Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions

Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state 13C and 15N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study.


Acetaminophen
The experimental 13 C and 15 N chemical shifts for acetaminophen used here were first reported in Ref [2]. Based on private communications with those authors, the referencing of the spectra reported there were corrected using new measurements on form I. Specifically, the original reported 15 N isotropic shifts from Ref [2] were shifted by +22.84 ppm to obtain properly referenced isotropic shifts on the neat nitromethane scale. These values were then converted to the solid NH 4 Cl scale as previously described. [1] Similarly, the revised form I 13 C resonances were shifted by +0.50 ppm relative to those published in Ref [2]. This correction reduces the discrepancy between the 13 C shifts from Ref [2] and those reported in Ref [3] from ∼0.9 ppm to ∼0.3-0.4 ppm. These referencing corrections from form I were then applied to forms II and III. Table S1: Experimental and predicted isotropic 13 C and 15 N chemical shifts for acetaminophen forms I, II and III. Predicted shifts are reported using the 2-body, cluster, and combined cluster/2-body models with charge embedding using the PBE0 density functional and both fragment and GIPAW calculations using the PBE density functional (in ppm). The raw chemical shieldings can be obtained from the empirically scaled chemical shieldings reported here using the linear regression parameters reported previously [1]    3 Testosterone Table S3: Experimental and predicted isotropic 13 C chemical shifts for testosterone. Predicted shifts are reported using the 2-body, cluster, and combined cluster/2-body models with charge embedding using the PBE0 density functional and both fragment and GIPAW calculations using the PBE density functional (in ppm). The raw chemical shieldings can be obtained from the empirically scaled chemical shieldings reported here using the linear regression parameters reported previously [1]

Analysis of Optimized Crystal Geometries
Figure S1 presents unit cell overlays between the experimental and relaxed crystal structures. Quantitative root-mean-square deviations in 15-molecule clusters (RMSD15 values) are reported in Table S4, with and without hydrogen atoms. The overlays and RMSD15 values demonstrate generally excellent agreement between the experimental and optimized structures, especially for heavy atoms. Of course, the use of fixed, experimental lattice parameters during the theoretical optimization helps ensure generally good agreement between the two sets of structures. For acetaminophen forms I and II, only minor deviations (e.g. in the form I methyl group) are observed between the experimental and optimized structures, and RMSD15 values are less than 0.1 Å for non-hydrogen atoms. Slightly larger differences are observed in the orientations of the rings in form III, leading to RMSD15 of 0.15 Å. For phenobarbital, subtle differences can be observed in the angle of the form II phenyl groups at the quaternary carbon, while the two form III structures are in excellent agreement. In α-testosterone, the rings are slightly displaced in the optimized structure relative to the experimental one, but the RMSD15 values are only 0.12 Å. For β-testosterone, the optimized heavy atom positions agree very well with experiment. If one includes hydrogen atoms, the RMSD15 values increase. Of course, hydrogen positions from x-ray diffraction are often unreliable, and in many cases the optimized bond lengths and angles look more reasonable than the experimental ones. In β-testosterone, the orientations of the water molecules also changes somewhat, which contributes to the 0.19 Å RMSD15 value there. In phenobarbital form II, the large 0.25 Å RMSD15 stems from differences in the rotation of the methyl groups and the orientations of the phenyl rings.
We also consider the structural similarities in the individual crystallographically unique monomers, with RMSD values listed in Table S5. RMSD values are ∼0.1 Å or less in all cases, with the maximum differences of up to ∼0.2 Å.

Testosterone
Form II Form III Figure S1: Overlays of experimental (colored by element) and optimized crystal structures (green).

Intra-and Intermolecular Contributions to Chemical Shielding
The fragment approach allows facile decomposition of the chemical shielding contributions arising from intra and intermolecular contributions. We analyze these features in two ways. First, we computed the chemical shieldings for each isolated, crystallographically-unique monomer (in the same intramolecular conformation as it adopts in the crystal, but with no other molecules or embedding charges around it). This gives the purely intramolecular shielding contributions, σ A isolated monomer . The difference between the isolated monomer shielding for atom A and the full crystalline chemical shielding for the same atom σ A crystal (as computed according to Eq 1 in the main paper) corresponds to the intermolecular contribution: To understand the role of intra-versus intermolecular contributions to the differences in shieldings observed among the different polymorphs/crystallographic environments, we then took the difference between for example, the form I and form II acetaminophen intra-and intermolecular shieldings: Note that the ∆σ notation here simply refers to the change in the shieldings, rather than corresponding to a two-body contribution ∆ 2 σ of the sort found in Eq 2 of the main paper. These differences were computed for each atom in acetaminophen. Analogous calculations were performed comparing the shieldings on monomers IIIa and IIIb from form III acetaminophen relative to form I. The same procedure was also repeated for phenobarbital form IIa, IIb, and IIc monomers against the form III one, and for αu and αv testosterone monomers relative to the β one. Form III phenobarbital and β-testosterone were chosen simply because they had only a single crystallographically unique monomer in the unit cell (Z = 1). RMS shielding changes are plotted for each case in Figure S2. From Figure S2, we observe that the changes in chemical shielding arising from intramolecular contributions among the different crystallographic environments are generally smaller than those arising from intermolecular contributions. In other words, while subtle changes in the monomer conformations do affect the chemical shieldings, changes in the intermolecular packing have a larger impact on the chemical shielding variations observed across these different crystal forms.
A second way to analyze the data comes from comparing the discrimination among different potential assignments using an embedded 1-body fragment model instead of the embedded 2-body one advocated in our previous work. Figure S3 presentsχ 2 plots for each of the three systems comparing the discrimination achieved by 1-body and 2-body models with both PBE and PBE0. For both acetaminophen and phenobarbital, the RMS errors obtained with the 1-body model are somewhat larger than those obtained with the 2-body one. More importantly, the discrimination among correct and incorrect assignments is notably larger with the 2-body models. For testosterone, the RMS errors for the correct assignment are surprisingly somewhat smaller with the 1-body model than the 2-body one (e.g. 1.75 vs 2.09 ppm for PBE0), but the discrimination is increased with the 2-body model.   Figure S3: Reduced χ 2 analysis using 13 C isotropic shifts illustrating the impact of pairwise contributions on the resolution of difference crystal environments. Results are reported for both the PBE0 and PBE density functionals using all acetaminophen, phenobarbital and testosterone polymorphs.