Concise NMR Approach for Molecular Dynamics Characterizations in

Article pubs.acs.org/JPCA

Concise NMR Approach for Molecular Dynamics Characterizations in Organic Solids Abil E. Aliev* and Denis Courtier-Murias Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, U.K. ABSTRACT: Molecular dynamics characterisations in solids can be carried out selectively using dipolar-dephasing experiments. Here we show that the introduction of a sum of Lorentzian and Gaussian functions greatly improve fittings of the “intensity versus time” data for protonated carbons in dipolar-dephasing experiments. The Lorentzian term accounts for remote intra- and intermolecular 1H−13C dipole−dipole interactions, which vary from one molecule to another or for different carbons within the same molecule. Thus, by separating contributions from weak remote interactions, more accurate Gaussian decay constants, Tdd, can be extracted for directly bonded 1H−13C dipole−dipole interactions. Reorientations of the 1H−13C bonds lead to the increase of Tdd, and by measuring dipolar-dephasing constants, insight can be gained into dynamics in solids. We have demonstrated advantages of the method using comparative dynamics studies in the α and γ polymorphs of glycine, cyclic amino acids L-proline, DL-proline and trans-4-hydroxy-L-proline, the Ala residue in different dipeptides, as well as adamantane and hexamethylenetetramine. It was possible to distinguish subtle differences in dynamics of different carbon sites within a molecule in polymorphs and in L- and DL-forms. The presence of overall molecular motions is shown to lead to particularly large differences in dipolardephasing experiments. The differences in dynamics can be attributed to differences in noncovalent interactions. In the case of hexamethylenetetramine, for example, the presence of C−H···N interactions leads to nearly rigid molecules. Overall, the method allows one to gain insight into the role of noncovalent interactions in solids and their influence on the molecular dynamics.

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In principle, 13C NMR can be used for dynamics characterizations. For example, the chemical shift anisotropy of 13C NMR can be used in the same manner as the anisotropy of 2H quadrupolar interactions.31−33 With the introduction of highfield solids NMR equipment, chemical shift anisotropy (CSA) measurements are becoming particularly useful (e.g., for aliphatic carbons with relatively small span of CSA).34,35 In addition, 1H−13C dipole−dipole interactions provide another source of information about dynamics.5,6 In a few early studies, dipolar-dephasing experiments have been shown useful for estimating motional averaging of dipolar interactions.36−40 It was found that for directly bonded 1H−13C pairs, the dependence of the signal intensity on the dephasing delay can be described using a Gaussian function.38 However, deviations from the simple Gaussian dependence were also observed.38,39 This inconsistency in “intensity versus time” dependences has considerably limited the application of the dipolar dephasing experiments, and only a handful of reports are known that have employed this technique. Here we show that dipolar-dephasing behavior of protonated carbons must be described using a sum of Gaussian and Lorentzian functions, as any given carbon remotely interacts

INTRODUCTION While solution NMR measurements are used extensively in organic and biomolecular research, the scale of applications of solid-state NMR is relatively modest. On one hand, solid-state NMR is technically more challenging, as there are several anisotropic interactions that are not averaged to zero.1−4 On the other hand, the presence of these anisotropic interactions increases the information content of solid-state NMR considerably compared to its solution-state counterpart.5−9 One of the reasons for relatively modest applications of solidstate NMR is due to the fact that X-ray and neutron diffraction techniques are successfully applied for structural characterization of solid materials. Clearly, solid-state NMR cannot compete with diffraction techniques when it comes to the amount and the quality of detail available from these techniques. In the field of dynamics characterizations, however, the leading position of solid-state NMR is well established.10−13 The most explored nucleus in this regard is deuterium, and it is, in principle, feasible to extract the geometry of motion using the analysis of wide-line and high-resolution 2H NMR spectra.14−23 The down side of 2H NMR, however, is that selective or full deuteration is required, which is not always feasible, while the application of natural-abundance measurements is still rather restricted due to its low abundance and relatively low Larmor frequency.24−30 © 2013 American Chemical Society

Received: June 28, 2013 Revised: July 23, 2013 Published: July 23, 2013 7855

dx.doi.org/10.1021/jp4064005 | J. Phys. Chem. A 2013, 117, 7855−7862

The Journal of Physical Chemistry A

Article

Figure 1. (a) Gaussian (eq 1) and (b) Gaussian+Lorentzian fittings (eq 2) of the methylene 13C intensities of glycine hydrochloride as a function of dipolar-dephasing period t at 20 T and νR = 4.4 kHz.

with other 1H nuclei (either intramolecular or intermolecular 1 H−13C interactions) and weak 1H−13C dipole−dipole interactions are best described using a Lorentzian function.39 This dependence is first verified using high-quality data obtained for glycine hydrochloride at 20 T, and then further explored for distinguishing subtle differences in dynamics of cyclic amino acids, polymorphs, and other organic solids.

middle of the dipolar-dephasing period t. Using experiments with varying t, the 13C signal intensity changes were measured to derive Tdd values. At least 20 different values of the dipolardephasing delay (t) between 1 and 50 μs were used. In the case of highly mobile adamantane, it was necessary to vary the dipolar-dephasing delay between 1 μs and 23 ms in order to achieve the necessary level of the signal decay. The estimated uncertainties in Tdd measurements were typically less than 3% of the measured values. For some of the solids studied, the chemical shift anisotropies were also measured using slow MAS at 2.5 kHz (20 T) and 1 kHz (7.05 T). The spectral deconvolution (as implemented in Bruker TopSpin software, version 2) was employed to determine integral intensities of spinning sidebands. The analysis of the spinning sideband intensities were used to derive the principal components (δ11, δ22 and δ33) of the CSA.44,45 In the standard convention, the principal components of the CSA, δ11, δ22 and δ33, are labeled according to the IUPAC rules:46 (i) principal components δ11 ≥ δ22 ≥ δ33; (ii) isotropic chemical shift δiso = (δ11 + δ22 + δ33)/3; (iii) span Ω = δ11 − δ33 (Ω ≥ 0). Under the Haeberlen−Mehring convention used in this work, the asymmetry of CSA indicates by how much the line shape deviates from that of an axial symmetry. The following definitions are used under the Haeberlen−Mehring convention:47,48 (i) principal components |δzz − δiso| ≥ |δxx − δiso| ≥ |δyy − δiso|; (ii) isotropic chemical shift: δiso = (δxx + δyy + δzz)/3; (iii) anisotropy Δσ = δzz − (δxx + δyy)/2; asymmetry η = (δyy − δxx)/(δxx − δiso), with 0 ≤ η ≤ 1.

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EXPERIMENTAL SECTION Organic solids studied in this work were received from SigmaAldrich and were used without further purification. Solid-state NMR experiments were carried out on a Bruker MSL300 spectrometer (7.05 T) at University College London and a Bruker AVANCE III 850 spectrometer (20 T) at the UK 850 MHz solid-state NMR facility at the University of Warwick. At 7.05 T, high-resolution solid-state 13C spectra were recorded using a standard 7 mm magic angle spinning (MAS) probe (Bruker). At 20 T, high-resolution solid-state 13C spectra were recorded using a standard 4 mm MAS probe (Bruker). In order to exclude the MAS dependence of dipolar-dephasing time constants, all measurements were carried out at the same MAS frequency. Thus, unless otherwise specified, the measurements were carried at the MAS frequency of 4.4 kHz with stability better than ±3 Hz. High-resolution solid-state 13C NMR spectra were recorded using cross-polarization (CP),41,42 MAS, and high-power 1H decoupling. Typical acquisition conditions for 13C CPMAS experiments at 7.05 T were 1H 90° pulse duration = 4 μs; contact time = 1.4 ms; recycle delay = 5 s; and continuous wave 1H decoupling. Typical acquisition conditions for 13C CPMAS experiments at 20 T were 1H 90° pulse duration = 3.5 μs; contact time = 1 ms; recycle delay = 5 s; and 1 H decoupling using the SPINAL-64 sequence.43 The recycle delays of 8−11 min were used in the case of cyclic amino acids L-proliene, DL-proline, and trans-4-hydroxy-L-proline with long 1 H spin−lattice relaxation times. The 1H and 13C chemical shifts are given relative to tetramethylsilane. The accuracy of the temperature controller used in this work was ±1 K and the long-term stability was better than ±0.5 K. The dipolar-dephasing measurements were carried out using MAS, CP and 1H decoupling. A modified pulse sequence by Alemany et al.38 was used in this work for measurements of dipolar-dephasing time constants (Tdd and TL, see Results and Discussion), which allows one to acquire less distorted dipolardephased spectra by introducing additional 180° pulses in the

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RESULTS AND DISCUSSION Dipolar-Dephasing in Rigid Solids. In order to investigate functional dependence of intensity (denoted as I) changes in 13C CP MAS spectra as a function dipolar-dephasing delay, we used signal intensity changes for the methylene carbons of glycine hydrochloride obtained at 20 T with a high signal-to-noise ratio (Figure 1). In Figure 1a, we employed a Gaussian function for fitting the experimental data: I = I0 exp( −t 2/Tdd 2) 7856

(1)



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where Tdd is the Gaussian dipolar-dephasing constant and t is the dephasing delay. In Figure 1b, we used a sum of Gaussian and Lorentzian functions: I = I0 exp( −t 2/Tdd 2) + IL exp(−t /TL)

(2)

where TL is the dipolar-dephasing constant in the Lorentzian term accounting for dephasing of remote 1H−13C dipolar interactions. The addition of the new term is justified by the fact that for any given 13C site there are remote intra- and intermolecular 1H−13C interactions present in organic solids, while the first Gaussian term accounts for strong C−H interactions of the 13C site with the directly bonded protons. The Lorentzian form of the function is selected for remote interactions, since it better fits dephasing of weak 1H−13C dipolar interactions.39 From comparison of two fittings, it is clear that eq 2 fits the experimentally measured dependence of intensities significantly better than eq 1. In particular, a nearly 4-fold improvement in the root-mean-square (rms) of fittings was found on changing from eq 1 to eq 2. The fitted values were Tdd = 36.8 ± 0.4 μs, I0 = 1.56 ± 0.02, TL = 53.6 ± 0.9 μs, and IL = −0.53 ± 0.05 (rms = 0.0103) on using eq 2 and Tdd = 33.1 ± 0.8 μs, I0 = 1.06 ± 0.01 (rms = 0.0372) on using eq 1. The negative sign of IL suggests that the effect of the Lorentzian term in eq 2 on the signal intensity may be opposite that of the Gaussian term. To summarize, the addition of the Lorentzian term accounts fully for the non-Gaussian deviation observed for the experimental data. Unlike the direct interactions, the remote 1H−13C interactions are expected to vary greatly for different C sites within a molecule or on comparing different solids. Besides, as the contribution to the overall intensity decay is relatively small for remote interactions, the accuracy of the TL determinations is expected to be poor, while their inclusion in eq 2 is expected to improve the accuracy and consistency of Tdd measurements. Therefore, in the following we mainly discuss the Tdd values derived for various solids using eq 2 and relate these to dynamics changes in solids. Polymorphs of Glycine. High-resolution solid-state 2H MAS NMR studies of the α and γ polymorphs of fully deuterated glycine (glycine-d5) were carried out previously.49,50 From the analysis of simulated 2H MAS NMR sideband patterns as a function of reorientational jump frequency (κ) for the −N+D3 group in glycine-d5, the experimentally observed differences in the 2H MAS NMR spectrum for the −N+D3 deutrons in the α and γ polymorphs was attributed to faster rate of reorientation of the −N+D3 group in the α polymorph compared to the γ polymorph.50 The Tdd values for the methylene carbons from the mixed Gaussian/Lorentzian fittings are 35.2 ± 0.4 and 37.1 ± 0.7 μs in the α and γ polymorphs, respectively, at 20 T. Despite the small difference observed, the higher value in the γ polymorph can be attributed to higher mobility of the methylene C−H bonds, i.e., the amplitude of small-angle librations about the C−Cα bond in the γ polymorph is likely to be slightly higher than that in the α polymorph. This result is in agreement with the known structures of glycine polymorphs (Figure 2), according to which the methylene hydrogen atom H4 (see the original notation51,52) in the α polymorph has two close oxygen atom neighbors (H···O, 2.39 Å, C−H···O, 137.4°; H···O, 2.45 Å, C− H···O, 140.0°),51 whereas in the γ polymorph there is only a single close H···O contact to one of the methylene protons (H5, H···O, 2.50 Å, C−H···O, 123.8°).52 Higher number of close contacts in the α polymorph compared to the γ polymorph is expected to lead to motionally more rigid C−H

Figure 2. Two 15-molecule clusters of glycine extracted from the crystal structures51,52 of (a) the α polymorph51 and (b) the γ polymorph.52 Intermolecular H···O close contacts for the central glycine molecule are highlighted.

bonds in the α polymorph, in agreement with the Tdd values measured. Previous studies have shown that small-angle librational motions can reduce the measured NMR parameters, such as 2H electric field gradient tensors, CSAs and dipolar couplings.10,53−55 Selective Dynamics Characterisations in Peptides. In Table 1 we compare the Tdd values for the methine carbons of the Ala residue in HO-Ala-Gly-H, HO-Gly-Ala-H, and HOAla1-Ala2-H derived from the mixed Gaussian/Lorentzian fittings. The minimum value of 53.6 μs at 20 T for the Cterminal Ala1 residue is one of the smallest values measured for a CH group and suggests that the corresponding Cα-H bond in Ala1 of HO-Ala1-Ala2-H is motionally static. The corresponding value for the N-terminal Ala2 residue is 58.0 μs, which is in favor of relatively high motional mobility of the Cα-H bond in Ala2 of HO-Ala1-Ala2-H. In terms of noncovalent interactions 7857



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Table 1. The Dipolar-Dephasing Constants Tdd (in μs) in Solid Dipeptides at 20 Ta 1

2

HO-Ala -Gly -H HO-Gly1-Ala2-H HO-Ala1-Ala2-H a

Cα(1)

Cα(2)

54.2 ± 1.1 (49.8) 34.5 ± 0.5 (39.6) 53.6 ± 0.7 (47.8)

34.1 ± 0.6 (45.1) 59.7 ± 0.9 (53.4) 58.0 ± 0.9 (50.1)

values of Tdd for corresponding carbons gradually decrease on going from L-proline to DL-proline and then to trans-4-hydroxyL-proline, we can conclude that the ring carbons are most rigid in trans-4-hydroxy-L-proline, while in L-proline their small-angle vibrational amplitudes near the equilibrium positions are the highest.58 There are differences in X-ray structures for zwitterionic forms of L-proline and DL-proline.59,60 Each of the carboxylic O atoms in L-proline is hydrogen-bonded to one of the N+H2 hydrogens with H···O distances of 2.69 and 2.71 Å.59 In DL-proline, however, one of the carboxylic O atoms is hydrogen-bonded to two N+H2 hydrogens with H···O distances of 2.71 and 2.84 Å.60 The C−H···O close contacts also show differences in L- and DL-proline. For example, in L-proline there is a 2.60 Å Cδ-Hδ3···O close contact,59 while in DL-proline the close contact is for the Cδ−Hδ2 hydrogen with the H···O distance of 2.69 Å.60 In both L- and DL-prolines there are also Cα-Hα···O close contacts (with H···O distances of 2.45 and 2.58 Å, respectively).59,60 Despite these differences, it is not possible to pinpoint the difference in the structure that leads to higher mobility of ring carbons in L-proline compared to DLproline. In trans-4-hydroxy-L-proline, however, there are four C−H···O close contacts for Cα−Hα, Cβ−Hβ2, Cδ−Hδ2, and Cδ−Hδ3 with relatively short H···O distances (2.43, 2.44, 2.22, and 2.54 Å, respectively),61 which explain the least vibrational mobility of the ring carbons in this amino acid compared to Land DL-proline. Adamantane and Hexamethylenetetramine. Adamantane has a very high symmetry (Td) and a cage-like globular skeleton. The adamantane molecules are randomly distributed among two distinguishable orientations related to each other by 90° rotation about the 4-fold axes of the crystal lattice.62 Adamantane is a typical example of rotator phase solid (also known as plastic crystalline phase), in which molecules reorient rapidly about their center of mass. Combined with the strong and sharp 13C NMR signals (with linewidths at half-height ∼3 Hz at 7.05 T), the high motional mobility makes adamantane a suitable solid for probing the dipolar-dephasing technique. Figure 3 shows the 13C signal intensities as a function of dephasing delay. Our fittings revealed that adamantane shows a Lorentzian decay:

The 13C chemical shifts are shown in brackets (in ppm).

present in the solid state, no significant differences were found for the Cα−H environments of Ala1 and Ala2;56 hydrogen bonds between COO− and N+H3 functionalities are present in the solid state, which are expected to equally restrict both the C- and N-terminal functionalities. However, there is an additional intermolecular hydrogen bond for the COO− group with the amide proton in the middle of the dipeptide (−CONH−).56 Furthermore, from the molecular structure of HO-Ala1-Ala2-H, it is apparent that librations of the C-terminal Ala1 residue is likely to involve restricted rotations about the Cα(Ala1)−N(Ala1) bond, whereas those of the N-terminal Ala2 residue is likely to involve restricted rotations about the Cα(Ala2)−C(Ala2) bond. As the Cα−C bond is longer than the Cα−N bond, the rotation about the Cα−C bond is expected to be less restricted than that about the Cα−N bond. Carbon Site Dynamics in L-Proline, DL-Proline, LHydroxyproline. At 20 T the Tdd value measured for the Cγ site (42.2 ± 0.8 μs) in L-proline is higher than that for the other two methylene sites Cβ (38.8 ± 0.9 μs) and Cδ (38.3 ± 0.6 μs). This suggests that the amplitude of small-angle vibrations about the equilibrium position is higher at the Cγ site compared to Cβ and Cδ sites. This result is also in agreement with the CSA measurements at 20 T using slow MAS at 2.5 kHz. The measured anisotropies (Δσ, ppm) and asymmetry parameters (η) were (Δσ/η): Cα −42.8 ± 0.4 ppm/0.81 ± 0.01, Cβ 34.7 ± 0.7 ppm/0 ± 0.01, Cγ 30.1 ± 0.6 ppm/0.55 ± 0.01 and Cδ 53.4 ± 0.5 ppm/0.66 ± 0.01, i.e., the reduced anisotropy for the Cγ site compared to the Cβ site is likely to be caused by higher motional amplitude for the Cγ site compared to the Cβ site. Similar results are also obtained at 7.05 T for L-proline (Table 2). In DL-proline, the Cγ site shows higher mobility

I = IL exp( −t /TL)

Table 2. The Dipolar-Dephasing Constants Tdd (in μs) of the Ring Carbons in the Solid State at 7.05 Ta L-proline DL-proline

trans-4-hydroxyL-proline a

Cα

Cβ

Cγ

Cδ

26.9 ± 0.8 (61.9) 26.3 ± 0.6 (59.9) 24.9 ± 0.4 (59.6)

21.5 ± 0.2 (32.8) 20.5 ± 0.3 (30.6) 20.8 ± 0.6 (39.4)

23.6 ± 0.2 (25.3) 21.2 ± 0.5 (25.9) 25.3 ± 0.2 (71.6)

21.5 ± 0.4 (46.3) 19.4 ± 0.4 (48.4) 19.3 ± 0.2 (56.6)

(3)

The rms of fitting is roughly 6 times better in the case of the Lorentzian fitting compared the Gaussian fitting. The use of mixed Gaussian/Lorentzian fitting did not show much improvement (∼12%) compared to a pure Lorentzian fit. Previously published data is also in favor of Lorentzian decay in the case of motionally mobile solids. According to Huang et al.,39 the decay rate of the 13C signal in dipolar-dephasing experiments depends on the strength of the dipole−dipole interactions between proton and carbon. As shown in this work, the slow decays characteristic for weak 1H−13C dipolar interactions in solids with high mobility of molecules can be fitted best by a first-order exponential decay (Lorentzian decay). We then studied hexamethylenetetramine (HMTA), which is similar to adamantane in terms of its molecular structure. The difference in the structures of these two molecules is that the CH groups of adamantane are replaced by nitrogen atoms in HMTA. Despite this similarity at a molecular level, HMTA does not show characteristic sharp lines in the 13C CPMAS NMR spectra. For example, the measured line width of 110 Hz at 7.05 T of the CH2 peak (at 73.8 ppm) is indicative of a

The 13C chemical shifts are shown in brackets (in ppm).

compared to the Cβ and Cδ sites. Torchia et al. have previously analyzed 2H wide-line line shapes of DL-[3,3,4,4,5,5-2H6]proline and have reported relatively high motional amplitudes of 22.1°, 29.0° and 10.8° for the respective β, γ, and δ positions of the proline ring.57 Although the actual values of motional amplitudes may show a model dependence, the 2H results nevertheless suggest higher mobility of the γ position compared to β and δ positions, in agreement with our results from dipolar-dephasing experiments. Here, we can also compare dynamics of various carbon sites in L-proline, DL-proline and trans-4-hydroxy-L-proline. As the 7858



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Figure 3. Lorentzian (left) and Gaussian (right) fittings of the experimentally measured 13C intensities (arbitrary units) of adamantane as a function of the dipolar-dephasing periods t (sec).

of Tdd in HMTA compared to adamantane confirms the relative immobility of HMTA molecules. The values of Tdd from either the Gaussian (18.8 ± 0.2 μs) or from the Gaussian+Lorentzian (18.2 ± 0.1 μs) fittings are slightly smaller than those measured for the α-polymorph of glycine at 7.05 T (19.4 ± 0.4 μs and 18.8 ± 0.3 μs, respectively). The latter suggests that the amplitudes of small angle vibrational motions are limited in HMTA compared to glycine. Although the choice of pure Gaussian function for the fitting is already giving a satisfactory result, we nevertheless emphasize that, unlike adamantane, a significantly better fit can be obtained using a mixed Gaussian/ Lorentzian function (Table 3 and Figure 5). As with glycine hydrochloride considered above, the use of the mixed function is physically meaningful in the case of motionally rigid HMTA, since there are both direct and remote 1H−13C dipolar interactions present in HMTA for any given carbon site. We have also studied the influence of MAS on Tdd and TL values using adamantane. As with the effect of molecular motions, the macroscopic spinning of the sample is expected to lead to averaging of 1H−13C dipole−dipole interactions. One would therefore expect the increase of Tdd and TL values on increasing the MAS frequency. The results of our measurements are given in Table 4 and support this expectation.

different molecular dynamics in HMTA compared to adamantane showing the line width of 3 Hz at 7.05 T of the CH2 peak (at 38.5 ppm). The examination of the crystal structure of HMTA63 reveal that there are 12 C−H···N hydrogen bonds in the crystal holding each molecule from reorientations about its center of mass (Figure 4). 2H NMR studies have been used in the past to study restricted dynamics of HMTA in the solid state.64 Here we show that dipolar-dephasing 1H−13C studies can be used for a straightforward characterization of the molecular dynamics without a need for isotope labeling. Regardless of the form of the dependence considered (Figure 5), the intensity decay constants Tdd or TL were less than 18.8 μs for CH2 carbons of HMTA at 7.05 T (Table 3). The significant decrease

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CONCLUDING REMARKS

We have shown that the introduction of a simple sum of Lorentzian and Gaussian functions shows greatly improved fittings of the “intensity versus time” data for protonated carbons in 1H−13C dipolar-dephasing experiments. The Lorentzian term accounts for remote intra- and intermolecular 1 H−13C dipole−dipole interactions, which vary from one molecule to another or for different carbons within the same molecule. Thus, by separating contributions from weak remote interactions more accurate Gaussian decay constants, Tdd, can be extracted for directly bonded 1H−13C dipole−dipole interactions. Reorientations of the 1H−13C bonds lead to the increase of Tdd values, and by measuring dipolar-dephasing constants, insight can be gained into relative dynamics of different carbon sites in a given solid. The main advantage of the dipolar-dephasing 1H−13C measurement is that it relies on

Figure 4. Arrangement of the HMTA molecules in the solid state. Three of the 12 C−H···N hydrogen bonds (with the H···N separation of 2.884 Å) holding each HMTA molecule are highlighted. 7859



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Figure 5. Gaussian (left) and mixed Gaussian/Lorentzian (right) fittings of the 13C signal intensity decay of the CH2 of HMTA as a function of the dipolar-dephasing periods t (sec).

Table 3. Dipolar-Dephasing Time Constants Tdd in Adamantane and Hexamethylenetetramine Measured at MAS Frequency of 4.4 kHz at Two Different Field Strengthsa solid

field, T

carbon

I0

Tdd, μs

IL

TL, μs

rms

adamantane

7.05

HMTA adamantane

7.05 20

CH2 CH CH2 CH2 CH CH2

0.10 ± 0.01 −0.14 ± 0.02 0.72 ± 0.01 0.20 ± 0.01 0.05 ± 0.01 1.38 ± 0.02

2983 ± 88 3187 ± 33 18.2 ± 0.1 3109 ± 0.60 6053 ± 175 33.8 ± 0.4

0.89 ± 0.01 0.81 ± 0.03 0.32 ± 0.02 0.81 ± 0.01 0.60 ± 0.01 −0.42 ± 0.06

4903 ± 20 4749 ± 86 16.0 ± 0.7 5565 ± 17 5558 ± 34 42.2 ± 0.9

0.0087 0.0076 0.0072 0.0061 0.0034 0.0184

HMTA a

20

The main component contributing to the signal decay is highlighted in bold letters.

of hexamethylenetetramine, for example, the presence of C− H···N interactions leads to nearly rigid molecules in the solid state. Overall, the method allows to gain insight into the role of noncovalent interactions in the solid state and their influence on the dynamics of molecules. The relative simplicity of the dipolar-dephasing experiment is expected to be particularly useful in detecting molecular motions in more complex systems such as proteins and intact bones.65 Preliminary measurements on collagen have shown that the influence of water on protein side chain and backbone can be monitored.66 As shown previously,40,66 the results of dipolar dephasing experiments could also be used to follow the changes in Tdd values as a function of temperature in order to gain a more detailed quantitative insight into the dynamic processes of interest. This technique is not restricted to 1H−13C pairs only and can be expanded to other pairs of nuclei, such as 1H−15N.

Table 4. The MAS Frequency Dependence of DipolarDephasing Time Constants TL and Tdd Measured for Adamantane at 7.05 T MAS frequency, kHz

TL, μs (CH)

Tdd, μs (CH)

TL, μs (CH2)

Tdd, μs (CH2)

4.4 2.2 0

4749 ± 86 2393 ± 31 412 ± 19

3187 ± 33 2864 ± 80 388 ± 31

4903 ± 20 2365 ± 62 630 ± 17

2983 ± 88 2717 ± 72 363 ± 12

a simple experimental setup with minimum hardware requirements. At the same time, this experiment is employed as a highresolution experiment (i.e., using MAS and proton decoupling), thus providing much needed sensitivity and selectivity for dynamics characterizations. The method provides particularly useful alternative to wide-line 2H NMR measurements, where selectivity of measurements is achieved using a laborious isotope labeling procedure. We have demonstrated the advantages provided by dipolardephasing measurements by comparative studies of the α and γ polymorphs of glycine, cyclic amino acids L-proline, DL-proline, and trans-4-hydroxy-L-proline, the Ala residue in different dipeptides, as well as differences in dynamics of structurally related cage molecules adamantane and hexamethylenetetramine. It was possible to distinguish subtle differences in dynamics of different carbon sites within a molecule in polymorphs and in L- and DL-forms. In addition, the presence of overall molecular motions can be detected, which leads to particularly large differences in Tdd values. In the majority of cases, the differences in dynamics in the solid state can be attributed to differences in noncovalent interactions. In the case

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank University College London (UCL) for the provision of access to NMR spectrometers and computational facilities. The UK 850 MHz solid-state NMR Facility used in this research was funded by EPSRC and BBSRC, as well as the University of Warwick, including partial funding through Birmingham Science City Advanced Materials Projects 1 and 7860



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2 supported by Advantage West Midlands (AWM) and the European Regional Development Fund (ERDF).

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