multinuclear solid-state nuclear magnetic resonance and...

Multinuclear Solid-State Nuclear Magnetic Resonance and DensityFunctional Theory Characterization of Interaction Tensors in TaurineLuke A. O’Dell,*,† Christopher I. Ratcliffe,† Xianqi Kong,‡ and Gang Wu‡

†Steacie Institute for Molecular Sciences, National Research Council, 100 Sussex Drive, Ottawa, Ontario, K1A 0R6, Canada‡Department of Chemistry, Queen’s University, 90 Bader Lane, Kingston, Ontario, K7L 3N6, Canada

*S Supporting Information

ABSTRACT: A variety of experimental solid-state nuclear magnetic resonance(NMR) techniques has been used to characterize each of the elements in2-aminoethane sulfonic acid (taurine). A combination of 15N cross-polarization magicangle spinning (CPMAS), 14N ultrawideline, and 14N overtone experiments enabled adetermination of the relative orientation of the nitrogen electric field gradient andchemical shift tensors. 17O spectra recorded from an isotopically enriched taurinesample at multiple magnetic fields allowed the three nonequivalent oxygen sites to be distinguished, and NMR parameterscalculated from a neutron diffraction structure using density functional theory allowed the assignment of the 17O parameters to thecorrect crystallographic sites. This is the first time that a complete set of 17O NMR tensors are reported for a sulfonate group.In combination with 1H and 13C MAS spectra, as well as a previously reported 33S NMR study, this provides a very broad setof NMR data for this relatively simple organic molecule, making it a potentially useful structure on which to test DFT calculationmethods (particularly for the quadrupolar nuclei 14N, 17O, and 33S) or NMR crystallography approaches.

1. INTRODUCTIONSolid-state nuclear magnetic resonance (NMR) spectroscopy isone of the premier techniques for the structural characterizationof materials, capable of providing detailed information on thelocal structure and dynamics in a broad range of systems. Forthe study of crystalline samples, a combination of solid-stateNMR experiments and density functional theory (DFT) calcu-lations can be particularly powerful. Gauge-including projectoraugmented wave (GIPAW) methods1 that take into accountthe infinite periodic lattice can be used to calculate NMRparameters to a high degree of accuracy, thereby allowingthe exquisite sensitivity of the measured NMR parameters to thecrystal or molecular structure to be fully exploited, for exampleto refine an X-ray diffraction structure. Such approaches arenow often referred to as NMR crystallography.2 Spin-half nucleisuch as 1H, 13C, or 29Si have been used to refine structures viatheir isotropic chemical shifts,3 chemical shift anisotropies,4 orspin diffusion properties.5 Parameters measured from quad-rupolar nuclei have also been used to refine crystal structures,6−9

but due to various associated difficulties such as low sensitivitiesor large anisotropic interactions, such nuclei are far moreseldom used in NMR crystallography. This is unfortunate, sincequadrupolar nuclei are capable of providing a wealth of localstructural information.10 In particular, the electric field gradient(EFG) offers a probe of the local electronic environment thatis highly sensitive to the surrounding structure, particularlyhydrogen bonding arrangements.Herein, we present multinuclear solid-state NMR measure-

ments for taurine, which features three challenging quadrupolarnuclei: 14N (nuclear spin I = 1), 17O (I = 5/2), and

33S (I = 3/2).This is therefore a potentially useful system on which to testout new experimental or computational methodologies. By use

of a combination of 15N and 14N methods, we obtain a full setof NMR parameters for the nitrogen site, including adetermination of the relative orientation of the EFG andchemical shift (CS) tensors. Parameters for the three non-equivalent oxygen sites are also obtained from an isotopicallyenriched sample and assigned to the correct crystallographicsites with the aid of DFT calculations. Solid-state 1H and 13CNMR spectra are also presented, which, in combination with aprevious 33S study,11 constitutes a near-complete set of NMRresults for this model system.

2. EXPERIMENTAL DETAILSa. Sample Details. For the solid-state 1H, 13C, 14/15N NMR

experiments, a natural abundance sample of taurine (>99%pure, purchased from Sigma Aldrich) was used. For the 17ONMR experiments, 17O-enriched taurine was synthesized in thefollowing manner. Sodium sulfite (300 mg, 2.38 mmol) wasdissolved in [17O]-water (1.16 g, 41% 17O-enriched, purchasedfrom CortecNet). The solution was kept at room temperaturefor 23 h. 2-Bromoethylamine hydrochloride (585 mg, 2.86 mmol)was then added to the solution. The mixture was stirred at 65 ±3 °C in an oil bath for 13 h. The [17O]-water was recovered.The residual material was refluxed in methanol (30 mL) for30 min, cooled to room temperature, collected (filtration), washedwith ethanol (2 × 10 mL), and dried at 80 °C. The crude productwas dissolved in 1 mL of 40% hydrobromic acid and filteredthrough sintered glass. Ethanol (35 mL) was added to the filtrateto precipitate out the product. The solid material was then washed

Received: November 10, 2011Revised: January 6, 2012Published: January 6, 2012

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© 2012 American Chemical Society 1008 dx.doi.org/10.1021/jp210844t | J. Phys. Chem. A 2012, 116, 1008−1014

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with ethanol (4 × 10 mL) and dried at 80 °C, giving 220 mg ofwhite solid (74% yield). The 17O enrichment of the productwas determined to be 23% by solution 17O NMR.b. Solid-State NMR Experiments. The 1H, 13C, and 15N

NMR spectra were recorded on an 11.7 T Bruker Avance IIIspectrometer using Varian double-resonance probes with a 3.2 mmrotor diameter and 20 kHz MAS rate for the 1H experiment and a4.0 mm rotor diameter and 10 kHz MAS rate for the 13C and 15Nexperiments. The 1H spectrum was acquired using a windowedDUMBO pulse sequence12 for homonuclear decoupling, with a2.8 μs π/2 pulse, a 24 μs DUMBO pulse length (ν1 = 71 kHz),a recycle delay of 5 and 4 scans acquired. For the 13C experi-ment, a 2 μs excitation pulse was applied with continuous-wave1H decoupling of ∼40 kHz power, a recycle delay of 2 min and32 scans acquired. The 15N spectrum was acquired with cross-polarization from the 1H nuclei using a 1H π/2 pulse of 4 μs,1.5 ms constant-amplitude contact pulses (ν1 = 55 kHz), arecycle delay of 2.5, and 1000 scans acquired. The 1H and 13Cspectra are referenced to tetramethylsilane and the 15N spectrumto solid NH4Cl.The 14N overtone NMR spectrum was recorded on a 21.1 T

Bruker Avance II spectrometer (Ultrahigh-field NMR Facilityfor Solids, Ottawa, Canada) using a home-built double-resonancestatic probe with a 7.0 mm inner-diameter coil size. A 25-μson-resonance excitation pulse (ν1 = 80 kHz as measured on the

2H nucleus, which is close in frequency to the 14N overtonetransition) was used with continuous-wave 1H decoupling of∼80 kHz power, a recycle delay of 1 s, and 50,000 scansacquired. The spectrum is referenced such that 0 kHz corre-sponds to exactly twice the 14N fundamental (single-quantum)frequency of solid NH4Cl.The 17O NMR spectra were recorded at 11.7 and 21.1 T on

Bruker Avance and Bruker Avance II spectrometers, respec-tively. The static and 1D MAS spectra were acquired using aspin−echo pulse sequence (π/2−τ−π/2−acquire). At 11.75 T,both nonspinning and MAS experiments were per-formed on a Bruker 4.0 mm double resonance MAS probe,the latter with a MAS rate of 12.0 kHz and 512 scans acquiredwith a recycle delay of 1 s. To obtain a high-quality staticspectrum at this field, 8854 scans were acquired with a recycledelay of 5 s. At 21.1 T, nonspinning experiments were per-formed on a home-built static probe with the sample packed ina 5.0 mm Teflon tube, while MAS and 3QMAS experimentswere performed on a Bruker 4.0 mm MAS probe with thesample packed in a Si3N4 rotor spinning at 12.5 kHz. For bothMAS and static spectra, a spin−echo sequence was used with apulse delay of 50 μs, 256 scans acquired and a recycle delay of20 s. In the 3QMAS experiment, the t1 increment wassynchronized with the sample spinning and a total of 48 t1increments were collected with 192 scans each and a recycledelay of 15 s.Spectral processing was carried out using the NUTS software

(Acorn NMR). The 17O spectra were simulated using Dmfit.13

The 14N overtone powder pattern was simulated usingRMNSim.14

c. DFT Calculations. DFT calculations were carried out ona neutron diffraction structure15 (CCSD code TAURIN03)using the CASTEP software16 and the Materials Studio 4.3program (Accelrys) running on a Linux server with 8 pro-cessing cores and 32 GB of RAM. Perdew, Burke, andErnzerhof (PBE) functionals were used with a plane wave basisset cutoff of 610 eV and a 3 × 1 × 2 Monkhorst-Pack k-spacegrid. Electric field gradient and chemical shielding tensors were

Figure 1. The molecular structure of taurine, taken directly from thecrystal structure15 with individual sites labeled.

Figure 2. (a) 1H NMR spectrum obtained from taurine at 11.7 T and 20 kHz MAS, using a windowed DUMBO homonuclear decoupling pulsesequence. The peak at 7.6 ppm corresponds to the three distinct NH3 protons, while the peak at 3.3 ppm arises from the four CH2 protons. (b)

13CNMR spectrum obtained from the same sample at 11.7 T and 10 kHz MAS. The two carbon sites are resolved with the peak at 46.5 ppmcorresponding to the carbon bonded directly to the sulfur and the peak at 35.8 ppm arising from the carbon bonded to the nitrogen.

The Journal of Physical Chemistry A Article

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calculated for all nuclei. Because of the relatively high degree ofaccuracy for this crystal structure, no geometry optimizationwas performed. DFT optimizations of the proton positions in thisstructure have previously been shown to yield calculated 14N and33S NMR parameters that agree less well with experimental valuesthan those obtained from the unoptimized structure.11

Calculated isotropic shielding values σcalc for1H, 13C, and 17O

were converted to isotropic chemical shifts δcalc using the ex-pression δcalc = σref − σcalc, with values for σref previously reported

as σref(1H) = 30.8 ppm, σref(

13C) = 170.0 ppm, and σref(17O) =

265 ppm.9 For 14N, the relation δcalc = 201.4 − 1.05σcalc wasused, having been determined in a previous study.17

To attempt to account for thermal vibrations in the DFTcalculations of the NMR parameters, a molecular dynamicssimulation was also carried out using the CASTEP software16

following a procedure recently reported.18 This used a cutoffenergy of 550 eV and a 3 × 1 × 2 Monkhorst Pack grid. Thetemperature was set at 290 K using a Nose thermostat in theNVT ensemble. The time step was set to 1 fs with a total timeof 6 ps.

3. RESULTS AND DISCUSSION3.1. 1H and 13C NMR Spectra. The zwitterionic molecular

structure of 2-aminoethane sulfonic acid (taurine) in its crys-talline form is shown in Figure 1. The crystal structure is mono-clinic with four molecules per unit cell and a cell volume of486 Å3.15 The asymmetric unit contains a single molecule, so allatoms in the molecule are crystallographically distinct, resultingin seven hydrogen sites, two carbon sites, three oxygen sites,and a single nitrogen and sulfur site.A 1H MAS NMR spectrum obtained from taurine at 11.7 T

is shown in Figure 2a. Two peaks are observed and are assignedto the NH3 protons (7.6 ppm) and CH2 protons (3.3 ppm) onthe basis of the isotropic chemical shifts calculated from thecrystal structure (Table 1). The calculated shifts for the fourcrystallographically distinct CH2 protons are clustered within0.5 ppm of each other, and the experimental 1H NMR peaksare not individually resolved even with the use of the DUMBO

Table 1. 1H and 13C Isotropic Chemical Shift Values for theSeven Crystallographically Distinct Hydrogen Sites and TwoDistinct Carbon Sites in Taurine, Calculated from theCrystal Structure Using DFTa

site calculated δiso/ppm experimental δiso/ppm

H1 8.1 7.6(1)H2 5.8H3 6.4H4 3.2 3.3(1)H5 3.7H6 3.4H7 3.4C1 43.9 46.5(1)C2 32.9 35.8(1)

aBecause of peak overlap, experimental 1H isotropic chemical shiftvalues correspond to the peak maxima for the two groups of sitesindicated.

Figure 3. (a) 15N CPMAS NMR spectrum of taurine at 11.7 T, (b) 14N overtone spectrum obtained from a static powder sample at 21.1 T, (c)simulation of the overtone powder pattern made using the parameters given in Table 2 (including the quadrupolar interaction and the chemical shiftanisotropy), and (d) simulation neglecting the effects of the chemical shift anisotropy.



homonuclear decoupling pulse sequence. The three NH3protons are also unresolved in the experimental spectrum,despite the calculated isotropic shift values being spread overa range of 2.3 ppm. The convergence of the NH3 protonchemical shifts to a single, relatively sharp peak is due tothe rotational dynamics of this amine group which are un-accounted for in the DFT calculations. There have been a largenumber of NMR studies of NH3 group rotations in crystallineamino acids, particularly 1H relaxation measurements19 and2H line shape studies,20 and typically, jump rates for the NH3groups in these systems are on the order of 106 s−1 at room tem-perature.20−22 The molecular dynamics simulation carried out onthis structure showed considerable librational motion of the NH3group, but interchange of the hydrogen sites was not observeddue to the extremely short time scale of the simulation (6 ps).To account for these fast thermal motions in our calculations, anew set of NMR parameters for all nuclei were obtained fromthe MD simulation by averaging the tensor elements calculatedfrom 46 individual frames spaced 50 fs apart. This approach wassuccessfully used previously to improve calculated 13C chemical shiftanisotropies;18 however, in this case it did not result in an improvedagreement with our experimental values for this system, and theseparameters are therefore not shown.The two carbon sites are well-resolved in the 13C NMR

spectrum with isotropic chemical shifts of 46.5 and 35.8 ppm(Figure 3), and on the basis of the calculated values (Table 1)these can be assigned to sites C1 and C2, respectively. Thisassignment is consistent with the observation of a much shorterspin−lattice relaxation time for the peak at 35.8 ppm. The C2carbon is directly bonded to a nitrogen site; therefore all C2carbons experience 13C−14/15N dipolar couplings, which willcontribute to relaxation (though we note that no residualdipolar splittings were observed for the C2 peak, being toosmall to resolve at this field). In contrast, C1 is bonded to asulfur site with a corresponding low abundance of the NMR-active 33S isotope (0.76%), thus contributions to spin−latticerelaxation from 13C−33S couplings will be insignificant. We notethat the calculated separation of these peaks (11.0 ppm), aquantity insensitive to errors in the value of σref(

13C) used,matches remarkably well with the experimental value (10.7 ppm).3.2. 14N and 15N NMR Spectra. An accurate isotropic

chemical shift for the nitrogen site (−6.0 ppm) was obtainedfrom the 15N CPMAS spectrum (Figure 3a). Along with thequadrupolar coupling constant (CQ) and asymmetry parameter(ηQ) that were recently determined11 using ultrawideline 14N

techniques,23 this provides constraints for the fitting of the 14Novertone powder pattern obtained at 21.1 T (Figure 3b). 14Novertone NMR spectra, in which the nuclei are irradiated atapproximately twice the Larmor frequency in order to directlyexcite and observe the Δm = 2 “overtone” transition,24 areinsensitive to the first-order quadrupolar interaction, which for14N is typically on the order of several MHz.25 The 14Novertone powder pattern widths are therefore typically on theorder of kHz, and perturbations due to both the second-orderquadrupolar interaction and chemical shift anisotropy can beresolved, particularly at high field strengths where the effects ofthe CSA are more pronounced. Such experiments thereforeprovide a potentially straightforward way of determining therelative orientations of the nitrogen EFG and CS tensors from apowder sample. The simulated 14N overtone powder pattern

Table 2. Experimental (Bold) and Calculated NMR Parameters for the Nitrogen and Three Nonequivalent Oxygen Sites inTaurinea

δiso/ppm Ω/ppm κ CQ/MHz ηQ α/deg β/deg γ/deg14N exptl −6.0(2) 18(5) −0.16(30) 1.19(1) 0.18(1) 270(50) 77(3) 90(15)14N calcd −9.1 12 0.05 1.29 0.36 251 86 35217O (O1) exptl 170.4(2) 88(10) 0.75(10) 6.70(2) 0.14(4) 90(10) −20(2) 90(10)17O (O1) calcd 178.2 115 0.36 −7.17 0.08 266 −15 25017O (O2) exptl 179.0(2) 88(10) 0.68(10) 6.65(2) 0.16(4) 0(10) 0(2) 0(10)17O (O2) calcd 187.3 88 0.53 −6.97 0.16 123 12 1217O (O3) exptl 187.4(2) 78(10) 0.69(10) 6.80(2) 0.05(4) 0(10) −5(2) 0(10)17O (O3) calcd 190.8 65 0.67 −6.76 0.04 10 −11 17

aCalculated isotropic shielding values were converted to chemical shifts δiso based on previously reported empirical relations for nitrogen17 andoxygen.9 Also shown are the span (Ω) and skew (κ) of the CS tensor, the quadrupolar coupling constant (CQ) and asymmetry parameter (ηQ), andthe Euler angles (α, β, and γ) describing the relative orientations of the CS and EFG tensors. Definitions of these parameters are standard and can befound elsewhere.17Parameters for the 33S nucleus are reported in reference 11.

Figure 4. Calculated orientations of the principal components of theelectric field gradient (purple, |V33| ≥ |V22| ≥ |V11|) and chemical shifttensors (green, δ11 ≥ δ22 ≥ δ33) of (a) nitrogen, (b) sulfur, and (c) thethree oxygen sites in the molecular frame of taurine.



shown in Figure 3c was fitted to the experimental spectrum bymanually adjusting the CS tensor parameters (the span Ω andskew κ) and Euler angles (α, β, and γ) while keeping δiso, CQ,and ηQ fixed to their experimental values. The resultant, completeset of 14N interaction parameters are presented in Table 2.Experimental uncertainties are larger for certain parametersthan others, indicating that these parameters had a relativelyminor effect on the shape of the simulated overtone powderpattern (e.g., the pattern shape was extremely sensitive to thevalue of the Euler angle β, but far less so to α). Overall, theagreement between the experimental and calculated 14N param-eters is reasonably good. The overestimation of the calculatedCQ by 100 kHz is of the same magnitude observed in a previous14N study.17 Some additional example simulations with alteredinteraction parameters are provided as Supporting Informationto illustrate the extent to which the shape of the static overtonepowder pattern changes as the parameters are adjusted.The relative orientation of nitrogen EFG and CS tensors can

also in principle be ascertained by fitting 14N MAS spinningsideband manifolds taking into account second-order cross-terms

between the quadrupolar and shielding interactions, but to thebest of our knowledge, such an approach has so far only beenapplied to cases where the two tensors are approximatelycoincident (e.g., nitrate or tetraalkylammonium ions).26 Thefitting of the static overtone powder pattern using constraintsfrom 15N and ultrawideline 14N experiments represents a morestraightforward approach that is analogous to the way Eulerangles are commonly determined for half-integer quadrupolarnuclei, where static central-transition powder patterns are fittedusing constraints from MAS spectra (vide infra).DFT calculations allow the (calculated) orientations of the

EFG and CS tensors to be visualized in the molecular frame,and this is illustrated for the nitrogen site in Figure 4a. Thelargest principal component of the EFG tensor (V33) and theleast shielded component of the CS tensor (δ11) are predictedto be aligned approximately parallel to the N−C bond. Theseorientations are consistent with previous DFT studies of aminogroups.27,28 The correct CS tensor orientation for the 33S nucleus,which was mislabeled in a previous publication,11 is also shownin Figure 4b for completeness. The least shielded component of

Figure 5. Experimental MAS (a and b) and static (c and d) 17O NMR spectra (black) obtained from an isotopically enriched sample of taurine at themagnetic field strengths shown. Spectra (a) and (b) were recorded at 12.5 and 12.0 kHz MAS, respectively. Asterisks denote spinning sidebands. Redtraces show fitted simulations, with the individual simulated lineshapes for sites O1, O2, and O3 shown below in green, purple, and blue, respectively.



the 33S CS tensor (δ11) lies approximately parallel to the S−Cbond.3.3. 17O NMR Spectra. Taurine has three inequivalent

oxygen sites in similar structural environments, but despiteconsiderable overlap of the 17O powder patterns, these sitescould be distinguished on the basis of multiple-field MAS andstatic NMR spectra (Figure 5). EFG parameters and isotropicchemical shifts were measured from the MAS spectra and thenfixed during fits of the static spectra, allowing the CS tensorsand Euler angles to be quantified. The calculated 17O param-eters for these sites show reasonably good agreement with theexperimental values, allowing the assignment of the NMRparameters to the correct crystallographic sites. The EFG andCS tensor orientations for all three oxygen sites are shown inFigure 4c. In all three cases, the largest principal component ofthe EFG tensor (V33) and the most shielded component of theCS tensor (δ33) are aligned approximately parallel to the O−Sbond. This is the first time that a complete set of 17O EFG andCS tensors have been determined for a SO3

− group.29

To further confirm the accuracy of the 17O NMR parameters,we obtained a 3QMAS spectrum from the enriched taurine. Asseen from Figure 6, three well-resolved peaks are observed inthe isotropic dimension. For 17O, the peak position along the iso-tropic dimension of a sheared 3QMAS spectrum is determined byFiso (ppm) = δiso (ppm) + (3/850)(CQ/ν0)

2(1 + ηQ2/3) × 10−6

(ppm).30 As seen from Figure 6, the excellent agreement betweenthe observed and predicted (using the 17O NMR parameters

shown in Table 2) peak positions confirms the accuracy of thereported parameters.For the sulfonate group in taurine, the observed values of CQ

(6.65−6.80 MHz) and δiso (170−187 ppm) for 17O are signif-icantly larger than those reported for p-toluenesulfonic acidmonohydrate (4.79 MHz and 140 ppm).31 Clearly, this discrep-ancy is due to the difference in hydrogen bonding between thetwo compounds. In p-toluenesulfonic acid monohydrate, each ofthe three sulfonate oxygen atoms is involved in a very strongO···H−O hydrogen bond with the O···O distance being 2.520,2.525, and 2.538 Å.32 In taurine, however, the sulfonate oxygenatoms are involved in weaker O···H−N hydrogen bonding withthe O···N distances ranging between 2.789 and 3.017 Å.15 Interest-ingly, among the three oxygen atoms in taurine, the isotropic che-mical shift appears to exhibit stronger sensitivity toward the strengthof hydrogen bonding than the quadrupole coupling constant.

4. SUMMARYExperimental NMR parameters have been obtained for 1H, 13C,14/15N, and 17O in crystalline taurine. The use of a combinationof 15N CPMAS, 14N static ultrawideline, and 14N overtone NMRspectroscopy provided a relatively straightforward method fordetermining the relative orientation of the nitrogen EFG andCS tensors. 17O NMR parameters were also measured for thethree nonequivalent oxygen sites using multiple-field static,MAS, and 3QMAS experiments. Along with a previous 33Sstudy,11 this constitutes a large and varied set of data on thisrelatively simple crystalline structure, making it a potentially usefulsystem on which to test DFT calculation methods or NMR crys-tallography approaches, particularly for the quadrupolar nuclei.NMR parameters calculated from an unoptimized neutron dif-fraction structure showed a good overall agreement with experi-mental values, though there appears to be some room for impro-vement. This may come from an improved crystal structure,more accurate computational methods (e.g., improved pseudo-potentials or methods that account for dynamics), or a combina-tion of the two. Ultimately, it is anticipated that more accurateDFT calculations for quadrupolar nuclei will allow a refinementof crystal structures such as this using the broad range of experi-mental NMR parameters available from such nuclei.

■ ASSOCIATED CONTENT*S Supporting InformationFurther examples of simulated 14N static overtone powderpatterns. This material is available free of charge via the Internetat http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected].

■ ACKNOWLEDGMENTSProf. Philip Grandinetti is thanked for providing the RMNSimsoftware used to simulate the 14N overtone spectra. Dr. AndreasBrinkmann is acknowledged for assistance in setting up the 1HDUMBO experiment and for helpful discussions. Access to the21.1 T NMR instrument was provided by the National Ultrahigh-Field NMR Facility for Solids, Ottawa (www.nmr900.ca). We aregrateful to Drs. Eric Ye and Victor Terskikh for assistance inrecording the 17O NMR spectra at 21.1 T. G.W. thanks theNatural Sciences and Engineering Research Council (NSERC)of Canada for support.

Figure 6. (a) Experimental 17O 3QMAS spectrum obtained from anisotopically enriched sample of taurine at 21.1 T. (b) Comparisonbetween calculated and observed peak positions along the isotropicdimension. The uncertainty in the experimental values is estimated tobe ±0.5 ppm.



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