Investigating discrepancies between experimental solid-state NMR and GIPAW calculation: N=C-N 13 C and OH···O 1 H chemical shifts in pyridinium fumarates and their cocrystals

An NMR crystallography analysis is presented for four solid-state structures of pyridine fumarates and their cocrystals, using crystal structures deposited in the Cambridge Crystallographic Data Centre, CCDC. Experimental one-dimensional, one-pulse 1 H and 13 C cross-polarisation (CP) magic-angle spinning (MAS) nuclear magnetic resonance (NMR) and two-dimensional 14 N- 1 H heteronuclear multiple-quantum coherence MAS NMR spectra are compared with gauge-including projector augmented wave (GIPAW) calculations of the 1 H and 13 C chemical shifts and the 14 N shifts that additionally depend on the quadrupolar interaction. Considering the high ppm (>10 ppm) 1 H resonances, while there is good agreement (within 0.4 ppm) between experiment and GIPAW calculation for the hydrogen-bonded NH moieties, the hydrogen-bonded fumaric acid OH resonances are 1.2 to 1.9 ppm higher in GIPAW calculation as compared to experiment. For the cocrystals of a salt and a salt formed by 2-amino-5-methylpyridinium and 2-amino-6-methylpyridinium ions, a large discrepancy of 4.2 and 5.9 ppm between experiment and GIPAW calculation is observed for the quaternary ring carbon 13 C resonance that is directly bonded to two nitrogens (in the -Solid-state NMR experiments were performed on: (1) a Bruker Avance III spectrometer, operating at 1 H and 13 C Larmor frequencies of 500.0 MHz and 125.8 MHz, respectively; (2) a Bruker Avance II+ spectrometer, operating at 1 H, 13 C and 14 N Larmor frequencies of 600.0 MHz, 150.7 MHz and 43.4 MHz, respectively; (3) a Bruker Avance III HD spectrometer, operating at 1 H, 13 C and 14 N Larmor frequencies of 700.0 MHz, 176.0 MHz and 50.6 MHz, respectively.


Introduction
The NMR crystallography approach has been increasingly utilised to provide a detailed characterisation of solid systems, whereby solid-state magic-angle spinning (MAS) NMR and density functional theory (DFT) calculations, in particular using the gauge including projector augmented wave (GIPAW) method, 1 are used alongside complementary techniques such as X-ray diffraction (XRD). [2][3][4][5][6] The power of GIPAW has been demonstrated in numerous applications, notably providing a link between crystal structures and NMR parameters, aiding both their development and validation [7][8][9] as well as adding further insight to investigations of intermolecular interactions. [10][11][12][13][14][15] A key consideration is the level of agreement between experiment and calculation. For 1 H and 13 C solid-state NMR of organic molecules, there is a typical maximum discrepancy corresponding to ~1% of the chemical shift range, i.e., ~0.2 ppm and ~2 ppm for 1 H and 13 C, respectively. [16][17][18][19][20] Specifically, Engel et al have recently performed a Bayesian analysis and determined a discrepancy between experiment and GIPAW calculation of 2.9 ± 0.7 ppm for 13 C in organic molecular solids. 21 It is also known that the gradient of a plot of experimental versus calculated chemical shielding often deviates from unity, see for example reference. 22 For 13 C, this results in an undercalculation at low chemical shifts and an overcalculation at high chemical shifts, e.g. methyl and carboxylate carbons, respectively, when a single reference shielding is used for the entire spectrum. An alternative approach is to use different reference shieldings for different parts of the spectrum. 18 Here we consider the four systems presented in Table 1. They are based on four differently substituted pyridine molecules and fumaric acid: specifically, two salts and two cocrystals of a salt are formed in the solid state. The structure of each system's asymmetric unit is given in Figure 1, alongside the atomic labels used throughout this work. Salt and cocrystal formation can alter the properties of a compound, such as stability, solubility and hygroscopicity, making them of considerable interest to pharmaceutical and agrochemical industries. [23][24][25][26] Salt formation in particular has been common practice in the development of active pharmaceutical ingredients for more than 25 years. 27 The observation of a salt or cocrystal form often depends on the position of a single proton, 9,28 making NMR crystallography methods extremely useful for their characterisation. In this paper, we report the identification of a 1 H and a 13 C specific chemical environment within the systems listed in Table 1 (this Table states the CSD reference and number as well as the original literature reference for the crystal structure, and also the shorthand names used here) whose chemical shifts exhibit larger than expected discrepancies between experiment and GIPAW calculation.

Results
We report here an NMR crystallography study of four related systems that are based on four differently substituted pyridine molecules and fumaric acid: specifically, two salts and two cocrystals of a salt.
Their crystal structures have been previously reported and deposited in the CCDC as listed in Table 1 (note that the experimental and GIPAW calculated results for 26L:F have been previously presented in Ref. 15 ). As noted above and expanded upon below, the focus of this paper is the identification of two specific chemical environments (see Fig. 2) for which there are significantly larger differences between their GIPAW calculated and experimental MAS NMR chemical shifts than expected. One discrepancy is for 1 H in a OH···O hydrogen bond and the other discrepancy is for a quaternary 13 C which is covalently bound to both a pyridinium nitrogen and an amino nitrogen. Fig. 3 shows 1D 1 H one-pulse MAS spectra for each system containing an OH···O hydrogen bond, with stick spectra corresponding to GIPAW calculated chemical shifts for the geometry optimised crystal structures. Note that the experimental COOH 1 H chemical shift for fumaric acid (FA) is taken from the literature. 51 Assignments are made with the aid of both 2D 14 N-1 H HMQC MAS NMR spectra (Fig. 4) and GIPAW calculation (SI, Tables S1-S5).

Figure 2: Chemical structures of the two environments which show large discrepancies between GIPAW calculated and experimental chemical shift: a 1 H in a OH···O hydrogen bond (left) and a quaternary 13 C between a pyridinium nitrogen and an amino nitrogen (right).
As has been reported previously, 15 in 26L:F (Fig. 3), H13 is observed at a lower ppm value experimentally compared with GIPAW calculation and can be assigned to the peak at 15.8 ppm (rather than 17.7 ppm as calculated). The other high-ppm 1 H resonance, corresponding to the NH + , has the same calculated chemical shift and is indeed seen experimentally at 17.7 ppm. The OH protons of FA, 25AMP:FFA and 25L:FFA also showed the largest discrepancy between experiment and calculation of the chemical shift. In the latter case, the experimental chemical shifts for the two OH protons in the system lie at δ iso exp = 13.4 ppm, at a lower ppm value than for the NH + proton, despite both being calculated at a higher chemical shift than this NH + environment. As in 26L:F, the NH + in 26AMP:F-H2, 25AMP:FFA and 25L:FFA is at a similarly high chemical shift to the OH resonances but in each case shows good agreement with the GIPAW calculated chemical shift (Table 4). This suggests that the OH···O discrepancy is not simply explained by the known temperature dependence of hydrogenbonded chemical shifts, [52][53][54][55][56][57][58][59] as this would also be expected to effect the NH + ··· − O proton.
The level of discrepancy between experiment and GIPAW calculation seen for each system is relatively consistent, with δ exp-calc ranging from 1.9 to 1.2 ppm in 26L:F and FA, respectively. The  Figure 1). For 25L:FFA (top right), a low intensity peak is observed between 17 and 18 ppm (denoted by ?); this is believed to correspond to a minority phase (note that this is largely obscured in the 1D 1 H-13 C CPMAS spectrum, presented below, due to both resonance overlap and the reduced signal to noise ratio).
lowest magnitude δ exp-calc of 1.2 ppm is for fumaric acid, where there is a neutral carboxylic acid/carboxylic acid hydrogen bond.   In 26AMP:F-H2, C9 is calculated at 151.3 ppm but is instead observed experimentally at 155.5 ppm. 25AMP:FFA shows an even greater discrepancy with the calculated chemical shift for C1 5.9 ppm lower than the experimental value of 153.8 ppm. By comparison, the quaternary carbons that sit at the analogous position in both 25L:FFA and 26L:F, directly bound to the pyridinium nitrogen, show excellent agreement between experiment and calculation with the largest discrepancy 0.2 ppm ( Table   5). As these are substituted with a methyl group rather than an amino group, the combination of amino and pyridinium interactions is thus correlated with the larger discrepancy between experiment and GIPAW calculation. No change in the 13 C chemical shift was observed when recorded at a 1 H Larmor frequency of 500 and 600 MHz (SI, Fig. S3), ruling out a shift of the 13 C chemical shift due to enhanced second-order quadrupolar effects from the two adjacent 14 N atoms. There is a known deviation from negative one in the gradient of a plot of experimental chemical shift against calculated chemical shielding, but this would be expected to affect the carboxyl and methyl carbons more significantly as they are further towards the edges of the chemical shift range. It is also of note that this would cause high-ppm 13 C environments to be calculated at a higher chemical shift than they are observed experimentally rather than lower, as seen for the amino substituted quaternary carbons discussed here.

Conclusions
An NMR crystallography study has been presented that reports 1 H, 13 C chemical shifts and 14 N shifts for four differently substituted pyridine molecules and fumaric acid that occur as two salts and two cocrystals of a salt in the solid state. The focus of this paper is on two chemical environments for which a greater discrepancy is observed between experiment and GIPAW calculated chemical shifts that goes beyond the typically encountered maximum of 1% of the chemical shift range. These are the 1 H in an OH···O hydrogen bond (which is observed 1.2-1.9 ppm below its calculated position) and a quaternary 13 C sitting covalently bound to both a pyridinium nitrogen and an amino nitrogen (which is observed 4.2-5.9 ppm above its calculated position). These discrepancies between experiment and GIPAW calculation stand out because of the great success of such GIPAW calculations in reproducing experimental chemical shifts.
For the 1 H chemical shifts of the hydrogen-bonded fumaric acid protons, it would be interesting to investigate the temperature dependence [52][53][54][55][56][57][58][59] to see if there are marked differences for the fumaric acid OH 1 H resonances as compared to the NH + 1 H resonances. In this context, there is also work that combines molecular dynamics with GIPAW simulation. [61][62][63][64][65] Note, however, that it is curious that this study has shown excellent agreement between experiment and GIPAW calculation for the NH + 1 H resonances even though the GIPAW calculation corresponds to 0 K. In addition, it would be interesting to investigate whether these discrepancies change if alternative calculation approaches are employed, such as the use of a hybrid DFT functional, e.g., PBE0 or the combination of a GIPAW calculation with a calculation on an isolated molecule at a higher level of theory, as described by Beran and coworkers. [66][67][68] experiment. Helpful discussions with Paul Hodgkinson and Chris Pickard are acknowledged. The calculated and experimental data for this study are provided as a supporting data set from WRAP, the Warwick Research Archive Portal at http://wrap.warwick.ac.uk/***.

Supporting Information
Tables of experimental and GIPAW calculated 1 H, 13 C chemical shifts and 14 N shifts; experimental and simulated PXRD patterns; comparison of 13 C CP MAS spectra recorded at two different magnetic fields (pdf).