Chia-Hsin Chen

Ieva Goldberga

Philippe Gaveau

Sébastien Mittelette

Jessica Špačková

Chuck Mullen

Ivan Petit

Thomas-Xavier Métro

Bruno Alonso

Christel Gervais

Danielle Laurencin
email: danielle.laurencin@umontpellier.fr

Looking into the dynamics of molecular crystals of ibuprofen and terephthalic acid using 17 O and 2 H NMR analyses

Oxygen-17 and deuterium are two quadrupolar nuclei that are of interest for studying the structure and dynamics of materials by solid state NMR. Here, 17 O and 2 H NMR analyses of crystalline ibuprofen and terephthalic acid are reported. First, improved 17 O-labelling protocols of these molecules are described using mechanochemistry. Then, dynamics occurring around the carboxylic groups of ibuprofen are studied considering variable-temperature 17 O and 2 H NMR data, as well as computational modelling (including molecular dynamics simulations). More specifically, motions related to the concerted double proton jump and the 180° flip of the H-bonded (-COOH)2 unit in the crystal structure were looked into, and it was found that the merging of the C=O and C-OH 17 O resonances at high temperatures cannot be explained by the sole presence of one of these motions. Lastly, preliminary experiments were performed with a 2 H-17 O diplexer connected to the probe. Such configurations can allow, among others, 2 H and 17 O NMR spectra to be recorded at different temperatures without needing to tune or to change probe configurations. Overall, this work offers a few leads which could be of use in future studies of other materials using 17 O and 2 H NMR.

Introduction

The potential of solid-state NMR techniques for helping study the structure and reactivity of complex (bio)molecular and materials systems has significantly increased in recent years, thanks to numerous developments made in terms of instrumentation (e.g., ultra-high magnetic fields, ultra-fast magic angle spinning -MASprobes), [START_REF] Gan | NMR spectroscopy up to 35.2T using a series-connected hybrid magnet[END_REF][START_REF] Ishii | Progress in proton-detected solid-state NMR (SSNMR): Super-fast 2D SSNMR collection for nano-mole-scale proteins[END_REF][START_REF] Penzel | Spinning faster: protein NMR at MAS frequencies up to 126 kHz[END_REF] pulse-sequence developments (e. g. [START_REF] Gan | NMR spectroscopy up to 35.2T using a series-connected hybrid magnet[END_REF] H-detected sequences, ultra-wide line and broadband acquisition methods), 2, 4-8 more efficient and/or selective isotopic enrichment approaches, [START_REF] Gupta | Segmental isotopic labeling of HIV-1 capsid protein assemblies for solid state NMR[END_REF][START_REF] Wong | Preparation of highly and generally enriched mammalian tissues for solid state NMR[END_REF][START_REF] Métro | Unleashing the Potential of 17 O NMR Spectroscopy Using Mechanochemistry[END_REF][START_REF] Hope | Revealing the Structure and Oxygen Transport at Interfaces in Complex Oxide Heterostructures via 17O NMR Spectroscopy[END_REF] as well as Dynamic Nuclear Polarization (DNP). [START_REF] Lilly Thankamony | Dynamic nuclear polarization for sensitivity enhancement in modern solid-state NMR[END_REF][START_REF] Hooper | Dynamic Nuclear Polarization (DNP) 101: A New Era for Materials[END_REF] Studies on challenging quadrupolar nuclei of low receptivity are increasingly being reported, including for some of the most « exotic » ones, [START_REF] Leroy | Recent advances in solid-state nuclear magnetic resonance spectroscopy of exotic nuclei[END_REF][START_REF] Bryce | New frontiers for solid-state NMR across the periodic table: a snapshot of modern techniques and instrumentation[END_REF] like [START_REF] Hafner | Ab-initio simulations of materials using VASP: Density-functional theory and beyond[END_REF] Ca, [START_REF] Śledź | New crystalline modification of terephthalic acid[END_REF] Ni, 87 Sr and 90 Zr, just to name a few. Moreover, investigations aiming at understanding the dynamics occurring at different timescales within (bio)molecular and materials systems are seen as highly important, not only because of the impact they can have on the NMR spectra and their acquisition conditions, but also and more importantly because of the insight they can provide on the properties of a given (bio)molecule or material. [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF][START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF][START_REF] Milić | Supramolecular Engineering for Formamidinium-Based Layered 2D Perovskite Solar Cells: Structural Complexity and Dynamics Revealed by Solid-State NMR Spectroscopy[END_REF][START_REF] Dunstan | Variable-Temperature Multinuclear Solid-State NMR Study of Oxide Ion Dynamics in Fluorite-Type Bismuth Vanadate and Phosphate Solid Electrolytes[END_REF][START_REF] Xiang | Toward understanding of ion dynamics in highly conductive lithium ion conductors: Some perspectives by solid state NMR techniques[END_REF] When it comes to studying dynamics in materials involving small organic molecules, [START_REF] Ishii | Progress in proton-detected solid-state NMR (SSNMR): Super-fast 2D SSNMR collection for nano-mole-scale proteins[END_REF] H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O are both attractive quadrupolar nuclei. [START_REF] Lu | Solid-State 17O NMR Reveals Hydrogen-Bonding Energetics: Not All Low-Barrier Hydrogen Bonds Are Strong[END_REF][START_REF] Wu | 17 O NMR studies of organic and biological molecules in aqueous solution and in the solid state[END_REF][START_REF] Wu | Solid-State 17 O NMR Study of Carboxylic Acid Dimers: Simultaneously Accessing Spectral Properties of Low-and High-Energy Tautomers[END_REF][START_REF] Catalano | Molecular dynamics of palmitic acid and lead palmitate in cross-linked linseed oil films: Implications from deuterium magnetic resonance for lead soap formation in traditional oil paintings[END_REF][START_REF] Kolokolov | Dynamics of Benzene Rings in MIL-53(Cr) and MIL-47(V) Frameworks Studied by 2H NMR Spectroscopy[END_REF][START_REF] Khudozhitkov | Characterization of Fast Restricted Librations of Terephthalate Linkers in MOF UiO-66(Zr) by 2H NMR Spin-Lattice Relaxation Analysis[END_REF][START_REF] Jiang | Thermally Activated Transient Dipoles and Rotational Dynamics of Hydrogen-Bonded and Charge-Transferred Diazabicyclo [2.2.2Octane Molecular Rotors[END_REF][START_REF] Dai | Solid-State 1H, 13C, and 17O NMR Characterization of the Two Uncommon Polymorphs of Curcumin[END_REF] This is notably true in crystals composed of molecules with carboxylic acid groups associated as dimers. Indeed, the dynamics of protons « hopping » between the H-bonded C=O and C-OH groups have been the object of much research, including using 2 H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O magnetic resonance techniques. [START_REF] Wu | Solid-State 17 O NMR Study of Carboxylic Acid Dimers: Simultaneously Accessing Spectral Properties of Low-and High-Energy Tautomers[END_REF][START_REF] Scheubel | High-resolution 1H, 2H, and 13C solid-state NMR of dimethylmalonic acid. Detection of a new mode of hydrogen motion[END_REF][START_REF] Kong | Solid-State 17 O NMR of Pharmaceutical Compounds: Salicylic Acid and Aspirin[END_REF][START_REF] Schmidt | Anomalous temperature dependence of nuclear quadrupole interactions in strongly hydrogen-bonded systems from first principles[END_REF] Among recent 2 H studies, Schmidt and Sebastiani's work showed by ab initio calculations that the 2 H quadrupolar parameters in strongly H-bonded systems could not be directly transposed into structural data such as bond lengths, due to the importance of non-linear effects and collective motions. [START_REF] Schmidt | Anomalous temperature dependence of nuclear quadrupole interactions in strongly hydrogen-bonded systems from first principles[END_REF] Regarding [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O, Wu and co-workers' investigations are worth highlighting: they demonstrated by using variable temperature [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR analyses that it is possible to study the concerted double-proton jumping, and estimate the energy asymmetry between the two Hbonded tautomers experimentally. [START_REF] Wu | Solid-State 17 O NMR Study of Carboxylic Acid Dimers: Simultaneously Accessing Spectral Properties of Low-and High-Energy Tautomers[END_REF] More generally speaking, when looking at the available literature, it appears that the information arising from 2 H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR analyses can potentially provide complementary information on the dynamic processes taking place within carboxylic acid dimers.

Considering the above context, the purpose of this article is to expand the possibilities for studying dynamics within molecular crystals by [START_REF] Ishii | Progress in proton-detected solid-state NMR (SSNMR): Super-fast 2D SSNMR collection for nano-mole-scale proteins[END_REF] H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR. Our studies were performed on two molecules: terephthalic acid and ibuprofen. Because of the very low natural abundance of both isotopes (Table 1), analyses were performed on enriched samples. First, improved [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-labelling protocols based on mechanochemistry are described for both molecules. [START_REF] Friscic | Mechanochemistry for Synthesis[END_REF] They were used to produce two doubly labelled compounds (enriched in [START_REF] Ishii | Progress in proton-detected solid-state NMR (SSNMR): Super-fast 2D SSNMR collection for nano-mole-scale proteins[END_REF] H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O), referred to as D-TA* and D-IBU*, which were isolated as molecular crystals (Scheme 1). Second, a variable temperature [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O MAS NMR study of D-IBU* is presented. The [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR spectra are discussed using complementary computational modelling studies, including molecular dynamics simulations and ab initio calculations of NMR parameters. Lastly, preliminary NMR investigations involving a 2 H- [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O diplexer connected to the NMR probe are presented.

This system was used in the case of D-TA*, enabling some of the 2 H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR experiments to be performed at different temperatures in a back-to-back fashion with no need to retune the probe. This configuration is not standard considering the very similar Larmor frequencies of both nuclei (Table 1).

Overall, the results presented in this manuscript will be of interest for future investigations of structure and dynamics using [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O and/or 2 H NMR. [START_REF] Pyykkö | Year-2017 nuclear quadrupole moments[END_REF] / 2.86 -25.58

Scheme 1. Structures of the doubly-labelled [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O and 2 H molecules: terephthalic acid (left) and ibuprofen (right). [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O labelling was achieved using mechanochemistry. [START_REF]The 17 O-labelling procedure leads to the predominant labelling of one oxygen per carboxylic group, but with both O atoms having the same probability to be enriched (which is why they are both highlighted in red[END_REF]

Experimental section

Isotopic labelling procedures for terephthalic acid and ibuprofen

The following reagents were used as received: ibuprofen (C13H18O2, Sigma Aldrich, ≥ 98% purity, racemic form, noted here IBU), terephthalic acid (C8H6O4, Janssen Chemicals, 98% purity, noted here TA), deuterated terephthalic acid (C8D4H2O4, with full deuteration on the aromatic cycle, 98% purity, Cambridge Isotope Laboratories, noted here D-TA) 1,1′-carbonyldiimidazole (C7H6N4O, TCI, >97% purity, noted here CDI). [START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF] O-labelled water was purchased from Eurisotop (isotopic composition indicated in the certificate of analysis: 97.1% D2O (> 99.96%, CAS 7789-20-0) was purchased from Sigma-Aldrich.

Reagent grade solvents were used in all purification protocols.

O-enrichment of terephthalic acid and deuterated terephthalic acid by mechanochemistry

The enrichment procedure was first optimised using [START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF] O-enriched water, due to its lower cost compared to [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-enriched water. Terephthalic acid (50 mg, 0.30 mmol, 1.0 eq) and CDI (107 mg, 0.66 mmol, 2.2 eq) were introduced in a stainless-steel grinding jar (10 mL inner volume) with two stainless steel balls (10 mm diameter). The jar was closed and subjected to grinding for 60 minutes in the MM400 mixer mill operating at 25 Hz. [START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF] O-labelled water (16 μL, 0.88 mmol, ~ 3 eq) was then introduced in the jar, and the mixture was subjected to further grinding for 60 minutes at 25 Hz. To help recover the product, non-labelled water (1 mL) was introduced in the jar, and the medium was subjected to grinding for 2 minutes at 25 Hz. Then, it was transferred to an Erlenmeyer flask (together with 2x1 mL of nonlabelled water, used here to rinse the grinding jar). The medium was acidified to pH ~ 1 by adding a few drops of concentrated HCl (6 mol.L -1 aqueous solution, ~ 15 drops). The white precipitate was immediately filtered on a glass frit, washed with 4x0.5 mL of a 1 mol.L -1 aqueous solution of HCl, and then with 0.5 mL of ultrapure water. The recovered solid was dried overnight under vacuum. Average yield (n = 3, n representing the number of independent labelling experiments performed): 43 mg, 86 %.

Average [START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF] O-enrichment level per oxygen, as determined by MS (n = 3) = 46 ± 1%.

For the preparation of the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] ).

O-enrichment of ibuprofen by mechanochemistry

The enrichment procedure was first optimised using [START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF] O-enriched water, due to its lower cost compared to [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-enriched water. Ibuprofen (120 mg, 0.58 mmol, 1.0 eq) and CDI (103 mg, 0.64 mmol, 1.1 eq) were introduced into a Retsch MM400 stainless steel grinding jar (10 mL inner volume) containing two stainless steel balls (10 mm diameter). The jar was closed and subjected to grinding for 30 minutes in the MM400 mixer mill operating at 25 Hz. [START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF] O-labelled water (99.3%, 16 µL, 0.87 mmol, 1.5 eq) was then added into the jar, and the mixture was subjected to further grinding for 30 minutes at 25 Hz. To help recover the product, non-labelled water (2 mL) was added into the jar, and the content was subjected to grinding for 2 minutes at 25 Hz. Then, the medium was transferred to a beaker (together with a sufficient amount of non-labelled water (8 mL) used here to rinse the jar). The medium was then acidified to pH ~ 1 with an aqueous solution of HCl (6 mol.L -1 , 18 drops). The white precipitate was filtered on a glass frit, and 2x5 mL of non-labelled water was used to help recover the rest of the product from the beaker. The product was washed with a 1 mol.L -1 aqueous solution of HCl and ultrapure water (3x1 mL of each), and then dried under vacuum. Average synthetic yield (n=3): 89 mg, 75%.

Average [START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF] O-enrichment level per oxygen, as determined by MS (n=3): 45 ± 2%.

For the preparation of the

General characterisation protocols of the enriched compounds

Infrared (IR) spectra were recorded on a Perkin Elmer Spectrum 2 FT-IR instrument. The attenuated total reflectance (ATR) measurement mode was used (diamond crystal), and measurements were performed in the 400-4000 cm -1 range.

Powder XRD analyses were carried out on an X'Pert MPD diffractometer using Cu Kα1 radiation (λ = 1.5406 Å) with the operation voltage and current maintained at 40 kV and 25 mA, respectively.

Diffractograms were recorded between 5° and 50° (or 60°) in 2θ, with a step size of 0.017°, and a time per step of 20 to 40 s.

Mass spectrometry (MS) analyses were performed on a Waters Synapt G2-S apparatus, using electrospray ionisation in negative mode in a range of 50-1500 Da. Capillary and cone voltages were set to 3000 V and 30 V, respectively. The source temperature was 100 °C and the desolvation temperature was set to 250 °C. Data were processed by MassLynxV4.1 software. For each product, a solution was prepared (in ethanol or DMSO, depending on the solubility), which were analysed fivetimes by ESI-MS.

1 H and [START_REF] Lilly Thankamony | Dynamic nuclear polarization for sensitivity enhancement in modern solid-state NMR[END_REF] C solution NMR spectra were recorded on an Avance III Bruker 600 MHz spectrometer equipped with a TCI Prodigy cryoprobe, using DMSO-d6 as a solvent. Chemical shifts were referenced to the residual solvent peaks at 2.50 ppm ( 1 H NMR spectra) and 39.52 ppm ( 13 C NMR spectra).

The melting points of ibuprofen (IBU) and its enriched counterparts (IBU* and D-IBU*) were measured on a Büchi B-540 Melting Point Apparatus. Samples were heated up to 70°C, and then with a ramp of 1 °C/min up to 80 °C. All measurements were done in triplicate (n = 3) and are reported in for D-IBU*. [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O MAS NMR chemical shifts were referenced to D2O at -2.7 ppm (which corresponds to tap-water at 0 ppm). The 17 O nutation experiment was also recorded using D2O at room temperature (with a natural abundance of 17 O).

The 2 H NMR experiments performed on the PhoenixNMR probe were carried out using a solid echo pulse sequence with a π/2 pulse length of 3.7 µs. [START_REF] Ishii | Progress in proton-detected solid-state NMR (SSNMR): Super-fast 2D SSNMR collection for nano-mole-scale proteins[END_REF] H MAS NMR experiments on D-TA* were performed with a MAS frequency of 5 kHz and rotor-synchronised echo delay of one rotor period (200 µs), and spectra were acquired using 14000 transients and recycle delay of 0.5 s. Static experiments were performed on D-IBU*, using an echo delay of 30 µs, and acquiring 122500 transients with a recycle delay of 0.5 s. [START_REF] Ishii | Progress in proton-detected solid-state NMR (SSNMR): Super-fast 2D SSNMR collection for nano-mole-scale proteins[END_REF] H chemical shifts were referenced to pure D2O at 4.6 ppm. The 2 H nutation experiment was also recorded using D2O at room temperature.

The 1 H nutation experiment was recorded using adamantane at room temperature with a MAS frequency of 10 kHz.

Variable-temperature studies were carried out under static or magic-angle spinning conditions (spinning at 5 or 18 kHz). In each situation, the temperature was calibrated using Pb(NO3)2. [START_REF] Bielecki | Temperature Dependence of207Pb MAS Spectra of Solid Lead Nitrate. An Accurate, Sensitive Thermometer for Variable-Temperature MAS[END_REF] When working under MAS conditions, careful attention was paid to the setting of the magic angle using KBr ( 79 Br resonance). The accuracy of the magic-angle at each temperature of analysis could be verified on D-TA*, by the absence of symmetric splitting of the 2 H resonance and sidebands under magic angle spinning (see supporting information, Figure S10). If judged necessary, the magic-angle was carefully reset at the temperature of interest using KBr.

Computational details

The NMR chemical shift calculations were performed within the DFT formalism using the QUANTUM-ESPRESSO (QE) [START_REF] Giannozzi | QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials[END_REF] software. The PBE generalised gradient approximation [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] was used and the valence electrons were described by norm-conserving pseudopotentials [START_REF] Troullier | Efficient pseudopotentials for plane-wave calculations[END_REF] in the Kleinman-Bylander form. [START_REF] Kleinman | Efficacious Form for Model Pseudopotentials[END_REF] The wave functions were expanded on a plane wave basis set with kinetic energy cut-off of 80

Ry. The shielding tensor was computed using the Gauge Including Projector Augmented Wave (GIPAW) [START_REF] Pickard | All-electron magnetic response with pseudopotentials: NMR chemical shifts[END_REF] approach, which permits the reproduction of the results of a fully converged all-electron calculation. Absolute shielding tensors are obtained. The isotropic chemical shift iso is defined as iso

= -[ - ref ],
where  is the isotropic shielding and  ref is the isotropic shielding of the same nucleus in a reference system as previously described. [START_REF] Métro | Unleashing the Potential of 17 O NMR Spectroscopy Using Mechanochemistry[END_REF] The principal components Vxx, Vyy, and Vzz of the electric field gradient (EFG) tensor are obtained by diagonalisation of the tensor. The quadrupolar interaction can then be characterised by the quadrupolar coupling constant CQ and the asymmetry parameter ηQ, which are defined as: CQ = eQVzz/h and ηQ = (Vyy -Vxx)/Vzz. The experimental values of the quadrupole moments of [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O (Q = -25.58 × 10 -30 m 2 ) and 2 H (Q = + 2.86 × 10 -30 m 2 ) [START_REF] Pyykkö | Year-2008 nuclear quadrupole moments[END_REF] were used to calculate CQ.

Two crystallographic structures of racemic ibuprofen (CCDC 1041383 and 128796) were tested as starting points. The geometry optimisation of all atomic positions (keeping cell parameters fixed to experimental values) was performed for both low-and high-energy tautomers using the VASP code [START_REF] Hafner | Ab-initio simulations of materials using VASP: Density-functional theory and beyond[END_REF] and a Monkhorst-Pack k-space grid size of 2 × 3 × 2. NMR parameters were then calculated keeping the relaxed atomic positions.

For the evaluation of the rotational barrier energy of the H-bonded (-COOH)2 dimeric unit in ibuprofen, the crystalline structure # CCDC 128796 was used as a starting point (because the ibuprofen dimer is at the centre of the unit cell, thereby facilitating the application of a geometrical torsion). The dihedral angle Car-C(H)-C-O was varied and constrained, while the geometry of the rest of the molecule was optimised, and the energy subsequently calculated.

AIMD (Ab-initio Molecular Dynamics) simulations were carried out with the CP2K code [START_REF] Vandevondele | Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach[END_REF] consisting in the Born-Oppenheimer MD (BOMD) with PBE electronic representation, including the Grimme (D3) correction for dispersion, [START_REF] Grimme | A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu[END_REF] GTH pseudopotentials, [START_REF] Goedecker | Separable dual-space Gaussian pseudopotentials[END_REF] combined plane-wave, and TZVP basis sets. [START_REF] Vandevondele | Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases[END_REF] The BOMD was performed using the NVT ensemble. The Nose-Hoover thermostat was used to control the average temperature at 300 K. Trajectories were accumulated over 20 ps with a time step of 0.5 fs. [START_REF] Ishii | Progress in proton-detected solid-state NMR (SSNMR): Super-fast 2D SSNMR collection for nano-mole-scale proteins[END_REF] H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR calculations were performed with QE every 400 steps, i.e., every 200 fs.

Results

Improved 17 O-enrichment protocols and preparation of doubly-labelled molecules

Due to the very low natural abundance of [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O and 2 H (Table 1), isotopic labelling is needed in order to be able to perform variable temperature solid-state NMR analyses in a reasonable time. While the deuteration of the carboxyl group can be easily achieved by exposure of the molecules to an excess of D2O, the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-labelling of the carboxylic oxygen atoms is not as straightforward, notably due to the high cost of [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-enriched water (1 mL of 90% [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-enriched water can cost up to ~ 2600 €). A previous study showed that terephthalic acid and ibuprofen could be enriched in [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O using mechanochemistry in a cost-efficient and user-friendly way. [START_REF] Métro | Unleashing the Potential of 17 O NMR Spectroscopy Using Mechanochemistry[END_REF] However, our enrichment levels only averaged to ~ 3-8 % per carboxylic oxygen for these molecules, which is ~ 2.5 to 7 times less than the maximum enrichment we could have expected based on the reactions and precursors involved. Hence, as part of this work, we first re-optimised the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-enrichment protocols for these two molecules.

The [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-labelling procedure we have developed involves two ball-milling steps, which are performed back-to-back and followed by IR spectroscopy: [START_REF] Métro | Unleashing the Potential of 17 O NMR Spectroscopy Using Mechanochemistry[END_REF][START_REF] Špačková | Unveiling the Structure and Reactivity of Fatty-Acid Based (Nano)materials Thanks to Efficient and Scalable 17O and 18O-Isotopic Labeling Schemes[END_REF] an activation of the carboxylic function using 1,1'-carbonyldiimidazole (CDI), followed by the hydrolysis of the acyl-imidazole intermediate using [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-enriched water. If either of these steps is incomplete, the final enrichment level decreases. We retested the reaction conditions for TA and IBU using [START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF] O-enriched water (due to its lower cost compared to [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-enriched water), and found that longer milling times (30-60 minutes, instead of 5-10 minutes)

were needed to ensure a better mixing of the reagents and full completion of activation and hydrolysis (see Figure S7 for illustrations in the case of IBU). We verified the reproducibility of the newly-optimised enrichment protocols and then used them for the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-labelling of terephthalic acid and ibuprofen. In the case of terephthalic acid, the optimised [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-enrichment protocol was applied to a deuterated form of the molecule (D-TA, fully deuterated on the aromatic cycle), while for ibuprofen, it was applied to the nonlabelled form of the molecule. The average [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-enrichment level per carboxylic oxygen achieved was ~ 20 % for D-TA* (when using ~ 40% [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-labelled water for the hydrolysis), and ~ 36% for IBU* (when using ~ 90% [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-labelled water for the hydrolysis). The mass spectra of the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-labelled molecules can be found in supporting information, together with other analyses that demonstrate the purity and crystallinity of the isolated molecules ( 1 H NMR, [START_REF] Lilly Thankamony | Dynamic nuclear polarization for sensitivity enhancement in modern solid-state NMR[END_REF] C NMR, and powder X-ray diffraction) (see Figures S1 to S6).

For ibuprofen, the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF]

Variable temperature 17 O MAS NMR of ibuprofen: experiments and computational modelling

The [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O MAS NMR spectra of D-IBU* were recorded at 14.1 T, while regulating the temperature between 0 and + 60°C (Figure 1). The [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O spectra show two second-order quadrupolar lineshapes at 0 °C, which correspond to the C=O and C-OH groups. These signals progressively merge as the temperature is increased, leading to a single resonance with a characteristic second-order quadrupolar lineshape at 60 °C. A similar observation had been made in our previous [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR study of nondeuterated ibuprofen. [START_REF] Métro | Unleashing the Potential of 17 O NMR Spectroscopy Using Mechanochemistry[END_REF] Fits of the spectra recorded at 0 °C and 60 °C can be found in supporting information (Figure S11). The fitted parameters at 0 °C (i.e. δiso = 308 ± 2 ppm and |CQ| = 7.9 ± 0.1 MHz for the C=O, and with δiso = 179 ± 2 ppm and |CQ| =7. Variable-temperature [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O MAS NMR spectra of D-IBU*. All [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR spectra shown here were recorded using the same acquisition conditions (including the same number of scans). The temperatures indicated correspond to the sample temperature inside the rotor at each spinning speed, as determined from calibrations using Pb(NO3)2. Tentative fits of the 0 °C and 60 °C spectra can be found in Supporting Information (Figure S11). « * » symbols correspond to spinning sidebands.

Although several polymorphs of racemic ibuprofen have been reported, [START_REF] Dudognon | Solid-Solid Transformation in Racemic Ibuprofen[END_REF] the most stable form was synthesized here, for which no polymorphic change is expected over the temperature range investigated by NMR. The changes in [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O solid-state NMR spectra around room temperature could, however, be due to (i) variations in the relative populations of the two tautomeric forms undergoing double proton jumps (Scheme 2a), [START_REF] Wu | Solid-State 17 O NMR Study of Carboxylic Acid Dimers: Simultaneously Accessing Spectral Properties of Low-and High-Energy Tautomers[END_REF] and/or (ii) 180° flips of the (-COOH)2 units (Scheme 2b), [START_REF] Filsinger | 17O NMR evidence for 180°-flips of (COOH)2 units in dimethylmalonic acid[END_REF] the latter motion having been suggested to exist for ibuprofen by Geppi and co-workers. [START_REF] Carignani | Detailed Characterization of the Dynamics of Ibuprofen in the Solid State by a Multi-Technique NMR Approach[END_REF] Both of these motions were further analysed, using additional computational simulations to help rationalise the observations made by [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR.

Scheme 2. Illustration of dynamics which can occur between H-bonded carboxylic acids, leading to interconversion between the two tautomeric forms: a/ concerted double proton jump and b/ concerted 180° flips of the H-bonded (-COOH)2 units.

First, the possible influence of concerted double proton jumps between the two tautomeric forms of ibuprofen on the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O MAS NMR data was looked into. Based on Wu and co-workers' recent work on a series of molecular crystals involving H-bonded carboxylic dimers, these motions can result in changes in [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR spectra with temperature, depending on the relative population of the tautomeric forms. [START_REF] Wu | Solid-State 17 O NMR Study of Carboxylic Acid Dimers: Simultaneously Accessing Spectral Properties of Low-and High-Energy Tautomers[END_REF] Such proton exchanges occur on the ps timescale and can participate in the averaging of [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR parameters between the two tautomeric forms. Here, a molecular dynamics simulation of racemic ibuprofen at 300 K was performed over a duration of 20 ps. This simulation brings evidence of the concerted double proton jumps, and shows the evolution of the calculated average [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR parameters of each oxygen (Figure 2), which appear to all progressively evolve towards averaged values.

R O O H R O O H H O O R H O O R R O O H R O O H H O O R H O O R a/ b/ Tautomer A Tautomer B
Nevertheless, a full averaging of the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR parameters could not be reached within the 20 ps timescale studied here.

Figure 2.

Molecular dynamics simulation of the structure of racemic ibuprofen, performed at 300 K, for a duration of 20 ps, with steps of 0.5 fs, with a focus on calculated [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR data. a/ Evolution of the H … O bond distances (in Å) in the dimer of the unit cell for which a concerted double 1 H jump was observed over the timescale of the calculation performed here (for the other dimer, no jump was observed); b/ Evolution of the DFT-calculated averaged [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR parameters for each oxygen site in this dimer (NMR parameters were calculated every 400 steps, i. e., every 200 fs; and for each new point calculated along the MD, the new value was averaged with the previous ones). For concerted double-proton jumps, the extent of averaging of the NMR parameters between both tautomers depends on the energy difference between the two forms and the analysis temperature. [START_REF] Wu | Solid-State 17 O NMR Study of Carboxylic Acid Dimers: Simultaneously Accessing Spectral Properties of Low-and High-Energy Tautomers[END_REF] In the case of racemic ibuprofen, Kolesov et al. reported an energy difference between both tautomers ~ 7.7 kJ/mol, based on Raman spectroscopy measurements. [START_REF] Demkin | Tautomeric Hydrogen Bond in Dimers of Ibuprofen[END_REF] In our case, starting from the crystalline structure of racemic ibuprofen, [START_REF] Ostrowska | High-Pressure Crystallization and Structural Transformations in Compressed R,S-Ibuprofen[END_REF] the energy difference between the tautomeric forms was calculated by DFT, yielding a value ~ 8.8 kJ/mol, 54 which is of the same order of magnitude as the experimental value of Kolesov. Using these energy differences and the DFT-calculated [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR parameters of each tautomer (Figure 3a), an approach similar to the one recently described by Wu and co-workers was then applied, [START_REF] Wu | Solid-State 17 O NMR Study of Carboxylic Acid Dimers: Simultaneously Accessing Spectral Properties of Low-and High-Energy Tautomers[END_REF] in order to see how the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR parameters may vary with temperature (Figure 3b). The most significant variations were observed for the isotropic chemical shifts. Yet, based on these calculations, a change of less than 10 ppm would have been expected for the « C=O » and « C-OH »-like resonances over the temperature range studied here (green-shaded region, Figure 2b), regardless of the energy difference chosen (8.8 or 7.7 kJ/mol). Similar conclusions would also have been expected for deuterated ibuprofen, for which an intermediate energy difference ~ 6.7 kJ/mol between the two tautomeric forms has been derived from Raman spectroscopy analyses. [START_REF] Demkin | Tautomeric Hydrogen Bond in Dimers of Ibuprofen[END_REF] Overall, this implies that no merging of the two [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O signals as observed in Figure 1 would have been expected to arise from concerted double 1 H-jumps only, on the basis of the calculated [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR parameters of the two tautomers and their energy difference. 8 kJ/mol (as calculated here by DFT for protonated ibuprofen) and of 7.7 and 6.7 kJ/mol (as determined experimentally by Raman for protonated and deuterated ibuprofen, respectively). [START_REF] Demkin | Tautomeric Hydrogen Bond in Dimers of Ibuprofen[END_REF] The region shaded in green corresponds to the temperature range studied here by [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR (i.e. between 0 and 60 °C). The equations used for the plot are recalled in the grey-shaded box [START_REF] Wu | Solid-State 17 O NMR Study of Carboxylic Acid Dimers: Simultaneously Accessing Spectral Properties of Low-and High-Energy Tautomers[END_REF] (in which the DFTcalculated values of δC=O and δC-OH of the two tautomeric forms given in Figure 3a were used).

The motion related to a concerted rotation of the (-COOH)2 group was then looked into. As mentioned above, the presence of this 180° -flip had already been proposed in racemic ibuprofen on the basis of comprehensive 1 H and 13 C NMR analyses. [START_REF] Carignani | Detailed Characterization of the Dynamics of Ibuprofen in the Solid State by a Multi-Technique NMR Approach[END_REF] Moreover, it is worth noting that the observations of the evolution of the variable-temperature [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O MAS NMR spectra of ibuprofen recall those reported by Wu and co-workers for nicotinic acid, in which the 180° rotation of an H-bonded -COOH unit was studied between ~ -20 and 100 °C (although in the latter case, it is a single -COOH moiety Hbonded to N which undergoes the 180° flip). Here, in contrast to the double proton jumps, the 180°-flip where H C motions in ibuprofen could not be made evident by molecular dynamics simulation due to the « short » timescale of our MD calculations. Nevertheless, the activation energy associated with this motion was evaluated by DFT, using an approach similar to the one proposed by Wu and co-workers for nicotinic acid. [START_REF] Lu | Solid-State 17O NMR Reveals Hydrogen-Bonding Energetics: Not All Low-Barrier Hydrogen Bonds Are Strong[END_REF] More specifically, starting from the published structure of racemic ibuprofen, the (-COOH)2 dimeric fragment was rotated (keeping all other atomic positions constant), and the energy difference for each torsion angle was then calculated after the relaxation of all atomic positions (except for those defining the dihedral angle). Some of the calculated geometries are shown in Figure 4. In doing so, it was found that the energy barrier is ~ 75-100 kJ/mol (the value depending on the direction chosen for the rotation of the (-COOH)2 unit). These values are very different from the one reported by Geppi on the basis of 1 H and [START_REF] Lilly Thankamony | Dynamic nuclear polarization for sensitivity enhancement in modern solid-state NMR[END_REF] C NMR analyses, which had estimated the barrier to ~ 13 kJ/mol. However, they are consistent with the energy barrier reported for (-COOH)2 180°-flips in other carboxylic dimers, for which values ranging from 50 to 85 kJ/mol have been reported. [START_REF] Scheubel | High-resolution 1H, 2H, and 13C solid-state NMR of dimethylmalonic acid. Detection of a new mode of hydrogen motion[END_REF][START_REF] Idziak | study of the molecular dynamics in crystalline trichloroacetic acid[END_REF] Part of the difference the value reported by Geppi may come from the fact that computationally, we are probing the rotation of the carboxylic group by « freezing » the rest of the structure, while in the experimental study, other motions are occurring within the crystal structure, [START_REF] Carignani | Detailed Characterization of the Dynamics of Ibuprofen in the Solid State by a Multi-Technique NMR Approach[END_REF][START_REF] Carignani | 13C Chemical Shielding Tensors: A Combined Solid-State NMR and DFT Study of the Role of Small-Amplitude Motions[END_REF][START_REF] Geppi | Molecular Properties of Ibuprofen and Its Solid Dispersions with Eudragit RL100 Studied by Solid-State Nuclear Magnetic Resonance[END_REF] which may indirectly facilitate the rotation of the carboxylic dimer. Overall, although the experimental and computational data shown here does not yet achieve a complete picture of the (-COOH)2 180° flip and double proton exchange processes occurring in racemic ibuprofen, it nevertheless demonstrates the added value of performing high-resolution [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR analyses and computational simulations to try to help understand these movements.

Figure 4.

DFT-evaluation of the activation energy for the rotation of the (-COOH)2 dimeric unit in crystalline racemic ibuprofen (using the CCDC crystal structure # 128796). Illustrations of some of the torsion angles are shown on the right (with C, O, and H in grey, red and white, respectively; not all atoms in the unit cell are displayed here for clarity).

Variable temperature analyses using a 1 H-2 H-17 O tuning configuration

To complement the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O MAS NMR study of the H-bonded carboxylic groups dynamics in D-IBU*, [START_REF] Ishii | Progress in proton-detected solid-state NMR (SSNMR): Super-fast 2D SSNMR collection for nano-mole-scale proteins[END_REF] H NMR experiments were carried out. Here, the possibility of performing 2 H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR analyses in a back-to-back fashion was investigated, using a diplexer connected to the probe for 1 H-2 H- [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] the NMR probe configuration can be attractive, especially to avoid hysteresis effects that can occur upon heating or cooling some crystalline phases.

A schematic illustration of the mode of connection of the diplexer to the NMR probe is shown in Figure 5a, with further details being provided experimental section. The nutations obtained upon calibration of RF pulses using D2O for 2 H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O, and adamantane for 1 H, are shown in Figure 5b. The loss in sensitivity of this triple resonance mode compared to the double resonance configuration was found to be reasonable (see supporting information, Figure S12). This probe configuration was first tested on the doubly-labelled D-TA* phase due to its higher weight percentage in both [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O and 2 H. The 2 H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O MAS NMR spectra were recorded between -30 and +60 °C (Figure 6). No significant changes were observed in the 2 H NMR. Although 2 H relaxation measurements may have led to observable differences, these were not performed at this stage. In the case of [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR, only subtle variations with temperature were observed. A tentative deconvolution of the spectra is shown in Figure S13 (supporting information), considering the presence of 2 resonances corresponding to « C=O » and « C-OH » like environments, in agreement with the previous [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR work reported for non-deuterated terephthalic acid. [START_REF] Métro | Unleashing the Potential of 17 O NMR Spectroscopy Using Mechanochemistry[END_REF] Due to the overlap of both resonances, MQMAS experiments at each temperature of analysis (or variable-temperature analyses at a second magnetic field) would have been needed to confirm the fitted parameters. Nevertheless, the small variations observed for D-TA* over this temperature range may reflect effects of H-bonding tautomerism and/or polymorphic changes of terephthalic acid. [START_REF] Kolesov | Proton delocalization and tunneling in terephthalic acid: Raman spectroscopic study[END_REF][START_REF] Goossens | Synchrotron X-ray diffuse scattering from a stable polymorphic material: terephthalic acid, C8H6O4[END_REF][START_REF] Beckham | Surface-Mediated Nucleation in the Solid-State Polymorph Transformation of Terephthalic Acid[END_REF][START_REF] Śledź | New crystalline modification of terephthalic acid[END_REF][START_REF] Davey | Morphology and polymorphism in molecular crystals: terephthalic acid[END_REF][START_REF] Meier | Structure and dynamics of terephthalic acid from 2 to 300 K: II. The temperature dependence of the disorder: A solid-state NMR study[END_REF][START_REF] Bailey | The crystal structure of terephthalic acid[END_REF] Indeed, on the one hand, previous studies in the literature have shown that the H-bonded carboxylic protons of terephthalic acid are dynamically disordered at room temperature, undergoing concerted double-proton jumps (Scheme 2a). [START_REF] Kolesov | Proton delocalization and tunneling in terephthalic acid: Raman spectroscopic study[END_REF][START_REF] Meier | Structure and dynamics of terephthalic acid from 2 to 300 K: II. The temperature dependence of the disorder: A solid-state NMR study[END_REF][START_REF] Pritchina | Raman spectra of terephthalic acid crystals in the temperature range 5K-300K. Spectroc[END_REF] The fact that the free enthalpy difference between both tautomeric forms has been estimated experimentally to only ~ 2 kJ/mol [START_REF] Meier | Structure and dynamics of terephthalic acid from 2 to 300 K: II. The temperature dependence of the disorder: A solid-state NMR study[END_REF] for terephthalic acid implies that small changes should be observable over the temperature range studied here (because this value is of the same order of magnitude as those reported for cinnamic acid and aspirin). [START_REF] Wu | Solid-State 17 O NMR Study of Carboxylic Acid Dimers: Simultaneously Accessing Spectral Properties of Low-and High-Energy Tautomers[END_REF] On the other hand, the variations in the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O MAS NMR spectra may also reflect the existence of several polymorphic forms of terephthalic acid. Out of the three polymorphs reported to date for this molecule, triclinic forms (I) and (II) have been the object of much attention. 59-62, 64, 66 Both consist of chains of terephthalic acid molecules, in which each molecule is hydrogen-bonded to 2 others through carboxylic acid dimer motifs. These chains are further assembled into 2D layers, which pack differently from one polymorph to the other. Moreover, when looking at the terephthalic acid motif itself, slightly different dihedral angles are found between the carboxylic function and the aromatic cycle when both polymorphs are compared. [START_REF] Bailey | The crystal structure of terephthalic acid[END_REF] Although both forms can be observed under ambient temperature and pressure, form (I) appears to be the least stable. Its transformation into form (II) has been studied both experimentally and computationally. [START_REF] Goossens | Synchrotron X-ray diffuse scattering from a stable polymorphic material: terephthalic acid, C8H6O4[END_REF][START_REF] Beckham | Surface-Mediated Nucleation in the Solid-State Polymorph Transformation of Terephthalic Acid[END_REF][START_REF] Davey | Morphology and polymorphism in molecular crystals: terephthalic acid[END_REF] More specifically, this transformation was found to occur above 70 °C, to be sensitive to pressure, and to be caused by a « surface-mediated nucleation » type of process, triggered by the movement of the supramolecular chains of terephthalic acid at the surface of the crystallites. [START_REF] Beckham | Surface-Mediated Nucleation in the Solid-State Polymorph Transformation of Terephthalic Acid[END_REF][START_REF] Davey | Morphology and polymorphism in molecular crystals: terephthalic acid[END_REF] In our case, given that D-TA* was obtained here as polymorph (I) (see Figure S1, supporting information), it is possible that the subtle modifications in the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR spectra upon heating are indicative of the onset of transformation into form (II), caused by the increase in temperature and possibly also pressure (due to the spinning). More specifically, [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR may indicate that changes in the local environment of the carboxylic functions precede more significant movements of the supramolecular chains. Although the observations made in [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR for D-TA* were not further investigated at this stage, they point to the interest of analysing molecular crystals by this technique, notably to help understand polymorphic transformations.

Using this 2 H- [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O probe configuration, preliminary 2 H NMR studies were also performed in the case of D-IBU*. The static 2 H NMR spectra revealed the presence of two main resonances (Figure 7a): one broad signal with a characteristic deuterium quadrupolar lineshape and a much sharper signal at the centre of the spectrum, the relative intensity of which was found to increase with temperature, under the measurement conditions used here (Figure S14, supporting information). The fitting of the broad 2 H NMR signal at each temperature was performed, yielding similar quadrupolar parameters between 0 and 60 °C, with |CQ| ~ 170 kHz and ηQ ~ 0.1 (Figure S14). These values are similar to those reported previously for supercooled and glassy states of deuterated ibuprofen, [START_REF] Bauer | Molecular Motions in Supercooled and Glassy Ibuprofen: Deuteron Magnetic Resonance and High-Resolution Rheology Study[END_REF] as well as for other crystal structures of organic molecules involving H-bonded carboxylic dimers. [START_REF] Poplett | 17O and 2H quadrupole double resonance in some carboxylic acid dimers[END_REF] Hence, this 2 H resonance is characteristic of (-COOD)2 dimeric structures in crystalline D-IBU*, with the 2 H NMR parameters being averaged between the two interconverting tautomeric forms of ibuprofen. The MD simulations and DFT calculations of 2 H NMR parameters associated with these double proton jumps are provided in Figures 7b and7c. In agreement with previous observations made by Sebastiani et al. [START_REF] Schmidt | Anomalous temperature dependence of nuclear quadrupole interactions in strongly hydrogen-bonded systems from first principles[END_REF] for H-bonded carboxylic acids, these calculations show that the « instantaneous » CQ values tend to follow the evolution of the longer O…H distance (Figure 7b, dashed vertical lines). [START_REF] Ishii | Progress in proton-detected solid-state NMR (SSNMR): Super-fast 2D SSNMR collection for nano-mole-scale proteins[END_REF] H NMR studies on supercooled and glassy ibuprofen, [START_REF] Bauer | Molecular Motions in Supercooled and Glassy Ibuprofen: Deuteron Magnetic Resonance and High-Resolution Rheology Study[END_REF] the fully motionally-narrowed 2 H NMR signal is observed here at a higher temperature (80 °C in Figure S9, vs 36 °C in ref. [START_REF] Bauer | Molecular Motions in Supercooled and Glassy Ibuprofen: Deuteron Magnetic Resonance and High-Resolution Rheology Study[END_REF] ). Overall, it is clear that 2 H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR spectra provide complementary information regarding the dynamics occurring around the carboxylic groups in racemic ibuprofen. It can be hypothesized that the progressive increase in mobility within ibuprofen crystals with temperature (especially around the carboxylic function) allows some molecules to behave as in a melt-like state, which may favour dynamics like the 180° (-COOH)2 flip to occur with energy barriers lower than the ones calculated by DFT, thereby explaining the observations made by [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR. However, more extensive investigations would be needed to confirm this.

Conclusion

In this article, three different aspects related to the structural analysis of molecular crystals containing carboxylic functions have been looked into. First, improved [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O labelling protocols based on mechanochemistry have been developed. This has allowed average enrichment levels exceeding 20% in [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O per carboxylic oxygen to be reached for two key molecules: (i) ibuprofen, a non-steoridal antiinflammatory drug which is seen as a « golden standard » for numerous investigations in pharmaceutical sciences aiming at improving drug formulations, and (ii) terephthalic acid, which is one of the most commonly-used ligands for the design of metal-organic frameworks (MOFs). In the latter case, the [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O labelling was performed here on a deuterated version of the terephthalic acid precursor (with deuteration on the aromatic ring), thereby leading to the formation of a doubly-labelled molecule, which would be of key interest for studying the structure and reactivity or a variety of MOFs, including the most complex ones. Such ligands should enable studying both the dynamics related to the 180°-flips of the aromatic ring (using 2 H NMR) and the binding properties to metal cations in a given system (using [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR).

Second, the experimental and computational study of [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O and 2 H enriched ibuprofen has shed light on the interest in looking at both of these nuclei when studying the dynamics occurring around the carboxylic groups. Although further investigations would be needed to fully understand the experimental observations, this work nevertheless complements previous studies on racemic ibuprofen crystals involving 1 H and [START_REF] Lilly Thankamony | Dynamic nuclear polarization for sensitivity enhancement in modern solid-state NMR[END_REF] C NMR, by underscoring the complexity of the molecular motions which take place around the carboxylic groups. More generally, this study shows how the NMR study of quadrupolar nuclei like [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O and 2 H may provide new opportunities for investigating polymorphic transitions of ibuprofen, [START_REF] Dudognon | Evidence for a New Crystalline Phase of Racemic Ibuprofen[END_REF] as well as its confined or « supercooled » states. [START_REF] Bauer | Molecular Motions in Supercooled and Glassy Ibuprofen: Deuteron Magnetic Resonance and High-Resolution Rheology Study[END_REF][START_REF] Adrjanowicz | Communication: Synperiplanar to antiperiplanar conformation changes as underlying the mechanism of Debye process in supercooled ibuprofen[END_REF][START_REF] Tielens | Molecular Picture of the Adsorption of Ibuprofen and Benzoic Acid on Hydrated Amorphous Silica through DFT-D Calculations Combined with Solid-State NMR Experiments[END_REF] Indeed, the polarity and H-bonding capability of carboxylic function implies that it is often key to interactions between molecules and with materials surfaces, meaning that direct insight into the local environment of the carboxylic atoms (among which oxygen) is important for detailed structure characterization purposes.

Lastly, we have presented some of the possibilities provided by combining 2 H- [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O diplexers to NMR probes for studying by NMR the 2 H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O nuclei at any given temperature, without having to change probe configurations. The RF-performance of the probe used along with the diplexer was shown to be suitable for such applications, as illustrated for both terephthalic acid and ibuprofen. While the experiments shown here were mainly performed in a back-to-back fashion, we will look into recording them using « double receiver » set-ups in future studies. Moreover, beyond these possibilities, the next step will consist of using such hardware configurations to perform multi-channel 2 H and [START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O correlation experiments. This pair of nuclear spins has not yet been studied due to the very similar Larmor frequencies of the two isotopes, but could offer new opportunities for helping understand further the structure of a variety of molecular and materials systems, considering that H and O are two atoms which are very often present. This is a point we will be looking into in the near future. Such instrumental developments will add to the ongoing effort to broaden the scope of heteronuclear correlations accessible to NMR spectroscopists with spin pairs of similar Larmor frequencies (e.g., [START_REF] Lilly Thankamony | Dynamic nuclear polarization for sensitivity enhancement in modern solid-state NMR[END_REF] C- [START_REF] Khudozhitkov | Characterization of Fast Restricted Librations of Terephthalate Linkers in MOF UiO-66(Zr) by 2H NMR Spin-Lattice Relaxation Analysis[END_REF] Al, 72-73 13 C- [START_REF] Grimme | A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu[END_REF] Sc, 73 13 C-81 Br… [START_REF] Makrinich | Distance measurements between carbon and bromine using a split-pulse PM-RESPDOR solid-state NMR experiment[END_REF] ).

  O-and 2 H-enriched phase (noted D-TA*), D4-terephthalic acid was used as a precursor, and the 17 O-labelling step was performed following the optimised[START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF] O-enrichment protocol described above using ~ 40%[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-labelled water for the hydrolysis step instead (yield: 42 mg; average[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O-enrichment level per oxygen, as determined by MS = 20 ± 1%). The 1 H and[START_REF] Lilly Thankamony | Dynamic nuclear polarization for sensitivity enhancement in modern solid-state NMR[END_REF] C solution NMR spectra, ESI-MS spectrum and XRD powder pattern of D-TA* are shown in supporting information (Figures S1 to S3

17 O

 17 NMR experiments were recorded using DFS (double frequency sweep) pulse sequence with a rotor-synchronised echo of one rotor period. The parameters were as follows: DFS pulse of 500 s (νRF( 17 O) ~ 7.4 kHz), with a sweep between 70 and 200 kHz, followed by a 17 O excitation pulse of 2 µs, echo delay of 55.55 µs, and a π-pulse of 4 µs. All experiments were performed with a MAS frequency of 18 kHz, recycle delay of 0.5 s, and the number of transients acquired was 2400 for D-TA* and 4000

  O-enriched compound was then re-suspended in the presence of an excess of D2O in order to exchange the carboxylic O-H group by O-D and form the doubly-labelled compound D-IBU*. This reaction was followed by IR spectroscopy by looking at the O-H vibration modes' replacement by O-D ones (see FigureS8). It is worth noting that after completion of the reaction, the NMR rotor was immediately packed and stored under vacuum in the freezer to avoid any back-exchange of the carboxylic deuterium with atmospheric humidity.

  3 ± 0.1 MHz for the C-OH) were in line with those reported previously for non-deuterated ibuprofen, and with results from GIPAW-DFT calculations on the crystal structure. 11 A tentative fit of the data recorded at 60 °C was also performed, resulting in intermediate δiso and |CQ| values (δiso = 244 ± 2 ppm and |CQ| =7.6 ± 0.1 MHz).

Figure 1 .

 1 Figure 1.Variable-temperature[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O MAS NMR spectra of D-IBU*. All[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR spectra shown here were recorded using the same acquisition conditions (including the same number of scans). The temperatures indicated correspond to the sample temperature inside the rotor at each spinning speed, as determined from calibrations using Pb(NO3)2. Tentative fits of the 0 °C and 60 °C spectra can be found in Supporting Information (FigureS11). « * » symbols correspond to spinning sidebands.

Figure 3 .

 3 Figure 3. a/ Representation of the 2 tautomeric forms of ibuprofen and their DFT-calculated 17 O NMR parameters (for the (-COOH)2 dimer) (not all atoms in the unit cell are shown here for clarity); b/ Temperature dependency of the[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O isotropic chemical shifts of the two tautomeric forms, for ΔE values of 8.8 kJ/mol (as calculated here by DFT for protonated ibuprofen) and of 7.7 and 6.7 kJ/mol (as determined experimentally by Raman for protonated and deuterated ibuprofen, respectively).[START_REF] Demkin | Tautomeric Hydrogen Bond in Dimers of Ibuprofen[END_REF] The region shaded in green corresponds to the temperature range studied here by[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR (i.e. between 0 and 60 °C). The equations used for the plot are recalled in the grey-shaded box[START_REF] Wu | Solid-State 17 O NMR Study of Carboxylic Acid Dimers: Simultaneously Accessing Spectral Properties of Low-and High-Energy Tautomers[END_REF] (in which the DFTcalculated values of δC=O and δC-OH of the two tautomeric forms given in Figure3awere used).

Figure 5 .

 5 Figure5. a/ Schematic representation of the connection mode of the diplexer to the NMR probe, and b/ nutations achieved on the 1 H, 2 H and[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O channels in triple resonance mode. The 810°/90° intensity ratio determined here for 2 H is 0.51.

17

 17

Figure 6 .

 6 Figure 6. Variable temperature[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O and 2 H NMR spectra of D-TA*, recorded under magic angle spinning conditions. The temperatures indicated correspond to the sample temperature inside the rotor, as determined from calibrations at different MAS speeds using Pb(NO3)2.

Figure 7 .

 7 Figure7. a/ Fit of the experimental static 2 H NMR spectrum of D-IBU* at 30°C, after symmetrisation of the 2 H lineshape (experimental spectrum in black, and its fit in red, considering two contributions, with in blue the H-bonded -(COOD)2 dimeric unit of D-IBU*, and in green the sharp mobile species. b/ Molecular dynamics simulation of the structure of racemic ibuprofen, performed at 300 K, with steps of 0.5 fs (shown here over a duration of ~ 15 ps), with a focus on calculated 2 H NMR data. Evolution of the H…O bond distances (in Å) in the dimer of the unit cell for which concerted double proton jump was observed over the timescale of the calculation, and evolution of the « instantaneous » DFTcalculated 2 H quadrupolar coupling constant CQ for this dimer (NMR parameters calculations were performed as a first approximation from the MD structures of protonated ibuprofen, every 200 steps, up to step # 14000, and then every 400 steps). c/ Evolution of the average calculated |CQ| values along with the MD timescale, showing that the 2 H |CQ| converges towards an average value.

Table 1 .

 1 Nuclear spin properties of 1 H, 2 H and 17 O

	1 H	2 H	17 O

(x10 -30 m 2 )

  [START_REF] Mandala | Structure and Dynamics of Membrane Proteins from Solid-State NMR[END_REF]

Table S1 (

 S1 supporting information). The 2 H and[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O NMR spectra of melted D-IBU* are shown in FigureS9.

	Solid-state NMR experiments

Solid-state NMR experiments were performed on a Varian VNMRS 600 MHz (14.1 T) spectrometer, using, in the vast majority of cases, a PhoenixNMR HXY probe equipped with a 3.2 mm probe head. The PhoenixNMR probe was tuned to 1 H (599.82 MHz), 2 H (92.07 MHz) and 17 O (81.33 MHz), using a 2 H-

[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF]

O diplexer. Conversion from multiple to single port tuning required a "special" tuning plug-in and diplexer built specifically for 2 H and 17 O. RF for 2 H and

[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF]

O from the NMR console goes through a PhoenixNMR diplexer that provides >100dBc isolation, and then into the probe on a single channel. The PhoenixNMR probe is adapted to provide an over-coupled double resonant structure for the 2 H and

[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF]

O frequencies, which in conjunction with the diplexer can allow the observation of one channel while irradiating on the other. Spectra were recorded under static or MAS conditions, with spinning speeds ranging from 5 to 18 kHz, depending on the sample. In the case of the 2 H-enriched ibuprofen (not labelled in 17 O), complementary 2 H MAS NMR experiments were performed on a Varian T3 HX probe, tuned to 2 H and 1 H, and spinning at 5 kHz.

  O tuning.Indeed, being able to analyse 2 H and[START_REF] Matlahov | Hidden motions and motion-induced invisibility: Dynamicsbased spectral editing in solid-state NMR[END_REF] O local environments at any given temperature without changing

			3.9°2
		c
		a
	Torsion angle	Relative energy
	(°)	(kJ/mol)
	3.9	0.0
	26.4	13.6	5.6°
	52.2	57.3
	57.3	63.3
	75.1	93.2
	95.6	83.5
	107.4	81.3
	125.3	62.2
	174.4	7.3	74.4°9
	272.6	100.1
	304.1	45.7
	328.2	11.2
			72.6°1

H MAS NMR a/ 17 O MAS NMR

	350	300	250	200	150	100	50	60 10 -30	°C °C °C	2000	b/ 2 -2000 -1000 0 1000
				δ( 17 O)/ ppm						δ( 2 H)/ ppm

  H NMR spectrum of D-IBU* at 30°C, after symmetrisation of the 2 H lineshape (experimental spectrum in black, and its fit in red, considering two contributions, with in blue the H-bonded -(COOD)2 dimeric unit of D-IBU*, and in green the sharp mobile species. b/ Molecular dynamics simulation of the structure of racemic ibuprofen, performed at 300 K, with steps of 0.5 fs (shown here over a duration of ~ 15 ps), with a focus on calculated 2 H NMR data. Evolution of the H…O bond distances (in Å) in the dimer of the unit cell for which concerted double proton jump was observed over the timescale of the calculation, and evolution of the « instantaneous » DFTcalculated 2 H quadrupolar coupling constant CQ for this dimer (NMR parameters calculations were performed as a first approximation from the MD structures of protonated ibuprofen, every 200 steps, up to step # 14000, and then every 400 steps). c/ Evolution of the average calculated |CQ| values along with the MD timescale, showing that the 2 H |CQ| converges towards an average value.The sharp central 2 H NMR resonance, on the other hand, is very weak at 0 °C, where it is centered at 5.2 ppm. At 60 °C, it becomes increasingly sharp and intense, and shifts to 9.4 ppm. Based on the observed chemical shifts and the 2 H NMR measurements also performed on melted D-IBU* (see Figures S9), this resonance appears to arise from different species: it is consistent with a small amount of residual liquid (mobile) water at 0 °C, and to the predominant presence of highly mobile ibuprofen at 60 °C (in a melt-like state, the melting temperature of ibuprofen being ~ 75 °C). It is worth noting that in comparison to previous variable-temperature

Acknowledgements

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No 772204; 2017 ERC-COG, MISOTOP project). NMR spectroscopic calculations were performed using HPC resources from GENCI-IDRIS (Grant 097535). Powder X-ray diffraction, mass spectrometry and solution NMR characterizations were performed with the support of the local Balard Plateforme d'Analyses et de Caractérisation (PAC Balard).