Giulia Mollica

Myriam Dekhil

Fabio Ziarelli

Pierre Thureau

Stéphane Viel

Quantitative Structural Constraints for Organic Powders at Natural Isotopic Abundance Using Dynamic Nuclear Polarization Solid-State NMR Spectroscopy

Keywords:

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Quantitative structural constraints for organic powders at natural abundance via dynamic nuclear polarization solid-state NMR** Giulia Mollica, Myriam Dekhil, Fabio Ziarelli, Pierre Thureau,* and Stéphane Viel* Abstract: A straightforward methodology is reported to quantitatively relate structural constraints based on 13 C- 13 C double-quantum buildup curves obtained by dynamic nuclear polarization (DNP) solidstate NMR to the crystal structure of organic powders at natural isotopic abundance. This methodology relies on the tremendous gain in NMR sensitivity provided by DNP (~50-fold here, which lowered the experimental time from a few years to a few days), and is sensitive to the molecular conformation and crystal packing of the studied powder sample (in this case theophylline). This allows crystal structures to be rapidly and effectively discriminated, and paves the way to three-dimensional structure elucidation of powders via the combination with powder X-ray diffraction, crystal prediction, and density functional theory computation of NMR chemical shifts.

Although single crystal X-ray diffraction (SCXRD) is currently unrivalled for the structural elucidation of organic compounds, it is typically inadequate when single crystals of sufficient size (or quality) are not available, and hence structure determination of microcrystalline powders remains highly challenging. In this context, NMR crystallography has emerged as a powerful technique by opening the way to ab initio structure determination of organic powders. [1] Precisely, powder X-ray diffraction (PXRD) and crystal structure prediction methods [2] can be combined to generate trial crystal structures that are refined using NMR experiments. One possible approach compares experimental chemical shifts with those computed by density functional theory (DFT) from a pool of trial crystal structures, the best match yielding the correct (or most likely) structure. However, because chemical shifts are not directly related to the crystal structure, their use as structural refinement constraints is not entirely satisfactory. In fact, 13 C chemical shifts were shown to be insufficiently sensitive for structure discrimination, whereas 1 H chemical shifts (which are sensitive to the crystal packing) showed limitations in case of reduced number of assigned resonances. [1a] Accessing alternative structural constraints is therefore desirable. Contrary to liquid-state NMR, however, where such constraints can be derived by nuclear Overhauser effect [START_REF] Neuhaus | The Nuclear Overhauser Effect in structural and conformational analysis[END_REF] or residual dipolar coupling [4] experiments, SSNMR still strives for similar experiments that could easily provide meaningful structural parameters. Studies on inorganic solids [5] indicate that dipolar couplings could be valuable candidates, but the high density of spins for abundant nuclei in organic compounds ( 1 H, or 13 C for uniformly enriched samples) drastically complicates the spin dynamics and prevents the measurement of long-range homonuclear spin couplings. [6] Analyzing rare spins such as 13 C or 15 N in natural abundance (NA) samples could alleviate this issue but the low NMR sensitivity precludes it. Recent work has shown, however, that SSNMR sensitivity of microcrystalline samples (with crystal widths ranging from 0.05 to 10 m) could be enhanced by highfield low-temperature magic-angle spinning (MAS) dynamic nuclear polarization (DNP). [7] DNP relies on the microwavedriven transfer of the electron spin polarization to nuclei, giving a maximum NMR signal enhancement equal to the ratio of the electron to nuclear magnetogyric ratios ( 660 for 1 H). As a result, sensitivity enhancements of 1 to 2 orders of magnitude can now be envisaged, [8] allowing two-dimensional (2D) dipolar and/or scalar correlation SSNMR experiments based on rare spins detection to be recorded on NA samples within reasonable times. [7,9] In particular, DNP-enhanced 2D double-quantum (DQ) dipolar correlation experiments have been recently used to probe qualitatively 1-bond or 2-bond 13 C- 13 C correlations in NA powders (via the comparison of cross-peak amplitudes obtained for specific mixing times), [7a,7b] and to estimate the distance between 29 Si-29 Si sites on the surface of silica nanoparticles (via numerical simulations). [9] Overall, 2D DQ 13 C- 13 C dipolar correlation experiments, while extremely challenging for NA samples due to the low 13 C natural abundance (1.1%), could provide significant constraints for structure determination of organic powders, but the required framework relating quantitatively 13 C-13 C cross-peak amplitudes to structural parameters has not been reported yet.

Here, we show how DNP-enhanced 2D 13 C-13 C DQ dipolar correlation experiments can be used to straightforwardly obtain quantitative data that are sensitive to the crystal structure of NA organic powders. We focused on theophylline (Figure 1a) available as a NA powder. Theophylline is a pharmaceutical compound representative of the current challenges found in structure determination: it has several polymorphic forms, [10] and, although it may form crystals suitable for SCXRD, its crystallization is far from straightforward. Moreover, the abovementioned ab initio NMR crystallography approach based on 1 H chemical shifts refinement failed to determine its correct crystal structure. [1a] Herein, the anhydrous polymorph of NA theophylline was incipiently wetted with a tetrabromoethane solution of the TEKPol biradical [11] (used as a source of electron spin polarization) and subsequently analyzed by DNP at 105 K. We obtained a DNP signal enhancement of 12 and an overall sensitivity enhancement of ~50 (see the Supporting information), [7a,7b,12] allowing DNP-enhanced 2D 13 C- 13 C DQ dipolar correlation spectra of NA theophylline to be recorded in Two such spectra with a short and a longer DQ excitation times ( DQ) are respectively shown in Figure 1a and 1b. The strongest correlations in Figure 1a arise mainly from 13 C- 13 C spin pairs separated by short distances (C1 C5, C3 C5), whereas weaker correlations due to 13 C- 13 C spin pairs separated by longer distances (C5 C6&C7, C5 C5) are observed in Figure 1b. More quantitatively, the amplitudes of each pair of 13 C- 13 C correlation peaks in a series of 2D DQ dipolar correlation spectra were measured and plotted as a function of DQ, yielding DQ build-up curves that were scaled to the 13 C CPMAS spectrum recorded under identical conditions (Figure 2). Due to the low 13 C natural abundance, the spin system only consists of isolated 13 C-13 C spin pairs. These data could thus be fitted with a straightforward analytical function based on the sum of the distinct 13 C- 13 C dipolar couplings that contribute to the correlation peak under study. This differs considerably from the complex many-body spin dynamics observed in spin networks ( 1 H, or 13 C for uniformly enriched samples). Figure 2 shows the analytical function plotted for the internuclear distances taken from the reference crystal structure of anhydrous theophylline previously determined by SCXRD and deposited in the Cambridge Structural Database (CSD entry code: BAPLOT06). [10a-c] This analytical function was also multiplied by a constant to scale the data and by an exponential decay to account for magnetic relaxation (see the Supporting Information). [13] The agreement between the experimental and the analytical 13 C-13 C DQ build-up curves in Figure 2 is excellent, showing trends that are clearly different depending on the observed 13 C-13 C DQ correlation peak. Importantly, these curves could only be perfectly reproduced by considering both the molecular conformation and the crystal packing of the theophylline crystal structure, which influenced the nature (intravs. intermolecular) of the involved dipolar couplings. This confirmed that 13 C-13 C DQ dipolar build-up curves obtained by DNP-enhanced SSNMR provided meaningful quantitative data that were sensitive to the crystal structure of the powder sample under study. In fact, attempts to reproduce these curves with alternative (but highly similar) theophylline crystal structures proved unsuccessful.

First, the sensitivity of our methodology to molecular conformation was studied by considering, in place of the reference structure (BAPLOT06), a virtual crystal structure that purposely differed from the reference only by an all-carbon atoms root-mean-square-deviation (rmsd) of 15 pm, while exhibiting otherwise identical space group and unit cell parameters. An rmsd of 15 pm is the precision that can be achieved with state-of-the-art NMR crystallography approaches based on chemical shift refinement. [1] Figure 3a compares the DQ build-up curve obtained experimentally for the C2-C5 correlation peak with those calculated from the virtual and reference crystal structures. This comparison could be more suitably evaluated using the goodness-of-fit coefficient of the involved C2 C5 spin pair ( 22-5), which was higher for the virtual (13.5) than for the reference (8.0) crystal structure. This confirmed that the DQ build-up curves, especially those involving medium-to-long range internuclear distances, could be used to detect small changes in molecular conformation (typical of conformational polymorphs). Second, the sensitivity to the crystal packing was studied by considering 3 different packing polymorphs of theophylline: the monoclinic, [10d] the monohydrate, [10b] and the high-temperature [10b] polymorphs (CDS entry codes: BAPLOT02, THEOPH02, and BAPLOT04, respectively). These polymorphs have almost identical molecular conformation but different unit-cell parameters. Moreover, BAPLOT02 and THEOPH02 have different space groups (P21/c and P21/n, respectively), whereas BAPLOT04 and BAPLOT06 have the same space group (Pna 21). For these polymorphs, deviations between calculated and experimental DQ build-up curves were observed for correlation peaks that primarily

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depend on intermolecular distances. This is shown in Figure 3b, where the analytical C6-C7 DQ build-up curves calculated for each theophylline polymorph are compared to the experimental data. The range of 2 6-7 values clearly shows that this correlation is sensitive to the crystal packing of the polymorphs. A similar trend was observed for C5-C5 (data not shown). Overall, a global 2 parameter including all 13 C-13 C spin pairs could be defined, which allowed these crystal structures to be sorted out and the reference crystal structure to be identified (Table 1).

In summary, we have shown that 13 C-13 C DQ dipolar build-up curves recorded by DNP-enhanced SSNMR on NA powders can be straightforwardly analyzed, providing quantitative data that are sensitive to the sample molecular conformation and crystal packing. This enables the rapid and effective discrimination of trial crystal structures of organic powders generated by NMR crystallography approaches, and will hence be highly valuable to existing PXRD, crystal prediction, and DFT-based chemical shift prediction methods for the tridimensional structure elucidation of organic powders at natural isotopic abundance. 63.0

Virtual structure ( 13 C RMSD=15 pm) [b] 84.0 BAPLOT02 [c] 98.0 BAPLOT04 [c] 94.0 THEOPH02 [c] 79.0 [a] Reference crystal structure determined by SCXRD. [b,c] Trial crystal structures selected to study the sensitivity of our methodology to molecular conformation [b] and crystal packing [c] .

Figure 3.

Sensitivity of the DQ build-up curves to the theophylline crystal structure. In a) and b), the solid line is the analytical DQ build-up curve calculated for the reference structure (BAPLOT06). The agreement between the calculated and experimental curves for a given i j spin pair is evaluated using the goodness-of-fit coefficient 2 i-j. In a), the experimental C2-C5 DQ build-up curve is shown together with that calculated for a virtual structure only differing from the reference structure by an all-carbon atoms rmsd of 15 pm (long-dashed curve). In b) the dot-dashed, dotted, and dashed curves are the analytical C6 C7 DQ build-up curves calculated for the monoclinic (BAPLOT02), monohydrate (THEOPH02), and high-temperature (BAPLOT04) packing theophylline polymorphs, respectively.

Figure 1 .

 1 Figure 1. DNP-enhanced 2D 13 C-3 C DQ dipolar correlation spectra of the anhydrous polymorph of NA theophylline impregnated with a TEKPol tetrabromoethane solution. Correlations between pairs of 13 C resonances appear in the DQ dimension at the sum of their chemical shifts. The DQ excitation time DQ is 0.5 and 2 ms in a) and b), respectively, leading to the observation of correlation peaks between 13 C spins separated by short and longer distances, respectively. The 13 C CPMAS spectrum is shown in the top projections and has been assigned according to the theophylline molecular structure shown in the left inset (* denotes spinning side bands).

Figure 2 .

 2 Figure 2. Double-quantum (DQ) build-up curves for selected pairs of 13 C dipolar correlation peaks shown by numbers on the top right of each graph (the bold number refers to the detected resonance). The experimental data points ( ) were obtained by integrating the correlation peaks obtained in a series of DNP-enhanced 2D 13 C-13 C DQ correlation spectra (see Figure 1) recorded for distinct DQ excitation time ( DQ) values. The solid lines represent an analytical function that considers the 13 C-13 C pairs involved in a specific correlation peak (see Supporting information for details and other curves).

Table 1 :

 1

	13 C-13 C DQ build-up curves goodness-of-fit coefficients	2 for different
	theophylline crystal structures (calculated using 8 distinct correlation peaks).
	Theophylline crystal structures	Goodness-of-fit coefficient	2
	BAPLOT06	[a]

Structure of organic powders:

A straightforward methodology is reported to quantitatively relate structural constraints based on 13


Pierre Thureau

Isaure Carvin

Fabio Ziarelli

Stéphane S Viel

Giulia Mollica

A Karplus Equation for the Conformational Analysis of Organic Molecular Crystals

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Accessing the atomic-level structure of functional materials is an essential prerequisite to understand the physical origin of their functionality. [1] Interestingly, functional materials composed of small organic molecules are very prone to polymorphism, i.e. they can assume different crystalline forms. [2] Because different polymorphs of the same chemical compound display distinct physicochemical properties, polymorphism might be an opportunity to tune the properties of a given functional material, with great value for industrial applications in pharmacy or energyrelated fields. [3] Recently, crystal structure prediction (CSP) has shown that polymorphism of organic molecular crystals is intimately linked with the conformational flexibility of the molecule. [4] The reverse is also true, i.e. the molecular conformation of flexible molecules in the solid state is strongly connected to the global crystal structure and cannot be simply inferred from the knowledge of the molecular geometry in the gas state or in solution. CSP methods have progressed in predicting molecular conformations for flexible molecules in the solid state. [5] However, because the dimensionality of the energy landscape increases with increasing the conformational degrees of freedom, obtaining good structural models from CSP to be used for solving the crystal structure of an unknown solid can be computationally very expensive for this kind of compounds. One approach to help structure determination of solids is to reduce the dimensionality of the landscape explored by CSP by providing constraints obtained experimentally. Solid-state nuclear magnetic resonance (SSNMR) is a very powerful approach to get atomic-level structural information on materials. Among the accessible NMR measurables, spin-spin J (or scalar) couplings are of exceptional value for conformational analysis. [6] In liquid-state NMR, the experimental dependence of three-bond J coupling constants ( 3 J) on torsional angles [7] through the well-known Karplus equations [8] has been extensively used for conformational analysis of small organic molecules, [9] peptides and proteins. [10] However, examples of the use of J couplings for structural analysis in the solid state are much more sparse in the literature, where they have mostly been reported for inorganic nuclei [11] and on disordered solids. [12] This difficulty is due to the fact that the scalar interaction between two spins can be several orders of magnitude smaller than the other active anisotropic spin interactions (e.g. quadrupolar, CSA, dipolar interactions), making it hardly detectable. This effect is exacerbated in the case of longrange scalar couplings, such as 3 J, which are characterized by correspondingly smaller coupling constants. Additionally, typical 3 J couplings in organic solids generate splitting patterns of a few Hz that are generally obscured in the SSNMR spectra by inhomogeneous line broadening, preventing the direct measurement of the corresponding coupling constant. Notwithstanding these experimental difficulties, several methodologies have been proposed to indirectly measure J couplings in solids, which are mostly based on the use of rotorsynchronized spin-echo experiments under magic-angle spinning (MAS) [13] on isotopically enriched samples. In several studies, Emsley, Brown and coworkers showed that spin echo experiments are very efficient to detect the presence of hydrogenbond mediated J couplings in organic solids ( 2h J). [14] For instance, JNN constants ranging between ca. 4 and 10 Hz could be measured in self-assembled guanosines, [15] showing very good agreement with the values computed by DFT on the corresponding periodic structures. [16] Recently, our group demonstrated that homonuclear 13 C-13 C 3 J couplings as small as 1 Hz can be measured in 13 C-enriched organic powders with the help of selective rotor-synchronized spin echo experiments. [17] Although these applications were useful to confirm or discover the presence of specific structural motifs, such as hydrogen bonds, no systematic attempt has ever been made, to the best of our knowledge, at obtaining quantitative structural information, such as torsional angles, from the value of J couplings in the solid state. With the support of first principles calculations, we show in this study that a simple Karplus relationship relates 13 C-13 C 3 J couplings -measured for a series of small 13 C-enriched organic solids only composed of C, N, O and H atoms -to the dihedral angle of the corresponding molecular fragment. Using the dihedral angles from the known crystal structures (see ESI), we parameterize a 13 C-13 C Karplus function for organic molecular crystals and we prove that it can successfully provide the dihedral angle in a polycrystalline solid compound of known structure, Lthreonine, with an accuracy of 10°. JCC values are plotted against the torsional angle of the molecular fragments in the corresponding crystal structure. The Karplus function reported by Berger for similar organic compounds in solution, [9] corresponding to Eq. 1, is shown as a dashed line. Labeling refers to Figure 1. Error bars for φ are approximately on the scale of the marker sizes. Color code is the same as Figure 1.

The existence of a Karplus dependence for three-bond carboncarbon J coupling constants ( 3 JCC) in the solid state was tested on a set of six organic molecules (of ca. 30 atoms). It is well known that, even in the liquid state, establishing dihedral angle dependence of 3 JCC can be complicated by substituent effects and through-space interactions. [7,18] Nonetheless, in this investigation, no particular restriction was applied to the choice of the compounds to be analyzed. On the contrary, the set of selected samples, although only composed of C, O, N and H atoms, was purposely chosen to include 3 JCC acting through various types of chemical bonds and heteroatoms in the solid state. Figure 1 shows the chemical structures of these compounds together with the molecular fragments corresponding to the 3 JCC taken into account in the analysis, indicated by dotted lines. The crystal structure of all these substances had been previously determined and deposited in the Cambridge Structural Database (CSD) with the entry references reported in Table 1. Table 1 also shows the dihedral angles (φ) for the CxyC molecular fragments (Figure 1) obtained after geometry-optimization of the corresponding CSD structures. The standard deviations associated with the values of dihedral angles were estimated from the CSD crystal structures before geometry optimization and are also reported in Table 1.

To assess the existence of a Karplus-like relationship between 3 JCC and the molecular conformation in the solid state, first principles calculations of JCC were performed using the optimized crystal structures of compounds A-F, as well as four additional crystal structures (namely anhydrous ampicillin, ibuprofen, flufenamic acid and cocaine), as inputs. A total of 22 computed which was obtained by Berger from multiple regression of 3 JCC measured on a set of 22 organic molecules in the liquid state. [9] We note that, because Karplus-like curves are symmetric with respect to φ=180°, we could have only shown the portion 0-180° of the curve (i.e. without specifying the sign of the torsional angle). However, the whole range 0-360° was shown here because the true angles were known from the crystal structures. Importantly, as explained in the ESI, the calculated value of 3 J47 for tyrosine (7.8 Hz), was halved to take into account the presence of two identical 3-bond coupling pathways. [7b, 19] In the absence of contributions from multiple coupling pathways, unexpectedly high values of 3 JCC (i.e. > 4 Hz), such as that observed for 3 J25 in glutamine, should be interpreted as an indication of the existence of planar fragments.

Table 1. Calculated and experimental 3 JCC corresponding to the CxyC three-bond molecular fragment for the investigated molecular crystals, together with their CSD entry reference. φ is the corresponding torsional angle in the geometry-optimized structure. Experimental standard deviations for dihedral angles are also

shown. The number of crystallographically distinct molecules composing the crystal asymmetric unit, Ζ', is also indicated. Figure 2 shows that Eq. 1 is in good agreement with the computed 3 JCC for the expected dihedral angles. As shown in Table S2 and Fig. S3 (ESI), these results are confirmed when analyzing all the 22 calculated couplings. Interestingly, for φ=180° (i.e. "E" fragments) 3 JCC span a large range, between 2.8 and 5.2 Hz. However, as explicitly mentioned by Krivdin, [7b] significant spread in 3 JCC in correspondence of the Karplus curve maxima (i.e. for φ=0° and φ=180°) was already observed by Marshall after analyzing a large number of saturated alicyclic alcohols, aldehydes and carboxylic acids in solution. [7b, 20] Moreover, this phenomenon was also observed in proteins [21] and carbohydrates. [22] Although a general explanation has not been reported, it has been observed that the presence of substituent groups with different electronegativity has a particularly strong impact on the J coupling values of planar fragments. [7b] We also note that, because the coefficient of the term in Cos(φ) is small in Eq. 1, this function defines a Karplus curve that is almost symmetric with respect to φ=90°, making it not very efficient to distinguish Z and E conformations. The results of this theoretical investigation on more than 20 computed 3 JCC strongly suggested that a Karplus-like behavior relates 3 JCC to dihedral angles in organic molecular crystals. We were interested to see whether these systems could be used to parameterize a Karplus function that could be subsequently used to extrapolate dihedral angles from the experimental measurement of 3 JCC. To this aim, 3 JCC were measured in the solid state with the help of selective spin-echo experiments for the same molecular fragments of the compounds A-F (see ESI). As described in Ref. [17] , these experiments allow 3 JCC as small as a few Hz to be measured accurately on 13 C-labeled samples. The measured 3 JCC are reported in Table 1.

As shown in Figure 3, the calculated and experimental 3 JCC show a very good agreement, the R 2 coefficient being 0.99. Interestingly, the 3 J47 and 3 J25 coupling constants measured for B and C, respectively, reflect well the large values previously computed on the full crystal lattices. Linear regression of these data using the function y=ax+b provides a=0.9 and b=-0.1, suggesting that, in the 1-8 Hz range, calculations tend to slightly underestimate the experimental coupling constants (or, viceversa, experiments to overestimate calculations). When the data are fitted by fixing a=1, the best fit is provided by y=x-0.5, indicating an average shift of -

Sample CSD entry Z' 3 JCC CxyC [a] φ [°] Calc [Hz] [b] Exp [Hz] [c] A HISTCM12 1

Hz between experimental and calculated values (see ESI).

We note that systematic deviations between computed and experimental J values have already been reported in the liquid state for small molecules and proteins. [9,21] Figure 4 shows the experimental 3 JCC values plotted versus the dihedral angles for the corresponding molecular fragments. As for the computed value, the experimentally measured value of 3 J47 for tyrosine (9.2 Hz), too, was halved to take into account the presence of two identical 3-bond coupling pathways (see discussion in the ESI). To obtain a Karplus function to be used for the conformational analysis of solid organic compounds, the 10 experimental [ 3 JCC, φ] pairs shown in Figure 4 were fitted to the generic Karplus function:

𝐽 ! "" (𝜑) = 𝐴 + 𝐵 𝐶𝑜𝑠(𝜑) + 𝐶 𝐶𝑜𝑠(2𝜑) (2)
providing the following parameterized Karplus equation:

𝐽 ! "" (𝜑) = 2.13 + 0.32 𝐶𝑜𝑠(𝜑) + 2.07 𝐶𝑜𝑠(2𝜑) (3)
We note that Eq. 3 was obtained using known torsional angles, which could hence be expressed in the range 0-360°, i.e. taking into account the sense of the torsion. However, because Karplus functions are symmetric with respect to φ=180°, Eq. 3 is not modified if all the torsional angles are defined between 0 and 180° (i.e. without taking into account the sign of the rotation). 3 JCC values are plotted against the torsional angle of the molecular fragments in the corresponding crystal structure. The Karplus function reported by Berger for similar organic compounds in solution, [9] corresponding to Eq. 1, is shown as a dashed line, while the Karplus-like function providing the best fit to the experimental values corresponds to Eq. 3. Labeling refers to Figure 1.

Error bars for φ are approximately on the scale of the marker sizes. Color code is the same as Figure 1.

It is interesting to note that the value of A in Eq. 3 is shifted by +0.46 Hz with respect to the same parameter for the Berger function, reflecting the previously discussed average shift of 0.5 Hz between the values of calculated and experimental 3 JCC. Moreover, we observe that the value of B is significantly larger in Eq. 3 than in Eq. 1, suggesting that Eq. 3 should be able to provide better discrimination between E and Z fragments.

The root mean square deviation (RMSD) between the experimental dihedral angles and the angles determined using Eq. 3 for the measured 3 JCC values was also estimated (see ESI). Bax and coworkers repeatedly used RMSD to evaluate the quality of parameterized Karplus functions for structural investigation of proteins in the liquid state. [21,23] Our data provided an RMSD of 6°.

Remarkably, this value is of the same order of magnitude as the accuracy obtained with 3 J, dipolar, or chemical shift-based methods for torsional angle determination in proteins or peptides (see for instance Refs. [24] ). As the sole example of Karplus-like function parameterized in the case of organic solids, Eq. 3 might hence be useful to estimate the dihedral angles in small organic solids from the simple measurement of the 3 JCC for the corresponding molecular fragment, without the need of first principle calculations. As discussed in the ESI, the uncertainty in torsional angle determination for the range of 3 JCC and σJ (i.e. the uncertainty associated with the experimental measurement of 3 JCC) shown in Table 1 (i.e. for 3 JCC >1 Hz and 0.2< σJ <0.4 Hz), can also be estimated from σJ to be less than 10°. This value is of the same order of magnitude of the RMSD calculated for Eq. 3.

The possibility of deducing φ from the measurement of 3 JCC using Eq. 3 was tested on the solid amino acid L-threonine. Figure S9 (ESI) shows that, for an experimentally measured 3 J13 value of 1.85 Hz, Eq. 3 predicts two possible dihedral angles for the 1-2-3-4 fragment of L-threonine in the range between 0° and 180° (i.e., only considering the absolute value of the torsional angle). Interestingly, one of these two torsional angles, indicated by a red arrow in Figure S9 and corresponding to 52°, differs by less than 10° from the true dihedral angle (61°, extracted from the CSD crystal structure of L-threonine after geometry optimization). This difference lies within the previously estimated uncertainty in angle determination, suggesting that Eq. 3 can be used to constrain the conformational search in organic molecular crystals in the solid state with the expected level of accuracy. Incidentally, we also note that the torsional angle of the 1-2-3-4 fragment of an isolated L-threonine molecule after geometry optimization in a vacuum supercell would be 71°. This observation confirms that crystal packing can induce substantial conformational rearrangement with respect to gas or liquid state and reinforces the importance of determining torsional angles in the solid state for reliable structural analysis.

In conclusion, we verified the opportunity of exploiting three-bond 13 C-13 C J couplings for the conformational analysis of solid organic compounds only composed of C, O, N and H atoms. With the support of DFT calculations on periodic structures, we observed that a Karplus-like function relates the values of the total calculated 3 JCC couplings to the dihedral angle φ of the corresponding molecular fragment. Surprisingly, calculations revealed that the predicted [ 3 JCC, φ] values display the same general Karplus behavior independently of the differences in substituent groups or supramolecular interactions present among the different molecular solids considered, the largest deviations being observed for planar fragments. Using 13 C-enriched powder samples, the 10 3 JCC of samples A-F were also measured experimentally with the help of rotor-synchronized spin echo experiments, confirming the type of relationship observed from calculations and showing that the calculated and experimental 3 JCC values are shifted by an average of 0.5 Hz. Best-fitting the experimental data with a Karplus-like function provided the first Karplus relationship ever reported for solid samples to the best of our knowledge. We demonstrated that this function allows the dihedral angle for the 1-2-3-4 molecular fragment of the solid amino acid L-threonine to be estimated within the expected angle accuracy of 10°. We expect that these findings will allow scalar couplings -today severely underexploited for the structural investigation of organic powders -to be included into current NMR crystallography approaches, providing structural information complementary to that obtained using other NMR measurables, such as chemical shifts and dipolar couplings [25] , and opening new avenues towards non-invasive structure determination of powders. Moreover, we anticipate that combining this information with crystal structure prediction will significantly improve crystal structure search, making structure solution for organic solids more rapid and reliable. Unlocking conformation of organic solids via solid-state NMR Three-bond J couplings accessed via solid-state NMR on organic solids are related to torsional angles via a simple Karplus relationship. This function constitutes a unique tool to probe the conformation of organic materials that is expected to significantly improve determination of crystal structures for powders.

Entry for the

  2h

Figure 1 .

 1 Figure 1. a) Chemical structures of the molecular crystals investigated: A, L-histidine HCl•H2O; B, L-tyrosine; C, L-glutamine; D, L-tryptophan; E, α-D-glucose; F, L-ascorbic acid. Red and blue numbers refer to 13 C-enriched and natural isotopic abundance carbon atoms, respectively, used for the experimental measurements of 3 J couplings. Dotted lines indicate the pathway of 3 J coupling through the three chemical bonds linking the two coupled carbon atoms, indicated with a plain circle. b) Torsional angle φ for the molecular fragment CxyC.

Figure 2 .

 2 Figure 2. Calculated 3 JCC for the set of organic molecular crystals investigated.

3

 3

3 JCC

 3 were analyzed (see ESI). For clarity, Figure2only shows the results of J calculations for molecules A-F, which are plotted as a function of the dihedral angle in the corresponding geometryoptimized crystal structure and compared to the following Karplus-like function: 𝐽 ! "" (𝜑) = 1.67 + 0.18 𝐶𝑜𝑠(𝜑) + 2.24 𝐶𝑜𝑠(2𝜑)

  [a] Numbering refers to carbon atoms, only, heteroatoms are indicated with their corresponding chemical symbol; [b] calculated 3 JCC values obtained after geometry optimizing the CSD structures with fixed unit-cell parameters; [c] experimental 3 JCC obtained as the average of the values measured observing each of the two carbon signals involved in the coupling; [d] 3 JCC receiving additive contributions from multiple three-bond paths: two equivalent pathways are available for the 3 J47 coupling in B, 4567 and 45'6'7 (see ESI); [e] for samples with Z'>1, only the 3 JCC for which the corresponding dihedral angle varies by less than 5° among the Z' non-equivalent molecules composing the asymmetric unit are retained for the analysis.

Figure 3 .

 3 Figure 3. Correlation between experimental and calculated 3 JCC for the molecular crystals investigated. R 2 coefficient is 0.99. The dashed line indicates linear regression of the data. Color code and labeling refer to Figure 1.

Figure 4 .

 4 Figure 4. Experimental 3 JCC for the set of organic molecular crystals investigated.3 JCC values are plotted against the torsional angle of the molecular fragments in the corresponding crystal structure. The Karplus function reported by Berger for similar organic compounds in solution,[9] corresponding to Eq. 1, is shown as a dashed line, while the Karplus-like function providing the best fit to the experimental values corresponds to Eq. 3. Labeling refers to Figure1. Error bars for φ are approximately on the scale of the marker sizes. Color code is the same as Figure1.

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Acknowledgements

The authors thank Prof. J. R. Yates for helpful discussions. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 758498). This work was granted access to the HPC resources of Aix-Marseille Université financed by the project Equip@Meso (ANR-10-EQPX-29-01) of the program "Investissements d'Avenir" supervised by the Agence Nationale de la Recherche. Keywords: crystal • dihedral angle • geometry • GIPAW • J coupling • NMR crystallography • NMR spectroscopy • scalar coupling • solid-state structures • vicinal coupling • polymorphism • powder • torsional angle.