The NMR response of boroxol rings: a density functional theory study

doi:10.1016/j.ssnmr.2004.08.004

Solid State Nuclear Magnetic Resonance

Volume 27, Issues 1–2, January 2005, Pages 5-9

https://doi.org/10.1016/j.ssnmr.2004.08.004 Get rights and content

Abstract

Cluster models of boron oxide glasses are studied computationally using density functional theory. It is shown that the isotropic chemical shielding of boron in boroxol rings is about 5 ppm less than for boron in non-ring ${BO}_{3 / 2}$ units, and that the quadrupole coupling in ring sites is about 0.1 MHz larger than in non-ring sites, confirming assignments made in glasses and crystalline model compounds. The chemical shielding anisotropy of these sites is computed and shown to be in agreement with recent experimental measurements. Furthermore, it is shown that the reason for the different responses is not the co-planarity of ${BO}_{3 / 2}$ groups bound in rings, but rather the contraction in the B–O–B bond angle from about $134^{\circ}$ in relaxed structures to $120^{\circ}$ as found in rings.

Introduction

The results of a variety of experiments on boron oxide glass have been interpreted as showing that the basic structural unit in this material is a planar ${BO}_{3}$ fragment, in which each oxygen atom bridges to a neighboring boron atom [1]. In addition, a number of experiments indicate that the linkage of three of these units into six-membered boroxol rings is actually quite prevalent, such that between 65% and 75% of the boron are contained in such rings. Experiments that have been thus interpreted include Raman spectroscopy [2], elastic and inelastic neutron scattering [3], [4], and nuclear quadrupole resonance [5]. It should also be noted that modelling studies of boron oxide glass structure have consistently failed to find significant concentrations of boroxol rings, or indeed clear evidence that the boron atoms occupy two distinct bonding environments of any kind [6], [7].

Nuclear magnetic resonance (NMR) has provided detailed spectroscopic evidence on this question. Experiments with a variety of high-resolution techniques consistently resolve two boron resonances, one shifted about 4 ppm downfield with respect to the other, and in an intensity ratio of about 3:1 [8], [9]. Based on experimental studies of model compounds [10], [11] and ab initio calculations [12], [13], the downfield site is assigned to the boroxol ring, while the upfield site is assigned to non-ring ${BO}_{3 / 2}$ units.

The purpose of this paper is two-fold: first, to confirm the ab initio calculation of the shielding and quadrupole coupling parameters of boron in boroxol rings and ${BO}_{3 / 2}$ groups with a different method than has been used previously, and, more importantly, to offer for the first time an explanation of why these two groups should differ in chemical shielding and quadrupole coupling at all. We find that the crucial distinction between the two units, as far as the NMR parameters are concerned, is the B–O–B bond angles made by the oxygen atoms linked to the central boron. In boroxol rings this angle is constrained to be $120^{\circ}$ , while in non-ring environments it relaxes to about $134^{\circ}$ . Co-planarity of neighboring ${BO}_{3 / 2}$ groups is shown not to play a role in determining the chemical shieldings.

Section snippets

Calculational methods

All calculations were carried out with the Amsterdam Density Functional code (ADF) [14], [15], [16]. Electric field gradients were also computed within ADF [17], and shielding tensors were calculated with the auxiliary program NMR [18], [19].

A variety of basis sets were used, to judge convergence, but all shielding tensor and electric field gradient tensor results are reported using a triple- $ζ$ basis of Slater-type orbitals augmented by two sets of polarization functions ( $3 d$ and $4 f$ ). Widely used

Results

The molecules studied include, first, ${BF}_{3}$ , for use as a shift reference. This choice was made so that the computed shieldings could be converted to chemical shifts for comparison with experiment, using a reference for which no solvent effects were necessary to consider. We also studied several models of borate clusters. The simplest was $B (OH)_{3}$ , that is, a trigonal boron terminated by hydroxyl groups. A more realistic model we studied for a network solid is ${BO}_{3} (B (OH)_{2})_{3}$ , which is a trigonal

Discussion

Summarizing the data in Table 1, our computations indicate an isotropic shielding of about 80 ppm for non-ring ${BO}_{3}$ units, when terminated by borates, and a shielding of about 75 ppm in ring structures. Furthermore, we computed a quadrupole coupling of 2.59 MHz for the non-ring unit and higher values, 2.66–2.71 MHz, in rings. Using the experimental shift in the gas phase of ${BF}_{3}$ of 9.4 ppm relative to ${BF}_{3} \cdot {Et}_{2} O$ [24], the standard boron shift reference, and our computed shieldings (Table 1), the

Conclusions

We report two primary conclusions. First, we confirmed by a high level of ab initio calculation the assignment of ${BO}_{3 / 2}$ NMR resonances in connected borate structures. Our results confirm that boroxol ring borons are deshielded by about 5 ppm relative to non-ring ${BO}_{3 / 2}$ groups, and that their quadrupole couplings are about 0.1 MHz larger. More importantly, we demonstrated by altering the structure of the ${BO}_{3 / 2}$ cluster that the structural feature responsible for this difference is not the

Acknowledgements

We thank Paul MacInnes for installation and support of ADF on the Institute for Research in Materials Beowulf Cluster, and we thank Professor Peter Kusalik and the IRM for making this computer available. We thank Professor Russ Boyd for helpful conversations. This work was supported with funds from the Canada Foundation for Innovation, the Atlantic Innovation Fund, the Canada Research Chairs program, and Dalhousie University.

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The values obtained are summarized in Table 3. The measured isotropic chemical shift, 18.5 and 14.0 ppm, are in good agreement with the values reported by different authors for BO3 units involved in three-membered boroxol rings (named R-BO3) and BO3 units forming chains (named NR-BO3) [32–37]. The NR-BO3 signal decreases progressively and disappears completely at X = 15.
Structural properties and ionic conductivity have been correlated in the XLi₂O-(100 − X)B₂O₃ vitreous system over a wide range of composition (X = 0–50 mol%). The structural evolution of the vitreous network as a function of the lithium oxide content was established at ambient temperature by ¹¹B and ⁷Li high resolution solid state NMR, while electrical conductivity has been measured by complex impedance spectroscopy from room temperature up to the glass transition temperature T_g. The ¹¹B NMR spectra indicate that starting from pure boron trioxide glass, the addition of alkali leads to a gradual transformation of BO₃ units into BO₄⁻. From X ≈ 30, the increase of Li⁺ content is also accompanied by the formation of Non-Bridging Oxygen (NBO). These specific structural changes have been used to interpret the conductive behavior of vitreous lithium borates. Indeed, measured on a wide range of composition, the direct conductivity (σ_dc) increases with the Li₂O content and exhibits a clear regime change at X ≈ 32, which can be correlated to the interaction of cations with BO₄⁻ units and NBO.
Determination of the bond-angle distribution in vitreous B<inf>2</inf>O<inf>3</inf> by 11B double rotation (DOR) NMR spectroscopy
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The B–O–B bond angle distributions for both ring and non-ring boron sites in vitreous B₂O₃ have been determined by ¹¹B double rotation (DOR) NMR and multiple-quantum (MQ) DOR NMR. The [B₃O₆] boroxol rings are observed to have a mean internal B–O–B angle of 120.0±0.7° with a small standard deviation, σ_R=3.2±0.4°, indicating that the rings are near-perfect planar, hexagonal structures. The rings are linked predominantly by non-ring [BO₃] units, which share oxygens with the boroxol ring, with a mean B_ring–O–B_non-ring angle of 135.1±0.6° and σ_NR=6.7±0.4°. In addition, the fraction of boron atoms, f, which reside in the boroxol rings has been measured for this sample as f=0.73±0.01.
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Boric acid, B(OH)₃, forms complexes in aqueous solution with a number of bidentate O-containing ligands, HL⁻, where H₂L is C₂O₄H₂ (oxalic acid), C₃O₄H₄ (malonic acid), C₂H₆O₂ (ethylene glycol), C₆H₆O₂ (catechol), C₁₀H₈O₂ (dioxynaphthalene) and C₂O₃H₄ (glycolic acid). McElligott and Byrne [McElligott, S., Byrne, R.H., 1998. Interaction of ${B(OH)}_{3}^{0}$ and ${HCO}_{3}^{-}$ in seawater: Formation of ${B(OH)}_{2} {CO}_{3}^{-}$ . Aquat. Geochem. 3, 345–356.] have also found B(OH)₃ to form an aqueous complex with ${HCO}_{3}^{- 1}$ . Recently Lemarchand et al. [Lemarchand, E., Schott, J., Gaillardeet, J., 2005. Boron isotopic fractionation related to boron sorption on humic acid and the structure of surface complexes formed. Geochim. Cosmochim. Acta 69, 3519–3533] have studied the formation of surface complexes of B(OH)₃ on humic acid, determining ¹¹B NMR shifts and fitted values of formation constants, and ¹¹B, ¹⁰B isotope fractionations for a number of surface complexation models. Their work helps to clarify both the nature of the interaction of boric acid with the functional groups in humic acid and the nature of some of these coordinating sites on the humic acid. The determination of isotope fractionations may be seen as a form of vibrational spectroscopy, using the fractionating element as a local probe of the vibrational spectrum. We have calculated quantum mechanically the structures, stabilities, vibrational spectra, ¹¹B NMR spectra and ¹¹B,¹⁰B isotope fractionations of a number of complexes B(OH)₂L⁻ formed by reactions of the type:using a 6-311G(d,p) basis set and the B3LYP method for determination of structures, vibrational frequencies and isotopic fractionations, the highly accurate Complete Basis Set-QB3 method for calculating the free energies and the GIAO HF method with a 6-311+G(2d,p) basis for the NMR shieldings. The calculations indicate that oxalic acid, malonic acid, catechol and glycolic acid all form stable complexes (ΔG < 0 for Reaction (1)),which are deshielded (less negative δ) vs. the (C₂H₅)₂OBF₃ reference by 3.6, 1.5, 6.5 and 5.4 ppm, respectively, and which are isotopically lighter than ${B(OH)}_{4}^{-}$ (more negative δ 11B) by 3‰, 2‰, 5‰ and 2‰, respectively. The calculated ¹¹B NMR shifts match well literature values and with the results of Lemarchand et al. (2005), while the calculated isotopic fractionations are also consistent with their results, but show much smaller deviations from ${B(OH)}_{4}^{- t}$ than indicated by these authors. This is a consequence of the use by Lemarchand et al. (2005) of a value of 1.0194 [Kakihana, H., Kotake, M., Satoh, S., Nomura, M., Okamoto, M., 1977. Fundamental studies on the ion-exchange separation of boron isotopes. Bull. Chem. Soc. Jpn. 50, 158–163.] for the ¹¹B,¹⁰B isotopic exchange equilibrium constant of the B(OH)₃, ${B(OH)}_{4}^{-}$ pair which is obsolete and should be replaced by the new purely experimentally determined value of 1.0285 for 0.63 molar ionic strength [Byrne, R.H., Yao, W., Klochko, K., Kaufman, A.J., Tossell, J.A., 2006. Experimental evaluation of the isotopic exchange equilibrium $^{10} {B(OH)}_{3} +^{11} {B(OH)}_{4}^{-} =^{11} {B(OH)}_{3} +^{10} {B(OH)}_{4}^{-}$ in aqueous solution. Deep-Sea Res. 1 (53), 684–688.] or 1.0308 for pure water [Klochko, K., Kaufman, A.J., Yao, W., Byrne, R.H., Tossell, J.A., 2006. Experimental measurement of boron isotope fractionation in seawater. Earth Planet Sci. Lett. 248, 276–285]. Given this correction the B(OH)₂L⁻ complexes are observed to be isotopically lighter than ${B(OH)}_{4}^{-}$ by only a few ‰. Changes in ¹¹B NMR shift and ¹¹B,¹⁰B isotope fractionations for the B(OH)₂L⁻ complexes, compared to ${B(OH)}_{4}^{-}$ , are found to be correlated to some extent with distortions of the O–B–O angles from tetrahedral values and/or with B–O bond strength sums. Similar free energies for the corner-sharing and 4-ring isomers of ${B(OH)}_{2} {CO}_{3}^{-}$ suggest a mechanism for creation of both BIII and BIV environments when B is incorporated into calcite.
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The NMR response of boroxol rings: a density functional theory study

Abstract

Introduction

Section snippets

Calculational methods

Results

Discussion

Conclusions

Acknowledgements

J. Non-Cryst. Solids

J. Magn. Reson.

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

Nuclear magnetic resonance absorption in glass. i. Nuclear quadrupole effects in boron oxide, soda-boric oxide, and borosilicate glasses

J. Chem. Phys.

Raman spectroscopy of crystalline and vitreous borates

Philips Res. Rep. (Suppl.)

A neutron diffraction investigation of the structure of vitreous boron trioxide

J. Non-Cryst. Solids

Fraction of boroxol rings in vitreous boron trioxide

Phys. Rev. B

Multiple boron sites in borate glass detected with dynamic angle spinning nuclear magnetic resonance

J. Non-Cryst. Solids

Network modification in potassium borate glassesstudies with NMR and Raman spectroscopies

J. Phys. Chem.