DOI: 10.1021/cg900538g
Predicting Multicomponent Crystal Formation: The Interplay between Homomeric and Heteromeric Interactions
2009, Vol. 9 4529–4532
Guangwen He,*,† Pui Shan Chow,† and Reginald B. H. Tan*,†,‡ † Institute of Chemical & Engineering Sciences, A*STAR (Agency for Science, Technology and Research), 1 Pesek Road, Jurong Island, Singapore 627833, and ‡Department of Chemical & Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576
Received May 19, 2009; Revised Manuscript Received July 1, 2009
ABSTRACT: Current approaches to improving physicochemical properties without changing desirable therapeutic behavior of active pharmaceutical ingredients include formation of multicomponent crystals such as salts and cocrystals. We report a technique that can provide a priori prediction for multicomponent crystal formation based on intermolecular pair interactions characterized using pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR). The accuracy of our prediction technique in comparison to the well-adopted ΔpKa rule of thumb is tested against 25 molecular pairs including protonated amines, nitrogen-protonated heterocyclic bases, phenols, and carboxylic acids dissolved in six solvents. While the ΔpKa rule results in numerous contradicting exceptions, our technique robustly predicts multicomponent crystal formation. These results reveal that the application of PGSE NMR for determining the self-diffusivities of molecules and subsequently the strengths of intermolecular interactions has the potential to be developed into a standard and robust protocol for the study of multicomponent solution chemistry.
*Corresponding author. Tel: (65) 6796 3779. E-mail: he_guangwen@ ices.a-star.edu.sg.
application, this rule of thumb is inadequate as shown by a recent review,7 in which the authors suggested that a crystal engineering approach based on complementary intermolecular interactions rather than just a single ΔpKa value should be applied for salt/cocrystal screening. The concept of forming appropriate supramolecular synthons to facilitate the design of multicomponent crystals has been widely adopted since its invention.3,4,20,21 However, examining the Cambridge Structural Database for a statistical analysis of suitable packing motifs to form synthons and to design new crystals still remains a time-consuming and laborintensive task. Furthermore, the outcomes of such searches usually serve as empirical guidelines that molecular association may exist between certain functional groups, rather than definitive answers for multicomponent crystal formation. The link between solution complexation and solid-state formation has been studied extensively in the literature.8,22-27 Higuchi and co-workers studied the solution complexation and revealed different binding tendencies of small organic molecules in aqueous solution that could shed some light on screening for cocrystallization tendency.26,27 Rodrı´ guez-Hornedo and coworkers8,23-25 constructed phase solubility diagrams of cocrystals based on solubility product and solution complexation and used these phase diagrams to explain how supersaturation is created to induce cocrystal formation. However, no a priori prediction for salt/cocrystal formation was made in these studies. Limited understanding of the solution physical chemistry often leads to difficulty in predicting which potential pairs of API and coformer form molecular salts or cocrystals effectively. The assembly of molecular structures resulting in either single- or multicomponent crystal formation relies on the details of the intermolecular interactions such as strength, extent, and preferred orientation. Considering a solution composed of two solutes and one solvent, it is hypothesized that if the homomeric interactions between the same solutes
r 2009 American Chemical Society
Published on Web 09/02/2009
Introduction Continuous improvement of the physicochemical properties of active pharmaceutical ingredients (APIs), such as solubility, bioavailability, dissolution rate, stability, hygroscopicity, crystallinity, and taste, represents an emerging area of research and development.1-5 Current approaches to improving solid-state properties without changing desirable therapeutic behavior include formation of alternative forms of APIs such as salts and cocrystals.6,7 Recent advances in cocrystal screening and prediction have facilitated the development of systematic approaches for the discovery and design of cocrystals to replace previous trial-and-error techniques. These advances include solubility-based approaches,8-10 thermal methods,11 near-infrared spectroscopic techniques,12 screening technique using pair interactions,13 computer simulation,14 and statistics-based design.15 Furthermore, the prediction of the likelihood and the strength of hydrogen bonding based on the basicity scale pKHB16 and the pKa slide rule17 could serve as an indication of possible cocrystal formation. However, few of these methods are able to distinguish between the probable formation of a cocrystal or a molecular salt. Molecular salts and cocrystals are both classified as multicomponent crystals. Salts are distinguished from cocrystals by the occurrence of proton transfer to form oppositely charged pairs. Presently, ΔpKa of an acid and a base is used as a rule of thumb to estimate the extent of proton transfer as an indication of the possible formation of salts.7 It is proposed that a salt would form if the difference in dissociation constants of the acid and the base, that is, ΔpKa (= (pKa)base - (pKa)acid) is greater than 3,18 and a negative ΔpKa will almost exclusively result in cocrystal formation.19 However, it is surmised that ΔpKa is incapable of predicting salt or cocrystal formation when its value falls between 0 and 3.18 Despite its wide
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are stronger than the heteromeric interactions between different solutes, single-component crystals are likely to form. On the contrary, multicomponent crystals such as salts and cocrystals might form if the heteromeric interactions dominate; the extent of the preferential heteromeric affinity will determine whether the resulting crystals are salts or cocrystals. In seeking facile experimental techniques to characterize the intermolecular pair interactions in solutions, we applied pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR) to measure long-time self-diffusivities of molecules of interest.13 The classical theory of molecular self-diffusion (Brownian motion) deals with the random movement of an individual solute particle due to stochastic collisions with other solute molecules and the solvent molecules in the surrounding medium. Therefore, a systematic measurement of molecular self-diffusion should provide useful information that correlates with intermolecular interactions. In this work, the hypothesis that PGSE NMR could be used as a tool in predicting the formation of multicomponent crystals and the extent of proton transfer between the acid and the base is tested against 25 molecular pairs including protonated amines, nitrogen-protonated heterocyclic bases, phenols, and carboxylic acids dissolved in six respective solvents (polar protic, polar aprotic, and nonpolar). The model systems chosen represent a complex situation where outcomes of solution crystallization of the molecular pairs range from 7 salts, 13 cocrystals to pairs that do not form any multicomponent crystals. The results provide a new perspective of how the fundamentals of intermolecular interactions in solutions could be correlated with the solid formation of single- or multicomponent crystals if these solutions are supersaturated appropriately. Experimental Section The model compounds used in this study are quinine (abbreviated as QUI), ethenzamide (ETZ), carbamazepine (CBZ), saccharin (SAC), (1R,2S)-(-)-ephedrine (EPH), 4,40 -bipyridyl (BPD), triethylenediamine (TED), 2-aminopyrimidine (APM), 4-(dimethylamino)pyridine (DMAP), 4-pyrrolidinylpyridine (PDP), paracetamol (PAC), 2-methoxy-4-nitrophenol (MNP), 4-nitrophenol (NP), ibuprofen (IBP), aspirin (ASP), p-aminobenzoic acid (PABA), succinic acid (SA), glutaric acid (GA), adipic acid (AA), pimelic acid (PA), maleic acid (MA), salicylic acid (SAL), and indole-2-carboxylic acid (ICA). Solvents used are ethanol (EtOH), methanol (MeOH), acetonitrile (ACN), ethyl acetate (EA), deuterium oxide (D2O), and methanol-d4 (MeOH-d4). Details of molecular pairs and experimental conditions can be found in the Supporting Information. Cocrystallization experiments were conducted by supersaturating the solutions through cooling or slowly evaporating the solvents. Single crystal X-ray diffraction (XRD) analysis on the resulting crystals was conducted using a Rigaku Saturn 70 CCD area detector with Mo KR radiation=0.71073 A˚ at 50 kV and 40 mA. The cell parameters of the resulting crystals were compared with those reported in the Cambridge Structural Database or peer-reviewed literature to confirm whether the resulting crystals are single- or multicomponent crystals. The long-time self-diffusivities of model compounds in solutions were measured using 1H pulsed gradient spin-echo nuclear magnetic resonance with a 400 MHz spectrometer at 296 K. The means and standard deviations of the Pair Interaction Index (vide infra) were approximated by performing Monte Carlo simulation, where random samples of K values were generated based on independent normal distributions with means and standard deviations obtained by linear regression (eqs 1 and 2).
He et al. All pKa values of the model compounds were calculated using ACD/pKa DB 11.0, Advanced Chemistry Development, Inc. Note that the pKa values obtained are at 298 K and zero ionic strength in aqueous solutions. On the basis of the above-mentioned calculated aqueous pKa, the pKa values in alcohol solutions were estimated using empirical equations reported in the literature.28 The values were rounded to the first decimal place.
Results and Discussion Solution Cocrystallization. Actual cocrystallization outcomes of all molecular pairs were determined in our lab and/ or extracted from the literature.7,11,13,29-35 These results are used to benchmark the accuracy of the ΔpKa rule of thumb and our prediction technique based on self-diffusion measurement using PGSE NMR. Long-Time Self-Diffusivity. According to Batchelor’s work,36 in a dilute multicomponent solution where solute molecules (two species i and j) are considered as hard spheres and the solvent may be regarded as a continuum, only bimolecular interactions between the solute particles and the interactions between solute particles and the solvent are significant. The long-time self-diffusivity of the solute molecules i and j in the solution can be respectively written as Di xj xi ¼ 1 þ Kii xi þ Kij xj ¼ 1 þ Kii þ Kij Di0 xi ðijÞ
¼ 1 þ Kii xi Dj ¼ 1 þ Kjj xj þ Kji xi ¼ 1 þ Dj0 ðijÞ
¼ 1 þ Kjj xj
ð1Þ ! xi xj Kjj þ Kji xj ð2Þ
These equations are valid only in the dilute limit when only pair interactions are considered. D and D0 are the absolute and Stokes-Einstein self-diffusivities of solute molecules, and x is the molar fraction of the solute. As shown in eq 1, for any given j concentration xj, the self-diffusivity of i decreases with increasing i concentration xi, suggesting that the mobility of i molecules is increasingly hindered when its own concentration increases. The pair contributions of the selfdiffusivity, Kii and Kij (whose values are usually negative), characterize mobility hindrance of self-diffusing solute i in the absence and presence of solute j, respectively. The values of K are the integral measures of the hydrodynamically weighted particle interactions. However, since eqs 1 and 2 are only valid in the dilute limit, K could not be used to characterize solution complexation. When solute molecules are treated as spherical particles in dilute systems, K µ f(exp(-μ/kT)), where μ is the pair interaction potential.36 The use of simple fluid theories to characterize the intermolecular interactions in solution by treating solute particles as impenetrable hard spheres with attractive tails has achieved qualitative and somewhat quantitative success.37 The general applicability of these theories has been independent of the particle size and the nature of the interaction potential. As a result, both solutes i and j should experience the same mobility hindrance when they are dissolved together into a solvent. This hypothesis can be experimentally verified in Figure 1, where Kii(ij) and Kjj(ij) are shown to be comparable to each other within experimental uncertainties, suggesting that the K’s are capable of characterizing particle interaction potential.
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Figure 1. Comparison of mobility hindrance Kii(ij) and Kjj(ij) for all molecular pairs in solutions. Figure 3. ΔpKa values of model molecular pairs. The dashed lines divide the different regions determined by the ΔpKa rule of thumb: salt formation for ΔpKa > 3; cocrystal formation for ΔpKa < 0; and inconclusive if 0 e ΔpKa e 3. Please see Figure 2 caption for the details of the solid symbols. Note that for model pairs SAC þ CBZ and SAC þ IBP, only the ΔpKa values in methanol are calculated and shown.
Figure 2. Pair interaction indices, (KijKji)/(KiiKjj), for model molecular pairs in solutions.
Intermolecular Interaction. The pair contributions of the self-diffusivity, Kii (Kjj) and Kij (Kji), are strongly correlated with the strengths of homomeric and heteromeric interactions respectively. Therefore, a group parameter, (KijKji)/(KiiKjj), defined as the Pair Interaction Index, is chosen to represent the relative magnitude of the heteromeric and homomeric pair interactions. This index was experimentally determined for each pair as an indicator of whether the formation of molecular salts or cocrystals is feasible. Figure 2 shows the values of the Pair Interaction Index, with respective experimental variabilities, for 25 different solute pairs. The symbols represent the outcomes of the crystallization experiments, namely, salt formation (diamonds), cocrystal formation (squares), or no multicomponent crystal formation (triangles). A Pair Interaction Index value of unity marks the boundary (solid line in Figure 2) of the two regions where either the homomeric or the heteromeric interactions dominate.
It clearly demarcates that there will not be multicomponent crystal formation when the index is less than unity because the homomeric interactions tend to be stronger. Therefore, single-component crystals are more likely to form. Our predictions successfully capture this phenomenon (triangles in Figure 2). On the other hand, when the index is greater than unity, that is, the heteromeric interactions are stronger, the distinction between the salt and cocrystal forming regions remains ambiguous. The magnitude of the index qualitatively indicates the extent of the proton transfer between the pair of organic acid and base, however, the direct quantitative correlation of the index and the strength of intermolecular interactions is not fully elucidated. Generally, we find that the differences in the indices of the salt and cocrystal forming pairs are statistically significant (e.g., the salt-cocrystal boundary is arbitrarily drawn as a dashed line at index=3) such that the index should also serve as a useful indicator of salt and cocrystal formation tendency. The three exceptional cases in our study are TED þ GA, APM þ PABA, and MNP þ PDP (shown in oval enclosure in Figure 2). These pairs form cocrystals in solution cocrystallization experiments but salt formation is suggested by the high values of indices. These discrepancies reveal several challenging areas in which our prediction technique could be improved: the index is only an integral measure of the strength of particle interaction but provides no information on the subtleties of the interaction such as hydrodynamic boundary conditions and preferred orientation, nor does it account for the asymmetry of particles; the index characterizes the particle interactions between solute molecules in solution, which is closely correlated with but not directly identical to the intermolecular interactions in the solid state. Screening for Multicomponent Crystal Formation Using the ΔpKa Rule of Thumb. A compilation of the ΔpKa values of model molecular pairs is shown in Figure 3 as a comparison with our proposed technique. The ΔpKa rule of thumb works reasonably well in predicting salt formation (diamonds); however, it is not as reliable in predicting cocrystal formation (squares), and is not able to predict the cases when no
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multicomponent crystals will form (triangles). The discrepancies between the predictions and the actual experimental outcomes are indicated in the oval enclosures. Childs et al.7 and Stahly38 have discussed extensively the limitations of the ΔpKa rule, suggesting that it should only be used as empirical guidance on initial screening for the tendency of multicomponent crystal formation, instead of as a predictive tool. Conclusion It is worth noting that the solvent plays a significant role in molecular mobility thus acting as either a facilitator or an inhibitor of the homomeric and heteromeric interactions. The prediction technique for multicomponent crystal formation has been tested against six solvents: (i) ethanol, methanol, acetonitrile, and ethyl acetate that are the actual solvents used in the solution cocrystallization experiments; (ii) deuterium oxide and methanol-d4 where significantly less amount of solute (up to 10-fold less, which is critical in multicomponent crystal screening for precious APIs) could be used for good PGSE NMR experiments. The resulting spectra show remarkably improved signal-to-noise ratio due to the suppressed solvent peaks. The prediction technique works well for all the solvents used. The agreement between our predictions and the outcomes of solution cocrystallization experiments of several groups of APIs and coformers including protonated amines, nitrogenprotonated heterocyclic bases, phenols, and carboxylic acids is revealing. A single prediction parameter, the Pair Interaction Index, robustly predicts the formation of single- or multicomponent crystals including salts and cocrystals reasonably well for the model systems under study. This technique could serve as a supplementary tool to the current state-of-the-art of multicomponent crystal prediction and screening. Lastly, besides prediction for salt/cocrystal formation, we emphasize that the application of PGSE NMR for determining the self-diffusivities of molecules and thereby the strengths of intermolecular interactions has the potential to be developed into a standard and robust protocol for the study of multicomponent solution chemistry. Acknowledgment. This work was supported by the Science and Engineering Research Council of A*STAR (Agency for Science, Technology and Research), Singapore. We thank Chacko Jacob and Liangfeng Guo for assistance in NMR experimentation, and Charles F. Zukoski for insightful discussions. Supporting Information Available: Experimental details. This material is available free of charge via the Internet at http://pubs. acs.org.
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