Assessment of the Stoichiometry of Multicomponent Crystals Using

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Assessment of the Stoichiometry of Multicomponent Crystals Using Only X-Ray Powder Diffraction Data Courtney K. Maguire, and Andrew P. J. Brunskill Mol. Pharmaceutics, Just Accepted Manuscript • DOI: 10.1021/mp5008458 • Publication Date (Web): 15 Apr 2015 Downloaded from http://pubs.acs.org on April 24, 2015

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Molecular Pharmaceutics

Assessment of the Stoichiometry of Multicomponent Crystals Using Only X-Ray Powder Diffraction Data Courtney K. Maguire* & Andrew P. J. Brunskill Merck Research Laboratories, Merck and Co., Inc., 126 E. Lincoln Ave., Rahway, New Jersey, 07065 Keywords: Crystal volume prediction, powder diffraction, powder indexing, solvate stoichiometry, co-crystal stoichiometry

ABSTRACT

Knowledge of the unit cell volume of a crystalline form and the expected space filling requirements of an API molecule can be used to determine if a crystalline material is likely to be multicomponent, such as a solvate, hydrate, salt, or a co-crystal. The unit cell information can be readily accessed from powder diffraction data alone utilizing powder indexing methodology. If the unit cell has additional space not likely attributable to the API entity, then there is either a void or another component within the crystal lattice. This “left over” space can be used to determine the likely stoichiometry of the additional component. A simple approach for calculating the expected required volume for a given molecule within a crystal using an atom based additive approach will be discussed. Coupling this estimation with the actual unit cell volumes and space group information obtained from powder indexing allows for the rapid

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evaluation of the likely stoichiometry of multicomponent crystals using diffraction data alone. This approach is particularly useful for the early assessment of new phases during salt, cocrystal, and polymorph screening, and also for the characterization of stable and unstable solvates.

INTRODUCTION

In the pharmaceutical industry, crystalline phases of the active pharmaceutical ingredient (API) and intermediates are preferred due to their stability, rejection of impurities, and robust processing.1 In many cases the crystal forms under investigation will be multicomponent, including salts, co-crystals, hydrates, or solvates.1 Multiple analytical tools are available for the characterization of multicomponent crystals to assess the identity and stoichiometry of the additional components. The primary characterization techniques will commonly be NMR, GC, HPLC, MS, TGA, vibrational spectroscopy or single crystal crystallography. In almost all situations, a powder X-ray diffraction pattern of the material under evaluation will be acquired. Usually this is solely for the purpose of determining crystallinity and as a “fingerprint” of the phase, rather than truly investigating the nature or composition of the phase. However, buried within the diffraction pattern is a wealth of additional information that is readily extracted to enrich understanding of the phase. In principle, the peak positions and intensities of the diffraction pattern contain all of the necessary information to solve the crystal structure2. However, often full structure solution from powder data is quite challenging, particularly for highly flexible molecules, and crystals with Z’ > 1. The first step to solving a crystal structure from powder data is the determination of the unit cell parameters and space group. The cell volume and symmetry alone can be utilized to make an assessment of the likely contents of the


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crystalline lattice by consideration of the expected molecular volume of the main and likely secondary components. Unit cell dimension and space group information is readily extracted utilizing well established and powerful powder indexing methodologies3-6.

Several approaches have been used to assess the likely cell volume based on the molecular formula, such as the Kempster-Lipson “18 Å³ rule”7, Hofmann atomic additive approach8, and the Ammon functional group based approach9. In all cases, predicted volumes based purely on expected composition assume efficient molecular packing as described by Kitaigorodsky10, whereby the crystalline lattice would not be expected to contain significant voids. Given this assumption, it is clear that a positive discrepancy between the experimental unit cell volume and the predicted volume occupied by the primary component will infer the presence of possible voids or more likely the presence of an additional component in the crystalline lattice. A simple approach that allows for rapid assessment of the likely stoichiometry of multicomponent crystals using powder X-ray diffraction data alone, without proceeding to the significantly more challenging full structure determination, is described within.


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METHODS X-ray Data Acquisition Powder X-ray Diffraction data were acquired on a Panalytical X-pert Pro PW3040 System with an X'celerator detector. The instrument was configured in the Bragg-Brentano configuration and equipped with a sealed tube Cu radiation source with monochromatization to Kα achieved using a Nickel filter. A fixed slit optical configuration was employed, with 1° divergence slits and 0.04° Soller slits. Data was acquired between 2 and 40° 2θ. Samples were prepared by gently pressing powdered sample onto a shallow cavity zero background silicon holder. Indexing Algorithms Powder indexing was performed using the X-Cell algorithm with subsequent Pawley refinement within Materials Studio Reflex module3. Database Extraction Pharmaceutically relevant solvents, counterions, and co-crystal formers were chosen for analysis, as they are likely guests in multicomponent crystals. The Cambridge Structural Database (CSD Version 5.35 + updates (Nov 2013)) was queried to identify single component and multicomponent structures in order to assess volume requirements against those predicted by the various approximations mentioned previously. Searches in ConQuest were conducted using the following filters:

organics only, no disorder, ≤0.075 R value, atoms with atomic mass ≤


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Bromine, room temperature structures, and no powder data. Room temperature structures were used since most powder diffraction data is collected under ambient conditions. Solvent Accessible Surface Boundary Calculations The volume occupied by the secondary component was assessed using Mercury11. At least ten structures that contained a given secondary component were chosen at random and each manually examined using Mercury to check for unoccupied void space. The volume requirements needed for the secondary component were calculated.

To do this, the secondary

component molecule was deleted from the structure and hydrogens of the main component normalized. The volume encompassed by the solvent accessible surface was calculated using a probe radius of 1.2 Å and an approximate grid spacing of 0.7 Å, which are the default values in the Mercury software. The void space determined was then averaged across the ten structures. The values were compared to those obtained from using the Kempster-Lipson method7, the Hofmann method8, and also simple space filling determined using the molecular mechanics software Spartan12.

Microsoft Excel was used to design the spreadsheet used for calculating

volume requirements. RESULTS AND DISCUSSION The commonly employed approaches for predicting unit cell volume based on molecular formula were investigated. The experimental cell volumes for 100 anhydrous pharmaceutical-like compounds were compared for two of the most commonly employed approaches for cell volume estimation. In the Kempster-Lipson (18Å³) rule, the estimated unit cell volume ( ) is simply the number of non-hydrogen atoms (N) in the compound multiplied by 18Å³, and this value is


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then multiplied by the number of molecules expected within the cell (Z). In the Hofmann approach, each atom type (ni), including hydrogens, is considered independently to calculate the expected molecular volume. The number of atoms of element i in the molecule is multiplied by the average volumes ̅ of that particular element. This is then multiplied by the expected number of molecules per cell (Z). Equations 1 and 2 describe these approaches.7, 8 Equation 1, Kempster-Lipson Cell Volume Estimation: = × 18 × Equation 2, Hofmann Cell Volume Estimation: = ∑ ̅ x Z Figures 1a and b show the correlation between the actual unit cell volumes and the predicted cell volumes for the Kempster-Lipson rule and the Hofmann approach, respectively. It is clear that the Hofmann volume estimate is superior to the Kempster-Lipson rule in predicting experimental volume. Both the slope and intercept for the Hofmann approach (Fig 1b) are superior to that of the Kempster-Lipson Rule (Fig 1a).


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Figure 1a: Comparison of Experimental vs Predicted Cell Volume of Selected Crystal Structures Using Kempster & Lipson (Rule of 18Å³) Approach

Figure 1b: Comparison of Experimental vs Predicted Cell Volume of Selected Crystal Structures Using Hofmann Approach Since the second component in multicomponent crystals would not be covalently bound and would associate via weaker interactions, such as hydrogen or ionic bonding, it was a concern that the Hofmann atomic volume estimates could not be applied directly and would have to be modified. To address this concern, multicomponent crystals for selected solvents and coformers/counterions were extracted from the CSD. Experimental cell volumes for


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multicomponent crystals were evaluated in the same manner as for the anhydrate structures. It was found that again the Hofmann approach was superior to the Kempster-Lipson approach for predicting the cell volumes for multicomponent crystals. (Figures 2a and b.) While the slope of the Hofmann plot indicates that it may slightly underestimate the volume, the intercept and the R2 are superior to that of the Kempster-Lipson plot.

Figure 2a: Comparison of Experimental vs Predicted Cell Volume of Selected Multicomponent Crystal Structures Using Kempster-Lipson (Rule of 18Å³) Approach

Figure 2b: Comparison of experimental vs predicted cell volume of Selected Multicomponent Crystal Structures using Hofmann Approach


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Utilizing the extracted multicomponent crystal structures used in Figure 2, the observed volume occupied by the secondary component was calculated and compared to the expected Hofmann volume for those components. To do this, the second component molecule atoms were removed from the crystal structure coordinate file and the resulting void volume calculated using a Solvent Accessible Surface Boundary approach with a probe radius of 1.2 Å and a grid spacing of 0.7 Å. Tables 1a and 1b show the predicted volume and the average observed volume for selected solvents and coformers/salt formers, respectively. Table 1a. Predicted Volumes and Average Observed Volumes for Selected Pharmaceutically Relevant Solvents

Solvent

Molecular Formula

Methanol Acetonitrile Ethanol Acetic Acid Acetone 2-Propanol n-Propanol t-Butanol Ethyl Acetate

CH4O C2H3N C2H6O C2H4O2 C3H6O C3H8O C3H8O C4H10O C4H8O2

Volume Volume Volume Volume requirements (Å³) - requirements (Å³)- requirements (Å³) requirements (Å³) Kempster-Lipson Space Filling CSD DB Hoffmann method method SPARTAN assessment 46 36 41 42 55 54 54 55 70 54 59 63 71 72 61 82 83 72 73 98 94 72 77 95 94 72 77 116 118 90 95 119 119 108 100 145


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Table 1b. Predicted Volumes and Average Observed Volumes for Selected Pharmaceutically Relevant Counterion/Co-Crystal Formers

Counterion/Co-Crystal Former

Molecular Formula

Acetic Benzoic Citric Fumaric Maleic L-Malic Oxalic L-Pyroglutamic Salicylic L-Tartaric Nicotinamide Saccharin Xylitol

C2H4O2 C7H6O2 C6H8O7 C4H4O4 C4H4O4 C4H6O5 C2H2O4 C5H7NO3 C7H6O3 C4H6O6 C6H6N2O C7H5NO3S C5H12O5

Volume Volume Volume Volume requirements (Å³) - requirements (Å³)- requirements (Å³) requirements (Å³) Kempster-Lipson Space Filling CSD DB Hoffmann method method SPARTAN assessment 71 72 61 82 150 162 127 160 204 234 159 192 121 144 103 120 121 144 103 128 143 162 113 136 83 108 71 72 151 162 119 123 162 180 133 166 154 180 121 127 149 162 124 145 197 216 152 198 187 180 143 167

Figure 3a. Hofmann Volume vs. Average Observed Volume from CSD for Selected Pharmaceutically Relevant Solvents


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Figure 3b. Hofmann Volume vs. Average Observed Volume from CSD for Selected Pharmaceutically Relevant Counterions/Co-Formers Figures 3a and 3b show that the mean observed volumes correlate quite well with the Hofmann estimates. Probe radius selection has a significant impact on the calculated void, and therefore any deviation of the slope from unity may not be meaningful13. Given the overall excellent estimation of the Hofmann approach for anhydrate and multicomponent crystals, further analyses were performed utilizing only the Hofmann atomic volume values and without any modification. Utilization of Volume Estimation for Assessment of Predicted Stoichiometry Unit cell parameters and volumes can be readily obtained from PXRD data by appropriate use of indexing and refinement algorithms. Therefore a PXRD pattern of a putative multicomponent crystal provides sufficient data to obtain the cell volume. Comparison of this volume and the Hofmann volume of the primary component should infer the likelihood of the presence of a second component. Further, the size of the “extra” volume should be related to the stoichiometry and identity of the second component. The assessment of this stoichiometry can be performed using Equation 3. Simply, the additional volume is calculated by subtracting the expected component 1 volume from the experimentally derived cell volume, and this is divided by the


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expected number of API molecules in the crystal form multiplied by the Hofmann volume for the expected second component. The expected value of Z can be inferred by consideration of multiplicity of the determined space group and the likely number of molecules in the asymmetric unit (Z’).

(Equation 3) As an example of the approach, PXRD patterns of two solvates (MeOH and EtOH) of Navarixin 14 were indexed.


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H 3C

O

O CH 3 N

O H 3C

N H

N H

CH3 OH

O

Scheme 1. Molecular Structure of Navarixin These patterns were collected on a standard laboratory diffractometer, configured in the BraggBrentano geometry and equipped with a sealed Cu tube radiation source and a Nickel beta-filter for monochromatization. Acquisition time was limited to six minutes to reflect standard data acquisition parameters for routine samples. Comparison of the experimental powder patterns and patterns calculated from the room temperature single crystal structures are shown in Figures 4a and 4b.

Simulated from SC-XRD

Experimental Powder Pattern

Figure 4a. Comparison of Methanol Solvate X-Ray Diffraction Patterns Determined by Both Powder and Single Crystal Diffraction


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Simulated from SC-XRD

Experimental Powder Pattern

Figure 4b. Comparison of Ethanol Solvate X-Ray Diffraction Patterns Determined by Both Powder and Single Crystal Diffraction Table 2 shows a comparison of the cell dimensions from the powder indexing and refinement, and from room temperature single crystal structure determinations. This clearly shows how indexing even a standard pattern results in a unit cell volume that is in excellent agreement with single crystal structure determination.


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Table 2: Comparison of Cell Dimensions from Single Crystal Structure Determination and Powder Indexing for Navarixin Solvates

Molecular Formula

Navarixin Methanol Solvate

Navarixin Ethanol Solvate

C21H23N3O5 • CH3OH

C21H23N3O5 • C2H5OH

429.5

443.5

Formula Weight (g/mol) Data Type /Temperature Crystal system, space group

SC-XRD / 293K

PXRD / 293K

Monoclinic, P21

SC-XRD / 293K

PXRD / 293K

Monoclinic, P21

a (Å)

9.4995(2)

9.5026(7)

9.7456(1)

9.7368(12)

b (Å)

9.7624(2)

9.7580(7)

10.0520(1)

10.0471(14)

c (Å)

12.7614(3)

12.7650(12)

12.3150(2)

12.3086(17)

β (°)

111.6656(6)

111.661(4)

107.9123(3)

107.918 (3)

1099.86

1100.06

1147.93

1145.70

Cell Dimensions

Cell Volume (Å3) Z (# of molecules per cell), Z’ (# of molecules per asymmetric unit) Calculated Crystal Density (g/cm³)

2,1

1.297

2,1

1.297

1.283

1.286

Using the molecular formula for the anhydrous Navarixin (C21H23N3O5), the calculations are as follows: Expected molecular volume of Navarixin = [21 x 13.87Å³] + [23 x 5.08Å³] + [3 x 11.8Å³] + [5 x 11.39Å³] = 500.46Å³


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Expected molecular volume of methanol

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= [1 x 13.87Å³] + [4 x 5.08Å³] + [1 x 11.39Å³] = 45.58Å³

Expected molecular volume of ethanol

= [2 x 13.87Å³] + [6 x 5.08Å³] + [1 x 11.39Å³] = 69.61Å³

Since the space group was determined to be P21 with a multiplicity of 2, then it would be expected that the cell would at most contain two molecules (Z = 2) of Navarixin. Therefore, the expected stoichiometry calculations for the two solvates are as follows: Expected Stoichiometry of MeOH solvate = [1100.06Å³ – 2 (500.46Å³)] / (2x45.58Å³) = 1.09 Expected Stoichiometry of EtOH solvate = [1145.7Å³– 2 (500.46Å³)] / (2x69.61Å³) = 1.04 While these stoichiometry calculations rarely result in perfectly integer (e.g. for mono, di, tri solvates) or fractional integer values (e.g. hemi or sesqui) it is a logical conclusion that the true stoichiometry will be easily deduced. In the Navarixin example, a monosolvate is predicted for both the MeOH (1.09 ≈ 1) and EtOH (1.04 ≈ 1) solvates, which agrees with the actual stoichiometry determined by SC-XRD. For these examples the void space diagrams were produced in Mercury by removing the solvent molecule. Figures 5a and 5b shows the void space diagrams for the two solvates.


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Figure 5a. Packing Diagram of Navarixin Methanol Solvate with Void Space Displayed After Solvent Removal

Figure 5b. Packing Diagram of Navarixin Ethanol Solvate with Void Space Displayed After Solvent Removal


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In the Navarixin example, the 1:1 stoichiometry of the MeOH and EtOH solvates is clearly correctly predicted. However, to assess the generality of this approach, the predicted stoichiometry was calculated for 100 of the multicomponent crystals included in Figure 2. In each case, using only the cell volume and the Z value from the structure, the likely stoichiometry was calculated. Figures 6a and 6b show the predicted stoichiometry for selected solvates and co-crystals/salts respectively. These examples cover multiple stoichiometric states including hemi, mono, sesqui and bis as well as varying second component size.

Figure 6a: Expected Stoichiometry of Multicomponent Crystals with Solvent as Secondary Component


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Figure 6b: Expected Stoichiometry of Multicomponent Crystals with Salt/Co-crystal Formers as Secondary Component In general, each secondary component shows the predicted stoichiometry centering around the true stoichiometry. However, it is clear that for smaller molecules such as methanol there is considerable scatter, but for larger molecules the predicted stoichiometry is more accurate. This is an expected result since the impact of small errors in the volume estimates will more greatly impact the predicted stoichiometry for small solvents. This can be demonstrated if one considers the estimated volume error per molecule for the anhydrate compounds used in Figure 1. Figure 7 shows volume error per molecule, using the Hofmann method, for the 100 anhydrate compounds against the actual molecular volume. The error appears randomly distributed and is not correlated with increasing compound size. The RMS volume error for these 100 compounds is approximately 12Å³, but even within this small dataset, errors as high as 30Å³ are encountered.


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Figure 7: Volume Error per Molecule for Selected Anhydrate Compounds Due to this potential for inherent volume error, the predicted stoichiometries for small second components should be treated with caution. With methanol for instance, a 23Å³ per molecule underestimate could result in the prediction of sesqui rather than mono stoichiometry. However, this can be tempered somewhat by the consideration of what crystal symmetries and values of Z’ commonly support non-integer stoichiometries15. For example, a space group with a mirror plane may be more likely to have hemi and sequi solvates involving solvent molecules that can have mirror symmetry. These solvent molecules may sit on the crystallographic mirror plane, thus being “shared” between two molecules. Further, if the molecular volume for an anhydrous form has been determined by indexing or SC-XRD, this may serve as a better estimate of the volume occupied by the primary component in the potential multicomponent crystal than using the Hofmann estimation.


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Similarly, this method should be applied with caution to water and small counterions, such as sodium and chloride. Although hydrates are ubiquitous and of great importance in the pharmaceutical development, the inherent errors in the volume estimation make this approach unsuited to assessing the likelihood of water incorporation. This technique has no chemical specificity, and is relying on the assumption of likely secondary components based on the knowledge of the composition of the crystallization system. This information will guide proper selection of complementary analytical techniques to provide definitive confirmation of the secondary component. In addition, if a particular crystal form could feasibly contain multiple guests components (e.g. mixed solvates, solvates of salts or cocrystals) this method can be applied, but assigning the voids to a particular component becomes inherently more complex.

Data Quality Required for Indexing Diffraction data used for indexing can range from high throughput screening data to synchrotron quality data. Ideally the material under evaluation should be phase pure but the many indexing algorithms are resilient to minor phase impurities. The unit cell can be determined wholly by the diffraction peak positions as long as the peak positions are determined accurately. The most powerful indexing algorithms can tolerate a certain amount of peak position error, due to issues such as sample displacement or transparency errors. However, zero point error should be minimized as much as possible by careful sample preparation. Further, sources of background, such as amorphous content or solvent scatter, will not affect peak positions. These tolerances allow this method to be applied to the analysis of unstable or labile solvates, which generally


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need to be analyzed as wet samples, usually under X-ray transparent film. Therefore this method can be freely applied to weakly crystalline solids, wetcake samples, and other varying quality diffraction data. When challenges are met in identifying a powder indexing solution, improving data resolution quality can be achieved by either improving in-house data acquisition (e.g. Kα1 monochromatization) or utilizing synchrotron radiation sources. CONCLUSION

A simple and rapid approach for calculating the expected required volume for a given molecule within a crystal using an atom based additive approach was presented. Coupling this estimation with the actual unit cell volumes and space group information obtained from powder indexing allows for the rapid evaluation of the likely stoichiometry of multicomponent crystals using diffraction data alone. Powder X-ray data is routinely gathered on pharmaceutical solids and application of this approach allows valuable information to be readily extracted without additional experimentation. This approach is particularly useful for the early assessment of new phases during salt, co-crystal, and polymorph screening, and also for the characterization of stable and unstable solvates.

The method described, coupled with complementary analytical

techniques, allows for a deeper understanding of the crystalline state of pharmaceutical solids, which is invaluable to the drug development process.


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AUTHOR INFORMATION Corresponding Author *Courtney K. Maguire, [email protected] ASSOCIATED CONTENT CSD extracted data, tables of predicted stoichiometries, atomic volume tables, Pawley refinement data and single crystal data is available as supplementary material. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENT The authors are appreciative of useful discussions and input from Narayan Variankaval, Alfred Y. Lee, Scott Shultz, and Siyan Zhang. ABBREVIATIONS SC-XRD: single crystal X-ray diffraction CSD: Cambridge Structural database PXRD: Powder X-ray diffraction REFERENCES 1. Lee, A.Y.; Erdemir, D.; Myerson, A.S. Crystal Polymorphism in Chemical Process Development. Annu. Rev. Chem. Biomol. Eng. 2011. 2, 259–80. 2. David, W.I.F., Shankland, K., McCusker, L.B., Baerlocher, Ch.,

Structure

Determination from Powder Diffraction Data, 2002. International Union of Crystallography, Oxford Science Publications


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Assessment of the Stoichiometry of Multicomponent Crystals Using

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