Introduction

Boronic acids, RB(OH)2, are a versatile class of compounds with applications in synthetic, biological, medicinal, and materials chemistry [1–32] and are widely used in the field of molecular recognition as chemical sensors for 1,2- and 1,3-diols. Boronic acid host compounds readily form boronate esters with saccharides in one of the few processes where a covalent bond can be rapidly made and subsequently broken [33]. When ortho-aminomethyl phenylboronic acids are rationally designed, the resulting boronate esters fluoresce due to subtle changes in Lewis acid–base chemistry of the proximal amine and the boron atom. A modification in the chemical structure adjacent to the boronic acid moiety can change the saccharide selectivity, pH range of operation, and fluorescence reporting abilities of the host compound.

Like their boronic acid counterparts, borinic acids, R1R2B(OH), have a variety of applications, e.g., in catalysis [34–36] and medicine [37–41], although their utility in molecular recognition is only beginning to be exploited [35, 36, 42–45]. Chudzinski et al. [42] recently highlighted this “neglected class of organoboron compounds” for diol recognition and detailed the effectiveness of diphenylborinic acid to preferentially bind the diol compounds catechol, L-lactic acid, and Alizarin Red S. Indeed, association constants for diphenylborinic acids bound to these particular substrates are nearly an order of magnitude larger than for similar boronic acids. Chudzinski et al. [42] speculated that this increase in affinity toward catechol, L-lactic acid, and Alizarin Red S could be a steric effect. However, there have been no systematic investigations of the structural and/or bonding differences in corresponding boronic and borinic acids that might help identify those features that affect their preference toward specific substrates.

The nature of the bonding surrounding the boron atom in both boronic and borinic acids is distinctive as a result of the empty p-orbitals on the trivalent boron atoms. Donor–acceptor interactions involving lone-pair orbitals on the hydroxyl oxygen atoms and these empty p-orbitals play a significant role in the nature of the boron–oxygen bonding. Lone-pair orbitals available from simple aliphatic substituents provide competitive donor–acceptor interactions that also impact the boron–oxygen bonding. Boronic acids differ from borinic acids by the presence of two boron–oxygen bonds and an intramolecular B–O–H…O hydrogen-bonding interactions inherent in the lower-energy endo-exo conformers of boronic acids [46–48]. These differences are expected to result in distinct steric and electronic properties of corresponding boronic and borinic acids that will influence their effectiveness as diol receptors to specific substrates. In this investigation, we compare the structure and bonding surrounding the trivalent boron atoms in the simple aliphatic boronic acids, R–B(OH)2 (R=H; NH2, OH, and F) and their related borinic acids, R–BH(OH), as a first step toward understanding their distinguishing properties.

Computational methods

Equilibrium geometries of all the molecules involved in this article were obtained using second-order Møller–Plesset perturbation theory with the frozen-core option, MP2(FC) [49], which neglects core–electron correlation; the Dunning–Woon aug-cc-pVTZ basis set was employed for all the geometry optimizations and the more complete aug-cc-pVQZ and aug-cc-pV5Z basis sets in selected optimizations [50–53]. Frequency analyses were performed analytically for all the compounds in this investigation at the MP2(FC)/aug-cc-pVTZ level to confirm that the geometry optimized structures were local minima on the potential energy surfaces (PESs). The GAUSSIAN 03 [54] and GAUSSIAN 09 [55] suits of programs were used for all the calculations. The geometry optimizations were followed by single-point calculations at the CCSD(FC)/aug-cc-pVTZ//MP2(FC)/aug-cc-pVTZ level to generate the QCI density for analyses of the bonding. Atomic charges were obtained from natural population analyses (NPA), and the bonding was analyzed with the aid of natural bond orbitals (NBOs). NBO version 3.1 embedded in GAUSSIAN 03 [54] and GAUSSIAN 09 [55] was used for all these calculations. The RESONANCE and E2PERT keywords were employed; the E2PERT command enables second-order perturbative estimates of donor–acceptor (bond–antibond) stabilization interaction energies, E(2), to be calculated in the NBO basis set [56–59]. Since NBO analyses using the (non-variational) MP2 density can be problematic, we consistently employed results from the HF/aug-cc-pVTZ and QCI densities [60]). NBOPro version 6.0 was used for visualization of natural bonding orbitals [61]. Atoms in molecules (AIM) calculations [62] using the MP2(FC)/aug-cc-pVDZ//MP2(FC)/aug-cc-pVDZ density were performed in selected cases to provide bond orders and atomic charge comparisons; the implementation in G03 [54] by Ciolslowski et al. [63, 64] was used for these calculations.

Results and discussion

Boron–oxygen bonding

R–B(OH)2 (R=H; NH2, OH, and F)

The optimized structures of the lowest-energy endo-exo conformers of R–B(OH)2 (R=H; NH2, OH, and F) are all planar at the MP2(FC)/aug-cc-pVTZ level [46–48, 65–70]. Selected structural parameters are shown in Fig. 1, and additional values are listed in Table 1a; the corresponding parameters from MP2(FC)/aug-cc-pVQZ and MP2(FC)/aug-cc-pV5Z optimizations are also given in Table 1a. Bond lengths for the higher-energy anti conformers are given in the footnotes to Table 1a.

Fig. 1
figure 1

Selected distances (Å) and angles (°) for the endo-exo conformers of the boronic acids H–B(OH)2, (H2N–B(OH)2), [HO–B(OH)2], and {F–B(OH)2} and for the cis conformers of the corresponding borinic acids calculated at the MP2(FC)/aug-cc-pVTZ//MP2(FC)/aug-cc-pVTZ level

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Table 1 Selected structural parameters of a. the boronic acids R–B(OH)2 (endo-exo) and b. the borinic acids R–BH(OH) (cis) (R=H; NH2, OH, F; X=H; N, O, F)
Full size table

Experimental structural data available for simple aliphatic boronic acids are rather limited. In 1981, Boggs and Cordell [65] presented approximate r0 structures of HB(OH)2 and FB(OH)2 based on earlier microwave studies in the gas phase reported by Kawashima et al. [71, 72]; the boron–oxygen distances were given as 1.353 and 1.366 Å for HB(OH)2 and as 1.360 and 1.365 Å for FB(OH)2. An experimental solid-phase boron–oxygen distance of 1.368 Å for B(OH)3 was given by Gajhede et al. [73]. Our calculated B–O distances, see Table 1a, are in reasonable agreement with these experimental values. More recently, Cyrański et al. [74] reported the results of an X-ray crystallographic study of n-butylboronic acid; the endo-exo monomers are arranged in centrosymmetric dimers in the crystal structure. The observed boron–oxygen distances are 1.3672(22) and 1.3795(20) Å, and the O–B–O angle is 116.048(135)° [75]; the corresponding values calculated at the MP2(FC)/aug-cc-pVTZ level for the gas-phase monomeric structure, 1.372 Å, 1.379 Å, and 117.4°, are in acceptable agreement with the crystallographic values, providing confidence in this computational level to generate sensible geometries for simple aliphatic boronic acids.

The MP2(FC)/aug-cc-pVTZ optimized boron–oxygen bond lengths, 1.386, 1.374, and 1.369 Å for the X–B–O–H cis-branch, and 1.379, 1.374, and 1.361 Å for the X–B–Ot–H trans-branch, X=N, O, and F, respectively) clearly decrease as the electronegativity of X increases [76, 77]. Improving the basis set to aug-cc-pVQZ or aug-cc-pV5Z results in a decrease in all the boron–oxygen distances by ca. 0.005 Å, see Table 1a, but does not alter the overall trend.

NBO analyses using either the HF or QCI densities with the aug-cc-pVTZ basis set identify only two boron–oxygen natural bonding orbitals for the endo-exo (and anti) conformers of H–B(OH)2, see Fig. 2, along with a total of four lone-pair orbitals, two on each oxygen atom. A similar description of the boron–oxygen bonding is also found for NH2–B(OH)2, OH–B(OH)2, and F–B(OH)2. However, second-order perturbative estimates of the donor–acceptor interaction energies, E(2) [56–59], available using the HF/aug-cc-pVTZ density in the NBO basis, indicate that significant stabilization is provided for each of these boron–oxygen bonds as a result of n O → n*B interactions involving the p-orbitals perpendicular to the planes of the molecules; the E(2) values for the cis and trans interactions of the endo-exo (anti) conformers are as follows: H, 65.0 and 66.2 kcal/mol (anti 68.5 kcal/mol); NH2, 55.6 and 58.8 kcal/mol (anti 58.3 kcal/mol); OH, 61.2 and 61.2 kcal/mol (anti 60.5 and 63.9 kcal/mol); and F: 63.3 and 66.6 kcal/mol (anti 66.4 kcal/mol). Clearly, the E(2) interaction energies increase in going from NH2 to OH and F as the electronegativity increases from N to F. Thus, NBO analyses suggest a model in which the boron–oxygen bonds in these simple aliphatic boronic acids are significantly stabilized by dative pπ–pπ interactions. This finding is in accord with the classification scheme for boron–oxygen bonding proposed by Straub [78] some 20 years ago. Based on a variety of experimental bond lengths, he proposed that boron–oxygen bonds with lengths in the range 1.36–1.37 Å have partial double bond character, BO. Indeed, the calculated boron–oxygen bond lengths for these simple boronic acids are generally in this Straub range, see Table 1a.

Fig. 2
figure 2

The two boron–oxygen natural bonding orbitals of the endo-exo conformer of H–B(OH)2, identified by the NBO analysis using HF densities with the aug-cc-pVTZ basis set

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This NBO description of the boron–oxygen bonding in H–B(OH)2, HO–B(OH)2, and F–B(OH)2 is rather different from that proposed by Mierzwa et al. [79] based on a topological analyses of the electron localization functions (ELFs). These authors found that the boron–oxygen bonds in H–B(OH)2, HO–B(OH)2, and F–B(OH)2 are each described by one V(B,O) attractor with average basin populations very close to 2.0e (2.05e, 1.99e, and 2.01e, respectively), indicative of single bonds. Furthermore, they found that the non-bonding electron density for each oxygen atom is characterized by a single V(O) basin with populations about 4.0e, i.e., two lone pairs of electrons on each oxygen atom. Mierzwa et al. [79] concluded that there is “no indication of dative pπ–pπ bonding” and that the partial double bonds “proposed by Straub are actually single B–O bonds” [78, 79].

The composition of the natural atomic hybrid orbitals of the boron–oxygen NBOs is given in Table 1SA of the Supplementary Materials. The p-character of the atomic hybrids on the boron atoms for the two distinct groups of boron–oxygen bonds for H2N–B(OH)2, HO–B(OH)2, and F–B(OH)2 using the QCI density (cis: sp 2.11, sp 2.00, and sp 1.91; trans: sp 2.14, sp 2.00, and sp 1.89) decreases, while the p-character of the atomic hybrids on the corresponding oxygen atoms (cis: sp 1.41, sp 1.47, and sp 1.52; trans: sp 1.39, sp 1.47, and sp 1.51) increases, as the electronegativity increases from N to F, in accord with Bent’s rule [80]. As would be expected, the NPA charge on the boron atoms for R–B(OH)2 become more positive (QCI: +1.13e, 1.21e, 1.29e) as the electronegativity of the substituent increases, see Table 2a, while the occupancies of the boron lone-pair orbitals decrease (QCI: 0.392e, 0.371e, and 0.353e for R=NH2, OH, and F) [80]. AIM charges based on the MP2(FC)/aug-cc-pVDZ density display the same trend.

Table 2 NPA charges (e) on the atoms in the a. boronic acids R–B(OH)2 (endo-exo) and b. borinic acids R–BH(OH) (R=H; NH2, OH, F) calculated from the MP2(FC)/aug-cc-pVTZ (top) and QCI(FC)/aug-cc-pVTZ (bottom) densities
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R–BH(OH) (R=H; NH2, OH, and F)

Optimized structures of the corresponding borinic acids, R–BH(OH) for (R=H; NH2, OH, and F), are also planar at the MP2(FC)/aug-cc-pVTZ level, and selected structural parameters are shown in Fig. 1, and additional values are listed in Table 1b. For comparing these R–BH(OH) structures, we specifically utilized conformers where the X–B–O–H dihedral angles (X=H; N, O, F) are cis, see Fig. 1. Although these acids lack the intramolecular B–O–H…O interactions inherent in the endo-exo conformers of the corresponding boronic acids, they retain possible intramolecular interactions of the form B–O–H…R. (The conformers of the borinic acids with the X–B–O–H dihedral angles in a trans arrangement were also optimized; bond lengths are given in the footnotes to Table 1. For X=N the trans conformer is ~1.8 kcal/mol lower in energy than the cis conformer, whereas for X=F the trans form is ~0.4 kcal/mol higher in energy.)

There is a paucity of experimental structural data for simple borinic acids. Borinic acid itself, H2BOH, is unstable, but its microwave structure has been reported by Kawashima et al. [77]: B–O = 1.352(4) Å, O–H = 0.967(14) Å, B–H = 1.200 Å (assumed), <B–O–H = 112.0(17)°, cis < H–B–O = 121.8(8)°, and trans < H–B–O = 117.2(8)°. Our calculated MP2(FC)/aug-cc-pVTZ structural parameters are in reasonable accord with these microwave values, see Fig. 1 and Table 1b, as well as with previous ab initio results [81–83]; improving the basis set to aug-cc-pVQZ and aug-cc-pV5Z does decrease the boron–oxygen bond length from 1.360 to 1.356 and 1.354 Å, respectively, in better agreement with the microwave value. Kawashima et al. [71] also observed F–BH(OH) by microwave spectroscopy in the hydrolysis of BF3 and diborane. They identified the observed conformer as trans, although they conjectured that the cis conformer would be lower in energy, consistent with what we found at the MP2(FC)/aug-cc-pVTZ level. No structural parameters were reported by Kawashima et al. [71].

The calculated boron–oxygen distance in H2B(OH), 1.360 Å at the MP2(FC)/aug-cc-pVTZ level, is 0.014 Å shorter than the corresponding distance in the H–B–O–H cis-branch of the endo-exo form of H–B(OH)2, 1.374, and 0.006 Å longer than either boron–oxygen distance in the anti form, see Table 1. In contrast to what we found for H–B(OH)2, NBO analyses using either the HF or QCI densities classify this boron–oxygen bond in H2B(OH) as a double bond, see Fig. 3. The calculated AIM boron–oxygen bond order for H2B(OH) using the MP2(FC)/aug-cc-pVDZ density is also greater than that of either boron–oxygen bonds in H–B(OH)2. Indeed, the boron–oxygen bonds in a variety of second-row borinic acids R–BH(OH) (R=Li, HBe, H2B, and H3C), where there are no competing lone pairs available for dative bonding to the boron atom, are all calculated to be slightly shorter than in their boronic acid analogs at the MP2(FC)/aug-cc-pVTZ level, and they are consistently classified as double bonds in NBO analyses using either the HF or QCI densities. Although Straub [78] did not consider H2B(OH) directly, he did classify the boron–oxygen bond in H2B(OCH3) as a double bond. The experimental gas-phase boron–oxygen bond length in H2B(OCH3) is 1.352 Å [84, 85], and the MP2(FC)/aug-cc-pVTZ geometry optimized value is almost the same, 1.351 Å. Mierzwa et al. [79] also performed a topological analysis of the ELF for H2B(OCH3) and found that the electron population of the V(B,O) basin was 2.22e and the electron population of the lone pair V(O) was only 3.29e, values indicative of some multiple bond character, but certainly not a double bond.

Fig. 3
figure 3

(left) top and (right) side views of the σ- and π-bonding orbitals of H2BOH. The NBO analysis using HF densities with the aug-cc-pVTZ basis set classified this bond as a double bond

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It is important to note that a definitive boron–oxygen double bond has been somewhat elusive. In 2005, Vidovic et al. [86] prepared and characterized the first Lewis acid-coordinated oxoborane in which the boron–oxygen bond retained significant double bond character. The X-ray boron–oxygen distance in the >B=O…AlCl3 moiety was 1.304(2) Å, much shorter than the boron–oxygen bond lengths in H2B(OCH3) and (CH3)2BOB(CH3)2, 1.352 and 1.359 Å, that Straub [78] classified as having B=O bonds, but much longer than the experimental B≡O triple bonds for HB≡O, 1.201 Å [87], or the MP2(FC)/aug-cc-pV5Z optimized length, 1.209 Å. Subsequently, geometry optimizations and NBO analyses showed that the core borocycle (–HN=CH–CH=CH–NH–B–)O at the heart of the Vidovic et al. [86] structure also had a B=O double bond in the gas phase; at the MP2(FC)/aug-cc-pVTZ level, the boron–oxygen distance in (–HN=CH–CH=CH–NH–B–)O is 1.270 Å [88]. Thus, it appears that a B=O double bond can be significantly shorter than the boron–oxygen bond found in H2B(OH) and that the Straub classification of B=O double bond lengths being ~1.35 Å may be closer to the upper limit for the boron–oxygen double bond length.

For the borinic acids H2N–BH(OH), HO–BH(OH), and F–BH(OH), where competitive donor–acceptor interactions involving the lone pairs on N, O and F are possible, the calculated boron–oxygen distances are ~0.01 Å shorter than those in the cis-branch of the corresponding boronic acids, compare Table 1a, b. In these three cases, however, NBO analyses using QCI densities classify the boron–oxygen bonds as single bonds, similar to what we found for the corresponding boronic acids. NBO analysis with the HF density also predicts the boron–oxygen bond in H2N–BH(OH) to be a single bond. However, the second-order stabilization energy associated with the nO → n*B interaction is 61.5 kcal/mol, some 6 kcal/mol greater than the corresponding value in the analogous boronic acid, H2N–B(OH)2. The HF density for F–BH(OH) characterizes the boron–oxygen bond as a double bond. Consistent with these NBO findings, AIM calculations predict the boron–oxygen bond orders for the borinic acids to be greater than those for either of the boron–oxygen bond orders in the analogous boronic acids.

The p-character of the atomic hybrid orbitals on the boron atoms associated with the boron–oxygen bonds in H2N–BH(OH), HO–BH(OH), and F–BH(OH) is greater than that for either of the boron–oxygen bonds in the corresponding boronic acids, compare Tables 1SA and 1SB. Consistent with what we observed for the boronic acids, the p-character on the boron atom decreases (QCI density: sp 2.31, sp 2.24, and sp 2.17), while the p-character on the oxygen atom increases (QCI density: sp 1.27, sp 1.30, and sp 1.33) as the electronegativity of the substituent increases.

The NPA and AIM charges on the boron atoms for the borinic acids are significantly less positive than for the corresponding boronic acids, see Table 2. The NPA occupation of the boron lone-pair orbital on the borinic acid is lower than that on the corresponding boronic acid, e.g., 0.267e for F–BH(OH) compared to 0.353e for F–B(OH)2.

Boron–nitrogen bonding

H2N–B(OH)2

The calculated boron–nitrogen bond length in H2N–B(OH)2 is 1.417 Å at the MP2(FC)/aug-cc-pVTZ level; the authors are unaware of any experimental value for this bond length. For comparison, we note that the corresponding bond lengths at this computational level for HN≡BH, H2N=BH2, and H3N → BH3 are 1.246, 1.395, and 1.652 Å, respectively; the experimental values for H2N=BH2 and H3N → BH3 are 1.391 Å [89, 90] and 1.672 Å [91] (for some interesting crystal structure comparisons, see [92]).

Straub’s [78] bond-length classification scheme for boron–nitrogen bonds is: B≡N, 1.22–1.26 Å; B=N, 1.34–1.41 Å; B–N, 1.65–1.67 Å; Paetzold [93] suggested similar values: B≡N, 1.26 Å; B=N, 1.41; B–N, 1.58 Å. For HN≡BH and H2N=BH2, the MP2(FC)/aug-cc-pVTZ boron–nitrogen bond lengths are clearly within Straub’s triple and double bond-length ranges, respectively, and the results of our NBO analyses using HF and QCI densities support these classifications [94–96]. Berski et al. [94] performed a topological ELF analysis of H2N=BH2 and found two bonding attractors V(B,N) localized above and below the symmetry plane, consistent with the usual Lewis formula; the total population of the two basins was nearly 4.0e consistent with a boron–nitrogen double bond.

For H2N–B(OH)2, the calculated MP2(FC)/aug-cc-pVTZ bond length is just outside the double bond range suggested by Straub [78], although the MP2(FC)/aug-cc-pVQZ and MP2(FC)/aug-cc-pV5Z lengths are slightly shorter, see Table 1a. NBO analyses using the QCI or HF densities identify only one boron–nitrogen natural bond orbital in H2N–B(OH)2. However, the second-order stabilization energy available using the HF density for the nN → n*B interaction is 76.8 kcal/mol, some 20 kcal/mol larger than that for either of the nO → n*B interactions, 55.6 and 58.8 kcal/mol, suggesting significant boron–nitrogen double bond character. Consistent with this finding, the calculated AIM boron–nitrogen bond order is larger than either of the two boron–oxygen bond orders.

The AIM and NPA charges clearly indicate that the nitrogen atom is more negatively charged than either of the oxygen atoms, see Table 2a. The natural atomic hybrids that compose the natural bond orbitals show that the boron–oxygen bonds involve greater p-character than the boron–nitrogen bond, see Table 1S.

H2N–BH(OH)

The calculated boron–nitrogen bond length for the borinic acid H2N–BH(OH) is 1.412 Å at the MP2(FC)/aug-cc-pVTZ level, ca. 0.005 Å shorter than the boron–nitrogen bond in the corresponding boronic acid; similar differences are at found at the higher levels, see Table 1a, b. To the author’s knowledge, there are no experimental structural parameters available for this acid. The calculated length of the boron–nitrogen bond is essentially at the upper limit of Straub’s suggested length for a double bond 1.34–1.41 Å [78]. NBO analyses using the QCI density identify the boron–nitrogen bond as a double bond, whereas the HF density classifies it as a single bond, albeit with a large nN → n*B second-order interaction energy of 85.8 kcal/mol, ~9 kcal/mol greater than for H2N–B(OH)2. Consistent with this finding, the calculated AIM boron–nitrogen bond order in H2N–BH(OH) is larger than the corresponding bond order in H2N–B(OH)2 at the MP2(FC)/aug-cc-pVDZ level.

The charge on the boron atom is less positive and the charge on the nitrogen atom is less negative in H2N–BH(OH) than in H2N–B(OH)2, see Table 2. As noted above for H2N–B(OH)2, the natural atomic hybrids that compose the natural bond orbitals show that the boron–oxygen bonds involve greater p-character than the boron–nitrogen bond, see Table 1S. The p-character of the natural atomic hybrids on the boron atom for the boron–nitrogen bond in H2N–BH(OH) (B:sp 1.97; N:sp 1.20) is greater than it is in H2N–B(OH)2 (B:sp 1.77; N:sp 1.31), whereas the reverse holds for the p-character of the nitrogen atom.

Boron–fluorine bonding

F–B(OH)2

The calculated boron–fluorine bond length in F–B(OH)2 is 1.338 Å at the MP2/aug-cc-pVTZ level and only slightly shorter at the MP2(FC)/aug-cc-pVQZ and MP2(FC)/aug-cc-pV5Z levels, 1.334 and 1.333 Å, see Table 1a, somewhat longer than the estimated experimental value, ~1.323 Å, which is based on results from F2B(OH) [65, 97]. In view of the lack of an experimental bond length for the boron–fluorine bond in F–B(OH)2, we calculated the length of a variety of boron–fluorine bonds in several related small molecules. The MP2/aug-cc-pVTZ level boron–fluorine bond lengths for BF(1Sg), H2BF, HBF2, and BF3 are 1.271, 1.326, 1.320, and 1.317 Å, respectively. These calculated lengths are consistently somewhat longer than the gas-phase experimental values: 1.263 Å [98], 1.316 Å [99], 1.311 Å [99], and 1.309 Å [100]. Using the more complete aug-cc-pVQZ and aug-cc-pV5Z basis sets, the calculated lengths of these bonds are shorter (BF: 1.265 and 1.2644 Å; H2BF 1.321 and 1.320 Å; HBF2: 1.316 and 1.315 Å; BF3: 1.313 and 1.312 Å), but remain slightly longer than the corresponding experimental values. For F–B(OH)2, the MP2(FC)/aug-cc-pVQZ and MP2(FC)/aug-cc-pV5Z fluorine–boron bond lengths are 1.334 and 1.333 Å, suggesting that the estimated experimental value of 1.323 Å may be somewhat short.

Straub’s [78] bond-length classification for boron–fluorine bonds is: B≡F, 1.21–1.26 Å; BF, 1.31–1.33 Å; B–F, 1.37–1.40 Å. As Straub clearly noted, there were good structural data for only one molecule with a B=F double bond, i.e., H2BF; interestingly, the experimental fluorine–boron bond length in this case, 1.316 Å [99], is in the range Straub classified as having only partial double bond character. NBO calculations on H2BF using either the HF or QCI densities identify two fluorine–boron bonds (σ and a π(dative)), along with and two lone pairs on the F atom. In contrast, corresponding NBO analyses for F2BH, where the experimental boron–fluorine bond length is 1.311 Å [99], find only two single boron–fluorine σ bonds and a total of six lone pairs on the F atoms. However, the second-order stabilization energy available using the HF density for the nF → n*B interaction is substantial, 54.9 kcal/mol, indicative of a partial boron–fluorine double bond, BF, consistent with Straub’s classification [78]. The experimental boron–fluorine bond length for BF3, 1.309 Å [100], is shorter than the corresponding bond lengths in either H2BF or HBF2. NBO analyses find a total of three sigma bonds, and the second-order stabilization energy available using the HF density for each nF → n*B interaction is 53.1 kcal/mol, similar to the value found for F2BH, suggesting partial double bonds, consistent with the Straub classification [78]. NBO analyses identify one boron–fluorine σ bond in F–B(OH)2, but the second-order nF → n*B interaction energy, 47.2 kcal/mol using the HF density, is only slightly smaller than the corresponding energies for BF3 or H2BF, indicative of a partial double bond.

Both AIM and NPA charges indicate that the charge on the fluorine atom is only about 55–60 % of the charge on the oxygen atoms, see Table 2. It is also interesting to note that the p-character of the atomic hybrids on the boron atom for the B–F bond sp 2.21 has greater p-character than for the B–O bonds, sp 1.89 and sp 1.91, see Table 1S.

F–BH(OH)

The calculated length of the boron–fluorine bond in F–BH(OH), 1.339 Å, is essentially the same as the corresponding bond length in F–B(OH)2, compare Table 1a, b. Although Kawashima et al. [71] detected F–BH(OH) in microwave experiments, no specific structural parameters were reported. Interestingly, a semi-experimental equilibrium structure of F2BOH has been generated in an extraordinary paper by Breidung et al. [101]. Our MP2(FC)/aug-cc-pVTZ optimized structure for this molecule is in acceptable agreement with their semi-experimental structure, e.g., our boron–oxygen distance is 1.355 Å compared to 1.3459(4) Å, and our boron–fluorine cis and trans distances are 1.333 and 1.323 Å compared to 1.322(6) and 1.316(6) Å.

NBO analyses using either the HF or QCI densities identify the boron–fluorine bond in F–BH(OH) as a single bond. Since the HF density identifies the boron–oxygen bond in F–BH(OH) as a double bond (see above), the largest second-order stabilization energy in this case involves delocalization from a fluorine lone-pair orbital into a boron–oxygen antibonding orbital; the value of E(2) for this nF → π*B-O interaction is 43.6 kcal. The boron–fluorine and boron–oxygen AIM bond orders are larger in F–BH(OH) than in F–B(OH)2.

Concluding remarks

Our systematic comparison of the boron–oxygen NBOs in R–B(OH)2 and R–BH(OH) (R=H; NH2, OH, and F) finds large nO → n*B second-order stabilization energies, indicating that the boron–oxygen bonds in these simple aliphatic boronic and borinic acids have a significant contribution from dative pπ–pπ bonding; indeed, π- and σ-bonds are identified in the NBO analyses of H2B(OH). Our analyses also show that the p-character of boron hybrid orbitals associated with the B–X (X=N, O, F) bonds is larger for the borinic acid than for the corresponding boronic acid. The results of geometry optimizations reveal that the boron–oxygen bond length in each borinic acid is shorter than either of the boron–oxygen bond lengths in the corresponding boronic acid. Furthermore, the boron–oxygen bond lengths in the X–B–Ot–H trans-branch of the endo-exo form of the boronic acids and for the X–B–O–H cis-branch of the boronic and borinic acids (X=N, O, and F, respectively) decrease as the electronegativity of X increases.

Further insight into the bonding in the corresponding boronic and borinic acids can be gained by evaluating the thermodynamics for the reaction R–B(OH)2 + R–BH2 → 2 R–BH(OH), in which the formal bonding in reactants and products is balanced in the spirit of homodesmotic reactions [102–105]. Using the endo-exo form for the boronic acids and the cis form of the borinic acids, the values of \(\Delta{\text{H}}_{298}^{0}\) for this reaction are −1.1, +1.6, −4.1 and −7.1 kcal/mol for R=H, NH2, OH, and F, respectively; using the anti form for the boronic acids, which eliminates the B–Ot–H…O intramolecular hydrogen bond, yields −2.1, −1.3, −8.1, and −7.7 kcal/mol. The exothermicity of these reactions suggests somewhat stronger bonding surrounding the boron atom in the borinic acids than in the boronic acids, consistent with the structural features noted above.

Our investigation highlights the significant differences in the strength and composition of the bonding and in the detailed structural features of simple aliphatic boronic and borinic acids that will affect their relative capabilities to bind to specific substrates. Future studies will include bulkier substituents and model substrates.