Ideal Molecular Conformation versus Crystal Site Symmetry - Crystal

Article pubs.acs.org/crystal

Ideal Molecular Conformation versus Crystal Site Symmetry Robert A. Pascal,, Jr.,*,†,‡ Christal M. Wang,‡,∥ Grace C. Wang,‡ and Lynn Vogel Koplitz§ †

Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States § Department of Chemistry, Loyola University, New Orleans, Louisiana 70118, United States ‡

S Supporting Information *

ABSTRACT: The X-ray structures of hydrocarbons that crystallize on special positions, and thus possess one or more crystallographic symmetry elements, were compared to DFT-calculated structures of the same hydrocarbons in the gas phase. Of the roughly 400 structures examined, at least 9% crystallize with a site symmetry that is not a subgroup of the symmetry of the ideal, lowest-energy, gas-phase structure. Thus, the crystal conformations of these molecules are very different from their ground-state conformations in the absence of packing forces, not merely modest distortions of their ideal structures. Most of the anomalous structures in our sample are higher-energy, inversion-symmetric conformations of molecules that possess chiral or polar ground-state conformations, suggesting that the well-known propensity of crystals to form with centers of inversion frequently leads molecules to adopt anomalous conformations in the solid state.

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INTRODUCTION X-ray diffraction is the most reliable experimental method for the determination of organic molecular structures, and diffraction data generally take precedence over spectroscopic data when assigning the three-dimensional structures of molecules. However, in a recent review1 of the structures of polycyclic aromatic compounds with significantly twisted conformations, we cited several examples of compounds with chiral, twisted ground-state conformations (having C2 or D2 symmetry) that had crystallized in achiral conformations (Ci, Cs, or C2h symmetry) of significantly higher energy (2−4 kcal/ mol, as judged by B3LYP/6-31G(d) calculations). In all but one case, these anomalous molecules occupy special positions in the crystal lattice and thus possess crystallographic inversion or mirror symmetry. Interestingly, for most of the molecules, there also exist closely related compounds, differing by some trivial substitution, that do crystallize in the expected chiral ground-state conformations.1 A representative example is compound 1 (Figure 1). In the crystal, this molecule resides on a special position with Cs symmetry, even though its ground state is calculated to have a C2-symmetric, twisted conformation.2 However, its simple methyl derivative 2 crystallizes with the expected twist.2 The crystal conformations of 1 and 2 are dramatically different, and examples of this sort raise two important questions concerning the solid-state structures of molecular crystals: (1) to what extent is the ideal conformation of a molecule reflected in its crystal conformation or crystallographic site symmetry, and (2) how frequently do molecules crystallize in anomalous conformations that are substantially different in geometry and/or energy from their “ideal” conformations (i.e., their ground-state conformations in the © 2012 American Chemical Society

Figure 1. Molecular structures of compounds 1 (above right) and 2 (below right). Hydrogen atoms have been omitted for clarity.

gas phase)? The case of the twisted acenes cited above suggests a surprisingly high rate for the latter: of the 95 X-ray structures cited in the review, six were anomalous (the review is comprehensive for molecules containing acene substructures with a twist of at least 30°).1 Is this class of compounds a special case, or is the phenomenon widespread? The relationship of molecular shape and crystal packing is hardly a new concern, dating at least to the work of Kitaigorodskii3 and extending to the present.4,5 With regard to the two specific questions posed above, the first has been answered to a very large degree by the remarkable work of Motherwell and co-workers.6 In this study, they were able to implement a “molecular-symmetry perception algorithm”,7 which allowed them to compare the exact or approximate Received: March 20, 2012 Revised: July 10, 2012 Published: July 11, 2012 4367

dx.doi.org/10.1021/cg300374w | Cryst. Growth Des. 2012, 12, 4367−4376

Crystal Growth & Design

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Before proceeding further, it is also important to define what is meant in this work by “distinct conformations”. For our purposes, all structures that reside anywhere within a single potential well are said to have the same conformation; we are not interested in small distortions from an ideal geometry. Thus, if two structures evolve to the same structure upon geometry optimization by some computational method, and the resulting structure represents a true potential minimum (a stationary point in a calculation that possesses no imaginary frequencies), then we consider those two structures to have the same conformation at this level of theory; if not, then they have distinct conformations. In addition, transition state structures (stationary points in a calculation that exhibit one imaginary frequency) are also considered to be distinct from the structures residing in adjacent potential wells. The Choice of Crystal Structures for Examination and the Assignment of Ideal Symmetries of the Molecular Structures. The version of the CSD employed for this study contains in excess of 400 000 entries,9 far too large a number for individual examination of each, but what would be an appropriate and manageable subset? We were drawn to this topic by the observation of ideally chiral molecules that had nonetheless crystallized on special positions with inversion or mirror symmetry; thus, anomalous structures might best be sought on such positions. Given that roughly one-half of all organic compounds crystallize in the space groups P1̅ (No. 2) and P21/c (No. 14),10 in which centers of inversion are the only special positions, we initially chose to examine hydrocarbons that had crystallized on inversion centers in these two space groups, at once limiting the intermolecular interactions in the crystals to van der Waals forces and reducing the total number of target structures to a few hundred. The specific search employed the following criteria: (1) The asymmetric unit contained only a single type of molecule; thus, all structures containing solvent of crystallization, ionic compounds, charge-transfer complexes, and host−guest complexes were excluded. (2) The molecule contained only carbon and hydrogen, with no more than 80 carbon atoms. (3) The conventional R(F) for the refinement of these structure was ≤0.08. (4) The structure contained no obvious evidence of disorder. (5) Z′ = 0.5 (ensuring that the molecule lies on a center of inversion, but also excluding, unfortunately, structures containing two independent molecules, each of which lies on a center of inversion). This search yielded 270 structures (redeterminations of the same structure are not counted in the total). Each of the structures possesses crystallographic C i symmetry, and this often corresponds to the ideal symmetry of the molecule or, even more commonly, to a subgroup of the ideal symmetry.11 Our chief interest is in a third possibility, that the ideal symmetry of the molecule does not include a center of inversion. Accordingly, each molecule was examined, and its probable ideal symmetry was assigned (based purely on chemical experience and intuition). Where the ideal symmetry of a molecule was thought to be uncertain, a conformational search was conducted by using molecular mechanics calculations (MMFF12), and promising conformations were further evaluated with semiempirical molecular orbital calculations (AM113). On the basis of these calculations, 51 structures were judged to require evaluation at a higher level of theory.

symmetry of each molecule in a large subset of the Cambridge Structural Database8 (CSD) with its corresponding crystallographic site symmetry. This approach permitted, in their own words, “a large-scale survey of structural data for which the symmetry of the occupied Wyckoff position and the symmetry of the molecule are both known unambiguously.”6 Unfortunately, this study does not address, indeed, it systematically avoids, question (2) above, because the “symmetry of the molecule” to which they refer is the exact or approximate symmetry observed in a particular crystal, and has no necessary correspondence to the ideal symmetry of the molecule in the absence of packing forces. Thus, the method of Motherwell would find that the molecular symmetry of compound 1 is Cs, but there is really no doubt, based on computational studies1 and a comparison to the crystal structures of nine very similar compounds, all of which are twisted,2 that the ideal symmetry of 1 is C2, and that its crystal conformation is an anomaly. This Article directly addresses question (2). We examine two moderately sized subsets of the CSD8,9 and attempt to determine, first by simple inspection of each structure and then by computational evaluation of suspected anomalous structures, whether each molecule adopts (at least approximately) its ideal conformation or instead adopts a distinctly different, higher energy conformation. Our findings are that (1) the frequency of such anomalous structures is slightly greater than the ∼6% frequency (6/95) observed for twisted polycyclic aromatics, (2) most of the anomalous structures in our sample are higher-energy, inversion-symmetric conformations of molecules with chiral or polar ground-state conformations, and (3) most of the anomalous structures may be represented by D2h- or C2h-symmetric drawings on the printed page, but which in reality must adopt structures of lower symmetry due to steric conflicts or angle strain.

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RESULTS AND DISCUSSION General Considerations for the Comparison of Experimental Molecular Structures with “Ideal” Structures. Given that several hundred thousand reliable crystal structures are collected in the CSD, and that the speed of modern computers makes the calculation of the gas-phase structures of small molecules a relatively simple matter, it should be easy to gather the data necessary to address the questions of conformation posed in the introduction. The chief problem is that each structure must be individually examined and its ideal symmetry or conformation assigned. This is a timeconsuming venture even if only chemical intuition and experience are employed to make the assignment, but frequently some sort of conformational search is also required, with evaluations of the relative energies of the various conformations by some computational method. In cases where the ideal and crystal conformations are distinct, then higher-level calculations are necessary to confirm the difference between the two and to provide a more highly accurate assessment of their relative energy. At the end of this process, we may be confident that any anomalous structure, initially suspected due to chemical intuition and ultimately confirmed by good-quality calculations, really is anomalous. Of course, it is inevitable that some structures judged initially to be “obviously” ideal, and thus not subjected to a more rigorous conformational analysis, are in fact anomalous. Thus, our estimates of the number of anomalous structures in the survey must be lower limits. 4368



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Table 1. Solid-State Hydrocarbon Structures from the Space Groups P1̅ and P21/c with Distinct Site Symmetry and Ideal Symmetry

relative E of optimized crystal conformation with respect to ideal conformation (kcal/mol) cmpd

CSD refcode

space group

calcd ideal symm

crystal site symm

symm of optimized crystal conf

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

GEGQUF LENNEX BIPHEN03 MATPIG CEVXAD JAKROC FEWHIZ QUPHEN WUXDIC ZZZNTQ01 TBUBEN10 NEKDUD XERHIM DEPXIF CEPXAW COVKAZ EBIGEB01 TEPBUT01

P1̅ P1̅ P21/c P21/c P21/c P21/c P21/c P21/c P21/c P21/c P21/c P1̅ P1̅ P21/c P21/c P21/c P21/c P21/c

C2 D2 D2 C2 D2 C2 D2 D2 C2 D2 D2 C2 C2 D2 D2 D2 C2 C2

Ci Ci Ci Ci Ci Ci Ci Ci Ci Ci Ci Ci Ci Ci Ci Ci Ci Ci

Ci C2h D2h (TS)b,d C2h (TS)b,d C2h C2h (TS)b,d Ci C2h (TS)b,c,d Ci (TS)b,d C2h (TS)b,c,d C2h Ci (TS)b,d Ci (TS)b,d C2h C2h C2h Ci C2h (TS)b

a

+6.8 +2.5 +2.2 +2.2 +2.2 +2.0 +1.9 +1.8 +1.8 +1.8 +1.8 +1.7 +1.6 +1.3 +1.2 +1.3 +0.7 +0.7

(+6.8) (+2.8) (+2.2) (+2.2) (+1.6) (+1.8) (+1.6) (+1.8) (+1.8) (+1.8) (+1.1) (+2.0) (+1.7) (+1.1) (+1.2) (+0.7) (+0.7) (+0.3)

The B3PW91/6-31G(d) E + ZPE is given first, and the B3LYP/6-311G(d,p) E is in parentheses. bThere is no inversion-symmetric minimum at either level of theory; the optimized crystal conformation is a transition state. cThe crystal conformation has approximate D2h symmetry. dContains a central biaryl substructure. a

crystallization in anomalous conformations has long been recognized and analyzed.19 Interestingly, all of the biaryl crystal conformations are transition states, not potential minima. It is important to note, however, that we are comparing the calculated energies of geometry-optimized crystal conformations with the calculated energies of the ideal conformations. The actual crystal conformations, which must exhibit additional distortions due to packing forces, will always be of even higher energy (in the gas phase). The Supporting Information contains a full list of the structures examined, with the molecules’ ideal and site symmetries, and brief notes on the results of the B3PW91/6-31G(d) calculations. This first search dealt only with molecules with crystallographic inversion symmetry, but would a more wide-ranging search find anomalous structures on other types of special

The relevant conformations of these molecules were subjected to geometry optimization and analytical frequency calculations at the B3PW91/6-31G(d) level of theory.14−17 The relative energies, including zero-point energy corrections, were used to assign the ideal conformations of the molecules. At this level, 25 of the 51 molecules prefer centrosymmetric conformations (usually, but not always, similar to the crystal conformations), but 26 (9.6% of the 270 total structures) possess acentric ideal conformations. However, for many of the 51 molecules, the difference in energy between the centric and acentric structures (ΔE) is less than 1 kcal/mol. Table 1 lists and illustrates the 18 anomalous structures where this ΔE ≥ 0.5 kcal/mol. Eight of these 18 molecules are relatively unhindered biaryls: derivatives of biphenyl that possess only hydrogen atoms at the ortho positions, and whose propensity for 4369



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Table 2. Solid-State Hydrocarbon Structures from Orthorhombic Space Groups with Distinct Site Symmetry and Ideal Symmetry

cmpd

CSD refcode

space group

calcd ideal symm

crystal site symm

symm of optimized crystal conf

21 22 23 24 25 26 27 28 29

HTRTBP10 QQQCIG01 PIFHIW CIMMAM JUXMEU INAPOC TAXPOX TAXQAK TAXQEO

Pnma Cmca Pnma Pbca Pbca Pbca Pbca Pbca Pbca

C1 D2 C2 D2 C2vd C2vd C2v C2v C2v

Cs C2h Cs Ci Ci Ci Ci Ci Ci

Cs (TS)b C2h (TS)c Cs (TS)b C2h Ci Ci C2h C2h C2h

relative E of optimized crystal conformation with respect to ideal conformation (kcal/mol)a +4.3 +3.7 +3.7 +1.9 +1.4 +1.3 +0.5 +0.5 +0.4

(+4.0) (+3.8) (+3.8) (+1.0) (+1.2) (+1.4) (+0.5) (+0.5) (+0.5)

The B3PW91/6-31G(d) E + ZPE is given first, and the B3LYP/6-311G(d,p) E is in parentheses. bThere is no Cs-symmetric minimum at either level of theory; the Cs structure is a transition state. cThere is no C2h-symmetric minimum at either level of theory; the C2h structure is a transition state. dThere exists a C2h structure of intermediate energy that is distinct from the Ci crystal conformation. a

Examination of Selected, Individual Anomalous Structures. The anomalous structures in Tables 1 and 2 fall, very broadly speaking, into three classes. The first consists of crowded, mostly polycyclic, aromatics (3, 4, 7, 9, 13, 22, 23) and crowded olefins (18−20, 24), the second is made up of the previously noted, unhindered biaryls (5, 6, 8, 10−12, 14, 15), and the third consists of large cyclophanes (17, 27−29) and related macrocycles (16, 25, 26). (Compound 21 fits none of these descriptions.) However, there is a common theme: the vast majority of the illustrated molecules can be represented as D2h-symmetric drawings on the printed page, and all but one of the remaining structures can be represented as C2h-symmetric drawings. (Again, compound 21 is the exception.) This should not be surprising, because distortions from D2h symmetry can lead both to common centrosymmetric point groups (C2h, Ci) and to common acentric point groups (D2, C2v, C2, Cs, C1), thus allowing the possibility of ideal and crystal conformations that are very different in shape but not too different in energy. Of course, none of these molecules can possess ideal D2h symmetry because of bond angle constraints or steric conflicts. Most adopt ideal symmetries that belong to chiral point groups, but C2v symmetry is also quite common. The relative energies of the ideal and crystal conformations differ widely, with no obvious pattern. For compounds 27−29, with a difference of only 0.5 kcal/mol, the crystal conformation would be adopted by one molecule in three in solution, but for compound 3, with a difference of 6.8 kcal/mol, one would expect the crystal conformation to be adopted by only one molecule in 100 000. This is probably close to the limit for such differences, at least for small molecules.21

positions? Accordingly, a search was conducted of all hydrocarbon structures in orthorhombic space groups that met criteria (1), (2), (3), and (4) above. This yielded a total of 391 structures. Again, every molecule was examined and its probable ideal symmetry was assigned, based first on experience and intuition, followed by conformational searches and AM1 calculations on questionable cases. A full breakdown of the ideal and site symmetries of these molecules is contained in the Supporting Information, but in aggregate, 379 molecules crystallize with a site symmetry equal to, or a subgroup of, their ideal symmetry, and the bulk of these (275) are molecules that crystallize on general positions. Among the 116 molecules that crystallize on special positions, ideally C2-symmetric molecules on C2-symmetric sites are the most common (23). However, 12 of the 116 structures are molecules that crystallize with site symmetries that are not subgroups of their ideal symmetries (as judged by AM1). Further evaluation of the conformations of these molecules at the B3PW91/6-31G(d) level left 9 of the 116 (7.8%) as truly anomalous, and these are listed and illustrated in Table 2. In contrast to Table 1, none of the entries in Table 2 are unhindered biaryls. Seven such hydrocarbons were found in orthorhombic space groups, but they did not crystallize in anomalous conformations. For each of the anomalous structures identified by B3PW91/ 6-31G(d) calculations after both searches, the assignment was checked by calculations at the higher B3LYP/6-311G(d,p) level.14,15,20 Both sets of calculations gave essentially the same results, and the relative energies of the ideal and optimized crystal conformations are listed in Tables 1 and 2 for both methods. 4370



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less stable, Cs conformation of 23 may be more efficient than packing of its twisted ideal conformation.

It is instructive to compare the ideal and crystal conformations of some of these molecules. Why the calculated ideal structure of a given molecule is the lowest energy conformation is usually clear, but the reason for adoption of a distinct, higher energy conformation in the solid state is often not. In some cases, one may gain insight by comparison of the anomalous structure to that of the same or a similar compound in a different crystal environment. Consider first the conformations of rubrene (22, Figure 2), as this molecule is most closely akin to compound 1 of the

Compound 3 (Figure 2) is also a tetracene derivative, in this case with a twisted, C2-symmetric ideal conformation and a Cisymmetric crystal conformation. Once again, the C2 conformation permits the peripheral phenyl and indeno rings to be further apart than in the Ci structure (the closest carbon− carbon contacts are 3.11 and 3.02 Å, respectively).24 Unlike the case of rubrene, the Ci conformation is a genuine potential minimum, not a transition state. Favorable π−π stacking of the more nearly planar cores of the Ci conformation is evident in the crystal structure of 3.27 Aromatic compounds with bulky alkyl, rather than aryl, substituents behave in much the same way. The crystal and ideal conformations of 1,2,4,5-tetra-tert-butylbenzene (13) and the very crowded naphthalene 4 are illustrated in Figure 3. The

Figure 2. Conformations of compound 22 (left) and compound 3 (right); crystal conformations are above and calculated ideal conformations below.

introduction. Rubrene has a linear polycyclic core that ideally prefers to adopt a twisted conformation, and the achiral crystal conformation observed in the solid state23 is calculated to be 3.8 kcal/mol higher in energy. As can be seen clearly in the figure, the crystal conformation requires that several sp2hybridized carbons in the tetracene core be pyramidalized, a distortion that gives rise to less favorable overlap of adjacent porbitals than the gentle twisting of the ideal structures. More importantly, in the crystal conformation the ipso carbons of the interior phenyl groups are only 2.83 Å apart,24 well within the sum of two carbons’ van der Waals radii, and the resulting steric conflict requires significant splaying of the phenyls. In the ideal conformation, the ipso carbons are 2.90 Å apart, and the phenyl splaying is less pronounced. Superior relief of steric conflict between peripheral substituents is a common determinant of the ideal conformation. Curiously, the C2h-symmetric crystal conformation of 22 is not even a potential minimum in the gas phase, but rather a conformational transition state! This was verified at the HF/631G(d), HF/6-311G(d,p), B3LYP/6-31G(d), B3LYP/6-311G(d,p), and B3PW91/6-31G(d) levels. What is the advantage of such a structure in the solid state? When the packing motif23 (not shown) is examined, the chief advantage of the achiral conformation appears to be favorable π−π stacking of the planar acene core. Such stacking is not easy for the twisted ideal conformation, but this is likely not the whole explanation. There exist crystal structures of two di-tert-butyl derivatives of rubrene: compounds 23 and 30, illustrated below. Compound 23 has already been identified as an anomalous structure; it crystallizes on a special position with Cs symmetry (see Table 1). Compound 30, however, crystallizes on a general position in a twisted conformation with approximate C2 symmetry. Most significantly, the crystals of 23 have a significantly greater density (1.184 g/cm3)25 than those of the isomeric 30 (1.141 g/cm3),26 lending support to the notion that the packing of the


nearly planar aromatic cores of both molecules in the Cisymmetric crystal conformations may look relatively “normal”, but they force tighter intramolecular contacts between the peripheral alkyl substituents than are found in the D2symmetric twisted ideal conformations. Thus, the shortest Cmethyl−Cmethyl distance in the crystal conformation of 13 is 3.36 Å, but in the calculated D2 conformation it is 3.41 Å. Similarly, the bridgehead carbons in the crystal conformation of 4 are only 3.14 Å apart, but in the D2 conformation the contact distance is relaxed to 3.19 Å. The brick-like shape of Ci-4 permits a tight packing in the crystal28 that is likely not possible for a twisted molecule, and the more compact shape of Ci-13 may provide similar advantages, but they are less obvious from its crystal structure.29 Of course, one may fall back upon the long-recognized preference for inversion-symmetric arrangements in the close 4371



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packing of molecules3,4 to account for these anomalous crystal structures. The relative merits of the crystal and ideal conformations of the remaining crowded aromatics, compounds 7 and 9, are analogous to the compounds discussed above, and the closely related, crowded olefins 18 and 24 (Figure 4) are also similar to

the crowded aromatic with respect to their ideal conformational preferences. Thus, the shortest Cmethyl−Cmethyl distances in the Ci crystal conformations of 18 and 24 are 3.26 and 3.25 Å, respectively, but the same contact distances in their D2symmetric ideal conformations are 3.34 and 3.31 Å, respectively. The more nearly rectangular structures of the Ci conformations may permit tighter packing in the solid state30,31 than would the chiral ground states. The reasons for the conformational preferences of the conjugated ethylene derivatives 19 and 20 are subtler than those of the preceding structures. These are much less crowded molecules, and the difference in energy between the optimized crystal conformations and the ideal conformations is only 0.7 kcal/mol for each. For compound 19, the slightly higher energy of the crystal conformation may be the result of the two “close” 2.82 Å hydrogen−hydrogen contacts32 where two phenyl rings are canted toward each other. In the ideal conformation, there is no H−H contact distance shorter than 3.69 Å. Compound 20 is more unusual. The Ci-symmetric crystal conformation is neither a minimum nor a transition state at any level of theory. Geometry optimization of this structure leads either to a Ci- or a C2h-symmetric transition state structure where the two central phenyl rings are perpendicular to the butadiene core (see Figure 5). This structure is the transition state for racemization of the chiral, propeller-like, C2-symmetric, ideal conformation. Because the phenyl rotations in compound 20 are almost unrestricted, the conformational potential surface for 20 is nearly flat. Thus, it is no surprise that 20 can adopt a Ci conformation that packs most efficiently in the crystal,33 but one must recognize that this conformation is geometrically, if


Figure 5. Conformations of compound 19 (left) and compound 20 (right). For 19, the crystal conformation is above and the calculated ideal conformation below; for 20, the crystal, optimized crystal, and ideal conformations are arranged from top to bottom. 4372



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conformational analysis of p-quaterphenyl is essentially the same and has been explored in part elsewhere.19c,d,i However, it is very important to note that, at least for p-quaterphenyl, the apparently planar crystal structure has been interpreted in terms of a dynamic disorder of nonplanar molecules,19c and such a phenomenon is a possibility for all other p-oligophenyls, even when there is no obvious evidence of disorder in the crystal.36 We now turn to macrocyclic structures, and Figure 7 illustrates two representative examples of such compounds that

not energetically, far from any potential minimum. Interestingly, there exists a structure in which compound 20 has cocrystallized with another, larger hydrocarbon.34 In this case, 20 also lies on a center of inversion, but it possesses a very nearly C2h-symmetric conformation that closely resembles the geometry-optimized crystal conformation illustrated in Figure 5. Eight structures in Table 1 contain central biaryl substructures, including biphenyl (5) itself. The optimized crystal conformations of these molecules are invariably inversion-symmetric transition state structures for rotation about the central biaryl bond. Because these biaryls contain only hydrogen atoms in the ortho positions, these conformational transition states are of low energy: 1.6−2.2 kcal/mol higher in energy than the twisted biaryl ground states. The propensity for symmetric biaryls to crystallize in such anomalous conformations is well-known and has been extensively analyzed.19 However, two of the molecules in Table 1, p-quaterphenyl (10) and p-sexiphenyl (12), deserve special attention, because their crystal conformations, like that of compound 20 discussed above, are far from any potential minimum or transition state. Consider the case of p-sexiphenyl. The crystal conformation35 (see Figure 6) is nearly planar, with approximate D2h


display anomalous crystal structures. A casual look at the Ci crystal and D2 ideal conformations of compound 16 gives no reason for a preference. A close examination of intramolecular contacts, however, shows that in almost every way the crystal conformation is slightly more crowded: the shortest Cmethyl− Cmethyl distances in the Ci conformation are 2.92 and 2.93 Å, but the D2 conformation has none shorter than 2.97 Å; the transannular contact distances for the terminal carbons of the butadiynes is 2.70 Å in the crystal, but 2.73 Å in the ideal conformation; a similar difference is seen for the interior carbons. The more compact Ci structure presumably packs more tightly and is observed in the crystal.37 The macrocyclic diynes 26 (Figure 7) and 25 (not shown) are much easier to understand. In the gas phase, these molecules prefer to have their polymethylene chains fully extended, but in the solid state, such a conformation would leave cavities that might not be easily filled with solvent molecules of crystallization. However, the introduction of a single gauche conformation on each side of the molecule permits the polymethylene chains to come into van der Waals contact over most of their length. The resulting lowersymmetry, slab-like structures pack easily with little empty space and no included solvent.38,39 The ideal conformations of 25 and 26 have C2v symmetry; however, there exist fully extended C2h conformations, distinct from the Ci crystal conformations and intermediate in energy between the crystal and ideal conformations. The most unusual structure in the sets is compound 21, which does not share any of the characteristics described above. In its ideal conformation (Figure 8), the triphenylmethyl group adopts the expected propeller conformation, and overall the molecule possesses C1 symmetry. In the crystal, the molecule adopts a Cs-symmetric conformation, which proves to be a transition state for the enantiomerization of the trityl propeller. Thus, the solid-state conformation of 21 is clearly an effect of crystal packing forces; free trityl groups rarely adopt Cs conformations. Interestingly, the cis isomer of compound 21

Figure 6. Conformations of p-sexiphenyl (12). The crystal conformation (∼D2h), the optimized crystal conformation (C2h), and calculated ideal conformation (D2) are arranged from left to right.

symmetry. Optimization of p-sexiphenyl at the B3PW91/631G(d) level under the constraint of D2h symmetry leads to a structure that is not a simple transition state, but a saddle point of order 5 (it has five imaginary frequencies) that is fully 9.1 kcal/mol higher in energy than the calculated D2-symmetric ground-state conformation, in which all pairs of rings can twist to avoid coplanarity. (There exist several additional conformations of D2 and C2 symmetry that are of virtually the same energy as the illustrated D2 conformation; they all share the property that no two adjacent rings are coplanar.) If, however, the crystal conformation is optimized under the constraint of only Ci symmetry (the same constraint that exists in the crystal), then a C2h-symmetric structure results, in which all but the center pair of rings are permitted to twist away from coplanarity. This structure is a genuine transition state (one imaginary frequency) and is only 1.8 kcal/mol above the ground state. It is clear then that p-sexiphenyl (and pquaterphenyl) crystallize in a roughly planar conformation not only to accommodate an inversion center, but also to benefit from extensive edge-to-face (herringbone) packing of the planar structures that is observed in the crystal.35 The 4373



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Figure 8. The crystal and ideal conformations of compound 21 (left, above and below, respectively) and a packing diagram for the crystal (right) in which the edge-to-face phenyls are indicated by solid atoms.

crystallizes on a general position,40 but it also adopts a conformation of nearly Cs symmetry. In this case, however, the ∼Cs conformation is the ground state and is stabilized by an intramolecular edge-to-face interaction between phenyl groups.40 In the packing of compound 21,41 it is an intermolecular interaction of this type (see Figure 8) that provides the needed stabilization of the transition state structure in the crystal. This work employed symmetry considerations to find anomalous structures, and in the preceding sections we have discussed only those cases where the crystal site symmetry was not a subgroup of the ideal molecular symmetry. However, it is also possible for two distinct conformations of a molecule to have the same symmetry, or for one to fall in a subgroup of the other. In the course of the conformational searches performed for this work, several such examples were found, but it is difficult to carry out a systematic search. The considerations that govern these molecules’ conformations are much the same as those considered previously, as the following three examples show. Many of the same considerations that govern the conformations of p-sexiphenyl (12, discussed above) also apply to p-quinquephenyl (31), with the exception that the ideal conformation of 31 possesses C2h symmetry. Because the crystal conformation possesses Ci symmetry, a subgroup of C2h, the structure does not appear anomalous on symmetry grounds. However, just as for p-sexiphenyl, the crystal conformation of pquinquephenyl is flat,35 having approximate D2h symmetry, and such a structure is calculated to be 7.5 kcal/mol higher in energy than the ground-state conformation. For p-oligophenyls with an odd number of rings, there exist low-energy conformations with both C2h and D2 (and C2) symmetry, in which all pairs of ring may twist away from coplanarity. In the case of 31, its D2 conformation is a mere 0.06 kcal/mol higher in energy than the C2h structure at the B3PW91/6-31G(d) level. As observed earlier for p-sexiphenyl, p-oligophenyls with an even number of rings can have only chiral (D2 or C2) lowenergy conformations because, to retain inversion symmetry, the two central rings must be coplanar. The crystal conformation of cyclophane 32 (space group P2 1 /c) possesses C i symmetry (and approximate C 2h symmetry),42 but it is 4.3 kcal/mol higher in energy than the distinct, fully extended, C2h ideal conformation (Figure 9). As with macrocycle 26, the extended conformation may not easily accommodate solvent of crystallization to fill the empty space, and so the molecule must introduce four gauche interactions in


the side chains to pack tightly. We previously observed a similar compression in the crystal structure of one of our triarylphosphine-containing cyclophanes,43 and this can scarcely be the only other example. The case of octaphenylnaphthalene44 (33, space group P212121) is very similar to the other crowded aromatics discussed above. The ideal conformation is twisted with D2 symmetry, but the C1 crystal conformation, with only approximate Ci symmetry, closely resembles a C2h minimum that is 3.6 kcal/mol higher in energy than the ideal. Experimental confirmation that the ideal symmetry of 33 is indeed D2 may be found in the six different X-ray structures of twisted octaarylnaphthalenes.1,45−47 We do not doubt that 4374



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many additional cases of distinct ideal and crystal conformations have gone undetected in our surveys, particularly among the numerous molecules possessing C1 symmetry.

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ASSOCIATED CONTENT

S Supporting Information *

(1) Lists of all crystal structures examined, giving each retrieved structure’s CSD refcode, space group number, Z, Z′, proposed ideal symmetry, site symmetry, and brief comments on the relative energies of various conformations; (2) an ASCII text file containing the calculated atomic coordinates and energies of the molecules discussed in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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CONCLUSIONS One should be cautious when assigning the ground-state conformation of a molecule based on a crystal structure in which the molecule resides on a special position (especially a center of inversion) in the crystal lattice. In the structural surveys reported herein, almost 10% of the hydrocarbons residing on inversion centers in the common space groups P 1̅ and P21/c in fact preferred chiral, or at least acentric, conformations in the absence of crystal packing forces. The CSD currently contains approximately 141 000 and 207 000 structures in P1̅ and P21/c, respectively, and 14% and 19% of the structures in these two space groups, respectively, contain molecules on centers of inversion.6 If the same rate of anomalous conformations prevails among nonhydrocarbons, then there must be in excess of 5000 anomalous structures of this type alone. Similarly, roughly 8% of the hydrocarbons residing on special positions in all orthorhombic space groups proved to have anomalous conformations, with the specific examples found in the space groups Pbca, Pnma, and Cmca. Although the numbers of hydrocarbons crystallizing on special positions (in orthorhombic space groups) with Ci, Cs, and C2 symmetry were comparable (35, 33, and 39, respectively, see the Supporting Information), centers of inversion were implicated in most of the anomalies. Indeed, among the roughly 1500 structures that we have surveyed for anomalous conformations, including nonhydrocarbons not reported here, we have yet to find a single, clear-cut example of a molecule with ideal Ci symmetry that crystallizes in a C2-symmetric conformation. This fully agrees with the work of Motherwell and co-workers, who found that when molecules possess Ci symmetry, then the inversion centers are retained in 99% of the corresponding crystal structures.6 Because symmetry considerations were employed to locate anomalous structures in this survey, we found that almost all of the anomalous structures could be represented as drawings containing multiple symmetry elements (i.e., D2h and C2h). This allows the actual molecules, which cannot retain such high symmetry due to bonding and steric constraints, to possess two or more conformations of lower symmetry and distinctly different shape, but of similar energy. The energy differences between the ideal and crystal conformations are usually small, so that for a molecule with ideal D2 symmetry, for example, there may be sufficient energy at room temperature to give significant populations of minor Ci or Cs conformations. This permits the adoption of these higher-energy conformations in the crystal when the packing is favorable. For those examples where the energy difference exceeds 4 kcal/mol, and thus fewer than one molecule in 1000 can adopt the anomalous conformation in solution, it is more difficult to see how crystallization of the anomalous conformation can occur. Finally, the vast majority of organic molecules crystallize on general positions, not special. Unfortunately, it is much more time-consuming to search the conformation space of asymmetric molecules, particularly when they possess many conformational degrees of freedom. There is no doubt that some such structures adopt anomalous high-energy conformations in the crystal, but we have insufficient data at present to comment on their frequency.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: (504) 862-3547. Fax: (504) 865-5596. E-mail: rpascal@ tulane.edu. Present Address ∥

Emory University, Atlanta, Georgia 30322, United States.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by National Science Foundation Grant CHE-0936862, which is gratefully acknowledged. We thank an anonymous referee for helpful suggestions.

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REFERENCES

(1) Pascal, R. A., Jr. Chem. Rev. 2006, 106, 4809−4819. (2) L’Esperance, R. P.; Van Engen, D.; Dayal, R.; Pascal, R. A., Jr. J. Org. Chem. 1991, 56, 688−694. (3) Kitaigorodskii, A. I. Organic Chemical Crystallography; Consultants Bureau: New York, 1961. (4) Brock, C. P.; Dunitz, J. D. Chem. Mater. 1994, 6, 1118−1127. (5) Motherwell, W. D. S. CrystEngComm 2010, 12, 3554−3570. (6) Pidcock, E.; Motherwell, W. D. S.; Cole, J. C. Acta Crystallogr., Sect. B 2003, B59, 634−640. (7) Cole, J. C.; Yao, J. W.; Shields, G. P.; Motherwell, W. D. S.; Allen, F. H.; Howard, J. A. K. Acta Crystallogr., Sect. B 2001, B57, 88−94. (8) (a) Allen, F. H.; Kennard, O.; Taylor, R. Acc. Chem. Res. 1983, 16, 146−153. (b) Allen, F. H. Acta Crystallogr., Sect. B 2002, B58, 380− 388. (9) CSD version 5.29 (November 2007) was employed. This was the version employed for our initial examination of the problem in 2008, and, for consistency, we have employed the same version for all subsequent searches. (10) Mighell, A. D.; Himes, V. L.; Rodgers, J. R. Acta Crystallogr., Sect. A 1983, A39, 737−740. (11) Ultimately, only 58 molecules (21%) were judged to be ideally Ci-symmetric, but 129 (48%) are C2h-symmetric, 46 (17%) are D2hsymmetric, and 18 (7%) are distributed among other centrosymmetric point groups. (12) Halgren, T. A. J. Comput. Chem. 1996, 17, 490−519. (13) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902−3909. (14) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley & Sons: New York, 1986; pp 63−100. (15) Becke, A. D. J. Chem. Phys. 1993, 98, 5648−5652. (16) Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244−13249. (17) The B3PW91 functional was employed because we have found B3PW91 to give both slightly better geometries18a and clearly superior isomer energies18b for light atom structures than the more common B3LYP functional. (18) (a) Pascal, R. A., Jr. J. Phys. Chem. A 2001, 105, 9040−9048. (b) Schreiner, P. R.; Fokin, A. A.; Pascal, R. A., Jr.; de Meijere, A. Org. Lett. 2006, 8, 3635−3638. (19) (a) Trotter, J. Acta Crystallogr. 1961, 14, 1135−1140. (b) Charbonneau, G.-P.; Delugeard, Y. Acta Crystallogr., Sect. B 4375



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1976, B32, 1420−1423. (c) Delugeard, Y.; Desuche, J.; Baudour, J. L. Acta Crystallogr., Sect. B 1976, B32, 702−705. (d) Baudour, J. L.; Delugeard, Y.; Rivet, P. Acta Crystallogr., Sect. B 1978, B34, 625−628. (e) Almenningen, A.; Bastiansen, O.; Fernholt, L.; Cyvin, B. N.; Cyvin, S. J.; Samdal, S. J. Mol. Struct. 1985, 128, 59−76. (f) Bastiansen, O.; Samdal, S. J. Mol. Struct. 1985, 128, 115−125. (g) Brock, C. P.; Minton, R. P. J. Am. Chem. Soc. 1989, 111, 4586−4593. (h) Baudour, J. L. Acta Crystallogr., Sect. B 1991, B47, 935−949. (i) Zhuralev, K. K.; McCluskey, M. D. J. Chem. Phys. 2001, 114, 5465−5467. (j) Zhuralev, K. K.; McCluskey, M. D. J. Chem. Phys. 2004, 120, 1841−1845. (20) (a) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785− 789. (b) Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200−206. (21) We have performed additional searches of the CSD (data not shown) with the goal of identifying anomalous structures, and the greatest difference in energy between the crystal and ideal conformations that we have found is 8.6 kcal/mol at the B3PW91/ 6-31G(d) level for CSD entry GOQVOX. Interestingly, in this case there are two polymorphs, one stabilized by intermolecular, the other by intramolecular hydrogen bonds. In the original report,22 the authors state, “At 90 °C the tetragonal needles [anomalous conformation]...turn, without melting, into the monoclinic cuboids [ideal conformation]...which melt at 171−172 °C.” (22) Merz, A.; Kronberger, J.; Dunsch, L.; Neudeck, A.; Petr, A.; Parkanyi, L. Angew. Chem., Int. Ed. 1999, 38, 1442−1446. (23) (a) Bulgarovskaya, I.; Vozzhenikov, V.; Aleksandrov, S.; Belsky, V. Latv. PSR Zinat. Akad. Vestis, Khim. Ser. 1983, 53−59. (b) Jurchescu, O. D.; Meetsma, A.; Palstra, T. T. M. Acta Crystallogr., Sect. B 2006, B62, 330−334. (24) For the close carbon−carbon contacts in anomalous conformations, we have cited the distances from the X-ray structures. Similar, but usually slightly longer distances are found in the geometryoptimized crystal conformations from which the energy differences are derived. Thus, for compound 14, the ipso carbons are 2.83 Å apart in the crystal structure, 2.85 Å apart in the calculated C2h conformation, and 2.90 Å apart in the calculated D2 ideal conformation. Similarly, for 3, the close carbon−carbon contact distances are 3.02 Å in the crystal structure, 3.03 Å in the calculated Ci conformation, and 3.11 Å in the calculated C2 ideal conformation. (25) Schuck, G.; Haas, S.; Stassen, A. F.; Kirner, H.-J.; Batlogg, B. Acta Crystallogr., Sect. E 2007, E63, o2893. (26) Schuck, G.; Haas, S.; Stassen, A. F.; Berens, U.; Batlogg, B. Acta Crystallogr., Sect. E 2007, E63, o2894 (CSD refcode PIFHOC). (27) Banide, E. V.; Ortin, Y.; Seward, C. M.; Harrington, L. E.; Muller-Bunz, H.; McGlinchey, M. J. Chem.-Eur. J. 2006, 12, 3275− 3286. (28) Matsuura, A.; Nishinaga, T.; Komatsu, K. Tetrahedron Lett. 1999, 40, 123−126. (29) Stam, C. H. Acta Crystallogr., Sect. B 1972, B28, 2715−2720. (30) Pilati, T.; Simonetta, M. Acta Crystallogr., Sect. C 1985, C41, 147−148. (31) Pilati, T.; Simonetta, M. Acta Crystallogr., Sect. C 1984, C40, 1407−1409. (32) For the determination of contact distances involving hydrogen, the C−H bond distances in the crystal structures have been “improved” to standard values derived from neutron diffraction. See notes and refs 11−14 in: Pascal, R. A., Jr. Eur. J. Org. Chem. 2004, 3763−3771. (33) Bats, J. W.; Urschel, B. Acta Crystallogr., Sect. E 2006, E62, o748−o750. (34) Huan, Z.; Yao, X.; Wang, R.; Wang, H.; Liu, W. Jiegou Huaxue (Chinese J. Struct. Chem.) 1993, 12, 383−386 (CSD refcode YAWLIR). (35) Baker, K. N.; Fratini, A. V.; Resch, T.; Knachel, H. C.; Adams, W. W.; Socci, E. P.; Farmer, B. L. Polymer 1993, 34, 1571−1587. (36) The reader may wonder whether dynamic disorder might be present in the other anomalous structures identified in the this work. Indeed, such dynamic disorder might be hidden by larger-than-normal thermal ellipsoids in long, narrow molecules such as the poligophenyls. However, for molecules of greater breadth, including

biphenyls bearing even simple substituents, small displacements near the center of the molecule would be greatly magnified at the periphery, and the resulting disorder would be obvious. (37) Houk, K. N.; Scott, L. T.; Rondan, N. G.; Spellmeyer, D. C.; Reinhardt, G.; Hyun, J. L.; DeCicco, G. J.; Weiss, R.; Chen, M. H. M.; Bass, L. S.; Clardy, J.; Jorgensen, F. S.; Eaton, T. A.; Sarkozi, V.; Petit, C. M.; Ng, L.; Jordan, K. D. J. Am. Chem. Soc. 1985, 107, 6556−6562. (38) Hellbach, B.; Gleiter, R.; Rominger, F. Synthesis 2003, 2535− 2541. (39) Gleiter, R.; Pflasterer, G.; Nuber, B. Chem. Commun. 1993, 454−456. (40) Cheetham, A. K.; Grossel, M. C.; Hope, D. A. O.; Weston, S. C. J. Org. Chem. 1993, 58, 6654−6661 (CSD refcode DHTRBP10). (41) Cheetham, A. K.; Grossel, M. C.; Newsam, J. M. J. Am. Chem. Soc. 1981, 103, 5363−5372. (42) Smith, B. B.; Hill, D. E.; Cropp, T. A.; Walsh, R. D.; Cartrette, D.; Hipps, S.; Shachter, A. M.; Pennington, W. T.; Kwochka, W. R. J. Org. Chem. 2002, 67, 5333−5337 (CSD refcode UGEVUX). (43) Chen, Y. T.; Baldridge, K. K; Ho, D. M.; Pascal, R. A., Jr. J. Am. Chem. Soc. 1999, 121, 12082−12087 (CSD refcode GOFWON). (44) Qiao, X.; Padula, M. A.; Ho, D. M.; Vogelaar, N. J.; Schutt, C. E.; Pascal, R. A., Jr. J. Am. Chem. Soc. 1996, 118, 741−745 (CSD refcode ZOPJOD). (45) Tong, L.; Ho, D. M.; Vogelaar, N. J.; Schutt, C. E.; Pascal, R. A., Jr. Tetrahedron Lett. 1997, 38, 7−10 (CSD refcode REBHOV). (46) Tong, L.; Ho, D. M.; Vogelaar, N. J.; Schutt, C. E.; Pascal, R. A., Jr. J. Am. Chem. Soc. 1997, 119, 7291−7302 (CSD refcodes RIQMAF, RIQMEJ, RIQMIN, RIQMOT). (47) Pascal, R. A., Jr.; Barnett, L.; Qiao, X.; Ho, D. M. J. Org. Chem. 2000, 65, 7711−7717 (CSD refcode QEYVEV).

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Ideal Molecular Conformation versus Crystal Site Symmetry - Crystal

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