Exploring the solubility of the carbamazepine-saccharin co-crystal; a

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Exploring the solubility of the carbamazepinesaccharin co-crystal; a charge density study Jonathan J. Du, Stephen A. Stanton, Slaiman Fakih, Bryson A. Hawkins, Peter A. Williams, Paul W. Groundwater, Jacob Overgaard, James A Platts, and David E Hibbs Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b01111 • Publication Date (Web): 13 Dec 2018 Downloaded from http://pubs.acs.org on December 18, 2018

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Crystal Growth & Design

Exploring the solubility of the carbamazepine-saccharin co-crystal; a charge density study

Jonathan J. Du1, Stephen A. Stanton1 Slaiman Fakih1, Bryson A. Hawkins1, Peter A. Williams1,4, Paul W. Groundwater1, Jacob Overgaard2, James A. Platts3 and David E. Hibbs1* 1School

of Pharmacy, Faculty of Medicine and Health, The University of Sydney, NSW 2006

Australia 2Department

of Chemistry, Center for Materials Crystallography, Aarhus University,

Langelandsgade 140, Aarhus C, DK-8000, Denmark 3School

of Chemistry, Cardiff University, Cardiff, CF10 3AT, UK

4School

of Science and Health, Western Sydney University, Locked Bag 1797, Penrith, NSW 2751

*Corresponding author: David E. Hibbs, [email protected] †Electronic supplementary information (ES) available. CCDC 1562074, 1474337 and 1562073. For ESI and crystallographic data in CIF or other electronic formats, see DOI: XXXXXXX

ACS Paragon Plus Environment

Crystal Growth & Design 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

Abstract Carbamazepine (CBZ) is used in the treatment of multiple neurological conditions. Although efficacious, its potential has been limited by its poor solubility, which means that patients are required to take very large doses to gain the desired effect. Co-crystals have been proposed as a means of improving the physico-chemical properties of pharmaceutical compounds while maintaining their efficacy. CBZ co-crystallised with saccharin (SAC) and nicotinamide (NIC) have previously been studied, with the CBZ-SAC crystal being more soluble than the commercially available product Tegretol, which only contains CBZ, while the nicotinamide cocrystal was found to be less soluble. High resolution X-ray crystallography has been carried out on the CBZ-SAC co-crystal and its individual constituents to determine which features of the electron density distribution contribute to the differing physical properties. The number of hydrogen bonds found for the CBZ, SAC and CBZ-SAC systems were 8, 5 and 10, respectively. Homosynthons (interactions between a pair of identical functional groups) are the primary bonding motif in CBZ and SAC, while a heterosynthon is also present in the co-crystal. Molecular electrostatic potential (MEP) maps show that co-crystallisation results in changes in distribution around the carboxamide group, thus accommodating heterosynthon formation and leading to subsequent charge redistribution across the CBZ molecule. Additional lattice energy calculations were not able to provide a definitive answer as to which system was most stable. Solid state entropy calculations revealed that the CBZ-SAC co-crystal had a higher entropy, providing explanations for the lower melting point and improved dissolution profile previously described. These investigations at an electronic level help to explain the greater solubility of the CBZ-SAC co-crystal compared to CBZ alone.


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Introduction Carbamazepine (CBZ), commercially known as Tegretol, is a neurological drug used in the treatment of epilepsy, trigeminal neuralgia and bipolar disorder1. CBZ acts by binding to α4β2 subunits on nicotinic receptors to reduce the frequency of voltage discharge of sodiumdependent channels1, 2. Although generally considered an efficacious drug, the poor solubility of CBZ has resulted in patients being required to take very large doses (from 100 mg up to 1.2 g per day) to achieve the desired therapeutic effects. Such high doses inevitably increase the occurrence of adverse effects thus limiting the use of CBZ in a wider patient population. Of the compounds which enter the drug development pipeline only a very small fraction make it to market; the overwhelming majority of compounds (over 90%) which do not make it to market fail during initial testing due to poor physico-chemical properties such as solubility (and hence bioavailability)3. Drug discovery programs thus invest a great deal of time and money into these products with very little or no return due to poor pharmacokinetic and pharmacodynamic profiles. Co-crystals have recently emerged as a viable means of increasing the number of drugs which may progress through the drug development pipeline4, 5. The FDA defines co-crystals as “solids that are crystalline materials composed of two or more molecules in the same crystal lattice” with the interactions between them governed by “non-ionic interactions” and “noncovalent interactions”6. A distinction should be made between co-crystals and salts; salt formation is one of the most common methods of improving some of the physico-chemical properties drugs, in particular solubility, however the ionic interaction between the two molecules formally involves a proton transfer. The association between the components of a cocrystal involve interactions such as hydrogen bonding, van der Waals, and π- π interactions. Thus, co-crystals offer an innovative means of developing suitable formulations for drugs with



poor physico-chemical properties, especially in cases where salt formation is not a viable option (when the drug has no functional groups which are ionisable at physiological pH). The ability of these systems to improve the physico-chemical properties of the drug, without modifying the chemical nature of the drug, and hence enhance its therapeutic effect in the body, also makes this a very attractive formulation option. As such, a greater understanding of the driving forces behind the formation of these systems is required to develop streamlined crystal engineering techniques 7, 8. Hickey et al. 9 demonstrated that a carbamazepine-saccharin co-crystal had an improved dissolution profile compared to the current commercial product Tegretol, which contains only CBZ and excipients. Box et al.10 compared the dissolution profiles of CBZ and its co-crystals with saccharin (SAC) or nicotinamide (NIC) and found differences between the dissolution profiles of pure CBZ and the CBZ-SAC and CBZ-NIC co-crystals. These differences in dissolution were attributed to the chemical characteristics of the co-former that was used. As can be seen below, co-crystallisation does not always lead to an improvement in physico-chemical properties, so that a greater understanding of why different co-formers result in different dissolution profiles is required to streamline the co-former selection process. High resolution X-ray diffraction has previously been used to determine the electron density distribution (EDD) in crystalline systems such as co-crystals11-16, giving information on the weak interactions which are known to be the driving force for the formation of these systems. El Hassan et al.17 recently published a study on the EDD of CBZ Form III, with a focus on the types of weak interactions present in the crystal. Here we present a comparative analysis of the EDD between CBZ Form III (1) and SAC (2) (Figure 1) and the CBZ-SAC co-crystal (3) with


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the aim of examining the different interactions present in the single crystal component and cocrystal and explaining perhaps why CBZ-SAC has a better dissolution profile than CBZ alone.



Figure 1: Chemical structures of carbamazepine (1) and saccharin (2).

Figure 2: ORTEP diagram of carbamazepine (CBZ) (1). Thermal ellipsoids are shown at 50% probability level18.


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Figure 3: ORTEP diagram of saccharin (SAC) (2). Thermal ellipsoids are shown at 50% probability level18.

Figure 4: ORTEP diagram of carbamazepine-saccharin (CBZ-SAC) co-crystal (3). Thermal ellipsoids are shown at 50% probability level18.



Methods Raw materials for the growth of crystals of (1) and (2) were purchased from Sigma Aldrich Pty Ltd, Castle Hill, NSW and used without further purification; crystals of (1) and (2) were grown via slow evaporation from ethanol and acetone respectively. Co-crystals of (3) were grown from the method described by Fleischman et al.19; by dissolving equimolar amounts of (1) and (2) in ethanol before mixing and the solution was then allowed to evaporate. Computational methods Single point (SP) calculations were carried out using the Gaussian 09 suite20 at the 6311++G** level of theory using the three parameter hybrid exchange function developed by Becke21 along with the exchange correlation potential, corrected via gradient develop by Lee et al.22. The long-range correction proposed by Tawada et al.23, 24 was also used (CAM-B3LYP). Topological analysis of the theoretical models was carried out using the AIMALL25 package while the XDPROP module of XD26 was used for the topological analysis of experimental data. Details on the collection, integration and reduction of data can be found in the supporting information. The dataset for (2) has been previously published as part of another charge density study11 and is used here for internal comparative purposes only. The multipole refinement procedure and alternative treatment of sulfur atoms method has been reported in previous publications11-13. Refer to Table 1 for selected crystallographic information from the independent atom model (IAM) and multipole (EXP) refinements.


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Table 1: Selected crystallographic information for (1), (2) and (3)

Formula Molecular Mass Crystal size (mm) Temperature (K) Crystal system Space group a (Å) b (Å) c (Å)  (o)  (o)  (o) Volume (Å3) Z Refinement Method No. of reflections collected No. unique Rint Completeness (%) No. reflections used c (g cm-1) F(000)  (mm-1) sin /max  range for data collection () Index ranges IAM Refinement Final R1, wR2 Goodness of fit Residual density (e Å-3) Multipole Refinement Nobs/Nvar R(F), R(F2), all data R(F), R(F2) > 3(F) Goodness of fit Residual density (e Å-3)

1 C15H12N2O 236.27 0.35 x 0.25 x 0.20 150 Monoclinic P21/n 7.491(2) 11.058(3) 13.785(3)

2 C7H5NO3S 183.18 0.30 x 0.25 x 0.20 150 Monoclinic P21/c 9.445(1) 6.922(1) 11.686(1)

92.90(2)

103.06(1)

1140.40(3) 4 Full-matrix leastsquares on F2 108988 18380 0.0565 98.2 43557 1.376 496 0.088 1.25 2.959-62.812 -14 ≤ h ≤ 18 -27 ≤ k ≤ 27 -34 ≤ l ≤ 34

744.30(1) 4 Full-matrix leastsquares on F2 170313 8965 0.0290 99.8 7800 1.635 376 0.394 1.28 3.445-65.615 -23 ≤ h ≤ 24 -17 ≤ k ≤ 17 -29 ≤ l ≤ 29

3 C15H12N2O⦁C7H5NO3S 419.45 0.4 x 0.2 x 0.2 150 Triclinic P1 7.468(2) 10.397(3) 12.676(3) 83.67(2) 85.66(2) 75.72(3) 946.78(5) 2 Full-matrix leastsquares on F2 294816 15558 0.0392 98.1 14199 1.471 436 0.208 1.00 2.714-45.309 -14 ≤ h ≤ 14 -20 ≤ k ≤ 20 -25 ≤ l ≤ 25

0.0501, 0.151 0.991 -0.38, 0.72

0.022, 0.072 1.094 -0.44, 0.62

0.0283, 0.094 1.023 -0.34, 0.58

28.9 0.0711, 0.0395 0.0356, 0.0368 1.198 -0.22, 0.25

24.3 0.0249, 0.0209 0.0150, 0.0204 3.058 -0.26, 0.17

18.0 0.0180, 0.0225 0.0141, 0.0224 1.114 -0.16, 0.18



Results and Discussion

Geometrical comparison The crystal structures of (1) and (2) each contain one molecule in the asymmetric unit while (3) contains one molecule each of (1) and (2) in the asymmetric unit. Refer to Figures 2 to 4 for ORTEP diagrams and the labelling scheme used. The X-ray structure of (1) was first reported in 198127, 28, with a more recent structure also reported in 198929, 200319, 30, 200831, 201132, 201317, 201533, 201634-36 and 201737. The X-ray structure obtained in this work was found to be in excellent agreement with data reported for a high resolution structure17 with mean differences in bond lengths and angles of 0.002 Å and 0.004° respectively. The structure of (2) was compared to results published by Bart38 in 1968 and mean differences of 0.008 Å and 0.010° for bond lengths and angles respectively. Crystal structures were also published for (2) in 1969 and 200540. The X-ray structure of (3) was compared to results published by Fleischman et al.19 with mean differences of 0.049 Å and 0.015° for bond lengths and angles respectively. Refer to Tables S4-21 (ESI) for a full list of bond lengths and angles.

Topological analysis Topological analysis of both SP and EXP models was carried out, with completeness being determined by satisfaction of the Poincaré-Hopf, or its crystalline equivalent, the Morse relationship41. Refer to Tables S22-27 (ESI) for details on the full topological analysis. There were very small differences in topological parameters between the EXP and SP models. The largest discrepancies between EXP and SP for the latter two systems was found in the topology of the S-O bonds, in accordance with previous findings11, 13. In both cases the EXP and SP models differ for ρbcp by approximately 0.2-0.3 eÅ-3 for each S-O bond and by 33-36 eÅ-5 for


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∇2ρρbcp. Both the EXP and SP models report an open shell interaction in S=O bonds, in accordance with its nature as a covalent bond. However, the less negative value of the Laplacian in the EXP model is reflected in (2) and (3) where there is a gap between the valence shell charge concentrations (VSCC) of the sulfur and oxygen atoms as seen in Figure 5. The discrepancy between the numerical and visual data shown in Figure 5 is attributed to the rapidly changing nature of the Laplacian in polar bonds, as found in previous studies 42, 43, as well as the fact that the Laplacian often changes sign near the BCP44-46. The solution to this problem lies in analysing the topology of the bond along the whole bond length as opposed to just at the BCP. Refer to Figures S4-5 (ESI) for ρ and -∇2ρ plotted against bond length for the S=O bonds in (2) and (3). The graphs of ρ vs. bond length are very similar and this is in accordance with the topological data reported above. In contrast, the experimental ∇2ρ is seen to change much more quickly than its theoretical counterpart and as such, small errors in determining the exact location of the bond critical points (bcp) may result in significant differences in ∇2ρbetween experiment and theory as discussed here.



(a)

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(b)


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(c)

(d)

Figure 5: -∇2ρ maps of the sulfoxide moiety in the EXP model for (a) (2), (b) (3) and in the SP model for (c) (2) and (d) (3). Hydrogen Bonds Koch et al.47 separated hydrogen bonds into two classes; classical and non-classical. Classical hydrogen bonds are defined as those where heteroatoms (X) are both donor and acceptor (X-H) within the hydrogen bond e.g. N-H, O-H groups bonded to N or O, while nonclassical bonds have a carbon atom as either hydrogen bond donor or acceptor. This definition is interpreted to also include oxygen bonded to atoms such as sulfur i.e. the S=O bonds present in (2) and (3). Topological analysis revealed a total of 5, 5 and 9 classical hydrogen bonds in (1), (2) and (3), respectively, with all bonds previously reported in the literature for (1) and (2) being found. C-H···π interactions were also found in (1) and (3). In (1), an aromatic hydrogen is directed towards one of the outer aromatic rings in CBZ, while in (3), the CBZ aromatic



hydrogen is substituted by one from the SAC molecule. Geometrical analysis of all hydrogen bonds found that the N-H···O bonds were most linear in each of the systems, with donorhydrogen-acceptor angles between 169-175° The C-H···C bonds were next most linear with an average bond angle of 142.4°. A total of 6 of these bonds were found, with three bonds having DHA angles greater than 150° and the other three having angles between 125 and 140°. C-H···O bonds were the least linear with all DHA angles less than 150°. It was also found that C-H···O bonds had the longest hydrogen to acceptor distances, these being almost exclusively over 2 Å, while N-H···O bonds had the shortest distances mostly (ranging from 1.75 - 2 Å) with one bond (N(2') - H(02')···O(1)) having a hydrogen to acceptor distance of 2.45 Å. Refer to Tables S28-30 (ESI) for full geometrical details of the hydrogen bonds. According to Koch et al.47, hydrogen bonds are characterised by a relatively low ρbcp and a positive ∇2ρbcp. All the hydrogen bonds discussed here were found to have these characteristics. All hydrogen bonds found in (1) and (2) were intermolecular and only one of the bonds found in (3) was located within the chosen asymmetric unit [N(1)-H(1A) ···O(1')], linking the carbamate group of the carbamazepine with the sulfoxide moiety of the saccharin forming the well-known heterosynthon. Refer to Figure 6 for diagrams of the interactions in (1), (2) and (3).


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(a)

(b)



(c) Figure 6: Selected synthon interactions in (a) (1), (b) (2) and (c) (3)48.

Hydrogen bond energies Hydrogen bond energies were approximated using the methods developed by Abramov49 and Espinosa50. Abramov initially proposed an expression for the kinetic energy (G) utilising the electron density, ρbcp. This was extended upon by Espinosa in conjunction with the Laplacian to obtain an expression for the potential energy (V). This provides an approximation of the bond energy. H-bonds can be separated into three groups according to their strength; weak (EHB < 20 kJ mol-1), moderate strength (EHB = 20-40 kJ mol-1) and strong (EHB > 60 kJ mol-1)51. Details of the hydrogen bonds as determined by topological analysis are reported in Tables 2 to 4 for (1), (2) and (3), respectively. Each system is held together almost exclusively by weak interactions,


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ranging from 2.7 – 19.0 kJ mol-1, with (1) and (2) each containing one moderately strong hydrogen bond; N(2') - H(01')···O(1') in (1) and N(1) - H(1A)···O(3) in (2). The N(2')-H(01')···O(1') bond found in (1) is symmetrical and forms the primary bonding motif. The two carbamazepine molecules are bonded in an anti-parallel fashion (see Figure 6a) which results in the aromatic tricyclic region being oriented in such a way that favourable interactions are present between the tricyclic aromatic rings. This orientation also gives rise to a C-H··· π interaction (C(11') - H(11')···C(3'), (-x+1, -y+1, -z+1)), with an estimated strength of 3.2 kJmol-1. Figure 7 shows the Laplacian and deformation density maps for selected hydrogen bonds in (1). The deformation density map of the homosynthon in (1) reflects what is observed in the Laplacian map, with the density around H(01') being polarised towards O(1') (-x, -y-1, -z). However, neither of the lone pairs on O(1') are directed towards the symmetry generated H(01'), instead they are directed in a perpendicular direction towards the intramolecular H(01') atom and other intermolecular interactions with H(8') and H(12'). The polarisation of the electron density towards the intramolecular H(01') may be a result of the N(2') atom being a hydrogen bond donor, forming interactions within the crystalline lattice thus causing a minor charge redistribution within the carboxamide group. The deformation density map in Figure 7d, illustrates the interaction between O(1') and hydrogens H(8') and H(12'), reveals the lone pair to be equally directed towards both atoms. The effect of the crystal field on the direction of the lone pairs of O(1') is also highlighted when compared to the Laplacian map of the same plane from gas phase calculations as seen in Figure 7b, where the lone pair is pointed directly at H(01'). The potential energy density of the gas phase hydrogen bond is calculated to be -0.14 Eh Å-3 with an estimated energy of 27.5 kJ mol-1, ~5 kJ mol-1 greater than the value obtained from experiment.



(a)

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(b)


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(c) (d) Figure 7: Topological diagrams of selected hydrogen bond interactions in (1); a.) -∇2ρ map of the O(1')-C(15')-N(2') plane from experiment b.) -∇2ρ map of the O(1')-C(15')-N(2') plane from theory, c.) deformation density map of the O(1')-C(15')-N(2') and d.) deformation density map of O(1'). Contours for (a) and (b) are plotted on a log scale (with range -800 to -0.001 and 0.001 to 800), while for (c) and (d), a scale of 0.1 e Å-3 was used. Positive lines indicate positive contours and dashed lines indicate negative contours.

An analogous situation is present in (2), where the N(1)-H(1A)···O(3) bond forms the homosynthon by bridging between the aromatic amine with the carbonyl oxygen to form the primary bonding motif between saccharin molecules; Figure 8 shows the Laplacian and deformation density maps for selected hydrogen bonds in (2). Similar to the findings for (1), the electron density localised around H(1A), is directed towards the acceptor O(3), due to the electronegativity difference, however both plots of the Laplacian and deformation density show an oxygen lone pair aligned to the hydrogen resulting in a significantly stronger bond in (2) compared to that in (1) (37.8 vs. 22.2 kJ mol-1) while the distances from the hydrogen and acceptor atoms to the critical point are similar. Figure 8c shows the other lone pair of O(3)



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interaction with intermolecular H(5); the non-linear alignment results in a weak bond (6.4 kJ mol-1).

2’)(a) (b) (c) Figure 8: Topological diagrams of selected hydrogen bond interactions in (2); a.) -∇2ρ map of the H(1A)-N(1)O(3) plane, b.) deformation density map of the H(1A)-N(1)-O(3) and c.) deformation density map of O(3). Contours for (a) are plotted on a log scale (with range -800 to -0.001 and 0.001 to 800), while for (b) and (c), a scale of 0.1 e Å-3 was used. Positive lines indicate positive contours and dashed lines indicate negative contours.

The bonding motifs and topology discussed above are carried over to the co-crystal, with the primary bonds in (1) and (2) being present in (3); the resulting heterosynthon represents the primary bonding motif in (3), forming a ‘cross shape’ containing a pair each of opposing carbamazepine and saccharin molecules. Analogous bonds are comparable in strength to the N(2')-H(01')···O(1') which is estimated to have a strength of 19.0 kJ mol-1 in (3), compared to 22.2 kJ mol-1 in (1). Similarly, the N(1)-H(1A)···O(3) is estimated to have a strength of 40.3 kJ mol-1 in (3) compared to 37.8 kJ mol-1in (2). Figure 9 shows the Laplacian and deformation density maps for the primary hydrogen bonding plane in (3). Both depictions show the lone pair of O(1') is directly aligned with H(01') while the same cannot be said of the lone pairs on O(1) towards H(02'). This explains the significant disparity in bond strength (~ 20 kJ mol-1) between


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the two primary bonds in (3). C-H··· π interactions can also be seen in (3) due to the analogous bonding of the carbamazepine molecules. This results in two interaction (C(5') - H(5')···C(7')(x+1, -y+1, -z+2) and ( C(3) - H(3)···C(3')( x, y-1, z)) with estimated strengths of 2.7 and 2.9 kJmol-1 respectively.

(a) (b) Figure 9: Topological diagrams of selected hydrogen bond interactions in (3); a.) -∇2ρ map of the O(1)O(1')-N(1) plane and b.) deformation density map of the O(1)-O(1')-N(1). Contours for (a) are plotted on a log scale (with range -800 to -0.001 and 0.001 to 800), a scale of 0.1 e Å-3 was used for (b). Positive lines indicate positive contours and dashed lines indicate negative contours.



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While the same number of hydrogen bonds were found in (1) and (3) on a per molecule basis, it should be noted they were formed competitively, i.e. formed according to Etter’s rules of hydrogen bonding52, 53 (the strongest donor will bind to the strongest acceptor etc.). In the solid state, therefore, the hydrogen bonds reported above are simply the strongest bonds which are capable of being formed. The polar nature of water will also result in the introduction of bonding interactions upon exposure to this solvent, which are likely to be more numerous than those in the solid state. In which case, the weak interactions which hold the system together are likely to dissociate to form stronger interactions with water, again in accordance with Etter’s rules. The increased number of molecules in the co-crystal also means there are more sites to which water molecules can potentially bind. CBZ has 2 hydrogen bond donors and 2 acceptors while SAC has 1 and 5; solvation of (3) thus results in 3 hydrogen bond donors and 7 acceptors. Both these mechanisms help to potentially explain the previously reported findings that (3) is more soluble than (1). Table 2: Topological analysis of hydrogen bonding in (1). Standard uncertainties have been omitted from the Table for clarity. They are closely scattered around 0.02 eÅ-3 (bcp) and 0.05 eÅ-5 (2bcp). BOND





(e Å-3)

(e Å-5)

0.10

3.36

0.03

ε

dH···bcp

dA···bcp

G

V

H

EHB

(Å)

(Å)

(Eh Å-3)

(Eh Å-3)

(Eh Å-3)

(kJ mol-1)

0.02

0.662

1.125

0.17

-0.11

0.06

22.2

0.87

0.35

0.904

1.544

0.04

-0.02

0.02

4.6

0.03

0.48

0.36

1.087

1.583

0.02

-0.02

0.01

3.1

0.04

0.44

0.93

1.082

1.784

0.02

-0.02

0.01

3.2

0.04

0.40

1.84

1.141

2.492

0.02

-0.02

0.01

0.04

0.39

1.29

1.655

1.773

0.02

-0.02

0.00

Intermolecular N(2') - H(01')···O(1')a C(8') -

H(8')···O(1')b

C(12') N(2') -

H(12')···O(1')c

H(02')···C(3')c

C(11') -

H(11')···C(3')d

Short Contacts C(5') ···C(10')c

Symmetry operators: a -x, -y, -z+1; b x-1, y, z; c x-0.5, -y+0.5, z-0.5; d -x+1, -y+1, -z+1.


3.2 3.4

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1 2 3 Table 3: Topological analysis of hydrogen bonding in (2). Standard uncertainties have been 4 omitted from the Table for clarity. They are closely scattered around 0.02 eÅ-3 (bcp) and 0.05 eÅ-5 5 (2bcp). 6 7 G V H dH···bcp dA···bcp   8 BOND ε 9 (Eh Å-3) (Eh Å-3) (Eh Å-3) (e Å-3) (e Å-5) (Å) (Å) 10 11 Intermolecular 12 a 0.629 1.150 13 N(1) – H(1A) ···O(3) 0.20 3.61 0.02 0.23 -0.20 0.03 14 15 C(2) - H(2)···O(2)b 0.905 1.465 0.04 1.00 0.41 0.05 -0.03 0.02 16 1.219 1.478 0.05 0.65 0.04 0.04 -0.03 0.01 17 C(3) - H(3)···O(2)c 18 d 1.018 1.476 0.05 0.73 0.14 0.04 -0.03 0.01 19 C(4) - H(4)···O(1) 20 C(5) - H(5)···O(3)e 1.052 1.396 0.07 0.96 0.03 0.05 -0.04 0.01 21 22 Short Contacts 23 a 1.806 1.545 0.03 0.33 1.49 0.02 -0.01 0.00 24 C(5) ···C(7) 25 Symmetry operators: a -x, -y+1, -z; b -x+1, y+0.5, -z+0.5; c -x+1, -y+2, -z; d x, -y+2.5, z-0.5; e -x, y26 0.5, -z-0.5. 27 28 Table 4: Topological analysis of hydrogen bonding in (3). Standard uncertainties have been 29 omitted from the Table for clarity. They are closely scattered around 0.02 eÅ-3 (bcp) and 0.05 eÅ5 30 (2bcp). 31 32 BOND ε G V H   dH···bcp dA···bcp 33 (eÅ-3) (eÅ-5) (Eh Å-3) (Eh Å-3) (Eh Å-3) 34 (Å) (Å) 35 Intermolecular 36 0.21 1.96 0.02 0.605 1.146 0.24 -0.21 0.04 37 N(1) - H(1A)···O(1') 38 N(2') - H(01') ···O(1')a 0.09 2.91 0.05 0.668 1.273 0.15 -0.1 0.05 39 40 N(2') - H(02')···O(1)a 0.07 0.90 0.09 1.141 1.399 0.05 -0.04 0.01 41 b 0.04 0.66 0.1 1.010 1.507 0.03 -0.02 0.01 42 C(13') - H(13')···O(2) 43 C(2) -H(2)···O(1)c 0.06 1.22 0.41 0.890 1.382 0.06 -0.04 0.02 44 0.08 2.79 0.03 0.644 2.255 0.14 -0.09 0.05 45 N(2') - H(01')···C(15')a 46 C(8') - H(8')···O(3)d 0.03 0.62 0.28 0.990 1.561 0.03 -0.02 0.01 47 48 C(5') - H(5')···C(7')e 0.03 0.37 0.23 1.136 1.780 0.02 -0.01 0.01 49 f 0.03 0.41 1.09 1.151 1.725 0.02 -0.01 0.01 50 C(3) - H(3)···C(3') 51 Short Contacts 52 g 0.04 0.32 0.30 1.643 1.751 0.02 -0.01 0.00 53 C(10') ···C(3) 54 C(1') ···C(3)f 0.04 0.36 0.08 1.654 1.755 0.02 -0.02 0.00 55 56 57 58 59 ACS Paragon Plus Environment 60

EHB (kJ mol-1)

37.8 5.2 5.2 5.3 6.4 2.4

EHB (kJ mol-1) 40.3 19.0 7.5 4.2 8.6 16.9 3.5 2.7 2.9 2.7 3.0


Symmetry operators: a -x, -y+1, -z+1; b -x+1, -y+1, -z+1; c -x+1, -y, -z+1; d -x, -y+1, -z+2; e -x+1, y+1, -z+2; f x, y-1, z; g x+1, y-1, z

Hirshfeld surfaces Three dimensional Hirshfeld surfaces, and the corresponding two dimensional fingerprint plots, were generated using the CrystalExplorer program54. The Hirshfeld surfaces can be found in Figures 10-12, in which areas where the strongest intermolecular interactions are present are highlighted in red. The parameter dnorm, which refers to the normalised contact distance in terms of de and di is plotted on the surface55. de is defined as the distance from the Hirshfeld surface to the nearest external nucleus while di is the distance from the surface to the nearest internal nucleus. Figures 13-15 show two-dimensional fingerprint plots for the complete molecules and specific interactions. In (1), N···H and O···H interactions play only a minor role, accounting for 13.2 and 2.2% of interactions, respectively; this can be attributed to the low number of these atoms in CBZ. The O···H bonds play a much more prominent role in (2), accounting for 53% of interactions. The position of the oxygen atoms bonded to sulfur in SAC, protruding away from the ring may contribute to this, as the lone pairs are more accessible to bonding partners; this is also reflected in the hydrogen bond analysis, although the oxygens are the only hydrogen bond acceptors in the molecule. In the co-crystal, O···H and N···H contributions are like that of (1) however a larger percentage was occupied by O···H bonds, with the SAC molecule producing extra hydrogen bonding partners. Both CBZ and SAC have aromatic features, and this is in evidence by C···H, C···C and H···H interactions accounting for most weak interactions across all three systems.


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(a) Figure 10: Hirshfeld surfaces for (1).

(b)


(b)



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(a)

(b)

(c)

(d)

(e)

(f)


(b)


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Figure 13: 2-Dimensional fingerprint plots of (1); (a) all interactions, (b) O···H interactions, (c) N···H interactions, (d) C···C interactions, (e) C···H interactions and (f) H···H interactions

(a)

(b)

(c)

(d) (f) (e) Figure 14: 2-Dimensional fingerprint plots of (2); (a) all interactions, (b) O···H interactions, (c) N···H interactions, (d) C···C interactions, (e) C···H interactions and (f) H···H interactions



(a)

(b)

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(c)

(d) (e) (f) Figure 15: 2-dimensional fingerprint plots of (3); (a) all interactions, (b) O···H interactions, (c) N···H interactions, (d) C···C interactions, (e) C···H interactions and (f) H···H interactions

Atomic Charges Integrated atomic basin charges were also determined from topological analysis of (1), (2) and (3). There was excellent agreement between the charges obtained from the EXP and SP models with mean differences of 0.001, 0.005 and 0.001e for (1), (2) and (3) respectively. The largest difference in charge in both (1) and (3) was found on C(15'), located on the carboxamide group of CBZ, with the EXP and SP models differing in charge by approximately 0.5e. The relative charge deficiency can be attributed to the delocalisation of electrons towards the neighbouring atom N(2'),


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which is heavily involved in hydrogen bonding in the formation of the homo- and heterosynthons mentioned previously. The charge delocalisation is further seen in N(1') which is more positive in the EXP compared to the SP model (by 0.2e), indicating electron movement towards the carboxamide group where excess charge is delocalised and involved in hydrogen bonding. Consequently, N(2') is more negative in the EXP model, by approximately 0.13e in both (1) and (3). Interestingly, there is a negligible charge difference on O(1') between the EXP and SP models. Further analysis of (2) reveals the largest difference in charge to be located on H(4) and N(1), with EXP reporting larger charges by 0.23 and 0.28e, respectively. The involvement of both atoms in the formation of intermolecular hydrogen bonds in (2) may be the cause of this difference. It can be seen that N(1) plays a crucial role in forming the bonding motif in (3), with a hydrogen bond strength of 40.3 kJ mol-1 (compared to 37.8 kJ mol-1 in (2)), however there is a negligible charge difference between the EXP and SP models in (3). This can be attributed to this hydrogen bond being present within the asymmetric unit and thus being accounted for in the SP calculations. The difference of 0.19e for N(1) (-1.11 and -1.30e for (2) and (3) respectively) in the EXP model supports this theory as electron density in the saccharin molecule is redistributed between (2) and (3), where the corresponding increase in electronegativity of N(1) is balanced by a reduced atomic population in O(3) from -1.11e in (2) to -0.99e in (3). Refer to Table S31 (ESI) for a full list of atomic charges obtained from multipole refinement.

Electrostatic Potential The molecular electrostatic potential (MEP) can be used to visualise the changes that occur when a molecule undergoes crystallisation, allowing greater insight to be gained into the



driving forces behind crystal formation, specifically, the movement of electrons between groups and atoms involved in weak interactions. Figures 16-18 show the MEP calculated from the EXP models for (1), (2) and (3) mapped onto an isosurface of ρ, which have been plotted on the same scale for comparability. Visual analysis of Figures 16-18 shows an even charge distribution across the aromatic regions for (1) and (2), with the heteroatoms being, as expected, electronegative. A contrast to this is seen in (3), where the charge on the saccharin has remained similar to that seen in (2), however the charge distribution in the aromatic region of CBZ has separated into two parts; the C(1) to C(6) aromatic ring becomes more electropositive (-0.65 to 0.32e), and the C(9) to C(14) aromatic ring becomes more electronegative (0.48 to 0.23e), in accordance with the increased number of short contacts reported in (3) in comparison to (1). This effect is further pronounced in (3) by the formation of π-π interactions, and charge redistribution involving the movement of electrons from the aromatic region of the CBZ molecule towards the carboxamide group due to the involvement of N(2) in multiple moderately strong hydrogen bonds. This movement generates a small dipole between N(1) and the edges of the aromatic ring.


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Figure 16: Molecular electrostatic potential maps of (1) mapped on an isosurface of ρ56.





Differences in atomic charge between CBZ and SAC can be quantified through an analysis of atomic charges and can be visualised through the MEP maps discussed above. In both cases, the main driving force behind the differences can be related to the types of hydrogen bonds they form (and the strength of these bonds). Atoms such as N(2) and N(1') have the largest differences in atomic charge due to their involvement primarily as hydrogen bond donors in the four main bonds which hold (3) together, however, in a complementary fashion, hydrogen bond acceptors may also display large differences in charge between systems. Although the effects of these interactions are most obvious on the donors and acceptors, as seen through the high degree of complementarity in the MEP maps, they also have a knock on effect to their surrounding atoms and molecules. The charge deficiency on C(15), due to N(2) being a hydrogen bond donor to some moderately strong hydrogen bonds, is an obvious example of this knock on effect. Although longer range charge redistribution effects may not be obvious in a comparison of the atomic charges, the formation of weaker interactions in the co-crystal may be an indicator of this, as any interaction requires a certain charge separation. The overall result is an increase in polarity across the surface of the crystal. Additionally, the molecular surface of the co-crystal, (3), is larger than that of (1), Combining these two factors results in a greater number of potential binding sites, which my explain the increased solubility of (3), compared to (1). Based on the differences reported here, it could be suggested that the increase in solubility is due to a greater dissolution rate of (3) compared to (1) in solution. This is in accordance with the results reported by Box et al.10 where peak concentration (~370 µg) was achieved after 11 and 77 minutes for (3) and (1) respectively. The oxygen atoms in the molecules were all involved in hydrogen bonding in all three systems, acting as hydrogen bond acceptors with O(1') and O(3) being bonded to carbon in


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carbamazepine and saccharin respectively while O(1) and O(2) were bonded to sulfur in saccharin. Table 6 shows the atomic charges of the oxygen atoms in all systems. The oxygen atoms bonded to sulfur had greater atomic charge compared to those bonded to carbon. The electronegativity of oxygen along with the greater number of electrons associated with sulfur explains this result. It is also seen that the oxygen atoms have greater charge in (1) and (2) compared to their counterparts in (3). Oxygen was involved in 3, 5 and 6 hydrogen bonds in (1), (2) and (3) respectively and the greater involvement results in charge distribution across a larger area leading to lower charge. The largest difference seen in O(1') with a difference of 0.22e between (1) and (3). This is due to its involvement in a bifurcated hydrogen bond in (3). Table 6: Atomic charges of oxygen atoms in (1), (2) and (3). Atoms O(1') (1) (3)

Pv -0.44 -0.28

Ω (EXP) -1.16 -0.94

Ω (DFT) -1.17 -1.18

O(1) (2) (3) O(2) (2) (3) O(3) (2) (3)

-0.59 -0.27 -0.52 -0.25 -0.41 -0.18

-1.27 -1.17 -1.19 -1.15 -1.11 -0.99

-1.30 -1.30 -1.30 -1.32 -1.11 -1.14

Lattice Energies The lattice energy of a crystal is a useful indicator of its solubility, with larger, more negative values indicating a more stable, less soluble, system. Generally, crystals with a higher lattice energy will require more energy to dissociate, but it should also be noted that the dissociation process also releases a certain amount of energy. Additionally, although the formation of a co-crystal implies a more stable structure due to stabilisation from a co-former,



this does not always lead to reduced solubility and dissolution in physical studies. How the individual components interact with the dissolution medium also plays a role. Lattice energies were calculated for all three systems to gain an understanding of the effects of charge redistribution resulting from the hydrogen bond formation and as observed in the atomic charge and electrostatic potential distributions. Two methods were used to calculate the lattice energy; those implemented by Gavezzotti in PIXEL57 and the CrystalExplorer (CE-B3LYP) approach5860,

and the component and total energies are shown in Table 7. Both methods evaluate the

interaction energies via a pairwise approach. In the PIXEL method, an ab initio calculation is initially performed to obtain the molecular electron density. The molecular electron density is then distributed over a grid into units, known as pixels and the energies are evaluated via numerical integration over these points. The CE-B3LYP approach uses monomer wavefunctions to estimate the components of the energy. Using the PIXEL method, the co-crystal is determined to be slightly more stable than CBZ, by approximately 7 kJ mol-1, while the CE-B3LYP method reports the inverse to be true, with CBZ more stable by 10 kJ mol-1. The benchmarking studies carried out by Turner et al.60 and Mackenzie et al.58 found there was excellent correlation between the values obtained from CE-B3LYP when compared to the PIXEL method and to published experimental sublimation energies59. The difference in values between (1) and (3) for both methods are within experimental error (roughly estimated as ca.10 kJ mol-1), while the differences between the two methods could be due to the difference in evaluation approaches. Our future studies in this area will be aimed at obtaining analogous experimental values. Table 7: Table of lattice energies for (1), (2) and (3) predicted by the CE-B3LYP method and the PIXEL program developed by Gavezzotti. Raw CE values refer to unscaled values, scaled values


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refer to those multiplied by the coefficients obtained from benchmarked calculations in Mackenzie et al.58. Energies are given in kJ mol-1. Coulombic Polarisation Dispersion Repulsion -97.9 -44.6 -160.6 129.4 -72.1 -25.7 -156.8 133 -76.2 -19.0 -136.6 82.2

Total -173.7 -121.6 -150.0

(1)

PIXEL (MP2/6-31G(d,p)) CE (B3LYP/6-31G(d,p) raw CE (B3LYP/6-31G(d,p) scaled

(2)


-117.4 -87.6 -92.5

-46.4 -25.4 -18.8

-109.1 -96.6 -84.1

101.5 116 71.7

-171.4 -93.5 -123.8

(3)


-115.5 -82.8 -87.5

-48.2 -27.8 -20.6

-134.3 -126.4 -110.1

118.0 126.3 78.1

-180.1 -110.6 -140.2

The hydrogen bond analysis above predicts that the total strength of the hydrogen bonds is approximately -36 and -105 kJ mol-1 (taken as the sum of estimated hydrogen bond energies from Tables 2 and 4), respectively, for (1) and (3), while the difference in lattice energies calculated by both methods is approximately 10 kJ mol-1. This disparity is reflected in the Coulombic component of the total energy, which differs between (1) and (3) by approximately 10 - 20 kJ mol-1. The more negative coulombic energy in (3) is offset by the larger dispersive forces in (1) by approximately 20-30 kJ mol-1. This highlights the fact that, although hydrogen bonds may play a large part in determining stability and other physical properties, other factors may also exert contributing effects. To further examine this possibility, we also investigated the solid state entropy of (1) and (3) using the method described by Madsen et al.61, 62. The THMA1463 program was used to obtain the three translational and three vibrational modes for both systems, which were subsequently used to calculate the solid state entropy using equation 1. Thermal parameters obtained from experiment performed at 150K were used as input and the THMA program was



Page 36 of 45

used to estimate the thermal parameters at 298K. The results of the calculations are shown in Table 8 along with their experimentally determined melting points. ℎ𝑣

ℎ𝑣

𝑆𝑣𝑖𝑏(𝑇) = 𝑛𝑅(𝑘𝑇[𝑒𝑘𝑇 ― 1]

―1

ℎ𝑣

― 𝑙𝑛[1 ― 𝑒

― 𝑘𝑇

(1)

])

Table 8: Values of solid state entropy for (1), (2) and (3). Values are given in J K-1 mol-1. Melting points (MP) are given in ᵒC. Temperature (K)

(1)

(2)

(3)

Entropy Temp

150

89.8

78.3

94.6

298

123.7

112

127.9

228.864

172.565

Melting point (MP) MP

190 - 19364

The co-crystal (3) has entropy than (1) and this can be attributed to the larger number of atoms within the system, resulting in more microstates and vibrational degrees of freedom. An inverse relationship was found between the melting points and solid state entropies of the systems. Thus, higher entropy, indicative of greater internal energy within the system, means that less external energy is required to cause the system to break apart. This is also in accordance with literature66, 67 and findings reported by Box et al.10 and Hickey et al.9 which reported that (3) had a better dissolution profile compared to (1), while the final amount of dissolved CBZ was comparable between the single product and co-crystal. This can be rationalised by our current findings, with the higher entropy of (3) meaning that less energy from the solvent is required to induce dissociation, hence accounting for the higher dissolution rate of (3); once CBZ is in solution, however, the solubility kinetics would be very similar.


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Conclusion Here we present an EDD study of CBZ (1), SAC (2) and the CBZ-SAC (3) co-crystal with the aim of providing an explanation for the improved dissolution profile of CBZ-SAC when compared to commercially available formulations of CBZ. High resolution single crystal X-ray crystallography was used to examine these systems at the electronic level. Topological analysis revealed a total of 5, 5 and 9 hydrogen bonds for (1), (2) and (3), respectively, with favourable aromatic interactions also present. The homosynthons present in (1) and (2), which form the primary bonding motifs in those systems, are also present in (3), albeit in the form of one homoand one heterosynthon, which result in the cross formation of opposing pairs of CBZ and SAC. A comparison of the atomic charges between the individual crystals and co-crystal reveals notable changes due to the involvement of N(2) in multiple hydrogen bonds, causing a charge deficiency in C(15), which in turn results in charge redistribution from the aromatic region in CBZ towards the carboxamide group. This generates a small dipole within the aromatic region thus making it more conducive to the formation of weak interactions. Similar changes can be seen in SAC. These changes are reflected in the MEP diagrams, where there is a high degree of complementarity in regions where there are moderately strong hydrogen bonds between donor and acceptor and aromatic regions do not display as even a charge distribution. This is believed to result in larger charge separation across the surface area of the co-crystal resulted in more potential binding sites when water is introduced. The lattice energy of each system was also calculated using the PIXEL and CE-B3LYP approaches with PIXEL reporting (3) to be more stable than (1) and CE-B3LYP reporting the opposite to be true. This highlights the need for further studies in this area to further investigate the accuracy of the energy contributions and to obtain experimental values. The solid state entropy of the systems was also investigated and was found to have an inverse relationship with the melting points. The entropy was also found to be



related to the dissolution rate; in both cases, higher entropy, taken to indicate that a system has more internal energy, means that less external energy from heat or solution is required to break the system apart. Overall, the formation of moderately strong hydrogen bonds, making (3) more stable than (1) in the solid state, also causes a charge redistribution across the CBZ molecule in the co-crystal, resulting in an increase in polarity of the system. The increased potential binding sites for water explain the previous findings in other papers that the CBZ-SAC co-crystal is more soluble than CBZ itself. Future research is aimed at examining the same properties of the CBZNIC co-crystal to gain insights into why it is less soluble.


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Supporting information SHADE anisotropic displacement parameters for hydrogen atoms, tables of experimental bond lengths and angles, details of topological analysis, residual density analysis, Hirshfeld surfaces and fingerprint plots. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgements DEH and PWG would like to thank The University of Sydney Bridging Support Scheme for funding. JD thanks The University of Sydney for an APA, the School of Pharmacy for research funding and the Sydney Informatics Hub at the University of Sydney for providing access to HPC Artemis. JO thanks the Danish National Research Foundation for financial support (DNRF-93). The authors would also like to thank Professor Mark Spackman for valuable discussions regarding lattice energy calculations for co-crystals.



References (1) Rossi, S., Australian Medicines Handbook 2016 (online). In ed.; Rossi, S., Ed. Australian Medicines Handbook Pty. Ltd: Adelaide, 2016. (2) Ortells, M. O.; Barrantes, G. E., Molecular modelling of the interactions of carbamazepine and a nicotinic receptor involved in the autosomal dominant nocturnal frontal lobe epilepsy. Br. J. Pharmacol. 2002, 136, 883-895. (3) Qiao, N.; Li, M.; Schlindwein, W.; Malek, N.; Davies, A.; Trappitt, G., Pharmaceutical cocrystals: An overview. Int. J. Pharm. 2011, 419, 1-11. (4) Almarsson, Ö.; Zaworotko, M. J., Crystal engineering of the composition of pharmaceutical phases. Do pharmaceutical co-crystals represent a new path to improved medicines? Chem. Commun. (Cambridge, U. K.) 2004, 1889-1896. (5) Blagden, N.; De Matas, M.; Gavan, P.; York, P., Crystal engineering of active pharmaceutical ingredients to improve solubility and dissolution rates. Adv. Drug Delivery Rev. 2007, 59, 617-630. (6) FDA, Regulatory Classification of Pharmaceutical Co-Crystals. In ed.; Services, U. S. D. o. H. a. H., Ed. Center for Drug Evaluation and Research 2016; p 8. (7) Springuel, G.; Norberg, B.; Robeyns, K.; Wouters, J.; Leyssens, T., Advances in Pharmaceutical Co-crystal Screening: Effective Co-crystal Screening through Structural Resemblance. Cryst. Growth Des. 2012, 12, 475-484. (8) Desiraju, G. R., Supramolecular Synthons in Crystal Engineering—A New Organic Synthesis. Angew. Chem., Int. Ed. Engl. 1995, 34, 2311-2327. (9) Hickey, M. B.; Peterson, M. L.; Scoppettuolo, L. A.; Morrisette, S. L.; Vetter, A.; Guzmán, H.; Remenar, J. F.; Zhang, Z.; Tawa, M. D.; Haley, S.; Zaworotko, M. J.; Almarsson, Ö., Performance comparison of a co-crystal of carbamazepine with marketed product. Eur. J. Pharm. Biopharm. 2007, 67, 112-119. (10) Box, K. J.; Comer, J.; Taylor, R.; Karki, S.; Ruiz, R.; Price, R.; Fotaki, N., Small-Scale Assays for Studying Dissolution of Pharmaceutical Cocrystals for Oral Administration. AAPS PharmSciTech 2016, 17, 245-251. (11) Du, J. J.; Váradi, L.; Williams, P. A.; Groundwater, P. W.; Overgaard, J.; Platts, J. A.; Hibbs, D. E., An analysis of the experimental and theoretical charge density distributions of the piroxicam–saccharin co-crystal and its constituents. RSC Adv. 2016, 6, 81578-81590. (12) Hibbs, D. E.; Austin‐Woods, C. J.; Platts, J. A.; Overgaard, J.; Turner, P., Experimental and theoretical charge density study of the neurotransmitter taurine. Chem.-Eur. J. 2003, 9, 1075-1084. (13) Lai, F.; Du, J. J.; Williams, P. A.; Váradi, L.; Baker, D.; Groundwater, P. W.; Overgaard, J.; Platts, J. A.; Hibbs, D. E., A comparison of the experimental and theoretical charge density distributions in two polymorphic modifications of piroxicam. Phys. Chem. Chem. Phys. 2016, 18, 28802-28818. (14) Nguyen, T. H.; Groundwater, P. W.; Platts, J. A.; Hibbs, D. E., Experimental and Theoretical Charge Density Studies of 8-Hydroxyquinoline Cocrystallized with Salicylic Acid. J. Phys. Chem. A 2012, 116, 3420-3427. (15) Nguyen, T. H.; Howard, S. T.; Hanrahan, J. R.; Groundwater, P. W.; Platts, J. A.; Hibbs, D. E., Experimental and Theoretical Charge Density Distribution in a Host-Guest System: Synthetic Terephthaloyl Receptor Complexed to Adipic Acid. J. Phys. Chem. A 2012, 116, 56185628.


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For table of contents use only Exploring the solubility of the carbamazepine-saccharin co-crystal; a charge density study

Jonathan J. Du1, Stephen A. Stanton1 Slaiman Fakih1, Bryson A. Hawkins1, Peter A. Williams1,4, Paul W. Groundwater1, Jacob Overgaard2, James A. Platts3 and David E. Hibbs1


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A carbamazepine-saccharin co-crystal was crystallised. Charge density studies were carried out to examine differences in the electron density distribution between the co-crystal and its constituents. This study aims to rationalise the improved solubility of the co-crystal in literature from an electron perspective with the goal of applying these insights into the development of pharmaceutical co-crystals.


Exploring the solubility of the carbamazepine-saccharin co-crystal; a

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