Comparison of Polymorphic Molecular Crystal Structures through

Comparison of Polymorphic Molecular Crystal Structures through Hirshfeld Surface Analysis Joshua J. McKinnon, Francesca P. A. Fabbiani, and Mark A. Spackman* Chemistry - M313, School of Biomedical, Bimolecular & Chemical Sciences, UniVersity of Western Australia, Crawley WA 6009, Australia

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ReceiVed NoVember 2, 2006; ReVised Manuscript ReceiVed December 14, 2006

ABSTRACT: Graphical tools based on Hirshfeld surfaces and two-dimensional (2D) fingerprint plots are shown to be valuable for visualizing and analyzing intermolecular interactions in polymorphs of molecular crystals and make the task of polymorph comparison easier and considerably faster. This is the direct result of the underlying principle behind the Hirshfeld surface, which embraces a “whole of structure” view of intermolecular interactions, rather than concentrating exclusively on assumed important (i.e., short) interactions. The subtle relationships between polymorphs of tetrathiafulvalene and p-dichlorobenzene are more easily discernible through comparison of Hirshfeld surfaces and fingerprint plots, rather than solely through conventional structure viewing, and differences and similarities among clearly distinct polymorphs of oxalic acid, terephthalic acid, and p-dichlorobenzene more readily emerge and can be easily catalogued in terms of specific atom‚‚‚atom interaction types. Conformational polymorphism makes the comparisons more challenging, and Hirshfeld surfaces provide sufficient information for piracetam, while for ROY (5-methyl-2((2-nitrophenyl)amino)-3-thiophenecarbonitrile, nicknamed ROY due to its red, orange, and yellow crystal forms) fingerprint plots are preferred, summarizing the major features of each crystal structure in a single, colored 2D plot. In addition to the successful applications to polymorph discrimination, improvements to the Hirshfeld surface approach are identified, the most notable being the breakdown of 2D fingerprint plots into specific atom‚‚‚atom contacts in the crystal. Introduction Polymorphism, the existence of more than one crystal structure for the same molecule, has been suggested as “an anathema to crystal engineering”,1 and the same might well be said about crystal structure prediction. Where those disciplines are concerned, at least in part, with understanding why a certain molecule crystallizes to give a particular crystal structure, the existence of polymorphism suggests that a definitive answer to this question may not exist. Although this is often seen as inconvenient, a complete understanding of polymorphism has become vitally important in areas where engineered crystals would be most desirable, in particular, the development of crystalline molecular materials in the pharmaceutical industry and for nonlinear optical applications. On a more fundamental level, the observation and structural characterization of polymorphic molecular crystal structures, complemented by modern crystal structure predictions, offer a unique opportunity to gain insight into the rich diversity of crystal-packing arrangements that may result from a small number of often quite subtle intermolecular interactions. The phenomenon of polymorphism has been variously described as anything from rare to universal. In 1965, McCrone suggested that “every compound has different polymorphic forms, and that, in general, the number of forms known for a given compound is proportional to the time and money spent in research on that compound”.2 More recently, Dunitz and Bernstein3 and Sarma and Desiraju4 have pointed to the low occurrence of polymorphism in the Cambridge Structural Database (CSD)5 to question McCrone’s assertion, while accepting that only limited conclusions can be drawn from the prevalence of flags identifying polymorphism in the CSD. As of the May 2006 update of the CSD, 9677 structures of a total of 380 864 feature the qualifier “polymorph”sjust over 2.5% of the total. This value is not likely to be representative of the * To whom correspondence should be addressed. Tel: +61 8 6488 3140. Fax: +61 8 6488 1005. E-mail: [email protected].

number of polymorphic structures that have been crystallized, since crystallographers may often just choose the “best looking” crystal from a batch where concomitant polymorphs exist.6 Alternatively, once a crystallization condition has been established, future crystallizations will often be performed under the same conditions, limiting the chance of producing a different polymorphic form in subsequent experiments, unless a crystallographer sets out on a specific search for polymorphism.3 Despite the plethora of data in the CSD, obtaining definitive information on the number of polymorphic crystal structures published for a particular compound remains nontrivial. In a recent exercise designed to extract from the CSD the “best” representative of each unique polymorph, van de Streek7 rejected ∼32% of entries in the CSD on the basis of criteria, such as high R-factors, disorder, etc., and clustered the remaining entries as polymorphs or redeterminations to obtain a final histogram of the frequency of occurrence of N polymorphs for a compound vs N (Figure 12 in that work). However, care must be taken when interpreting the histogram, as it is not made clear from the caption that N is the number of “polymorphs” detected by the algorithm, rather than the actual number of observed polymorphs. An example is p-dichlorobenzene, one of the two compounds for which five “polymorphs” were detected, while only three distinct forms exist (see further discussion below). Polymorphism is of particular importance in industrial processes, where different physical properties of polymorphic forms can substantially alter the viability and quality of a manufactured product. This is particularly so for the design and production of drugs in the pharmaceutical industry, as varying physical properties between different polymorphs can affect shelf life and durability, solubility, as well as bioavailability and manufacturing of the drug.8 As the well-known controversy and patent litigation over the polymorphic forms of ranitidine hydrochloride showed,9,10 detailed knowledge of different polymorphic forms of a drug is also important commercial information for drug companies.

10.1021/cg060773k CCC: $37.00 © 2007 American Chemical Society Published on Web 02/22/2007

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On the basis of the above considerations, the need for an understanding of intermolecular interactions in the context of crystal packing and polymorphism becomes evident. The ongoing difficulty involved in investigating and quantifying structural differences between polymorphs has been most succinctly described by Bernstein: “Even for the trained and practised 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”.10 A serious impediment to a clear understanding of intermolecular interactions in polymorphic structures is the difficulty associated with clearly visualizing the three-dimensional (3D) structures, particularly with the aim of understanding the often subtle similarities and differences between them. This is despite the substantial advances in computing speed and interactive computer graphics that have become available on desktop and laptop computers in recent years. We recently presented11 a detailed review of the application of the Hirshfeld surface12 to the understanding and description of a wide variety of molecular crystal structures, and it was clear from that work that graphical tools based on the Hirshfeld surface and the associated twodimensional (2D) fingerprint plot13 offered considerable promise for exploring packing modes and intermolecular interactions in molecular crystals. Since the publication of that review, Hirshfeld surfaces have been applied to the polymorphism of CS2,14 piracetam,15 cyclopropylamine,16 R-glycylglycine,17 L-serine,18 benzene,19 naphthalene, phenanthrene, and pyrene,20 and a series of triarylcarbonyl derivatives.21 While almost all of those papers focused on the effects of pressure, in the present work we focus attention on the application of the same graphical and computational tools to address the general frustration expressed by Bernstein in the quote above. To accomplish this, we investigate several polymorphic systems comprising the most common intermolecular interactions, and ranging from the small, rigid, and relatively straightforward (oxalic acid, p-dichlorobenzene, terephthalic acid) to the more complicated (tetrathiafulvalene) and the challenges presented by conformational polymorphism (piracetam and ROY). Our objective is to determine where Hirshfeld surface-based tools can be used to advantage in analyzing these systems, where they offer little advantage over conventional tools, and to identify directions for future improvements. In the following discussion, we rely on many of the concepts introduced in our recent topical review,11 directing the reader to sections of that article when required, and we will assume the reader is familiar with them. Computational Methods Molecular Hirshfeld surfaces partition crystal space into smooth, non-overlapping, interlocking molecular volumes. Inside the Hirshfeld surface the electron distribution due to a sum of spherical atoms for the molecule (the promolecule) dominates the corresponding sum over the crystal (the procrystal), and the Hirshfeld surface is defined implicitly where the ratio of promolecule to procrystal electron densities equals 0.5. As it depends intimately on the molecular geometry, the location and orientation of nearest and more distant neighboring molecules, and the nature (radial extent) of specific atom types that make close contacts with the molecule in question, the Hirshfeld surface reflects in considerable detail the immediate environment of a molecule in a crystal. For a given crystal structure and set of spherical atomic electron densities, the Hirshfeld surface is unique,11 and it is this property that suggests the possibility of gaining additional insight into the polymorphism of molecular crystals.

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Any number of different properties can be encoded on the Hirshfeld surfaces, and some of these have been explored in detail. For each point on the surface, two colored distance properties are defined: de, the distance from the point to the nearest nucleus external to the surface, and di, the distance to the nearest nucleus internal to the surface.22 In addition, two further colored properties based on the local curvature of the surface can be specified.23 CurVedness is a measure of “how much shape”; low values of curvedness are associated with essentially flat areas of the surface, while areas of sharp curvature possess a high curvedness and tend to divide the surface into patches associated with contacts between neighboring molecules. Shape index is a measure of “which shape”, and it can be sensitive to very subtle changes in surface shape, particularly in areas where the total curvature (or the curvedness) is very low. An important attribute of this property is that where the shape index of two surface regions differs only by a sign, complementary “stamp” and “mould” pairs can be readily identified. 2D fingerprint plots13 are derived from the Hirshfeld surface by plotting the fraction of points on the surface as a function of the pair (di, de). Each point on the standard 2D graph represents a bin formed by discrete intervals of di and de (0.01 × 0.01 Å), and the points are colored as a function of the fraction of surface points in that bin, with a range from blue (relatively few points) through green (moderate fraction) to red (highest fraction). To date, all fingerprint plots have used the standard range of fractions spanning 0.1% of surface area, but to facilitate more detailed visual comparison between plots, some fingerprint plots presented below use an enhanced color scale, spanning a range of 0.033% (i.e., enhanced by a factor of 3). Because of the direct dependence of Hirshfeld surfaces on a given molecular environment, the number of Hirshfeld surfaces that are unique in a given crystal structure depends on the number of crystallographically independent molecules in the corresponding asymmetric unit. This implies that for structures with Z′ > 1, the number of unique Hirshfeld surfaces is greater than one and that for structures with Z′ < 1 the unique portion of the Hirshfeld surface is not the entire surface (e.g., for a Z′ ) 0.5 structure with a molecule residing on an inversion center, the patterns of intermolecular interactions are the same on each side of the molecule). On a more subtle note, for a noncentrosymmetric molecule in a centrosymmetric space group, two visually different Hirshfeld surfaces may be generated for a particular molecule, depending on the selection made among all possible symmetry-related molecules in the unit cell. These two surfaces are related to one another by an inversion operation but generate identical fingerprint plots, and particular care should be taken during surface visualization to enable a meaningful comparison. We emphasize that the size and shape of a Hirshfeld surface reflects the interplay between different atoms and intermolecular contacts in a crystal, and hence the surfaces necessarily reflect different intermolecular interactions. Colored surface mapping of the small number of functions described above represents our present attempts to extract that information in a way that can be exploited as much as possible, and since the surfaces and corresponding fingerprint plots are unique for any crystal structure, and consequently for any polymorph, they offer the promise of a powerful tool for elucidating and comparing intermolecular interactions and for identifying common features and trends in specific classes of compounds. For the first time in our research into the applications of Hirshfeld surface-based tools, we make use of CrystalExplorer,

Polymorphic Molecular Crystal Structures

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Figure 1. Left: Hirshfeld surfaces of the R- and β-forms of oxalic acid surrounded by a cluster of neighboring molecules. Hydrogen bonds are indicated by thin black lines, and the surface property is de. Right: corresponding 2D fingerprint plots for the two polymorphs.

a new computer program for calculation and display of Hirshfeld surfaces and 2D fingerprint plots, developed in collaboration with coworkers at the University of Western Australia and available for download.24 CrystalExplorer accepts a structure input file in CIF format, and because internal consistency is important when comparing one structure with another, for the generation of Hirshfeld surfaces all bond lengths to hydrogen (or deuterium) atoms are set to typical neutron values (C-H ) 1.083 Å, O-H ) 0.983 Å, N-H ) 1.009 Å).25 Fingerprint plots can be interrogated interactively alongside the corresponding Hirshfeld surfaces by clicking on a (di, de) pair of interest, which results in the highlighting of the region(s) on the surface matching that particular pair of distances. For detailed comparison between Hirshfeld surfaces, mapped properties, and fingerprint plots for a number of related structures, it is also essential to avoid comparing results from structures obtained at widely separated temperatures. In the following discussion, we compare between crystal structures determined at the same temperature wherever possible, but where some polymorphs are only observed at lower temperatures, the effect on the various maps and plots should be borne in mind when drawing conclusions. Results and Discussion Oxalic Acid. The two known polymorphs of oxalic acid possess very different crystal structures.26 The stable R-form (Pbca) exhibits a strong 3D network of hydrogen bonds and close contacts, while the crystal structure of the metastable β-form (P21/c) is dominated by the formation of infinite chains of hydrogen-bonded molecules based on a centrosymmetric R22(8)27 carboxylate dimer motif, with much weaker interactions between chains.28 The crystal-packing diagrams of both forms (Figure 1) illustrate the packing of the β-form quite

effectively, but the structure of the R-form is considerably more difficult to visualize in this way. The molecular Hirshfeld surfaces generated for the two oxalic acid structures (Figure 1) have distinctly different shapes, reflecting the very different packing modes of the two polymorphs, although the Hirshfeld volumes (i.e., VH, the volumes enclosed by the respective surfaces) of the two forms are almost identical (R: 75.41 Å3; β: 75.34 Å3). In both structures, each molecule participates in four hydrogen bonds (in the R-form, two of these are equivalent, while in the β-form all four are equivalent by symmetry), and so hydrogen-bonding contacts necessarily dominate both crystal structures for this small molecule. The Hirshfeld surface of the β-form features the characteristic pattern of the R22(8) cyclic hydrogen bond interaction on the de surface at the ends of the molecule,29 while the hydrogen-bond network of the R-form is shown by the large red spot on the de surface near the carbonyl acceptor (1) and the small yellow dot at the hydrogen-bond donor (2). Inspection of the fingerprint plots in Figure 1 clearly highlights the major packing differences between these crystal structures: the β-form features the diffuse region of blue points between the hydrogen bond spikes, which are characteristic of the cyclic hydrogen-bond dimer motif, while this feature is absent from the fingerprint plot of the R-form. The fingerprint plots also show that the hydrogen bond is shorter in the β-form (H‚‚‚O distance of 1.69 Å) than in the R-form (1.83 Å), and the broader hydrogen-bond fingerprint in the R-form is a result of the smaller O-H‚‚‚O angle (146.6°, compared with 174.1° for the β-form). The O-H‚‚‚O angle can be easily discerned from the Hirshfeld surfaces because the surface adjacent to both the donor and the acceptor involved in a particular hydrogen bond is perpendicular to the vector connecting the donor and acceptor atoms.


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Figure 2. Hirshfeld surfaces and 2D fingerprint plots for the polymorphs of p-dichlorobenzene. For each polymorph the Hirshfeld surface is shown mapped with curvedness (left), shape index (center), and de (right). As all three molecules lie on an inversion center, the reverse side of each Hirshfeld surface exhibits the same features as that shown.

p-Dichlorobenzene. As discussed in the introduction, there are only three known polymorphic forms for p-dichlorobenzene. The high-temperature β-form crystallizes from the melt at 328 K, transforming reversibly to the R-form at 304 K. A third form, γ, crystallizing below 273 K, can be irreversibly converted to the R-form on heating. A fourth polymorph, δ, has been reported to exist at ambient temperature at pressures above 0.3 GPa,30 but recent high-pressure powder-diffraction studies showed no evidence of this.31 p-Dichlorobenzene has been the subject of several crystallographic studies, though only Wheeler and Colson have published structures for all three known forms at the same temperature (100 K).32,33 The polymorphism and phase transformations of p-dichlorobenzene have been studied extensively by experimental31,34,35 and theoretical35,36,37 methods. Wheeler and Colson33 noted a trend in the number of short Cl‚‚‚Cl contacts (which they define as contacts less than 3.9 Å) for the three phases, with five Cl‚‚‚Cl contacts to each chlorine observed in the γ-phase, four such contacts in the R-phase, and three in the high-temperature β-phase. Our analysis of the Wheeler and Colson structural data shows that the R-phase has two Cl‚‚‚Cl contacts shorter than 3.90 Å to each chlorine atom but also has two additional Cl‚‚‚Cl contacts at 3.93 Å, highlighting the fact that using such arbitrary distance criteria, and focusing on a single atom‚‚‚atom contact type, can be misleading when comparing crystal structures. Hirshfeld surfaces and fingerprint plots can easily circumvent this as they enable

the visualization of all the intermolecular contacts surrounding the entire molecule. The Hirshfeld surfaces for the three forms of p-dichlorobenzene are shown in Figure 2.38 From the Hirshfeld surfaces, it is clear that the crystal structures of the R- and β-forms must be related to one another, while the γ structure is significantly different. Above the plane of the molecule, inspection of the adjacent red and blue triangles on the shape index surface of the R- and β-forms shows that the π‚‚‚π stacking interaction is almost identical in these crystal structures. In contrast, the γ-form shows a large indentation above the surface characteristic of a C-H‚‚‚π contact; the region around the hydrogen at bottom-right of the same surface shows the corresponding convex region identifying the C-H‚‚‚π “donor” group. The 2D fingerprint plots in Figure 2 clearly show the similarities as well as gross and subtle differences between the three forms of p-dichlorobenzene, reflecting the information provided by visual inspection of the Hirshfeld surfaces, while also providing additional insight into the crystal structures. From them, it is clear that H‚‚‚H contacts (which appear where de ≈ di at or shorter than the H-atom van der Waals radius of 1.20 Å) are closer in the R-form than in the β-form and essentially absent in the γ-form. The nature of the green spikes in the region marked 1 on each of the plots is similar for the R- and β-forms and results from a Cl‚‚‚H contact that is slightly shorter in the R-form (2.86 Å) than in the β-form (2.92 Å). In both structures,



Figure 3. Crystal-packing diagrams for the three polymorphic forms of p-dichlorobenzene. Cl‚‚‚Cl contacts are indicated by thin black lines, and it can be seen that the stacking motif in the β-form is shared by the R-form.

these spikes are broadened slightly by a second Cl‚‚‚H contact at 3.05 Å (β) and 2.98 Å (R). The corresponding feature on the 2D fingerprint plot for the γ-form is qualitatively different and closely resembles the fingerprint for a C-H‚‚‚π interaction (as seen for the example of benzene, Figure 11 in our recent article11), with the sharp green part of the streak similar to the Cl‚‚‚H contacts seen for the R- and β-forms also visible; this fingerprint in the γ-form actually results from the superposition of features due to a Cl‚‚‚H contact at 2.88 Å and a C-H‚‚‚C contact at 2.84 Å. The 2D fingerprint plots are distinctive in regard to the Cl‚ ‚‚Cl contacts that occur in each structure. The R- and γ-forms both feature bent Cl‚‚‚Cl contacts, with θ1 ) 166°, θ2 ) 92° for the R-form and θ1 ) 155°, θ2 ) 85° for the γ-form.39 The fingerprint for this contact is bright red, slightly broad, and reasonably short, extending from just shorter than 1.9 Å [or half the Cl‚‚‚Cl distance of 3.73 Å (β) and 3.79 Å (γ)] on the fingerprint plot, to about 2.0 Å. In contrast, the approximately linear Cl‚‚‚Cl contact in the β-form (θ1 ) θ2 ) 169°), which at 3.39 Å is significantly shorter, produces a very long, sharp fingerprint, extending from 1.7 Å to at least 2.0 Å on the fingerprint plot. The Cl‚‚‚Cl contact is visible on the shape index surface for the γ-form as a distinctive blue cross, labeled 2 on the surface, while for the R- and β-forms the same feature at the ends of the molecules is not visible in the orientation shown. The crystal-packing diagrams in Figure 3 confirm the observations made from the Hirshfeld surfaces and 2D fingerprint plots above. The almost identical nature of the molecular stacks in the R- and β-forms is clear (R is related to β by doubling of the a-axis and a rotation of molecules in alternate layers), and the packing diagrams also show that the major structural difference between these two polymorphs is the relationship between adjacent molecular stacks through the Cl‚‚‚Cl contacts. Conversely, the crystal-packing diagram of the γ-form provides much less immediate insight into the actual packing of this structure. Terephthalic Acid. There are currently 10 structures published in the CSD (November 2005), and inspection of their cell constants suggests the existence of at least three polymorphs, possibly four, although terephthalic acid is known to crystallize in only three polymorphic forms. Forms I and II are triclinic (P1h) and can be obtained by recrystallization from aqueous solutions at ca. 150 °C.40 Form III is monoclinic (C2/m) and was recently prepared by thermal hydrolysis of 1,4-dicyanoben-

zene.41 Domenicano et al.42 obtained a triclinic modification of terephthalic acid and suggested that it might be a new modification. However, SlÄedz´ et al.41 demonstrated convincingly that the powder diffraction pattern of this form is similar to that of form I, and the only difference between the two crystal structures lies in the choice of unit cell. In the triclinic polymorphs, the terephthalic acid molecule resides on an inversion center, giving Z′ ) 0.5, while in the monoclinic modification it resides on a special position of site symmetry 2/m, giving Z′ ) 0.25. Dynamic disorder of the hydrogen-bonded proton occurs in all polymorphs, as confirmed by temperature-dependent neutron diffraction studies for form I.43 This has implications for the generation of Hirshfeld surfaces and fingerprint plots, and there are two possible ways to deal with this disorder: (i) generate surfaces by incorporating fractional occupancies for the proton positions in the computation of the promolecule and procrystal electron densities; (ii) assume a totally ordered structure by assigning site occupancy of unity to one of the possible sites. Although CrystalExplorer can readily handle option (i) provided details of disorder are included in the CIF files (but, as noted by van de Streek,7 the CSD does not yet include site occupancies), we prefer to assume ordered protons in the present work and note that this necessitated a change in the space group for TEPHTH13, which can only be C2/m if the hydrogen-bonded proton is disordered over two equivalent sites. Common to the crystal packing of all three polymorphs is the formation of hydrogen-bonded chains through a centrosymmetric R22(8) dicarboxylic acid cyclic dimer motif, and these chains in turn form 2D layers of various kinds. The packing of the three polymorphs is characterized by different arrangements of the chains into layers. Hirshfeld surfaces offer improved and unambiguous polymorph assignment through comparison of single color plots, rather than manual or automated investigation of cell parameters, packing diagrams, and intermolecular interactions. Figure 4 shows Hirshfeld surfaces for all five room-temperature crystal structures of terephthalic acid, and we have chosen to map shape index on these surfaces as it is the most sensitive to small changes in surface curvature, although either curvedness or de would probably also suffice for this comparison (and 2D fingerprint plots should be amenable to automatic pattern matching for this purpose). The assignment of polymorphic forms is immediately obvious from Figure 4 and interfaced with


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Figure 4. Hirshfeld surfaces mapped with the shape index for five CSD entries of terephthalic acid unambiguously show the relationships between the various structures.

Figure 5. Hirshfeld surfaces and 2D fingerprint plots for the three polymorphs of terephthalic acid. For each polymorph, the Hirshfeld surface is shown mapped with curvedness (left), shape index (center), and de (right), and the fingerprint plots have been enhanced by a factor of 2 to highlight the features due to C‚‚‚C contacts.

a resource such as the CSD, computation and display of these surfaces would enable rapid comparison between reported structures. Hirshfeld surfaces and fingerprint plots for the three polymorphs of terephthalic acid are shown in Figure 5.44 All three fingerprint plots show a prominent pair of spikes with diffuse regions of points in between, a pattern characteristic of a cyclic hydrogen-bonding motif. The spikes in form III are shorter, indicating a longer hydrogen bond. The red points at de ) di ≈ 1.8 Å, visible on the fingerprint plots of forms I and III, are characteristic of π‚‚‚π interactions, and it is notable that they are almost absent in form II, where π‚‚‚π interactions are not as significant in the crystal structure. A conspicuous red line appears for form III at de + di ≈ 3.8 Å, indicating a substantial

fraction of C‚‚‚C contacts. π‚‚‚π interactions are evident on the Hirshfeld surface as a large flat region across the molecule, which is most clearly visible on the curvedness surfaces. The pattern of red and blue triangles on the same region of the shape index surface is another characteristic of π‚‚‚π interactions. Blue triangles represent convex regions due to ring carbon atoms of the molecule inside the surface, while red triangles represent concave regions due to carbon atoms of the π-stacked molecule above it. The pattern of alternating red and blue triangles with local 3-fold symmetry is indicative of offset π‚‚‚π stacking interactions characteristic of graphite-like layers, and this type of stacking is evident in form III but not in forms I and II. Figure 6 shows the Hirshfeld surfaces of the three different polymorphs of terephthalic acid in the context of their crystal-



Figure 6. Crystal-packing diagrams for the three polymorphs of terephthalic acid, with Hirshfeld surfaces mapped with de.

packing arrangements. An imprint due to the adjacent benzene ring is clearly visible on the de surface, reflecting the offset stacking arrangement in the crystal. The de surface clearly conveys the position of neighboring aromatic rings above the plane of these molecules, where the center of the benzene ring corresponds to a local peak in de and appears as a deep blue spot on the surface (depicted in Figure 6 in a pseudo-hexagonal environment as a result of the choice of range for de). While this spot is centered on the central lower portion of the surfaces for form III, it is found at an offset in form I, thereby providing further evidence to the different offsets in π‚‚‚π stacking in the two forms. Tetrathiafulvalene. Tetrathiafulvalene (TTF) is an efficient electron donor that has been regularly used, along with its derivatives, in the construction of organic charge-transfer crystals with high conductivity,45 such as the TTF/TCNQ complex.46,47 The system has been recently shown to be trimorphic, exhibiting a monoclinic modification (R-form:48 P21/c; Z′ ) 0.5), a triclinic modification stable at high temperatures49 (β-form:50 P1h; Z′ ) 2, with four unique half-molecules in the asymmetric unit), and a second triclinic modification (γ-form:51 P1h; Z′ ) 1 with two unique half-molecules in the asymmetric unit).52 As noted by Ellern et al., structures containing more than one unique molecule, but with each molecule lying on a crystallographic center of symmetry, are rares notable examples include the isostructural pair of azobenzene53 and transstilbene54sand those that are reported are often the result of incorrect (lower symmetry) space group assignment.55 Because Hirshfeld surfaces are necessarily unique and reflect the immediate environment of the molecules in question (and not their space group assignment) their use enables a rapid and easy visual comparison of the independent molecules in the structure and can immediately reveal whether the assignment of Z′ > 1 is correct. From a first investigation of the Hirshfeld surfaces of the R and γ polymorphs depicted in Figure 7, it is clear that both molecules in the γ-form are in almost identical environments to the molecule in the R-form. This can be readily concluded from comparison of the Hirshfeld surfaces mapped with any of the three different properties, and especially from the 2D fingerprint plots. This is perhaps not surprising, as γ-TTF is closely related to R-TTF: the a-axis is doubled, and the asymmetric unit now contains two half-molecules (which would have been related by the a-axis in R-TTF but for a rotation of ∼5° about an axis perpendicular to the molecular plane). The crystal structure of R-TTF is based on π‚‚‚π stacking of molecules, as emphasized by the complementary (interlocking) blue and red diamonds on the shape index surface and the large flat region delineated by a blue outline on the curvedness

surface. The 2D fingerprint plot for this form reflects this packing arrangement with a concentration of points surrounding the red region along the diagonal, and corresponding to S‚‚‚S, C‚‚‚S, and C‚‚‚C contacts between molecules in stacks, as well as between stacks. The shortest S‚‚‚S contacts in the R-form (3.41 Å) are between molecules in separate stacks and appear on the fingerprint plots as the start of the sharp green/red diagonal line at de ) di ) 1.7 Å. This contact occurs in the area labeled 1 on the de surface, but does not feature as a red spot on the de surface because S‚‚‚S contact distances are large in comparison with others such as C-H‚‚‚S. The change in color from pale blue/green to red on the fingerprint plot starting at de ) di ≈ 1.8 Å corresponds to an additional S‚‚‚S contact at 3.58 Å as well as the start of the interlayer contacts, the shortest being a C‚‚‚C contact at 3.62 Å. Stacks of molecules in both γ-TTF and R-TTF are linked by relatively close C-H‚‚‚C, C-H‚‚‚S, and H‚‚‚H contacts, as well as S‚‚‚S contacts. The de surfaces of all molecules in Figure 7 feature two bright red spots at the top of the surface, which are due to a close approach of a pair of hydrogen atoms from the end of an adjacent molecule (see packing diagram in Figure 8). This contact is responsible for the split H‚‚‚H feature, because, while this contact involves a pair of H‚‚‚H contacts, the geometry of this contact (shown in the packing diagram) means that it also involves C‚‚‚H contacts at 3.05 and 3.25 Å. Thus, the feature reflects the partial C‚‚‚H nature of the contact and is split across the de ) di diagonal. The red regions on the sides of the de surfaces for these polymorphs of TTF arise from close C-H‚‚‚S contacts and contribute to the broad feature labeled 2 in Figure 7; the other contribution to this feature comes from H‚‚‚C contacts. Note that in R-TTF the contact labeled 3 produces a small red (concave) spot on the shape index surface, a feature characteristic of other weak hydrogen bonds (e.g., chloromethane; see Figure 56 of ref 11). In the γ polymorph contact regions between the Hirshfeld surfaces of the two molecules in the asymmetric unit are visible, and it is possible to identify complementary regions in the fingerprint plots, where one molecule acts as a donor and the other one as an acceptor. The most striking of these complementary features are the regions marked 4 in Figure 7, which correspond to C-H‚‚‚S contacts: molecule A acts as a C-H‚‚‚S donor (and the H‚‚‚S distance is closer than in R-TTF), while molecule B acts as a C-H‚‚‚S acceptor. As the published crystal structure of β-TTF does not include hydrogen atom positions, discussion of close intermolecular contacts in the original structural paper50 was necessarily limited to concentrating on S‚‚‚S contacts. For the present analysis, hydrogen atom positions were added at standard positions, and it is clear from what follows that H‚‚‚S and H‚‚‚C contacts


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Figure 7. Hirshfeld surfaces and 2D fingerprint plots for the polymorphs of TTF. For each polymorph the Hirshfeld surface is shown mapped with curvedness (left), shape index (center), and de (right).

Figure 8. Crystal-packing diagram for R-TTF showing three columns of stacked molecules; a similar packing motif is observed in γ-TTF.

cannot be ignoredsthey contribute significantly to the crystal packing of this structure, as well as the other two polymorphs. In β-TTF, there are four different molecules in the unit cell, and none is in an environment similar to the other two polymorphs. While this is easily confirmed by visual inspection of the Hirshfeld surfaces and fingerprint plots in Figure 9, it is much less obvious when analyzing the crystal structure by conventional methods, such as comparison of packing diagrams, where a detailed structural analysis becomes rather challenging. From the 2D fingerprint plots, it is evident that all four molecules in β-TTF show a considerably greater range of values in de and di, whereas both R- and γ-TTF are considerably more compact, thereby suggesting that the structure of β-TTF is much less dense than the other two. This is confirmed by comparing the density values obtained by diffraction experiments, although it should be noted that while the R and β structures were

determined at room temperature, the structure of the γ-form was determined at 150 K. On further analysis, the most notable characteristic of the β polymorph is the absence of the layered stacking that is present in the other two modifications. Instead, each molecule features large depressions visible on the top of the de surfaces due to one (molecules C and D) or two (molecules A and B) C-H‚‚‚π contacts. It is clear from the four surfaces in Figure 9 that this structure features two identifiable pairs of molecules in similar environments. This is corroborated by the earlier analysis by Ellern et al., who pointed out that the structure is characterized by two chains of molecules, each consisting of alternating crystallographically independent molecules. One chain contains molecules A and D, while the other contains molecules C and B, as shown in the crystal-packing diagram in Figure 10. From investigation of the surfaces and packing diagram, it is clear that the molecular chains are quite similar. Molecules A and B each have their molecular plane roughly perpendicular to the direction of propagation of the chain, while molecules C and D are both aligned approximately parallel to the direction of propagation. This arrangement results in a similar chemical environment and therefore similar Hirshfeld surfaces for molecules A and B (the perpendicular molecules) and for molecules C and D (the parallel molecules). The packing diagram (Figure 10) shows that the two C-H‚‚‚π contacts above the plane of molecules A and B, features that are clearly conspicuous on their de surfaces, are the result of close contact from hydrogen atoms in two different molecules. This information is also available from the curvedness surface on the right of Figure 9, where the blue “seams” of high curvedness surround the surface patches corresponding to each nearest neighbor in



Figure 9. Hirshfeld surfaces and 2D fingerprint plots for the four molecules in β-TTF. For each molecule, the Hirshfeld surface is shown mapped with curvedness (left), shape index (center), and de (right).

Figure 10. Crystal-packing diagram for β-TTF showing the relationship between pairs of molecules forming ribbons and the interactions between ribbons. Dashed lines indicate close S‚‚‚S contacts (red), C-H‚‚‚C contacts (blue), and C-H‚‚‚S contacts (green).

the crystal. These blue seams between the two regions of C-H‚‚‚π interaction effectively delineate patches contacted by each nearest neighbor in the crystal. The 2D fingerprint plots for the four independent TTF molecules of the β polymorph show very clearly how the pseudo-symmetry of the fingerprints can disappear in structures with Z′ > 1.0, because intermolecular contacts can now occur between crystallographically distinct molecules. Deciphering the

various intermolecular interactions in this particular case is a complicated process, even with the aid of the 2D plots. However, the fingerprints highlight subtle differences in the chemical environments of the four molecules that are not immediately evident from the Hirshfeld surface pictures and certainly not evident from a crystal-packing diagram. For example, there is just one close H‚‚‚H contact in the crystal, clearly occurring between molecules B and D (labeled 5 in Figure 9), and this is visible on the de surface of molecule B as a small orange spot at the top-left of the de surface (5 in Figure 9); a similar spot at the end of molecule D is not visible in the view chosen for the figure. As mentioned above, several H‚‚‚C and H‚‚‚S contacts occur in this crystal, and because of the significant size difference between carbon and sulfur atoms, where these occur on the same 2D fingerprint plots (for instance, molecule C), the separate contacts are resolved into two spikes (labeled 6 in Figure 9). Even when these spikes appear in isolation, the distance of the spike from the diagonal can be used to distinguish between H‚‚‚C and H‚‚‚S contacts. The fingerprint plots for molecule A shows a spike at top left (7) due to a hydrogen in molecule A approaching a sulfur in another molecule (this must be either molecule C or D from the fingerprint plots; the packing diagram confirms that this is in fact molecule C). The other spike in


Figure 11. Contacting patches highlighted on the curvedness surfaces of β-TTF. When the top molecules are rotated 180° as shown, then the highlighted patches for molecules B and C, and A and D, fit together exactly.

this plot (8) has its point closer to the diagonal and is due to a carbon atom in molecule A approaching a hydrogen atom (in molecule D). The shape of individual patches of the curvedness surface that are surrounded by blue regions of high curvedness are particularly suitable for qualitatively visualizing regions of similarity and disparity between different surfaces. Where this examination shows a high degree of similarity, other properties of the surface can be used to determine in a more quantitative manner the subtle difference between parts of the surfaces. In the case of β-TTF, this situation can be illustrated by the regions above the molecular plane of molecules C and D in Figure 9. Here, the shapes of the two patches traced in blue on the curvedness surface are almost identical, but the examination of the de surface shows that the C-H contact above the ring (marked by the orange spot) is slightly shorter on the surface of molecule D than of molecule C. The curvedness map can also be used to determine the crystal-packing patterns without having to view a crystal-packing diagram. Figure 11 shows the contact patch mentioned above highlighted on the curvedness surfaces for molecules B and A and the complementary patches for molecules C and D, respectively. Piracetam. The polymorphism of the drug compound piracetam (2-oxo-pyrrolidineacetamide) has been investigated recently by Fabbiani et al.,15 who reported a new, high-pressure, crystal form. In addition to this new polymorph (form IV), three other forms of piracetam are known, and their crystal structures have been determined at room temperature. Piracetam has also been the test case for a new approach to crystal structure prediction of conformationally flexible molecules,56 which successfully identified the most likely candidate structure for form IV, independently of the X-ray determination. Using a combination of Hirshfeld surfaces, fingerprint plots, and packing diagrams, Fabbiani et al. have already provided a detailed analysis of the four polymorphs of piracetam, but that work did not present Hirshfeld surfaces. For that reason, we focus here only on the Hirshfeld surfaces and refer the reader to ref 15 for a discussion of the corresponding fingerprint plots and packing diagrams. The conformational differences between molecules in the various forms have been summarized by Fabbiani et al., and they originate almost entirely from the rotation of the amide moiety relative to the pyrrolidine ring. Because of this piracetam provides a relatively straightforward introduction to the challenges presented by conformational flexibility, and in Figure 12 we compare Hirshfeld surfaces for molecules in all four forms with the pyrrolidone ring in a common orientation.57 From the figure, it is readily seen that the molecules in forms I, II, and

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III share a similar conformation, with the amide carbonyl oxygen pointing toward the ring; molecules in forms II and III have almost identical conformations. In contrast, the amide group is rotated by almost 180° for molecules in form IV. Hirshfeld surfaces presented in this common orientation provide immediate insight into the similarities and differences in intermolecular contacts for these four polymorphs. At a very basic level, since de is mapped over the same range (0.8-2.3 Å) for all surfaces, the relative fractions of blue on the surface (i.e., large distances from the surface to nuclei in neighboring molecules) reflect differences in density: form I is the least dense, forms II and III are of similar density, and form IV is obviously the most dense. Form IV also exhibits many more short contacts, especially obvious from the greater number of yellow spots on the bottom view of the surface, and this is typical for high-pressure structures. The top views for forms II and III are almost identical, not simply because they have closely similar conformations, but because they participate in the same hydrogen-bonding motif in the crystal, namely, the formation of R22(8) cyclic dimers (associated with the bright red spot characteristic of a hydrogen bond acceptor on the top views, adjacent to the amide oxygens), with the dimers linked by hydrogen bonds between the second amide hydrogen and the pyrrolidone oxygen atom of a neighboring molecule to form an R44(18) pattern (associated with the red spot on the lower right of the surfaces). The back sides of the Hirshfeld surfaces for forms II and III differ considerably, with the yellow indentation above the pyrrolidine ring for form III indicating a contact akin to a weak C-H‚‚‚C interaction. Additional details can be readily gleaned from Figure 12, such as the orientation of individual hydrogen bonds (e.g., in forms II, III, and IV the hydrogen bond acceptor is near the extension of the amide CdO bond vector, while in form I the amide oxygen accepts a hydrogen bond from an acceptor side-on to the CdO bond), and the number and relative proximity of hydrogen bonds (e.g., the pyrrolidone oxygen atom participates in one short and one longer hydrogen bond in forms II, III, and IV, but only one in form I), but much greater insight is obtained by interactive rotation of these surfaces in real time. Reproduction of different views of a surface in a 2D medium such as the printed page is no substitute for interactive graphics. ROY. 5-Methyl-2-((2-nitrophenyl)amino)-3-thiophenecarbonitrile, nicknamed ROY due to its red, orange, and yellow crystal forms, is the organic polymorphic record-holder with nine known concomitant polymorphs at room temperature.58,59 These are named after their color and crystal form: yellow prisms (Y), red prisms (R), orange needles (ON), orange plates (OP), yellow needles (YN), orange-red plates (ORP), red plates (RPL), yellow, discovered in 2004 (Y04), and Y04 transformed (YT04). The structures of the first six polymorphs and the last have been solved recently by single-crystal methods. Comparing the crystal structures of the seven polymorphs for which detailed 3D information is available is a serious challenge, especially given the substantial conformational changes that occur in the polymorphs (e.g., the phenyl-thiophene angle (θthio), which correlates with polymorph color, varies between 22° and 113°). 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 because of the substantial conformational differences between polymorphs it is problematic to compare surfaces surrounding molecules in different conformations as well as different environments. Because of this our discussion of the polymorphs of ROY is based largely on the comparison of fingerprint plots



Figure 12. Hirshfeld surfaces mapped with de for the four forms of piracetam. Two sides of each surface are shown: in the same orientation as the molecular structure on the left (referred to in the text as top), and the reverse side obtained by a rotation of 180° about the vertical axis (referred to as bottom).

(Figure 13), which are remarkably dissimilar from one another and give the first indication that the corresponding crystal structures are fundamentally and substantially different.60 The most obvious differences lie in the shape (this is connected to major structural difference) and in the relative spread of data points, especially the sparse points at high de and di, which to a good approximation give an indication of significant voids in the structures. The presence of these regions on the 2D plots does not allow at present a quantitative analysis of the “free space” available in a given structure as the number of data bins that make up these regions can be very low and is not easily conveyed by the available coloring palette. For example, ORP and ON are the least dense structures, but Y also has many points at high de and di, yet is the second densest polymorph. Analysis of this region is prone to over-interpretation when comparing different structures; a meaningful analysis requires a careful interactive investigation of the correspondence between a particular de and di fingerprint pair, void regions, Hirshfeld surfaces, and crystal-packing diagrams. Here we note that the void region on ON is formed in the proximity of sulfur atoms and methyl groups in neighboring molecules, which form conspicuous channels that run down the crystallographic a-axis. The extraction of quantitative information and visualization of

void regions in a given crystal structure is an area that we are currently investigating. According to the discussion of the structures by Yu et al.,58,59 all ROY polymorphs are characterized by an intramolecular hydrogen bond between the amino and nitro groups (not visible on the Hirshfeld surface, which by definition envelops all intramolecular contacts and only depicts intermolecular contacts), but they remark that only polymorphs Y and YT04 exhibit weak intermolecular hydrogen bonds. However, even a cursory investigation of the fingerprint plots suggests otherwise: the presence of “spikes” of various length and thickness off the plot diagonal is a feature common to all fingerprints in Figure 13. This is indeed a rather crowded region, at least in comparison with the fingerprint plots presented earlier for the polymorphs of simpler, more rigid structures, although most of the spikes in Figure 13 can be readily resolved. In our earlier analysis, similarly positioned spikes and wings were ascribed to the presence of strong or weak hydrogen bonding, or short C-H‚‚‚π contacts, and from Figure 13 we conclude that all seven ROY structures have at least one short H‚‚‚X contact characteristic of an intermolecular hydrogen bond. From Table 1 we see that the dominant close contacts are H‚‚‚N and H‚‚‚ O, some of which are considerably shorter than the sum of van


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Figure 13. 2D fingerprint plots for the seven ROY polymorphs; the plots have been enhanced by a factor of 3 to highlight the features due to C‚‚‚C contacts. Table 1. Intermolecular Contacts to H Atoms Shorter than 0.97dvdW for the Polymorphs of ROYa H...H dvdWb R OP ORP ON Y YN YT04

2.40 2.05†

H...C

H...N

H...O

2.90 2.78†

2.75 2.55 2.47, 2.58 2.51 2.50 2.30

2.72 2.38†, 2.63 2.61† 2.40 2.56 2.51 2.38 2.63

2.18, 2.27† 2.41

a

Contacts labeled † involve methyl H atoms, and contact distances in bold denote cyclic motifs. b dvdW is the sum of van der Waals radii from Bondi.62

der Waals radii.61 Of course, some of these hydrogen bonds are rather weak in terms of hydrogen-bonding parameters and are at the limit of being classified as such, but they nevertheless represent notable intermolecular contacts in the context of crystal packing. The presence of many different atom types, and therefore many possible intermolecular interactions, makes a detailed analysis of these fingerprint plots more challenging, and we emphasize that even though we do not present any Hirshfeld surfaces, such a detailed analysis requires a meticulous manual investigation of the corresponding surfaces via interactive computer graphics. All the contacts listed in Table 1 are in fact present in all polymorphs to some degree, but they often overlap with features due to other intermolecular interactions or occur

at longer distances, and do not emerge from visual investigation of the plots alone. Whether features due to the shortest of these intermolecular hydrogen bonds (Table 1) are evident on the fingerprint plots depends on several factors, for example the length of each hydrogen bond or the presence of other intermolecular contacts that occur over similar di and de ranges, which would overlap with the hydrogen-bonding spikes, thereby making them less visible. It is now clear how decomposition of the fingerprint plots into specific individual interaction-type‚ ‚‚interaction-type plots would be more meaningful, and this is another area that we are currently exploring and which will be the subject of a future publication. To demonstrate how assignment of these diagnostic spikes can be performed even for structures of this complexity, Figure 14 reproduces the fingerprint plot for the R polymorph, with the major spikes and shoulders assigned to various H‚‚‚X contacts, alongside a plot of the same interactions on a crystalpacking diagram. The spacing of the various spikes from the plot diagonal reflects the differences in size (van der Waals radii) of the acceptor (X) atoms. The spike closest to the diagonal arises from the overlap of a -H2C-H‚‚‚O contact at 2.38 Å and a phenyl-C-H‚‚‚O contact at 2.63 Å. The contact labeled 2 is the centrosymmetric dimer involving two identical C-H‚‚‚N contacts at 2.55 Å, and that labeled 1 involves a close -H2C-H‚‚‚CN contact at 2.78 Å. The closest C-H‚‚‚S contacts occur at 3.35 Å and show up on the fingerprint plot as small shoulders on the sides of the plot. The complementary nature of the fingerprint plots and the packing diagrams is apparent



Figure 14. Assignment of key features in the 2D fingerprint plot for form R of ROY. The four contacts labeled on the packing diagram on the left are identified with the sharpest spikes on the fingerprint plot.

from Figure 14. Where the former is capable of identifying important close contacts without recourse to tables of contact distances relative to van der Waals radii, the packing diagram clearly shows that the contacts labeled 1 and 2 are both cyclic, and together form a continuous chain motif. The other close contacts also form chains, with 3 running across the figure from left to right, and 4 from top to bottom. Another feature visible in some of the fingerprint plots for the ROY polymorphs is the spike along the plot diagonal characteristic of H‚‚‚H contacts. Whereas this is very prominent in OP, which exhibits the shortest contact of this type (Table 1), as well as in YN, it is very long in Y and R. Of course H‚‚‚H contacts are also present in the other structures, but the absence of a sharp feature indicates that those that are present occur at longer and similar distance ranges. In the plots of ORP and YN, a distinct splitting of the H‚‚‚H fingerprint is noticeable (in YN this arises from a different contact to the one giving the sharp and close contact). This splitting occurs when the shortest contact is between three atoms, rather than a direct two-atom contact.11 The short H‚‚‚H contact of 2.05 Å deserves comment, since this is significantly shorter than the sum of H-atom van der Waals radii of 1.20 Å.62 Such a short contact may be a result of the orientational disorder or it could reflect an average orientation of the H atoms in the methyl group, although this does not seem to be the case here. Unusually short contacts are rare but not unknown. For example, a very short but real contact ) dmin 1.02 Å is observed in the crystal structure of of dmin e i pyrene-II,63 and to our knowledge the shortest intermolecular H‚‚‚H contact in an organic crystal structure is that of the unstable polymorph of 1,2,3,5-tetra-O-acetyl-β-D-ribofuranose, with a H‚‚‚H distance of 1.949(7) Å.64 The existence of these short contacts, usually thought to be repulsive in nature, appears to be in accordance with the recent concept of H‚‚‚H interactions as bonding and stabilizing interactions in a crystal structure.65 Table 1 also highlights short H‚‚‚O and H‚‚‚N contacts that form cyclic dimer motifs in the crystal structures, and all six dimers are illustrated in Figure 15. Dunitz and Gavezzotti66 have recently applied Gavezzotti’s Pixel semi-classical density sums (SCDS) method67 to six of the polymorphs of ROY, with a focus on the energetics of individual molecular pairs. This method incorporates a realistic electrostatic energy based on ab initio

electron densities, as well as polarization, dispersion, and repulsion contributions to the energy. The two similar centrosymmetric dimers observed for R and ORP are both computed to have binding energies of 25 kJ mol-1 (these dimers are labeled R E and OP C in ref 66), as does the dimer in YN (YN C in ref 66), while the dimer in OP (OP A) is more strongly bound, with a computed energy of 42 kJ mol-1. Dunitz and Gavezzotti did not identify the bifurcated dimer in ON, and YT04 was not included in their analysis. Despite the obvious appeal of identifying short atom-atom contacts and various hydrogen-bonding motifs in these polymorphs, in ranking the most important molecular pairs in the six polymorphs on the basis of energy, Dunitz and Gavezzotti observe that all but one of the lowest energy pairs involve stacking of either or both of the nitrophenyl and thiophenecarbonitrile rings (the exception is the cyclic dimer in OP, Figure 15). In other words, dispersion interactions are substantially stronger than the weak hydrogen bonding in these structures, and they also comprise an important part of the so-called hydrogen-bond energies. Those authors conclude that “As new evidence keeps accumulating, it becomes more and more evident that the cohesive energy in organic crystal structures is not amenable to simple reasoning based on intermolecular atom-atom bonding interactions. Rather, it is mainly the interactions between the molecules and not between the individual atoms that provide the best basis for analyzing and understanding the cohesive energy of organic crystals”. Chen et al.59 have ranked the crystal energies of six polymorphs of ROY (based on their enthalpies) as follows: YN (highest energy, least stable at 0 K), ON, OP, R, YT04 and Y (lowest energy, most stable at 0 K), spanning a narrow energy range of ca 3 kJ mol-1; melting and melting/eutectic data on ORP could not be measured due to shortage of material. The relative crystal energies computed by Dunitz and Gavezzotti are in excellent agreement with the experimental ranking, but lattice energies span a range of 13 kJ mol-1 (22 kJ mol-1 when conformational energy differences are taken into account). It would naturally be very satisfying if Hirshfeld surfaces and fingerprint plots could be used directly to assess the energy ranking of polymorphs, but the energy differences involved are typically very small, and the complex interplay between various contributions to the total free energy of a crystal structure imply


McKinnon et al.

Figure 15. Cyclic hydrogen-bonded dimer motifs in the ROY polymorphs. Those observed in R, ORP, YN, and OP are centrosymmetric, the dimer in ON involves a bifurcated contact to the NO2 group with two nearly identical H‚‚‚O distances, and the dimer in YT04 incorporates both H‚‚‚N and H‚‚‚O close contacts.

that a Hirshfeld surfaces energy-matching process would be likely to depend on a quantitative, as well as qualitative, analysis, which is beyond the scope of this work but is an area that is currently being explored. Conclusions Through this work we have demonstrated how Hirshfeld surfaces and fingerprint plots are a valuable and rapid tool for visualizing and analyzing intermolecular interactions in polymorphs of molecular crystals, thereby making the task of polymorph comparison easier and more rapid. In particular, the subtle relationships between some polymorphs (e.g., R- and γ-TTF, and R- and β-p-dichlorobenzene) are more easily discernible through comparison of Hirshfeld surfaces and fingerprint plots rather than solely through conventional structure viewing. Conversely, structural differences and similarities between clearly distinct polymorphs (e.g., R- and β-oxalic acid, and R- and γ-p-dichlorobenzene) stand out more evidently and can be easily catalogued in terms of specific atom‚‚‚atom interaction types. This is the direct result of the underlying principle behind the Hirshfeld surface, i.e., embracing a “whole of structure” view of intermolecular interactions, rather than concentrating exclusively on assumed important (i.e., short) interactions. Hirshfeld surfaces and fingerprint plots proved to be particularly suited for comparing environments of structures with Z′ > 1 (e.g., β- and γ-TTF) where the complex interplay between crystallographically unique molecules could be rationalized in terms of complementary regions. Where conformational polymorphism occurs, Hirshfeld surfaces may sometimes be used as the sole basis for comparison, as observed for piracetam, while for ROY fingerprint plots become the preferred method for polymorph comparison, enabling the visualization of the major features of a crystal structure as a whole in a single, colored 2D plot. However, underlying all of these analyses is a detailed interaction between the Hirshfeld surfaces, fingerprint plots, and more conventional crystal-packing diagrams, all of which can be performed in real time on modern personal computers. In this sense, the figures that we have chosen represent only a small subset of those used in our investigations of each system. Although the power of Hirshfeld surfaces and fingerprint plots lies in the visualization of the environment around one molecule in terms of its intermolecular contacts with its neighboring molecules, rather than between individual atoms, this method has currently some shortcomings. In particular, as exemplified

by the analysis on ROY, fingerprint plots are not very sensitive to differences in contact geometries and where the complexity of the molecule probed increases either through size, diversity of atom type or conformational flexibility, the number and type of intermolecular interactions is inevitably likely to increase. This results in the inconvenient problem of overlap of the same type of contact or even in some cases of different types of contacts on the fingerprint. We believe this problem could be circumvented by breaking down the 2D fingerprint plots into specific atom‚‚‚atom contacts in the crystal, and this is an area we are currently exploring. This development would enable extracting quantitative information on the relative contribution of each contact type and could prove useful when attempting to rank the importance of specific intermolecular interactions. Rather than contradicting the earlier statement on the importance of viewing the crystal structure in its entirety, this effort recognizes the importance of first understanding the crystal structure as a whole and subsequently being able to focus on specific families of intermolecular contacts. Acknowledgment. This research has been supported by the Australian Research Council. One of the authors (F.P.A.F.) would like to thank DEST (Department of Education, Science and Training of the Australian government) for the award of an Endeavour Research Fellowship. References (1) Bernstein, J.; Henck, J. O. Cryst. Eng. 1998, 1, 119-128. (2) 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. (3) Dunitz, J. D.; Bernstein, J. Acc. Chem. Res. 1995, 28, 193-200. (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) Allen, F. H.; Bellard, S.; Brice, M. D.; Cartwright, B. A.; Doubleday, A.; Higgs, H.; Hummelink, T.; Hummelink-Peters, B. G.; Kennard, O.; Motherwell, W. D. S.; Rodgers, J. R.; Watson, D. G. Acta Crystallogr. 1979, B35, 2331-2339. Allen, F. H.; Kennard, O.; Taylor, R. Acc. Chem. Res. 1983, 16, 146-153. Allen, F. H. Acta Crystallogr. 2002, B58, 380-388. (6) Bernstein, J.; Davey, R. J.; Henck, J. O. Angew. Chem. Int. Ed. 1999, 38, 3441-3461. (7) van de Streek, J. Acta Crystallogr. Sect B. 2006, 62, 567-579. (8) Haleblian, J.; McCrone, W. J. Pharm. Sci. 1969, 58, 911-929. Bernstein, J. In Computer-Assisted Modeling of Receptor-Ligand Interactions. Theoretical Aspects and Applications to Drug Design; Rein, R., Golombek, A., Eds.; Alan R. Liss, Inc.: New York, 1989; Beyer, T.; Day, G. M.; Price, S. L. J. Am. Chem. Soc. 2001, 123, 5086-5094.

Polymorphic Molecular Crystal Structures (9) Seddon, K. R. In Crystal Engineering: The Design and Application of Functional Solids; Seddon, K. R., Zaworotko, M., Eds.; Kluwer Academic: Amsterdam, 1999; pp 1-28. (10) Bernstein, J. Polymorphism in Molecular Crystals; Clarendon Press: Oxford, 2002. (11) McKinnon, J. J.; Spackman, M. A.; Mitchell, A. S. Acta Crystallogr. 2004, B60, 627-668. (12) McKinnon, J. J.; Mitchell, A. S.; Spackman, M. A. Chem. Eur. J. 1998, 4, 2136-2141. Spackman, M. A.; Byrom, P. G. Chem. Phys. Lett. 1997, 267, 215-220. (13) Spackman, M. A.; McKinnon, J. J. CrystEngComm 2002, 4, 378392. (14) Dziubek, K. F.; Katrusiak, A. J. Phys. Chem. B. 2004, 108, 1908919092. (15) Fabbiani, F. P. A.; Allan, D. R.; Parsons, S.; Pulham, C. R. CrystEngComm 2005, 7, 179-186. (16) Lozano-Casal, P.; Allan, D. R.; Parsons, S. Acta Crystallogr. 2005, B61, 717-723. (17) Moggach, S. A.; Allan, D. R.; Parsons, S.; Sawyer, L. Acta Crystallogr. 2006, B62, 310-320. (18) Moggach, S. A.; Marshall, W. G.; Parsons, S. Acta Crystallogr. 2006, B62, 815-825. (19) Budzianowski, A.; Katrusiak, A. Acta Crystallogr. 2006, B62, 94101. (20) Fabbiani, F. P. A.; Allan, D. R.; Parsons, S.; Pulham, C. R. Acta Crystallogr. 2006, B62, 826-842. (21) Bacchi, A.; Bosetti, E.; Carcelli, M.; Pelagatti, P.; Pelizzi, G.; Rogolino, D. CrystEngComm 2006, 8, 233-244. (22) For meaningful comparison between surfaces, the mapping range for de is the same for all surfaces in each figure in the present work, although it may differ between figures. (23) Koenderink, J. J.; van Doorn, A. J. Image Vision Comput. 1992, 10, 557-565. (24) Wolff, S. K.; Grimwood, D. J.; McKinnon, J. J.; Jayatilaka, D.; Spackman, M. A. CrystalExplorer 1.5; University of Western Australia, Perth, Australia, 2006 (http://www.theochem.uwa.edu.au/ CrystalExplorer). (25) Allen, F. H.; Kennard, O.; Watson, D. G.; Brammer, L.; Orpen, A. G.; Taylor, R. J. Chem. Soc. Perkin Trans. 2 1987, S1-S19. (26) Thalladi, V. R.; Nu¨sse, M.; Boese, R. J. Am. Chem. Soc. 2000, 122, 9227-9236. Derissen, J. L.; Smit, P. H. Acta Crystallogr. 1974, B30, 2240-2242. (27) Etter, M. C. Acc. Chem. Res. 1990, 23, 120-126. Etter, M. C.; MacDonald, J. C.; Bernstein, J. Acta Crystallogr. 1990, B46, 256262. Bernstein, J.; Davis, R. E.; Shimoni, L.; Chang, N. L. Angew. Chem. Int. Ed. Engl. 1995, 34, 1555-1573. (28) Structures chosen from the CSD were OXALAC06 (R-form) and OXALAC04 (β-form). Each is the room-temperature structure with the lowest crystallographic R-factor for that form. (29) This feature is described in detail in Section 3.4.1 of ref 11. (30) Sankaran, H.; Sharma, S. M.; Sikka, S. K.; Chidambaram, R. Pramana 1986, 27, 835-839. (31) Ibberson, R. M.; Wilson, C. C. J. Phys.: Condens. Matter 2002, 14, 7287-7295. (32) Wheeler, G. L.; Colson, S. D. Acta Crystallogr. 1975, B31, 911913. (33) Wheeler, G. L.; Colson, S. D. J. Chem. Phys. 1976, 65, 1227-1235. (34) Reynolds, P. A. Acta Crystallogr. 1977, A33, 185-191. (35) Boese, R.; Kirchner, M. T.; Dunitz, J. D.; Filippini, G.; Gavezzotti, A. HelV. Chim. Acta 2001, 84, 1561-1577. (36) Mirsky, K.; Cohen, M. D. Acta Crystallogr. 1978, A34, 346-348. Royer, J.; Skalli, M.; Bayard, F.; Decoret, C. J. Cryst. Growth 1993, 130, 280-286. (37) Oonk, H. A. J.; Van Genderen, A. C. G.; Blok, J. G.; Van der Linde, P. R. Phys. Chem. Chem. Phys. 2000, 2, 5614-5618. Thiery, M. M.; Rerat, C. J. Chem. Phys. 2003, 118, 11100-11110. Dunitz, J. D.; Gavezzotti, A. HelV. Chim. Acta 2002, 85, 3949-3964. Day, G. M.; Price, S. L. J. Am. Chem. Soc. 2003, 125, 16434-16443. (38) Structures chosen from the CSD were DCLBEN07 (R-form), DCLBEN06 (β-form) and DCLBEN03 (γ-form). (39) The angles are defined in Figure 54 of ref 11.

Crystal Growth & Design, Vol. 7, No. 4, 2007 769 (40) Bailey, M.; Brown, C. J. Acta Crystallogr. 1967, 22, 387-391. (41) Sledz, M.; Janczak, J.; Kubiak, R. J. Mol. Struct. 2001, 595, 77-82. (42) Domenicano, A.; Schultz, G.; Hargittai, I.; Colapietro, M.; Portalone, G.; George, P.; Bock, C. W. Struct. Chem. 1990, 1, 107-122. (43) Fischer, P.; Zolliker, P.; Meier, B. H.; Ernst, R. R.; Hewat, A. W.; Jorgensen, J. D.; Rotella, F. J. J. Solid State Chem. 1986, 61, 109125. (44) Structures chosen from the CSD were TEPHTH07 (form I), TEPHTH12 (form II), and TEPHTH13 (form III). (45) Bechgaard, K. In Structure and Properties of Molecular Crystals; Pierrot, M., Ed.; Elsevier: Amsterdam, 1990; pp 235-295. (46) Kistenmacher, T. J.; Phillips, T. E.; Cowan, D. O. Acta Crystallogr. 1974, B30, 763-768. (47) Coppens, P. Phys. ReV. Lett. 1975, 35, 98-100. (48) Cooper, W. F.; Kenny, N. C.; Edmonds, J. W.; Nagel, A.; Wudl, F.; Coppens, P. J. Chem. Soc. Chem. Commun. 1971, 889-90.; Cooper, W. F.; Edmonds, J. W.; Wudl, F.; Coppens, P. Cryst. Struct. Commun. 1974, 3, 23-26. (49) Venuti, E.; Della Valle, R. G.; Farina, L.; Brillante, A.; Vescovi, C.; Girlando, A. Phys. Chem. Chem. Phys. 2001, 3, 4170-4175. (50) Ellern, A.; Bernstein, J.; Becker, J. Y.; Zamir, S.; Shahal, L. Chem. Mater. 1994, 6, 1378-1385. (51) Batsanov, A. S. Acta Crystallogr. 2006, C62, o501-o504. (52) Structures chosen from the CSD were BDTOLE10 (R-form) and BDTOLE02 (β-form). The CIF file for the γ-form of TTF (150 K structure) was downloaded from the Acta Crystallographica website, http://www.iucr.org. (53) Brown, C. J. Acta Crystallogr. 1966, 21, 146-152. (54) Hoekstra, A.; Meertens, P.; Vos, A. Acta Crystallogr. 1975, B31, 2813-2817. (55) Marsh, R. E.; Herbstein, F. H. Acta Crystallogr. 1983, B39, 280287.; Marsh, R. E.; Herbstein, F. H. Acta Crystallogr. 1988, B44, 77-88.; Herbstein, F. H.; Marsh, R. E. Acta Crystallogr. 1998, B54, 677-686.; Marsh, R. E. Acta Crystallogr. 1999, B55, 931-936. (56) Nowell, H.; Price, S. L. Acta Crystallogr. 2005, B61, 558-568. (57) Structures chosen from the CSD were BISMEV05 (form I), BISMEV (form II), BISMEV01 (form III), and BISMEV04 (form IV). All except BISMEV05 are room temperature structures; BISMEV05 is the single crystal redetermination of form I at 150 K (ref 15), the original RT structure for form I (BISMEV03) being based on powder data and having amide H atoms placed in idealized pyramidal positions. (58) Yu, L.; Stephenson, G. A.; Mitchell, C. A.; Bunnell, C. A.; Snorek, S. V.; Bowyer, J. J.; Borchardt, T. B.; Stowell, J. G.; Byrn, S. R. J. Am. Chem. Soc. 2000, 122. (59) Chen, S.; Guzei, I. A.; Yu, L. J. Am. Chem. Soc. 2005, 127, 98819885. (60) Structures chosen from the CSD were QAXMEH (ON), QAXMEH01(Y), QAXMEH02 (R), QAXMEH03 (OP), QAXMEH04 (YN)QAXMEH05 (ORP), and QAXMEH12 (YT04). (61) In Table 1, we compare the internuclear separation with the sum of van der Waals radii from Bondi (ref 62) but use a cutoff of 97% of this sum to acknowledge that the precise values of van der Waals radii are somewhat arbitrary, and many different choices could be made. This does not mean that we regard contact distances longer than this separation as unimportant; the 97% cutoff serves merely to identify the very shortest close contacts in each structure for correlation with the spikes in the fingerprint plots in Figure 13. (62) Bondi, A. J. Phys. Chem. 1964, 68, 441-447. (63) Dunitz, J. D.; Gavezzotti, A. Acc. Chem. Res. 1999, 32, 677-684. (64) Bombicz, P.; Czugler, M.; Tellgren, R.; Ka´lma´n, A. Angew. Chem. Int. Ed. 2003, 42, 1957-1960. (65) Matta, C. F.; Herna´ndez-Trujillo, J.; Tang, T. H.; Bader, R. F. W. Chem. Eur. J. 2003, 9, 1940-1951. (66) Dunitz, J. D.; Gavezzotti, A. Cryst. Growth Des. 2005, 5, 21802189. (67) Gavezzotti, A. J. Phys. Chem. B. 2002, 106, 4145-4154. Gavezzotti, A. J. Phys. Chem. B. 2003, 107, 2344-2353.

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Comparison of Polymorphic Molecular Crystal Structures through

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