Do 12-Membered Cycloalkane Rings Only Exist As One Conformation

Oct 18, 2012 - Though the conformation of the PMDI-12 molecules as a whole may differ, examination of the conformation of the 12-membered ring indicat...
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Do 12-Membered Cycloalkane Rings Only Exist As One Conformation in the Solid-State? A Detailed Solid-State Analysis Involving Polymorphs of N,N′‑Biscyclododecyl Pyromellitic Diimide Sanaz Khorasani, Manuel A. Fernandes,* and Christopher B. Perry Molecular Sciences Institute, School of Chemistry, University of the Witwatersrand, PO Wits 2050, Johannesburg, South Africa S Supporting Information *

ABSTRACT: Conformational flexibility in molecules plays a key role in many chemical and biological processes. It is a common belief that the larger the cycloalkane the more flexible it will be, and the more conformations it will adopt. While theoretical studies have shown that cyclododecane has many possible conformations, they have also consistently shown that one conformation is slightly more stable. In this work, we examine the effect of substitution and crystal packing on the conformation of singly substituted cyclododecane rings. This has been done by exploiting polymorphism in an attempt to induce new conformations in a specific molecule, as well as by examining structures reported in the Cambridge Structural Database (CSD). To this end, three polymorphs of N,N′-biscyclododecyl pyromellitic diimide (PMDI-12) have been identified and their structures elucidated. To rationalize the differences between the various polymorphs, molecule···molecule interaction energies have been calculated using atom−atom potential methods. Though the conformation of the PMDI-12 molecules as a whole may differ, examination of the conformation of the 12-membered ring indicates that it is conformationally identical in all three polymorphs. Examination of 20 other organic and organometallic structures containing this group in the CSD, indicates that they have the same conformation (only one possible exception in the 34 rings examined in this work), which suggests that the 12-membered ring adopts a single conformation ([3333] with D2 symmetry) in the solid-state that is relatively unaffected by crystal packing.

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“square” conformer of unsubstituted cyclododecane, denoted by [3333] (Figure 3) in Dale’s nomenclature,4 has the lowest strain energy. (The numbers in the brackets refer to the number of C−C bonds between the “corner” atoms of the ring.) The next most stable are the [2334] (4.5 kJ mol−1), [1434] (7.3 kJ mol −1 ), and [2343] (10.3 kJ mol −1 ) conformations. Kolossváry and Guida5 have also shown that the [3333] conformation occupies a deep global minimum: the conversion to the [2334] conformation is associated with a 29.9 kJ mol−1 energy barrier. While the conformational behavior of unsubstituted cyclododecane is well-known, it would be interesting to see whether substitution at a single point coupled with solid-state packing effects (intermolecular forces) would allow a conformation other than the [3333] to crystallize out. Consequently, in this work we incorporated two 12-membered cycloalkane rings into a pyromellitic anhydride molecule (PMDI-12) in an attempt to use conformational flexibility to create conformational polymorphs, and in turn use polymorphism to distort the 12-membered rings. In addition, we chose to work with PMDI-12 (1) because the lack of groups capable of strong hydrogen bonds allows the influence of other intermolecular interactions to be evaluated and possibly classified into favored arrangements of molecules or motifs as

INTRODUCTION Polymorphism occurs when more than one structure or arrangement of molecules in a crystal lattice results in a different energy minimum. Differences in crystal structure may be due to differences in intermolecular interactions resulting in an alternative packing arrangement (packing polymorphs) or differences in molecular conformation. Polymorphs are useful because they often display very different properties as is wellknown in the pharmaceutical and pigment industries. These differences in properties also allow the influence of intermolecular interactions on molecular structure to be examined.1 In short, molecular conformational flexibility is a possible path toward inducing polymorphism (a potentially useful materials design approach), but in turn, polymorphism allows conformational flexibility to be examined. As a route toward inducing conformational polymorphism,1,2 we chose to work with a 12-membered ring (cyclododecane) because it is a large cycloalkane, and it is relatively easy to obtain in the large amounts required for a conformational polymorphism study, where many crystallization experiments are required. It is also considered the first member of the largering cycloalkanes.3 Because of the inherent flexibility of this molecule, it is reasonable to expect that it would be able to adopt a wide range of stable conformations. Possible conformations for unsubstituted cyclododecane have been extensively searched for and studied by several authors3−7 by means of molecular mechanics methods. All agree that the © 2012 American Chemical Society

Received: June 4, 2012 Revised: October 10, 2012 Published: October 18, 2012 5908

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are commonly described in structures containing classical hydrogen bonds. To increase the pool of 12-membered rings analyzed, all structures containing singly substituted 12membered rings in the Cambridge Structural Database8 (CSD) have also been examined and the results combined with those experimentally obtained in this work.

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Table 1. Crystallographic Information for Polymorphs I−III formula formula weight temperature (K) wavelength (Å) crystal system space group a (Å) b (Å) c (Å) α (deg) β (deg) γ (deg) V (Å3) ρcalcd (g/cm3) Z data/params R1/wR2 GOF

EXPERIMENTAL SECTION

Synthesis. PMDI-12 (1) was synthesized according to an established method.9 Pyromellitic dianhydride (2 g, 9.16 mmol) was dissolved in THF (5 mL) and added to a solution of cyclododecylamine (3.36 g, 18.3 mmol) dissolved in THF (5 mL). The resulting white solid was filtered off, dissolved in acetic acid (30 mL), and refluxed for 12 h. The mixture was then slowly cooled to room temperature over a 4 h period, resulting in white crystals (polymorph I in the first synthesis; II in the subsequent syntheses), which were filtered off. 1H (500 MHz, CDCl3): δ = 8.22 (s, 2H, Ar−H), 4.50− 4.53 (m, 2H, CHN), 2.14−2.19 (m, 4H, CH2), 1.75−1.79 (m, 4H, CH2), 1.57−1.60 (m, 4H, CH2), 1.40−1.42 (m, 32H, CH2);.13C (500 MHz, CDCl3): δ = 166.7 (CO), 137.0, 117.9, 47.9 (CHN), 28.2 (CH2), 24.2 (CH2), 24.0 (CH2), 22.7 (CH2), 22.5 (CH2). Melting point: 206−209 °C. Crystal Structure Solution and Refinement. Intensity data were collected at −100 °C on a Bruker APEX II CCD area detector diffractometer with graphite monochromated Mo Kα radiation (50 kV, 30 mA). The collection method involved ω-scans of width 0.5° and 512 × 512 bit data frames. The crystal structures were solved by direct methods. Non-hydrogen atoms were first refined isotropically followed by anisotropic refinement by full matrix least-squares calculations based on F2. Hydrogen atoms were first located in the difference map then positioned geometrically and allowed to ride on their respective parent atoms. Data collection: APEX2.10 Cell refinement: SAINT.11 Data reduction: SAINT. Program used to solve structure: SHELXS97.12 Program used to refine structure: SHELXL-97.12 Molecular graphics: ORTEP-3 for Windows13 and SCHAKAL-99.14 Software used to prepare material for publication: WinGX15 and PLATON.16

I

II

III

C34H48N2O4 548.74 173(2) 0.71073 triclinic P1̅ 7.0557(2) 7.6048(2) 15.1267(5) 96.046(2) 96.701(2) 106.338(1) 765.39(4) 1.191 1 3692/181 0.044/0.098 1.029

C34H48N2O4 548.74 173(2) 0.71073 monoclinic C2/c 19.5309(7) 10.1243(4) 17.5617(6) 90 121.951(1) 90 2946.50(19) 1.237 4 3567/181 0.042/0.099 1.021

C34H48N2O4 548.74 173(2) 0.71073 triclinic P1̅ 8.1128(9) 11.0482(11) 17.788(2) 89.267(4) 79.228(4) 78.377(4) 1533.7(3) 1.188 2 5377/361 0.049/0.091 0.678

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RESULTS AND DISCUSSION Analysis of crystals obtained directly from the first molecular synthesis resulted in the discovery of polymorph I. Recrystallization from ethyl acetate led to the polymorph II. Polymorph III was initially obtained by crystallization of the melt on a hotstage microscope (reported in Table 1) but was later discovered to be more easily obtained through slow evaporation from chloroform. (See Figure S1 in the Supporting Information for photographs of all three polymorphs.) All three polymorphs have been structurally characterized using X-ray diffraction; I and II crystallize in triclinic P1̅ and monoclinic C2/c, respectively, with half a molecule in the asymmetric unit, while III crystallizes in triclinic P1̅ with two half molecules (each half referred to as molecule A and B in the text) in the asymmetric unit (Table 1, Figure 1). As it is centrosymmetric, the molecule crystallizes across a center of inversion in all three structures. The molecules in I and II are conformationally similar (rmsd = 0.1007 Å; all non-hydrogen atoms superimposed by leastsquares) and as a consequence these two structures can be classed as packing polymorphs. Molecules A and B in III (rmsd

Figure 1. ORTEP diagrams (50% probability level) for polymorphs (a) I, (b) II, (c) molecule A, and (d) molecule B of polymorph III. Only the asymmetric unit has been labeled; the other half of each molecule is related by a center of inversion.

= 0.0894 Å) are also similar to each other but are different from those in I and II (Figure 2); the rmsd is 0.5012 Å between I and III-B for example. As a consequence, III is a conformational polymorph of I and II. Selected bond lengths and angles within the molecules are reported in Table 2. The bond lengths in all the molecules are consistent with each other. The largest difference between the conformations in I and II and those in III is due to rotation of the 12-membered ring around the N1− C1 bond, in addition to bending of the 12-membered ring away from a vector defined by the N1−C1 bond. As a consequence, 5909

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significantly more energetic than III-A which is a little unexpected for two molecules which are so conformationally similar. Though the PMDI-12 molecule in the polymorphs I and II is conformationally different from those in III, it is interesting to note that the 12-membered rings have essentially the same conformation (see Figure S2 in the Supporting Information). The conformation adopted is the square-like [3333] conformation, which has been predicted in several papers3−7 as the most stable conformation for a 12-membered cycloalkane ring. To see if this conformation is the most common one in the solid state in general, a search for structures containing singly substituted 12-membered rings (a twelve membered ring with all hydrogen atoms present, minus one for the substitution was used as a fragment; see Supporting Information) in the Cambridge Structural Database8 (CSD; Version 5.33, 2012 release with Nov 2011 update) was carried out resulting in 20 compounds (see Table S1 in the Supporting Information for Refcodes). A superimposition of the alkane rings from these structures and the three polymorphs reported here (34 rings in total) is shown in Figure 3. The overlay indicates that, with one

Figure 2. Superimposition (by least-squares fit of the pyromellitic imide atoms) of the PMDI-12 molecule in the three polymorphs showing the conformational differences between the various molecules. The conformations of the molecules in I and II are similar, while the molecules A and B from III are also similar to each other. The conformations of the molecules in III are, however, different from those in I and II.

Table 2. Selected Bond Lengths (Å) and Torsion Angles (deg) for Molecules in Polymorphs I, II, and III N(1)−C(1) N(1)−C(13) N(1)−C(16) C(1)−C(2) C(1)−C(12) N(1)−C(1)−C(7) N(1)−C(1)−C(8) C(13)−N(1)−C(1)− C(2) C(13)−N(1)−C(1)− C(12) C(16)−N(1)−C(1)− C(2)

I

II

III-A

III-B

1.477 1.401 1.392 1.532 1.525 151.7 166.6 −70.0

1.477 1.399 1.398 1.537 1.532 153.7 167.8 −69.0

1.488 1.395 1.397 1.525 1.524 139.0 153.0 −79.8

1.480 1.399 1.402 1.506 1.546 139.1 153.7 −76.4

58.4

59.3

49.1

52.6

105.4

107.4

107.6

113.2

Figure 3. Least squares superimposition (all atoms) of 12-membered rings from structures reported in the CSD shown from the top of the ring and two side views. The substituted carbon has been set as C1 in all the structures. Included are the 12-membered rings from the three PMDI-12 polymorphs reported here. All the structures (34 rings in total) have the same [3333] conformation with the one exception of NOCSED which is indicated by the arrows.

there is a ∼13° increase in the angle of bending of the 12membered ring toward O2 as shown by the N1−C1−C7 and N1−C1−C8 angles, and rotational differences of ∼4−10° about the N1−C1 bond resulting in torsion angle differences in the various molecules as shown in Table 2. To determine which of these conformations is most the stable, the relative energies of the molecules were calculated with the M0617 DFT functional and the 6-31++G(d,p) basis set, using Gaussian-09.18 In this calculation, the crystal geometry of the C, O, and N atoms were kept frozen while the H atom positions were allowed to optimize. This was done to correct for the fact that H atoms in crystal structures determined by X-rays are geometrically and not experimentally placed. From these calculations, the relative energy of the molecules were found to be 1.8 kJ mol−1, 0 kJ mol−1, 2.8 kJ mol−1 and 17.7 kJ mol−1 for molecules I, II, III-A, and III−B, respectively. The equivalent calculation with the B3LYP19 functional gave the relative energies of these molecules as 6.6, 0, 9.0, and 26.9 kJ mol−1, respectively. The conformation of the molecule in II is therefore the most stable followed by the conformationally similar molecule in I. The conformation of molecule III−B is the most energetic of these and also

exception, the 12-membered rings of all the compounds analyzed crystallize in the [3333] conformation (a square composed of 3 atoms per side as defined by Dale’s notation) or some slightly distorted version thereof. The average torsion angles (°) around the cycloalkane ring for the 33 rings that have the [3333] conformation are as follows: 162(6)/ −68(4)/ −68(2)/ 158(6)/ −68(4)/ −69(4)/ 162(7)/ −68(4)/ −68(5)/ 158(6)/ −69(4)/ −68(3). These are consistent with the values predicted for the [3333] conformation of unsubstituted cyclododecane3,6 with approximate D4 symmetry. Whether the [3333] conformation of unsubstituted cyclododecane has D2 or D4 symmetry has been discussed in theoretical studies.3−7 In general, the answer depends on the molecular mechanics method used: calculations using MM220 suggest that the [3333] conformation of unsubstituted cyclododecane has D2 symmetry, while calculations using MM321 suggest that the molecule has D4 symmetry6,7 (see also Supporting Information Table S2). The difference between the two symmetries is an elongation in one direction of the [3333] “square”, which converts the ring from D4 to D2 symmetry. Overlaying the cyclododecane rings from the crystal structures 5910

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using the substituted atom (C1) as a guide results in a ring with approximate D4 symmetry as shown by the torsion angles above. When the torsion angles from the experimental structures are rearranged by starting from the largest torsion angle (ring substitution being ignored) and working around the ring, then the following average torsion angles (deg) is obtained for the 33 rings analyzed: 167(3)/ −69(5)/ −68(4)/ 154(3)/ −69(4)/ −68(3)/ 165(3)/ −68(3)/ −70(3)/ 155(4)/ −68(4)/ −69(4) (Supporting Information Table S3). The standard deviations are now smaller, and the result now shows that the average [3333] conformation of the structures examined has D2 symmetry. This result also shows that substitution does not have a clear influence on the direction of elongation of the [3333] ring. The only exception that does not have the [3333] conformation is one of the rings in the NOCSED22 structure (NOCSED Ring 2 in Supporting Information Table S1 and Figure S3). This particular ring is best described as approximately having a [13332] conformation. The torsion angles (deg) around the cycloalkane ring are as follows: 137.46/ −29.05/ −98.35/123.30/ −20.52/ −98.29/143.42/ −38.04/ −92.25/117.51/ −11.74/ −104.12. These angles are completely different from any of the low energy conformations predicted by Anet and Rawdah3 and Saunders6: only these authors have listed torsion angles for their computed conformations. The most acute angle in the conformations predicted by these researchers is about 50°, while at least three torsion angles in the NOCSED ring are less than 30°, and none of the angles reach the 160° typical of the [3333] conformation. The presence of the [3333] conformation in 33 out of the 34 rings examined indicates that it is a very stable conformation. The existence of the NOCSED exception suggests that it is possible to distort the 12-membered ring but with difficulty. It is noteworthy that examining the crystal packing in the structure of NOCSED does not reveal any significant close contacts to the ring; also the ring does not seem to interact sterically with the rest of the molecule. The cause of the distortion (if real) is therefore not clear. The ORTEP diagram of NOCSED reported in the paper does show slightly larger than normal ellipsoids suggesting that some unresolved disorder may be present. However, most of the ellipsoids are reasonable so it is unlikely that it would convert into the [3333] conformation if a disorder model was applied. During this study, we attempted to obtain an alternative conformation by melting a sample of II and allowing it to resolidify (at around 170 °C) which led to the first crystals of III. Heating a sample of II to around 220 °C (above its melting point), and keeping it at this temperature for a few minutes before allowing it to resolidify, led to the formation of an amorphous plastic like material after several cycles of heating and cooling: possibly because of the 12-membered ring or the PMDI-12 as a whole adopting other conformations. FTIR spectra of the three polymorphs together with a spectrum from a sample of polymorph III after several melting and solidification cycles are given in the Supporting Information. The lack of classical hydrogen bonds (O−H···O, N−H···O, etc) means that these structures are stabilized by weak hydrogen bonds and dispersive forces. The geometries of the most significant weak interactions for each polymorph are listed in Tables 3 and 4. Each of the three polymorphs has a different packing arrangement because of the role different weak interactions play in each structure. Polymorphs I and III are both stabilized by

Table 3. C−H···O Interaction Geometries for Polymorphs I−III (Å, deg) D−H···A

D−H

C11−H11B···O2a C17−H17···O2b C7−H7B···O2c C12A−H12A···O2Bd C11B−H11C···O1Ae C12B−H12C···O1Bf C12A−H12C···O2Bf

H···A

polymorph I 0.99 2.54 0.95 2.41 polymorph II 0.99 2.706 polymorph III 0.99 2.56 0.99 2.60 0.99 2.52 0.99 2.56

D···A

D−H···A

3.352(2) 3.213(2)

139 142

3.533(3)

141

3.509(4) 3.508(4) 3.349(4) 3.511(5)

160 152 141 160

a −1 + x, y, z. bx, 1 + y, z. c−x, 1 − y, −z. d−1 + x, y, z. e1 + x, −1 + y, z. f1 − x, −y, 1 − z.

Table 4. C−H···π and CO···π Interaction Geometries for Polymorphs I−III (Å, deg) D−H···A

X···Cg

C10−H10B···Cga C10−H10B···Cgb C16A−O2A···Cg1c C16B−O2B···Cg2d

polymorph I 2.67 polymorph II 2.82 polymorph III 3.503(3) 3.419(3)

C···Cg

C−X···Cg

3.615(2)

159

3.608(2)

137

3.988(4) 3.855(4)

104.8(2) 102.0(2)

a Cg = C14−C15−C17−C14−C15−C17; 1 − x, −y, −z. bCg = C14− C15−C17−C14−C15−C17; −x, −y, 1/2 − z. cCg1 = N1B−C13BC14B−C15B−C16B; −x, 1 − y, 1 − z. dCg2 = N1A−C13A−C14A− C15A−C16A; 1 − x, 1 − y, 1 − z.

significant C H···O interactions, while only one relatively weak C−H···O interaction is present in II (Table 3). In the case of I, molecules interact with each other through C−H···π interactions to form a ribbon of molecules along the [110] direction (Figure 4a and 4b). Each of these molecules also interacts with neighboring molecules through C−H···O interactions to form another ribbon along the b axis (Figure 4c). The combination of the C−H···π and C−H···O interactions results in a slab of molecules parallel to the (001) plane. The 12-membered rings, which define the edges of each of these slabs, then interact through dispersion forces with those of the neighboring slabs resulting in the observed packing (Figure 4a). A distinctive feature of this polymorph is that each pyromellitic diimide component effectively has 6 closest neighbors, two of which are the 12-membered rings from neighboring molecules above and below it, while the remaining four are neighboring pyromellitic diimide groups. This is a consequence of the nature of the C−H···O interactions which occur between the pyromellitic diimide components, a feature which is unique to this polymorph. The pyromellitic diimide groups therefore interact with each other within a slab but are isolated from those on the neighboring slab by the 12membered rings. In the case of II, the only apparently significant C−H···O interaction is very weak as shown by the long H···O distance in Table 2, and involves an interaction between a 12-membered ring and an imide oxygen on a neighboring molecule (Figure 5c). This difference results in an alternative crystal packing 5911

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Figure 4. Crystal packing and weak interactions in I: (a) packing diagram in which each molecule interacts via C−H···π interactions to form a ribbon of molecules along the [110] direction (see Figure 5b for an equivalent ribbon present in II); (b) the C−H···π interaction in more detail; (c) C−H···O interactions acting between the pyromellitic diimide groups and which link the C−H···π ribbons shown in panel b along the b axis.

Figure 5. Crystal packing (a), C−H···π (b), and C−H···O interactions (c) in II. As in I, the structure is composed of C−H···π interaction (indicated with dotted lines in panels a and b) stabilized ribbons of molecules. Each ribbon interacts through C−H···O interactions to neighboring ribbons (c).

arrangement in II even though it shares many structural similarities with I. As in I, molecules are held together by C− H···π interactions to form a ribbon of molecules (Figure 5b). Neighboring ribbons then interact with each other through the weak C−H···O interaction which results in each pyromellitic diimide component being surrounded by 12-membered rings. As a consequence, the packing in this structure is completely different to I. In this case, each pyromellitic diimide component is surrounded by 6 nearest neighbors which are all 12membered rings. The pyromellitic imide groups are therefore isolated from the others in this polymorph which is a feature unique to this polymorph. In polymorph III, the two molecules (A and B) stack alternately (···A···B···A···B···) on each other to create a stack of molecules along the a axis (Figure 6). A feature of this structure is that the molecules in a stack interact with each other through CO···π interactions (a dipole induced dipole interaction) and not through π···π interactions (Table 4). Though these visually appear to interact with each other through π...π interactions they are in fact too far from each other to interact

in this way. (Lattice energy calculations indicate that the interaction between molecules in a stack does have a large dispersion component as will be shown later.) As a consequence molecules A and B are not coplanar but lie instead at an angle of 22.96(2)°, which is presumably due to steric interference of the 12-membered rings on neighboring molecules within the stack (Figure 6c). This is interesting as the 12-membered ring as been pushed in toward the center of the stack by ∼13° (as discussed earlier) and not away from it as one would expect. Regardless of the cause of A and B not stacking in a coplanar manner, the result is a small space between these molecules which is clearly visible when viewing a space filling diagram of the stack side on (see Supporting Information Figure S4). This is probably the main reason why at 1.188 g cm−3 the crystal density of polymorph III is low compared to polymorph II which has a crystal density of 1.237 g cm−3. It is, however, comparable to polymorph I which has a crystal density of 1.191 g cm−3. 5912

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would like to identify motifs composed of molecule···molecule interactions, which are energetically favorable and structure determining, in an analogous way to that which is routinely done by analyzing close contacts in crystal structures of samples containing H-bonding. As a consequence, lattice energy calculations were carried out using the atom potential methods OPROP 23 (with the UNI force field, 24,25 both being implemented as part of the OPiX suite of programs23) and AA-CLP (part of the CLP suite of programs26 that now supersedes OPiX) to identify the most significant molecule···molecule interactions stabilizing the various polymorphs. The merits of this approach for identifying structure determining interactions have been discussed.27−29 AA-CLP has a useful feature of being able to break down each molecule···molecule interaction into four energy components contributing to the total energy of the interaction: coulombic, polarization, dispersion, and repulsion. This is often useful for understanding the nature of the interaction between the two molecules. As prescribed within the OPiX and CLP manuals, all H-atom positions were first recalculated within each program suite with a C−H distance of 1.08 Å as part of the calculation procedure. The results of these calculations are given in Table 5. The values calculated using OPROP are in general larger but compare reasonably well with those obtained using the AACLP method. More importantly, the two calculation methods consistently indicate which individual molecule···molecule interactions contribute most to the stability of each structure, and as a consequence, are most likely to be structuredetermining. The two methods also consistently identify the next most important interactions contributing 10 kJ mol−1 or more to the stability of each structure, though the relative magnitude of each molecule···molecule interaction calculated by each method does differ. The geometries of the most stable molecule···molecule interactions in each polymorph are shown in Figure 7 (see also Figures S5−S8 in the Supporting Information). The most important molecule...molecule arrangement in both polymorphs I and II is the one enabling the cyclic C−H···π interaction (Figure 7a and 7c). This leads to the C−H···π stabilized ribbons in polymorphs I and II and is therefore at least partially structure-determining in both structures (Figures 4 and 5). What determines the overall structure in both these polymorphs is the relative importance of the remaining molecule···molecule interactions in each of these polymorphs. In the case of I, only two molecule...molecule interactions (other than the C−H···π) contribute more than 15 kJ mol−1 to the stability of the structure. One of these (x, 1 + y, z contributing −52.1 kJ mol−1 according to OPROP) involves the C−H···O interaction stabilizing molecules along the b axis shown in Figure 4c. Calculating the energy of this interaction with AA-CLP indicates that it is also the interaction with the greatest Coulombic contribution to its stability. It is also interesting that the Coulombic contribution to the stability of each polymorph is by far the highest in polymorph I while relatively insignificant in II and III. It should be noted that the author of CLP has shown that the AA-CLP method underestimates the Coulombic contribution to the stability of a structure. This shortcoming is compensated by the polarization term.26 It is therefore likely that the Coulombic contribution to the stability of I is even greater than the values given in Table 5 suggest. For II, three molecule···molecule interactions (other than the C−H···π) contribute more than 15 kJ mol−1 to the stability of

Figure 6. Crystal packing (a), C−H···O (b), and CO···π interactions (c) in III. In this case PMDI-12 crystallizes with two molecules in the asymmetric unit, which have been indicated as A and B on the diagrams. These stack on each other by what appear to be π···π interactions but which are really CO···π interactions as shown in (c). C−H···O interactions occur within the stack, and between neighboring stacks as shown in panel b.

In general, the evaluation of crystal packing by examining close contacts does not give a complete picture of which interactions contribute most to the stability of each polymorph. In this case, the lack of classical hydrogen bonding makes the evaluation of the contribution of the different interactions to the stability of each polymorph even more difficult. Ideally, one 5913

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Table 5. Molecule···Molecule Interaction Energies Contributing the Most to the Stability of Polymorphs I−III as Calculated Using OPROP23 and AA-CLP26 (kJ mol−1)a symmetry (molecule pair) 1 + x, 1 + x, x, 1 + 1 + x, x, 1 +

1 + y, z y, z y, z 1 + y, −1 + z y, −1 + z

−x, y, 0.5 − z 0.5 − x, 0.5 + y, 0.5 − z 0.5 + x, −0.5 + y, 1 + z 0.5 + x, 0.5 + y, 1 + z x, y, 1 + z

OPROP/UNI −70.8 −56.2 −52.1 −19.3 −11.1 −75.9 −39.1 −36.8 −30.7 −10.9

x, y, z (AB) x, −1 + y, z (AB) 1 + x, y, z (AA) 1 + x, y, −1 + z (AA) x, y, 1 + z (AA)

−108.3 −28.2 −27.1 −26.0 −8.7

x, y, z (BA) x, −1 + y, z (BA) 1 + x, y, z (BB) x, 1 + y, z (BB) 1 + x, −1 + y, z (BB) 1 + x, −1 + y, −1 + z (BA)

−108.3 −28.2 −25.1 −19.9 −18.0 −8.0

AA-CLP (total)

AA-CLP (Coulombic)

AA-CLP (polarization)

polymorph I −64.9 0.6 −14.0 −51.3 −7.9 −13.1 −43.9 −13.8 −14.0 −19.4 0.1 −5.1 −11.6 0.4 −3.7 polymorph II −59.9 3.5 −13.9 −33.0 −3.4 −9.4 −28.9 0.2 −8.7 −29.1 −0.7 −8.5 −11.5 −0.1 −3.3 polymorph III (interaction environment around molecule A) −86.3 −1.2 −21.2 −21.2 −1.3 −7.4 −27.8 0.1 −8.4 −26.4 −0.4 −6.5 −9.2 −0.1 −2.7 polymorph III (interaction environment around molecule B) −86.3 −1.2 −21.2 −21.2 −1.3 −7.4 −25.5 0.6 −8.4 −12.7 −2.0 −6.2 −17.1 −1.1 −5.4 −8.6 0.1 −2.6

AA-CLP (dispersion)

AA-CLP (repulsion)

−76.0 −50.4 −53.4 −20.8 −15.5

24.5 20.1 37.2 6.4 7.2

−73.8 −33.9 −35.1 −36.8 −12.3

24.2 13.7 14.8 16.8 4.2

−103.2 −26.7 −33.1 −29.6 −7.8

39.3 14.1 13.5 9.8 1.5

−103.2 −26.7 −34.3 −17.8 −16.3 −11.1

39.3 14.1 16.6 13.4 5.8 5.0

a The molecule pairs involved in the various interactions for polymorph III are also indicated. Diagrams for each molecule pair can be found in the Supporting Information.

Figure 7. Arrangement of molecules contributing most to the stability of the three polymorphs: (a) C−H···π interaction in I (1 + x, 1 + y, z; OPROP energy = −70.8 kJ mol−1); (b) molecules involved in ribbon forming C−H···O interactions in I (x, 1 + y, z; OPROP energy = −52.1 kJ mol−1); (c) C−H···π interaction in II (−x, y, 0.5 − z; OPROP energy = −75.9 kJ mol−1); (d) CO···π interaction between molecules A and B within a π···π stack in III (x, y, z; OPROP energy = −108.3 kJ mol−1).

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support much weaker C−H···O interactions in most cases and only dispersion forces in others. As a consequence they contribute only about 25% of the stability of the stacking interaction. In the case of molecule A, four interactions from surrounding molecules contribute more than 15 kJ mol−1 to the stability of the structure. Two of these involve interactions between molecules A and B, while the remaining two involve interactions between two A molecules. In the case of molecule B, five interactions from surrounding molecules contribute more than 15 kJ mol−1 to the stability of the structure. As in molecule A, two of these involve interactions between molecules A and B, while the remaining three involve interactions between two B molecules. The results of the lattice energy calculation at 0 K using AACLP and OPROP are given in Table 6. Since the molecules in the three polymorphs have different conformations, the contribution of the intramolecular energies (relative to the molecule in polymorph II) as determined with M06/6-31+ +G(d,p) have been added to the lattice energies to obtain the relative energy of each polymorph. The order of crystal densities as listed in Table 1 are 1.188, 1.191, and 1.237 g cm−3 for polymorphs III, I, and II, respectively. Higher crystal densities are taken to usually indicate stronger interactions between the molecules in a structure.1 Assuming that the polymorph with the highest crystal density is the most stable suggests that polymorph II is the most stable followed by I and then III. The calculations (Table 6) indicate that polymorph II is the most stable of the three polymorphs at 0 K followed by I. The least stable of the three polymorphs is III. It is interesting to note that in this work we obtained polymorph I on only one occasion after the crystals precipitated out during the first synthesis of this compound. Further crystallizations from subsequent synthesis attempts led to polymorph II. Recrystallization from isopropanol at room temperature also leads to polymorph II. While checking the homogeneity of the polymorph I sample by powder X-ray diffraction, we found that grinding leads to its conversion to polymorph II, which is not surprising as the two structures are very similar. These results coupled with a DSC scan of polymorph I (Supporting Information Figure S10a) indicate that it is probably monotropically metastable with respect to the other polymorphs. Polymorph III was first obtained after solidification of a melt at around 170 °C but was also obtained by crystallization from acetic acid during later syntheses. We have also been able to grow polymorph III by slow evaporation from chloroform but this may be due to polymorph contamination of laboratory equipment and clothing. Finally, we have carried out several DSC studies of polymorphs II and III to see if the relationship between the polymorphs is enantiotropic (Supporting Information Figure S10), but the results suggest the likely presence of additional polymorphs near the melting point of this compound.

the structure, one more than polymorph I. All of these include C−H···O interactions between the 12-membered ring and the pyromellitic diimide component (see Supporting Information Figure S6). It is interesting to note that one C−H···O interaction is listed in Table 3 for II, while the lattice energy program indicates that two others are also significant when coupled with other atom...atom contacts present in the respective molecule...molecule interactions (Supporting Information Figure S6). The reason for this is that the C− H···O interactions listed in Table 3 are those found when using standard distance and angle criteria, while the additional C− H···O interactions would have been listed as very long and as a consequence unlikely. The combination of each of these molecule···molecule interactions results in a distinctive feature of polymorph II where the pyromellitic diimide components are isolated from each other. The interaction environment around each molecule is also more uniform, which results in this polymorph having the lowest lattice energy and being more stable than the others when the sum of these interactions is taken into account (Table 6). A similar case has been Table 6. Lattice, Intramolecular, and Total Energies for Polymorphs I−III (kJ mol−1) at 0 Ka OPROP/UNI lattice energy intramolecular energy total energyb lattice energy intramolecular energy total energyb lattice energy intramolecular energy total energyb

polymorph I −236.6 1.8 −234.8 polymorph II −260.4 0 −260.4 polymorph III −236.7 10.3c −226.4

AA-CLP −234.1 1.8 −232.3 −238.4 0 −238.4 −221.6 10.3c −211.3

a

Lattice energies were calculated using OPROP or AA-CLP, while the relative intramolecular energies (relative to molecule B from polymorph III) were calculated with the M06 DFT functional using Gaussian-09 and a 6-31++G(d,p) basis set. bSum of the lattice (intermolecular) and intramolecular energies to give the total energy per mole in a particular polymorph. cPolymorph III contains two molecules in the asymmetric unit. As a consequence the average energy of these two molecules (the per mole value) has been added to account for the contribution of the intramolecular energies to this polymorph.

highlighted by Nangia,2 where experimental evidence and lattice energy calculations indicate that polymorph 3 of tosylhydrazone is more stable than polymorph 1, even though a N−H···O hydrogen bond present in polymorph 1 is absent in polymorph 3. This result also shows that an analysis of atom···atom interactions in the form of close contacts may not be enough when evaluating the characteristics of one polymorph with respect to another (see also refs 27−29). There are two molecules in the asymmetric unit of III, and the calculations indicate that the molecule···molecule interaction environment is different for each molecule. The strongest molecule···molecule interaction by far occurs in polymorph III. This particular geometry supports the CO···π interactions between molecules A and B in this structure creating the stacks distinctive to this structure (Figure 7d). The remaining molecule...molecule arrangements in this structure

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SUMMARY Three polymorphs of PMDI-12 have been obtained and their crystal structures elucidated. Polymorphs I and II differ mainly in crystal packing and can therefore be classified as packing polymorphs. Molecules in III have a different conformation to those in I and II and, as a consequence, III can be regarded as a conformational polymorph of I or II. The conformation of the 12-membered ring is, however, relatively unchanged in each polymorph. Extracting structures with singly substituted 12 membered rings from the CSD (both organic and organo5915

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(9) Barooah, N.; Baruah, J. B. J. Mol. Struct. 2008, 872, 205−211. (10) APEX2, version 2.0-1; Bruker AXS Inc.: Madison, WI, U.S.A., 2005. (11) SAINT+, version 6.0 (includes XPREP and SADABS); Bruker AXS Inc.: Madison, WI, U.S.A., 2005. (12) Sheldrick, G. M. Acta Crystallogr., Sect. A 2008, 64, 112−122. (13) Farrugia, L. J. J. Appl. Crystallogr. 1997, 30, 565. (14) Keller, E. University of Freiberg, Germany, 1999. (15) Farrugia, L. J. J. Appl. Crystallogr. 1999, 32, 837−838. (16) Spek, A. L. Acta Crystallogr., Sect. D 2009, 65, 148−155. (17) Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, 157−167. (18) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö .; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussion 09, Revision A.02; Gaussian Inc.: Wallingford, CT, 2009. (19) (a) Vosko, S. H.; Wilk, L.; Nusait, M. Can. J. Phys. 1980, 58, 1200−1211. (b) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785−789. (c) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623−11627. (d) Becke, A. D. J. Chem. Phys. 1993, 98, 5648−5652. (20) Allinger, N. L. J. Am. Chem. Soc. 1977, 99, 8127−8134. (21) Allinger, N. L.; Yuh, Y. H.; Lii, J.-H. J. Am. Chem. Soc. 1989, 111, 8551−8566. (22) Chen, C.-T.; Liao, S.-Y.; Lin, K.-J.; Lai, L.-L. Adv. Mater. 1998, 3, 334−338. (23) Gavezzotti, A. OPiX, A computer program package for the calculation of intermolecular interactions and crystal energies; University of Milano: Milan, Italy, 2003. (24) Filippini, G.; Gavezzotti, A. Acta Crystallogr., Sect. B 1993, 49, 868−880. (25) Filippini, G.; Gavezzotti, A. J. Phys. Chem. 1994, 98, 4831−4837. (26) Gavezzotti, A. New J. Chem. 2011, 35, 1360−1368. (27) Dunitz, J. D.; Gavezzotti, A. Angew. Chem., Int. Ed. 2005, 44, 1766−1787. (28) Dunitz, J. D.; Gavezzotti, A. Cryst. Growth Des. 2005, 5, 2180− 2189. (29) Zipp, C. F.; Fernandes, M. A.; Marques, H. M.; Michael, J. P.; Perry, C. B. Cryst. Growth Des. 2011, 11, 1431−1436.

metallic compounds were examined), and superimposing the 12-membered rings and those obtained in this work on each other, indicates that the 12-membered rings almost exclusively adopt a square like [3333] conformation regardless of the type of substitution on the ring. This has large consequences if the reason for choosing a 12-membered ring was its assumed conformational flexibility. Unlike other cycloalkane rings, cyclododecane has a dominant conformation that has been theoretically shown to be very stable. In this work, singly substituted cyclododecane has shown itself to be relatively unaffected by polymorphism. Examining structures from the CSD has also shown that the conformation of singly substituted 12-membered rings are relatively unaffected by chemical substitution. In molecules capable of classical hydrogen bonding, close contacts can be used to identify important structure forming motifs which are usually described by means of graph sets. However, it is not possible to use close contacts to identify structure determining arrangements of molecules (motifs) in structures of compounds such as PMDI-12, which are not capable of classical hydrogen bonds. The use of lattice energy calculations to identify important arrangements of molecules that are structure determining and hence fulfill the same role as hydrogen bonding motifs in structures containing strong hydrogen bonds is therefore required. In this work, calculated molecule···molecule interactions have been used to identify a structure-determining arrangement of molecules (motif) common to polymorphs I and II. They have also helped identify the most important, and probably structure determining, interactions in the various polymorphs.

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ASSOCIATED CONTENT

S Supporting Information *

Crystal coordinates as CIF files for polymorphs I−III. This material is available free of charge via the Internet at http:// pubs.acs.org. The CIF files can also be obtained from the Cambridge Crystallographic Data Centre (CCDC) as 873577− 873579.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +27-11-7176723. Fax: +27-11-7176749. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to thank the University of the Witwatersrand and the South African National Research Foundation (GUN 77102), Pretoria for financial support.

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REFERENCES

(1) Bernstein, J. Polymorphism in Molecular Crystals; Oxford University Press: New York, 2002; pp 40−41, 164−165. (2) Nangia, A. Acc. Chem. Res. 2018, 41, 595−604. (3) Anet, A. L.; Rawdah, T. N. J. Am. Chem. Soc. 1978, 100, 7166− 7171. (4) Dale, J. Top. Stereochem. 1976, 9, 199−270. (5) Kolossváry, I; Guida, W. C. J. Am. Chem. Soc. 1993, 115, 2107− 2119. (6) Saunders, M. J. Comput. Chem. 1991, 12, 645−663. (7) Christensen, I. T.; Jørgensen, F. S. J. Comput.-Aided Mol. Des. 1997, 11, 385−394. (8) Allen, F. H. Acta Crystallogr., Sect. B 2002, 58, 380−388. 5916

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