Measuring multiple 17 O– 13 C J -couplings in naphthalaldehydic acid: a combined solid state NMR and density functional theory approach †‡

A combined multinuclear solid state NMR and gauge included projected augmented wave, density functional theory (GIPAW DFT) computational approach is evaluated to determine the four heteronuclear 1 J ( 13 C, 17 O) couplings in solid 17 O enriched naphthalaldehydic acid. Direct multi-field 17 O magic angle spinning (MAS), triple quantum MAS (3QMAS) and double rotation (DOR) experiments are initially utilised to evaluate the accuracy of the DFT approximations used in the calculation of the isotropic chemical shifts ( d iso ), quadrupole coupling constants ( C Q ) and asymmetry ( Z Q ) parameters. These combined approaches give d iso values of 313, 200 and 66 ppm for the carbonyl (C Q O), ether (–O–) and hydroxyl (–OH) environments, respectively, with the corresponding measured quadrupole products ( P Q ) being 8.2, 9.0 and 10.6 MHz. The geometry optimised DFT structure derived using the CASTEP code gives firm agreement with the shifts observed for the ether ( d iso = 223, P Q = 9.4 MHz) and hydroxyl ( d iso = 62, P Q = 10.5 MHz) environments but the unoptimised experimental XRD structure has better agreement for the carbonyl group ( d iso = 320, P Q = 8.3 MHz). The determined d iso and Z Q values are shown to be consistent with bond lengths closer to 1.222 Å (experimental length) rather than the geometry optimised length of 1.238 Å. The geometry optimised DFT 1 J ( 13 C, 17 O) coupling to the hydroxyl is calculated as 20 Hz and the couplings to the ether were calculated to be 37 (O–C Q O) and 32 (O–C–OH) Hz. The scalar coupling parameters for the unoptimised experimental carbonyl group predict a 1 J ( 13 C, 17 O) value of 28 Hz, whilst optimisation gives a value of 27 Hz. These calculated 1 J ( 13 C, 17 O) couplings, together with estimations of the probability of each O environment being isotopically labelled (determined by electrospray ionisation mass spectrometry) and the measured refocussable transverse dephasing ( T 2 0 ) behaviour, are combined to simulate the experimental decay behaviour. Good agreement between the measured and calculated decay behaviour is observed.


Introduction
In comparison to other prominent organic functionalities, the inception and formation of the C-O bond is a relatively poorly understood process despite its fundamental prominence in many branches of organic, organometallic and industrial chemistry, and chemical engineering. 1 The production of ethers, acetals and ketals, and the initiation of hydrolysis reactions rely intrinsically on the relative strength of the C-O bond in its particular environment. 2 Some well-established industrial processes are underpinned by the formation of C-O bonds to yield industrial scale commercial products. The Paternò-Büchi reaction is a photochemical process that forms C-O bonds in natural products syntheses, and the Williamson ether synthesis is a widely used industrial process for ether formation. 3,4 Furthermore, hydrogen bonding to the oxygen atom in C-O bonds, (e.g. in esters) can affect their strengths, and may play a role in enzymatic processes pertaining to numerous biological and biomedical applications. 5 More recently, initiatives on biomass utilization have employed homogeneous catalysis for the activation and functionalization of ether C-O sigma (s) bonds for F capture and remediation. 6 The high chemical specificity and ability to probe short range interactions enables solid state NMR to investigate the relationship between a negative O-centred nucleophile and a sp 2 hybridized electrophilic C centre. In this study solid naphthalaldehydic acid (1) and its 2 H-naphthalaldehydic acid (2) counterpart, depicted in Fig. 1(a) and (b), respectively, will be examined using this technique to characterise C-O bonding arrangements with varying strength. This molecule represents a unique structural motif which possesses three O-based functionalities which are in close proximity within the six-membered lactone crown of the naphthalaldehydic structure, thus introducing numerous C-O bonding scenarios. A recent report describes a series of salts in which the lactone ring has opened to produce isolated aldehyde and carboxylate groups, and the n-p* CÁ Á ÁO interactions and H-bonding scenarios between them. 7 Some prominent examples of this overall phenomenon included the efficacy and structure-function properties of aspirin, 8 and the stabilisation of chirality in protein and polymer structures. [9][10][11][12][13] The measurement of scalar (or J-) couplings between directly bonded or closely proximate NMR active nuclei are routinely exploited to aid molecular structure determination. 14 Scalar coupling values are quantifiable entities emanating from the hyperfine interactions between neighbouring nuclei and is transmitted through the bonding electrons, providing information about connectivity and dynamics between atomic positions. 15 In typical solution state NMR experiments on organic and inorganic compounds, the determination of such couplings can be attained from basic 1D experiments; this is due to fast Brownian motion (on the timescale of the NMR experiment) removing the anisotropic components of all interactions present, thus resulting in high resolution isotropic data. However, it should be emphasised that J-couplings in solution involving the 17 O nucleus (particularly 1 J( 13 C, 17 O) couplings) are typically elusive due to the fast quadrupole relaxation of the 17 O nucleus. 16 In contrast, the residual inhomogeneous broadenings commonly experienced in solids usually preclude J couplings between common nuclei ( 1 H, 13 C, 15 N, 31 P, 29 Si, 17 O, etc.) from being measurable in direct observation experiments. Solid state NMR experiments rarely succeed in the achieving the spectral resolution attainable in the solution state because of the existence of higher order cross terms which cannot be completely averaged by MAS, residual dipolar interactions and distributions of isotropic chemical shifts due to structural disorder. 17 However, developments in high speed magic angle spinning (MAS), 18 effective heteronuclear decoupling and pulse sequence development, 19 higher magnetic field strengths, and the GIPAW DFT computation of NMR parameters [20][21][22][23] have all contributed to improved resolution and introduced new rationales for interpreting solid state NMR data. These advances have stimulated a renewed interest in undertaking J-coupling measurements in the solid state.
The aim of this study is to establish a combined methodology which uses first principles density functional theory (DFT) J-coupling calculations using the CASTEP code and heteronuclear ( 13 C-17 O) spin echo-based experiments to determine the 1 J( 13 C, 17 O) couplings within the various C-O moieties of naphthalaldehydic acid which is a complex lactone arrangement with three O-containing functionalities in close proximity. This approach provides a natural complement to single crystal X-ray structure determinations and charge density studies that can collectively interrogate the relative strength of C-O bonds and could be extended to CÁ Á ÁO interactions and bond formation scenarios. Solid state NMR J-coupling measurements are typically achieved using J-resolved or INADEQUATE experiments, or specific variants of these sequences. [24][25][26][27][28][29] A key feature of these spin echo-based experiments is that they refocus the evolution of all terms that appear as offsets, including those that are directly induced by chemical shift distributions. 30 This has critical implications for solid state NMR experimentation as the utilisation of these methods allows the indirect detection of J-couplings, even when inhomogeneous broadenings impede its direct observation and measurement from the more routinely acquired 1D data. As the 17 O nucleus has an extremely low natural abundance (0.037%), there exists a dearth of measured 1 J( 13 C, 17 16 This work represents the first study to implement a combined computational and experimental approach to measure multiple 1 J( 13 C, 17 O) couplings in a more complex organic system to further investigate C-O bond characteristics.

Experimental section
Synthesis Maximum 17 O enrichment of naphthalaldehydic acid 1 with optimal homogeneity was achieved by dissolving the solid (200 mg, 1 mmol) in dioxane (4 ml) whilst stirring under nitrogen, Fig. 1 (a) The structures of the naphthalaldehydic acid variants with the hydroxyl group (1) and the deuterated hydroxyl group (2) as evaluated in this study. The numbering scheme and labels defining the carbonyl (CQO, C 11 ) and hydroxyl (C-OH, C 12 ) positions, and the colour scheme denoting the O environments is conserved throughout the manuscript. The experimental (orange) and CASTEP-DFT geometry optimized (purple) bond lengths are also illustrated and summarised in Table 3. (b) The crystal packing scheme of solid naphthalaldehydic acid showing the H-bonding between stacks of molecules related by a twofold screw axis.
with 90% 17 O labelled water (Cortecnet, 0.45 ml) being added. Phosphorus pentachloride (B2 mg) was added and the mixture warmed to 75 1C for 24 h. The reaction was cooled, the solvent evaporated in vacuo, and the residue left to dry at 45 1C for 1 h. Toluene (18 ml) was added and the mixture heated to reflux, filtered through a warm glass filter funnel, and the filtrate left to crystallise at room temperature to give white crystals (122 mg, 60%), m.p. 165-166 1C. To test the selectivity of the 17 O enrichment process, a less vigorous process was used where the initial reflux stage was conducted in THF (bp 66 1C) instead of dioxane (which was heated to 75 1C), using a reaction time of only 6 h and a lower 17 O concentration of 40% (Cortecnet, 0.45 ml).
The naphthalaldehydic acid (100 mg) was deuterated by dissolving the product in dichloromethane (20 ml), and the filtered solution shaken with D 2 O (99%, 2 Â 2 ml). The dichloromethane solution was dried with anhydrous sodium sulphate, filtered and evaporated to give the mono-deuterated material. 1

Solid state NMR
The solid state 1 H MAS NMR measurement was undertaken at 14.1 T using a Bruker Avance-II+ 600 spectrometer operating at a 1 H Larmor frequency of 599.4 MHz. The data was acquired using a Bruker 1.3 mm triple resonance probe spinning at 60.0 kHz. A single pulse experiment was implemented using a 1.25 ms pulse duration (flip angle of p/4) and a recycle delay of 180 s. This 1 H MAS NMR data was referenced to the primary standard of tetramethylsilane (TMS, d iso = 0 ppm). A corresponding 2 H MAS NMR measurement was undertaken at 11.7 T on a Bruker Avance-III 500 spectrometer operating at a 2 H Larmor frequency of 76.8 MHz. This data was acquired using a 4 mm Bruker MAS double resonance probe operating at a 5 kHz spinning frequency. A single pulse experiment was implemented using a 1.75 ms pulse duration (flip angle of p/4) and a recycle delay of 3 s was determined. The 2 H MAS spectrum was referenced to d-chloroform (CDCl 3 , d iso = 7.26 ppm) which was compared to the primary reference of TMS-d 12 (d iso = 0 ppm). 32 The 13 C MAS NMR data was acquired at 11.7 T using a Bruker Avance-III 500 spectrometer operating at a 13 C Larmor frequency of 125.8 MHz. A 1 H-13 C cross-polarisation MAS (CPMAS) experiment was implemented using a Bruker 4 mm double resonance probe which enabled a rotation frequency of 10 kHz. A variable amplitude (70-100%) CPMAS experiment employed an initial 1 H p/2 pulse of 2.5 ms, a contact period of 5 ms, a recycle delay of 600 s and a 1 H decoupling field of B100 kHz during acquisition. The 13 C CPMAS NMR data was referenced to the primary standard of tetramethylsilane (TMS, d iso = 0 ppm) via a secondary solid alanine reference (d iso (CH 3 ) = 20.5 ppm, d iso (CH) = 50.5 ppm and d iso (COOH) = 177.8 ppm). The measurement of the 1 J( 13 C, 17 O) coupling constants were performed using a modified spin-echo experiment as previously described by Hung et al. 16 A 1 H-13 C CP preparation of magnetisation (see above) was followed by a refocussing p pulse (CP-t-p-t) on both the 13 C and 17 O channels thus forming an echo. The 13 C and 17 O p pulse duration on each channel was 6 ms. The t delays were incremented from 0 to 15 ms, with 100 kHz of 1 H decoupling applied throughout. The 2D 1 H-13 C Lee-Goldberg heteronuclear correlation experiment used the same cross polarisation preparation as described above and implemented homonuclear Lee-Goldberg 1 H- 1 34 simulation package to determine the experimental isotropic chemical shift (d iso ) and quadrupole (C Q , Z Q ) NMR parameters (see Table 1 and Fig. 3(a), (c) and (e), respectively). The CASTEP calculated NMR parameters for d iso , 1 J OC , C Q and Z Q (see Tables 2 and 3) were used as input into the SIMPSON 4.2.1 35 simulation package to generate a direct comparison between experimental and calculated data. The SIMPSON input files are given in Table S3 (ESI ‡).

First principle DFT geometry optimisation and magnetic resonance calculations
All density functional theory (DFT) calculations were performed using the CASTEP 16.1 21 code which employs Kohn-Sham DFT methodology using periodic plane-waves under the ultrasoft pseudopotential approximation. The generalized gradient approximation for the exchange correlation energy was employed using the Perdew-Burke-Ernzerhof solids functional (PBE-sol). Pseudopotentials were generated 'on-the-fly' using the standard Accelrys Software Materials Studio pseudo-atom definitions. Each calculation was converged with respect to basis-set size and Brillouin zone k point sampling to at least an accuracy of 0.4 mH (B0.000002% of total energy) per atom for each of the systems under investigation. To confirm this level of energy convergence was sufficient to produce accurate ionic forces, energy minimisation with respect to ionic positions was repeated with increasing plane wave cut off energy and density of k points within the Monkhorst-Pack Brillouin zone grid. This level of convergence was achieved using a plane wave cut-off energy of 900 eV for system, and by invoking k point Monkhorst-Pack grids of 3 Â 2 Â 2.
Geometry optimisation and H position optimisation calculations were performed on all systems using the over-converged values described previously to ensure accurate forces. For these structural optimisations, the lattice parameters were kept fixed whilst the atomic positions were optimised to a force tolerance of 0.05 eV Å À1 , a maximum ionic displacement of 1 Â 10 À3 Å and a total energy change of 2 Â 10 À5 eV per atom. NMR parameter calculation of the chemical shift, 22,36 electric field gradient tensors 20 and J-couplings 23,37 invoked the gauge included projector augmented wave (GIPAW) DFT method which extended the pseudopotential (valence electron approximation) approximation to recover all electron charge densities. This approach demonstrated that the NMR parameters depend more sensitively upon the electron density than the total energy, so each NMR parameter will be more sensitive to basis set truncation errors than to total energies. This is compensated for by the over-convergence of the basis set to a level which experience suggests will produce fully converged NMR parameters. Consequently, these calculations were completed      38 These calculations used the same basis set convergence (0.4 mH) as the original calculations to minimise the propagation of errors.

Results and discussion
The homogenous 17 O enrichment of solid naphthalaldehydic acid 1 was achieved by heating to 75 1C in 90% 17 O labelled water under acid catalytic conditions in hot dioxane for 24 h, with the resulting product recrystallized from toluene. The electrospray ionisation mass spectrometry (ESI-MS) of the resultant anion suggested that it was characterised by a ratio of triply labelled: doubly labelled: mono labelled molecules of B6 : 4 : 1. A recently reported single crystal X-ray structure determination of 1 shows that the head group is essentially a closed lactone ring arrangement supporting the three proximate O positions referred to as carbonyl (CQO), ether (-O-) and hydroxyl (-OH) groups for the purpose of the remaining discussion. However, open ring configurations can be realised when molecule 1 is deprotonated to give salts with various cations which exhibit interactions between the negatively charged carboxylate (CO 2 À ) anion and the aldehyde (CHQO) functionality (see Scheme 1 below). 7 As observed in Fig. 1(b), the crystalline salt naphthalaldehydic acid 1 has a cyclic lactone structure with only one crystallographically unique molecule comprising the asymmetric unit of the crystal. There exists intermolecular H-bonding between the CQO functionality and the -OH moiety on an adjacent molecule constrained by a twofold screw axis, with the two symmetry related H-bonds associated with each molecule assuming an OÁ Á ÁO distance of 2.754(4) Å. 7 There is an anomeric interaction between the two O atoms attached to the methine C leading to a short C-OH bond length of 1.387 Å and a long C-O(CQO) bond length of 1.477 Å due to donation of lone pair electron density from the hydroxyl O atom into the adjacent methine CH-O(CQO) bond. 7 In comparison, a typical unperturbed C-O bond length is usually observed to fall between these values at B1.43 Å. 39 The 1 H MAS NMR data from naphthalaldehydic acid measured at 14.1 T under fast MAS conditions (n r = 60 kHz) is shown in Fig. 2(a). This spectrum shows a single broad resonance with no individual proton environments able to be resolved from this signal, despite the acquisition of this data under high field and fast MAS conditions. The aromatic, hydroxyl and methine 1 H species are all expected to appear at similar isotropic chemical shifts (d 6.8-8.4 ppm in solution), and the strong homogeneous 1 H-1 H dipolar interaction broadens all resonances thus resulting in a single unresolved feature. It is possible that both the 1 H and 13 C resonances suffer from anisotropic bulk magnetic susceptibility (ABMS) broadening, however this broadening typically only increases the linewidth by B1 ppm. 40 These problems are commonly observed in highly complex aromatic systems and heavy (but not complete) deuteration of the sample is required to significantly increase spectral resolution. 41 The 17 O labelled naphthalaldehydic acid sample 1 was selectively deuterated at the hydroxy position to form a doubly 17 O/ 2 H enriched variant 2 (see Fig. 1(a)) to investigate (and reduce) the potential of 1 H motional modulation effects on the 17 O MAS and DOR NMR data (vide infra). The 2 H MAS NMR data from this quadrupolar (I = 1) nucleus shown in Fig. 2(b) depicts a broad satellite transition spectrum with a 2 H quadrupole coupling constant (C Q ) of B200 kHz being measured from the simulation of this data. Previous measurements of 2 H C Q values from various enriched -OD arrangements demonstrate that C Q occurs within the range of B190-290 kHz; 42,43 the C Q characterising the -OD moiety in this hydroxyl-lactone species represents a value at the low end of this range thus suggesting that partial motional averaging of this interaction is evident. This value is significantly smaller than the predicted C Q value of B308 kHz as computed using the CASTEP code (see Table S1 in the ESI ‡). These DFT calculations in their basic form do not account for rotation, vibration or libration of the -OD bond, hence any subsequent motional averaging of the static quadrupole interaction is not modelled. Recently, it has been suggested that dueteration can also reduce the point symmetry of the moiety. 44 It is important to note that the d iso ( 2 H) for the -OD species is B8.0 ppm, and this is corroborated by the 1D 1 H MAS and 2D 1 H-13 C HETCOR MAS NMR data depicted in Fig. 2(a) and (d). The 2D 1 H-13 C HETCOR data of Fig. 2(d) clearly shows that all protonated C species are correlated with the broad 1 H resonance at B8.0 ppm, indicating that the d iso (-OH) value is not resolved from the more intense 1 H resonances associated with the aromatic protons. Collectively, the observations of a more deshielded 1 H chemical shift (d iso ( 1 H) B8.9 ppm) and a Scheme 1 partial motional averaging of the 2 H quadrupole interaction (C Q B200 kHz) indicates that the bond covalence characterising the -OH group is of intermediate strength, while the intermolecular H-bonding interaction inherent to the crystal structure of 1 (influencing the -OH proton) is weak. 31,38 Solid state 17 Fig. 4 clearly demonstrates the chemical purity of this system, and that very high structural order is reflected by the absence of any distributions in the chemical shift and/or distributions of quadrupole NMR parameters. Previous studies have established that H-bond motion can modulate the multiple quantum excitation and evolution processes in the MQMAS experiment thus inducing detrimental effects on the resolution observed in the F1 dimension, however this is also not observed here. 38 Simulation of the 17 O 1D data for the CQO species (i.e. the most deshielded 17 O environment) yields an isotropic chemical shift of d iso = 313 ppm and quadrupole parameters of C Q = 8.2 MHz/Z Q = 0.03. A 17 O d iso value of this magnitude is low compared to a ketone group, but it is within the reported limits of typical carboxylic acid and lactone functionalities. 46,47 Conversely, the observed 17 O resonance from the hydroxyl (-OH) species is the most shielded (d iso = 66 ppm) and represents a larger quadrupole interaction with C Q = 9.6 MHz/Z Q = 0.81. Both sets of 17 O quadrupole parameters measured for both the CQO and the -OH groups are in firm agreement with previously reported data in the literature observed for amino acidÁHCl salts. 38,46,48 The high Z Q value for the -OH species, and corresponding low Z Q value for the CQO species are typical for 17 O nuclei bonded to larger conjugated aromatic moieties. 38,49 In previous studies on amino acids, it has been reported that the 17 O asymmetry parameter (Z Q ) is close to zero for CÁ Á ÁO distances in a CQO functionality of B1.22 Å, while it appears to increase rapidly for longer bond lengths. Simulation of the 17 O resonance from the ether (-O-) linkage (located between the CQO and -OH resonances) in this lactone structure yields an isotropic chemical shift of d iso = 200 ppm and quadrupole parameters of C Q = 8.9 MHz/Z Q = 0.25. All isotropic chemical shift and quadrupole parameters characterising the three O species comprising this lactone structure are in agreement with previously reported values for the lactone of 2-[1,2,3-17 O 3 ]acetylbenzoic acid which is the only other reported labelled lactone structure studied by solid state NMR. 47 Despite the use of high magnetic fields in this study, no chemical shift anisotropy (CSA) contributions were required to facilitate the accurate simulation the data in Fig. 3(a)-(c), suggesting that CSA influences are small in comparison to the dominant quadrupole interaction and subsequently eliminated by MAS.
The CQO bond length of 1 measured in the single crystal X-ray structure determination at 100 K is 1.222 Å, and the DFT  geometry optimisation yields a longer CQO bond length of 1.238 Å. From Table 3, the measured 17 O d iso value of the CQO value is 313 ppm (from MAS NMR); when this value is introduced to eqn (2) a bond length of 1.223 Å is predicted, suggesting the room temperature NMR measurements are in firm agreement with the single crystal X-ray structure determination (performed at 100 K) despite the large temperature difference between the two measurements. Correspondingly, as the MAS NMR measured 17 O Z Q value of the carbonyl is close to zero, then it can be presumed that the bond length is closer to the unoptimized 1.222 Å, as any CQO bond length significantly above 1.2 Å gives a Z Q 4 0 value. 53 Support for the crystallographic derived structure by highly accurate 17 O solid state NMR measurements is necessary to gauge the temperature variations between the NMR (298 K) and crystallographic (100 K) measurements. These observations infer that accurate calculated 1 J( 13 C, 17 O) couplings can be obtained from DFT-CASTEP calculations (notionally undertaken at 0 K) on high quality crystal structure data.
From inspection of the spectral and computationally generated data exhibited in Fig. 3 and Tables 1 and 2, there exists a very strong correlation between the directly measured and simulated 17 O MAS NMR data (see Fig. 3(a), (c) and (e), and Table 1) and the GIPAW DFT calculated 17 O NMR interaction parameters from a geometry optimised structure of 1 using the CASTEP code (see Fig. 3 Table 2). In particular, the experimentally determined -OH data (d iso = 66 ppm, C Q = 9.6 MHz, Z Q = 0.81), -O-data (d iso = 200, C Q = 8.9, Z Q = 0.25) and CQO data (d iso = 313 ppm, C Q = 8.2 MHz and Z Q = 0.03) show an excellent agreement with the corresponding DFT results (-OH, d iso = 62 ppm, C Q = 9.5 MHz, Z Q = 0.85; -O-, d iso = 223ppm, C Q = 9.3 MHz, Z Q = 0.25; CQO, d iso = 307 ppm, C Q = 8.1 MHz and Z Q = 0.31) when geometry optimisation is implemented. These correlations are marginally stronger than those derived from calculations using non-geometry optimised structures; this is particularly evident when comparing the MAS NMR measured and DFT calculated -OH d iso values when geometry optimisation is omitted. In this case, a discrepancy of B40 ppm exists. Nevertheless, the strength of the above correlations suggests that the GIPAW DFT method represents a very sound approximation for describing the electronic configuration of O species in organic solids, and this approach thus presents a solid foundation on which to underpin 1 J( 13 C, 17 O) coupling calculations in the naphthalaldehydic acid system 1. The DFT calculations also highlight that both geometry optimised and direct calculations on the X-ray derived structure need to be considered when calculating the 1 J( 13 C, 17 O) couplings in this system.

(b), (d) and (f) and
Unlike the conventional MAS NMR technique, the DOuble Rotation (DOR) experiment involves spinning the sample about two angles to enable averaging of both the P 2 and P 4 terms of the 4th order Legendre polynomial, which describes the angular dependences of the second order quadrupole interaction. The first order quadrupole broadening is reduced by sample rotation around the familiar magic angle of 54.71 with respect to B 0 , while the second order quadrupole broadening is eliminated by simultaneous rotation at 54.71 and a second angle of 30.61 with respect to the magic angle. The two major advantages that the DOR NMR technique offers are, (a) the observed (featureless) centre-of-gravity shift (d cg ) yields greater resolution than conventional MQMAS experiments which are limited by the number of attainable slices defining the F1 dimension, and (b) the DOR experiment uses a single pulse excitation experiment in comparison to two-pulse or three-pulse MQMAS experiments which possess limited pulse efficiencies. The greater resolution and superior signal-to-noise ratio afforded by the DOR technique is met with technical challenges; sample rotation at two angles simultaneously is difficult to stabilise, and the limited rotational rates achievable by the inner and outer rotors introduces large residual spinning sideband manifolds which necessitate acquisitions at multiple spinning rates to isolate the central transition. 33,54 For a quadrupolar nucleus such as 17 O, the apparent centreof-gravity shift (d cg ) is comprised of both field independent isotropic chemical shift (d iso ) and field dependent second-order quadrupole shift (d (2) Q,iso ) components: For the central transition of an I = 5/2 nucleus such as 17 O, eqn (4) reduces to: where n 0 is the 17 O Larmor frequency and P Q is the quadrupole product (related to the quadrupole coupling constant, C Q ,) which is defined by: Hence, for featureless data that precludes simulation of the central transition spectrum to ascertain the characteristic NMR parameters, this approach enables variable B 0 field data to be analysed graphically via the linear relationship of eqn (5), thus allowing d iso to be determined from the y-intercept and P Q to be elucidated from the slope. [55][56][57][58][59] High resolution data afforded by the 17 O DOR technique allows some subtle aspects of motion affecting the O positions to be detected. The characterisation of these properties is an important prerequisite to the measurement and calculation of 1 J CO couplings. Table 1 summarises the d iso and P Q data elucidated from the variable field (14.1, 11.7 and 9.4 T) 17 O DOR measurements and the graphical approach outlined above for 1 (see Fig. 5(a)-(d)) and 2 (see Fig. 5(e)-(h)). Each spectrum shows the centre-of-gravity shifts (d cg ) identified; these were isolated from the spinning sideband manifolds by varying the spinning frequency of the outer rotor over a range of 1.3-1.9 kHz. From the undeuterated system 1 the determined 17  Previous studies have demonstrated that the deuteration of protonated oxo functionalities in solid organic systems improves the resolution obtained in the 17 O DOR experiment. This is achieved by damping the heteronuclear dipolar proton coupling which homogenously broadens the 17 O resonance. [60][61][62][63] This is corroborated by the data in Fig. 5 where the 17 O resonance for the -OD (see Fig. 5(e)-(h) for 2) moiety is significantly narrower and of greater intensity than its -OH counterpart (see Fig. 5(a)-(d) for 1), especially at the higher fields of 11.7 and 14.1 T. As observed from Table 1 and Fig. 5(d) and (h), the data for the CQO and -O-moieties from the undeuterated sample 1 show an inferior overall correlation on the linear regression and greater errors on each individual measurement in comparison to their counterparts from the deuterated sample 2. This is a consequence of the broader 17 O resonances due to proton motion in the H-bond which induces additional cooperative modes of motion throughout the other O functionalities. Furthermore, for the CQO and -O-moieties the measured d iso and P Q values from the DOR experiment closely corroborate those reported from the MAS, MQMAS and geometry optimised DFT (GO-DFT) data. In comparison, for both samples 1 and 2 the overall correlations described in the linear regression for the -OH species are inferior to those described above for the CQO and -O-moieties. As suggested above, a reduced correlation for the -OH data (sample 1) is expected to emanate from proton heteronuclear dipolar coupling in the H-bonded arrangement; however, the -OD data (sample 2) exhibits a more reduced correlation and much larger errors. This contradicts previously Results from undeuterated naphthalaldehydic acid 1 are given in a, b and c, and results from deuterated naphthalaldehydic acid 2 are given in e, f and g. The outer rotor frequencies are denoted as 'OR', and the inner:outer rotor frequency ratios are labelled 'ratio'. From plots of centre-of-gravity (d cg ) for each DOR resonance against 1/n 0 2 (d, h), d cg is observed to be field (or n 0 ) dependent through second order quadrupole effects from the spin I = 5 / 2 17 O nucleus such that d cg (ppm) = d iso (ppm) À (3/500 Â P Q 2 /n 0 2 ) Â 10 6 , thus permitting graphical estimates for d iso (y intercept) and P Q (slope) for molecules 1 and 2.
reported evidence that proposes sample deuteration reduces these errors, promoting more resolved 17 O DOR data, and enables more accurate measurements of the d iso and P Q parameters. 33 This anomaly suggests that the reduced correlations/larger errors from 2 originate from lower point energy of the OD bond and results in an isotope effect on the NMR parameters. 62,63 The deuteration procedure of 17 Fig. 4(d) where 17 O MAS NMR data from the deuterated sample 2 (which originated as sample 1) exhibits greatly inferior signal/noise in comparison to sample 1 shown in Fig. 4(b). These complex isotope affects clearly directly influence upon the 17 O d iso and P Q parameters characterising each O environment, and the deuteration of molecule 1 can produce measured NMR parameters which are not directly comparable to those calculated from the single crystal derived structure. The process of deuteration of hydroxyl environments to reduce heteronuclear dipolar coupling, and potentially reduce the point symmetry of the moiety, is occasionally employed in the literature. Here, we show this is not best employed when trying to accurately compare diffraction derived DFT NMR parameters and the experimental MAS data. Overall, the GIPAW DFT-derived C Q and Z Q parameters show a strong correlation with the MAS and MQMAS achieved parameters, therefore for the following 1 J determinations the experimentally determined parameters will be used.
The spin echo dephasing data from the (undeuterated) naphthalaldehydic acid system 1 is presented in Fig. 6, and the measured heteronuclear 1 J( 13 C, 17 O) coupling constants are summarised in Table 3. This study represents only the second measurement of 1 J( 13 C, 17 O) coupling constants in the solid state. While the first was demonstrated on a doubly 13 C/ 17 O labelled solid glycineÁHCl sample, 16 this work focusses on a uniformly labelled 17 O system which possesses multiple O positions which are in close proximity.
A CT-selective 17 O p-pulse in a heteroncuelar spin echo experiment only refocuses the central-transition (CT) spin states, consequently confining the dephasing behaviour of the 13 C signals observed in Fig. 6 to only those 13 C spins bonded to 17 O spins in the +1/2 or À1/2 CT spin states. Presuming 100% 17 O enrichment of an isolated 13 C-17 O two spin system, only 1/3 of 13 C spins attached to 17 O CT (+1/2 or À1/2) spin states will show a cosine J-modulation, while the other 2/3 of the 13 C spins will show no cosine modulation as they couple to the satellite transition (ST) +5/2, +3/2, À3/2 or À5/2 spin states. Hence, a J-resolved experiment utilising a CT-selective 17 O pulse for a 13 C-17 O spin pair will exhibit a cosine modulation (presuming no T 2 0 contribution) that goes from an initial signal intensity of 1, down to a minimum signal of S(t) het = 0.33, with a 0.66 signal intensity for a J-evolution time of 1/2 J. However, the relatively broad nature (B41 kHz) of the multiple 17 O environments in naphthalaldehydic acid means uniformly exciting the three oxygen environments required non-selective pulses, therefore accurate SIMPSON simulations are required to evaluate the data with respect to the pulse lengths used, and fitting the decay using a function is challenging. J C11-C1 , 1 J C12-O2 , 1 J C12-OH and 1 J C12-C9 ) and simulated using the SIMPSON 4.2.1 package. The contributions from n J-couplings (n 4 2) are predicted by CASTEP to be minimal and are therefore ignored. The experimental quadrupole coupling constants, which are in good agreement with the DFT results, are used throughout. As SIMPSON does not consider T 2 0 , then these were measured using a simple homonuclear spin-echo. The experimental and predicted behaviour S(t) het = 0 ms is normalised to an intensity of 1. The individual compositions, derived from experimental quadrupole parameters, CASTEP 1 J couplings and numerical SIMPSON simulations are deconvoluted in Fig. S1 and S2 (ESI ‡), up to 32 ms, the results were multiplied with the T 2 0 results and their enrichment probabilities: p O1O2 = p O3O4 = 80%; probabilities that C 11 or C 12 is directly bonded to two enriched 17 O species, p O1 = p O2 = p O3 = p O4 = 7.5%; probabilities that C 11 or C 12 is directly bonded to one enriched 17 O species, p none = 5%; probability that C 11 or C 12 are not directly bonded to any enriched 17 O species. Therefore, C 11 = 0.85 Â SIMPSON output of 1 J C11Q , 1 J C11-O , 0.075 Â 1 J C11QO , 0.075 Â 1 J C11-O , 1. 1% (natural abundance 13 C) Â 1 J C11-C1 , all multiplied by a T 2 0 of 14 ms. An example of the SIMPSON input file is given in the ESI, ‡ Table S3. As the natural abundance of the 13 C isotope is 1.1%, these species will induce minor contributions to the dephasing curve and therefore these were considered in the DFT derived SIMPSON simulations.
All data presented in Fig. 6 were acquired using a modified spin echo sequence as detailed by Hung et al., 16 with the simulation of each multi-component spin echo dephasing curve being achieved using SIMPSON. 45 An analytical expressions for deriving isolated 1 J-couplings have been developed by Duma et al., with the quadrupolar contributions to the scalar coupling explored by Perras and Bryce. 64,65 SIMPSON 4.2.1 cannot simulate multiple 1 J-couplings with multiple quadrupole coupling constants. Therefore, the simulation was broken up into their individual one-bond components and multiplied together. The p pulse length (6 ms, 41 kHz), was also considered in the SIMPSON calculation to account for any errors or issues caused by finite pulse lengths, this pulse length was chosen as it is the same as the linewidth of the three oxygen environments.
The output of the SIMPSON simulations were then scaled to represent the oxygen enrichment, which was determined by high-resolution ESI-MS. This gave the following probabilities, p: p O1O2 = p O3O4 = 80%; probabilities that C 11 or C 12 is directly bonded to two enriched 17 O species, p O1 = p O2 = p O3 = p O4 = 7.5%; probabilities that C 11 or C 12 is directly bonded to one enriched 17 O species, p none = 5%; probability that C 11 or C 12 are not directly bonded to any enriched 17 Fig. 3 and 4(b)) provides a uniformly labelled product for 1 which is thus preferred for this study, in comparison to the labelled product derived from shorter and milder (THF, 66 1C, 6 h) reaction conditions (see Fig. 4(c)) which highlights a preferential 17 O enrichment of the -OH position. The DFT derived SIMPSON outputs do not consider the transverse relaxation contribution to the decays, therefore T 2C11 0 and T 2C12 0 were measured using a homonuclear spin echo sequence and upon these the 1 J( 13 C, 17 O) coupling modulation is superimposed. These times are estimated by conventional homonuclear 13 C spin echo (p/2-t-p-t-acquire) measurements to be 14 AE 2 ms and 10 AE 4 ms for the C 11 and C 12 positions, respectively. The GIPAW DFT calculated 1 J( 13 C, 17 O) coupling constants for the O positions are derived from the single crystal structure determination of 1, 7 with these calculations being performed on both the geometry optimised and the experimental structures, coupled with associated dispersion corrections. These results are summarised in Table 3. Key to the effectiveness of this computational approach for these 1 J( 13 C, 17 O) coupling constants is the highly accurate characterisation of 1 involving the more routinely GIPAW DFT calculated NMR parameters such as d iso , C Q and Z Q as presented in Fig. 3, and Tables 1 and 2, which demonstrates that the ultrasoft 'on-the-fly' O pseudopotential is particularly optimised for 17 O NMR measurements in organic solids. This provides the simulation of the dephasing characteristics for C 11 and C 12 shown in Fig. 6(a) and (b) using the calculated 1 J( 13 C, 17 O) coupling constants ( 1 J CO1 , 1 J CO2 , 1 J CO3 and 1 J CO4 ) with greater statistical importance.
As the C 11 and C 12 positions are not 13 C labelled, the spin echo intensities at larger evolution times are difficult to determine, as they cannot be accurately discriminated from the noise. The error in each data point grows cumulatively for increasingly longer evolution times; as observed from Fig. 6, these dephasing measurements were truncated at a maximum evolution time of 15 ms. The contributions from neighbouring proton species are removed by high power 1 H (100 kHz) decoupling during the evolution and acquisition periods; however, the X J couplings to neighbouring 13 C spins are not suppressed. The 1 J-coupling from C 11 to C 1 and C 12 to C 9 are 58 and 39 Hz, respectively. As the natural abundance of the 13 C isotope is 1.1%, these species will induce minor contributions to the dephasing curve and therefore these were considered in the DFT derived SIMPSON simulations. Extended homonuclear 1 J( 13 C, 13 C) contributions are predicted by CASTEP to have an insignificant contribution to the decay (Table S2, ESI ‡), and as there is no 13 C labelling in the structure, the maximum contribution of this 1 J( 13 C, 13 C) coupling is 1.1% of cos(pJ CC t) to the overall result, these may account for a minor source of error in the observed decay. Using high power decoupling limits the acquisition times you can safely record the data, therefore the cosine modulation feature which is predicted at a t between 20 to 24 ms was not possible to observe. This would also be challenging to reproduce accurately due to reduced signal-to-noise at these larger t delays and the need for high power decoupling at these extreme lengths is likely to cause damage to the probe.
Despite these sources of error, the results presented in Fig. 6 suggest that overall methodology invoked above appears to be a robust approach for calculating multiple 1 J( 13 C, 17 O) couplings in a complex arrangement containing multiple oxo functionalities in the solid state. In particular, it is evident that GIPAW DFT calculations of 1 J( 13 C, 17 O) coupling constants are accurate as observed by the strong correlation between the experimental dephasing behaviour and the simulated S(t) het behaviour (adopting the isolated spin system approximations above) using calculated values of 1 J CO1 , 1 J CO2 , 1 J CO3 and 1 J CO4 from CASTEP. The correlation between the calculated data using the proposed model and the experimental data is excellent for the three nuclear spin system involving C 12 which is directly bonded to the methine (-O-) and hydroxyl (-OH) moieties (i.e. 1 J CO3 and 1 J CO4 ). It should be noted that the reduced correlation describing C 11 involves 1 J CO1 coupling to the CQO moiety which is influenced by intramolecular H-bonding to the -OH species in an adjacent molecule. Furthermore, the errors in the C 11 heteronuclear spin echo experiment were larger, due to insufficient signal to noise, possibly due to less efficient cross polarisation.
It is interesting to note that the magnitudes of the two 1 J( 13 C, 17 O) couplings to the central ether -O-linkage reflect the corresponding bond lengths involved. The 1 J( 13 C, 17 O) coupling constant for the shorter bond length CQO species is 37 Hz (carbonyl C-O bond length: 1.338 Å), which is larger than the coupling constant of 32 Hz to the more distant CH-OH (methine C-O bond length: 1.490 Å). In contrast, the 1 J( 13 C, 17 O) coupling constant between the methine C and the -OH species is smaller than that to the ether -O-atom (20 Hz cf. 32 Hz) despite having a significantly shorter bond length (1.379 Å cf. 1.490 Å). As mentioned above, -OH motion within the weak H-bonding arrangement can modulate and diminish the magnitude of this 1 J( 13 C, 17 O) coupling, however the bond angle disposition as proposed by the Karplus relationship may also contribute to this marked reversal in this trend. 15,66 Although calculations 67 and measurements 68 of 1 J( 13 C, 17 O) coupling constants characterising the CO and CO 2 gas phase systems have been reported (measured/calculated; 16.4/17.2 Hz and 16.1/17.1 Hz, respectively), the only existing measurement of 1 J( 13 C, 17 O) couplings ascertained from a real solid state system pertains to glycineÁHCl where 1 J(CQO) = 25 Hz and 1 J(C-OH) = 28 Hz. 16 The determined 1 J ( 13 C, 17 O) coupling constants that characterise solid naphthalaldehydic acid 1 summarised in Table 3 are comparable to these previous values, and this study reports the first 1 J( 13 C, 17 O) measurements on ether -O-linkages. This work has demonstrated that measurements of 1 J( 13 C, 17 O) coupling constants is not limited to selectively labelled highly isolated spin systems in small molecules, and that this information can be elucidated from larger and more complex spin systems which are isotopically enriched by more routine synthetic methods.

Conclusions
A combined 17 O MAS, 3QMAS and DOR NMR approach has been utilised to accurately characterise the O positions in naphthalaldehydic acid 1 and to assess the accuracy of the first principles GIPAW DFT calculations for deriving the associated 17 O NMR parameters. The initial phase of this study demonstrated that 17 O NMR parameters such as the isotropic chemical shift (d iso ) and quadrupole parameters (C Q , Z Q ) were well correlated with those emanating from the GIPAW DFT calculations using the CASTEP code. Heteronuclear 1 J( 13 C, 17 O) measurements were undertaken on this system which possesses multiple O functionalities in the hydroxy lactone head group of the molecule. These measurements represent the first assessment of multiple 1 J( 13 C, 17 O) couplings from a single molecule in the solid state, and they were also evaluated against the scalar coupling calculations resulting from first principles GIPAW DFT calculations and SIMPSON simulations. For the modified spin-echo dephasing experiment focussing on the C 11 and C 12 positions in 1, the dephasing of the magnetisation in each case relates to two three-spin ( 17 O-13 C-17 O) systems in which the O positions are enriched. This experiment cannot isolate the individual 1 J( 13 C, 17 O) contributions and a weighted average dephasing curve is produced which can only be deconvoluted by simulation using 1 J( 13 C, 17 O) couplings from the GIPAW DFT calculations as the SIMPSON input, hence the reliance on accurate DFT prediction in this study. The resultant simulated spin-echo dephasing curves produced are in good agreement (within error) with those experimentally derived.
The geometry optimised DFT structure derived using the CASTEP code gives a firm agreement with the experimentally measured shifts observed for the ether (d iso = 223, P Q = 9.4 MHz) and hydroxyl (d iso = 62, P Q = 10.5 MHz) groups, however the unoptimised experimental structure has better agreement for the carbonyl group (d iso = 320, P Q = 8.3 MHz). The determined d iso and Z Q values for the latter are shown to be consistent with bond lengths closer to 1.222 Å emanating from the unoptimised experimental XRD structure, rather than the geometry optimised length of 1.238 Å. The geometry optimised DFT 1 J( 13 C, 17 O) coupling to the hydroxyl is calculated as 20 Hz and the 1 J CO couplings to the ether oxygen were calculated to be 37 (O-CQO) and 32 (O-C-OH) Hz. These measurements are all within error of the experimental echo decays.

Conflicts of interest
There are no conflicts to declare.