Application of the Method of Molecular VoronoiâDirichlet Polyhedra for

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Application of the method of molecular Voronoi–Dirichlet polyhedra for analysis of non-covalent interactions in crystal structures of flufenamic acid – the current record-holder on the number of structurally studied polymorphs Viktor N. Serezhkin, and Anton V. Savchenkov Cryst. Growth Des., Just Accepted Manuscript • Publication Date (Web): 12 May 2015 Downloaded from http://pubs.acs.org on May 13, 2015

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Crystal Growth & Design

Cover Page APPLICATION OF THE METHOD OF MOLECULAR VORONOI–DIRICHLET POLYHEDRA FOR ANALYSIS OF NON-COVALENT INTERACTIONS IN CRYSTAL STRUCTURES OF FLUFENAMIC ACID – THE CURRENT RECORD-HOLDER ON THE NUMBER OF STRUCTURALLY STUDIED POLYMORPHS

Viktor N. Serezhkin*, Anton V. Savchenkov** Samara State University, Samara, Russian Federation

ABSTRACT: Crystal chemical analysis of 8 polymorphs of flufenamic acid (FFA, C14H10NO2F3) – the current record-holder on the number of structurally characterized polymorphic modifications – was carried out using the method of molecular Voronoi–Dirichlet polyhedra. It was proved, that every polymorph of FFA, as every polymorph of the previous record-holder ROY (C12H9N3O2S), has a unique set of types of intra- and intermolecular non-covalent interactions.

FFA C14H10NO2F3

ROY C12H9N3O2S

*Anton V. Savchenkov +7 92 76 96 87 65 [email protected] 1 Akademika Pavlova street Samara State University 443011 Samara Russian Federation ACS Paragon Plus Environment

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APPLICATION OF THE METHOD OF MOLECULAR VORONOI–DIRICHLET POLYHEDRA FOR ANALYSIS OF NONCOVALENT INTERACTIONS IN CRYSTAL STRUCTURES OF FLUFENAMIC ACID – THE CURRENT RECORD-HOLDER ON THE NUMBER OF STRUCTURALLY STUDIED POLYMORPHS Viktor N. Serezhkin*, Anton V. Savchenkov** Samara State University, Samara, Russian Federation

ABSTRACT: Crystal chemical analysis of 8 polymorphs of flufenamic acid (FFA, C14H10NO2F3) – the current record-holder on the number of structurally characterized polymorphic modifications – was carried out using the method of molecular Voronoi–Dirichlet polyhedra. It was proved, that every polymorph of FFA, as every polymorph of the previous

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record-holder ROY (C12H9N3O2S), has a unique set of types of intra- and intermolecular noncovalent interactions.

1. INTRODUCTION Interest in polymorphism is being sustained for almost two centuries from its discovery by Mitscherlich.1–6 Up to date there are tens of thousands of crystal structures marked as polymorphs in Cambridge Structural Database7 (CSD) and Inorganic Crystal Structure Database8 (ICSD). The ongoing increase in the number of substances presenting polymorphism strengthens the idea of its universality, stated half a century ago by McCrone9: “… every compound has different polymorphic forms and … the number of forms known for a given compound is proportional to the time and money spent in research on that compound”. In recent years, a lot of effort was put into studying conformational polymorphism of molecular crystals, which is defined as the existence of different conformers in the structures of different polymorphs.10 One of the most studied compound possessing conformational polymorphism is the pharmaceutical intermediate ROY11 (5-methyl-2-[(2-nitrophenyl)amino]-3thiophenecarbonitrile). For a long time ROY held the record on the number of structurally characterized polymorphic modifications with 7 polymorphs in the CSD.7 Such rich polymorphism attracted many researchers,2,12–15 though one of the key questions raised by Bernstein1 was not replied: “Can the differences in energetic environment be understood on the basis of particular intermolecular interactions?” To answer this question we analyzed the polymorphic system of ROY using the method of molecular Voronoi–Dirichlet polyhedra (VDP), which earlier proved its efficiency in the analysis of intermolecular interactions in crystal structures of various substances.16,17 Using the method of molecular VDP it was shown, that each


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out of 7 different polymorphs of ROY is characterized by a unique set of intra- and intermolecular interactions.18 In 2012, López-Mejías et al. published a paper19 devoted to nine polymorphs of non-steroidal anti-inflammatory drug flufenamic acid (FFA). FFA (Figure 1) has 8 structurally characterized forms, what makes it the current record-holder on polymorphism as stated in the title of the work by López-Mejías et al.19 The authors experimentally and theoretically characterized relative stability of 8 polymorphs,19 though fundamental reasons of polymorphism of FFA are not discussed. Structural features of 8 polymorphs, containing 27 crystallographically independent molecules of FFA, are discussed only in terms of three torsion angles and no numerical characteristics of packing of molecules are provided in the research.19

HO

O

O N H N

CF3

+

O

–

H N

S

N

flufenamic acid (FFA) C14H10NO2F3

5-methyl-2-[(2-nitrophenyl) amino]-3-thiophenecarbonitrile (ROY) C12H9N3O2S

Figure 1. Molecular structures of FFA and ROY. The idea of using Hirshfeld surfaces for analysis of intermolecular interactions in different polymorphs was earlier tested by McKinnon et al. on the example of ROY.2 The authors came to a conclusion, that «For ROY, detailed comparison of features on Hirshfeld surfaces reproduced on the printed page does not bring any obvious advantage over conventional packing diagrams», and that «a detailed analysis requires a meticulous manual investigation of the corresponding surfaces via interactive computer graphics».2 In our opinion, such method of “manual” analysis


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of intermolecular interactions in the structures of polymorphs will inevitably lead to subjectivism, dependent on how much “meticulous” the researcher is. The difficulty of visual comparison of various crystal structures was well denoted by Bernstein1: «Even for the trained and practiced eye, a single crystal structure of a molecular solid is rarely understood with ease, so that comparison of two or more crystal structures, even involving the same molecule in polymorphic structures, can be an exercise in frustration». The effort to explain conformational origins of polymorphism of FFA was recently attempted by Delaney et al.20 However, the authors concentrated only on 2 most common forms, known for more than 30 years.21,22 Using terahertz spectroscopy and solid-state density functional theory (DFT), the authors20 were able to find the most stable form out of two polymorphs. They have also shown, that “the hydrogen-bonding scheme and total London dispersion forces were essentially the same for both polymorphs, while interactions of the permanent dipoles of the molecules were the main reason for the energetic differences”. The aim of the current work was to apply the method of molecular VDP for examination of peculiarities of non-covalent interactions in the crystal structures of all 8 structurally characterized polymorphs of the current record-holder on polymorphism – the FFA. 2. EXPERIMENTAL SECTION The corresponding reference codes from the CSD7 for eight structurally characterized polymorphs of FFA are FPAMCA, FPAMCA11–FPAMCA17, and for seven structurally characterized polymorphs of ROY are QAXMEH, QAXMEH01–QAXMEH05, QAXMEH12. The procedure of crystal chemical analysis using Voronoi–Dirichlet tessellation and details of


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the method of molecular VDP can be found in the cited literature.16–18,23–25 The basics of the method are discussed further, which will be useful for discussion. The VDP of an atom A surrounded by atoms Y is a convex polyhedron of minimum volume, containing this atom, and bounded by perpendicular planes, which pass through middle points of segments A–Y, connecting atom A with all other atoms Y. Each face of a VDP belongs to two atoms and corresponds to a certain interatomic interaction A–Y. All A–Y contacts can be unambiguously sorted out into chemical bonds A–X and non-covalent interactions A/Z using the method of intersecting spheres.26 Faces of a VDP are also characterized by a rank of face24 (RF), which shows the number of chemical bonds in the shortest chain connecting A and Y. Thus, for all chemical bonds RF = 1, for intramolecular non-covalent interactions RF > 1 and for intermolecular interactions RF = 0. Molecular VDP results from the integration of VDP’s of atoms comprising a molecule. During this procedure all inner faces, corresponding to chemical bonds (RF = 1) and intramolecular interactions (RF > 1), vanish inside a molecular VDP. Therefore, the faceting of a molecular VDP is formed only by faces with RF = 0, and each of them corresponds to a certain contact between two atoms of neighboring molecules. As an example, Figure 2 shows molecular VDP’s of two different conformers of FFA with reference codes FPAMCA11 and FPAMCA.

(a)

(b)


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Figure 2. Molecular VDP’s of two different conformers of FFA in the structures of crystals FPAMCA11 (a) and FPAMCA (b). Atomic VDP’s of atoms of different chemical elements are depicted with different colors. It should be stressed, that all calculations within the method of molecular VDP are based only on crystallographic characteristics of compounds and do not require any crystallochemical radii, quantum chemical estimations or a priori judgment. It is also important that all types of interatomic interactions without exception are taken into account, what eliminates the human factor in the analysis of crystal structures. 3. RESULTS AND DISCUSSION Corresponding reference codes from the CSD7 will be further used for identification of 8 structurally characterized polymorphs of FFA. Calculations using the method of molecular VDP showed, that the average numbers of intra- and intermolecular non-covalent interactions for all 27 crystallographically independent molecules of FFA are equal to 64 and 299 respectively (Tables S1, S2). According to the criterion of conformational polymorphism27 all 27 molecules present different conformers of FFA, as every one of them has a unique set of intramolecular interactions, varied by RF (Table S2). This agrees with the results of the work by López-Mejías et al.19 Atoms of 5 different chemical elements in the composition of FFA molecule (C14H10NO2F3) can possibly realize 15 types of interatomic contacts. Partial contributions of intermolecular contacts (∆A/Z) of a certain type can be unambiguously estimated as the ratio of areas of faces of VDP’s, corresponding to such contacts, to the total area of molecular VDP. The sum of partial contributions of all 15 types of intermolecular (or intramolecular ∆#A/Z) interactions is equal to 100%: ∆FF + ∆FO + ∆FN + ∆CF + ∆HF + ∆OO + ∆NO + ∆CO + ∆HO + ∆NN +


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∆CN + ∆НN + ∆CC + ∆НС + ∆НН = 100%. Detailed characteristics of all non-covalent interactions of 27 crystallographically independent molecules of FFA polymorphs are listed in Tables S1 and S2 in Supporting information. More than 96% of surface area of molecular VDP’s of FFA correspond to 10 out of 15 types of contacts (F/F, C/F, H/F, C/O, H/O, C/N, Н/N, C/C, Н/С and Н/Н), which are present in all polymorphs of FFA (Figure 3). In all cases the most significant contacts are H/F, H/O, Н/С and Н/Н, corresponding to ∼10–30% of surface area of molecular VDP each. 35% ∆,

FPAMCA FPAMCA11 FPAMCA12 FPAMCA13 FPAMCA14 FPAMCA15 FPAMCA16 FPAMCA17

30 25 20 15 10 5 0 F/F

C/F

H/F C/O H/O C/N H/N C/C H/C H/H

Figure 3. Partial contributions (∆, %) of 10 types of intermolecular interactions present in 8 polymorphic modifications of FFA. For polymorphs with Z` > 1 the mean values are shown. The remaining 5 types of intermolecular contacts (O/F, N/F, O/O, N/O and N/N) are not necessarily present in all polymorphs of FFA and therefore are considered as distinguishing interactions. For example, in the FPAMCA13 polymorph all 5 types of interactions are found, while in the FPAMCA polymorph only O/O interactions are present (Figure 4).


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Figure 4. Partial contributions (∆, %) of 5 types of distinguishing intermolecular interactions in 8 polymorphic modifications of FFA. For polymorphs with Z` > 1 the mean values are shown. Figure 4 and Table S1 show, that 6 out of 8 polymorphs of FFA have unique sets of types of distinguishing intermolecular interactions. The only exceptions are modifications FPAMCA14 and FPAMCA15, each involving N/N and O/O intermolecular interactions (Figure 4). However these two polymorphs differ by intramolecular interactions, as shown further. All polymorphs of FFA involve 9 out of 15 types of intramolecular interactions (F/F, C/F, H/F, C/O, H/O, H/N, C/C, H/C and H/H), which contribute up to 99–100% of all non-covalent intramolecular contacts (Figure 5). Three out of 15 intramolecular contacts, namely O/F, N/F and N/N, do not appear in any of the FFA polymorph, as O and N atoms are shielded from F atoms and there is only one N atom in the molecule.


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∆#35 ,%

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FPAMCA FPAMCA11 FPAMCA12 FPAMCA13 FPAMCA14 FPAMCA15 FPAMCA16 FPAMCA17

30 25 20 15 10 5 0 F/F

C/F

H/F

C/O

H/O

H/N

C/C

H/C

H/H

Figure 5. Partial contributions (∆#, %) of 9 types of intramolecular interactions present in 8 polymorphic modifications of FFA. For polymorphs with Z` > 1 the mean values are shown. The remaining 3 types of non-covalent intramolecular contacts (O/O, N/O and C/N) are also distinguishing for FFA polymorphs. Figure 6 and Table S2 show, that polymorphic modifications FPAMCA14 and FPAMCA15, having the same set of intermolecular interactions, differ significantly by intramolecular interactions. The FPAMCA14 polymorph involves O/O, N/O and C/N intramolecular interactions, while in the FPAMCA15 polymorph only C/N intramolecular interactions are present. Thus, every polymorph of FFA has a unique set of types of intra- and intermolecular non-covalent interactions, what in our opinion is the key reason for the existence of polymorphic modifications of FFA.


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Figure 6. Partial contributions (∆#, %) of 3 types of distinguishing intramolecular interactions in 8 polymorphic modifications of FFA. For polymorphs with Z` > 1 the mean values are shown. The application of the rank of faces (RF) of VDP’s for analysis of interatomic interactions reveals various features of molecular crystal structures, which are not recognizable when using conventional methods. For example, in the polymorphs of FFA intramolecular H/F contacts cover about 12.5% of all interactions with RF > 1 (Figure 5). The RF values of H/F contacts are equal to 4 or 8. Contacts H/F with RF = 4 were found in all 27 crystallographically independent molecules of FFA. Such interactions arise between F atoms of –CF3 groups and two nearest H atoms of the same benzene ring (in particular, atom H# on Figure 7a). The shortest H#⋅⋅⋅F distances for contacts with RF = 4 in 27 conformers of FFA are equal to 2.34 – 2.54 Å (Table S3).

(a)

(b)

Figure 7. Two conformations of 27 crystallographically independent molecules of FFA: (a) – «cis»; (b) – «trans». Red dotted lines designate intramolecular H/F contacts with RF = 4 (a) and RF = 8 (b). Chemical bonds depicted as thick lines define the values of RF. Mentioned in the text H*/Н contacts with RF = 6 arise between H* atom and the nearest H atom from the right benzene ring.


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On the other hand, intramolecular H/F contacts with RF = 8 are not present in every FFA conformer (Table S3). It is easy to count, that the path of 8 chemical bonds leads from the F atom to the H atom of the left benzene ring (marked as H* on Figure 7). As can be seen from Figure 7a, such H*/F interaction with RF = 8 is possible only if the right benzene ring is rotated on 180° around the N–C bond (Figure 7b). Thus, all 27 crystallographically independent molecules of FFA have one of two conformations: «cis» (Figure 7a) or «trans» (Figure 7b). The difference between these two conformations is evident from comparison of molecular VDP’s of corresponding molecules: FFA conformer in FPAMCA11 (Figure 2a) has “cis” conformation, and in FPAMCA (Figure 2b) – “trans” conformation. It is also worth noting, that FFA molecules are not flat as shown on Figures 1 and 7. The dihedral angle between planes of two benzene rings in 27 conformers of FFA is in the range of 34–54°. Two benzene rings of FFA molecule cannot lie in the same plane due to intramolecular H*/H contacts with RF = 6 (Figure 7) and H*⋅⋅⋅Н distance of about 2.2 Å. If the molecule was flat, the H*⋅⋅⋅Н distance would be less than 1 Å. The “trans” structures correspond to 14 out of 27 crystallographically independent molecules of FFA. The shortest H*⋅⋅⋅F distances in molecules with “trans” structures (Figure 7b) are equal to 3.63–4.46 Å, while in molecules with “cis” structures (Figure 7a) such distances are not less than 6.09–6.36 Å. According to the method of molecular VDP, intramolecular H*/F contacts with RF = 8 are involved only in 4 out of 14 FFA molecules with “trans” structures (Table S3). In the other 10 molecules such H*/F interactions are shielded by atoms of the same and neighboring molecules. In the end, we provide a comparison of non-covalent interactions of the current record-holder on polymorphism – FFA (C14H10NO2F3) and the previous one – ROY11 (C12H9N3O2S). Both


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compounds consist of atoms of five chemical elements. Labelling F and S atoms as X atoms provides the same set of possible interatomic interactions in FFA and ROY (Figure 8). 30% ∆, 25 20

a

ROY FFA

15 10 5 0 H/H H/C C/C H/N C/N N/N H/O C/O N/O O/O H/X C/X X/N X/O X/X #, % ∆35

30 25

b

20 15 10 5 0 H/H H/C C/C H/N C/N N/N H/O C/O N/O O/O H/X C/X X/N X/O X/X

Figure 8. Comparison of partial contributions of intermolecular (∆, %, a) and intramolecular (∆#, %, b) non-covalent interactions in the structures of FFA (C14H10NO2F3) and ROY (C12H9N3O2S) polymorphs, averaged over 27 crystallographically independent molecules for FFA and over 7 crystallographically independent molecules for ROY. Х atoms represent either F (FFA) or S (ROY) atoms. Figure 8 shows, that intermolecular interactions as well as intramolecular ones in the crystal structures of ROY and FFA are quite similar. The most important non-covalent interactions in both compounds are H/H, H/C, H/O and H/X. Evident differences are noticeable for intermolecular H/N contacts: their partial contribution in the case of FFA is strongly decreased due to fewer number of N atoms in the composition of the molecule and lesser accessibility of sp2 hybridized N atoms, shielded by three bonded atoms (H and 2C). On the other hand, as FFA molecule possess three times as many F atoms as ROY possess S atoms, the significant increase of partial contribution of intermolecular H/X contacts in the case of FFA is not surprising. For the same reason partial contributions of non-covalent X/X interactions are higher in the case of


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FFA. In the case of ROY intramolecular X/X interactions are totally impossible (as there is only one X atom in the molecule), and intermolecular X/X contacts are distinguishing and realize only in 2 out of 7 polymorphs. 4. CONCLUSION As earlier on the example of ROY, we conclude, that every polymorph of FFA is characterized by a unique set of intra- and intermolecular interactions. Appearance (or disappearance) of theoretically possible types of non-covalent interactions due to conformational changes inevitably affects enthalpy and entropy of polymorphs, and consequently affects Gibbs free energy, that defines their relative stability. Thus, every polymorph of FFA corresponds to a certain (local in the general case) minimum of free energy, dependent on the set of intra- and intermolecular interactions involved. In our opinion, the ninth, yet not structurally studied polymorph of FFA will have its own unique set of non-covalent interactions. ASSOCIATED CONTENT Supporting Information. Characteristics of inter- and intramolecular interactions and peculiarities of intramolecular H/F interactions of 27 crystallographically independent molecules in crystals of FFA polymorphs. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * [email protected] ** [email protected]


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Notes The authors declare no competing financial interests. ABBREVIATIONS CSD, Cambridge Structural Database; DFT, density functional theory; FFA, flufenamic acid; ICSD, Inorganic Crystal Structure Database; ROY, 5-methyl-2-[(2-nitrophenyl)amino]-3thiophenecarbonitrile; VDP, Voronoi–Dirichlet polyhedron. REFERENCES (1) Bernstein, J. Polymorphism in Molecular Crystals. Oxford University Press, New York City, 2002. (2) McKinnon, J.J.; Fabbiani, F.P.A.; Spackman, M.A. Cryst. Growth Des. 2007, 7, 755. (3) Dunitz, J. D.; Bernstein, J. Acc. Chem. Res. 1995, 28, 193. (4) Sarma, J. A. R. P.; Desiraju, G. R. In Crystal Engineering: The Design and Application of Functional Solids; Seddon, K. R., Zaworotko, M., Eds.; Kluwer Academic: Amsterdam, 1999; pp 325-356. (5) Kitaigorodskii, A. I. Molecular crystals and molecules. Academic Press, New York, 1973. (6) Brittain, H.G. Polymorphism in Pharmaceutical Solids. Informa Healthcare; 2 edition. July 27, 2009. 656 p. (7) Allen, F.H. Acta Cryst. 2002, B58, 380. (8) Belsky, A.; Hellenbrandt, M.; Karen, V.L.; Luksch, P. Acta Cryst. 2002, B58, 364.


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(9) McCrone, W. C. In Physics and Chemistry of the Organic Solid State; Fox, D., Labes, M. M., Weissberger, A., Eds.; Wiley-Interscience: New York, 1965; Vol. 2; pp 725-767. (10) Cruz-Cabeza, A. J.; Bernstein, J. Chem. Rev. 2014, 114, 2170. (11) Chen, S.; Guzei, I.A.; Yu, L. J. Am. Chem. Soc. 2005, 127, 9881. (12) Yu, L.; Stephenson, G.A.; Mitchell, C.A. et al. J. Am. Chem. Soc. 2000, 122, 585. (13) Mitchell, C.A.; Yu, L.; Ward, M.D. J. Am. Chem. Soc. 2001, 123, 10830. (14) Yu, L. J. Phys. Chem. A. 2002, 106, 544. (15) Smith, J.R.; Xu, W.; Raftery, D. J. Phys. Chem. B. 2006, 110, 7766. (16) Serezhkin, V.N.; Prokaeva, M.A.; Pushkin, D.V.; Serezhkina, L.B. Russ. J. Inorg. Chem. 2009, 54, 1412. (17) Savchenkov, A.V.; Klepov, V.V.; Vologzhanina, A.V. et al. CrystEngComm. 2015, 17, 740. (18) Serezhkin, V.N.; Pushkin, D.V.; Serezhkina, L.B. Crystallogr. Rep. 2010, 55, 554. (19) López-Mejías, V.; Kampf, J.W.; Matzger, A. J. Am. Chem. Soc. 2012, 134, 9872. (20) Delaney, S.P.; Smith, T.M.; Korter, T.M. J. Mol. Struct. 2014, 1078, 83. (21) McConnell, J. F. Cryst. Struct. Commun. 1973, 2, 459. (22) Krishna Murthy, H. M.; Bhat, T. N.; Vijayan, M. Acta Cryst. 1982, B38, 315.


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(23) Serezhkin, V.N. Some features of stereochemistry of U(VI). Structural Chemistry of Inorganic Actinide Compounds. Elsevier Science, 2007. P. 31–65. (24) Shevchenko, A.P.; Serezhkin, V.N. Russ. J. Phys. Chem. 2004, 78, 1598. (25) Serezhkin, V.N.; Serezhkina, L.B.; Vologzhanina, A.V. Acta Cryst. 2012, B68, 305. (26) Serezhkin, V.N.; Mikhailov, Yu.N.; Buslaev, Yu.A. Russ. J. Inorg. Chem. 1997, 42, 1871. (27) Serezhkin, V.N.; Serezhkina, L.B. Crystallogr. Rep. 2012, 57, 33.


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For Table of Contents Use Only Application of the method of molecular Voronoi–Dirichlet polyhedra for analysis of noncovalent interactions in crystal structures of flufenamic acid – the current record-holder on the number of structurally studied polymorphs Viktor N. Serezhkin, Anton V. Savchenkov Synopsis. Crystal chemical analysis of 8 polymorphs of flufenamic acid (FFA) – the current record-holder on the number of structurally characterized polymorphic modifications – using the method of molecular Voronoi–Dirichlet polyhedra revealed, that every polymorph of FFA, as every polymorph of the previous record-holder ROY, has a unique set of types of intra- and intermolecular non-covalent interactions.


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