High-Z' and twinning behavior in 3,4-dinitro­benzoic acid

The title compound, C₇H₄N₂O₆, (I), crystallizes in P with Z' = 4, but with no approximate or pseudosymmetry. The crystals were nonmerohedrally twinned, with at least four twin components related to the major moiety by 180° rotations around the real b and c axes, and by 180° rotation around the a* axis. The excessive twinning is not caused by a phase change from an untwinned room-temperature higher-symmetry polymorph. The mol­ecules are planar chiral and, owing to the tilt angle of the nitro groups and the position of protonation, there are altogether eight conformers possible. Six of these theoretically possible eight conformers are realized in the solid-state structure of (I). Packing analysis and force-field calculations indicate that the largest part of the packing inter­actions does not originate from the hydrogen-bonding inter­actions, as one might initially be tempted to assume; [pi]-[pi] stacking and O_nitro...[pi] inter­actions between neighboring mol­ecules of (I) seem to be the dominant factor that determines the packing observed in the structure of this nitro-substituted benzoic acid derivative.

S1. Comment

Structures which crystallize with Z' > 1, i.e. structures that are built from more than one chemically identical but crystallographically distinct entity, have over the last decades become one of the focal points of crystallographic research. Around 8.8% of molecular solids crystallize with more than one crystallographically independent molecule per unit cell (Anderson et al., 2006), but at this time the reasons for the phenomenon of crystallization are still not well understood. High-Z' structures are often associated with commensurate modulation, which can help to avoid mismatch of spacing between molecules in a simpler parent structure with a lower Z' value (Hao et al., 2005). Pseudo-symmetry or structure modulation is however not a necessary requirement for crystallization with Z' > 1, and most high-Z' structures cannot be reduced to a simpler parent structure with fewer crystallographically unique molecules. The two most cited reasons for the Z ' > 1 phenomenon, for both modulated and/or not [non?] modulated structures, are the non-self-complementary shape of the molecules, and competing strong directional interactions (Steed, 2003; Desiraju, 2007; Anderson & Steed, 2007; Anderson et al., 2008). Specifically pointed out also was the formation of centrosymmetric synthons in combination with chirality of the molecules (Anderson et al., 2006). As a consequence of these incompatibilities, there are many structures for which the observed Z' > 1 crystal does genuinely represent the most stable form as the particular molecule simply cannot pack in a higher symmetry without generating highly unfavorable steric interactions, creating large lattice voids or sacrificing highly stabilizing, directional interactions.

3,4-Dinitro-substituted benzoic acids are important precursors for the production of peripherally substituted metallotetraaza[14]annulenes (MTAAs). MTAAs are porphyrin analogs with either a planar or saddle-shaped geometry depending on the substituents placed on the diiminato framework of the molecule (Weiss et al., 1976, 1977; Ricciardi et al., 1995; Mandon et al., 1987; Wooodruff et al., 1976). MTAAs have been extensively studied because when partially oxidized they become electronically conducting materials, while in their reduced forms they are electronic insulators. They can also be polymerized chemically or electrochemically via coupling at the diiminato proton (Ricciardi et al., 1995; Bailey et al., 1984, 1986a,b; Hochgesang & Bereman, 1988; Miry et al., 2000). Electrochemically polymerized MTAAs are of particular value owing to the fact that their red/ox potentials can be tuned depending on the electron-donating or -withdrawing characteristics of the peripheral substituents. In addition to their unique electrochemical properties, they also have interesting optical properties, being black in the oxidized form and golden in their reduced form. During our investigations into the synthesis and properties of MTAAs, we attempted to synthesize several derivatives of (I) as starting materials for the synthesis of MTAAs. As the structure of the parent 3,4-dinitrobenzoic acid was yet unknown, we attempted to establish its single-crystal structure for comparison and reference purposes. The structures of 2,4-dinitrobenzoic acid [Cambridge Structural Database (CSD) refcode BIPJUF [ref]] and 2,5-dinitrobenzoic acid (CSD refcode DAJXUH [ref]) had been reported in the 1980s by Krygowski and coworkers (Wieckowski & Krygowski, 1985; Grabowski & Krygowski, 1985), and for 3,5-dinitrobenzoic acid two polymorphs (CSD refcode CUKCAM01 in P2₁/c and CUKCAM02 and in C2/c) have been described (Prince et al. 1991; Kanters et al., 1991; Domenicano et al., 1990). The structure of 3,4-dinitrobenzoic acid was, however, suspiciously unknown.

Initial attempts to grow single crystals of (I) and collect data were hampered by a tendency of the compound to form excessively twinned crystals. Crystals of (I) were grown from a variety of solvents, including water, ethanol–water and deuterated chloroform (see Experimental). Crystals did readily form from all of these solvents and all crystallization attempts yielded the same solvent-free polymorph, but specimens from all batches suffered from excessive non-merohedral twinning. Prompted by the excessive twinning the samples were also analyzed by scanning electron microscopy (SEM) analysis. A representative selection of crystals were mounted on carbon tape and Pd–Au coated for SEM analysis. Crystals imaged by SEM were typically rod shaped, with lengths of up to ca 0.4 mm, and on average slightly less than 100 µm wide, but much smaller crystals were also present. Most crystals were intergrown and clearly not single, with crystals aligned at various angles between 60 and 80°, leading to intersecting rods as shown in Fig. 1(a), or at angles less than 10°, thus forming frayed rods with an irregular shape instead of clear crystal faces. Some crystals, such as the specimen shown in Fig. 1(b), appeared well formed with clearly defined crystal faces. Even these well formed crystals, however, showed clear signs of twinning in the form of layers that stretch throughout the crystals along the long axis of the rods (dark and light gray layers as seen in Fig. 1b). The thickness of the twin domains varies between just a few and up to a few dozen micrometres. At the resolution of the SEM images the layered twin domains formed this way are perfectly parallel with another, thus not affecting the shape or macroscopic appearance of the crystallites. The SEM images thus revealed that all specimens selected were macroscopically twinned, but even the largest twin domains were only a few dozen micrometres thick, thus making it impossible to isolate an untwinned sample still large enough to use for single-crystal X-ray diffraction with a normal laboratory sealed-tube X-ray source. Based on the SEM micrograph observations we thus screened multiple crystals from all batches for both diffraction intensity and degree of twinning (see Refinement for details). The least twinned specimens had still at least four major twin components which originated from the major moiety by 180° rotations around the real b and c axes, and by a 180° rotation around the a* axis. In all samples for which partial data were collected the data overlap of neighboring spots was substantial, with many spots showing multiple consecutive overlaps in a 'chain of pearls' fashion, and many diffraction spots were thus automatically rejected by the integration program (SAINT; Bruker, 2009). For a recent example of a twinned structure suffering from similar excessive consecutive peak overlay problems, see e.g. Kumar et al. (2010). The crystal of (I) eventually selected for a complete data collection (a fragment of a larger crystal) showed a rejection rate of around 30–40%, and collection of a full sphere of data via ω scans led to a 96% complete data set up to 25° (with molybdenum radiation). Additional collection of ϕ scans did not significantly increase the completeness of the data set any further. The distribution of the data among the four twin domains is shown in Table S1 in the Supplementary material, and the exact twin matrices identified by the integration program are given in Table S2.

The title compound crystallizes in space group P1 and with four crystallographically independent molecules per unit cell. A displacement ellipsoid plot of the symmetry-independent molecules A through D is shown in Fig. 2. The configurations of the four independent molecules in the lattice show substantial variation. There are four independent variables that formally define the molecular geometry of the 3,4-dinitrobenzoic acid molecules upon crystallization and freezing out of fast equilibration through either proton transfer or rotation of nitro groups. The 3,4-dinitro substitution makes the molecules planar chiral. The place of protonation at the carboxylic acid group in relation to the position of the nitro groups transforms the two planar chiral enantiomers into two diastereomeric pairs of enantiomers. The nitro groups in the molecules of (I) are, however, not co-planar with the plane of the phenyl ring, thus adding two more variables that define the molecular geometry of the molecules. In common to all four molecules observed in the solid-state structure are the approximate absolute values of the angles between the phenyl and nitro groups, which vary between 26.4 (2) and 64.8 (2)°. Also in common to all molecules is that the direction of rotation of the two nitro groups within each molecule is necessarily linked, i.e. the nitro groups in each molecule are tilted in the same direction in order to avoid close O_nitro-to-O_nitro contacts between neighboring substituents. The tilt direction of the NO₂ groups can thus be handled as one single variable for each molecule. Adding this variable to the inherent planar chiral nature of the molecule and the position of protonation creates eight possible enantiomers for the molecules of (I), or four diastereomeric pairs of enantiomers. Of the possible four types of diastereomers, three are realized in the solid-state structure of (I). Taking the centrosymmetry of the structure into account, six of the theoretically possible eight enantiomers are observed. Fig. 3 shows how the molecules are related. A least-squares overlay of molecules A and D (red and orange [in the electronic version of the paper]) shows them to have identical conformations with both the position of protonation as well as the tilt direction of the nitro groups being the same with respect to the position of the nitro substituents. In molecules B and C the site of protonation is switched when compared to A and D. In B and C the hydroxy group is located on the same side as the nitro group, in A and D [it is] on opposite sides. B and C are, in contrast to A and D, not superimposable with each other and form members of two different groups of diastereomers differentiated by the tilt direction of the nitro groups (Fig. 3).

The tilt angles of the nitro groups against the planes of the benzene rings are mostly within the ranges seen in other aromatic nitro compounds. Only for molecule C is one of the dihedral angles significantly larger than one would expect [64.8 (2)°, plane of C2C—C7C, N1C against C4C, N1C, O3C, O4C], and a comparison with other similar molecules flagged this torsion angle as unusually large. Out of 10 000 entries in the CSD, only 618 had nitro-phenyl torsion angles of 65° or higher. It should be noted that molecule C also carries the smallest of all nitro-phenyl torsion angles, 26.4 (2)° for the nitro group of N2C, and steric interaction of this nitro group, which is nearly coplanar with the aromatic ring, is a possible reason for the unusually large nitro-phenyl torsion angle of 64.8 (2)° for the nitro group of N1C. All other molecular parameters of all four molecules are within the expected ranges for this type of molecule [CSD Mogul geometry check (Macrae et al., 2008; CCDC, 2009), based on CSD V5.32, November 2010 (Bruno et al., 2002)].

The molecules are arranged as dimers connected via pairwise hydrogen bonds with the motif typical for carboxylic acids [graph-set motif R²₂(8)]. Molecules A form pairs with molecules D, and molecules B with C (Fig. 4). Both dimers are pseudo-centrosymmetric with the nitro groups in the 3- and 4-positions of the two benzene rings related by non-crystallographic inversion centers located in the center of the hydrogen-bonded carboxylic acids, but none of the dimers are actually centrosymmetric in the solid state (no crystallographic inversion centers relate the two molecules of the dimers with each other).

Both the AD as well as the BC dimers are arranged in double layers of parallel dimers with a substantial π···π-stacking interaction component. The distances of the average molecular planes of the dimers, as defined by all non-hydrogen atoms aside of [apart from?] the nitro O atoms of each dimer, are 3.447 Å for the plane of the AD dimers and 3.349 Å for that of the BC dimers.

Individual pairs of dimers are, however, slightly offset as shown in Fig. 5 for the pair of AD dimers. The dimers are closest towards the center of the pair of dimers with a distance between planes there being less than 3 Å (the H1D···O2D distance is 2.937 Å, indicating the possibility of the hydrogen bond from O1D—H1D being bifurcated and having in addition to the main hydrogen bond towards O2A a smaller component towards O1D). Towards the tail ends of the pair of dimers the planes are moving further apart, probably due to the tilting of the nitro groups of molecule D which exhibit through their oxygen atoms close contacts with the π-electron density of the nitro and phenyl groups of molecule A. Fig. 5 shows a summary of these interactions: red dotted lines symbolize O–H···O hydrogen bonds (including the possible weak H1D···O2D interaction), blue dotted lines represent significant π···π-stacking interactions at the center of the pairs of dimers, and black dotted lines show the most important O_nitro···π interactions towards the fringe of the double dimeric assemblies.

The BC pairs of dimers are arranged in a similar but slightly different way (Fig. 6). The center of symmetry that connects the two dimers is, as in the case of AD, shifted, but not along the direction of the axis of the dimers, but perpendicular to this axis. The BC dimers thus are shifted sideways against each other and do mostly not come to rest atop of one another. As a consequence, the number of direct contacts involving the π···π stacking interactions is much lower for the BC pairs of dimers than it was for AD, and no possible additional hydrogen bonding interactions between the dimers are possible. O_nitro···π interactions are limited to that of one nitro-oxygen of molecule B to one nitro π-system of molecule C.

The pairs of dimers, both AD and BC, are translated along the a axis of the cell leading to infinite double strands of π-stacked parallel molecules. Perpendicular to the a axis the infinite AD and BC strands are tilted against each other and arranged in a herringbone fashion (Fig. 7). The tilt angle of the planes, again defined by all non-hydrogen atoms with the exception of the nitro O atoms of each AD and BC dimer, is 65.69°.

Using UNI force-field calculations, approximate energies for intermolecular potentials were estimated (Gavezzotti, 1994, Gavezzotti & Filippini, 1994), yielding a total packing energy of -527.0 kJ mol^-1. Intermolecular potentials given are the sum of coulombic, polarization, dispersion and repulsion terms as defined in the PIXEL method. Hydrogen-atom positions were normalized prior to the calculations, O—H distances to 0.993, C—H distances to 1.089 Å. Among the significant interactions found were of course the intermolecular potentials associated with the two R²₂(8) hydrogen-bonding interactions, with -40.9 and -32.3 kJ mol^-1 for the CB and the AD dimers, respectively. These interactions were however not the strongest interactions, but were ranked by the force-field calculation only as fourth and sixth. Altogether six substantial interactions with a stabilization energy of over 30 kJ mol^-1 were detected, with four of them, including the strongest ones, being stacking interactions between the molecules of (I). The largest intermolecular potential, at -45.6 kJ mol^-1, is observed between two of the C molecules across a crystallographic inversion center. The second strongest, at -44.4 kJ mol^-1 nearly as pronounced, is a stacking interaction between molecules A and D. In this case the molecules are parallel to one another, and not related by inversion symmetry. Interestingly, all strong interactions above 30 kJ mol^-1 are between either the A and D, or between the B and C molecules. No such interactions are found between A and B or C, or D and B or C, thus indicating the formation of two separate `regions' or `clusters' within the structure with no strong interactions between molecules of the two regions. The force-field calculations thus agree with and substantiate the results of the sum of the individual interactions as discussed in the packing arrangements section above, but indicate that the largest part of the packing interactions do not originate from the hydrogen-bonding interactions, as one might initially be tempted to assume; indeed the π···π stacking and O_nitro···π interactions between neighboring molecules of 3,4-dinitrobenzoic acid molecules are the dominant factor that determines the packing observed in the structure of this nitro-substituted benzoic acid.

Equivalent calculations were performed for the 2,4- and 2,5- and the two 3,5-isomers of dinitrobenzoic acid [BIPJUF, DAJXUH (Wieckowski & Krygowski, 1985; Grabowski & Krygowski, 1985); CUKCAM01 in P2₁/c (Prince et al. 1991), CUKCAM02 and in C2/c (Kanters et al., 1991; Domenicano et al., 1990)]. The two polymorphs of the 3,5-isomer are structurally related, and the conformations of the molecules and their arrangement in hydrogen-bonded dimers in the two structures are virtually identical. The packing of the dimeric units is also related, with layers two molecules thick along the a axes of both structures being superimposable. The structures are distinguished by the nature of the successive layers along this axis: in the primitive P2₁/c structure the third and fourth layer are located in the next unit cell and are created by translation; in CUKCAM02 the third and fourth layer are part of the larger C-centered cell and a result of the twofold axis present only in this double-volume cell but not in the primitive setting of CUKCAM01 (overlays and comparisons of CUKCAM01 and CUKCAM02 are provided as supplementary figures S1 and S2).

The force-field calculations performed for the 2,4- and 2,5- and the two 3,5-isomers of dinitrobenzoic acid do not mirror the results for 3,4-dinitrobenzoic acid. In all of these four structures the R²₂(8) hydrogen-bonding interactions were significantly more pronounced than in 3,4-dinitrobenzoic acid, with individual intermolecular potentials between -46.59 and -48.61 kJ mol^-1 (for the P2₁/c polymorph of the 3,5-isomer and the 2,4-isomer, respectively). Only for the 2,5- isomer was the intermolecular potential associated with the R²₂(8) hydrogen bond not the strongest individual interaction. In this molecule an intermolecular interaction associated with a strong symmetric π-stacking interaction with an interplanar separation of 3.54 Å was attributed -49.32 kJ mol^-1, versus -47.74 kJ mol^-1 for the potential associated with the R²₂(8) hydrogen bond. These results point towards a substantial weakening of the hydrogen-bonding interactions in 3,4-dinitrobenzoic acid when compared to its 2,4- and 2,5- and the two 3,5-isomers, with stabilization energies for the two hydrogen bonds in the 3,4-isomer that are around 7 and 15 kJ mol^-1 weaker than their counterparts in the 2,4- and 2,5- and the two 3,5-isomers. Compared to other aromatic carboxylic acid dimers the weakening of the hydrogen bonds in 3,4-dinitrobenzoic acid seems to be even more pronounced. Values reported by Gavezotti using the same method (PIXELS) were generally lower than -50 kJ mol^-1 and clustered around -70 kJ mol^-1 (Gavezzotti, 2008).

An analysis of the actual hydrogen-bonding parameters in the structure of (I) does provide some additional evidence for a diminished hydrogen-bonding strength. The O···O distances within all five structures are, after correction for the different data-collection temperatures (the current data set was collected at 100 K, all others at room temperature), comparable with each other, but those of the 3,4-isomer appear to be somewhat elongated when compared to those of the other isomers. The values for the 2,4- and 2,5- and the two 3,5-isomers at room temperature are 2.656, 2.622, 2.633 and 2.636 Å; those for the 3,4-isomer at 100 K are 2.607 (4) and 2.619 (4) Å for the AD dimer, and 2.604 (4) and 2.615 (4) Å for the BC dimer. Correction of these values for the difference in data-collection temperature, e.g. by 0.048 Å as was observed for 2,4,6-trimethylbenzoic acid (CSD entries TMBZAC02 to TMBZAC05, Wilson & Goeta, 2004), would raise the O···O distances above those observed for the other isomers by 0.021 and 0.025 Å for the BC and the AD dimers, respectively. While these values might be able to explain some of the weakening of the hydrogen bonds, they seem not substantial enough to explain the full 7 and 15 kJ mol^-1 loss in stabilization predicted by the UNI force-field calculations. The total packing energies per molecule indicated a slightly more favorable packing arrangemnet for the 2,4- and 2,5- and the two 3,5-dinitrobenzoic acids when compared to the 3,4-isomer (-132.88, -135.13, -132.11 and -133.37 kJ mol^-1 versus -131.75 kJ mol^-1 per molecule, respectively).

In their 2006 paper on the prevalence of large Z' values in systems that can form tightly hydrogen-bonded dimeric structures Steed and coworkers (Anderson et al., 2006) analyzed carboxylic acid derivatives and similar molecules for their tendency to form high-Z' structures. For carboxylic acid derivatives such as the title compound they found that there is indeed a connection between the ability of a system to form an R²₂(8) COOH dimer motif and the number of crystallographically independent molecules in the structure, but that this Z' behavior is limited to only chiral carboxylic acid structures. If they crystallize in a non-chiral setting they do not behave significantly differently from other organic compounds as a whole [chiral structures containing the COOH dimer motif crystallize with Z' > 1 in 13.9% of cases, compared with 10.7% for achiral carboxylic acids and 8.8% of structures in the CSD as whole (Anderson et al., 2006)].

High Z' values are often associated with pseudo-symmetry, and pairs of molecules tend to be related to each other by approximate translations, rotations or centers of symmetry. Many of these structures only deviate slightly from higher symmetry with only small energetic differences between the high-Z' form and a (hypothetical) higher-symmetry form. As a consequence higher-temperature polymorphs can often be found in which the differences between crystallographically independent molecules present in the low-temperature polymorph are lost. Often associated with a phase change from a higher-symmetry high-temperature form to the lower-symmetry low-temperature form is twinning (pseudo-merohedral and/or non-merohedral). As the crystals of the title compound are heavily twinned by several non-merohedral twin operations, the structure was thus investigated for the possible presence of pseudo-symmetry or temperature-dependent phase changes. A PLATON analysis for missed symmetry did not however yield any additional pseudo-symmetry or pseudo-translation, even with the most relaxed search criteria (Spek, 2009). This is in agreement with the already described presence of six of the theoretically possible eight enantiomers in the crystal structure (see molecular geometry discussion). The presence of so many conformationally different molecules makes an arrangement of similar entities related by pseudo-symmetry and especially pseudo-translation difficult to realize.

To more confidently rule out any pseudo-symmetry as the cause for either the high Z' value or the pronounced twinning the crystals were tested for the possible presence of a phase change between room temperature and 100 K. The unit cells found at room temperature differed only marginally from those at 100 K, and no difference with regard to the degree or type of twinning was observed. The presence of twinning at room temperature, and not only upon cooling to 100 K, is also confirmed by the room temperature SEM images (Fig. 1), which revealed clear signs of excessive twinning for all crystals analyzed. The structure of (I) described here thus seems to be a genuine Z' = 4 structure with no approximate or pseudo-symmetry, and the excessive twinning observed is not caused by a phase change from an untwinned room-temperature higher-symmetry polymorph. This is also supported by the fact that crystals of (I) grown by three different methods from different solvents yielded the same polymorph and all crystals from all batches showed the same types of twinning, regardless of the way they had been grown (slow cooling of a hot aqueous solution, slow evaporation of a chloroform solution, or vapor diffusion of water into an ethanol solution at constant temperature). This points towards the observed polymorph of (I) with Z' = 4 to be the actual thermodynamically most stable crystal form (but this cannot be ascertained with absolute surety, of course), which raises the question of what causes the molecule to crystallize in this complicated high-Z' structure. Reasons for compounds to crystallize with more than one crystallographically independent molecule are manifold, and no single principle can be found to be responsible to explain the Z' > 1 phenomenon. However, some causes seem to be observed on a regular basis that are associated with a higher than usual tendency to crystallize with Z' > 1: a non-self-complementary shape of the molecules, and competing strong directional interactions (Steed, 2003, Desiraju, 2007, Anderson & Steed, 2007, Anderson et al., 2008). For 3,4-dinitrobenzoic acid, both of these causes seem to be playing some role, but especially competition between strong directional hydrogen-bonding interactions and other less directional but in their sum equally strong forces such as π···π stacking and O_nitro···π interactions seem to affect the molecules' ability to pack in a simple regular arrangement. The packing with a high Z' value is made easier by the number of possible conformations that the molecule can assume. By realizing six of the eight energetically comparable conformers in the solid state 3,4-dinitrobenzoic acid is able to achieve a solid-state arrangement in which competition between hydrogen-bonding, π···π stacking and O_nitro···π interactions are balanced to a degree to allow for effective packing with a total packing energy similar to that observed for the other isomers of dinitrobenzoic acid that do not suffer that much from packing frustration as the 3,4-isomer.

Related literature

For related literature, see: Anderson & Steed (2007); Anderson et al. (2006, 2008); Bailey et al. (1984, 1986a, 1986b); Bruker (2005, 2008, 2009); Bruno et al. (2002); CCDC (2009); Desiraju (2007); Domenicano et al. (1990); Gavezzotti (1994, 2008); Gavezzotti & Filippini (1994); Grabowski & Krygowski (1985); Hao et al. (2005); Hochgesang & Bereman (1988); Kanters et al. (1991); Kumar et al. (2010); Macrae et al. (2008); Mandon et al. (1987); Miry et al. (2000); Prince et al. (1991); Ricciardi et al. (1995); Sheldrick (2008); Spek (2009); Steed (2003); Weiss et al. (1976, 1977); Wieckowski & Krygowski (1985); Wilson & Goeta (2004); Wooodruff et al. (1976).

S2. Experimental

3,4-Dinitrobenzoic acid (99%) was obtained from Alfa-Aesar. Crystallization was first accomplished by serendipitous crystal formation from deuterated chloroform in an NMR tube. Crystals from this batch, and from other attempts using chloroform as the solvent, yielded only excessively twinned samples not suitable for X-ray diffraction (see Refinement section for details regarding the twinning). Slow diffusion of water into a solution of (I) in ethanol yielded well formed crystals, but the crystals were still excessively twinned and none of several setups with different solvent and compound ratios yielded crystals suitable for X-ray single-crystal diffraction. In another attempt to obtain X-ray-quality crystals deionized water was used and crystallization was achieved by heating of small samples of either saturated solutions to boiling followed by slow cooling, or by slow cooling of room-temperature solutions to 277.5 K. The crystals obtained that way were somewhat improved with less [fewer] twin domains and diffraction spot overlaps, but still not suitable for collection of a usable X-ray data set. An increase of both solvent volume and sample amount (using a 100 ml Erlenmeyer flask and several grams of 3,4-dinitrobenzoic acid) to achieve a decreased cooling rate and slower crystal growth (and thus larger domain sizes and less twinning) did still lead to crystals that were mostly excessively twinned. Among the bulk of these samples some crystals were however identified as possible candidates for data collection, and these specimens were chosen for crystal screening (see Refinement section).

S3. Refinement

The crystals of the sample were found to be excessively non-merohedrally twinned. SEM imaging of several representative crystals indicated the presence of macroscopic twin domains, but individual domains were not larger than just a few micrometres, and on average much smaller (see Fig. 1b). Multiple crystals were screened and orientation matrices for the twin components were identified using the program CELL_NOW (Bruker, 2005). From the tested crystals about half a dozen were selected for partial data collection based on their diffraction power, the number of twin components present, and the degree of overlap of the twin components. All of these final crystals had at least four major twin components created from the major component by 180° rotations around the real axes [0 1 0] and [0 0 1], and by 180° rotation around the reciprocal axis (1 0 0). In all samples for which partial data were collected the data overlap of neighboring spots was significant with many spots showing multiple consecutive overlaps in a 'chain of pearls' fashion, and many diffraction spots were thus automatically rejected by the integration program (SAINT; Bruker, 2009). Most integrated data showed rejection rates of 50% and above. Attempts to collect data at a larger crystal-to-detector distance did not significantly lower the number of rejected reflections. The crystal selected for a complete data collection (a fragment of a larger crystal) showed a rejection rate around 30–40%. Data were collected with 90 s exposure time per frame at 100 K. Collection of a hemisphere of data using ω scans yielded a data set slightly less than 80% complete. Collection of the other half of the full sphere led to a 93% complete data set up to 26.37° in θ, and 96% to 25°. Additional collection of ϕ scans did not significantly increase the completeness of the data set any further.

The twin laws found by CELL_NOW for the final crystal chosen were a rotation from the first domain by a 180° about reciprocal axis 0 1 0 (domain 2), a 180° rotation about reciprocal axis 0 0 1 (domain 3) and 180° rotation about the real axis 1 0 0 (domain 4).

The distribution of the data among the four twin domains is shown in Table S1, and the exact twin matrices identified by the integration program in Table S2.

The final data were corrected for absorption using TWINABS (Bruker, 2008), and the structure was solved using direct methods with only the non-overlapping reflections of component 1. Using the HKLF 5 least-square refinement method for non-merohedrally twinned as specified in SHELXL (Sheldrick, 2008), the structure was refined with all reflections of component 1 (including all overlapping diffraction spots) with a resolution better than 0.8 Å, resulting in BASF values of 0.071 (1), 0.191 (1), and 0.061 (1).

The total number of reflections given (_diffrn_reflns_av_R_equivalents) is before the cutoff at 0.8 Å. The R_int value given is for these reflections and is based on agreement between observed single and composite intensities and those calculated from refined unique intensities and twin fractions before the cutoff at 0.8 Å.

H atoms attached to carbon atoms were positioned geometrically and constrained to ride on their parent atoms, with C—H distances of 0.95 Å, and with U_iso(H) = 1.2 U_eq(C). The hydroxy H atoms were refined in calculated positions at a fixed C—O—H angle, but the C—C—O—H dihedral angle and the O—H distance were allowed to refine [AFIX 148 command in SHELXTL (Sheldrick, 2008), and with U_iso(H) = 1.5 U_eq(O). The O—H distances in the four crystallographically independent molecules were restrained to be the same within a standard deviation of 0.02 Å.

Computing details

Data collection: APEX2 (Bruker, 2009); cell refinement: SAINT (Bruker, 2009); data reduction: SAINT (Bruker, 2009) and TWINABS (Bruker, 2008; Sheldrick, 2008); program(s) used to solve structure: SHELXTL (Bruker, 2003; Sheldrick, 2008); program(s) used to refine structure: SHELXTL (Bruker, 2003; Sheldrick, 2008); molecular graphics: SHELXTL (Bruker, 2003; Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Bruker, 2003; Sheldrick, 2008) and publCIF (Westrip, 2010).

Figures

	Fig. 1. SEM micrographs of crystals of 3,4-dinitrobenzoic acid. a) a selection of crystals typical of the the batch as a whole at 100 × magnification. b) a not intergrown crystal at 400 × magnification showing the layering of twin domains (lighter and darker areas within apparently single crystals). Crystals were gold-palladium coated for SEM imaging.
	Fig. 2. Plot of the crystallographically independent section of the structure of 3,4-dinitrobenzoic acid. Displacement ellipsoids of non-hydrogen atoms are at the 50% level. Hydrogen atoms are represented as capped sticks.
	Fig. 3. Least squares overlay of molecules A and D (red and orange) and B and C (blue and green) in top and side view. Molecules A and D have identical conformations with both the position of protonation as well as the tilt direction of the nitro groups being the same. In molecules B and C the site of protonation is switched when compared to A and D. B and C are not superimposable with each other and are differentiated by the tilt direction of the nitro groups.
	Fig. 4. Packing view of the structure of 3,4-dinitrobenzoic acid, viewing direction down the a-axis. Colour coding as in Figure 3.
	Fig. 5. Pairs of dimers of molecules A and D (colour coding as in Figure 3). Red dotted lines are O–H···O hydrogen bonds (including the weak H1D···O2D interaction), blue dotten lines are significant π···π stacking interactions, black dotted lines are Onitro···π interactions.
	Fig. 6. Pairs of dimers of molecules B and C (colour coding as in Figure 3). Red dotted lines are O–H···O hydrogen bonds, blue dotted lines are significant π···π stacking interactions, black dotted lines are Onitro···π interactions.
	Fig. 7. Depiction of the infinite double strands of π stacked parallel molecules, view down the a-axis. Perpendicular to the a-axis the infinite AD and BC strands are tilted against each other and arranged in a herringbone fashion with a tilt angle of the planes (indicated in opaque red) of 66.15°.

3,4-dinitrobenzoic acid

Crystal data

C7H4N2O6	Z = 8
Mr = 212.12	F(000) = 864
Triclinic, P1	Dx = 1.750 Mg m^−3
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 7.373 (6) Å	Cell parameters from 1266 reflections
b = 13.06 (1) Å	θ = 2.8–23.7°
c = 16.800 (12) Å	µ = 0.16 mm^−1
α = 89.633 (12)°	T = 100 K
β = 88.194 (12)°	Rod, colourless
γ = 84.838 (11)°	0.25 × 0.09 × 0.06 mm
V = 1610 (2) Å^3

Data collection

Bruker AXS SMART APEX CCD diffractometer	7991 independent reflections
Radiation source: fine-focus sealed tube	6572 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.088
ω scans	θmax = 26.4°, θmin = 1.2°
Absorption correction: multi-scan (TWINABS; Bruker, 2008)	h = −9→9
Tmin = 0.935, Tmax = 1.000	k = −16→16
34980 measured reflections	l = 0→20

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.062	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.164	H atoms treated by a mixture of independent and constrained refinement
S = 1.07	w = 1/[σ^2(Fo^2) + (0.0505P)^2 + 4.2636P] where P = (Fo^2 + 2Fc^2)/3
7991 reflections	(Δ/σ)max < 0.001
552 parameters	Δρmax = 0.33 e Å^−3
6 restraints	Δρmin = −0.39 e Å^−3

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
C1A	−0.1748 (6)	0.3161 (3)	0.4909 (2)	0.0173 (9)
C2A	−0.0332 (5)	0.2391 (3)	0.5214 (2)	0.0174 (9)
C3A	−0.0812 (6)	0.1502 (3)	0.5586 (2)	0.0171 (8)
H3A	−0.2058	0.1375	0.5645	0.021*
C4A	0.0520 (6)	0.0804 (3)	0.5869 (2)	0.0183 (9)
C5A	0.2346 (6)	0.1005 (3)	0.5777 (3)	0.0205 (9)
C6A	0.2837 (6)	0.1872 (3)	0.5405 (3)	0.0222 (9)
H6A	0.4087	0.1987	0.5338	0.027*
C7A	0.1499 (6)	0.2583 (3)	0.5126 (2)	0.0207 (9)
H7A	0.1823	0.3198	0.4875	0.025*
C1B	0.7176 (6)	−0.0138 (3)	0.1083 (2)	0.0183 (9)
C2B	0.5747 (6)	0.0529 (3)	0.1506 (2)	0.0159 (8)
C3B	0.6206 (6)	0.1303 (3)	0.2004 (2)	0.0171 (8)
H3B	0.7447	0.1383	0.2103	0.021*
C4B	0.4850 (6)	0.1945 (3)	0.2350 (2)	0.0177 (9)
C5B	0.3016 (6)	0.1809 (3)	0.2224 (2)	0.0176 (9)
C6B	0.2568 (6)	0.1034 (3)	0.1751 (2)	0.0197 (9)
H6B	0.1326	0.0935	0.1673	0.024*
C7B	0.3934 (6)	0.0393 (3)	0.1385 (3)	0.0194 (9)
H7B	0.3629	−0.0144	0.1049	0.023*
C1C	0.9087 (6)	0.1878 (3)	−0.0053 (2)	0.0178 (9)
C2C	0.7653 (6)	0.2655 (3)	0.0249 (2)	0.0188 (9)
C3C	0.8125 (6)	0.3551 (3)	0.0590 (2)	0.0184 (9)
H3C	0.9368	0.3676	0.0630	0.022*
C4C	0.6772 (6)	0.4254 (3)	0.0868 (2)	0.0174 (9)
C5C	0.4949 (6)	0.4060 (3)	0.0828 (2)	0.0194 (9)
C6C	0.4483 (6)	0.3167 (3)	0.0484 (2)	0.0180 (9)
H6C	0.3242	0.3031	0.0457	0.022*
C7C	0.5842 (6)	0.2477 (3)	0.0182 (2)	0.0187 (9)
H7C	0.5537	0.1873	−0.0076	0.022*
C1D	0.4717 (6)	0.4964 (3)	0.3902 (2)	0.0170 (8)
C2D	0.3322 (6)	0.5598 (3)	0.3452 (2)	0.0171 (9)
C3D	0.3801 (6)	0.6451 (3)	0.3028 (2)	0.0164 (8)
H3D	0.5029	0.6619	0.2997	0.020*
C4D	0.2451 (6)	0.7050 (3)	0.2655 (2)	0.0161 (8)
C5D	0.0660 (6)	0.6779 (3)	0.2694 (2)	0.0174 (9)
C6D	0.0197 (6)	0.5930 (3)	0.3103 (2)	0.0182 (9)
H6D	−0.1029	0.5758	0.3125	0.022*
C7D	0.1539 (6)	0.5326 (3)	0.3486 (2)	0.0177 (9)
H7D	0.1246	0.4729	0.3770	0.021*
N1A	−0.0013 (5)	−0.0088 (3)	0.6303 (2)	0.0228 (8)
N2A	0.3814 (5)	0.0241 (3)	0.6020 (2)	0.0271 (9)
N1B	0.5386 (5)	0.2818 (3)	0.2794 (2)	0.0203 (8)
N2B	0.1543 (5)	0.2460 (3)	0.2618 (2)	0.0229 (8)
N1C	0.7358 (5)	0.5192 (3)	0.1224 (2)	0.0226 (8)
N2C	0.3469 (5)	0.4803 (3)	0.1116 (2)	0.0209 (8)
N1D	0.2907 (5)	0.7989 (3)	0.2250 (2)	0.0194 (8)
N2D	−0.0796 (5)	0.7408 (3)	0.2288 (2)	0.0203 (8)
O1A	−0.1239 (4)	0.3942 (2)	0.45596 (18)	0.0220 (7)
H1A	−0.226 (3)	0.434 (2)	0.438 (3)	0.033*
O2A	−0.3398 (4)	0.2973 (2)	0.50174 (17)	0.0214 (7)
O3A	−0.1339 (5)	−0.0484 (2)	0.6085 (2)	0.0298 (7)
O4A	0.0881 (4)	−0.0377 (3)	0.6878 (2)	0.0348 (8)
O5A	0.3854 (5)	−0.0613 (3)	0.5745 (2)	0.0385 (9)
O6A	0.4935 (5)	0.0548 (3)	0.6453 (2)	0.0440 (10)
O1B	0.6778 (4)	−0.0780 (2)	0.05976 (18)	0.0221 (7)
O2B	0.8836 (4)	0.0019 (2)	0.12393 (19)	0.0240 (7)
H2B	0.964 (3)	−0.046 (3)	0.097 (3)	0.036*
O3B	0.6498 (4)	0.2651 (3)	0.33030 (19)	0.0304 (8)
O4B	0.4718 (4)	0.3668 (2)	0.25907 (18)	0.0258 (7)
O5B	0.1795 (5)	0.2772 (2)	0.32821 (19)	0.0303 (8)
O6B	0.0139 (4)	0.2636 (3)	0.2254 (2)	0.0304 (8)
O1C	0.8676 (4)	0.1124 (2)	−0.04249 (18)	0.0223 (7)
O2C	1.0745 (4)	0.2049 (2)	0.00943 (18)	0.0218 (7)
H2C	1.155 (3)	0.156 (3)	−0.016 (3)	0.033*
O3C	0.8151 (5)	0.5749 (2)	0.0772 (2)	0.0316 (8)
O4C	0.7067 (5)	0.5325 (3)	0.1929 (2)	0.0341 (8)
O5C	0.3770 (4)	0.5703 (2)	0.11290 (19)	0.0275 (7)
O6C	0.2021 (4)	0.4465 (3)	0.1316 (2)	0.0330 (8)
O1D	0.4206 (4)	0.4250 (2)	0.43327 (18)	0.0201 (6)
H1D	0.516 (4)	0.398 (3)	0.463 (2)	0.030*
O2D	0.6364 (4)	0.5201 (2)	0.38426 (17)	0.0209 (6)
O3D	0.4215 (4)	0.7928 (2)	0.17913 (19)	0.0272 (7)
O4D	0.1949 (5)	0.8771 (2)	0.24225 (19)	0.0280 (7)
O5D	−0.0465 (4)	0.7665 (3)	0.16074 (19)	0.0295 (8)
O6D	−0.2213 (4)	0.7614 (3)	0.2664 (2)	0.0293 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C1A	0.017 (2)	0.020 (2)	0.015 (2)	−0.0031 (17)	0.0000 (16)	−0.0020 (17)
C2A	0.014 (2)	0.020 (2)	0.018 (2)	0.0006 (16)	−0.0024 (16)	−0.0004 (17)
C3A	0.015 (2)	0.020 (2)	0.016 (2)	−0.0038 (16)	0.0000 (16)	−0.0010 (17)
C4A	0.018 (2)	0.019 (2)	0.018 (2)	−0.0015 (17)	0.0002 (17)	−0.0006 (17)
C5A	0.018 (2)	0.024 (2)	0.019 (2)	0.0014 (17)	−0.0009 (17)	−0.0016 (18)
C6A	0.012 (2)	0.032 (2)	0.024 (2)	−0.0069 (18)	−0.0019 (17)	0.0026 (19)
C7A	0.022 (2)	0.023 (2)	0.018 (2)	−0.0056 (18)	−0.0002 (18)	−0.0005 (18)
C1B	0.019 (2)	0.017 (2)	0.020 (2)	−0.0057 (17)	−0.0048 (17)	0.0019 (17)
C2B	0.018 (2)	0.015 (2)	0.015 (2)	−0.0053 (16)	−0.0028 (16)	0.0032 (16)
C3B	0.018 (2)	0.017 (2)	0.017 (2)	−0.0031 (16)	−0.0061 (16)	0.0030 (17)
C4B	0.022 (2)	0.018 (2)	0.014 (2)	−0.0053 (17)	−0.0041 (16)	−0.0010 (17)
C5B	0.016 (2)	0.018 (2)	0.019 (2)	−0.0018 (16)	−0.0005 (16)	0.0012 (17)
C6B	0.016 (2)	0.022 (2)	0.022 (2)	−0.0050 (17)	−0.0034 (17)	−0.0010 (18)
C7B	0.018 (2)	0.021 (2)	0.020 (2)	−0.0058 (17)	−0.0027 (17)	−0.0025 (18)
C1C	0.020 (2)	0.021 (2)	0.013 (2)	−0.0049 (17)	−0.0026 (17)	0.0026 (17)
C2C	0.023 (2)	0.020 (2)	0.013 (2)	−0.0045 (17)	−0.0002 (17)	−0.0017 (17)
C3C	0.015 (2)	0.023 (2)	0.018 (2)	−0.0066 (17)	−0.0024 (16)	0.0003 (18)
C4C	0.017 (2)	0.020 (2)	0.016 (2)	−0.0083 (17)	−0.0016 (17)	−0.0008 (17)
C5C	0.019 (2)	0.022 (2)	0.018 (2)	−0.0023 (17)	−0.0009 (17)	0.0006 (17)
C6C	0.014 (2)	0.022 (2)	0.019 (2)	−0.0041 (17)	−0.0021 (16)	−0.0030 (17)
C7C	0.020 (2)	0.021 (2)	0.017 (2)	−0.0062 (17)	−0.0056 (17)	−0.0020 (17)
C1D	0.018 (2)	0.017 (2)	0.0157 (19)	−0.0004 (16)	0.0017 (16)	−0.0033 (17)
C2D	0.017 (2)	0.018 (2)	0.016 (2)	−0.0011 (16)	−0.0013 (16)	−0.0042 (17)
C3D	0.014 (2)	0.019 (2)	0.016 (2)	−0.0035 (16)	0.0021 (16)	−0.0031 (17)
C4D	0.020 (2)	0.0136 (19)	0.014 (2)	−0.0021 (16)	0.0001 (16)	−0.0032 (16)
C5D	0.017 (2)	0.019 (2)	0.016 (2)	−0.0003 (16)	−0.0028 (16)	−0.0024 (17)
C6D	0.014 (2)	0.022 (2)	0.020 (2)	−0.0032 (16)	−0.0004 (16)	−0.0001 (17)
C7D	0.019 (2)	0.018 (2)	0.016 (2)	−0.0045 (17)	−0.0007 (17)	−0.0006 (17)
N1A	0.022 (2)	0.0224 (19)	0.023 (2)	0.0036 (16)	0.0001 (16)	0.0021 (16)
N2A	0.0170 (19)	0.034 (2)	0.030 (2)	−0.0006 (16)	−0.0002 (17)	0.0045 (18)
N1B	0.024 (2)	0.0207 (19)	0.0173 (18)	−0.0059 (15)	−0.0023 (15)	−0.0030 (15)
N2B	0.025 (2)	0.0200 (18)	0.024 (2)	−0.0045 (15)	0.0015 (16)	−0.0037 (16)
N1C	0.0195 (19)	0.0219 (19)	0.027 (2)	−0.0035 (15)	−0.0056 (16)	−0.0041 (17)
N2C	0.021 (2)	0.023 (2)	0.0183 (18)	−0.0006 (16)	−0.0010 (15)	−0.0026 (15)
N1D	0.0165 (18)	0.0232 (19)	0.0191 (18)	−0.0043 (15)	−0.0059 (15)	0.0000 (15)
N2D	0.019 (2)	0.0190 (18)	0.023 (2)	−0.0036 (15)	−0.0043 (15)	−0.0026 (15)
O1A	0.0197 (16)	0.0194 (15)	0.0270 (17)	−0.0025 (12)	−0.0026 (13)	0.0063 (13)
O2A	0.0135 (15)	0.0297 (17)	0.0217 (16)	−0.0042 (12)	−0.0032 (12)	0.0044 (13)
O3A	0.0291 (18)	0.0257 (17)	0.0362 (19)	−0.0094 (14)	−0.0033 (15)	−0.0007 (15)
O4A	0.0244 (18)	0.044 (2)	0.034 (2)	0.0030 (15)	−0.0009 (15)	0.0180 (16)
O5A	0.031 (2)	0.0273 (19)	0.056 (2)	0.0049 (15)	−0.0008 (17)	0.0039 (17)
O6A	0.0259 (19)	0.052 (2)	0.054 (2)	0.0047 (17)	−0.0183 (18)	0.001 (2)
O1B	0.0196 (15)	0.0217 (15)	0.0255 (16)	−0.0031 (12)	−0.0037 (13)	−0.0080 (13)
O2B	0.0146 (15)	0.0242 (16)	0.0334 (18)	−0.0003 (13)	−0.0034 (13)	−0.0101 (14)
O3B	0.0275 (18)	0.0338 (18)	0.0302 (18)	−0.0006 (14)	−0.0123 (15)	−0.0114 (15)
O4B	0.0364 (19)	0.0177 (16)	0.0239 (17)	−0.0042 (14)	−0.0041 (14)	−0.0030 (13)
O5B	0.037 (2)	0.0308 (18)	0.0234 (17)	−0.0043 (15)	0.0058 (15)	−0.0093 (14)
O6B	0.0191 (17)	0.0307 (18)	0.041 (2)	−0.0001 (14)	−0.0027 (15)	−0.0021 (15)
O1C	0.0193 (15)	0.0206 (15)	0.0279 (17)	−0.0068 (12)	−0.0009 (13)	−0.0073 (13)
O2C	0.0130 (15)	0.0285 (17)	0.0241 (16)	−0.0026 (12)	−0.0023 (12)	−0.0079 (13)
O3C	0.035 (2)	0.0243 (17)	0.0375 (19)	−0.0121 (15)	0.0001 (16)	−0.0002 (15)
O4C	0.039 (2)	0.0361 (19)	0.0282 (19)	−0.0086 (16)	−0.0064 (15)	−0.0118 (15)
O5C	0.0293 (18)	0.0222 (16)	0.0305 (18)	−0.0009 (13)	0.0007 (14)	−0.0033 (14)
O6C	0.0179 (17)	0.0388 (19)	0.043 (2)	−0.0075 (14)	0.0023 (14)	−0.0074 (16)
O1D	0.0158 (15)	0.0212 (15)	0.0232 (16)	−0.0003 (12)	−0.0016 (12)	0.0048 (13)
O2D	0.0134 (14)	0.0261 (16)	0.0236 (16)	−0.0026 (12)	−0.0024 (12)	0.0002 (13)
O3D	0.0218 (17)	0.0293 (17)	0.0301 (17)	−0.0034 (13)	0.0046 (14)	0.0059 (14)
O4D	0.0337 (19)	0.0169 (16)	0.0331 (18)	−0.0026 (14)	0.0035 (14)	−0.0002 (14)
O5D	0.0300 (18)	0.0344 (19)	0.0243 (17)	−0.0030 (14)	−0.0059 (14)	0.0084 (14)
O6D	0.0169 (17)	0.0325 (18)	0.0379 (19)	0.0008 (14)	−0.0027 (14)	−0.0004 (15)

Geometric parameters (Å, º)

C1A—O1A	1.255 (5)	C5C—N2C	1.466 (6)
C1A—O2A	1.270 (5)	C6C—C7C	1.373 (6)
C1A—C2A	1.483 (6)	C6C—H6C	0.9500
C2A—C3A	1.384 (6)	C7C—H7C	0.9500
C2A—C7A	1.398 (6)	C1D—O1D	1.254 (5)
C3A—C4A	1.373 (6)	C1D—O2D	1.281 (5)
C3A—H3A	0.9500	C1D—C2D	1.485 (6)
C4A—C5A	1.398 (6)	C2D—C3D	1.385 (6)
C4A—N1A	1.448 (5)	C2D—C7D	1.391 (6)
C5A—C6A	1.361 (6)	C3D—C4D	1.374 (6)
C5A—N2A	1.470 (6)	C3D—H3D	0.9500
C6A—C7A	1.384 (6)	C4D—C5D	1.397 (6)
C6A—H6A	0.9500	C4D—N1D	1.460 (5)
C7A—H7A	0.9500	C5D—C6D	1.365 (6)
C1B—O1B	1.234 (5)	C5D—N2D	1.473 (5)
C1B—O2B	1.294 (5)	C6D—C7D	1.381 (6)
C1B—C2B	1.473 (6)	C6D—H6D	0.9500
C2B—C7B	1.386 (6)	C7D—H7D	0.9500
C2B—C3B	1.388 (6)	N1A—O3A	1.214 (5)
C3B—C4B	1.363 (6)	N1A—O4A	1.224 (5)
C3B—H3B	0.9500	N2A—O5A	1.208 (5)
C4B—C5B	1.403 (6)	N2A—O6A	1.215 (5)
C4B—N1B	1.457 (5)	N1B—O3B	1.209 (5)
C5B—C6B	1.360 (6)	N1B—O4B	1.224 (5)
C5B—N2B	1.462 (6)	N2B—O5B	1.216 (5)
C6B—C7B	1.382 (6)	N2B—O6B	1.221 (5)
C6B—H6B	0.9500	N1C—O4C	1.209 (5)
C7B—H7B	0.9500	N1C—O3C	1.220 (5)
C1C—O1C	1.236 (5)	N2C—O5C	1.216 (5)
C1C—O2C	1.294 (5)	N2C—O6C	1.228 (5)
C1C—C2C	1.477 (6)	N1D—O3D	1.213 (5)
C2C—C7C	1.383 (6)	N1D—O4D	1.219 (5)
C2C—C3C	1.384 (6)	N2D—O6D	1.213 (5)
C3C—C4C	1.366 (6)	N2D—O5D	1.214 (5)
C3C—H3C	0.9500	O1A—H1A	0.9345
C4C—C5C	1.394 (6)	O2B—H2B	0.9311
C4C—N1C	1.472 (5)	O2C—H2C	0.9282
C5C—C6C	1.380 (6)	O1D—H1D	0.9202
O1A—C1A—O2A	124.6 (4)	C4C—C5C—N2C	121.7 (4)
O1A—C1A—C2A	118.2 (4)	C7C—C6C—C5C	118.9 (4)
O2A—C1A—C2A	117.1 (4)	C7C—C6C—H6C	120.5
C3A—C2A—C7A	120.4 (4)	C5C—C6C—H6C	120.5
C3A—C2A—C1A	120.7 (4)	C6C—C7C—C2C	120.5 (4)
C7A—C2A—C1A	118.9 (4)	C6C—C7C—H7C	119.7
C4A—C3A—C2A	119.7 (4)	C2C—C7C—H7C	119.7
C4A—C3A—H3A	120.1	O1D—C1D—O2D	124.1 (4)
C2A—C3A—H3A	120.1	O1D—C1D—C2D	118.2 (4)
C3A—C4A—C5A	119.3 (4)	O2D—C1D—C2D	117.7 (4)
C3A—C4A—N1A	118.9 (4)	C3D—C2D—C7D	121.7 (4)
C5A—C4A—N1A	121.7 (4)	C3D—C2D—C1D	119.9 (4)
C6A—C5A—C4A	121.6 (4)	C7D—C2D—C1D	118.4 (4)
C6A—C5A—N2A	117.5 (4)	C4D—C3D—C2D	118.2 (4)
C4A—C5A—N2A	120.7 (4)	C4D—C3D—H3D	120.9
C5A—C6A—C7A	119.4 (4)	C2D—C3D—H3D	120.9
C5A—C6A—H6A	120.3	C3D—C4D—C5D	120.1 (4)
C7A—C6A—H6A	120.3	C3D—C4D—N1D	119.0 (4)
C6A—C7A—C2A	119.6 (4)	C5D—C4D—N1D	120.9 (4)
C6A—C7A—H7A	120.2	C6D—C5D—C4D	121.6 (4)
C2A—C7A—H7A	120.2	C6D—C5D—N2D	117.8 (4)
O1B—C1B—O2B	123.4 (4)	C4D—C5D—N2D	120.6 (4)
O1B—C1B—C2B	120.9 (4)	C5D—C6D—C7D	118.9 (4)
O2B—C1B—C2B	115.7 (4)	C5D—C6D—H6D	120.6
C7B—C2B—C3B	120.3 (4)	C7D—C6D—H6D	120.6
C7B—C2B—C1B	119.2 (4)	C6D—C7D—C2D	119.6 (4)
C3B—C2B—C1B	120.5 (4)	C6D—C7D—H7D	120.2
C4B—C3B—C2B	119.0 (4)	C2D—C7D—H7D	120.2
C4B—C3B—H3B	120.5	O3A—N1A—O4A	124.5 (4)
C2B—C3B—H3B	120.5	O3A—N1A—C4A	117.8 (4)
C3B—C4B—C5B	120.6 (4)	O4A—N1A—C4A	117.6 (4)
C3B—C4B—N1B	117.4 (4)	O5A—N2A—O6A	125.8 (4)
C5B—C4B—N1B	121.8 (4)	O5A—N2A—C5A	117.9 (4)
C6B—C5B—C4B	120.3 (4)	O6A—N2A—C5A	116.2 (4)
C6B—C5B—N2B	118.3 (4)	O3B—N1B—O4B	125.6 (4)
C4B—C5B—N2B	121.4 (4)	O3B—N1B—C4B	117.9 (3)
C5B—C6B—C7B	119.5 (4)	O4B—N1B—C4B	116.4 (3)
C5B—C6B—H6B	120.2	O5B—N2B—O6B	125.1 (4)
C7B—C6B—H6B	120.2	O5B—N2B—C5B	117.9 (4)
C6B—C7B—C2B	120.3 (4)	O6B—N2B—C5B	117.0 (4)
C6B—C7B—H7B	119.9	O4C—N1C—O3C	126.3 (4)
C2B—C7B—H7B	119.9	O4C—N1C—C4C	117.9 (4)
O1C—C1C—O2C	123.7 (4)	O3C—N1C—C4C	115.7 (4)
O1C—C1C—C2C	120.3 (4)	O5C—N2C—O6C	125.5 (4)
O2C—C1C—C2C	116.0 (4)	O5C—N2C—C5C	117.4 (4)
C7C—C2C—C3C	120.7 (4)	O6C—N2C—C5C	117.1 (4)
C7C—C2C—C1C	119.3 (4)	O3D—N1D—O4D	126.1 (4)
C3C—C2C—C1C	120.0 (4)	O3D—N1D—C4D	117.5 (4)
C4C—C3C—C2C	118.9 (4)	O4D—N1D—C4D	116.3 (3)
C4C—C3C—H3C	120.6	O6D—N2D—O5D	126.2 (4)
C2C—C3C—H3C	120.6	O6D—N2D—C5D	117.0 (4)
C3C—C4C—C5C	120.6 (4)	O5D—N2D—C5D	116.7 (4)
C3C—C4C—N1C	116.4 (4)	C1A—O1A—H1A	109.5
C5C—C4C—N1C	123.0 (4)	C1B—O2B—H2B	109.5
C6C—C5C—C4C	120.4 (4)	C1C—O2C—H2C	109.5
C6C—C5C—N2C	117.8 (4)	C1D—O1D—H1D	109.5
O1A—C1A—C2A—C3A	−178.3 (4)	C1C—C2C—C7C—C6C	177.5 (4)
O2A—C1A—C2A—C3A	1.1 (6)	O1D—C1D—C2D—C3D	174.0 (4)
O1A—C1A—C2A—C7A	2.3 (6)	O2D—C1D—C2D—C3D	−4.1 (6)
O2A—C1A—C2A—C7A	−178.3 (4)	O1D—C1D—C2D—C7D	−4.2 (6)
C7A—C2A—C3A—C4A	0.0 (6)	O2D—C1D—C2D—C7D	177.6 (4)
C1A—C2A—C3A—C4A	−179.5 (4)	C7D—C2D—C3D—C4D	1.7 (6)
C2A—C3A—C4A—C5A	0.1 (6)	C1D—C2D—C3D—C4D	−176.5 (4)
C2A—C3A—C4A—N1A	175.9 (4)	C2D—C3D—C4D—C5D	−1.3 (6)
C3A—C4A—C5A—C6A	−0.8 (6)	C2D—C3D—C4D—N1D	176.0 (4)
N1A—C4A—C5A—C6A	−176.5 (4)	C3D—C4D—C5D—C6D	0.5 (6)
C3A—C4A—C5A—N2A	−175.4 (4)	N1D—C4D—C5D—C6D	−176.7 (4)
N1A—C4A—C5A—N2A	8.9 (6)	C3D—C4D—C5D—N2D	−179.3 (3)
C4A—C5A—C6A—C7A	1.4 (7)	N1D—C4D—C5D—N2D	3.5 (6)
N2A—C5A—C6A—C7A	176.2 (4)	C4D—C5D—C6D—C7D	−0.1 (6)
C5A—C6A—C7A—C2A	−1.3 (6)	N2D—C5D—C6D—C7D	179.7 (4)
C3A—C2A—C7A—C6A	0.7 (6)	C5D—C6D—C7D—C2D	0.5 (6)
C1A—C2A—C7A—C6A	−179.9 (4)	C3D—C2D—C7D—C6D	−1.3 (6)
O1B—C1B—C2B—C7B	3.4 (6)	C1D—C2D—C7D—C6D	176.9 (4)
O2B—C1B—C2B—C7B	−178.5 (4)	C3A—C4A—N1A—O3A	36.9 (6)
O1B—C1B—C2B—C3B	−175.0 (4)	C5A—C4A—N1A—O3A	−147.4 (4)
O2B—C1B—C2B—C3B	3.0 (6)	C3A—C4A—N1A—O4A	−141.4 (4)
C7B—C2B—C3B—C4B	−2.2 (6)	C5A—C4A—N1A—O4A	34.3 (6)
C1B—C2B—C3B—C4B	176.2 (4)	C6A—C5A—N2A—O5A	−120.2 (5)
C2B—C3B—C4B—C5B	1.9 (6)	C4A—C5A—N2A—O5A	54.7 (6)
C2B—C3B—C4B—N1B	−173.0 (3)	C6A—C5A—N2A—O6A	56.5 (6)
C3B—C4B—C5B—C6B	−0.3 (6)	C4A—C5A—N2A—O6A	−128.6 (5)
N1B—C4B—C5B—C6B	174.4 (4)	C3B—C4B—N1B—O3B	−52.5 (5)
C3B—C4B—C5B—N2B	177.2 (4)	C5B—C4B—N1B—O3B	132.6 (4)
N1B—C4B—C5B—N2B	−8.1 (6)	C3B—C4B—N1B—O4B	124.4 (4)
C4B—C5B—C6B—C7B	−1.0 (6)	C5B—C4B—N1B—O4B	−50.4 (5)
N2B—C5B—C6B—C7B	−178.6 (4)	C6B—C5B—N2B—O5B	144.6 (4)
C5B—C6B—C7B—C2B	0.8 (6)	C4B—C5B—N2B—O5B	−33.0 (6)
C3B—C2B—C7B—C6B	0.9 (6)	C6B—C5B—N2B—O6B	−34.5 (6)
C1B—C2B—C7B—C6B	−177.6 (4)	C4B—C5B—N2B—O6B	147.9 (4)
O1C—C1C—C2C—C7C	6.5 (6)	C3C—C4C—N1C—O4C	−113.3 (4)
O2C—C1C—C2C—C7C	−173.9 (4)	C5C—C4C—N1C—O4C	65.0 (6)
O1C—C1C—C2C—C3C	−173.1 (4)	C3C—C4C—N1C—O3C	64.5 (5)
O2C—C1C—C2C—C3C	6.5 (6)	C5C—C4C—N1C—O3C	−117.2 (5)
C7C—C2C—C3C—C4C	0.7 (6)	C6C—C5C—N2C—O5C	−152.4 (4)
C1C—C2C—C3C—C4C	−179.7 (4)	C4C—C5C—N2C—O5C	25.3 (6)
C2C—C3C—C4C—C5C	1.7 (6)	C6C—C5C—N2C—O6C	26.8 (6)
C2C—C3C—C4C—N1C	−180.0 (4)	C4C—C5C—N2C—O6C	−155.5 (4)
C3C—C4C—C5C—C6C	−1.9 (6)	C3D—C4D—N1D—O3D	49.8 (5)
N1C—C4C—C5C—C6C	179.8 (4)	C5D—C4D—N1D—O3D	−133.0 (4)
C3C—C4C—C5C—N2C	−179.6 (4)	C3D—C4D—N1D—O4D	−128.7 (4)
N1C—C4C—C5C—N2C	2.2 (6)	C5D—C4D—N1D—O4D	48.6 (5)
C4C—C5C—C6C—C7C	−0.2 (6)	C6D—C5D—N2D—O6D	45.9 (5)
N2C—C5C—C6C—C7C	177.5 (4)	C4D—C5D—N2D—O6D	−134.2 (4)
C5C—C6C—C7C—C2C	2.6 (6)	C6D—C5D—N2D—O5D	−133.6 (4)
C3C—C2C—C7C—C6C	−2.9 (6)	C4D—C5D—N2D—O5D	46.3 (5)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1A—H1A···O2D^i	0.93	1.71	2.619 (4)	163
O2B—H2B···O1C^ii	0.93	1.70	2.615 (4)	169
O2C—H2C···O1B^ii	0.93	1.68	2.604 (4)	172
O1D—H1D···O2A^iii	0.92	1.75	2.607 (4)	154

Symmetry codes: (i) x−1, y, z; (ii) −x+2, −y, −z; (iii) x+1, y, z.