A curious case of dynamic disorder in pyrrolidine rings elucidated by NMR crystallography

A pharmaceutical exhibits differing dynamics in crystallographically distinct pyrrolidine rings despite being nearly related by symmetry, with one performing ring inversions while the other is constrained to torsional librations. Using 13 C solid-state magic-angle spinning (MAS) NMR and DFT calculations, we show that this contrast originates from C-H···H-C close contacts and less efficient C-H···π intermolecular interactions observed in the transition state of the constrained pyrrolidine ring, highlighting the influence of the crystallographic environment on the molecular motion. the uncertainty the Summary. Pseudosymmetric pyrrolidine groups exhibiting distinct dynamics are investigated by solid-state NMR and DFT, uncovering the origins to this contrast.

Pharmaceutical products are most often manufactured in their solid forms, benefiting the patient with a convenient route of administration. 1 During the development stage, this solid form is thoroughly characterized in order to identify potential risks associated with stability, polymorphic conversion, 2, 3 and the ability to form hydrates or solvates. 4 Characterization may include X-ray crystallography and using the derived structural model to assess the risks of making a particular solid form into a medicine. The occurrence of crystallographic disorder arising from mobility (i.e. dynamic structural disorder) or the accessibility of multiple conformations/orientations (i.e. static structural disorder) poses several challenges in the risk assessment, due in part to the uncertainty on the atomic positions.
Here, we combine solid-state NMR and DFT calculations in an NMR crystallography approach to investigate a development compound, 1a, which features a curious case of structural disorder. Despite there being two molecules in the asymmetric unit (Z' = 2) each related by pseudosymmetry, surprisingly only one of the two pyrrolidine groups in the structural model appears to be disordered. The solid-state NMR experiments allow the motion and thermodynamic parameters to be characterized in 1a via 13 C spinlattice relaxation time measurements, while the computations allow the origins of these contrasting dynamics to be understood.
The compound investigated herein, 1a, consists of the salt (the counterion is referred to as "a") of a pharmaceutical compound (1) in a 1:1 stoichiometric equivalence. The structural model, determined by X-ray crystallography at 150 K, suggests the presence of a pair of 1a related by C 2 pseudosymmetry, with the disorder in one of the pyrrolidine groups of 1 breaking this symmetry. As shown in Fig. 1a, where the red dotted lines represent the rest of the undisclosed structure, a pyrrolidine group appears to be relatively "ordered" (henceforth referred to as C ord ), while the other group appears to be disordered (henceforth referred to as C dis ) over two positions with occupancies of 0.5 each. However, while C ord appears to be ordered, the situation is ambiguous as its anisotropic displacement ellipsoids 29 have some distortions (see Figure S3 of the ESI), suggesting the presence of vibrations. The crystallographic environment surrounding the two pyrrolidine groups differ in that C dis interacts more closely with the counterion a while C ord interacts primarily with other molecules of 1. All contacts (within 3 Å) involving the pyrrolidine groups are shown in Figure S4 of the ESI. In order to confirm the contrast in the dynamics of the pyrrolidine groups, variable temperature 1 H-13 C cross polarisation (CP) magic- angle spinning (MAS) solid-state NMR experiments and 13 C spinlattice relaxation time measurements, T 1 ( 13 C), have been performed.
When there are two molecules in the asymmetric unit, a doubling of 13 C resonances can be observed if the crystallographic environments between otherwise chemically equivalent sites are sufficiently distinct. As shown in Fig. 1b, a 13 C chemical shift difference of 2.2 ppm is observed between C ord (( 13 C) = 26.7 ppm) and C dis (( 13 C) = 24.5 ppm). The 13 C signals have been assigned to their sites in the structural model using gauge-including projector augmented-wave (GIPAW) 30 DFT calculations as part of CASTEP. 31 The calculations were performed for both conformations of C dis , and the average GIPAW calculated ( 13 C) chemical shifts are 26.7 ppm and 24.3 ppm for C ord and C dis , respectively, resulting in a computed difference of 2.4 ppm. These calculated results, shown on Fig. 1b as sticks, are in excellent agreement with the experimental results.
As the pyrrolidine groups consist of saturated heterocycles, they can exhibit dynamics in the form of ring inversions, 32, 33 analogous to those observed in cyclohexane. 10,34 In order to investigate the dynamics, 1 H-13 C solid-state CP MAS NMR and T 1 ( 13 C) measurements were performed at 10°C steps between 0°C and 60°C. As shown in Fig. 2a, there are no significant changes to the 13 C chemical shifts of C ord or C dis as the temperature is increased, and this is also true for all the other resonances (not shown on the figure). Supported by differential scanning calorimetry (see Figure S5 of the ESI), this suggests that no phase changes or major structural changes are occurring between these temperatures.
The T 1 ( 13 C) at 20°C for C ord and C dis were 9.7 s and 1.4 s, respectively, and all T 1 ( 13 C) values are shown on Fig. 2b and have been tabulated in Table S1 of the ESI. These short T 1 ( 13 C) suggest that both C ord and C dis are dynamic. To place these values into context, the T 1 ( 13 C) at 20°C of the rigid carbons of 1a are >100 s, whereas the T 1 ( 13 C) of rotating methyl groups on 1a are 11 s and 15 s at 20°C. The relationship between T 1 ( 13 C), the correlation times (τ c ), and the activation energy are well known, and have been interpreted using the Bloembergen-Purcell-Pound model. [35][36][37] Assuming it follows the Arrhenius equation, measuring the T 1 ( 13 C) relaxation times as a function of the temperature allows for the activation energy to be extracted (see Eq. S1 to S3 of the ESI). As we have employed a fixed dipolar coupling constant using a C-H bond length of 1.09 Å and assume no motional averaging of the dipolar coupling, the value of τ 0 is an estimate and was not further considered in our analysis.
A plot of T 1 ( 13 C) as a function of the temperature is shown in Fig.  2b, with the fits using Eq. S1 to S3 being in excellent agreement with the experimental results (R c ² > 0.96). The extracted activation energies are 11 ± 2 kJ mol 1 for C ord and 16 ± 3 kJ mol 1 for C dis , with all parameters being summarized in Table 1. The higher activation energy of C dis has been attributed to dynamics in the form of ring inversions, which is also supported by the X-ray structure. In contrast, having a single favourable conformation, short T 1 ( 13 C) relaxation times, and anisotropic displacement ellipsoids suggesting the presence of vibrations, we associate the lower experimental activation energy of C ord to torsional librations rather than ring inversions. The activation energy of C dis is very similar in value with the calculated energy of 17.2 kJ mol 1 for the pyrrolidine group in proline performing a ring inversion. 38 In order to understand why C dis is capable of exhibiting ring inversions while C ord is only librating, transition state calculations were performed using CASTEP. These calculations search for the energy maximum between two conformations (puckered up & down) using the linear synchronous transit method. 39,40 Each model was optimized with constrained unit cell parameters prior to the calculations, and the transition state calculations were performed individually for both C ord and C dis . In the case of C ord , while only a single position was observed experimentally, a tentative structure for the second conformation was generated through modelling and DFT optimizations.
The calculations performed on the full structures, shown as teal diamonds in Fig. 3, indicate that the two conformations of the pyrrolidine group, puckered up (left) and down (right), have approximately equal energies for C dis , whereas a 22.3 kJ mol 1 energy difference is observed for C ord . These results suggest that both conformations of C dis are energetically favourable, while only the conformation that was experimentally observed in the structural model for C ord is favourable. Further, the calculated transition state energy barrier for C dis relative to the puckered down conformation is 17.8 kJ mol 1 , in excellent agreement with the experimentally measured activation energy of 16 ± 3 kJ mol 1 . We propose that this energy barrier is low enough to permit the pyrrolidine ring to undergo dynamics in the form of ring inversions, with both conformations of C dis being accessible. In contrast, the transition state energy of a ring inversion for C ord is 31.7 kJ mol 1 relative to the starting geometry, which is not in agreement with the experimental show the fits using Eq. S1 to S3 of the ESI and the values from Table 1. Table 1. Experimental thermodynamic parameters obtained from fitting the T 1 ( 13 C) in Fig. 2b for 1a using Eq S1 to S3 (see the ESI), including the correlation coefficient (R c ²), as compared to the DFT-calculated activation energies performed on complete ring inversions.

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Please do not adjust margins NMR results of 11 ± 2 kJ mol 1 . The clear discrepancy between the computational and experimental results for C ord suggests that for this ring, the barrier for a ring inversion is too high, and thus the libration is observed experimentally. † To understand why C dis is exhibiting ring inversions while C ord is only librating, a series of structural models were created. The first set of models consisted of structure 1a but the counterions "a" have been removed while maintaining periodicity (red squares), and the second set consisted of completely isolating either molecule of 1 in a cell enlarged by 9 Å along the a, b, and c axes of the unit cell (purple circles). These models allow interactions arising from the crystal packing to be removed selectively. 41 As shown in Fig. 3, there is a clear contribution to the transition state energies from crystal packing. The intermolecular interactions involving C ord and C dis can be identified based on the molecules involved, either between two molecules of 1 (denoted here as 1···1) or between molecules of 1 and a (denoted here as 1···a). In the case of C dis , removing the counterion a has lowered the calculated energy barrier by 5.1 kJ mol 1 , whereas a reduction of 2.8 kJ mol 1 was observed upon isolating the molecule 1 that has C dis . In contrast, isolating the molecule 1 that has C ord reduced the energy barrier of C ord by 17.2 kJ mol 1 , whereas removing the counterion a merely reduced the barrier by 1.2 kJ mol 1 . Notably, in the isolated molecule of 1, the energy of both conformations of C ord are now nearly the same, and the energy barriers are similar for both C dis and C ord due to the removal of the intermolecular interactions. Evidently, the intermolecular interactions involving C ord and C dis are distinct, with 1···1 interactions playing a larger role in the energy barrier for C ord and 1···a interactions being more important for C dis .
The interactions in the structural model were analysed in detail and are shown in Fig. 4, illustrating all atoms within distances shorter than the sum of their van der Waals radius and near hydrogen atoms for both conformations (puckered up & down) of both pyrrolidine rings. C ord exhibits mostly 1···1 interactions (Fig 4. a, b), whereas C dis presents both 1···1 and 1···a interactions (Fig 4. c, d). In the case of C dis , there are six and eight atoms within this specified radius of any hydrogen atom in the ring when puckered up and down, respectively, compared to eight and ten atoms for C ord in the same conformations.
The significance of these interactions was further investigated using DFT calculations performed on molecular cluster models (tabulated in Table S2 of the ESI), [42][43][44] noting that 1···a interactions have highly stabilizing energies due to their opposing charges. Interestingly, the energies of the 1···a interactions involving C dis are very similar for both conformations, with values of 166.3 kJ mol 1 and 167.2 kJ mol 1 when puckered up and down, respectively. This difference may have been reflected in the CASTEP calculations as a slightly higher stability of the puckered down conformation of C dis (see Fig.  3). Meanwhile, there is a much larger disparity in the energies of the interactions involving both conformations for C ord . For example, the contributions from 1···1 interactions from beneath the ring (relative to Fig. 1a) is 51.8 kJ mol 1 when C ord is puckered up (experimentally observed conformation), and 62.3 kJ mol 1 when puckered down (not experimentally observed). The differences in these interaction energies may partially explain the origin of the energy gap of 22.3 kJ mol 1 between both conformations of C ord in the CASTEP calculations performed on the full structure of 1a (see Fig. 3), and why a single librating conformation is observed in the structural model.
In order to decompose the intermolecular contributions to the energy barriers for the dynamics of C dis and C ord , the approach discussed above was applied to the transition states obtained from the DFT calculations (see Table S2 of the ESI). In this case, the energies involving specific intermolecular interactions were computed for the transition states and compared to the puckered up / down conformation, for both C dis and C ord . The energy barrier for the ring inversions of C dis appears to originate primarily from the weakening of C-H···O interactions originating from 1···a, with a difference of 7.4 kJ mol 1 between the puckered up conformation and the transition state, thus destabilizing the transition state of C dis . This further supports the results obtained from the calculations presented in Fig. 3b, where removing the counterion reduced the energy barrier of C dis . However, the overall calculated energy barrier (17.8 kJ mol 1 ) is still small enough to allow ring inversions to occur. In terms of C ord , the destabilizing 1···1 interactions originates mainly from a build-up of close contacts between neighbouring pyrrolidine hydrogens (C-H···H-C), and in part due to less efficient C-H···π Fig. 3 Calculated relative energies as a pyrrolidine group achieves a ring inversion performed on models of (a) C ord and (b) C dis using: the original structural model of 1a (teal diamonds), 1a maintaining periodicity but with the counterion removed (red squares), and isolated molecule of 1 (purple circle). A depiction of the models are shown above, represented by balls and sticks, providing a frame of reference of the conformations.

Fig. 4
Diagrams showing all atoms within distances shorter than the sum of their van der Waals radius and near hydrogen atoms in either pyrrolidine groups of the optimized structural models of 1a when: (a) C ord is puckered up, (b) C ord is puckered down, (c) C dis is puckered up, (d) C dis is puckered down. The structure in (b) was obtained from DFT optimizations and has not been experimentally observed. The arrows highlight the carbon atoms of interest. interactions in the transition state. Overall, this imposes a much greater energy barrier for a ring inversion to occur (31.7 kJ mol 1 ), and results in a higher relative energy for the puckered down conformation. This explains why a significant reduction in the energy barrier for C ord was observed in the isolated molecule (cf. Fig. 3a).
In order to investigate the wider significance of the phenomenon investigated here, we have searched the Cambridge Structural Database (version 5.41) 45 for disordered pyrrolidine rings using the structure on Fig 1a as the search query. Full details on the analysis can be found in section 4 of the ESI. We have identified 179 examples where the pyrrolidine ring exhibits structural disorder, with 20 structures having a Z' = 2 and a case of contrasting disorder akin to our compound 1a (see Table S3 of the ESI). Further, pyrrolidine ring inversions are shown to have implications on the structure of proline 38,46,47 and proline-containing peptides. 48,49 Evidently, disorder in pyrrolidine rings is not a rare occurrence, and is likely also the case for other five-membered rings. The approach demonstrated here of combining solid-state NMR and DFT calculations may help to unravel these cases of disorder, while providing a theoretical framework for their origins. Interestingly, while intermolecular interactions have previously been shown to play a role in dynamics, 50-54 their influence has been manifested here as two pseudosymmetric pyrrolidine groups exhibiting distinct dynamics.

Conclusions
In conclusion, the disorder observed in C dis of compound 1a has been attributed to the occurrence of dynamics in the form of ring inversions with an activation energy of 16 ± 3 kJ mol 1 . Despite the pseudosymmetry of the structure (Z' = 2), ring inversions were only observed for C dis while C ord was constrained to torsional librations with an activation energy of 11 ± 2 kJ mol 1 . DFT calculations suggest that the constraints on C ord originate from neighbouring C-H···H-C and less effective C-H···π intermolecular interactions between 1···1 in the transition state and the ring inversion product. Meanwhile, the counterion plays a more direct role in the ring inversions of C dis , albeit with a weaker effect. The strategy of combining solid-state NMR and DFT calculation has allowed thorough details on the disorder to be extracted individually for both rings, overall providing significant improvements to the structural understandings of 1a.

Conflicts of interest
There are no conflicts to declare.