Conformational Polymorphism - Chemical Reviews (ACS Publications)

Review pubs.acs.org/CR

Conformational Polymorphism Aurora J. Cruz-Cabeza*,† and Joel Bernstein‡,§ †

Van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands Faculty of Natural Sciences, New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, United Arab Emirates § Department of Chemistry, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva, Israel 84120 ‡

8.4. Pressure-Induced Conformational Polymorphism 8.5. What Difference Can Length Make? 8.6. Pharmaceuticals and Conformational Polymorphism 9. Consequences of Conformational Change 10. Conclusions and Outlook Author Information Corresponding Author Notes Biography Acknowledgments References

CONTENTS 1. Introduction 2. Methods 2.1. Crystal Structures 2.1.1. The Cambridge Structural Database and the Creation of the Polymorphic Data Set 2.1.2. Comparison of Polymorphs 2.2. Molecules 2.2.1. Data Retrieval 2.2.2. Molecular Degrees of Flexibility (DOFlex) 2.2.3. Comparison of Molecular Geometries 2.2.4. Gas-Phase Optimizations and Energies 3. Refinement of the Polymorphic Dataset 4. Concepts: Conformations, Conformers, and Polymorphs 5. Identifying Conformational Change 5.1. rmsd[r]-crystal Limits 5.2. Torsion Variation Limits 5.3. rmsd[r]-crystal versus max(Δθ) 5.4. Are My Polymorphs Conformational? 6. Energetic Cost of Conformational Variations 7. Statistics on Conformational Polymorphism 7.1. Polymorphism in the CSD 7.2. Molecular Flexibility and Conformational Polymorphism 7.3. Torsion-Angle Change, R-Bond Nature, and Conformational Polymorphism 8. Notorious Cases of Conformational Polymorphism 8.1. Molecular Shape and Conformational Polymorphism 8.2. Synthetic Memory and Conformational Polymorphism 8.3. Concomitant Conformational Polymorphism

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1. INTRODUCTION The century following the determination of the first crystal structure by the Braggs1 has yielded encyclopedic precise information on molecular geometry. The interatomic distances for virtually any pair of atoms that can form a bond are known to high precision.2 Similar information is available for angles and torsion angles formed by atoms in molecules. The torsion angles in a molecule are of particular interest because, together, they define the molecular shape, which is intimately related to the chemical and physical properties of the molecule. Until the late 1960s, the difficulty in performing a crystal structure determination somewhat limited the number of determined crystal structures and, consequently, the amount of geometric information available. Although there was recognition of the possibility that the molecular shape found in a crystal structure might differ from that in other media (mostly because of lack of information to the contrary), it was generally assumed that the molecular shape in the crystal was “the molecular shape”. As crystal structure determinations became increasingly facile at the beginning of the 1970s, a number of studies were published of a molecule in different crystal structures exhibiting different molecular shapes. The only rationale for this phenomenon, termed conformational polymorphism, was that the crystal environment might play a role in determining the molecular shape, thus tempering the assumption that the molecular shape observed in a crystal is identical to that to be found in fluid media. Some of the questions that arise from these observations are as follows: How is the phenomenon defined? How can it be recognized? How common is it? How different are the molecular shapes in those compounds exhibiting conformational polymorphism? What conformational energies are

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Received: May 7, 2013 Published: December 18, 2013 © 2013 American Chemical Society

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group; therefore, only two atomic coordinates need be determined to solve the structure. The first X-ray determination of a conformationally flexible molecule, cyclohexane, was reported by Hassel and Kringstad in 1930,26 even though 40 years earlier, Sachse27,28 had suggested that cyclohexane was a flexible molecule facilitating a variety of conformations. Prior to Hassel and Kringstad’s work, it was not known in which conformation the molecule existed, and Hassel and Kringstad showed that cyclohexane was in the chair conformation in the crystal rather than the boat conformation. Since that work, cyclohexane and its derivatives have become perhaps the iconic cornerstones of research in stereochemistry.29,30 To properly address the subject of conformational polymorphism, one must address the definitions of the terms “conformation” and “conformer”. The terms have been understood and applied in a number of ways, despite the existence of formal IUPAC definitions. According to the IUPAC recommendations, a conformation is “the spatial arrangement of the atoms affording distinction between stereoisomers which can be interconverted by rotations about formally single bonds”, whereas a conformer “is one of a set of stereoisomers, each of which is characterized by a conformation corresponding to a distinct potential energy minimum”.31 Chemists and chemical crystallographers have understood variations on these definitions, and the historical development and use of the terms prior to the formal IUPAC definition reflects some of that variety. In 1962, Eliel noted that conformation “is used to denote any one of the infinite number of momentary arrangements of the atoms in space that result from rotation about single bonds”.29 More recently, Glusker and Trueblood define it as “One of the likely shapes of a molecule. Generally applied to molecules for which there is a possibility for rotation about bonds. Different rotational positions about bonds are represented by torsion angles.”32 Although, conceptually, a “momentary arrangement in space” might be equivalent to “shape”, the working definition requires some metric parameters (i.e., torsion angles). About 30 years earlier, though, Dunitz included the element of energy in the definition: “Of all possible spatial arrangements of atoms in a molecule ... those that correspond to potential energy minima are known as conformations. The definition, like the concept itself, is imprecise ... how are we to know whether a proposed spatial arrangement corresponds to a potential energy minimum or not? ... Generally, conformations are arrangements that arise by rotation about bonds, and they may be described by specification of relevant torsion angles. Moreover, we can be reasonably confident that any particular arrangement of atoms observed in a molecular crystal cannot be far from an equilibrium structure of the isolated molecule. X-ray analysis thus provides information about the preferred conformations of molecules although it has nothing to say about the energy differences between conformations or the energy barriers that separate them.”30 Consistent with Dunitz’s definition, in this review we incorporate energy into our working definition of conformer. Any change in a given single rotatable bond (henceforth Rbond) of a molecule always affords a new conformation, but it affords a new conformer only if the conformational change goes through a potential energy barrier into a different potential energy well. Intermolecular interactions present in organic crystals are generally not sufficient to significantly perturb bond lengths and bond angles, but for those molecules that do exhibit

associated with conformational polymorphism? Why is it important to identify this phenomenon? To answer these questions, this review explores the development and current status of conformational polymorphism, the convergence of two central and recurring themes in structural chemistry: polymorphism and molecular conformation. Individually, each has a long and rich history in the development of chemistry that highlights the significance of the merging of the two into an important component of current molecular science. Polymorphism was first recognized in 1822 by Mitscherlich, when he noted the difference in physical and chemical properties in different crystals of arsenates and phosphates.3,4 The earliest example of a polymorphic organic compound was that of benzamide, first studied by Liebig and Wöhler5 in 1832, for which it took over 170 years for the first appearing but fleeting metastable form to be determined.6 There was considerable activity in the study and utilization of polymorphism during the century following the Liebig−Wöhler article;7−13 however, as analytical methods advanced, producing and publishing numbers became easier than producing pictures and descriptions of different crystals, which resulted in a waning of interest in polymorphism in the middle decades of the 20th century. A recent gradual renaissance was brought about by the confluence of a number of factors: the increasing recognition that different polymorphs of the same substance can exhibit very different properties and the possibility of utilizing polymorphs as ideal systems for the study of structure− property relations; the increasing facility for carrying out singlecrystal structure determinations for the structural characterization and comparison of polymorphs; the recognition of the relevance to the pharmaceutical industry and the publicity attending a number of high-profile patent litigations involving questions dealing with polymorphism; and finally, the ease with which color photographs of crystals can be prepared and published in the mainstream scientific literature, thus facilitating the reproduction and recognition of published polymorphic crystal forms. A number of books have documented this renaissance.14−16 Molecular conformation and the recognition of the importance of the three-dimensional structure of molecules dates to the seminal work by Pasteur on the optical isomers of tartaric acid.17 This was essentially contemporary with Kekulé’s proposal for the structure of benzene based on the tetravalence of carbon18 that also advanced the concept of the tetrahedral carbon atom.19−21 Following the discovery of the diffraction of X-rays by crystals in 1912, there was a flurry of activity in developing techniques to utilize the phenomenon to determine the structure of crystals, leading to the awarding of the Nobel Prize to the father and son Bragg for the structure of sodium chloride.1 The structure of diamond22 provided the metrics of the tetrahedral carbon atom (1.54 Å CC bond length and 109.5° CCC angle), whereas that of graphite23,24 confirmed the planarity of the benzene ring, the aromatic CC bond length of ∼1.40 Å, and the 120° CCC bond angle. Although structural science has advanced significantly in the intervening ∼90 years, the values for these fundamental geometric parameters have not changed significantly since these first determinations. The first determination of the crystal structure of an organic compound was that of hexamethylenetetramine, carried out by Dickinson and Raymond in 1923.25 The solution of this crystal structure in those early days was actually made possible by the fact that the molecule is a rare example of an organic substance crystallizing in a cubic space 2171


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the current context, polymorphsare given those six letters plus two numbers. The “best-R-factor” subset of the CSD does not contain crystal structure redeterminations; only the unique structure with the lowest R factor is kept. In building this bestR-factor subset (annually provided with the CSD), structure redeterminations are identified and removed using an algorithm that compares crystal structures based on comparisons of simulated powder X-ray diffraction (PXRD) patterns.40 In addition to redeterminations, potentially wrong structures are also eliminated (including structures with R factors of >10%), together with structures exhibiting positional disorder of heavy atoms. Therefore, the resulting list contains only structures of high quality with no disorder. Thus, any refcode family containing more than one refcode within the best-R-factor list corresponds to a polymorphic family. Crystallographic data were retrieved from the CSD version 5.33 (Nov. 2011 release) using Conquest.41 Searches on the subset of polymorphic structures were restricted to the best-Rfactor list, including crystal structures of one single organic molecule (no multicomponent crystals) limited to the most common atomic elements in organic molecules (C, H/D, N, O, S, and halogens). Only structures with all of their threedimensional atomic coordinates determined (with the exception of hydrogen atoms) were retrieved, and polymeric structures were removed. The search returned 2935 different crystal structures containing 1366 polymorphic molecules. 2.1.2. Comparison of Polymorphs. Crystal structures of polymorphs were compared using the COMPACK algorithm.42 For each structure, COMPACK generates a cluster of molecules (generally ca. 20) consisting of a central molecule and a specified number of its closest neighbors to provide a localized representation of the crystal structure. For a pair of structures, correlation of selected atoms for the central molecule is carried out, and the molecular clusters are superimposed maximizing the number of overlapping molecules under certain distance and angle tolerances. COMPACK returns the number of matched molecules between clusters (N = 1−20), together with a root-mean-square deviation value of their atomic positions (rmsdN). A command-line version of the COMPACK algorithm, as implemented in Mercury’s materials module,43 was used for crystal structure comparison using a cluster size of 20 molecules and the standard tolerances.

torsional degrees of freedom, various polymorphs can exhibit different molecular conformations and, more importantly, different conformers. Crystal forces might play a role in determining the conformation of a molecule in the solid state and, in particular, in the phenomenon of conformational polymorphism, the subject of this review. Historically, the explicit connection between polymorphism and molecular conformation as conformational polymorphism was apparently first made by Corradini in 197333 and shortly thereafter by Panagiotopoulos et al.34 The first attempt to utilize conformational polymorphs to quantify the relationship between crystal forces and molecular conformation was made by one of the coauthors.35 Although increasing numbers of articles and reviews on the subject of polymorphism have been published, there have been only a few limited subsequent attempts at compiling the instances of conformational polymorphism and summarizing our knowledge of the phenomenon.36,37 Three possible reasons behind the lack of such a complete review are (1) the exponential increase in crystal structure data available; (2) the difficulty of identifying a polymorph as a conformational polymorph from literature data alone, that is, without appropriate statistical and analytical tools; and (3) the lack of awareness of the practical importance of conformational polymorphism. For instance, in the course of the preparation of a 1978 article, one of the coauthors sought to include some literature examples of polymorphic structures in which the molecular conformations differed. This search was carried out using “traditional” methods, often scanning journals by hand and then punching cards to serve as input to geometry programs, first to calculate and compare geometries and then the appropriate ORTEP plots. Developments in hardware and software and the creation of the invaluable Cambridge Structural Database (CSD)38 have transformed the field and permit us now to define the term itself more precisely and to survey the structural literature to place the concept into perspective. The term has, in fact, become part of the lingua franca of structural chemistry: a recent query to Web of Knowledge located 740 references containing “conformational polymorphs” or “conformational polymorphism” in the context of crystallography. The review is organized as follows: We first provide a description of the choice of the data set, followed by the precise definition of terms in the context of the review, the statistical variations of molecular parameters and methods to evaluate them, examples of conformational polymorphism, and the energetic manifestations and consequences of conformational change in polymorphs.

2.2. Molecules

2.2.1. Data Retrieval. Molecular geometries were retrieved from the crystal structures and exported as molecular files using Conquest.41 OpenBabel was used for molecular format conversions and the addition of hydrogen atoms44 to molecules with unresolved hydrogen atom positions. 2.2.2. Molecular Degrees of Flexibility (DOFlex). The most common method of defining molecular flexibility is by specifying the number of R-bonds. Some algorithms, however, do not account for cyclic groups or groups attached to triple bonds as rotatable. Here, we refer to a molecule’s degree of flexibility (DOFlex) as the sum of (1) the number of acyclic Rbonds, (2) the number of groups attached to triple bonds, and (3) the number of aliphatic cycles that could potentially also change their geometry. Terminal groups such as CH3, NH2, and OH are not taken into account because of the lack of accuracy in the determination of hydrogen atom positions with X-ray diffraction. These molecular descriptors were calculated using the ChemAxon cheminformatics plugin.45

2. METHODS 2.1. Crystal Structures

2.1.1. The Cambridge Structural Database and the Creation of the Polymorphic Data Set. The CSD38 currently holds structural information on over 650000 crystal structures of organic and organometallic compounds.39 In the CSD, all crystal structures containing the same chemical compound(s) are stored in a unique refcode family consisting of six letters. Usually, the first crystal structure of a refcode family is given the six-letter refcode only, whereas any further structures of the same chemical compound(s)redeterminations under the same or different conditions or, specifically in 2172


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2.2.3. Comparison of Molecular Geometries. TORMAT46 was used to compare molecular geometries. A TORMAT comparison of conformations of molecules in crystal structures A and B of a compound returns a mapping of atoms of the B conformation onto the A conformation. If there are symmetry-related atoms in the molecule, various atom mappings are possible; thus, TORMAT returns the mapping that results in the lowest root-mean-square deviation between atomic positions, namely, rmsd[r]. The TORMAT rmsd[r] value is calculated according to the equation rmsd[r ] (Å) =

⎛ ∑N (r A − r B)2 ⎞ i ⎜ i=1 i ⎟ ⎜ ⎟ N atoms ⎝ ⎠

3. REFINEMENT OF THE POLYMORPHIC DATASET We proceeded to refine our original polymorphic data set retrieved from the best-R-factor list of the CSD. Polymorphs in this data set were identified as unique based on differences in PXRD patterns from other polymorphs of the same molecule, plus low-quality structures and structures with disorder of heavy atoms were also eliminated. Comparing crystal structures based on PXRD patterns similarity is very fast and is the only suitable way to identify and remove structure redeterminations from large databases such as the entire CSD.40 On one hand, the method is not infallible, and indeed, we detected a few instances in which real polymorphs were removed because of the similarities between PXRD patterns in different polymorphs are high. On the other hand, PXRD patterns can be significantly altered by small changes in atomic fractional coordinates or anisotropic cell expansions, and although the algorithm accounts for some of these factors, in some cases, the same polymorph determined under more extreme conditions might not be identified as the same crystal structure. For this reason, we used COMPACK42 to further compare the original polymorphic data set and eliminate redeterminations that were not identified with the PXRD comparison algorithm only. Crystal structures were compared in pairs within each polymorphic family (families of two polymorphs required one comparison, families of three required three, families of four required six, etc.). The original 2935 crystal structures (containing 1366 polymorphic molecules) required a total of 2786 COMPACK comparisons. Of these, 87 pairs of crystal structures were found to match 20 molecules within the tolerances allowed, and one pair of crystal structures was found to be a misclassification in the CSD, their molecules being isomers but not the same compound (KETTUY01 and KETTUY10).50 Pairs of crystals matching 20 of 20 molecules in a cluster indicate that these two structures are very similar if not identical. The rmsd20 value indicates how close the two structures are. Figure 1 shows a histogram of rmsd20 values for

(1)

where r refers to the atomic position of atom i in conformations A/B and the summation runs over the heavy atoms in the molecule (Natoms). Hydrogen atoms are ignored in these conformational comparisons, and inversion is allowed so that enantiomers can be compared accordingly. In addition to the TORMAT comparison data, we also calculated the maximum difference for any torsion angle of a given pair of molecules, max(Δθ). TORMAT identifies all noncyclic bonds as rotatable excluding terminal hydrogen atom rotations (e.g., CH3, NH2, and OH, because there is often considerable imprecision in the positions of the hydrogen atoms) and rotations of groups attached to triple bonds (because these rotations cannot be measured with a classic torsion angle). The visual superposition of molecules was performed with Mercury. 2.2.4. Gas-Phase Optimizations and Energies. Molecular energetics were determined by gas-phase geometry optimizations carried out with density functional theory including dispersion corrections (DFT-d) at the B97-D/ccpVTZ level of theory using the Gaussian 0947 package. The functional B97-D includes van der Waals corrections as derived by Grimme and co-workers.48,49 Starting molecular geometries were taken as reported in the polymorphic crystal structures. In cases where hydrogen atom positions were unresolved, these were added to the reported heavy atoms using the procedure implemented in OpenBabel, which uses information on the atomic hybridizations.44 Two consecutive geometry optimizations were performed per conformation: (i) a constraint optimization in the gas phase, in which R-bonds were constrained to the observed values in the crystal structures but other geometric parameters were allowed to optimize (Ecrys), and (ii) a relaxed optimization in the gas phase (Egas), in which all parameters in the molecule were allowed to optimize. Frequency calculations were not performed, but “tight” criteria were used for convergence. Three values of relative energy were calculated per A−B pair of conformations

Figure 1. rmsd20 histogram for the 87 pairs of crystal structures matching 20 molecules of a 20-molecule cluster with COMPACK. A visual overlay of YAMHID02/YAMHID03 with rmsd20 = 0.7 Å is given as an illustration.

ΔEgas − crys(A) = Ecrys(A) − Egas(A)

those 87 pairs found as being the same within the COMPACK tolerances. Pairs of structures with large rmsd20 values show some structural changes due to variations in the experimental conditions. For example, SALOXM03 and SALOXM05 have rmsd20 = 0.44 Å and correspond to the same crystal structure determined at different pressures (ambient and 2.37 GPa),51 and YAMHID02 and YAMHID03 have rmsd20 = 0.7 Å and correspond to the same crystal structure determined at higher and lower temperatures (253 K 52 and 173 K 53 ). A

ΔEgas − crys(B) = Ecrys(B) − Egas(B) ΔEgas − gas(AB) = |Egas(B) − Egas(A)|

ΔEgas−crys(A/B) is the adjustment energy for the conformations in polymorphs A/B and ΔEgas−gas(AB) is the conformational energy difference between gas-phase conformers A and B. 2173


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correspond to distinct energy minima of the gas-phase potential energy surface (gas-PES). Does the definition of conformer hold in the solid state? In a crystal, molecular geometries represent minima on the crystal potential energy surface (crystal-PES): minima of the sum of the intra- and intermolecular energy. A crystal environment is clearly different from the gas phase because of the presence of neighboring molecules and the effect of these molecules on the molecular conformations. For the majority of neutral molecules, equilibrium geometries of molecules in their crystal structures are essentially close to their gas-phase equilibrium geometries.55 This observation has important consequences. For example, it is possible to use conformational data in crystals for the successful generation of ligand conformations.56,57 Similarly, gas-PES conformers are used as starting geometries to successfully predict crystal structures of flexible molecules.58,59 There are, however, some notable exceptions to this observation, namely (a) charged species (e.g., zwitterions)60 and (b) molecules crystallizing in special symmetry positions (e.g., biphenyl).61 A very appropriate approximation to the conformationcrystal problem is, therefore, to use gas-phase equilibrium geometries of molecules to unambiguously establish whether two molecular geometries in different crystals are representative conformations of two different conformers. When referring to conformations in crystal structures, it is important to differentiate between two phenomena: (a) conformational adjustment and (b) conformational change. On one hand, conformational adjustment always occurs for any flexible molecule in a crystal, to some extent, even if minimal. The flexible molecule adjusts to the crystal environment by slightly varying its conformation to minimize the lattice energy of the crystal (intra- and intermolecular energy). In the adjustment, a small conformational energy penalty is paid (adjustment energy, ΔEgas−crys) to improve the intermolecular interactions in the crystal. On the other hand, conformational change involves a change of gas-phase conformer: It requires going uphill on the gas-PES; over the energy barriers; downhill into a different potential energy well; and finally, conformational adjustment of the new gas-phase conformer to its crystal structure. The relative energy of two different gas-phase conformers is referred to here as ΔEgas−gas. These concepts are illustrated in Figure 3. We can illustrate these definitions with the well-studied polymorphic molecule ROY (i.e., for the three colors of the various polymorphs: red, orange, yellow) as an example. ROY crystallizes in at least nine different polymorphs, the structures

representation of the structure overlay of YAMHID02/03 is given as an example in Figure 1. How different two crystal structures should be for them to be considered polymorphs is a subject of debate. Experimental conditions such as temperature or pressure do certainly affect crystal structure. Gavezzotti stated that “structures without a substantial change in the three dimensional symmetry operations should strictly be referred to not as polymorphs but as modulations or phases”.54 Although such an approach requires considerable subjective analysis, we tend to share Gavezzotti’s view; moreover, because we are particularly interested in conformational polymorphs, structures matching 20 of 20 molecules with the COMPACK algorithm must perforce have similar conformations and were removed from the polymorphic data set. The polymorphic data set was also searched for pairs of enantiopure chiral/racemic structures. These pairs are not polymorphs unless racemization is possible, and they were also removed, because they indeed have different compositions. We found eight families of refcodes (16 crystal structures) consisting of chiral molecules crystallizing as enantiopure and racemic pairs, which we eliminated from the data set. In summary, the data set used in this review consisted of 1297 polymorphic molecules (Mpol) comprising 2770 crystal structures (Cpol). A summary of the retrieval and filtering process is presented in Figure 2.

Figure 2. Summary of the data retrieval and refinement process. Numbers in blue refer to crystal structures, and numbers in black refer to molecules.

4. CONCEPTS: CONFORMATIONS, CONFORMERS, AND POLYMORPHS Because this review deals with conformational polymorphs, it is essential to distinguish between conformations and conformers following the IUPAC recommendations noted briefly in the Introduction. The result of a variation of any torsion angle in a molecule is a new conformation. If, in addition to a change in torsion angle, there is a change in potential energy well in the new conformation, the new conformation is also a conformer. Not all pairs of conformations are conformers, only those that

Figure 3. Schematic representation of the concepts of “conformational change” and “conformational adjustment”. 2174


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of seven of which have been determined by X-ray diffraction methods.62−64 These seven determined polymorphs crystallize with seven different conformations as defined by the torsion angle θ (Figure 4). These seven conformations, however, can

Larger rmsd[r]-crystal values indicate significant changes in conformations across polymorphs. Small rmsd[r]-crystal values, on the other hand, indicate that the conformational variations are small, mainly adjustments of the same gas-phase conformer to a different polymorph. The shape of the histogram of rmsd[r]-crystal values (Figure 5) illustrates that changes in

Figure 4. Gas-phase potential energy surface of ROY as a function of the torsion angle θ (B97-D/cc-pVTZ). The experimental conformations found in the seven determined ROY polymorphs are plotted as red and yellow circles.

Figure 5. rmsd[r]-crystal histogram (0.1 Å bin) for all conformation comparisons among all polymorphs (3166 TORMAT comparisons).

conformations across polymorphs are continuous. The rmsd[r]crystal histogram resembles, in principle, a Gaussian distribution with large deviations because of the high tail. To accurately assess conformational relationships between these conformations according to our definition, therefore, we need to make use of energy calculations. Instead of generating gas-PES for all these molecules (which would be an extremely expensive task, particularly for those flexible molecules with many degrees of freedom), we followed the procedure depicted in Figure 6. Conformations were

be grouped into two distinct conformational regions confined to the two gas-phase conformers of ROY: the local minimumenergy conformer (θ ≈ 40°) and the global minimum-energy conformer (θ ≈ 140°). The conformations observed in the different polymorphs are “adjustments” of the two gas-phase conformers to the seven different crystalline environments (Figure 4). Thus, the conformations found in polymorphs QAXMEH, QAXMEH02, QAXMEH03, and QAXMEH05 are adjustments of the local minimum-energy conformer (red circles), whereas the conformations found in polymorphs QAXMEH01, QAXMEH04, and QAXMEH12 are adjustments of the global minimum-energy conformer (yellow circles). Conformations in red are related to conformations in yellow by conformational change. In the context of polymorphism of flexible molecules, two polymorphs whose independent conformations are related by conformational adjustment are referred to here simply as polymorphs, because the conformations populate the same potential well. If, in addition to adjustment, these conformations are related by conformational change, we refer to them as conformational polymorphs. Thus, for ROY, polymorphs QAXMEH/02/03/05 are related to QAXMEH01/04/12 by conformational polymorphism.

Figure 6. Schematic representation of the optimization procedure employed.

optimized in the gas phase constraining R-bonds to the values observed in the crystal structures. After the constraint optimizations, full optimizations (allowing all parameters to be optimized) were performed. Conformations were compared before (rmsd[r]-crystal) and after (rmsd[r]-gas) full geometry optimization. Because of the large data set (3166 pairs of conformations, which required 7198 unique DFT-d calculations), we filtered the data into a more manageable and representative subset. First, only the most differing pair of conformations (largest rmsd[r]-crystal value) per polymorphic molecule was taken.

5. IDENTIFYING CONFORMATIONAL CHANGE 5.1. rmsd[r]-crystal Limits

To assess the conformational variability of the molecules in our polymorphic data set (1297 polymorphic molecules, 2770 crystal structures), a total of 3166 conformation comparisons across polymorphs were required. Each conformation comparison returned a TORMAT rmsd[r] value that is referred to as rmsd[r]-crystal because the conformations being compared are those found in the experimental crystal structures. 2175


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Second, as judged from visual inspection, most pairs of conformations with rmsd[r]-crystal between 0−0.3 Å appeared to be adjustments of the same gas-phase conformers only; we, therefore, chose to take only pairs of conformations with rmsd[r]-crystal values of >0.225 Å for further calculations. In this way, our data set was reduced to 549 pairs of conformations in total (requiring 2196 gas-phase DFT-d calculations), 452 pairs of which optimized successfully during the entire DFT-d procedure. The data set of 452 pairs of conformers was subdivided into two sets: (i) 141 pairs related by conformational adjustment only (CA data set, rmsd[r]-gas < 0.1 Å) and (ii) 311 pairs related by conformational change (CC data set, rmsd[r]-gas > 0.1 Å). We chose rmsd[r]-gas < 0.1 Å for distinguishing between change and adjustment because it was noted that pairs of conformers with 0 Å < rmsd[r]-gas < 0.1 Å differed only in hydrogen atom positions (together with some small readjustments of some heavy atoms). Because we cannot be certain about hydrogen atom positions originally taken from X-raydetermined geometries, these conformers were counted as being only conformational adjustments as well. rmsd[r]-gas values are plotted against rmsd[r]-crystal values in Figure 7, where the two tendencies (adjustment and change) are depicted as a dashed orange line (conformational adjustment only) and a dashed blue line (conformational change).

Figure 8. Relative frequencies of conformational change (blue) and adjustment (orange) as functions of rmsd[r]-crystal (452 pairs of conformations).

increases slowly to a maximum of 25%. Above the cutoff of 0.375 Å, this frequency rises to 54%. Identifying conformational change and adjustment by optimizing all pairs of conformations in all polymorphs with a suitable computational model is an expensive task and is clearly impractical for large data sets or for routine crystallographic use. We have achieved the optimization of 452 pairs of conformations when our original data set consisted of 3166 pairs. Thanks to these data, we were able to derive an approximate rmsd[r]-crystal cutoff of 0.375 Å that could be very valuable for readily distinguishing between conformational change and adjustment. Because almost 70% of the original conformations have rmsd[r]-crystal < 0.225 Å, we estimate that this cutoff of 0.375 Å will place ∼90% of the pairs with the correct conformational relationship across the entire range of rmsd[r]-crystal values. There will no doubt be some outliers from these classifications, particularly for rmsd[r]-crystal values for which the certainty of conformational change is less (between 0.4 Å of ∼50% and 0.65 Å of ∼80%). Figure 9

Figure 7. Scatter plot of rmsd[r]-gas versus rmsd[r]-crystal values for 454 pairs of conformations optimized at the B97-D/cc-pVTZ level of theory.

Clearly, large values of rmsd[r]-crystal represent conformational change, and smaller values more often represent conformational adjustments only. The relative frequency (in percent) of pairs of conformations related by conformational change/adjustment was plotted as a function of rmsd[r]-crystal in Figure 8. The data are binned using rmsd[r]-crystal intervals of 0.05 Å. Each bin contains a number of optimized pairs of conformers, and thus, we can determine the percentage that optimize to the same gas-phase minimum (orange, conformational adjustment only) or different gas-phase minima (blue line, conformational change). Figure 8 shows that the largest change in relative frequencies occurs at rmsd[r]-crystal values between 0.35 and 0.4 Å. Using 0.375 Å as a midvalue of that range, below this cutoff of rmsd[r]-crystal, the number of conformations that optimize to different gas-phase minima

Figure 9. Refcode family, rmsd[r]-crystal, and superimposed conformations for three pairs of crystal conformations that optimized to the same gas-phase conformer.

illustrates the overlay of three pairs of conformations with rmsd[r]-crystal > 0.375 Å that optimize to the same gas-phase conformer but would be misclassified as conformational polymorphs using the proposed rmsd[r]-crystal cutoff. Finally, one should also notice that this cutoff was derived from the data contained in the CSD. Most of these molecules have between 10 and 50 atoms. Hence, this rmsd[r]-crystal cutoff might be less applicable for larger molecules. Although 2176


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we also tried to derive an rmsd[r]-crystal cutoff based on molecular size, no correlations were found.

question, we proceeded to analyze our data set of optimized conformations. From the data set of 452 molecules optimized in the previous section, we took a subset of 267 pairs of conformations of molecules having at least one flexible R-bond and no additional conformational degrees of freedom. We then plotted the relative frequencies of conformational change (blue line) and adjustment (orange line) as functions of max(Δθ) in this subset (Figure 11). We observe that, up to max(Δθ) = 25°

5.2. Torsion Variation Limits

Using the rmsd[r]-crystal cutoff of 0.375 Å as an indication of the type of conformational variation in comparing two conformations is a very convenient approximation when comparing a large set of polymorphs and molecules of different nature. However, if one is to look at a particular molecule and all of the sources of molecular flexibility for this molecule arise from variations in acyclic R-bonds, the most facile and most precise way of determining the variation relationship between two conformations is by examining torsion-angle changes in Rbonds. One needs to look only at the maximum change in any R-bond, max(Δθ), of a pair of conformations. If the change in torsion angle results in a passage to a different energy well, as demonstrated in Figure 3, then these two conformations are related by conformational change. Yet, how can one know when a variation in an R-bond corresponds to a new conformer? That can be determined by examining the CSD distributions of R-bond values. For example, we calculated the gas-PES for propanol (blue line) and the R-bond distribution for a bond of the type C(sp3)CH2CH2O(sp3) from the CSD (grey surface) (Figure 10). Whereas the gas-PES requires a few hours of calculations,

Figure 11. Relative frequencies of conformational change (blue) and adjustment (orange) as functions of max(Δθ) (subset of 267 DFT-doptimized pairs of conformations containing flexibility due to acyclic bonds only).

[limit of the bin of the histogram at max(Δθ) = 20°], 100% of the conformational pairs are related only by conformational adjustment. For 25° < max(Δθ) < 45°, 92% of pairs are related by conformational adjustment only. On the other hand, for max(Δθ) > 95°, 99% of pairs of conformations correspond to different gas-energy minima, so there is clear conformational change. Only one pair of conformations related by adjustment was observed at max(Δθ) = 120°. For 45° < max(Δθ) < 95°, in approximately 50% of the cases, conformational variations correspond to conformational change, whereas in the other 50%, they are conformational adjustment. In summary, when comparing two different conformations (with flexible R-bonds only, no aliphatic rings or triple bonds), we can easily calculate the maximum torsion-angle deviation and state the following: • For max(Δθ) < 25°, they are related by conformational adjustment only. • For 25° ≤ max(Δθ) < 45°, they are related by conformational adjustment (92% chance). • For 45° ≤ max(Δθ) < 95°, it is not possible to make a prediction, and the R-bonds need to be analyzed individually. • For max(Δθ) ≥ 95°, they are related by conformational change (99% chance).

Figure 10. Gas-PES for propanol (B97-D/cc-pVTZ) and CSD distribution for an R-bond of the type C(sp3)CH2CH2O(sp3).

torsion-angle distributions from the CSD are generated within seconds using MOGUL.65 They both represent the same situation: maxima of the CSD lie at the minima of the gasPES.55 From the CSD distribution in Figure 10, two very valuable pieces of information about torsion variability can be extracted: (i) In 94% of the instances, this R-bond adjusts to a maximum of 40° around the gas-phase energy minimum geometry.66 (ii) A change of Δθ ≈ 120° clearly indicates a change of conformational energy minimum and, thus, a conformational change. Thus, if two polymorphs of a molecule contain an R-bond of the type CCCO and this R-bond changes between conformations by ∼120°, one can unambiguously say that these two conformations correspond to two different gas-phase conformers and, hence, they are conformational polymorphs. Is it possible to define particular torsion-angle variations that would be indicative of conformational change or simply adjustment for an R-bond of any nature? To answer this

5.3. rmsd[r]-crystal versus max(Δθ)

We have established practical cutoffs for determining whether two conformations are related by conformational change when comparing deviations of their atomic positions (rmsd[r]-crystal) or R-bonds [max(Δθ)]. To find the relationships between these two measures, max(Δθ) was plotted against rmsd[r]crystal in Figure 12 (for pairs of polymorphic molecules with at 2177


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of data points. A more illustrative representation of the data is given in Figure 14. Average max(Δθ) values (represented as

Figure 12. Scatterplot of max(Δθ) versus rmsd[r]-crystal for a subset of conformation comparisons (2373 comparisons of polymorphic molecules having at least one R-bond).

Figure 14. Average values of max(Δθ) (circles) and standard deviations (error bars) calculated for every 0.1-Å rmsd[r]-crystal value.

least one R-bond, 2373 data points). We also plotted the rmsd[r]-crystal cutoff of 0.375 Å for change and the max(Δθ) cutoffs for adjustment (45°) and change (95°) as orange lines. Areas 1 and 3 in Figure 12 correspond to those for which both the rmsd[r]-crystal and max(Δθ) cutoffs agree, whereas areas 2 and 4 represent those for which there is a lack of agreement in the classification between the two cutoffs. Area 1 corresponds to pairs of conformations that undergo only adjustments to different polymorphic crystal structures, whereas area 3 corresponds to pairs of conformations that change. Ninetytwo percent of the data lie in areas 1 and 3 for which both the rmsd[r]-crystal and max(Δθ) predictions are in agreement. There are 167 observations in area 4 (7%) and only 10 in area 2 (0.4%). Observations in area 4 are due to two factors: (i) dubious cases of change/adjustment that would need further evaluation with an energy model and (ii) pairs of conformations for which the main conformational changes are due not to the rotation of the acyclic R-bonds but to other sources of molecular flexibility. For example, conformational changes involving aliphatic rings (Figure 13, top) or groups

circles) and their standard deviations (error bars) were calculated for data binned in 0.1 Å rmsd[r]-crystal intervals and are plotted in Figure 14. rmsd[r]-crystal is linearly correlated with max(Δθ) only below the rmsd[r]-crystal cutoff of 0.375 Å, when the variation between conformations is due to conformational adjustment only. Above the cutoff, the calculated averages have little meaning because of the very large standard deviations. We noticed that the maximum standard deviation below the cutoff is 13° or 26°, representing the entire span around the average value. This 26° value corresponds to the max(Δθ) = 25° derived in the previous section, which is the max(Δθ) value for which one can be 100% confident that conformations only adjust. The lack of correlation between max(Δθ) and rmsd[r]-crystal beyond 0.375 Å can be attributed to three causes. First, the existence of other sources of flexibility not measurable with max(Δθ) (as noted earlier, see Figure 13). Second, changes in R-bonds by the same Δθ at different positions in the molecule might result in very different rmsd[r]-crystal values depending on the shape of the molecule and the location of the R-bond. Third, for any given value of max(Δθ), the conformation of a flexible molecule can result from a change in one R-bond only or in several rotations at the same time, which would potentially result in a much larger rmsd[r]-crystal value. This is exemplified in Figure 15 for two pairs of conformations. On

Figure 13. Two examples of pair of conformations with rmsd[r]-crystal > 0.375 Å and max(Δθ) < 45°.

around triple bonds (Figure 13, bottom). Hence, provided that all sources of molecular flexibility arise from acyclic classic Rbonds, the derived rmsd[r]-crystal and max(Δθ) cutoffs should be, in ∼95% of cases, in good agreement. It is possible to discern some degree of correlation between rmsd[r]-crystal and max(Δθ) only in area 1, below the rmsd[r]crystal cutoff (0.375 Å). Upon crossing that threshold, any semblance of correlation is lost, with almost random scattering

Figure 15. Examples of two pairs of conformations having the same max(Δθ) value but very different rmsd[r]-crystal values. 2178


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certainty. Values in the middle (0.25−1 Å) change in certainty as in Figure 8. Thus, a pair of polymorphs with rmsd[r]-crystal = 0.4 Å would be classified as conformational polymorphs with only 54% certainty, whereas for rmsd[r]-crystal = 0.75 Å, the certainty is 70%. In cases of less certainty, further energy calculations are recommended.

one hand, in TOHVAO (we use refcodes here to refer to the molecules in question), changes about only one R-bond in a terminal position in the molecule result in a small rmsd[r]crystal value. On the other hand, in TUMDIP, changes about three R-bonds in the molecule (by more than 95°, plus another three between 45° and 95°) result in a much larger rmsd[r]crystal value. This pair of examples clearly demonstrates how max(Δθ) and rmsd[r]-crystal can be correlated only when there is conformational adjustment but can never be correlated when there is conformational change.

6. ENERGETIC COST OF CONFORMATIONAL VARIATIONS Having determined the algorithm for dealing with the geometric aspects of defining conformational polymorphism, we now turn to the energetics of the phenomenon. Histograms of change and adjustment energies (Figure 17) were generated

5.4. Are My Polymorphs Conformational?

For an absolute identification of conformational polymorphism, energy calculations are recommended because energy is indeed part of the definition. However, as derived from the analyses above, certain (more accessible) structural parameters can also be used to identify the phenomenon with relatively high confidence. We propose a decision tree for the crystallographer (or crystal engineer) to identify the conformational relationship between two polymorphs A and B (Figure 16) when the use of

Figure 17. Histograms of conformational adjustment (orange, N = 904) and conformational change (blue, N = 311) energies (1 kJ/mol per bin). Dashed lines illustrate the cumulative percentages of the distributions.

from the data obtained in the DFT-d optimization procedure for the 452 pairs of conformations (sections 5 and 2). This resulted in a total of 904 values of ΔEgas−crys (adjustment energies) and 311 values of ΔEgas−gas (conformational change energies) arising from those pairs of the data set that involved conformational change. The two histograms have very similar shapes, both with a maximum at ΔE = 1 kJ/mol, but they illustrate the energetics of two different phenomena. The histogram for conformational adjustment in Figure 17 (orange line) quantifies the conformational energy penalty involved in placing an equilibrium gas-phase conformer into a crystal. Almost 50% of the crystal conformations in our data set differ in energy from their gas-phase conformers by less than 2.5 kJ/mol (∼RT at room temperature), ∼70% by less than 4.5 kJ/mol, and ∼90% by less than 10.5 kJ/mol (Figure 17, orange line). This illustrates that, indeed, conformations in crystals remain very close in energy to their gas-phase conformers. Adjustment energies of this scale can easily be compensated by improvements of the intermolecular interactions. The remaining ∼10% of the conformations (98 cases) have higher ΔEgas−crys energies (from ∼10.5 to 57 kJ/mol). These higherenergy adjusted conformations mostly correspond to sugars, which contain several OH groups. Sugars often have one or several intramolecular hydrogen bonds in the gas-phase conformer, whereas in the crystal, these OH groups undergo small rotations to satisfy the formation of other intermolecular hydrogen bonds. Small deviations of these OH or NH2 terminal groups come at a high energetic cost (because the intramolecular hydrogen bond deviates from an optimal

Figure 16. Decision tree to identify the conformational relationship between polymorphs A and B with structural data only.

energy calculations is not possible. If conformations A and B have one or more torsion angles with Δθ > 95°, they are conformational polymorphs. If this is not the case, one can examine CSD distributions of all possible R-bonds, flexible rings of the molecule, and conformations around triple bonds. If there is at least one conformational feature in clearly distinct areas of the distributions for conformations in A and B, then they are conformational polymorphs (see Figure 10 for an example). If not, one can compare conformations using Mercury and calculate an rmsd[r]-crystal value. If rmsd[r]crystal(AB) > 0.375 Å, then they are conformational polymorphs. Whereas the use of the max(Δθ) cutoff of 95° and the indications of the CSD distributions will provide an answer of high certainty, the use of the rmsd[r]-crystal cutoff will vary in accuracy depending on its value. The accuracy of the rmsd[r]crystal prediction can be correlated with the graph in Figure 8. Very high (>1 Å) and very low ( 95°). The remaining 5% represent a mixture of both change and adjustment. The magnified distribution in the range of changes in Figure 24 exhibits two maxima at ∼110° and ∼170°. The maximum at ∼170° illustrates conformational changes for, for example, many planar substituents of a benzene ring (a carboxylic acid, or amide group) that have two (probably isoenergetic) minima in the gas-PES at θ ≈ 0° and 180°, and so, Δθ ≈ 180°. Substituents on C(sp3)−C(sp3) type R-bonds, on the other hand, have two minima in the gas-PES at θ = 60° and 180° and, hence, maxima at Δθ ≈ 110°. The widths of the bands at Δθ ≈ 110° and Δθ ≈ 170° illustrate the fact that conformational change is also accompanied by some adjustment. Only ∼11% of R-bonds actually change conformation. Yet, are all R-bonds equally prone to change and adjust? To understand how R-bonds of different chemical natures have different propensities for change or adjustment, we classified Rbonds according to the nature and hybridization of the atoms involved in them. We found a total of 479 unique natures of Rbonds. As a measure of their propensity to “change”, we calculated how often an R-bond of that nature changed (approximated as Δθ > 70°) as a percentage of the total observations. As a measure of their propensity to “adjust”, we calculated their average torsion-angle adjustment value (Δθ). A summary of the R-bond nature, number of comparisons recorded in the polymorphic data set (Ntor), and propensity to change and adjust is given in Table 2 for R-bonds with at least 94 data points. The information in Table 2 clearly indicates how the propensity to change and adjust varies for Rbonds of different chemical natures. For example, a pure alkane chain C3C3C3C3 (R-bond 13, superscripts indicate the hybridization of the C atom) changes conformation in only 6% of cases, adjusting, on average, by 3.1°, whereas an R-bond of nature OC3C3O changes conformation in 22% of cases, adjusting, on average, by 7.1°. The R-bonds found to be most prone to change and adjust are summarized in Figure 25. It is not surprising that the Rbonds most prone to change (e.g., C3C3NamCam) are present in the molecules showing the largest number of conformational polymorphs in the CSD (e.g., chlorpropamide and tolbutamine, Figure 22). Similarly, the R-bonds found to be most prone to adjust are found in molecules with rich polymorphic behavior, such as the fenamic acid derivatives or the sulfonamide drugs.

Figure 23. Frequencies of polymorphism (orange bars) and conformational polymorphism (blue bars) as functions of the polymorphic molecule’s degrees of flexibility.

tional flexibility is obviously a necessary condition for conformational polymorphism, it is not a sufficient condition. 7.3. Torsion-Angle Change, R-Bond Nature, and Conformational Polymorphism

To this point, we have considered the overall conformation of a molecule based on the ensemble of conformational parameters. We now pose the question of whether the chemical nature of individual R-bonds plays a role in the tendency to result in conformational polymorphism. Thirty-six percent of the polymorphic molecules in the CSD exhibit conformational polymorphism, but how often does an individual R-bond actually change conformation? We extracted a total of 9323 individual torsion-angle comparisons (Ntor) from the 3166 TORMAT comparisons among conformations across polymorphs. Data on the comparison of torsion angles were analyzed, binned in intervals of 10°, and a histogram of Δθ (θA − θB) was produced (Figure 24). Figure 24 illustrates the torsion-angle variability within our polymorphic set of molecules containing R-bonds (1045 polymorphic molecules of the 1297 contain at least one Rbond). The maximum of the Δθ histogram lies at Δθ = 0°,

8. NOTORIOUS CASES OF CONFORMATIONAL POLYMORPHISM 8.1. Molecular Shape and Conformational Polymorphism

Although some conformational polymorphs do not necessarily undergo significant changes in their overall molecular shape, there are several examples of striking shape changes in conformational polymorphs in the CSD. The largest polymorphic molecules in the CSD (161−177 atoms and 52−57 Rbonds) consist of triglycerides (YIXTAB, QESJII, YIXTEF, QESJOO).118,119 A triglyceride is an ester derived from a molecule of glycerol and three fatty acids. Three of them have conformational polymorphs (YIXTAB, YIXTEF, QESJOO) exhibiting the largest rmsd[r]-crystal differences between any

Figure 24. Histogram of torsion-angle variability for a total of N = 9323 comparisons of torsion angles among polymorphs. 2183


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Table 2. Nature of R-Bonds, Number of Comparisons Recorded in the Polymorphic Data Set (Ntor), and Their Propensity to Change and Adjusta no.

torsion nature

Ntor

change in Ntor (%)

average ΔθAdjust (deg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

C3C3NamCam OC3C3O CarCarOCar CarCarNamCam CarCarOC3 C2OC3C3 C2C3C3C3 CarCarC3O CarCarC3C3 CarCarC2O CarCarC2C2 CarCarC2O C3C3C3C3 CarCarNpl3Car CarCarSO2 CarCarN3C3 CarCar C2N2 CarCarN3O C3NamCamO CarNamCamO CarCarCarCar C3OCO

94 171 125 133 329 214 105 116 133 177 222 348 882 97 154 132 222 472 157 156 201 354

27 22 21 21 20 16 13 12 12 10 9 7 6 6 4 4 4 3 2 1 1 1

12.0 7.1 20.2 13.3 8.8 16.0 7.1 16.9 8.9 11 8.8 9.8 3.1 18.5 17.3 9.7 9.9 10.3 5.1 4.8 13.3 6.9

Figure 26. Bent and linear conformations of two saturated triglycerides as in YIXTAB and YIXTEF.

a

Superscripts represent hybridization (i.e., C3 = C sp3, C2 = C sp2) or chemical nature (Car = aromatic carbon, Cam = amidic carbon) for carbon atoms and number of bonded atoms for nitrogen atoms (i.e., N3 = N bonded to 3 atoms; N2 = N bonded to 2 atoms). Figure 27. Conformations of (top) bis(4-bromobenzensulfonyl)amine as in polymorphs YABKUI and YABKUI01 and (bottom) an oligothiophene derivative as in polymorphs KISQEJ and KISQEJ01.

formations is also observed for three oligothiophene derivatives (KISQEJ/01 and KISQUZ/01), one of which is illustrated in Figure 27.121 8.2. Synthetic Memory and Conformational Polymorphism

Conformational polymorphs of molecules with restricted flexibility can carry “synthetic memory”. For example, the bisurea macrocycle shown in Figure 28 was synthesized using two different methods. When the synthetic route utilized reactants Figure 25. R-bonds found most prone to change (left) and adjustment (right) in the polymorphic data set.

pair of polymorphs in the CSD of 10.80, 10.91, and 12.2 Å, respectively. The saturated glycerides in particular (YIXTAB and YIXTEF) show two polymorphs with two very distinct conformations: a bent V-shaped conformation and a linear conformation (Figure 26). Probably the smallest polymorphic molecule (30 atoms) exhibiting the largest relative change in molecular shape (with rmsd[r]-crystal = 3.25 Å) is bis(4-bromobenzensulfonyl)amine (YABKUI).120 One R-bond changes by almost 180° from a folded to an unfolded type of conformation (Figure 27). Although the hydrogen bonding of the two conformations remains very similar, the way the aromatic rings interact with neighboring molecules differs considerably between the two polymorphs. A very similar folded/unfolded pair of con-

Figure 28. Synthetic methods used for the preparation of the bis-urea macrocycle and schematic representations of their conformations as found in the two conformational polymorphs ZILQOA and ZILQOA01. 2184


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free to change conformation (Figure 28, top), the stable anti conformer (ZILQOA)122 was obtained and crystallized. When a rigid reactant in a syn conformation was employed in the synthesis, the macrocycle was first made and crystallized in the metastable syn conformer (ZILQOA01).123 Although the energy difference between these anti and syn conformers is 9 kJ/mol according to our B97d calculations, the energy of interconversion between them was calculated elsewhere to be over 120 kJ/mol (with semiempirical methods).123 A similar phenomenon occurs for the hexabenzocoronene molecule in APUDEV that crystallizes with a contorted highenergy conformer upon direct crystallization from synthesis (Figure 29).124 Even though classic measures of molecular

Figure 30. Conformations of 1,3-bis(m-nitrophenyl)urea as found in the alpha (SILTOW),127 beta (SILTOW01),128 and delta (SILTOW11)126 polymorphs.

Figure 29. (Left) High-energy and (right) low-energy conformations adopted by a fluorinated benzocoronene molecule with refcode APUDEV.

flexibilities would classify this molecule as rigid, the high-energy contorted conformer is first observed because of the cyclization route and is kinetically arrested. Upon heating above 100 °C, the metastable form containing the strained conformer (with a relative conformational energy of 42 kJ/mol) transforms into the stable conformer and crystallizes into a different conformational polymorph.

Figure 31. Four different conformations found in the four known conformational polymorphs of the hexa-host molecule hexakis(4cyanophenyloxy)benzene.

8.4. Pressure-Induced Conformational Polymorphism

The use of high pressure for the compression of already known forms or high-pressure crystallization techniques has recently been found to provide a new way of obtaining new polymorphs, including conformational polymorphs.130 Perhaps the most illustrative case of the appearance of a conformational polymorph under high-pressure crystallization conditions is that of piracetam, a drug used for the treatment of disorders of the nervous system. Three polymorphs of piracetam have been known since the early 1980s (forms I−III,131,132 BISMEV/02/ 03). The three polymorphs contain the same local gas-phase conformer (ΔEgas−gas = 12.3 kJ/mol, b97d/cc-pVTZ) with small adjustments to the different polymorphs. The crystallization of piracetam at high pressure resulted in the appearance of two new polymorphs (BISMEV04/07),133,134 one of which, form IV, corresponds to a conformational polymorph (BISMEV04, Figure 32) that contains a substantially adjusted conformation of the global minimum-energy conformer (Figure 32, left). Although this conformation corresponds to the global minimum-energy gas-phase conformer, it has an adjustment energy of 11 kJ/mol, whereas forms I−III and V contain slightly adjusted conformations (maximum adjustment energy of 2 kJ/mol) of the local gas-phase energy minimum. Conformational polymorphism induced by pressure has been observed for various materials including pharmaceuticals

8.3. Concomitant Conformational Polymorphism

There are many examples in our data set and in the literature in which clearly different conformational polymorphs crystallize concomitantly.125 In fact, Groth’s original concomitant polymorphs happened to be a pair of conformational polymorphs (and a hydrate structure) of the molecule 1,3bis(m-nitrophenyl)urea (SILTOW).126 A more recently discovered polymorph also crystallizes concomitantly with the other two under different experimental conditions. The lattice energies of these three conformational polymorphs have been calculated to lie within 1 kJ/mol of each other.126 Their conformations (Figure 30) are known to differ in energy by less than 6 kJ/mol, with energy barriers between them of less than 10 kJ/mol [SCF/6-31G(d,p)].126 Another example of concomitant conformational polymorphism is that of the molecule hexakis(4-cyanophenyloxy)benzene (POPGUX),129 which crystallizes from solution as a solvate. Crystallization of this hexa-host from the melt, however, yields four unsolvated conformational polymorphs: Forms I and II crystallize concomitantly from a slow cooling of the melt, forms I and III crystallize concomitantly upon rapid cooling, whereas form IV crystallizes by applying stress to the molten amorphous phase (Figure 31). 2185


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Drug molecules in the CSD with at least three different conformers in multiple polymorphs include chlorpropamide,108−112 aripiprazole,141 axitinib,96 furosemide,142 N-(4′methoxyphenyl)-3-bromothiobenzamide,143 diflorasone diacetate,144 acitretin,145 and tolbutamide.113−116 The conformational polymorphism of the HIV drug ritonavir146−148 has attracted particular attention because of the spontaneous appearance of the stable polymorph, which compromised the drug bioavailability, approximately 2 years after the drug had been launched. The polymorphic appearance resulted in the drug being removed from the market in 1998 for a year for reformulation to overcome the seriously lower bioavailability of the new, more stable form. A similar example, also involving a conformational polymorph, was reported more recently for the Parkinson’s disease drug rotigotine.149

Figure 32. (Top) Gas-phase conformers and (bottom) crystal conformations as found in the five polymorphs of piracetam (BISMEV, orange; BISMEV02, black; BISMEV03, green; BISMEV04, pink; BISMEV07, red).

9. CONSEQUENCES OF CONFORMATIONAL CHANGE The first important consequence of conformational change in polymorphism is that conformational polymorphs are more likely to differ in their properties than polymorphs. Why? Many physicochemical properties of compounds (e.g., dipole moment, molecular shape, color) are conformation-dependent. In the case of conformational adjustment, a single gas-phase conformer adapts to different polymorphs. The adjusted conformations in the different polymorphs are structurally and energetically very close to the same gas-phase conformer. Consequently, the physicochemical properties of such adjusted conformations are also close to those of that unique gas-phase conformer. Compounds crystallizing with the same conformer in different polymorphs have the same molecular properties (slightly adjusted) but different solid-state properties. In the case of conformational change, however, different gas-phase conformers adapt to different polymorphs. Although the changed conformations might have similar energetics, they can display significant structural changes. Hence, the physicochemical properties of such changed conformations can vary significantly. As a consequence, compounds crystallizing with different conformers in different polymorphs can exhibit both different molecular properties and different solid-state properties. This statement can be exemplified with ROY. The polymorphs of ROY adopting conformations close to the local minimum-energy gas-phase conformer display modulated shades of red and orange (Figure 4, red circles), whereas those adopting conformations close to the global minimum-energy gas-phase conformer display shades of yellow (Figure 4, yellow circles).64 The colors of these polymorphs are strongly dependent on their conformations. Another striking example of property change in conformational polymorphs is that of ritonavir. The solubility of form II is one-fourth that of form I.146 The exceptional conformational change exhibited by ritonavir in forms I and II might be an added factor influencing the dramatic change in solubility. Having computed dipole moments for our set of optimized pairs of conformations in polymorphs (452 pairs, section 5), we proceeded to quantify the extent of molecular dipole moment changes in polymorphs and conformational polymorphs. Eighty-seven percent of crystal conformations related by adjustment differ in dipole moment by less than 0.5 D, and 97% differ by less than 1.5 D (Figure 34). The subset of crystal conformations related by conformational change, however, behaves very differently. Only 44% of crystal conformations related by conformational change differ in dipole moment by less than 0.5 D, and 67% differ by less than 1.5 D. Therefore,

(BISMEV),133,134 energetic materials (PUBMUU),135 and amino acids (LCYSTN).136 8.5. What Difference Can Length Make?

Quinacridones are materials widely used as pigments because of their color and luminescent properties. We noted two families of polymorphs for the dibutyl- (WAMFAS)137 and dicetyl(NULTIY)138 substituted quinacridones. These two compounds share the core quinacridone structure (responsible for the luminescent properties) but have alkane chain substituents of different lengths (4 carbon atoms for the butyl-substituted and 16 carbon atoms for the cetyl-substituted). To our surprise, the compound with the shortest alkane chain exhibits four polymorphs containing three different conformers (WAMFAS01/02/03/04), whereas that with the longest alkane chain exhibits two polymorphs with identical conformations (Figure 33).

Figure 33. (Top) n-Dibutyl-substituted quinacridone in four polymorphs and displaying three different conformers (WAMFAS01/02/03/04) and (bottom) n-dicetyl-substituted quinacridone in two polymorphs and displaying one unique conformer (NULTIY/ NULTIY01).

8.6. Pharmaceuticals and Conformational Polymorphism

Conformational polymorphism has often been observed in pharmaceuticals.139 In fact, many of the molecules exhibiting the richest polymorphic behavior in the CSD are bioactive. This is perhaps a consequence of the facts that drug molecules often have many degrees of flexibility (5.6 rotatable bonds, on average)140 and their polymorphic behavior is often studied extensively. 2186


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temperatures, two main conformers of ritonavir exist in solution, but “the interconversion between them requires significant energy and would not be expected to occur spontaneously”.146 This observation correlates well with the fact that form II is apparently reluctant to nucleate, perhaps because of the difficulty of accessing the conformation exhibited in this form, unless certain impurities or seeds are present in solution. As a final note, and following on the second consequence, although it is known that flexible molecules have a reduced tendency to crystallize,150 there is still a “lack of understanding of the role of conformation in determining the outcome of crystallizations”.151 Despite recent advances, predicting and controlling152 the conditions of crystallization of conformational polymorphs still remains a largely unattainable goal. To our knowledge, there has only been one study in which a metastable conformational polymorph has been crystallized by carefully designing an inhibitor that mimicked the conformation found in the stable polymorph.153 As part of a grand strategy to make progress in this field, knowledge of conformations in solution and crystallization must clearly be further developed to understand the mechanisms of nucleation and growth of conformational polymorphs at the molecular level.154

Figure 34. Histogram of changes in molecular dipole moment for crystal conformations related by adjustment (orange, N = 141) and change (blue, N = 311).

33% of crystal conformations related by change exhibit a significant change in polarity (>1.5 D) as a result of the conformational change. Significant changes in molecular polarity are very likely to influence various properties of the resulting conformational polymorphs. The second important consequence of conformational change in polymorphism relates to the “accessibility” of the different conformers. Crystal conformations related by conformational adjustment are located in the same potential energy well. They are derived from the same gas-phase conformer. Crystal conformations related by conformational change, however, are located in different energy wells of the molecular conformational potential energy surface. Hence, in principle, the transition from one conformational polymorph to another involves the crossing of a conformational energy barrier, whereas no conformational energy barrier exists between conformations related by adjustment. In practice, these molecules are embedded in a crystal environment so that a change in molecular conformation accompanying a polymorphic phase transition within the crystal might be prevented by the ensemble of steric factors due to neighboring molecules. However, when the crystal is dissolved, the steric factors due to the crystal structures disappear, but the energy barrier for conformational change remains. To go from one conformer to another conformer in solution, this energy barrier still needs to be crossed. This might have important consequences for the accessibility of the conformer and, hence, the ultimate accessibility of the conformational polymorph. Although low-energy barriers allow the existence of several low-energy conformers in solution, high-energy barriers can prevent that phenomenon and, hence, make it difficult to observe polymorphs with conformers that are harder to access. This was illustrated in some examples in section 8. Whereas there are molecules whose various conformers are easily accessible in solution and crystallize concomitantly because of the low conformational energy barriers (section 8.3),126 molecules whose conformers are related by very highenergy barriers would never convert unless a different synthetic route were followed123 or the systems were heated to very high temperatures (section 8.2). An intermediate example is perhaps that of ritonavir. According to NMR experiments at different

10. CONCLUSIONS AND OUTLOOK In this review, we have provided an unambiguous definition of conformational change and conformational polymorphism, as well as a quantitative basis for the likelihood of its appearance. The key findings on the connections between conformations and polymorphs are summarized as follows: (a) Conformational adjustment and conformational change are different phenomena (section 4). (b) Two polymorphs are conformational polymorphs only if their conformations are related by conformational change (section 4). (c) Conformational change requires a change of gas-phase conformer and, hence, crossing of an energy barrier (section 4). (d) Identification of conformational change requires energy calculations (section 4). (e) As an approximation, structural rules (derived in this review) can also be used to identify conformational change and, hence, conformational polymorphism (section 5). (f) Energy differences associated with conformational variations of small organic molecules in different polymorphs are usually small (section 6). (g) Higher-energy conformations in crystals are rare but possible for (i) molecules that are able to break an intramolecular interaction in favor of a strong intermolecular interaction and (ii) molecules that crystallize in special symmetry positions (section 6). (h) Thirty-six percent of polymorphic molecules in the CSD exhibit conformational polymorphism (section 7). (i) Chlorpropamide has the largest number of conformational polymorphs in the CSD (section 7). (j) R-bonds of different natures have different propensities to change and adjust (section 7). (k) Propensities to change and adjust for R-bonds of different natures were presented (section 7). 2187


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(l) Polymorphic molecules containing R-bonds that are prone to change are more likely to exhibit conformational polymorphism (section 7). (m) Polymorphic molecules containing R-bonds that are prone to both change and adjust are likely to display a rich polymorphic landscape (e.g., chlorpropamide). (n) A number of outstanding representative cases of conformational polymorphs were presented and discussed (section 8). (o) Identification of conformational polymorphism is very important for two main reasons: (i) conformational polymorphs might differ in properties more significantly

Aurora J. Cruz-Cabeza (left) earned a Masters Degree (2004) in Heterogeneous Catalysis from the University of Córdoba, Spain, and a Ph.D. (2008) in Physical Chemistry from the University of Cambridge, U.K. There, she worked with Prof. William Jones, Dr. Graeme Day, and Dr. Sam Motherwell. Her Ph.D. thesis was awarded the PANalytical thesis prize in physical crystallography. She then worked as a senior research scientist at the materials science department at Pfizer Global Research, Sandwich, U.K. There, she developed and applied computational techniques to assess polymorphism and design cocrystals of pharmaceutical materials. In 2009, she joined the Cambridge Crystallographic Data Centre as a research fellow of the Pfizer Institute for Pharmaceutical Materials Sciences. During this period, she used computational techniques in conjunction with crystal structure database analysis to understand various aspects of crystal and molecular structure. Cruz-Cabeza currently holds an NWO VENI fellowship at the University of Amsterdam, where she studies static and dynamic phenomena in organic crystals. Her current research focuses on polymorphism, conformational polymorphism, tautomerism in molecular crystals, formation of multicomponent crystals, and simulation of disorder in crystalline lattices. She has authored over 30 research articles and a book chapter and regularly contributes to Crystal Structure Prediction Blind Tests.

than polymorphs and (ii) some conformational polymorphs might be harder to crystallize because their conformers are less accessible experimentally (section 9). The phenomena of polymorphism and conformational polymorphism still remain largely unpredictable.155 In this review, we have attempted to provide more precise and quantitative definitions and concepts, and we have compiled data on conformational polymorphism from the CSD and the literature. The knowledge derived and summarized here refers to polymorphic molecules only. For example, statement h above states that, if a molecule is polymorphic and contains Rbonds that are prone to change, then it is more likely to exhibit conformational polymorphism; the molecule, however, has to be polymorphic first. The present data provide no information or guidelines regarding the tendency of molecules to be polymorphic; if they are polymorphic, but only if they are polymorphic first, then the observations above on conforma-

Joel Bernstein (right) was born in Cleveland, OH, in 1941. After obtaining a B.A. degree at Cornell University, he earned a Ph.D. degree in physical chemistry at Yale University for research on the solid-state spectroscopy of organic compounds. Following two-year postdoctoral stints in X-ray crystallography with Ken Trueblood at UCLA and in organic solid-state chemistry with Gerhardt Schmidt at the Weizmann Institute of Science in Rehovoth, Israel, he joined the faculty of the newly established Ben-Gurion University of the Negev, where he was the incumbent of the Carol and Barry Kaye Professorship of Applied Science in the Department of Chemistry until January 2010 and is now Professor Emeritus. As of May 2010, Bernstein is also affiliated with the newly founded New York University Abu Dhabi as Global Distinguished Professor. His research interests center on the organic solid state, with particular emphasis on understanding and utilizing polymorphism, structure−property relationships, hydrogen-bonding patterns and graph sets, and organic conducting materials. He has published over 180 research and review articles and book chapters on these subjects and is the sole author of a book entitled Polymorphism in Molecular Crystals, published by Oxford University Press and translated into Russian. In 1999, he was elected a Fellow of the American Association for the Advancement of Science and has served as a consultant to a many multinational pharmaceutical

tional polymorphism apply. We deal with the issue of the tendency of molecules toward polymorphism in a separate work.156 Finally, the information compiled here coupled with knowledge-based predictions of polymorphism157,158 could produce a very valuable polymorph risk-assessment tool. Because of the potentially more important property changes displayed by conformational polymorphs, anticipating a more stable conformational polymorph to appear would be of extreme value to many industries.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 2188


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companies and as a testifying witness in patent litigations on the solidstate chemistry of drugs. His career has been punctuated by visiting professorships at the University of Illinois, Cornell University, the University of Minnesota, the University of Barcelona, and the University of Bologna; a visiting scientist position at the Cambridge Crystallographic Data Centre; and two years (2010-2011) as Professor-at-Large at the University of Western Australia, Perth.

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Conformational Polymorphism - Chemical Reviews (ACS Publications)

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