Dynamic Disorder and Electronic Structures of Electron-Precise

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Dynamic Disorder and Electronic Structures of ElectronPrecise Dianionic Diboranes: Insights from SolidState Multinuclear Magnetic Resonance Spectroscopy Y. T. Angel Wong, Johannes Landmann, Maik Finze, and David L. Bryce J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 26 May 2017 Downloaded from http://pubs.acs.org on May 26, 2017

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Journal of the American Chemical Society

Dynamic Disorder and Electronic Structures of Electron-Precise Dianionic Diboranes: Insights from Solid-State Multinuclear Magnetic Resonance Spectroscopy Y. T. Angel Wong,‡ Johannes Landmann,£ Maik Finze,*,£ and David L. Bryce*,‡ ‡

Department of Chemistry and Biomolecular Sciences & Centre for Catalysis Research and Innovation, University of Ottawa, Ottawa, Ontario, Canada K1N6N5

£

Institut für Anorganische Chemie, Institut für nachhaltige Chemie & Katalyse mit Bor (ICB), Julius-MaximiliansUniversität Würzburg, Am Hubland, 97074 Würzburg, Germany ABSTRACT: The J(11B, 11B) coupling constants of various salts of the electron-precise hexacyanodiborane(6) dianion, [B2(CN)6]2-, were obtained using 11B double-quantum filtered (DQF) J-resolved solid-state nuclear magnetic resonance (SSNMR) spectroscopy. Our results show that the magnitude of the DQF J splitting is influenced by both the crystallographic symmetry of the system and the presence of dynamics. The splittings are amplified by a factor of 3 as compared to the corresponding theoretical J coupling constants for cases where 1) there is an absence of dynamics but the boron pairs are crystallographically equivalent, or 2) the boron pairs are crystallographically inequivalent but are rendered magnetically equivalent on the timescale of the experiment due to dynamic disorder, which was identified by 11B and 13C SSNMR experiments. Consequently, molecular motions need to be taken into consideration when interpreting the results of DQF J-resolved experiments, and, conversely, these experiments may be used to identify dynamic disorder. Variable temperature NMR data support the notion of three different motional processes with correlation times ranging from 102 to 106 s-1 over the temperature range of 248 to 306 K. When molecular motion and crystallographic symmetry are both accounted for, the J(11B, 11B) coupling constants for various [B2(CN)6]2- salts were measured to range from 29.4 Hz to 35.8 Hz, and their electronic origins were determined using natural localized molecular orbital and natural bond orbital analyses. The coupling constants were found to strongly correlate to the hybridization states of the boron orbitals which form the B – B bonds and to the strength of the B – B bonds. This study provides a novel tool to study dynamics in ordered and disordered solids, and provides new perspectives on electron-precise dianionic diboranes featuring 2-centre 2-electron bonds in the context of related compounds featuring multiply and singly-bonded boron spin pairs.

Introduction Electronic and molecular structures are frequently explored via the indirect nuclear spin-spin (J) coupling interaction observed in nuclear magnetic resonance (NMR). This interaction can provide valuable insights into the nature of chemical bonding as it originates from the orbital overlap of two atoms. For instance, the homonuclear and heteronuclear J couplings involving spin-½ nuclei are often utilized for conformational and structural investigations of organic and biological systems.1-5 However, the spectral fine structure arising from the J coupling between a pair of quadrupolar nuclei (I > 1/2) is, in comparison, more difficult to detect and thus less commonly employed. In solution, the measurement of the J couplings for a pair of quadrupolar nuclei is rarely feasible due to rapid quadrupolar relaxation, while in the solid state, anisotropic quadrupolar spectral broadening often masks the relatively small effects of J coupling, thereby preventing the extraction of the J coupling constants. Various NMR

techniques have proven effective in measuring the homonuclear quadrupolar J coupling constants for powdered samples;6-13 however, many of these techniques require either additional probe hardware or relatively tedious spectral analysis procedures. Recently, our group has reported the homonuclear J coupling constants for a series of quadrupolar nuclei (e.g., J(11B, 11B), and J(71Ga, 71Ga)) in the solid state using several easily implemented J-resolved NMR experiments,7,9-11,13 one of which is the doublequantum filtered (DQF) J-resolved sequence.9,11,13 In this experiment, the J coupling information is extracted into the indirect dimension using a spin echo, and an INADEQUATE block is executed before the spin echo for double quantum filtering. As a result, simple doublets are obtained in the indirect dimension, and the splittings between these doublets are directly related to the corresponding J coupling constants. Using this technique, strong correlations between the J coupling constants and various electronic properties have been reported. For ex-

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ample, the J(11B, 11B) coupling constants for a series of diborane, diborene, and diboryne compounds were observed to correlate to the hybridization states of the boron orbitals responsible for the B – B bond, as well as the bonding energies of the B – B bonds.11,13 This suggests that given enough empirical data, electronic properties can be directly extracted from J coupling constants without the need for computational simulations. The doublet splittings observed in the DQF J-resolved spectra are dependent on both the magnitude of the J coupling constant and the magnetic equivalency of the

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Figure 1. Discrimination via B J-resolved SSNMR spectroscopy between pairs of (a) magnetically equivalent and (b) non-equivalent boron spin pairs in samples devoid of largescale molecular dynamics. Samples are (a) bis(catecholato)diboron and (b) its NHC-complexed analogue. Adapted from ref. 9.

nuclear pair under study.9,11,13,14 For a pair of magnetically inequivalent nuclei, the J splittings are equal to J, while for a pair of magnetically equivalent nuclei, the J splittings are amplified by a factor of (2S+3)(2S-1)/4, where S is the spin quantum number.9 For solids that do not exhibit molecular motions, a pair of nuclei is considered to be magnetically equivalent if they are related by a specific symmetry operation (e.g., Ci, Sn>1, C2 and a mirror plane, or Cn>3 along the bond and C2 relating the nuclei);15 therefore under favorable conditions the magnitude of the J splittings can directly provide information on the crystallographic symmetry of the system. This was consistently observed for previously studied diboron compounds.9,11,13 These systems did not exhibit dynamic behavior, and for a pair of boron nuclei (S = 3/2) related by an inversion center, the corresponding J splittings were always measured to be 3J. On the other hand, for a pair of inequivalent borons, the J splittings were always equal to J (Figure 1). Apparent magnetic equivalence can also arise as a result of dynamics and this is best exemplified by considering the three protons on a methyl group. For solids undergoing molecular motion, if the exchange is fast on the NMR timescale, sites which are inequivalent under slow exchange on the NMR timescale could be rendered effectively equivalent.16-19 This relation between the time scale of the molecular motion and magnetic equivalence suggests that the presence of dynamics could result in symmetry-amplified J splitting for a pair of crystallographical-

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ly distinct nuclei, thereby confounding the extraction of the J coupling constants from the DQF J-resolved spectra. However, this has yet to be explored as previous studies were performed only on static systems.9,11,13 Since accurate measurement of the J coupling constant is necessary for elucidating electronic properties, it is important to investigate the potential effects of molecular dynamics on the appearance of the spectra. Moreover, if dynamic disorder can induce symmetry-amplified J splittings for pairs of crystallographically inequivalent boron spins, then DQF Jresolved experiments could potentially be employed as a novel tool for detecting molecular motions. In recent years, there has been a growing interest in developing compounds bearing electron-precise B – B bonds due to their wide range of potential applications in synthetic chemistry.20-33 Since chemical behaviors depend on electronic properties, insights into the electronic structures of these diboron systems should prove to be valuable for understanding their reactivity and to facilitate rational design. However, previous solid-state NMR (SSNMR) experiments relating the J(11B, 11B) coupling constants and the corresponding electronic structures were only performed on systems where the B – B bond is formed from boron orbitals with a p-orbital hybridization index of 1 to 2,9,11,13 and to our knowledge, none have been performed on systems encompassing electron-precise 2c2e B(sp3) – B(sp3) bonds. Recently, a series of stable hexacyanodiborane(6) dianion ([B2(CN)6]2-) salts with electron precise B – B bonds (i.e., 2c-2e B(sp3) – B(sp3)) were synthesized and observed to display a variety of crystallographic behaviors.23 Pairs of boron nuclei of some of these salts were found to be crystallographically equivalent, while others were found to be distinct. Salts which contain non-equivalent boron atoms could perhaps exhibit dynamics as the structures were also observed via diffraction techniques to be disordered. As such, these salts serve as excellent models for 1) examining how dynamics can impact the corresponding DQF J-resolved spectra, and 2) developing a relation between the electronic features of electron-precise B – B bonds and the corresponding J(11B, 11B) coupling constants, thereby providing a useful benchmark for the future studies of these systems. Here, we demonstrate how molecular dynamics associated with boron spin pairs can affect the corresponding 11B DQF J-resolved spectra using various [B2(CN)6]2- salts (Figure 2, [Mg(DMF)6][B2(CN)6] (1), [Cu(DMSO)6][B2(CN)6] (2), K2[B2(CN)6] (3), [nBu4N]2[B2(CN)6] (4), and [BMPL]2[B2(CN)6] (5, [BMPL] = 1-butyl-1-methylpyrrolidinium)) as archetypes. The presence and/or absence of dynamics was first assessed independently by 13C and 11B SSNMR spectroscopy, and the conclusions reached were then employed to analyze the corresponding 11B DQF J-resolved spectra. Natural bond orbital (NBO) and natural localized molecular orbital (NLMO) analysis of the J(11B, 11B) coupling constants were conducted to determine the electronic origins of the J couplings. The coupling constants were also analyzed based on the hybridization states of the boron orbitals and the bonding energy of the B – B bonds as to correlate


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the measured J coupling constants to the electronic properties of the systems.

precipitate of 2 was filtered off and dried in air. Yield 530 mg (0.746 mmol, 90%). Raman (solid): 2254 (s, ν̃(CN)), 2218 (s, ν̃(CN)), 2205 (s, ν̃(CN)), 2197 cm−1 (vs, ν̃(CN)). IR (solid): 2197 cm-1 (ν̃(CN)). Elemental analysis calcd (%) for C18H36B2CuN6O6S6, C 30.45, H 5.11, N 11.84, S 27.09; found: C 30.13, H 5.24, N 11.48, S 27.84. DSC: Two overlapping endothermic processes starting at approximately 110 °C with maxima at 190 and 211 °C were detected that are rationalized by loss of DMSO. 3. 11B SSNMR Spectroscopy

2-

Figure 2. Structure of the [B2(CN)6] salts investigated in this study, where Z = Mg(DMF)6 (1), Cu(DMSO)6 (2), K2 (3), [nBu4N]2 (4), or [BMPL]2 (5).

Experimental 1. General Aspects The hexacyanodiborane(6) dianion salts (H3O)2[B2(CN)6], K2[B2(CN)6] (3), [nBu4N]2[B2(CN)6] (4), [BMPL]2[B2(CN)6] (5), Mg[B2(CN)6], and Cu[B2(CN)6] were synthesized as described in the literature.23 IR spectra were recorded with a Bruker Alpha spectrometer with an apodized resolution of 4 cm−1 in the attenuated total reflection (ATR) mode in the region of 4000–400 cm−1 using a setup with a diamond crystal. Raman spectra were measured on a Bruker IFS-120 with an apodized resolution of 2 or 4 cm–1 using the 1064 nm excitation line of a Nd/YAG laser on crystalline samples contained in melting point capillaries in the region of 4000–80 cm–1. Elemental analyses (C, H, N, S) were performed either with a Euro EA3000 instrument (HEKA-Tech, Germany) or with an Elementar Vario MICRO cube instrument (Elementar Analysensysteme, Germany). Differential scanning calorimetry (DSC) was performed with a DSC 204 F1 Phoenix (Netzsch, Germany) in the temperature range of 20580 °C with a heating rate of 5 K∙min–1 and a constant gas flow of 40 mL∙min–1 N2. 2. Synthesis and characterization of hexacyanodiborane(6) dianion salts [Mg(DMF)6][B2(CN)6] (1). Similar to the method described earlier, Mg[B2(CN)6] was obtained from (H3O)2[B2(CN)6] and Mg powder in aqueous solution.23 Mg[B2(CN)6] (200 mg, 1.00 mmol) was dissolved in hot DMF (10 mL), filtered, and the solution was slowly cooled to room temperature. The crystalline colorless [Mg(DMF)6][B2(CN)6] (1) was filtered off and dried in a vacuum. Yield 390 mg (0.609 mmol, 61%). Raman (solid): 2198 cm−1 (vs, ν̃(CN)). IR (solid): 2196 cm−1 (vs, ν̃(CN)). Elemental analysis calcd (%) for C24H42B2MgN12O6, C 45.00, H 6.61, N 26.24; found: C 44.95, H 6.62, N 26.23. DSC: Three overlapping endothermic processes starting at approximately 95 °C with maxima at 105, 119, and 158 °C were observed that are presumably due to loss of DMF and may be accompanied by additional phase transitions. [Cu(DMSO)6][B2(CN)6] (2). Reaction of (H3O)2[B2(CN)6] with CuCl2∙2H2O in water gave blue Cu[B2(CN)6] as described in the literature.23 Cu[B2(CN)6] (200 mg, 0.829 mmol) was dissolved in hot DMSO (6 mL) and slowly cooled to room temperature. The blue, crystalline

All 11B NMR experiments were conducted using a Bruker Avance III NMR spectrometer (B0 = 9.4 T, νL(11B) = 128.38 MHz) equipped with a 4 mm triple resonance MAS probe. The spectra were recorded at room temperature, and the chemical shifts were referenced externally using solid sodium borohydride (δiso(11B) = 42.06 ppm with respect to F3B∙O(C2H5)2). In order to reduce the boron background signal of the probe, the 11B MAS and static spectra were acquired using the Hahnecho sequence (π/2−τ1−π−τ2−acquire) with TPPM decoupling.34 A π/2 pulse length of 1.9 μs, optimized to maximize the central transition (CT) signal was used, and a recycle delay of 2 s was employed. The echo delay was 77.15 μs. A total of 16 to 3200 scans were collected for each spectrum, and the samples were spun at a frequency of 12.5 kHz for the 11B MAS experiments. The experimental J(11B, 11B) coupling constants were measured using the DQF J-resolved sequence (π/2 – NτR – π – NτR – π/2 – τ1 – π/2 – NτR + t1/2 – π – NτR + t1/2 – acquire) with TPPM decoupling.34 For the DQF J-resolved experiments, double frequency sweeps were also executed for signal enhancement.35 The MAS frequency was 12 kHz, and the recycle delays were 2 s. A 20 μs CT selective π/2 pulse was used, and a DQF delay of 208 μs to 4.5 ms was employed. A total of 32 t1 increments, with 256 scans per increment, were collected using an incremented delay of approximately 389 μs. The spectral splittings were analyzed by fitting the observed lines to a mixed Gaussian/Lorentzian and the precision reported reflects the errors reported by the automated fitting procedure. Additional details on variable-temperature (VT) experiments are provided in the Supporting Information. 4. 13C SSNMR Spectroscopy 1

H→13C cross-polarization (CP) experiments were conducted under MAS and stationary conditions with a Bruker Avance III NMR spectrometer in a magnetic field of 9.4 T (νL(13C) = 100.61 MHz) with a 4 mm triple resonance MAS probe. All spectra were collected at room temperature, and the chemical shifts were referenced externally to solid glycine (δiso(13C=O) = 176.4 ppm with respect to TMS). SPINAL-64 decoupling36 was executed and π/2 pulse lengths ranging from 2.5 to 4.9 μs were employed. Contact times ranging from 2000 to 4000 μs were used and the recycle delays were set to 2 s. For the MAS experiments, samples were spun at 13 kHz and RAMP CP was employed. Proton contact power was not ramped for static experiments. In order to obtain a suitable signal-tonoise ratio, 4000 to 40000 scans were recorded per



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2-

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Figure 3. The crystal structures of the [B2(CN)6] anion of samples 1, 2, 3, 4 and 5, illustrating the presence of crystallographic disorder in 1, 3 – 5. Samples 1, 2, and 3 contain pairs of crystallographically equivalent boron nuclei, whereas samples 4 and 5 contain pairs of inequivalent boron nuclei.

spectrum. Additional details on VT experiments are provided in the Supporting Information. Bruker TopSpin 3.0 software was used for all NMR data processing. For the Hahn-echo experiments, the recorded FIDs were left-shifted to the echo maxima. Spectral fitting was accomplished using WSolids137 and EXPRESS.38 5. Density Functional Theory Calculations For all of the samples, the input structures were generated from the atomic coordinates of the hexacyanodiborane(6) dianions as obtained from the published crystal structures (CCDC numbers: 1049207, 1049194, 1049218, 1054696, and 1054695). Sites with low partial occupancies (minor disorder sites) were removed for samples with crystallographic disorder (i.e., 1, 3, 4, and 5). The 11B EFG tensors, the J(11B, 11B) coupling constants, and the 13C magnetic shielding tensors were computed using the Amsterdam Density Functional program (ADF, version 2012 and version 2016)39, and the calculations were executed using the revPBE functional with the TZ2P basis set. Optimized structures of the dianions were not used, as the optimization process expectedly resulted in identical geometries for all five samples. Use of the experimental geometries provided good agreement with experiment for these samples (vide infra). The NLMO and NBO analyses of the J(11B,11B) coupling constants were accomplished using the NBO program (ver. 5.0)40 that is incorporated into ADF.

6. Single-crystal X-ray diffraction Crystal data for [Cu(DMSO)6][B2(CN)6] (2) were collected at 298 K on a Bruker X8-Apex II diffractometer with a CCD area detector and multi-layer mirror or graphite monochromated Mo-Kα radiation (λ = 0.71073 Å). Complex salt 2 crystallizes in the trigonal space group R-3 (no. 148) with Z = 3, and cell dimensions of a = b = 14.0349(13) and c = 15.6390(15) Å, and V = 2667.8(6) Å3; ρcalc. = 1.326 Mg∙m–3, µ(Mo–1 Kα) = 1.004 mm , F(000) = 1107. The structure was solved by intrinsic phasing methods (SHELXT).41,42 Refinement is based on full-matrix least-squares calculations on F2 (SHELXL).42,43 A total of 9273 reflections were collected (2.12 < θ < 26.75) with 1269 independent reflections, 100 variables, and without restraints. All non-hydrogen atoms were refined anisotropically. For all CH moieties idealized bond lengths and angles were used and the isotropic displacement parameters of the H atoms were tied to the equivalent isotropic displacement parameters of the respective parent C atom. Calculations were carried out using the ShelXle graphical interface.44 The final refinement resulted in R1[Fo2 > 2σ(Fo2)] = 0.061, wR2 = 0.133 (all data), S = 1.047, and ∆ρmax/∆ρmin +0.542 and –0.400 e∙Å–3. The molecular structure diagram was drawn with the program Diamond 4.3.0.45 Crystallographic data have been deposited with the Cambridge Crystallographic Data


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Centre. These data can be obtained free of charge on quoting the depository number CCDC-1521872 from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif. 7. Powder X-ray diffraction Samples for powder diffraction were ground in a mortar and placed into Lindemann glass capillaries (Ø 0.5 mm). Diffraction data were collected on a Bruker AXS D8 Discover powder X-ray diffractometer equipped with a LynxEye detector in transmission geometry. X-ray radiation (Cu-Kα1; λ = 154.06 pm) was focused with a Goebel mirror, whereas Cu-Kα2 radiation was eliminated by use of a Ni absorber. Diffraction patterns were recorded and analyzed using the Bruker AXS Diffrac-Suite.

and 11B SSNMR experiments on 4 and 5 in order to determine if these borons undergo molecular motion. Firstly, according to the X-ray diffraction data,23 there are a total of 60 and 44 non-equivalent carbons for 4 and 5, respectively, contributed from both the anion and the cation. Hence, if these samples feature static disorder, we would anticipate 60 13C signals for 4 and 44 13C signals for 5 to be observed under MAS (ignoring resolution issues for the moment), with each peak corresponding to a distinct carbon. Yet, far fewer 13C signals were detected for 4 and 5 (Figure 5). Even when generously allowing for fortuitous spectral overlap between peaks, these muchreduced numbers suggest dynamic disorder of the samples since molecular motion can induce

Results and discussion 13

1. Identification of dynamic disorder via 11B SSNMR and C SSNMR

We hypothesized that the presence of dynamics may induce effective equivalency between two nuclear sites, meaning that symmetry-amplified J splittings may be expected in the 11B DQF J-resolved spectra of dynamically disordered systems even if the spins are non-equivalent in the static diffraction structure. To test this hypothesis, we first identified samples with pairs of crystallographically distinct borons (unrelated by a symmetry element) which display dynamic disorder at room temperature. From single-crystal X-ray crystallographic data,23 sample 2 was found to be crystallographically ordered, while samples 1, 3, 4, and 5 were found to be crystallographically disordered (Figure 3). Since the initial crystallographic study on 2 was performed at 100 K and because the powder diffraction pattern at 298 K did not match the simulated pattern, the structure was re-determined (Figure 4). At 298 K, the Cu atom of the complex cation [Cu(DMSO)6]2+ is located on a 3-bar axis resulting in disorder of the DMSO ligands. The two different positions have occupancies of 1/3 and 2/3, reflecting Jahn-Teller distortion due to the d9 configuration of copper. The [B2(CN)6]2– anion is located on a center of inversion and reveals no disorder as observed for the low-temperature phase. The homogeneity of crystalline 2 was proven by powder X-ray diffraction, and the experimental and the simulated patterns are in excellent agreement (Figure 4). Samples of 1, 3, 4, and 5 were also studied by powder X-ray diffraction (Figure S3-S6). All samples contained a single crystalline phase except for 5, which consists of at least two slightly different crystalline phases. One of these corresponds to the crystal structure reported earlier.23 Tempering of 5 at 100 °C for 1 h resulted in conversion of the sample into this crystal phase, and the tempered sample was employed for the NMR studies. Furthermore, each pair of borons in samples 1, 2, and 3 is related by an inversion center, whereas the borons in samples 4 and 5 were found to be unrelated by any operations (Figure 3). Consequently, samples 4 and 5 contain sets of crystallographically non-equivalent borons, and we conducted a series of 13C

Figure 4. Structure of [Cu(DMSO)6][B2(CN)6] (2) in the crystal at 298 K (view along [001]; displacement ellipsoids at 15% probability) (top), and the simulated and experimental X-ray diffraction powder patterns of 2 (bottom).

equivalency between various sets of carbons if the rate of exchange is fast on the NMR time scale, thereby reducing the number of peaks detected in the spectra.19 The crystal structures of 4 and 5 (Figure 3) show that the nitrile carbons are disordered. Since these carbons are directly bonded to the boron atoms, it is reasonable to suppose that if the borons are dynamically disordered then these carbons will be as well. Therefore, the type of disorder (i.e., static or dynamic) associated with the nitrile carbons can provide insight into the dynamics of the



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Figure 5. Solid state C CP/MAS NMR spectra of 4 and 5 recorded at room temperature and at 9.4 T. The spinning frequency was 13 kHz. Asterisks (*) denote spinning sidebands, while the solid triangles (▼) denote the carbon signals arising from the nitrile carbons. Inserts show expansion of the region from 12 ppm to 30 ppm. 13

of 0 ppm to 100 ppm arise from the C of the corresponding cations. The full range spectra are given in Figure S8.

13

Figure 6. The nitrile signal of 4 and 5 obtained by static C CP SSNMR (black trace), as denoted by the asterisk. Spectra were recorded at 9.4 T and at 33°C. The spectra simulated from best fit are shown as the red trace; see Table 1 for simulation parameters. The remaining signals located in the range

boron atoms. In order to determine the nature of the disorder of the nitrile carbons, our analysis of the 13C SSNMR spectra will now solely focus on the region where the corresponding peaks are expected to be observed (ca. 108 to 168 ppm)46-50. From the 13C MAS NMR spectra (Figure 5), only one broad peak at 131.1 ppm corresponding to the nitrile carbons was noted for samples 4 and 5, instead of up to 24 and 8, as predicted by X-ray diffraction, respectively. As compared to the remainder of the 13C signals, the line shapes for the nitrile carbons show asymmetric broadening. The nitrile carbon line widths were measured to be 198.3 Hz for 4 and 206.3 Hz for 5, while the line widths of the other carbon signals were found to range from 40.8 Hz to 166.8 Hz for 4 and 42.9 Hz to 122.8 Hz for 5. At first glance, this may suggest peak overlap as a potential explanation for the observation of a single nitrile carbon peak. However, it is unlikely that the line widths observed result from the nearly perfect overlap of 24 or 8 peaks (for 4 or 5, respectively). Nevertheless, in order to gain more insight into the dynamics of the nitrile moieties, static 13C experiments were also conducted (Figure 6). The experimental NMR parameters and the corresponding DFT values are given in Table 1. The δiso data


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determined from the static 13C spectra were in good agreement with the corresponding MAS experimental values (131.1 ppm for 4 and 5), the computational results, and also literature values for a range of nitriles (ca. 108 to 168 ppm).46-50 However, as compared to both the literature and the DFT values, the experimental chemical shift (CS) tensor spans, Ω, were found to be greatly reduced. For solids without dynamic disorder, i.e., AgCN, CuCN, salts (M = nBu4N, K, and Tl), M[Au(CN)2] Pb(H2O)[Au(CN)2]2, Pb[Au(CN)2]2 and various Kn[M(CN)4] salts (M = Zn, Cd, Hg, and Au, n = 1 or 2), the Ω of nitrile carbons have been reported to range from 328 ppm to 361 ppm.46-50 Similar values (348 ppm to 352 ppm) were also obtained from our DFT calculations, which were determined using stationary models. Yet, the static 13C NMR experiment revealed a Ω of only 30 ppm and 69 ppm for samples 4 and 5, respectively. Furthermore, the skew (κ) was calculated to range from 0.95 to 0.96; however, it was experimentally measured to be ~0 for 4 and -0.46 for 5. Since the effects of the CS tensors on the static 13C spectra can be expected to average under rapid molecular motion,51-53 the marked decrease in the experimental Ω on the order of 80 to 90%, and the deviation of the experimental κ from the theoretical values for a static structure, further indicates that the nitrile groups of samples 4 and 5 are dynamically disordered. To quantitatively assess the impact of dynamics on the C NMR line shape, we recorded a series of lowtemperature spectra of sample 4 (Figure 7). The spectra then were analyzed using EXPRESS software which simulates the effects of Markovian jump dynamics. As the temperature is lowered from 33°C to -25°C, the powder pattern evolves to one which reflects the full static (unaveraged) 13C chemical shift tensor. Further lowering of the temperature did not change the spectra further. The static low-T span value of 348 ppm that was used in the simulations is that obtained from DFT calculations on a static molecule, and is also in good accord with room temperature data acquired for sample 3, which does not exhibit dynamics at room temperature (Ω = 328 ppm; see Supporting Information). On the basis of the statically disordered structures (at 100 K) of some of the dianionic diboranes shown in Figure 3, we considered which types of motions would be reasonable and which would result in magnetic equivalence of the boron atoms in the high temperature limit. We first examined the effect of a threefold jump of the three CN groups bonded to boron about the B-B axis (process ‘A’): this is entirely analogous to a methyl group rotation. Theory (and the simulations) shows that such a motion will result in a powder pattern which is scaled by (3cos2θ – 1)/2 (where θ is the angle between the unique component of the CS tensor and the axis of rotation, equal to 71° for 4), which in this case is equal to approximately -0.34. This motion alone therefore is not enough to account for the experimental observations. We thus proceeded to consider an additional set of motions (processes ‘B’ and ‘C’) which would render the boron atoms magnetically equivalent in the fast-motion limit. These two-fold jump motions involve reorientations

of the whole dianionic diborane moiety to rapidly sample crystallographic positions as identified in the disordered single-crystal diffraction structures (see the MPG files and accompanying description in the Supporting Information). Again, rapid motion of this type alone is not sufficient to account for the experimental observations. However, when the methyl-type rotation and the reorientations of the dianionic diborane moiety are considered together (processes A, B, and C), the experimental data are reproduced (Figure 7). Figure S13 of the Supporting Information shows that none of the three modes of motion alone, or any pair of these motions, can account for the experimental spectrum. All three modes are required simultaneously. The rates of motion for the three dynamic processes are provided in Table S4 of the Supporting Information. There is of course an important caveat inherent this analysis: while we believe that the dynamics proposed are physically reasonable, it cannot be claimed that these are the only possible ways to fit the data.

13

13

Figure 7. (a) Experimental C CP SSNMR spectra recorded for a stationary sample of 4 at 9.4 T at temperatures ranging from 306 K to 173 K. Asterisks denote the nitrile carbon signals of interest, which were simulated (b) with EXPRESS in order to extract the rates for three motional processes A, B, and C (Table S4). The remaining experimental signals arise from the BMPL cation. Additional simulation parameters (angles and CS tensor values) are given in Table S5.



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Table 1. Experimental and theoretical 13C CS tensors of the nitrile carbons of samples 4 and 5. The experimental results were obtained from static 13C NMR spectra at 33°C, while the calculated results were computed using the revPBE functional with the TZ2P basis set. sample

carbon a site

4

5

theoretical δiso / ppm

Ω / ppm

experimental

b

κ

δiso / ppm

Ω / ppm

κ

131.0 ± 1.0

30 ± 7

0.00 ± 0.20

135.2 ± 1.2

69 ± 10

-0.46 ± 0.06

1

129.8

348

0.96

2

129.6

349

0.96

3

130.2

349

0.95

4

129.6

348

0.95

5

129.5

348

0.95

6

129.4

348

0.95

1

132.2

352

0.96

2

132.4

352

0.95

3

132.4

352

0.95

4

132.8

352

0.95

5

131.5

350

0.95

6

131.5

350

0.95

a

b

Each number corresponds to a crystallographically distinct nitrile carbon in the major disorder site. Only one carbon signal was resolved in the corresponding NMR spectra of 4 and 5, as shown in Figure 6.

from many crystallographically distinct carbons, all coupled to 11B and 10B and 14N – it is not realistic to model so many effects to a partially resolved powder pattern of low signalto noise. With regards to the timescale, it is well-known that 13C chemical shift tensors report on dynamics in the 102 to 104 s-1 range (in this case the span of the unaveraged chemical shift tensor at 9.4 T is about 30 kHz), and the rates obtained by spectral fitting vary from 102 s-1 for the two anion reorientation modes at 248 K to 106 s-1 for the nitrile rotation mode in the high-temperature limit (306 K) (see Supporting Information).

11

Figure 8. B Hahn echo MAS spectra of 2, 4, and 5. Experiments were performed at room temperature with a spinning frequency of 12.5 kHz and at 9.4 T. Asterisks (*) denote impurities.

Given the overlap of the powder pattern of interest with the 13 C resonances due to the cation, it is impossible to unambiguously fit each spectrum over the range of temperatures (consider for example that at low temperature, the spectrum should result from the superposition of contributions

To further probe this dynamic disorder, we performed a series of 11B SSNMR experiments to investigate the motions of the boron atoms in these samples. Consistent with the results obtained from our 13C experiments, the 11B data also indicates dynamic disorder of the [B2(CN)6]2- dianion. For both samples (4 and 5), a single pseudoLorentzian 11B signal for [B2(CN)6]2- was detected under MAS (Figure 8). The absence of spectral features arising from quadrupolar interactions was attributed to the pseudo-tetrahedral environments of the boron nuclei, resulting in small quadrupolar interactions and therefore minimal second-order quadrupolar broadening. This is in agreement with our calculations, where CQ values for the two inequivalent borons in the major disorder site were calculated to be -0.94 MHz and -0.96 MHz for 4, and -0.80 MHz and -0.79 MHz for 5. Furthermore, as compared to the corresponding signal of sample 2, which once again consists of a pseudo-Lorentzian line shape as the CQ were calculated to have similar values (-0.88 MHz) owing to the pseudotetrahedral environment the boron nuclei are in, the line widths of the signals from samples 4 and 5 are noticeably narrower (FWHM = 388.2 Hz, 203.9 Hz, and 214.8 Hz for 2, 4, and 5, respectively; Figure 8). Since the dianion of 2 does


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Table 2. Experimental (J(11B, 11B)exp.) and theoretical (J(11B, 11B)calc.) J(11B, 11B) coupling constants, B – B σ-bonding NBO energies (σ(B – B) NBO energy), and the p-orbital hybridization indexes of the B – B bonds (hybridization index) of the series of [B2(CN)6]2- salts investigated in this study. All theoretical results were calculated using the revPBE functional with the TZ2P basis set. sample

a.

11

11

J( B, B)exp. / Hz

a

11

11

J( B, B)calc. / Hz

σ(B – B) NBO energy / a.u.

hybridization index

1

31.8 ± 0.2

26.9

-0.066

2.90

2

29.4 ± 0.3

24.9

-0.061

2.99

3

31.7 ± 0.4

28.1

-0.067

2.83

4

35.8 ± 0.4

30.3

-0.072

2.76

5

33.7 ± 0.5

28.2

-0.070

2.84

The

precision

reflects

the

errors

reported

by

the

automated

spectral

fitting

procedure

employed.

was once again observed. As mentioned, for both samples, only one 11B signal was detected for [B2(CN)6]2-; however, the number of distinct boron sites for 4 and 5 were found to be 8 and 4, respectively, by X-ray diffraction.23 With the caveat that fortuitous overlap of up to 8 resonances is always a slim possibility, this disagreement was again attributed to the presence of rapid dynamics, resulting in equivalence between the various sites, and a single NMR resonance. More importantly, since each NMR signal corresponds to a distinct boron, the single peak observed in the 11B MAS spectra thus indicates that all of the boron nuclei in 4 and 5 are at least chemically equivalent on the timescale of the experiment.

11

Figure 9. Solid-state B NMR spectra of 2 and 4 obtained using the Hahn echo sequence under stationary conditions (room temperature, Bo = 9.4 T).

not exhibit any crystallographic disorder (X-ray diffraction indicates that 2 only has one pair of equivalent borons as illustrated in Figure 3)23, the reduction in line width seen for 4 and 5 is consistent with the presence of dynamics of the dianion in these two samples. This effect has been previously reported for the 11B nuclei of carborane, where the 11B line widths were observed to be remarkably narrow as a result of isotropic reorientation in the solid state.54,55 Further evidence for dynamics in 4 comes from the static 11B NMR experiments shown in Figure 9, where the resonance for sample 4 (FWHM = ca. 1710 Hz) was sharper than that of sample 2 (FWHM = ca. 5547 Hz) owing to motional averaging of the quadrupolar and magnetic shielding interactions. (We were unable to draw similar conclusions from the static 11B NMR spectrum of sample 5 due to the presence of impurities, resulting in peak overlap (Figure S7).) Referring again to the 11 B MAS NMR spectra of 4 and 5 (Figure 8), a discrepancy between the number of NMR signals and the number non-equivalent atoms as detected by X-ray diffraction

Variable-temperature 11B MAS NMR experiments were carried out on 4 to further probe the dynamic processes (see Supporting Information). We attempted to model the change in CT half-height line width as an Arrhenius process. An apparent activation energy of 9.1 kJ mol-1 is obtained (after subtracting a rough estimate of the inherent static line width); considering that activation energies for methyl group rotation are often on the order of 12 kJ mol-1,56 our result seems too low to be physically meaningful. This problem is attributed to the simultaneous contributions from the three different dynamic processes proposed above. A further complication in trying to apply a simple Arrhenius analysis to the 11B CT line widths arises from the 11B-11B and 11B-10B dipolar coupling interactions which are gradually reintroduced as the temperature is lowered. Nevertheless, these variable-temperature experiments provide further evidence for the existence of dynamic disorder in 4. Our inability to observe the 11B satellite transition spinning sidebands at room temperature also suggests the presence of at least one dynamic process on the µs timescale. 2. 11B DQF J-resolved SSNMR Spectroscopy 11

B DQF J-resolved SSNMR experiments were performed on all five of the samples. The resulting spectra are provided in Figure 10, and the experimental and theoretical J(11B, 11B) coupling constants are reported in Table 2. As expected, the splittings given by the DQF J-resolved peaks of samples 1 (95.3 Hz), 2 (88.3 Hz), and 3 (95.0 Hz) are amplified by a factor of three as compared to the calculated J(11B, 11B) values (26.9 Hz, 24.9 Hz, and 28.1 Hz for 1, 2, and 3, respectively) due to the presence of a crystallo-



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graphic inversion center between the two boron nuclei (Figure 3). Conversely, even though the boron nuclei of samples 4 and 5 are non-equivalent according to the Xray data recorded at 100 K for 4 and 298 K for 5 (Figure 3),23 we still anticipate the J splittings to be symmetryamplified by a factor of three since they are expected to be magnetically equivalent as a result of dynamics. Indeed, the J splittings (107.3 Hz for 4, 101.2 Hz for 5) were observed to be three times larger than the calculated J(11B, 11 B) values (30.3 Hz for 4, 28.2 Hz for 5). This illustrates that molecular dynamics results in an effective magnetic equivalence of the boron spins, and that this effect manifests itself in the DQF J-resolved spectra. Consequently, dynamic disorder needs to be taken into consideration when performing DQF J-resolved NMR experiments in order to correctly extract the J coupling constants; or, from an alternative point of view, these experiments can potentially be employed to determine if dynamic disorder is present, if the symmetry of the system and approximate magnitude of the J(11B, 11B) values are known a priori. As already mentioned in the Introduction, it has been solidly established in previous work that, in the absence of molecular dynamics, splittings of J or 3J are consistently measured for systems containing non-equivalent or magnetically equivalent spin pairs, respectively (Figure 1).

Table 3. The main NLMO contributions to the J(11B, 11B) coupling constants of the [B2(CN)6]2- salts studied in this work. Calculations were performed using the revPBE functional with the TZ2P basis set. sample

B core NLMO / %

B – B bonding NLMO / %

1

71.4

39.1

2

71.8

40.7

3

70.5

39.7

4

69.5

40.1

5

71.6

37.7


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Journal of the American Chemical Society of dynamics is decreasing as the temperature is decreased. A loss of some signal intensity is also consistent with that expected from simulations of the transition from full magnetic equivalence to chemical equivalence.57 For diborane systems without dynamic disorder, the experimental J(11B, 11B) coupling constants have been reported to correlate linearly with the corresponding theoretical values,13 illustrating that the coupling constants can be retrieved using DFT calculations. As shown in Figure 11, we obtained a good agreement between the calculated and experimental J(11B, 11B) coupling constants for the [B2(CN)6]2- dianions (Jexp. = 1.14Jcalc. + 0.89 Hz; R2 = 0.90). The deviation of R2 from linearity was attributed to the input structures that were employed for the J(11B, 11B) calculation since they were based on the atomic coordinates of the major disorder sites only and the calculations were performed under static conditions (at T = 0 K). Thus, for samples with dynamic disorder, the input structures do not fully represent the real system, contributing to small differences between the theoretical and the experimental 11 J(11B, B) coupling constants. As compared

11

Figure 10. The indirect dimension of the B DQF J-resolved SSNMR spectra of 1, 2, 3, 4, and 5 recorded at room temperature and at 9.4 T with a spinning frequency of 12 kHz. The J splittings were found to be amplified by a factor of 3 for all samples since 1 – 3 consist of pairs of crystallographically equivalent borons, while 4 and 5 are dynamically disordered. 11 11 The corresponding J( B, B) values are given in Table 2.

The two-dimensional J-resolved 11B MAS NMR spectra also clearly depend on temperature. For 4, the spectral splitting of 3J is observed over the high-temperature range from 33°C to 11°C, but the signal-to-noise ratio plummets over this same range (see Supporting Information). Therefore, in this case the effect of a reduced dynamical rate seems to manifest itself in the 11B relaxation time constants (perhaps a decreased T2) and/or some sort of interference process which leads to a loss of signal. We attempted to record spectra with recycle delays double and triple those used in our room temperature experiments, but were not able to observe a signal in the indirect dimension at temperatures below 11°C. While we were thus unable to observe a doublet with reduced splitting equal to J, these VT experiments are nevertheless consistent with our hypothesis and suggest that the rate

Figure 11. Correlation between the experimental and theo11 11 11 retical J( B, B) coupling constants as obtained from B DQF J-resolved SSNMR spectroscopy and as calculated using 2 revPBE/TZ2P, respectively, (J = 1.14Jcalc. + 0.89 Hz, R = 0.90). Data taken from Table 2.

to other previously studied diboron systems,11,13 the J(11B, 11 B) values of the electron-precise [B2(CN)6]2- salts are consistently substantially smaller. According to the literature, the J(11B, 11B) coupling constants for diboranes were found to range from 98 to 136 Hz,13 and for diboron derivatives with higher B – B bond orders, the measured J coupling constant varied from 75 to 187 Hz.11 Alternatively, the J(11B, 11 B) coupling constants of the [B2(CN)6]2- salts were observed to range from 29.4 to 35.8 Hz, which is in good agreement with the value of 33.2 Hz derived from simulation of the ABX pattern of the 13C NMR spectrum of [11B2(13CN)(CN)5]2– in CD3CN solution.23 The magnitude of the J(11B, 11B) coupling constants has been reported to correlate inversely with various electronic metrics of the sys-



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tems, such as the hybridization state of the boron orbitals and the B – B bond energies.11,13 Since the [B2(CN)6]2- dianions contain single B – B bonds where the boron orbitals are expected to be sp3 hybridized, the corresponding J(11B, 11 B) values are anticipated to be smaller than in the previously studied diboron systems which had less boron p – orbital contribution to the B – B bond (ca. sp1 to sp2 hybridized). To confirm this line of reasoning, NBO and NLMO analyses were conducted.

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NBOs are localized orbitals (usually 1– to 2–center) which provide a depiction of the wavefunction, ѱ, that is closely related to the classical Lewis structure, whereas NLMOs are expansions of the NBOs and are more delocalized.58,59 The corresponding analysis can be employed to elucidate the electronic origins of the J couplings and to investigate the electronic features of the system. From our calculations, the main NLMO contribution to the J couplings for all of the samples was found to arise from the boron core orbitals (ca. 70%) and the B – B σ-bonding orbitals (ca. 40%) (Table 3). Information regarding the electronic properties of [B2(CN)6]2- was also obtained (Table 2), enabling a correlation between the J(11B, 11B) coupling constants and the electronic properties to be accomplished. Similar to what was previously reported,13 an increase in the J(11B, 11B) values was correlated to a decrease in B – B σ-bonding NBO energy and p-orbital hybridization index of the boron orbitals responsible for the B – B bond (Table 2 and Figure 12), thus illustrating the ability of J coupling constants to assess the strength of the B – B bonds, as well as the nature of the boron bonding orbitals for systems bearing 2c-2e B(sp3) – B(sp3) bonds. This also explains the difference between our results and the much larger literature values. Previous studies were only performed on B – B bonds formed from boron orbitals with p-orbital hybridization index of ca. 1 to 2 and B – B σbonding NBO energies of ca. -0.3 to -0.4,11,13 whereas [B2(CN)6]2- comprises B(sp3) – B(sp3) bonds and therefore the boron orbitals have greater p-orbital character, and the corresponding B – B bonds are also weaker (NBO energies of ca. -0.07). Accordingly, the J(11B, 11B) coupling constants of the [B2(CN)6]2- salts can be expected to be smaller. Conclusions

Figure 12. Correlation between the experimentally obtained 11 11 J( B, B) coupling constants and (a) the B – B σ-bonding 2 NBO energies (J = -300ENBO + 12.7 Hz, R = 0.99), and (b) the degree of p-orbital hybridization, m, of the boron orbitals responsible for the B – B bonds (J = -63.5m + 215 Hz, 2 2R = 0.97). The black squares correspond to the [B2(CN)6] dianions studied in this work, the red squares correspond to the diborane compounds studied in ref. 13, and the blue squares correspond to the diborene and diboryne systems investigated in ref. 11. The p-orbital hybridization index for the diborene and diboryne compounds were converted from the corresponding σB-B s-character given within ref. 11 by assuming only p and s orbitals of the borons contribute to the bonding interaction. Line of best fit was derived using dibo2rane data only. Inserts show the correlation for [B2(CN)6] only and the respective values are given in Table 2.

This work has provided new insights into two distinctly important areas of chemistry and materials science: the chemical bond and molecular dynamics. Understanding the nature of the chemical bond occupies a prime position in the pantheon of chemical research. This contribution has provided novel insight, via J couplings measured from advanced two-dimensional NMR experiments, into the nature of the 2c-2e bond in a series of electron precise dianionic diboranes. The measured coupling constants have been shown, with the aid of computational chemistry, to differ substantially from the values obtained for other diboron systems including diboranes, diborenes, and diborynes. Somewhat surprisingly, it is remarkable that the correlations presented in Figure 12 hold over such a wide range of bonding energies and hybridization states, suggesting the generality of the methods described herein for characterizing the electronic structures associated with heretofore unexplored bonding environments and other novel systems. To the best of our knowledge, this is the first SSNMR investigation into the relationship between the J(11B, 11B) coupling constants of 2c-2e B(sp3) – B(sp3) systems and their respective electronic structures. Molecular dynamics in solids is a fascinating and important field with diverse applications ranging from molecular machinery to topochemical transformations and


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more. The present contribution has described a novel NMR effect whereby molecular dynamics of nonequivalent nuclear spin pairs changes the appearance of the spectrum in a predictable and useful manner. This effect can be used in two senses, depending on the nature of the system. First, if one has independent knowledge of the symmetry relationship between two spins, the effect can be used to detect the presence or absence of dynamics in the system. Or, if one has independent knowledge of the presence or absence of dynamics, the effect can be used to provide information on the equivalence or nonequivalence of the spin pair. This effect therefore provides unique information on the structure and dynamics of solids.

ASSOCIATED CONTENT Supporting Information. IR, Raman, and additional NMR spectra; powder X-ray diffractograms; cif for 2; information on variable-temperature NMR experiments; modelling of the effects of dynamics on the NMR spectra; MPG files. This material is available free of charge via the Internet at http://pubs.acs.org

AUTHOR INFORMATION Corresponding Authors *[email protected]; [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENTS D. L. B. thanks the Natural Sciences and Engineering Research Council of Canada for funding. M. F. thanks Merck KGaA (Germany) for generous support and Thomas C. Schäfer and Sven H. Zottnick for the powder diffraction experiments. Dr. Glenn Facey is thanked for his valuable assistance with low-temperature NMR experiments. Mr. Jason (Yue) Zhang and Dr. Bryan Lucier are thanked for helpful discussions concerning spectral simulations.

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Dynamic Disorder and Electronic Structures of Electron-Precise

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