Cocrystals Help Break the âRulesâ of Isostructurality: Solid Solutions

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Cocrystals help breaking the “rules” of isostructurality: solid solutions and polymorphism in the malic/tartaric acid system. Aurora J. Cruz-Cabeza, Monica Lestari, and Matteo Lusi Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b01321 • Publication Date (Web): 15 Dec 2017 Downloaded from http://pubs.acs.org on December 16, 2017

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Crystal Growth & Design

Cocrystals help breaking the “rules” of isostructurality: solid solutions and polymorphism in the malic/tartaric acid system. Aurora J. Cruz-Cabeza,a Monica Lestarib and Matteo Lusi*b. a

School of Chemical Engineering and Analytical Science, University of Manchester, M13 9PL Manchester, United Kingdom.

b

Department of Chemical Sciences, Bernal Institute, University of Limerick, Limerick, Republic of Ireland.

Solid_solutions; Cocrystals; Racemates; Polymorphism; Isostructurality.

Crystalline solid solutions have the potential to afford tunable materials for pharmaceutical and technological applications. Unfortunately, these poorly understood phases are difficult to obtain and, hence, to study. In fact, commonly accepted empirical rules prescribe that only molecules of similar size and electron distribution are mutually soluble in the solid state. Here, despite the evident structural and electronic differences, the enantiomers of malic acid and tartaric acid are crystallized together in variable stoichiometric ratio to produce both cocrystals and solid solutions. In some cases, physical mixtures are observed. The composition and polymorphism of the crystalline products is explained by DFT-d molecular substitution calculations for the cocrystallized molecules in different (known) structures. At the same time, from a crystal

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engineering perspective, the behavior of this complex system is rationalized thanks to the existence of intermediate cocrystal forms that merge the structural features of the pure molecular components.

Introduction: In the past decades, chemists have pursued the idea of engineering crystal structures with predictable properties.1-4 Such crystals have potential uses as chemical intermediates in synthesis (topochemical reactions) and separation processes, or as products in pharmaceutical or material sciences. The most successful approach in crystal engineering involves the rationalization and exploitation of supramolecular forces to co-crystallize multiple molecular species in a stoichiometric ratio: supramolecular compounds.5-10 Ideally, a virtually infinite library of neutral and ionic species, which can be used as chemical building blocks, would enable the realization of crystal structures with the desired properties. On the other hand, the finite (discrete) differences in size, shape and charge between those building blocks might limit the degree of control over such phases. Alternatively, crystalline materials can be “engineered” by preparing multicomponent crystals of variable stoichiometry: solid solutions. These phases are the crystalline counterpart of liquid solutions.11 Hence, as for liquid solutions, their stoichiometry is not limited to an integer or rational number but it can be varied in continuum (at least within certain limits). In this sense,


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stoichiometric control is the key for a fine and predictable modification of structures and properties. Solid solutions of salts have been systematically investigated since the second half of 19th century.12-14 Around the same time the first examples of organic solid solutions have also been reported.15,16 Recently, solid solutions of molecular and network crystals have been receiving growing attention.17-22 For example, we have shown that these phases can enable fine-tuning of unit cell metrics,23 polymorphism,24 thermal stability25 and mechanical response to stimuli26 in molecular and network crystals. Unfortunately, solubility in the solid state is relatively rare. Indeed crystallization is regarded as a purification technique to afford either pure substances or supramolecular adducts (cocrystals) and the existence of stable stoichiometric compounds is generally regarded as the nemesis of solid solutions. The limited solid-state solubility of molecules represents a major limitation to the development of new solid solutions. To date there are no exact recipes to predict whether two molecules are mutually miscible in a solid. The concepts of isomorphicity and isostructurality have been used as empirical guidelines to identify potential solid solutions.27,28 Kitaigorodskii observed that molecules or ions are likely to form a solid solution if they are similar in structure and size, as well as electronically.29 For example, solubility is expected between chloride and bromide molecular analogues. In contrast, hydrogen/hydroxyl substituted pair of molecules tend to be less miscible because the OH group is generally involved in a H-bond that is precluded to the unsubstituted molecule. It has been shown that solid-state solubility of two molecules can be enhanced by the use of a third component that behaves as a “solid solvent”.30 Within the crystal, the third component can


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co-dissolve with the other species in a homogeneous three-component solid solution31 or it can act as a coformer in a cocrystal, while the other components mutually substitute each other. The latter case has been referred to as a cocrystal solid solution.32 Perhaps earlier examples of this type of materials are represented by enantiomeric systems33,34 and inclusion compounds.35 More recently pharmaceutical28,32,34 and porous36 cocrystal solid solutions have also been reported. Cocrystal solid solutions could be particularly advantageous in crystal engineering since variable stoichiometry introduces further complexity to multicomponent crystals.37,38 Hence the structural and chemical diversity that is typical of supramolecular cocrystals can be combined with the potential for fine-tuning that is proper of solid solutions. On the other hand, there are cases in which multicomponent phases need to be avoided. For example, when partial solvation or hydration is the undesired consequence of recrystallization or exposure to atmospheric water vapours,39,40 or when the formation of a multicomponent crystal prevents molecular separation and chiral resolution.41 For all these reasons, a deeper understanding of these phases is critical. Malic and tartaric acids are chiral dicarboxylic acids largely used by the food and pharmaceutical industries as excipients, preservatives or as regulators in fermentation processes.42 They also have physiological activity being involved in the muscles metabolism. The two molecules are structurally related. L-tartaric acid (L-t) can be seen as a derivative of Dmalic acid (D-m) in which one hydrogen atom has been substituted by a hydroxyl group. D-m acid has one chiral centre (absolute configuration R) whilst L-t has two chiral centres of (absolute configuration R,R). For simplicity, D-m and L-t acid can be seen as “homochiral” (R) molecule whilst L-malic acid (L-m) and D-tartaric acid (D-t) are the (S) mirror images (figure 1). A meso- isomer of tartaric acid also exists that will not be discussed here.


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Figure 1: Fischer projection of D-m, L-m, L-t and D-t.

Table 1. Summary of known crystal structures of malic and tartaric acid as enantiopure, racemic and 1:1 cocrystaline forms.* Enantiopure Substances

Racemic Compounds §

Chirality

CSD Refcode

S. G.

Zˈ

L-t (R,R)

TARTAC

P21

1

D-t (S,S)

TARTAC24

P212121

1

COFRUK10

P21

2

Tartaric Acid

CSD Refcode

S. G.

D+L-t (S,S+R,R)

ZZZDUI01

P-1

1

DLMALC (α)

Cc

1

DLMALC11 (β)

P21/c

1

L-t : L-m (R,R+S)

NIGYOV (I)

P1

1+1

D-t : D-m (S,S+R)

NIGYOV01 (III)

P21

1+1

L-m (S) Malic Acid

§

Chirality

Zˈ

D+L-t (R+S)

D-m (R) 1:1 Cocrystals Tartaric:Malic Acid

L-t : D-t (R,R+R) D-t : L-t (S,S+S)

Unknown

§

*ZZZDUI01 and NIGYOV, and DLMALC and NIGYOV01 are isostructural. S.G. = Space Group

The pure enantiomers of both molecules crystallise in the monoclinic P21 space group; however the two forms are not isostructural (Cambridge Structural Database, CSD,43 Refcodes COFRUK10 and TARTAC, table 1).44,45 A second polymorph of enantiopure tartaric acid crystallizes in the P212121 space group (TARTAC24).46 Racemic forms for both molecules are also reported: a non-centrosymmetric Cc47 and a centrosymmetric P21/c48 form for malic acid (DLMALC and DLMALC11), and a P-1 structure for tartaric acid (ZZZDUI01).49


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A first cocrystal of L-m (S) and L-t (R,R) was reported by Aakeröy et al. in the P1 space group (NIVYOG);50 two other polymorphs were reported by Jones.51 Form II was identified by powder X-ray diffraction (PXRD) and differential scanning calorimetry (DSC) but no structural details are available. Form III (P21, NIVYOG01) is monotropically related to form I and form II and was obtained by heating the other two.51 Notably form I of the cocrystal is isosotructural to the DL-tartaric acid racemate (ZZZDUI01) whilst form III is isostructural to the DL-malic acid form α (DLMALC). Furthermore Jones described how mechanochemical cocrystallization of malic and tartaric acid racemates can be exploited for chiral resolution.51 Together, the D- and L- enantiomers of malic and tartaric acids constitute a four-component system known to produce racemates, cocrystals, polymorphs and solvates. Such diversity makes this system particularly interesting from the crystallographic and crystal engineering point of view. Here malic and tartaric acids are further investigated with the aim of producing solid solutions. For clarity, we will refer to the various solid phases in this paper by their CSD refcodes (table 1).

Results: A.1. L-malic:D-tartaric acid (“homochiral” solid solutions) The grinding of L-m, one chiral centre (S), with a small amount of D-t, two chiral centres (S,S), in the presence of a drop of ethanol produces a white microcrystalline powder. PXRD shows that the Braggs’ peaks of the enantiopure malic acid structure (COFRUK10 phase) shift regularly to lower 2θ values (larger unit cell) as the ratio of tartaric acid increases until the


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cocrystal composition is reached (i.e. 1:1) This evidence suggests that a solid solution is produced (figure 2, left). On further addition of D-t, however, peaks of a new phase appears alongside those of the cocrystal structure. The new phase is isostructural to the enantiopure structure TARTAC. Remarkably, the peak positions of both phases in the physical mixture keep shifting as a function of composition, as expected for two solid solutions (figure 2, left). Variable temperature PXRD measurements reveal that the phases with COFRUK10 structure, at both 1:1 and intermediate compositions, melt at around 140 °C. The same measurements show that the tartaric acid structure (TARTAC) remains crystalline until about 160 °C (ESI S3 and S4). Upon cooling, the molten phases produce an amorphous paste, which highlights the importance of the mechanochemical method to produce homogenous and crystalline solid solutions.

Figure 2: PXRD patterns of L-m acid and D-t ground together in varied ratio (left) and stability of L-m and D-t as physical mixtures as well as pure phases at 1:0, 1:1 and 0:1 compositions (right). The dashed lines are not real but are drawn to link the calculated energy.

Table 2: Summary of the crystal structures


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Lm:Dt 1.48:0.58 5.1031(2) 9.2582(3) 11.6220(4) 90 93.362(2) 90

a (Å) b (Å) c (Å) α (°) β (°) γ (°) Vol. 548.14(3) (Å3) Space P21 group Moiety (C4H6O5)1.42 formul (C4H6O6)0.58 a Mr 277.47 D. 1.681 (g/cm3) Z 2 R 0.0382 reflect. 1656 *

Lm:Dt 1:1 5.1194(2) 9.3082(4) 11.4952(5) 90 92.682(2) 90

Lm:Dt 0.14:0.86 6.1883(5) 5.9822(5) 7.7304(6) 90 100.227(3) 90

Dm:Lm(1) 1:1* 13.068(4) 8.727(3) 4.8855(17) 90 103.238(7) 90

Dm:Lm(2) Lm:Lt 1:1* 1:1 13.046(2) 4.8476(5) 8.762(2) 8.8656(9) 4.8922(9) 12.6341(12) 90 90 103.407(16) 97.700(2) 90 90

547.17(4)

281.63(4)

542.3(3)

543.96(19)

P21

P21

C2/c

(C4H6O5) (C4H6O6)

(C4H6O5)0.14 (C4H6O6)0.86

248.18

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Lm:Dm:Lt 1:0.25:0.75 4.900(3) 8.934(5) 12.818(7) 90 98.508(14) 90

Lm:Dt:Lt 0.3:0.7:1 4.8793(4) 6.5557(5) 9.2038(7) 74.541(3) 88.189(3) 76.694(3)

Dm:Lm:Dt:Lt 1:1:1:1 4.8779(7) 6.4726(10) 9.2890(14) 74.097(6) 87.370(6) 77.637(6)

538.08(9)

554.9(5)

276.00(4)

275.49(7)

C2/c

P21

P21

P1

P-1

C4H6O5

C4H6O5

(C4H6O5) (C4H6O6)

147.85

268.18

268.18

284.18

280.18

295.38

284.34

1.725

1.743

1.642

1.637

1.754

1.677

1.777

1.714

2 0.0470 2501

2 0.0526 1279

2 0.0976 508

2 0.1244 424

2 0.0542 3358

2 0.0867 1774

1 0.0663 1535

1 0.2243 906

(C4H6O5)1.25 (C4H6O5)0.30 (C4H6O6)0.75 (C4H6O6)1.70

(C4H6O5) (C4H6O6)

the exact composition could not be determined .

Recrystallization by solvent evaporation of the product of manual grinding affords quality single crystals for single crystal X-ray diffraction (SXRD). Structure refinement shows that single crystals obtained from the microcrystalline product at intermediate compositions are disordered, confirming their solid solutions nature (table 2). On the contrary, single crystals at 1:1 composition are ordered cocrystals in which each co-former occupies a unique crystallographic position. The stability of the three known enantiopure phases for malic acid and tartaric acid (COFRUK10, TARTAC and TARTAC24) were investigated via molecular substitution calculations (see methods) using accurate DFT-d models. It is important to note that only ordered models were considered. The stability of the various ordered phases containing L-m and D-t in 1:0, 1:1 and 0:1 ratios were calculated and plotted in figure 2 (right). For pure L-m, the COFRUK10 structure is the most stable. For 1:1 L-m:D-t, the COFRUK10 structure is the most stable phase as an ordered 1:1 cocrystal but the TARTAC structure for the same composition is only 0.2 kJ/mol above in energy. For 0:1 composition, the TARTAC


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structure is the most stable. This is in good agreement with the outcome of the grinding experiments. We notice, however, that the physical mixture of enatiomerically pure phases at 1:1 composition is predicted to be slightly more stable than the ordered cocrystal by 1.8 kJ/mol. This energy difference is small and may be compensated by entropic factors, especially if disorder is present. Currently, however, the computation of such effects is non-trivial and it is excluded from the energy calculations.

A.2. L-malic:D-malic acid (enantiopure crystals, scalemic solid solutions and racemates) Two polymorphs of the L-m and D-m racemate, respectively (S) and (R) configuration, are reported (DLMALC and DLMALC11). PXRD suggests that manually co-grinding equimolar amount of D-m and L-m produces the racemic form β (DLMALC11, P21/c - table 1), which is recognisable by the small 111 peak at around 18.5° in 2θ (figure 3 left). DFT-d Energy calculations indicate that form β is more stable than form α by just over 1 kJ/mol. Grinding L-m and D-m in a scalemic ratio between 1:1 and 2:1 produces a powder pattern similar to the one calculated for form α (DLMALC, Cc): absence of the peak at 18.5° in 2θ. Enantiomeric enrichment also results in a progressively shifting of the diffraction peaks toward higher angles (smaller unit cell dimensions). Enantiomeric ratio higher than 2:1 produces a polycrystalline mixture containing the malic acid racemate and the pure enantiomer in excess (figure 3 left). Recrystallization of the racemic powder affords quality single crystals. SXRD analysis reveals that they are isometric to form α and structure refinement indicates that both D- and L-malic acid molecules are disordered over two positions with equal occupancy, hence resulting in a centrosymmetric C2/c structure. The quality of the data did not allow establishing whether the


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observed symmetry is a consequence of twinning or of positional disorder. In fact, precession images shows the presence of week reflections [100], which should be absent in the C centred space group (ESI). Recrystallization of the 2:1 scalemic phase produces crystals but small size and poor quality prevented satisfactory refinement and determination of the enantiomeric composition. Nonetheless, two single crystals with slightly different unit cells were isolated. (see table 2).

Figure 3: PXRD patterns of samples containing L-m and D-m ground together in varied ratio (left). Stability of the physical mixture of the entantiopure D-m and L-m phases and the DLmalic acid crystal forms at L-m:D-m compositions of 1:0, 1:1 and 0:1 and (right). The dashed lines are not real but are drawn to link the calculated energies.

Again, the grinding results agree very well with the substitution calculations presented in figure 3 (right). In all cases, the most stable phase is achieved. The energy graph as a function of D-m composition in figure 3 right is very informative. At 1:1 compositions, form β of the racemate (DLMALC11) is the most stable phase and very close in energy to form α. At pure Lm or pure D-m compositions, however, the enantiopure crystal form (CUFRUK10) is the most


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stable one closely followed by form α. Hence, DFT calculations correctly predict the observed change in the rank of stability from enantiopure to α and to β forms, as the racemic composition is reached. Moreover, by assuming an ideal (linear) relationship between composition and energy for each form at non-stoichiometric composition (dashed lines in figure 3), a qualitative estimate of the stability window for each crystal form can be inferred.

A.3. L-malic:L-tartaric acid and D-tartaric:L-tartaric acid (“heterochiral” and racemic physical mixtures) When L-m, (S) configuration, and L-t, (R,R) configuration, are ground together with ethanol, a physical mixture is obtained that contains the known form I of the cocrystal (NIVYOG) together with the crystal form of the pure molecules in excess (COFRUK10 and TARTAC respectively). In such mixture, the peak position of each phase remains constant and only their relative intensities change with composition. The qualitative conclusions of PXRD visual inspection are confirmed by the Rietveld analysis that quantifies the relative amount of malic acid, tartaric acid and cocrystal phases (ESI S1 and table 1). Similarly, grinding a scalemic mixture of L-t and D-t in the same conditions affords a mixture of both the known cocrystal and enantiomerically pure phase (ESI S2 and T2). Therefore, no solid solution appears to be formed, but a mixture of the stoichiometric cocrystals plus the excess enantiopure phases. Recrystallization of the polycrystalline mixtures affords only known cocrystals and enantiomerically pure single crystals whose details are not reported for convenience. However, in recrystallizing the L-m:L-t microcrystalline powder at 1:3 composition, a unique single crystal was isolated that could be solved as a novel P21 structure. The refinement confirms it to


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be a 1:1 L-m:L-t cocrystal, although the malic acid appears disordered in two orientations rotated of 180° from each other. The powder pattern calculated for the new cocrystal matches some, but not all, the peaks of reported for form II by Jones.51 Theoretical calculations for the ordered 1:1 cocrystals show that NIVYOG is the most stable form, NIVYOG01 (obtained at high temperature by Jones et al) is the highest energy metastable form and the new P21 form (obtained only from a mixture at 1:3 ratio) is an intermediate polymorph only 0.8 kJ/mol above the original P1 form NIVYOG (table 3). The observation of this new P21 form may be possible due to entropic gains associated with the observed disorder. Table 2. Summary of known stoichiometric cocrystals for L-malic and L-tartaric acid. The relative stability of the ordered 1:1 forms is given.

CSD Refcode

Form

S. G.

NIVYOG New form NIVYOG01

I III

P1 P21 P21

Relative Energy (kJ/mol) 0.0 0.8 4.4

Ref. 50

Aakeröy This Study 51 Jones

The stability of physical mixtures as well as the possible phases for the L-m:L-t system, is calculated at three different compositions as shown in figure 4. The three cocrystal phases NIVYOG, NIVYOG01 and the new P21 form become very unstable as the composition differs from 1:1. The physical mixtures are indeed predicted to be significantly more stable than solid solutions of all cocrystal phases at compositions other than the 1:1. This is in excellent agreement with the experimental observations and explains why no solid solution can be obtained for this system.


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Figure 4: Stability of L-m:L-t physical mixtures as well as possible solid solutions at L-m:L-t compositions of 1:0, 1:1 and 0:1. The energy of NIVYOG01 at 1:0 composition is out of the scale of this graph. Dashed lines are not real but are drawn to link the calculated energies. The red rectangle magnifies a section of the graph.

B. Three- and four-component systems. The synthesis of the three-component solid solution of L-m (S), D-m (R), and L-t (R,R) was attempted via solid state grinding. When a small amount D-m in the malic acid racemate (DLMALC) is substituted by L-t, a phase is formed, which is isostructural to the one of the malic acid racemate (L-m:D-m:L-t = 3:2:1 in figure 5). Such phase presents a reduced crystallinity as witnessed by the peak broadening in the PXRD. Poor crystallinity is also observed in the recrystallization experiments, which failed to produce large enough crystals for SXRD. Further substitution of D-m with L-t affords a different phase, isomorphous to the tartaric acid racemate (ZZZDUI01) also isostructural with form I of the cocrystal (L-m:D-m:L-t = 3:1:2 in figure 5). The latter structure is maintained upon replacement of L-m with D-t in the L-m:D-t:L-t solid solution. For both phases, the diffraction peaks shifting is consistent with the


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formation of a solid solution (figure 5). These phases cannot be considered polymorphs of each other because their crystal composition is different. Indeed, polymorphism is observed upon heating the L-m:D-m:L-t = 3:1:2 phase to about 130 °C (ESI S5). The polymorphic transition temperature for such intermediate stoichiometry phase is about 10 °C lower than the one reported by Jones for the form I to form III L-m:L-t cocrystal. On the contrary, the series of L-m:D-t:L-t solid solutions show no phase transitions other than the product melting/decomposition (as observed in ESI S6). Once melted, both samples resolidify as amorphous.

Figure 5: PXRD patterns of the three-component (left) and four-component (right) systems. The red circles highlights the minor difference observed between the powder patterns for the Lm:L-t = 1:1 and the L-m:D-t:D-m:L-t = 1:1:1:1 phases.

Single crystals at intermediate composition were obtained by solvent evaporation from ethanol. Their analysis confirms the disordered and variable stoichiometry expected for a solid solution.


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The two enantiomeric pairs can also be mixed together in a four-component system. The stoichiometric variation results in a series of powders whose diffraction patterns match those obtained for the three-component cases at similar composition. The main discrepancy is observed for D-m:L-m:D-t:L-t composition of 5:1:5:1 where a phase mixture is observed (figure 5 right). Furthermore, small differences in the powder pattern might indicate that the fourcomponent system is not a mixture of two binary cocrystals (figure 5). SXRD measurements of the recrystallized sample at 1:1:1:1 composition, which was solved in the P-1 space group, revealed the disordered nature of the structure. Unfortunately, refinement did not allow the determination of its stoichiometry.

Discussion: L-m and D-t are relatively similar molecules that differ for an extra –OH group in tartaric acid. L-m has one chiral centre of (S) configuration whilst D-t has two chiral centres of (S,S) configurations. The different number of hydroxyl groups in these compounds is sufficient to determine different H-bond motifs and packing in the (known) crystal forms of the pure substances. Hence, the complete solubility observed in this study contrasts with the principle of isomorphicity27,28 and Kitaigorodskii’s rules for solid solutions.29 At the same time, the two molecules form a stable 1:1 cocrystal that could be responsible for the observed mutual solubility. Enantiopure malic acid has two molecules in the asymmetric unit. The hydroxyl groups of the independent molecules are H-bonded to each other and set 2.95 Å apart (O-O distance see S8). In the solid solution at ≅ 7:3 L-m:D-t composition, one of the crystallographically independent


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molecules of malic acid is partially replaced by D-t while the other remains fully occupied. In this structure, the interaction distance increases to 3.05 Å perhaps due to steric effects. Moreover the extra hydroxyl group establishes a second H-bond interaction with the hydroxyl group of the fully occupied malic acid (O-O distance = 2.79 Å). In the 1:1 L-m:D-t cocrystal, one of the malic acid is fully replaced by the molecule of tartaric acid. In this case, the mentioned O-O distances increase to 3.06 and 2.83 Å respectively (see S8). When the amount of tartaric acid increases over 50%, the cocrystal structure is not produced anymore. A new structure isomorphous to the one of pure tartaric acid appears with only one molecule in the asymmetric unit. In the 1:6 L-m:D-t solid solution, the presence of malic acid reduces the H-bond distance between the partially occupied hydroxyl group and the carboxylate group to 2.85 (from 2.90 Å in the pure tartaric acid crystal). The other interaction distances remain roughly constant (see S8). Ultimately, these two molecules originate two pure crystals, a cocrystal and two series of solid solutions. At least from a crystallographic point of view, the solid solution isostructural to the malic acid form should be regarded as a cocrystal solid solution whereas the tartaric acid form is a proper solid solution (figure 4). The existence of intermediate cocrystal forms can also explain the three- (and four-) component solid solutions. In fact, although the malic and tartaric acid racemates are structurally different, they are, each, isomorphous to one polymorph of the L-m:L-t cocrystal. The L-m:Dm:L-t solid solution can assume two different forms depending on the D-m:L-t ratio. In this side of the phase diagram, the tartaric acid rich sample (isostructural to the cocrystal form I) converts to the malic acid rich sample (isostructural to the cocrystal form III) at high temperature. On the contrary, the L-m:D-t:L-t solid solution has only one form regardless of temperature and composition. It must be noted that, the L-m:D-m:L-t and the L-m:D-t:L-t solid solutions are not


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the same because the disorder occurs on different coformers. Then two series of solid solutions are produced alongside to the three malic acid:tartaric acid cocrystal forms and the malic acid and tartaric acid racemates (figure 6).

Figure 6: Schematic representation of stoichiometric and non-stoichiometric forms for the Lm:D-t (top) and L-m:D-m:L-t and L-m:D-t:L-t series (bottom).

All the structures are characterised by the same chain of dicarboxylc acids, which are sustained by the classic ܴଶଶ (8) H-bond. The differences lies in the way those chains pack on each other. The malic acid racemate (forms α and β) and the cocrystal form III have the same packing. The sequence of successive layers for these structures can be described as ABA (figure 7). The layers in the new cocrystal form have a similar sequence but the intermediate layer is shifted outward respect to the page plane: ABˈA sequence. On the other hand the tartaric acid racemate and the cocrystal form I have a common ABˈC.


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Figure 7: comparison of the crystal packing for malic acid racemate α (violet) and β (purple), L-m:L-t cocrystal form I (orange), new form (green) and form III (blue), and tartaric acid racemate (red).

Figure 8: from left to right: malic acid racemate forms α and β; L-m:D-t cocrystal form III, form II and form I; tartaric acid racemate. The malic acid hydroxyl oxygen is in green for clarity. In the disordered structures, only one position is represented.

Although the structures of the stoichiometric crystals can be grouped into just the three packing types, the different number of hydroxyl groups and their positions generates six unique H-bond networks (figure 8). In the solid solutions, some interactions are present only in part depending on the concentration of each molecule in the structure. Noticeably, the H-bond networks in the malic acid racemate form β and the cocrystal form III extends in the two


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dimensions whereas in the other structures H-bonds extend also in the direction perpendicular to the plane. Finally, the similarity of forms α and β of malic acid racemate might explain the malic acid scalemic phase. In fact, despite having the same ABA packing, the two forms differ in the order and orientation in which the enantiomer repeat. In form α, each chain alternates D- and Lenantiomers. In form β the chains are homochiral (figure 5 and S10). A scalemic phase of malic acid can then be seen as a combination of forms α and β: different proportions of form α and β character would allow enantiomeric enrichment. Unfortunately single crystal refinement and analysis did not provide definitive answer.

Experimental details and methods: Mechanochemical synthesis: All the mechanochemical reactions were performed by grinding together the reagents (about 0.5 mmol) in the appropriate ratio in an agate mortar with one or two drops of ethanol for about 5 minutes. Details are provided in the ESI. Powder diffraction analysis: all the products of the mechanochemical synthesis were analysed by powder X-ray diffraction (PXRD) on a Panalytical Empyrean diffractometer in flat stage configuration (Bragg-Brentano θ/θ geometry) equipped with a Cu sealed tube source (λKα1,2 = 1.540562 and 1.544398 Å respectively). Rietveld analysis52 of the diffractograms were performed with the X-pert Highscore Plus suit of software to determine the sample composition and to refine the unit cell dimensions of known phases. Variable temperature measurements were performed under nitrogen atmosphere on a Panalytical X-pert Pro diffractometer equipped with


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an Anton-Paar TK400 stage. All the samples were scanned between 5 and 30° (2θ) under a 1 ml/min stream of N2. Single crystal growth and analysis: recrystallization of selected powders was attempted by dissolving few milligrams (a small spatula) of the mechanochemical products in ethanol and letting the solvent slowly evaporating in air (over 3 to 4 days). Single crystals were analysed at room temperature by single crystal X-ray diffraction on a Bruker Quest diffractometer equipped either with a sealed tube Mo generator (λKα = 0.71073 Å) and Photon 100 CMOS detector or a microfocus Cu generator (λKα = 1.54178 Å) and a Photon II CMOS detector at room temperature. Data were integrated with SAINT 8.37A and corrected for absorption using empirical methods (SADABS)53 based upon symmetry-equivalent reflections combined with measurements at different azimuthal angles. Crystal structures were solved and refined against all F2 values using the SHELXTL 2013/154 through the XSEED interface.55 In the disordered structures, the occupancy of hydroxyl groups were expressed in terms of a ‘free variable’. Nonhydrogen atoms were refined anisotropically and hydrogen atoms were placed in calculated positions, either refined using idealized geometries (riding model) or distance constrains, and assigned fixed isotropic displacement parameters. Computational Methods: Crystal structures of all pure systems were retrieved from the Cambridge Structural Database,43 their refcodes are summarised in table 1. In addition, the structure of the new L-malic:L-tartaric acid cocrystal reported in this study was also studied. In total, eight different crystal structures were considered (ZZZDUI01/NIVYOG, DLMALC11, DLMALC, COFRUK10, TARTAC, TARTAC24, NIVYOG01 and the new cocrystal phase).


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The molecular structures in the crystal structures above were then modified as required in order to compute the stability of the different crystal forms with different content of L-m:D-m and/or L-t:D-t. The generated model was then geometry optimised using a DFT-d model as described below. Six models were produced for each structure. For example, for NIVYOG, the crystal structure was optimised with the following compositions L-m:L-t 1:1 (original, “pseudoracemic”), L-m:D-t 1:1 (chiral), L-m:D-m 1:1 (racemic), L-t:D-t (racemic), L-m (chiral) and Dt (chiral). We refer to this as substitution calculations since the crystal structure is the same but the model is generated by substituting molecular models. This 48 generated models were then geometry optimised using the plane wave code VASP version 5.4.1.56-59 All possible structural parameters (unit cell parameters as well as atomic positions) were allowed to optimise freely. The PBE functional60 was used with PAW61,62 and the Tkatchenko and Scheffler van der Waals corrections.63 The Brillouin zone was sampled using the Monkhorst–Pack approximation64 and a variety of k-point grids with increasing number of kpoints until the form energies converged. Structural relaxations were halted when the calculated force on every atom was less than 0.003 eV Å-1. A single molecule (for each of the molecular models) was optimised in the gas-phase using a fixed large super-cell. The lattice energy of the models were calculated by subtracting the electronic energy of a single molecule in the gas-phase from the electronic energy of a single molecule in the given crystal structure.

Conclusions: This work shows that L-m and D-t form a series of solid solutions throughout the whole range of composition. A scalemic solid solution of D-m and L-m is also being reported, although


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solubility of these molecules seem be more limited, to around the racemic composition. The, three-component solid solutions of D-m:L-m:L-t and L-m:L-t:D-t have also been demonstrated whereas only non-definitive evidences have been produced for the existence of four-component crystal forms. The four-component molecular system constituted by D-m, L-m, D-t and L-t represents an example of the complexity and structural richness that can be encountered in crystallography and crystal engineering. The racemates, stoichiometric cocrystals, solid solutions and scalemic solid solutions forms discussed in this paper sum to the already known polymorphs, hydrates and solvates known for these molecules. Such diversity makes the correct identification of each phase a delicate task that tests the technical limits of crystallographic, chemical and computational analysis. The solid solutions reported here are observed despite the different molecular structure and the crystal forms of the pure compounds, which contradicts the empirical rules for solid-state solubility. Molecular substitution calculations in the various crystal structures involved were found to be a good mean of rationalising the solid solutions. In all cases, the most stable phase was produced. Hence this work demonstrates that, at least in this case i) commonly used empirical rules for solid state solubility may be too rigid; ii) molecular substitution calculations in the crystal structures of the compounds can help predicting the product of crystallisation for stoichiometric and non-stoichiometric phases, at least when entropic factors are not critical. From a crystal engineering perspective, the observed solid solutions can be rationalized through the existence of stable 1:1 cocrystal forms that bridges the structures and the interaction


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observed in the pure, single component structures. If this behaviour was proven general, we speculate that stoichiometric cocrystalline phases could be exploited to design and synthesize unexpected solid solutions.

Supporting Information. Electronic Supporting Information (ESI) are available free of charge from http://pubs.acs.org and include: experimental details; PXRD and VTPXRD data; Rietveld analysis summary; figures relative to SXRD analysis. Crystal Information Files for all the structures can be obtained from the CCDC database: 1574933-1574941.

Corresponding Author *Department of Chemical Sciences, Bernal Institute, University of Limerick, Limerick, Republic of Ireland [email protected]

Funding Sources The work of Monica Lestari and Matteo Lusi was funded by Science Foundation Ireland for funding through the SFI-SIRG grant number 15/SIRG/3577.

References:


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(1) Pepinsky, R. Crystal engineering: new concept in crystallography. Phys. Rev. A: At. Mol. Opt. Phys. 1955, 100, 971. (2) Schmidt, G. M. J. Photodimerization in the solid state. Pure Appl. Chem. 1971, 27, 647678. (3) Adams, J. M.; Pritchard, R. G.; Thomas, J. M. Preparation and X-ray crystal structure of guanidinium oxalate dihydrate monoperhydrate: a novel example of crystal engineering. J. Chem. Soc., Chem. Commun. 1976, 358-359. (4) Jones, W.; Ramdas, S.; Theocharis, C. R.; Thomas, J. M.; Thomas, N. W. Crystal engineering of photodimerizable cyclopentanones. Comparison of chloro- and methylsubstitution as solid-state steering groups. J. Phis. Chem. 1981, 85, 2594-2597. (5) Desiraju, G. R. Crystal Engineering: The design of Organic Solids; Elsevier Amsterdam, 1989. (6) Etter, M. C. Encoding and decoding hydrogen-bond patterns of organic compounds. Acc. Chem. Res. 1990, 23, 120-126. (7) R. Lewis, G.; Guy Orpen, A. A metal-containing synthon for crystal engineering: synthesis of the hydrogen bond ribbon polymer [4,4[prime or minute]-H2bipy][MCl4] (M = Pd, Pt). Chem. Commun. 1998, 1873-1874. (8) Braga, D.; Grepioni, F. Organometallic crystal engineering: prospects for a systematic design. Coord. Chem. Rev. 1999, 183, 19-41. (9) Almarsson, O.; Zaworotko, M. J. Crystal engineering of the composition of pharmaceutical phases. Do pharmaceutical co-crystals represent a new path to improved medicines? Chem. Commun. 2004, 1889-1896. (10) Metrangolo, P.; Neukirch, H.; Pilati, T.; Resnati, G. Halogen Bonding Based Recognition Processes: A World Parallel to Hydrogen Bonding†. Acc. Chem. Res. 2005, 38, 386-395. (11) Glasstone, S. Textbook of Physical Chemistry; D. Van Nostrand Company, Inc., 1940. (12) Mitscherlich, E. Ueber die Kristallisation der Salze in denen des Metal der Basis mit zwei proportionen Sauertoff ver buden ist. Abh. Königl. Akad. Wiss. Berlin 1820, 11. (13) Pitkin, L. XLIII.—ISOMORPHOUS SALTS AND FRACTIONAL CRYSTALLIZATION. J. Am. Chem. Soc. 1880, 2, 408-410. (14) Retgers, J. W. Beiträge zur Kenntnis des Isomorphismus II. Z. Phys. Chem 1890, 5, 436466. (15) Ciamician, G. L.; Garelli, F. Solid solutions. Zeit. physikal. Chem. 1897, 22, 134-135. (16) Bruni, G.; Gorni, F. Solid solutions and isomorphous mixtures of saturated and nonsaturated open-chain compounds. I. and II. Real. Accad. dei Lincei 1899, 8, 454-463, 570-459. (17) Braga, D.; Cojazzi, G.; Paolucci, D.; Grepioni, F. A remarkable water-soluble (molecular) alloy with two tuneable solid-to-solid phase transitions. Chem. Commun. 2001, 803804. (18) Ferlay, S.; Hosseini, W. Crystalline molecular alloys. Chem. Commun. 2004, 788-789. (19) Natarajan, R.; Magro, G.; Bridgland, L. N.; Sirikulkajorn, A.; Narayanan, S.; Ryan, L. E.; Haddow, M. F.; Orpen, A. G.; Charmant, J. P. H.; Hudson, A. J.; Davis, A. P. Nanoporous Organic Alloys. Angew. Chem. Int. Ed. Engl. 2011, 50, 11386-11390. (20) Furukawa, H.; Müller, U.; Yaghi, O. M. “Heterogeneity within Order” in Metal–Organic Frameworks. Angew. Chem. Int. Ed. Engl. 2015, 54, 3417-3430. (21) Mishra, M. K.; Ramamurty, U.; Desiraju, G. R. Solid Solution Hardening of Molecular Crystals: Tautomeric Polymorphs of Omeprazole. J. Am. Chem. Soc. 2015, 137, 1794-1797.


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Page 25 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(22) Thomas, S. P.; Sathishkumar, R.; Guru Row, T. N. Organic alloys of room temperature liquids thiophenol and selenophenol. Chem. Commun. 2015, 51, 14255-14258. (23) Adams, C. J.; Haddow, M. F.; Lusi, M.; Orpen, A. G. Crystal engineering of lattice metrics of perhalometallate salts and MOFs. Proc. Natl. Acad. Sci. USA 2010, 107, 1603316038. (24) Adams, C. J.; Gillon, A. L.; Lusi, M.; Orpen, A. G. Towards polymorphism control in coordination networks and metallo-organic salts. CrystEngComm 2010, 12, 4403-4409. (25) Schur, E.; Nauha, E.; Lusi, M.; Bernstein, J. Kitaigorodsky Revisited: Polymorphism and Mixed Crystals of Acridine/Phenazine. Chem. Eur. J. 2015, 21, 1735-1742. (26) Nauha, E.; Naumov, P.; lusi, m. Fine-tuning of a thermosalient phase transition by solid solutions. CrystEngComm 2016. (27) Nath, N. K.; Nangia, A. Isomorphous Crystals by Chloro–Methyl Exchange in Polymorphic Fuchsones. Cryst. Growth Des. 2012, 12, 5411-5425. (28) Shemchuk, O.; Braga, D.; Grepioni, F. Alloying barbituric and thiobarbituric acids: from solid solutions to a highly stable keto co-crystal form. Chem. Commun. 2016, 52, 11815-11818. (29) Kitaigorodskii, A. I. Mixed crystals; Springer‐Verlag: Berlin, 1984; Vol. 33. (30) Lusi, M.; Vitorica-Yrezabal, I. J.; Zaworotko, M. J. Expanding the Scope of Molecular Mixed Crystals Enabled by Three Component Solid Solutions. Cryst. Growth Des. 2015, 15, 4098-4103. (31) Bruni, G. Solid solutions in mixtures of three substances. Atti Real. Accad. Lincei 1900, 9, 232-241. (32) Oliveira, M. A.; Peterson, M. L.; Klein, D. Continuously Substituted Solid Solutions of Organic Co-Crystals. Cryst. Growth Des. 2008, 8, 4487-4493. (33) Srisanga, S.; ter Horst, J. H. Racemic Compound, Conglomerate, or Solid Solution: Phase Diagram Screening of Chiral Compounds. Cryst. Growth Des. 2010, 10, 1808-1812. (34) Chen, S.; Xi, H.; Henry, R. F.; Marsden, I.; Zhang, G. G. Z. Chiral co-crystal solid solution: structures, melting point phase diagram, and chiral enrichment of (ibuprofen)2(4,4dipyridyl). CrystEngComm 2010, 12, 1485-1493. (35) le Roex, T.; Nassimbeni, L. R.; Weber, E. Clathrates with mixed guests. Chem. Commun. 2007, 1124-1126. (36) Hasell, T.; Chong, S. Y.; Schmidtmann, M.; Adams, D. J.; Cooper, A. I. Porous Organic Alloys. Angew. Chem. Int. Ed. Engl. 2012, 51, 7154-7157. (37) Rekis, T.; Be̅rziņš, A.; Orola, L. n.; Holczbauer, T.; Actiņš, A.; Seidel-Morgenstern, A.; Lorenz, H. Single Enantiomer’s Urge to Crystallize in Centrosymmetric Space Groups: Solid Solutions of Phenylpiracetam. Cryst. Growth Des. 2017. (38) Coquerel, G.; Tamura, R. In Disordered Pharmaceutical Materials; Wiley-VCH Verlag GmbH & Co. KGaA: 2016, p 135-160. (39) Zencirci, N.; Gstrein, E.; Langes, C.; Griesser, U. J. Temperature- and moisturedependent phase changes in crystal forms of barbituric acid. Thermochim. Acta 2009, 485, 33-42. (40) Braun, D. E.; Bhardwaj, R. M.; Arlin, J.-B.; Florence, A. J.; Kahlenberg, V.; Griesser, U. J.; Tocher, D. A.; Price, S. L. Absorbing a Little Water: The Structural, Thermodynamic, and Kinetic Relationship between Pyrogallol and Its Tetarto-Hydrate. Cryst. Growth Des. 2013, 13, 4071-4083. (41) Grandeury, A.; Condamine, E.; Hilfert, L.; Gouhier, G.; Petit, S.; Coquerel, G. Chiral Discrimination in Host−Guest Supramolecular Complexes. Understanding Enantioselectivity and


25


Page 26 of 27

Solid Solution Behaviors by Using Spectroscopic Methods and Chemical Sensors. J. Phys. Chem. B 2007, 111, 7017-7026. (42) Deshpande, S. S. Handbook of Food Toxicology; Taylor & Francis, 2002. (43) Groom, C. R.; Bruno, I. J.; Lightfoot, M. P.; Ward, S. C. The Cambridge Structural Database. Acta Crystallogr. Sect. B 2016, 72, 171-179. (44) van der Sluis, P.; Kroon, J. Structure of (-)-malic acid. Acta Crystallogr. Sect. C 1989, 45, 1406-1408. (45) Okaya, Y.; Stemple, N. R.; Kay, M. I. Refinement of the structure of d-tartaric acid by Xray and neutron diffraction. Acta Crystallogr. 1966, 21, 237-243. (46) Callear, S. K.; Hursthouse, M. B. D-Tartaric Acid, 2008, Crystal Structure Report Archive, University of Southampton. (47) van Loock, J. F. J.; van Havere, M.; Lenstra, A. T. H. Bull. Soc. Chim. Belg. 1981, 90, 61. (48) van der Sluis, P.; Kroon, J. The structure of (+/-)-malic acid, (+/-)-C4H6O5. Acta Crystallogr. Sect. C 1985, 41, 956-959. (49) Luner, P. E.; Patel, A. D.; Swenson, D. C. (+/-)-Tartaric acid. Acta Crystallogr. Sect. C 2002, 58, o333-o335. (50) Aakeröy, C. B.; Cooke, T. I.; Nieuwenhuyzen, M. The crystal structure of the molecular cocrystal L-malic acid L-tartaric acid (1/1). Supramol. Chem. 1996, 7, 153-156. (51) Eddleston, M. D.; Arhangelskis, M.; Friscic, T.; Jones, W. Solid state grinding as a tool to aid enantiomeric resolution by cocrystallisation. Chem. Commun. 2012, 48, 11340-11342. (52) Rietveld, H. A profile refinement method for nuclear and magnetic structures. J. Appl. Crystallogr. 1969, 2, 65-71. (53) M. Sheldrick, G. In Current Pharmaceutical Design; Göttingen, U. o., Ed. 1996. (54) Sheldrick, G. M. A short history of SHELX. Acta Crystallographica Section A 2008, 64, 112-122. (55) Barbour, L. J. X-Seed — A Software Tool for Supramolecular Crystallography. J. Supramol. Chem. 2001, 1, 189-191. (56) Kresse, G.; Hafner, J. Ab initio. Physical Review B 1993, 47, 558-561. (57) Kresse, G.; Hafner, J. Ab initio. Physical Review B 1994, 49, 14251-14269. (58) Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science 1996, 6, 15-50. (59) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B 1996, 54, 11169-11186. (60) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. (61) Blöchl, P. E. Projector augmented-wave method. Physical Review B 1994, 50, 1795317979. (62) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Physical Review B 1999, 59, 1758-1775. (63) Tkatchenko, A.; Scheffler, M. Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data. Phys. Rev. Lett. 2009, 102, 073005. (64) Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations. Physical Review B 1976, 13, 5188-5192.


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The mechanochemical co-crystallization of malic acid and tartaric acid affords solid solutions and cocrystalline solid solutions that seem to break the rules of isostructurality and Kitaigorodskii guidelines for solid-state solubility. The new phases can be rationalized, not just in spite, but thanks to the existence of stable cocrystalline intermediates.


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Cocrystals Help Break the âRulesâ of Isostructurality: Solid Solutions

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