Testing the limits of NMR crystallography: the case of caffeine–citric acid hydrate.

The crystal structure of a new 1 : 2 caffeine–citric acid hydrate cocrystal is presented. The caffeine molecules are disordered over two positions, with the nature of the disorder confirmed to be static by 13C solid-state NMR. NMR linewidths in statically disordered systems reflect the distribution of local chemical environments, and this study investigates whether the disorder contribution to 13C linewidths can be predicted computationally. The limits of NMR crystallography calculations using density functional theory are tested by investigating how geometry optimisation conditions affect calculated NMR parameters. Careful optimisation is shown to reduce differences between 13C constants of symmetry-related sites to about 0.1 ppm. This is just sufficient to observe a correlation between calculated and experimental linewidths, and also show that systematic errors associated with geometry optimisation do not compromise other applications of “NMR crystallography”. In addition, the unit cell enthalpies calculated after careful optimisations provide insight into why the disordered structure is adopted.


Testing the limits of NMR crystallography: the case of caffeine-citric acid hydrate -Supplementary Information
shows that the calculation time and number of iterations in the optimisation increases as the convergence conditions are tightened. The calculation times are highly variable, reflecting variations in performance of the HPC platform, and so the number of iterations is the more meaningful parameter. Unsurprisingly, variable unit cell optimisations take the longest time and require the largest number of iterations to converge.
Increasing the tightness of the convergence conditions causes the number of warnings in the optimisation to increase, particularly the "complex landscape" warning. The over-tightening of the force tolerance probably contributes to the increased number of warnings in [3-D]- . However, no warnings were observed in [3], despite the large number of iterations required. In comparison, no dispersion correction was used in [2] and the convergence criteria were looser but "complex landscape" warnings were still present in nearly half of the optimisations.
Electronic Supplementary Material (ESI) for CrystEngComm. This journal is © The Royal Society of Chemistry 2016 The variation in unit cell parameters for the 16 simulated disorder structures was relatively small, with the majority of the parameters changing by roughly 1%. The unit cell length along the c axis reduced by a moderate 2% in all cases during the optimisations. The 1212 pair showed a significant lowering in final energy relative to the other structures, which is reflected by the particularly large change in the angles, which all deviate away from 90˚ upon optimisation. Apart from the 1111 pair, which retains a monoclinic crystal system, the symmetry of the other structures drops to triclinic. The sign of the change in α and β angles from 90˚ is not physically significant.

Fig. S3 shows that the total heavy atom RMSD is correlated with the mean energy difference between symmetry-related pairs as expected. [3-DC] and [3-DO] result in the lowest RMSDs between symmetry-related pairs, though [3-DC]
is not considered to be as physical, as discussed in the main text.

Linewidth Simulation
The homogeneous contribution to the 13 C linewidth consists of a "nonrefocussable linewidth", ∆ ′ = 1 2 ′ , assumed to be Lorentzian in nature, where T 2 ', is the time-constant for decay of the 13 C magnetisation under spin-echo conditions. T 2 ' values and subsequently Δ' values were calculated from spin-echo experiments, as described the main text, for both CCA and the 1:1 cocrystal. The inhomogeneous contribution, Δ inhomog , includes the broadening due to disorder, ABMS and quadrupolar effects from the nitrogen atoms in caffeine. The latter effects were simply estimated to be the same as those of the 1:1 ordered caffeine-citric acid cocrystal, and calculated by subtracting Δ' from the experimental linewidths for the 1:1 cocrystal, see Table S3. Although the ABMS contribution will be different between the system, they are constant for a given sample and so do [1] [2] not affect the quality of correlation in Fig. 6. The inhomogeneous contributions were modelled using a Gaussian lineshape. The site-specific Δ' values for CCA (Table S2) and Δ inhomog values from the 1:1 cocrystal (Table S3) were used as the input linewidths for a Python script that used pNMRsim 1 to calculate synthetic 13 C spectra for each caffeine site from the isotropic chemical shifts read from the 16 .magres files using the MagresPython 2 library. The sum of these spectra over the 16 disorder structures gave a single spectrum per site, the linewidths of which were deconvoluted in Gsim 3 and tabulated in Table S4.