis set were employed for the calculations.

Experimentally and/or computationally derived distances between the boron and oxygen atoms, a key parameter in any discussion of bond order¹⁰⁵, the calculated composition of the molecular orbitals at a variety of MP2/cc and DFT/6−311++G(d,p) levels, and the computed NRT bond orders at the BVP86/(svp)tzvp-Ahlrichs levels are consistent with the presence of a boron-oxygen triple bond in H−BO, H₂N−BO, and various (acyclic) conformers of HN=CH−CH=CH−NH−BO in vacuo. Using the COSMO BVP86/(svp)tzvp models to simulate the long-range effects of an aqueous medium, the boron-oxygen bond in H−BO was still best described as a triple bond, whereas for H₂N−BO and HN=CH−CH=CH−NH−BO(1a, 1b) this bond appears to be more appropriately described as intermediate between a double and triple bond. Incorporating several explicit water molecules in the vicinity of the boron-oxygen bond during the optimization of complexes of H₂N−B≡O and HN=CH−CH=CH−NH−BO(1a), to account for short-range/site-specific effects on the boron-oxygen bonding, often resulted in the corresponding boronic acid, suggesting that in an aqueous environment the presence of H₂N−B≡O or HN=CH−CH=CH−NH−BO(1a, 1b) would be short-lived. The boron–nitrogen bond in H₂N−B≡O and HN=CH−CH=CH−NH−B≡O(1a, 1b) was predominantly a single bond in vacuo, but was predicted to have substantial double bond character by the COSMO BPV86/tzvp aqueous media model.

At all the MP2(FC)/(aug)-cc-pVxZ and DFT/6−311+G(d,p) computational levels we employed in this investigation, the (−NH=CH−CH=CH−NH−B−)O borocycle, 1c (C_2v symmetry), was ~30 kcal/mol lower in energy than any of the HN=CH−CH=CH−NH−B≡O acyclic conformers we found, see Table 1 and Table 5S. All indications are that the boron-oxygen bond in this borocycle is predominantly a double bond, in accord with the available experimental results on (−N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−B−)O²⁴. The calculated lengths of the two boron-nitrogen bonds in 1c and (−N(C₆F₅)=C(CH₃)−CH=C(CH₃)−N(C₆F₅)−B−)O were identical, a measure of the extent of electron delocalization in this conformer.

The hydration reactions,

$$\mathrm{H}\mathrm{N}=\mathrm{C}\mathrm{H}-\mathrm{C}\mathrm{H}=\mathrm{C}\mathrm{H}-\mathrm{N}\mathrm{H}-\mathrm{B}\mathrm{O}(\mathbf{1}\mathbf{a},\mathbf{1}\mathbf{c})+{\mathrm{H}}_2\mathrm{O}\to \mathrm{H}\mathrm{N}=\mathrm{C}\mathrm{H}-\mathrm{C}\mathrm{H}=\mathrm{C}\mathrm{H}-\mathrm{N}\mathrm{H}-\mathrm{B}{(\mathrm{O}\mathrm{H})}_2,$$

were calculated to be highly exothermic; the calculated values of ΔH⁰₂₉₈ for 1a and 1c were −49.4 and −32.6 kcal/mol respectively at the MP2(FC)/cc-pVDZ level, an indication of the amount of energy stored in the boron-oxygen bond in these compounds. Furthermore, the calculated value of ΔH⁰₂₉₈ for the trimerization reaction of HN=CH−CH=CH−NH−BO(1a) to form the ((NH=CH−CH=CH−NH)₃B₃O₃) boroxine structure was −141.1 kcal/mol at the MP2(FC)/cc-pVDZ computational level These findings help to quantify the high-energy content of BO multiple bonds.