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 co-

crystallized molecules in different (known) structures. At the same time, from a crystal

1

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,

2

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

3

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 D-

malic 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.

4

COOH

HHO

COOH

HH

COOH

OHH

COOH

HHO

COOH

OHH

COOH

HH

COOH

HHO

COOH

OHH

L-malic acid D-malic acid L-tartaric acid D-tartaric acid

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 Chirality CSD Refcode S. G.§ Zˈ

Tartaric AcidL-t (R,R)

D-t (S,S)

TARTAC

TARTAC24

P21

P212121

1

1D+L-t (S,S+R,R) ZZZDUI01 P-1 1

Malic AcidL-m (S)

D-m (R)COFRUK10 P21 2 D+L-t (R+S)

DLMALC (α)

DLMALC11 (β)

Cc

P21/c

1

1

1:1 Cocrystals

Tartaric:Malic Acid

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

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

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

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

NIGYOV (I)

NIGYOV01 (III)

P1

P21

1+1

1+1

*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

5

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

6

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

7

Lm:Dt1.48:0.58

Lm:Dt1:1

Lm:Dt0.14:0.86

Dm:Lm(1)1:1*

Dm:Lm(2)1:1*

Lm:Lt1:1

Lm:Dm:Lt1:0.25:0.75

Lm:Dt:Lt0.3:0.7:1

Dm:Lm:Dt:Lt1:1:1:1

a (Å) 5.1031(2) 5.1194(2) 6.1883(5) 13.068(4) 13.046(2) 4.8476(5) 4.900(3) 4.8793(4) 4.8779(7)

b (Å) 9.2582(3) 9.3082(4) 5.9822(5) 8.727(3) 8.762(2) 8.8656(9) 8.934(5) 6.5557(5) 6.4726(10)

c (Å) 11.6220(4) 11.4952(5) 7.7304(6) 4.8855(17) 4.8922(9) 12.6341(12) 12.818(7) 9.2038(7) 9.2890(14)

α (°) 90 90 90 90 90 90 90 74.541(3) 74.097(6)

β (°) 93.362(2) 92.682(2) 100.227(3) 103.238(7) 103.407(16) 97.700(2) 98.508(14) 88.189(3) 87.370(6)

γ (°) 90 90 90 90 90 90 90 76.694(3) 77.637(6)

Vol. (Å3) 548.14(3) 547.17(4) 281.63(4) 542.3(3) 543.96(19) 538.08(9) 554.9(5) 276.00(4) 275.49(7)

Spacegroup P21 P21 P21 C2/c C2/c P21 P21 P1 P-1

Moietyformul

a(C4H6O5)1.42 (C4H6O6)0.58

(C4H6O5) (C4H6O6)

(C4H6O5)0.14 (C4H6O6)0.86 C4H6O5 C4H6O5 (C4H6O5)

(C4H6O6)(C4H6O5)1.25(C4H6O6)0.75

(C4H6O5)0.30(C4H6O6)1.70

(C4H6O5)(C4H6O6)

Mr 277.47 248.18 147.85 268.18 268.18 284.18 280.18 295.38 284.34

D.(g/cm3) 1.681 1.725 1.743 1.642 1.637 1.754 1.677 1.777 1.714

Z 2 2 2 2 2 2 2 1 1

Rreflect.

0.03821656

0.04702501

0.05261279

0.0976508

0.1244424

0.05423358

0.08671774

0.06631535

0.2243906

* 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

8

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

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

9

(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

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 DL-

malic 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.

10

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 L-

m or pure D-m compositions, however, the enantiopure crystal form (CUFRUK10) is the most

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

11

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

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. Relative Energy(kJ/mol) Ref.

NIVYOG I P1 0.0 Aakeröy50

New form - P21 0.8 This StudyNIVYOG01 III P21 4.4 Jones51

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

12

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.

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

13

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

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 re-

solidify as amorphous.

14

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 L-

m: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.

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 four-

component 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

15

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

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).

16

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:D-

m: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

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 L-

m:D-t (top) and L-m:D-m:L-t and L-m:D-t:L-t series (bottom).

17

All the structures are characterised by the same chain of dicarboxylc acids, which are sustained

by the classic R22(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.

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).

18

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

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 L-

enantiomers. 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:

19

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

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’. Non-hydrogen atoms

20

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).

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, “pseudo-

racemic”), L-m:D-t 1:1 (chiral), L-m:D-m 1:1 (racemic), L-t:D-t (racemic), L-m (chiral) and D-

t (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 k-

points until the form energies converged. Structural relaxations were halted when the calculated

21

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

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

22

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

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

23

*Department of Chemical Sciences, Bernal Institute, University of Limerick, Limerick, Republic

of Ireland matteo.lusi@ul.ie

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.

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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.

28