The challenging case of the theophylline–benzamide cocrystal

Theophylline has been used as an active pharmaceutical ingredient (API) in the treatment of pulmonary diseases, but due to its low water solubility reveals very poor bioavailability. Based on its different hydrogen-bond donor and acceptor groups, theophylline is an ideal candidate for the formation of cocrystals. The crystal structure of the 1:1 benzamide cocrystal of theophylline, C₇H₈N₄O₂·C₇H₇NO, was determined from synchrotron X-ray powder diffraction data. The compound crystallizes in the tetra­gonal space group P4₁ with four independent mol­ecules in the asymmetric unit. The mol­ecules form a hunter's fence packing. The crystal structure was confirmed by dispersion-corrected DFT calculations. The possibility of salt formation was excluded by the results of Raman and ¹H solid-state NMR spectroscopic analyses.

S1. Introduction

Theophylline (tp) has been used as an active pharmaceutical ingredient (API) for diverse applications since the beginning of the 20t h century (Gremels, 1928; Smith et al., 1935). Recently, tp is used as a powerful bronchodilator and respiratory stimulant treating apnea in infants, as well as acute and chronic asthma (Hendeles & Weinberger, 1983). Due to its low water solubility, this API reveals very poor bioavailability. Based on its different hydrogen-bond donor and acceptor groups, tp is an ideal candidate for the formation of cocrystals (Alhalaweh et al., 2013; Ban et al., 2009; Heiden et al., 2012; Childs et al., 2007; Trask et al., 2006). Cocrystals are multicomponent crystalline systems consisting of uncharged organic compounds stabilized via inter­molecular forces, including hydrogen bonds, π–π inter­actions or halogen bonds (Aakeröy & Salmon, 2005). Cocrystallization with an appropriate coformer allows rendering distinct physicochemical properties of a given API, whereas the molecular structure of the drug and its pharmaceutical affect remains unaffected (McNamara et al., 2006; Good & Rodríguez-Hornedo, 2009; Trask et al., 2005, 2006; Chieng et al., 2009). Cocrystals are of greatinter­est in pharmaceutical research to improve the water solubility of an API in order to decrease the required dosages in the tablets. The possibility to tune crystal structures based on crystal-engineering considerations and to broaden the knowledge on structure–property relationships increases the current inter­est (Sun, 2009). In the present study, we present the crystalline structure of the 1:1 theophylline–benzamide cocrystal determined from synchrotron X-ray powder diffraction data.

S2. Experimental

S2.1. Synthesis and crystallization

Anhydrous theophylline (99%, Sigma–Aldrich, Germany) and benzamide (>=99.5%, Sigma–Aldrich, Germany) were obtained commercially and were used without further purification. Since no single crystals could be obtained by slow evaporation from diverse solvents, the synthesis of the 1:1 cocrystal (in the following abbreviated as the tp:ba cocrystal) was conducted by grinding in a ball mill (MM400, Retsch, Germany) at a frequency of 30 Hz for 25 min. A 10 ml steel vessel with two steel balls (diameter 10 mm) was used for a total load of 1 g. The rea­cta­nts were neat ground in an equimolar ratio.

S2.2. Raman spectroscopy

Raman measurements were performed on a Raman RXN1™ Analyzer (Kaiser Optical Systems, France). The spectra were collected using a laser with a wavelength of λ = 785 nm and a contactless probe head (working distance 1.5 cm, spot size 1.0 mm). Raman spectra were recorded with an acquisition time of 5 s and 5 accumulations. NIR excitation radiation at λ = 785 nm and an irradiation of 6.6 W cm⁻² were performed.

S2.3. Solid-state NMR spectroscopy

¹H MAS NMR measurements were performed on a Bruker AVANCE600 spectrometer using a 2.5 mm double-bearing magic angle spinning (MAS) probe (Bruker Biospin) and applying a spinning speed of 25 kHz. The spectra were recorded with a π/2 pulse length of 2.75 µs, a recycle delay of 300 s and an accumulation number of 32. Existent ¹H rotor and probe background signals were suppressed using the EASY experiment (Jaeger & Hemmann, 2014a,b). Adamantane served as secondary field standard with a ¹H chemical shift of 1.78 p.p.m.

¹H–¹³C CPMAS experiments were run in a 4 mm rotor with a spinning speed of 12.5 kHz (Hartmann & Hahn, 1962). The cross polarization (CP) contact time was 2 ms and the proton spin-lockfield was ramped linearly (ramped-CP) down to 50% of the initial value (Cook et al., 1996). ¹H Two-Pulse Phase Modulation (TPPM) decoupling was applied (Bennett et al., 1995). The ¹³C chemical shifts were referenced to adamantane with 38.5 p.p.m.

S2.4. Synchrotron X-ray diffraction

The powder X-ray diffraction (PXRD) pattern of the tp:ba cocrystal used for structure solution was recorded at the Powder diffraction beamline of the Australian Synchrotron (Melbourne, Australia) at an energy of 12.4012 keV and a beam current of 200 mA using a Si (111) double-crystal monochromator. A Mythen one-dimensional microstrip detector was used to record the scattering intensity (Wallwork et al., 2007). The PXRD patterns were recorded for 10 min.

S2.5. Indexing and structure solution

The synchrotron X-ray powder pattern of the tp:ba cocrystal was indexed using the program DICVOL (Boultif & Louër, 1991). The structure was solved using the simulated annealing routine implemented in the DASH program (David et al., 2006). As starting conformation for the tp and ba molecules, the values of the Cambridge Structural Database (CSD; Groom & Allen, 2014) entries BAPLOT01 (Reference?) and BZAMID05 (Reference?) were used. For the initial structure solution, the configurations of the molecules (two molecules of tp and ba) were kept rigid.

S2.6. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. The structure refinement was carried out by the Rietveld method using the program TOPAS (Rietveld, 1967, 1969; Coelho, 2007). A Pawley refinement was performed including the background, zero-point error, unit-cell parameters, peak-width and peak-asymmetry parameters. For the Rietveld refinements, restraints were applied for all bond lengths, bond angles and planar groups. The data were tested for preferred orientation using the approach of March & Dollase (Dollase, 1986). However, no significant preferred orientation was found. The Rietveld refinement included the atomic coordinates, profile parameters, unit-cell parameters, scale, background,and one overall isotropic displacement parameter for the C, N and O atoms of each molecule. H atoms were included with B_iso(H) = 1.2B_iso(parent atom).

S2.7. Lattice energy minimizations

The crystal structure of the tp:ba cocrystal was optimized by lattice-energy minimizations using dispersion-corrected density functional theory (DFT-D). Calculations were performed by the program GRACE (generation, ranking and charaterization engine; Avant-garde Materials Simulation, 2016) that uses the VASP code for single-point DFT calculations (Dollase, 1986; Kresse & Furthmüller, 1996; Kresse & Hafner, 1993). The PBE functional was combined with an empirical dispersion correction (Neumann & Perrin, 2005). Unit-cell parameters and atomic coordinates of all atoms were optimized without any restraints or constraints. For calculation details, see van de Streek & Neumann (2014).

S3. Results and discussion

S3.1. Solid-state 1H MAS NMR and Raman spectroscopy

The solid-state ¹H MAS NMR (ssNMR) spectrum of the tp:ba cocrystal presented in Fig. 1 shows that the signal of the acidic proton of tp at 14.5 p.p.m. is high-field shifted in the cocrystal spectrum (Baias et al., 2013). Based on this shift it can be assumed that the proton is bridged weaker to ba in the cocrystal as in pure tp, concluding that a the tp:ba cocrystal consists of neutral molecules without a proton transfer from tp to ba. The observed line broadening in the ssNMR spectrum of the cocrystal indicates that the structure may contain more than one symmetrically independent tp (and ba) molecule, which was proven by ¹³C NMR investigations (see Fig. S1 in the Supporting information). The splitting of the tp and ba peaks confirms the presence of independent molecules in the cocrystal lattice.

The Raman data depicted in Fig. 2 support the result of the ssNMR investigations. The absorption bands of the carbonyl groups of tp at 1665 and 1707 cm⁻¹ are only slightly shifted in the cocrystal spectrum (1643 and 1690 cm⁻¹). For a salt formation a shift of 30–40 cm⁻¹ to lower frequencies is expected. Additionally, the stretching band of the secondary amino group at 3123 cm⁻¹ would disappear and instead a new absorption band of the ammonium group would occur between 2000 and 2200 cm⁻¹ (Childs et al., 2007). Since this stretching band shifts in the cocrystal by 5 cm⁻¹ only, a salt formation can be ruled out.

S3.2. Structure determination

Indexing was performed on different laboratory and synchrotron X-ray powder patterns of the tp:ba cocrystal. The X-ray powder diagrams could be indexed unambiguously with a tetra­gonal unit cell with the figures of merit M(20) = 138.8 and F(20) = 510.6 (de Wolff et al., 1968; Smith & Snyder, 1979). Based on the unit-cell volume of V = 2765 ų, a value of Z = 8 is reasonable. A Pawley refinement with this unit cell in P4, i.e. without systematic extinctions, led to a χ² value of 13.9.

The determination of the space group was difficult. Bayesian statistical analysis (Markvardsen et al., 2001) within the program DASH led to P4₂/n or P4₁2₁2 as most probably space groups, each with Z' = 1. In both space groups, the tp and ba molecules had to be positioned on a general position, since Wyckoff positions with site symmetry 1 or 2 cannot be occupied by tp or ba molecules, which both have the molecular symmetry m (C_s). However, all attempts to solve the structure in P4₂/n or P4₁2₁2 from the synchrotron data by real-space methods with simulated annealing using the programs DASH were unsuccessful. Attempts in several other tetra­gonal space groups failed too. Using FOX instead of DASH or laboratory data instead of synchrotron data did not help either (Favre-Nicolin & Cerný, 2002). The manual assessment of the systematic extinctions from the visually absent reflections leads to the following reflection conditions:

(1) hkl: none, corresponding to a primitive Bravais lattice

(2) hk0: h + k = 2n, corresponding to an n-glide plane parallel to (001)

(3) 0kl: none, excluding glide planes parallel to (100)

(4) hhl: none, excluding glide planes parallel to (110)

(5) 00l: l = 4n, corresponding to a 4₁ or 4₃ screw axis.

(6) 0k0, k = 2n, which is included in (2), but would point to a 2₁ screw axis parallel to [010], if the n-glide planes were absent.

(7) hh0: ambiguous (one visible reflection only)

However, the determination of systematic extinctions from the X-ray powder data bears uncertainties due to the high peak overlap, especially in the high 2θ region. For example, reflection condition (2) was based only on the absence of three reflections (010, 210 and 030), and for the 00l reflections the condition l = 4n differed from l = 2n only by the reflections 002 and 006, which were visually absent. The only unambiguous observation was the absence of systematic extinctions of the hkl, 0kl and hhl reflections.

Furthermore, the reflection conditions were contradictory to each other. A 4₁ or 4₃ screw axis cannot be combined with an n-glide plane perpendicular to it. 1 Obviously, at least one of the observed `reflection conditions' was not due to a systematic extinction, but by reflections with accidentally low intensities. The neglect of condition (2) leads to the extinction symbol P4₁2₁–, which corresponds to the space groups P4₁2₁2 and P4₃2₁2. (These two space groups cannot be distinguished from each other from powder data of an achiral compound, because all Friedel pairs systematically overlap, hence P4₃2₁2 was not considered further.) If, on the other hand, reflection condition (5) were only 00l: l = 2n, the space group would be P4₂/n. Hence, the manual determination of systematic extinctions again led to P4₁2₁2 (or P4₃2₁2) and P4₂/n as the most likely space groups.

We ran further trials in P4₁2₁2 and P4₂/n, but without success. We also tested, whether the ba molecule could be situated on the 4₂ axis with site symmetry 2 in P4₂/n, which would cause a twofold orientational disorder of the benzamide molecule, with the O atom being disordered with the amino group. However, the DASH runs did not give sensible results. Similarly, a solution trial in P4₂/n with a disordered ba molecule using two independent molecules with occupancies of 0.5 each, failed.

Although none of the structural models obtained hitherto gave a satisfactory fit to the powder pattern, a visual inspection of the `best of the wrong solutions', i.e. of the models with the lowest χ² values in each space group, revealed that most structures showed a common packing motif: Along the c axis, the structures consisted of four layers of molecules. Within these layers, all molecules were oriented with their molecular planes parallel to (130) and (310), in some other structures parallel to (30) and (310). However, all structures had χ² values of more than 200, which indicated that the assumed crystal symmetries were not the correct ones.

Finally, we considered which crystal symmetries are statistically frequent. We used the statistics of structural classes published by Belsky et al., which contains not only the space groups, but also the number of independent molecules and the molecular site symmetries (Chernikova et al., 1990; Belsky et al., 1995). Out of 19642 investigated organic homomolecular structures, 126 were tetra­gonal with Z = 8. From these structures, the most frequent crystal symmetries were (site symmetries in brackets):

– P4₁2₁2, Z = 8 (1): 49 structures

– P4₂/n, Z = 8 (1): 20 structures

– P2₁c, Z =8 (1): 12 structures

– I, Z = 8 (1): 7 structures

– I4₁/a, Z = 8 (2): 6 structures

– P4₁, Z = 8, Z' = 2 (1,1): 5 structures

– I4₁cd, Z = 8 (2): 5 structures

This statistics again pointed to the space groups P4₁2₁2 and P4₂/n, which were incorrect for the tp:ba cocrystal. Since the hkl, 0kl and hhl reflections clearly did not show any systematic extinction, all other space groups could be ruled out, except P4₁. Hence, we tried to solve the structure of the tp:ba cocrystal in P4₁, Z = 8 with four independent molecules (two tp and two ba) per asymmetric unit.

In P4₁, the crystal structure could be solved from the synchrotron powder pattern by simulated annealing with DASH. In order to reach a better statistic, the number of simulated annealing runs was increased from 25 to 100. The best solution was obtained with a profile χ² value of 33.0 and an intensity χ² value of 47.5. With slightly higher R values, several structures were obtained, which showed a similar molecular packing, but with one or more molecules rotated by 180° around their long molecular axis.

Subsequently, the structure with the lowest χ² value was refined by the Rietveld method using the program TOPAS. The molecular geometry was restrained using restraints on bond lengths, bond angles and planar groups. The Rietveld refinement converged with a smooth difference curve and confidence values of R_p = 1.86% and R_wp = 2.41% (see Fig. 3).

1^? The combination 4₁/n is impossible, because the application of a 4₁ screw operation to a perpendicular n-glide plane generates a second n-glide plane which is parallel to the first one, but shifted by (0, 0, 1/4). If the symmetry operation of the first glide plane is (x', y', z') = (x + 1/2, y + 1/2, −z), that of the second glide plane will be (x', y', z') = (x + 1/2, y + 1/2, −z + 1/2). A consecutive application of both glide planes to an atom on the general position (x, y, z) results in an atom situated at (x + 1, y + 1, z + 1/2), which is equivalent to (y, y, z + 1/2), and denotes a translational copy of the original atom, shifted by (0, 0, 1/2). Hence, every atom has a translational copy shifted by c/2 and the unit cell consists of two identical parts. Thus the unit cell can be transformed by c' = c/2. Thereby the 4₁ screw axes change to 4₂ screw axes. The same argumentation holds for the combination 4₃/n.

S3.3. Proof of the correctness of the crystal structure

A crystal structure of an achiral compound in a chiral space group with Z' ≥ 2 should always be regarded with caution, since it may easily be a case of missed symmetry (Herbstein & Marsh, 1998; Marsh & Spek, 2001; Clemente, 2003). This is especially critical for structures determined from powder data. For example, the low-temperature structure of 4-methyl­pyridine N-oxide, determined by X-ray powder and neutron powder diffraction, was originally published in 2006 in P4₁ (Z = 32 and Z' = 8) (Damay et al., 2006). Indeed, the published atomic coordinates do not show any higher symmetry. Later, a rerefinement led to P4₁2₁2 (Z' = 4) (Palatinus & Damay, 2009). However, for the tp:ba cocrystal there are several facts indicating that the space group is actually correct:

(1) The broadening of the signals in the ¹H MAS NMR spectrum indicates Z' > 1.

(2) There are only two translationengleiche supergroups of P4₁, i.e. P4₁2₁2 and P4₁22. However, the clear orientation of the molecular planes parallel to (130) und (310) contradicts the existence of twofold rotation or screw axis parallel to [100] or [110]. Furthermore, extensive structure solution attempts in P4₁2₁2 failed. Klassengleiche supergroups, such as I4₁ or P4₂ (c' = 2c), can be excluded, because the unit-cell parameters are unambiguous, and the Bravais lattice is clearly primitive.

(3) The molecular packing does not show a higher symmetry. The two formula units within the asymmetric unit are clearly symmetrically independent, and not related by any symmetry element, even not a local one. The hydrogen-bond pattern of the two tp molecules is different from each other; the same is valid for the two ba molecules. Also a rotation of one or more molecules around the long molecular axis does not lead to identical hydrogen-bond patterns.

The correctness of the crystal structure was finally proven by a lattice-energy minimization using dispersion-corrected DFT calculations, including an optimization of the lattice parameters. Upon optimization, the protonation state did not change, and the resulting structure did not show any additional symmetry. Lattice parameters and atomic coordinates changed only slightly. A recent survey of 215 crystal structures, which were solved from powder data and published in IUCr journals, revealed, that during a DFT-D optimization under these conditions, the mean deviation of non-H atoms should be less than 0.35 Å. In the case of higher deviations, the structure is likely either to be incorrect or to exhibit special features such as disorder or unusual thermal expansion (van de Streek & Neumann, 2014). For the tp:ba cocrystal, an r.m.s. value of 0.139 Å could be found. Hence, the crystal structure of the tp:ba cocrystal should be correct. The overlay of the solved crystal structure (red) and the DFT-calculated structure (blue) are presented in Fig. 4.

S3.4. Crystal structure

The tp:ba cocrystal crystallizes in the tetra­gonal space group P4₁ and reveals a slightly higher density than the rea­cta­nts. Two crystallographically independent tp and two independent ba molecules are present in the asymmetric unit (tp1, tp2, ba1, and ba2; Fig. 5). Dimers are formed between tp1 and ba1 molecules and tp2 and ba2 molecules. A dimer between ba1 and tp1 is formed including the carbonyl group and amide group and the secondary amino group and carbonyl group of tp1. The ba2 molecule forms a similar dimer to the tp2 molecule.

The dimers are arranged in sheets. The unit cell contains four sheets, with molecules at z ~~1/8, 3/8, 5/8 and 7/8 (Fig. 6). Within each sheet, all molecules are parallel (Fig. 7). The molecules of the first and third sheets are oriented almost exactly in the (310) direction, and those of the second and fourth sheets in the (30) direction. This leads to a hunter's fence arrangement (Fig. 8). The sheets are connected by hydrogen bonds between the molecular dimers: The amino group of the ba1 molecule forms a hydrogen bond to an imidazole N atom of a tp molecule in a neighbouring sheet, whereas the amino group of the ba2 molecule connects to the O atom of a tp molecule in a neighbouring sheet. This leads to a one-dimensional hydrogen-bond network parallel to the [001] direction.

S4. Conclusion

Based on synchrotron powder data, the extraordinary structure of the theophylline–benzamide cocrystal could be solved. Typically, the API theophylline cocrystallizes with benzamide-similar coformers in monoclinic space groups. However, when theophylline is ground under neat conditions with benzamide the tetra­gonal 1:1 cocrystal is formed in the space group P4₁. DFT-D calculations proved the correctness of this structure solution. Solid-state NMR investigations and Raman spectroscopy confirm that the cocrystal consists of neutral molecules, thus excluding a salt formation.

Structure description

Theophylline (tp) has been used as an active pharmaceutical ingredient (API) for diverse applications since the beginning of the 20t h century (Gremels, 1928; Smith et al., 1935). Recently, tp is used as a powerful bronchodilator and respiratory stimulant treating apnea in infants, as well as acute and chronic asthma (Hendeles & Weinberger, 1983). Due to its low water solubility, this API reveals very poor bioavailability. Based on its different hydrogen-bond donor and acceptor groups, tp is an ideal candidate for the formation of cocrystals (Alhalaweh et al., 2013; Ban et al., 2009; Heiden et al., 2012; Childs et al., 2007; Trask et al., 2006). Cocrystals are multicomponent crystalline systems consisting of uncharged organic compounds stabilized via inter­molecular forces, including hydrogen bonds, π–π inter­actions or halogen bonds (Aakeröy & Salmon, 2005). Cocrystallization with an appropriate coformer allows rendering distinct physicochemical properties of a given API, whereas the molecular structure of the drug and its pharmaceutical affect remains unaffected (McNamara et al., 2006; Good & Rodríguez-Hornedo, 2009; Trask et al., 2005, 2006; Chieng et al., 2009). Cocrystals are of greatinter­est in pharmaceutical research to improve the water solubility of an API in order to decrease the required dosages in the tablets. The possibility to tune crystal structures based on crystal-engineering considerations and to broaden the knowledge on structure–property relationships increases the current inter­est (Sun, 2009). In the present study, we present the crystalline structure of the 1:1 theophylline–benzamide cocrystal determined from synchrotron X-ray powder diffraction data.

Raman measurements were performed on a Raman RXN1™ Analyzer (Kaiser Optical Systems, France). The spectra were collected using a laser with a wavelength of λ = 785 nm and a contactless probe head (working distance 1.5 cm, spot size 1.0 mm). Raman spectra were recorded with an acquisition time of 5 s and 5 accumulations. NIR excitation radiation at λ = 785 nm and an irradiation of 6.6 W cm⁻² were performed.

¹H MAS NMR measurements were performed on a Bruker AVANCE600 spectrometer using a 2.5 mm double-bearing magic angle spinning (MAS) probe (Bruker Biospin) and applying a spinning speed of 25 kHz. The spectra were recorded with a π/2 pulse length of 2.75 µs, a recycle delay of 300 s and an accumulation number of 32. Existent ¹H rotor and probe background signals were suppressed using the EASY experiment (Jaeger & Hemmann, 2014a,b). Adamantane served as secondary field standard with a ¹H chemical shift of 1.78 p.p.m.

¹H–¹³C CPMAS experiments were run in a 4 mm rotor with a spinning speed of 12.5 kHz (Hartmann & Hahn, 1962). The cross polarization (CP) contact time was 2 ms and the proton spin-lockfield was ramped linearly (ramped-CP) down to 50% of the initial value (Cook et al., 1996). ¹H Two-Pulse Phase Modulation (TPPM) decoupling was applied (Bennett et al., 1995). The ¹³C chemical shifts were referenced to adamantane with 38.5 p.p.m.

The powder X-ray diffraction (PXRD) pattern of the tp:ba cocrystal used for structure solution was recorded at the Powder diffraction beamline of the Australian Synchrotron (Melbourne, Australia) at an energy of 12.4012 keV and a beam current of 200 mA using a Si (111) double-crystal monochromator. A Mythen one-dimensional microstrip detector was used to record the scattering intensity (Wallwork et al., 2007). The PXRD patterns were recorded for 10 min.

The synchrotron X-ray powder pattern of the tp:ba cocrystal was indexed using the program DICVOL (Boultif & Louër, 1991). The structure was solved using the simulated annealing routine implemented in the DASH program (David et al., 2006). As starting conformation for the tp and ba molecules, the values of the Cambridge Structural Database (CSD; Groom & Allen, 2014) entries BAPLOT01 (Reference?) and BZAMID05 (Reference?) were used. For the initial structure solution, the configurations of the molecules (two molecules of tp and ba) were kept rigid.

The crystal structure of the tp:ba cocrystal was optimized by lattice-energy minimizations using dispersion-corrected density functional theory (DFT-D). Calculations were performed by the program GRACE (generation, ranking and charaterization engine; Avant-garde Materials Simulation, 2016) that uses the VASP code for single-point DFT calculations (Dollase, 1986; Kresse & Furthmüller, 1996; Kresse & Hafner, 1993). The PBE functional was combined with an empirical dispersion correction (Neumann & Perrin, 2005). Unit-cell parameters and atomic coordinates of all atoms were optimized without any restraints or constraints. For calculation details, see van de Streek & Neumann (2014).

The solid-state ¹H MAS NMR (ssNMR) spectrum of the tp:ba cocrystal presented in Fig. 1 shows that the signal of the acidic proton of tp at 14.5 p.p.m. is high-field shifted in the cocrystal spectrum (Baias et al., 2013). Based on this shift it can be assumed that the proton is bridged weaker to ba in the cocrystal as in pure tp, concluding that a the tp:ba cocrystal consists of neutral molecules without a proton transfer from tp to ba. The observed line broadening in the ssNMR spectrum of the cocrystal indicates that the structure may contain more than one symmetrically independent tp (and ba) molecule, which was proven by ¹³C NMR investigations (see Fig. S1 in the Supporting information). The splitting of the tp and ba peaks confirms the presence of independent molecules in the cocrystal lattice.

The Raman data depicted in Fig. 2 support the result of the ssNMR investigations. The absorption bands of the carbonyl groups of tp at 1665 and 1707 cm⁻¹ are only slightly shifted in the cocrystal spectrum (1643 and 1690 cm⁻¹). For a salt formation a shift of 30–40 cm⁻¹ to lower frequencies is expected. Additionally, the stretching band of the secondary amino group at 3123 cm⁻¹ would disappear and instead a new absorption band of the ammonium group would occur between 2000 and 2200 cm⁻¹ (Childs et al., 2007). Since this stretching band shifts in the cocrystal by 5 cm⁻¹ only, a salt formation can be ruled out.

Indexing was performed on different laboratory and synchrotron X-ray powder patterns of the tp:ba cocrystal. The X-ray powder diagrams could be indexed unambiguously with a tetra­gonal unit cell with the figures of merit M(20) = 138.8 and F(20) = 510.6 (de Wolff et al., 1968; Smith & Snyder, 1979). Based on the unit-cell volume of V = 2765 ų, a value of Z = 8 is reasonable. A Pawley refinement with this unit cell in P4, i.e. without systematic extinctions, led to a χ² value of 13.9.

The determination of the space group was difficult. Bayesian statistical analysis (Markvardsen et al., 2001) within the program DASH led to P4₂/n or P4₁2₁2 as most probably space groups, each with Z' = 1. In both space groups, the tp and ba molecules had to be positioned on a general position, since Wyckoff positions with site symmetry 1 or 2 cannot be occupied by tp or ba molecules, which both have the molecular symmetry m (C_s). However, all attempts to solve the structure in P4₂/n or P4₁2₁2 from the synchrotron data by real-space methods with simulated annealing using the programs DASH were unsuccessful. Attempts in several other tetra­gonal space groups failed too. Using FOX instead of DASH or laboratory data instead of synchrotron data did not help either (Favre-Nicolin & Cerný, 2002). The manual assessment of the systematic extinctions from the visually absent reflections leads to the following reflection conditions:

(1) hkl: none, corresponding to a primitive Bravais lattice

(2) hk0: h + k = 2n, corresponding to an n-glide plane parallel to (001)

(3) 0kl: none, excluding glide planes parallel to (100)

(4) hhl: none, excluding glide planes parallel to (110)

(5) 00l: l = 4n, corresponding to a 4₁ or 4₃ screw axis.

(6) 0k0, k = 2n, which is included in (2), but would point to a 2₁ screw axis parallel to [010], if the n-glide planes were absent.

(7) hh0: ambiguous (one visible reflection only)

However, the determination of systematic extinctions from the X-ray powder data bears uncertainties due to the high peak overlap, especially in the high 2θ region. For example, reflection condition (2) was based only on the absence of three reflections (010, 210 and 030), and for the 00l reflections the condition l = 4n differed from l = 2n only by the reflections 002 and 006, which were visually absent. The only unambiguous observation was the absence of systematic extinctions of the hkl, 0kl and hhl reflections.

Furthermore, the reflection conditions were contradictory to each other. A 4₁ or 4₃ screw axis cannot be combined with an n-glide plane perpendicular to it. 1 Obviously, at least one of the observed `reflection conditions' was not due to a systematic extinction, but by reflections with accidentally low intensities. The neglect of condition (2) leads to the extinction symbol P4₁2₁–, which corresponds to the space groups P4₁2₁2 and P4₃2₁2. (These two space groups cannot be distinguished from each other from powder data of an achiral compound, because all Friedel pairs systematically overlap, hence P4₃2₁2 was not considered further.) If, on the other hand, reflection condition (5) were only 00l: l = 2n, the space group would be P4₂/n. Hence, the manual determination of systematic extinctions again led to P4₁2₁2 (or P4₃2₁2) and P4₂/n as the most likely space groups.

We ran further trials in P4₁2₁2 and P4₂/n, but without success. We also tested, whether the ba molecule could be situated on the 4₂ axis with site symmetry 2 in P4₂/n, which would cause a twofold orientational disorder of the benzamide molecule, with the O atom being disordered with the amino group. However, the DASH runs did not give sensible results. Similarly, a solution trial in P4₂/n with a disordered ba molecule using two independent molecules with occupancies of 0.5 each, failed.

Although none of the structural models obtained hitherto gave a satisfactory fit to the powder pattern, a visual inspection of the `best of the wrong solutions', i.e. of the models with the lowest χ² values in each space group, revealed that most structures showed a common packing motif: Along the c axis, the structures consisted of four layers of molecules. Within these layers, all molecules were oriented with their molecular planes parallel to (130) and (310), in some other structures parallel to (30) and (310). However, all structures had χ² values of more than 200, which indicated that the assumed crystal symmetries were not the correct ones.

Finally, we considered which crystal symmetries are statistically frequent. We used the statistics of structural classes published by Belsky et al., which contains not only the space groups, but also the number of independent molecules and the molecular site symmetries (Chernikova et al., 1990; Belsky et al., 1995). Out of 19642 investigated organic homomolecular structures, 126 were tetra­gonal with Z = 8. From these structures, the most frequent crystal symmetries were (site symmetries in brackets):

– P4₁2₁2, Z = 8 (1): 49 structures

– P4₂/n, Z = 8 (1): 20 structures

– P2₁c, Z =8 (1): 12 structures

– I, Z = 8 (1): 7 structures

– I4₁/a, Z = 8 (2): 6 structures

– P4₁, Z = 8, Z' = 2 (1,1): 5 structures

– I4₁cd, Z = 8 (2): 5 structures

This statistics again pointed to the space groups P4₁2₁2 and P4₂/n, which were incorrect for the tp:ba cocrystal. Since the hkl, 0kl and hhl reflections clearly did not show any systematic extinction, all other space groups could be ruled out, except P4₁. Hence, we tried to solve the structure of the tp:ba cocrystal in P4₁, Z = 8 with four independent molecules (two tp and two ba) per asymmetric unit.

In P4₁, the crystal structure could be solved from the synchrotron powder pattern by simulated annealing with DASH. In order to reach a better statistic, the number of simulated annealing runs was increased from 25 to 100. The best solution was obtained with a profile χ² value of 33.0 and an intensity χ² value of 47.5. With slightly higher R values, several structures were obtained, which showed a similar molecular packing, but with one or more molecules rotated by 180° around their long molecular axis.

Subsequently, the structure with the lowest χ² value was refined by the Rietveld method using the program TOPAS. The molecular geometry was restrained using restraints on bond lengths, bond angles and planar groups. The Rietveld refinement converged with a smooth difference curve and confidence values of R_p = 1.86% and R_wp = 2.41% (see Fig. 3).

1^? The combination 4₁/n is impossible, because the application of a 4₁ screw operation to a perpendicular n-glide plane generates a second n-glide plane which is parallel to the first one, but shifted by (0, 0, 1/4). If the symmetry operation of the first glide plane is (x', y', z') = (x + 1/2, y + 1/2, −z), that of the second glide plane will be (x', y', z') = (x + 1/2, y + 1/2, −z + 1/2). A consecutive application of both glide planes to an atom on the general position (x, y, z) results in an atom situated at (x + 1, y + 1, z + 1/2), which is equivalent to (y, y, z + 1/2), and denotes a translational copy of the original atom, shifted by (0, 0, 1/2). Hence, every atom has a translational copy shifted by c/2 and the unit cell consists of two identical parts. Thus the unit cell can be transformed by c' = c/2. Thereby the 4₁ screw axes change to 4₂ screw axes. The same argumentation holds for the combination 4₃/n.

A crystal structure of an achiral compound in a chiral space group with Z' ≥ 2 should always be regarded with caution, since it may easily be a case of missed symmetry (Herbstein & Marsh, 1998; Marsh & Spek, 2001; Clemente, 2003). This is especially critical for structures determined from powder data. For example, the low-temperature structure of 4-methyl­pyridine N-oxide, determined by X-ray powder and neutron powder diffraction, was originally published in 2006 in P4₁ (Z = 32 and Z' = 8) (Damay et al., 2006). Indeed, the published atomic coordinates do not show any higher symmetry. Later, a rerefinement led to P4₁2₁2 (Z' = 4) (Palatinus & Damay, 2009). However, for the tp:ba cocrystal there are several facts indicating that the space group is actually correct:

(1) The broadening of the signals in the ¹H MAS NMR spectrum indicates Z' > 1.

(2) There are only two translationengleiche supergroups of P4₁, i.e. P4₁2₁2 and P4₁22. However, the clear orientation of the molecular planes parallel to (130) und (310) contradicts the existence of twofold rotation or screw axis parallel to [100] or [110]. Furthermore, extensive structure solution attempts in P4₁2₁2 failed. Klassengleiche supergroups, such as I4₁ or P4₂ (c' = 2c), can be excluded, because the unit-cell parameters are unambiguous, and the Bravais lattice is clearly primitive.

(3) The molecular packing does not show a higher symmetry. The two formula units within the asymmetric unit are clearly symmetrically independent, and not related by any symmetry element, even not a local one. The hydrogen-bond pattern of the two tp molecules is different from each other; the same is valid for the two ba molecules. Also a rotation of one or more molecules around the long molecular axis does not lead to identical hydrogen-bond patterns.

The correctness of the crystal structure was finally proven by a lattice-energy minimization using dispersion-corrected DFT calculations, including an optimization of the lattice parameters. Upon optimization, the protonation state did not change, and the resulting structure did not show any additional symmetry. Lattice parameters and atomic coordinates changed only slightly. A recent survey of 215 crystal structures, which were solved from powder data and published in IUCr journals, revealed, that during a DFT-D optimization under these conditions, the mean deviation of non-H atoms should be less than 0.35 Å. In the case of higher deviations, the structure is likely either to be incorrect or to exhibit special features such as disorder or unusual thermal expansion (van de Streek & Neumann, 2014). For the tp:ba cocrystal, an r.m.s. value of 0.139 Å could be found. Hence, the crystal structure of the tp:ba cocrystal should be correct. The overlay of the solved crystal structure (red) and the DFT-calculated structure (blue) are presented in Fig. 4.

The tp:ba cocrystal crystallizes in the tetra­gonal space group P4₁ and reveals a slightly higher density than the rea­cta­nts. Two crystallographically independent tp and two independent ba molecules are present in the asymmetric unit (tp1, tp2, ba1, and ba2; Fig. 5). Dimers are formed between tp1 and ba1 molecules and tp2 and ba2 molecules. A dimer between ba1 and tp1 is formed including the carbonyl group and amide group and the secondary amino group and carbonyl group of tp1. The ba2 molecule forms a similar dimer to the tp2 molecule.

The dimers are arranged in sheets. The unit cell contains four sheets, with molecules at z ~~1/8, 3/8, 5/8 and 7/8 (Fig. 6). Within each sheet, all molecules are parallel (Fig. 7). The molecules of the first and third sheets are oriented almost exactly in the (310) direction, and those of the second and fourth sheets in the (30) direction. This leads to a hunter's fence arrangement (Fig. 8). The sheets are connected by hydrogen bonds between the molecular dimers: The amino group of the ba1 molecule forms a hydrogen bond to an imidazole N atom of a tp molecule in a neighbouring sheet, whereas the amino group of the ba2 molecule connects to the O atom of a tp molecule in a neighbouring sheet. This leads to a one-dimensional hydrogen-bond network parallel to the [001] direction.

Based on synchrotron powder data, the extraordinary structure of the theophylline–benzamide cocrystal could be solved. Typically, the API theophylline cocrystallizes with benzamide-similar coformers in monoclinic space groups. However, when theophylline is ground under neat conditions with benzamide the tetra­gonal 1:1 cocrystal is formed in the space group P4₁. DFT-D calculations proved the correctness of this structure solution. Solid-state NMR investigations and Raman spectroscopy confirm that the cocrystal consists of neutral molecules, thus excluding a salt formation.

Synthesis and crystallization

Anhydrous theophylline (99%, Sigma–Aldrich, Germany) and benzamide (>=99.5%, Sigma–Aldrich, Germany) were obtained commercially and were used without further purification. Since no single crystals could be obtained by slow evaporation from diverse solvents, the synthesis of the 1:1 cocrystal (in the following abbreviated as the tp:ba cocrystal) was conducted by grinding in a ball mill (MM400, Retsch, Germany) at a frequency of 30 Hz for 25 min. A 10 ml steel vessel with two steel balls (diameter 10 mm) was used for a total load of 1 g. The rea­cta­nts were neat ground in an equimolar ratio.

Refinement details

Crystal data, data collection and structure refinement details are summarized in Table 1. The structure refinement was carried out by the Rietveld method using the program TOPAS (Rietveld, 1967, 1969; Coelho, 2007). A Pawley refinement was performed including the background, zero-point error, unit-cell parameters, peak-width and peak-asymmetry parameters. For the Rietveld refinements, restraints were applied for all bond lengths, bond angles and planar groups. The data were tested for preferred orientation using the approach of March & Dollase (Dollase, 1986). However, no significant preferred orientation was found. The Rietveld refinement included the atomic coordinates, profile parameters, unit-cell parameters, scale, background,and one overall isotropic displacement parameter for the C, N and O atoms of each molecule. H atoms were included with B_iso(H) = 1.2B_iso(parent atom).

Computing details

Cell refinement: TOPAS Academic (Coelho, 2007); data reduction: DASH (David et al., 2006); program(s) used to solve structure: DASH (David et al., 2006); program(s) used to refine structure: TOPAS Academic (Coelho, 2007); molecular graphics: DIAMOND (Crystal Impact, 2014); software used to prepare material for publication: publCIF (Westrip, 2010).

Figures

	Fig. 1. ^1H MAS NMR spectra of the tp:ba cocrystal and the reactants without the spinning side bands.
	Fig. 2. Raman spectra of the tp:ba cocrystal and the reactants tp and ba.
	Fig. 3. Rietveld refinement of the crystal structure of the tp:ba cocrystal. X-ray intensity for the cocrystal tp:ba cocrystal at ambient conditions as a function of diffraction angle 2θ. The observed pattern (black circles), the best Rietveld fit profile (red line), the reflection positions (blue tick marks), and the difference curve (grey line) of observed and calculated profiles are shown. The energy was 12.4012 keV (λ = 1.0004 Å). The confidence values Rp', Rwp' and Rexp' denote values with background subtraction.
	Fig. 4. Overlay of the experimental crystal structure from powder data (red) and the calculated structure by DFT-D investigations (blue) (a) of a molecular section and (b) the unit cell of the tp:ba cocrystal.
	Fig. 5. Structure motif of the tp:ba cocrystal. H atoms not involved in the hydrogen bonding have been omitted for clarity. Colour key: C atoms grey, O atoms red and N atoms iblue. Green dashed lines indicate hydrogen bonds.
	Fig. 6. The crystal structure of the tp:ba cocrystal, viewed along the a axis. H atoms not involved in the hydrogen bonding have been omitted for clarity. Colour key: C atoms grey, O atoms red and N atoms iblue. Green dashed lines indicate hydrogen bonds.
	Fig. 7. One sheet of parallel molecules in the crystal structure of the tp:ba cocrystal. The view direction is along [001].
	Fig. 8. The crystal structure of the tp:ba cocrystal. The view direction [001].

Theophylline–Benzamide (1/1)

Crystal data

C7H8N4O2·C7H7NO	F(000) = 1264
Mr = 301.31	Dx = 1.446 Mg m^−3
Tetragonal, P41	Synchrotron radiation
Hall symbol: P 4w	µ = 0.11 mm^−1
a = 10.281404 (12) Å	T = 293 K
c = 26.15892 (6) Å	Particle morphology: tablet
V = 2765.19 (1) Å^3	white
Z = 8	cylinder, 10 × 0.5 mm

Data collection

Australien Synchrotron XRD beamlime diffractometer	Data collection mode: transmission
Primary focusing, Si 111 monochromator	2θmin = 2.0°, 2θmax = 82.32°, 2θstep = 0.01°
Specimen mounting: 0.5 mm glass capillary

Refinement

Refinement on Inet	Excluded region(s): none
Least-squares matrix: full with fixed elements per cycle	86 parameters
Rp = 1.86	42 restraints
Rwp = 2.41	0 constraints
Rexp = 1.19	H-atom parameters constrained
R(F) = 1.86	Weighting scheme based on measured s.u.'s w = 1/σ[Yobs]^2
χ^2 = 1.388	(Δ/σ)max = 0.001
21236 data points

Special details

Geometry. Bond distances, angles etc. have been calculated using the rounded fractional coordinates. All su's are estimated from the variances of the (full) variance-covariance matrix. The cell e.s.d.'s are taken into account in the estimation of distances, angles and torsion angles

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

	x	y	z	Uiso*/Ueq
C1	0.1498 (4)	0.0405 (3)	0.83153 (17)	0.04569
C2	0.2867 (4)	0.0950 (5)	0.83190 (17)	0.04569
C3	0.0824 (4)	0.0163 (3)	0.78716 (16)	0.04569
C4	0.0872 (4)	0.0125 (3)	0.87810 (16)	0.04569
O5	0.3562 (7)	0.0928 (8)	0.8714 (2)	0.04569
N6	0.3367 (5)	0.1401 (5)	0.78775 (16)	0.04569
C7	−0.0444 (4)	−0.0346 (3)	0.78751 (16)	0.04569
H8	0.1232 (17)	0.0346 (19)	0.7525 (7)	0.05483
C9	−0.0368 (4)	−0.0372 (3)	0.87881 (16)	0.04569
H10	0.132 (2)	0.0281 (19)	0.9107 (7)	0.05483
H11	0.4037 (16)	0.2066 (18)	0.7941 (6)	0.05483
H12	0.301 (2)	0.1603 (17)	0.7535 (7)	0.05483
C13	−0.1038 (4)	−0.0614 (3)	0.83266 (16)	0.04569
H14	−0.0885 (17)	−0.0496 (18)	0.7539 (7)	0.05483
H15	−0.0799 (18)	−0.0560 (18)	0.9115 (7)	0.05483
H16	−0.1916 (17)	−0.0965 (15)	0.8319 (8)	0.05483
N17	0.7730 (7)	0.6654 (5)	0.64541 (16)	0.04569
C18	0.8154 (8)	0.5652 (5)	0.61405 (17)	0.04569
C19	0.7909 (5)	0.6478 (4)	0.70053 (18)	0.04569
C20	0.7209 (9)	0.7856 (5)	0.63011 (17)	0.04569
N21	0.7964 (7)	0.5792 (4)	0.56265 (16)	0.04569
O22	0.8566 (8)	0.4635 (6)	0.6313 (3)	0.04569
H23	0.842 (2)	0.572 (2)	0.7074 (9)	0.05483
H24	0.833 (2)	0.7219 (16)	0.7137 (6)	0.05483
H25	0.7094 (18)	0.6372 (18)	0.7163 (7)	0.05483
C26	0.7094 (9)	0.7880 (5)	0.57544 (17)	0.04569
O27	0.6833 (8)	0.8667 (6)	0.6600 (2)	0.04569
C28	0.7514 (9)	0.6932 (5)	0.54358 (16)	0.04569
C29	0.8441 (4)	0.4766 (4)	0.52873 (15)	0.04569
N30	0.6674 (6)	0.8883 (4)	0.54528 (16)	0.04569
N31	0.7320 (8)	0.7255 (6)	0.4945 (2)	0.04569
H32	0.8650 (18)	0.3993 (16)	0.5481 (6)	0.05483
H33	0.9193 (18)	0.5080 (19)	0.5119 (7)	0.05483
H34	0.778 (2)	0.4566 (19)	0.5042 (7)	0.05483
C35	0.6858 (8)	0.8458 (5)	0.49707 (17)	0.04569
H36	0.6192 (17)	0.9567 (15)	0.5552 (7)	0.05483
H37	0.6616 (18)	0.9010 (18)	0.4665 (7)	0.05483
C38	0.4621 (3)	0.6599 (4)	0.11543 (16)	0.04569
C39	0.4087 (5)	0.7961 (4)	0.11160 (17)	0.04569
C40	0.4862 (3)	0.6035 (4)	0.16187 (16)	0.04569
C41	0.4870 (3)	0.5905 (4)	0.07091 (16)	0.04569
O42	0.4048 (8)	0.8562 (7)	0.0695 (2)	0.04569
N43	0.3792 (9)	0.8545 (5)	0.15581 (16)	0.04569
C44	0.5347 (3)	0.4781 (4)	0.16483 (16)	0.04569
H45	0.470 (2)	0.652 (2)	0.1954 (7)	0.05483
C46	0.5354 (3)	0.4657 (4)	0.07265 (16)	0.04569
H47	0.4707 (17)	0.6314 (17)	0.0377 (7)	0.05483
H48	0.384 (2)	0.9498 (18)	0.1531 (7)	0.05483
H49	0.390 (4)	0.8328 (19)	0.1928 (6)	0.05483
C50	0.5598 (3)	0.4082 (4)	0.12160 (16)	0.04569
H51	0.5510 (18)	0.4415 (19)	0.1997 (7)	0.05483
H52	0.5531 (18)	0.4163 (17)	0.0405 (7)	0.05483
H53	0.5930 (16)	0.3202 (19)	0.1253 (7)	0.05483
N54	0.1707 (5)	0.7227 (7)	0.28773 (16)	0.04569
C55	0.0647 (5)	0.6927 (9)	0.31895 (17)	0.04569
C56	0.1536 (4)	0.6994 (4)	0.23330 (18)	0.04569
C57	0.2901 (5)	0.7765 (9)	0.30278 (17)	0.04569
N58	0.0846 (4)	0.6955 (7)	0.37094 (16)	0.04569
O59	−0.0371 (6)	0.6510 (9)	0.3009 (3)	0.04569
H60	0.0681 (18)	0.6635 (18)	0.2267 (8)	0.05483
H61	0.163 (2)	0.7789 (16)	0.2160 (6)	0.05483
H62	0.2181 (19)	0.6392 (17)	0.2224 (6)	0.05483
C63	0.2911 (5)	0.7926 (8)	0.35765 (17)	0.04569
O64	0.3734 (6)	0.8011 (7)	0.2725 (3)	0.04569
C65	0.1937 (5)	0.7532 (8)	0.38978 (16)	0.04569
C66	−0.0245 (4)	0.6597 (4)	0.40385 (14)	0.04569
N67	0.3892 (5)	0.8377 (7)	0.38882 (16)	0.04569
N68	0.2225 (5)	0.7774 (9)	0.4390 (2)	0.04569
H69	−0.0970 (16)	0.6329 (17)	0.3839 (7)	0.05483
H70	−0.0488 (17)	0.732 (2)	0.4239 (7)	0.05483
H71	0.003 (2)	0.5886 (17)	0.4248 (7)	0.05483
C72	0.3439 (5)	0.8239 (7)	0.43681 (17)	0.04569
H73	0.4590 (15)	0.8864 (19)	0.3792 (7)	0.05483
H74	0.395 (2)	0.8583 (19)	0.4671 (9)	0.05483

Geometric parameters (Å, º)

O22—C18	1.215 (9)	C19—H24	0.942 (18)
O27—C20	1.207 (8)	C29—H34	0.96 (2)
O59—C55	1.226 (9)	C29—H32	0.967 (17)
O64—C57	1.194 (9)	C29—H33	0.947 (19)
O5—C2	1.257 (7)	C35—H37	1.012 (19)
O42—C39	1.263 (7)	C57—C63	1.445 (6)
N17—C19	1.465 (6)	C63—C65	1.369 (7)
N17—C20	1.405 (8)	C56—H61	0.939 (17)
N17—C18	1.387 (7)	C56—H60	0.969 (19)
N21—C29	1.463 (6)	C56—H62	0.951 (19)
N21—C28	1.355 (7)	C66—H69	0.950 (17)
N21—C18	1.366 (6)	C66—H71	0.957 (19)
N30—C35	1.348 (6)	C66—H70	0.94 (2)
N30—C26	1.368 (7)	C72—H74	1.01 (2)
N31—C35	1.327 (9)	C1—C2	1.515 (6)
N31—C28	1.341 (7)	C1—C4	1.408 (6)
N30—H36	0.899 (17)	C1—C3	1.375 (6)
N54—C57	1.403 (8)	C3—C7	1.405 (6)
N54—C55	1.396 (7)	C4—C9	1.374 (6)
N54—C56	1.455 (6)	C7—C13	1.358 (6)
N58—C66	1.462 (6)	C9—C13	1.413 (6)
N58—C65	1.361 (8)	C3—H8	1.017 (19)
N58—C55	1.376 (6)	C4—H10	0.982 (19)
N67—C72	1.347 (6)	C7—H14	1.001 (19)
N67—C63	1.377 (7)	C9—H15	0.982 (19)
N68—C72	1.338 (8)	C13—H16	0.971 (18)
N68—C65	1.344 (7)	C38—C41	1.390 (6)
N67—H73	0.911 (18)	C38—C39	1.507 (6)
N6—C2	1.347 (6)	C38—C40	1.369 (6)
N6—H12	0.990 (19)	C40—C44	1.385 (6)
N6—H11	0.985 (18)	C41—C46	1.377 (6)
N43—C39	1.338 (6)	C44—C50	1.365 (6)
N43—H49	0.999 (17)	C46—C50	1.433 (6)
N43—H48	0.984 (19)	C40—H45	1.023 (19)
C20—C26	1.435 (6)	C41—H47	0.980 (19)
C26—C28	1.353 (8)	C44—H51	1.001 (19)
C19—H23	0.96 (2)	C46—H52	0.999 (19)
C19—H25	0.940 (19)	C50—H53	0.97 (2)
C18—N17—C19	116.8 (5)	N67—C63—C57	129.2 (5)
C18—N17—C20	127.2 (4)	N68—C65—C63	111.9 (5)
C19—N17—C20	115.9 (4)	N58—C65—N68	127.5 (5)
C18—N21—C28	120.1 (4)	N58—C65—C63	120.6 (4)
C18—N21—C29	118.2 (5)	N67—C72—N68	113.6 (5)
C28—N21—C29	121.0 (4)	N54—C56—H60	110.3 (13)
C26—N30—C35	104.5 (4)	N54—C56—H61	108.4 (11)
C28—N31—C35	103.6 (5)	N54—C56—H62	108.5 (11)
C35—N30—H36	127.0 (13)	H61—C56—H62	110.5 (16)
C26—N30—H36	126.7 (12)	H60—C56—H62	109.4 (16)
C55—N54—C57	127.3 (4)	H60—C56—H61	109.8 (17)
C55—N54—C56	116.2 (4)	N58—C66—H71	107.6 (13)
C56—N54—C57	116.5 (4)	N58—C66—H70	109.4 (12)
C55—N58—C66	117.6 (4)	H70—C66—H71	111.2 (16)
C65—N58—C66	122.0 (4)	H69—C66—H70	109.1 (16)
C55—N58—C65	119.3 (5)	N58—C66—H69	110.6 (11)
C63—N67—C72	105.3 (5)	H69—C66—H71	109.0 (16)
C65—N68—C72	103.3 (5)	N68—C72—H74	125.1 (13)
C72—N67—H73	126.0 (13)	N67—C72—H74	120.8 (13)
C63—N67—H73	126.8 (12)	C2—C1—C3	122.7 (4)
C2—N6—H11	111.2 (10)	C2—C1—C4	119.7 (4)
H11—N6—H12	105.4 (15)	C3—C1—C4	117.6 (4)
C2—N6—H12	135.0 (13)	O5—C2—N6	119.6 (5)
C39—N43—H48	111.9 (12)	N6—C2—C1	118.5 (4)
H48—N43—H49	106.7 (16)	O5—C2—C1	121.8 (5)
C39—N43—H49	135.4 (16)	C1—C3—C7	122.0 (4)
N17—C18—N21	117.3 (5)	C1—C4—C9	120.8 (4)
O22—C18—N17	121.9 (5)	C3—C7—C13	120.0 (4)
O22—C18—N21	120.4 (6)	C4—C9—C13	120.5 (4)
O27—C20—C26	127.4 (6)	C7—C13—C9	119.2 (4)
N17—C20—C26	109.3 (5)	C7—C3—H8	117.2 (11)
O27—C20—N17	123.1 (5)	C1—C3—H8	120.8 (11)
N30—C26—C20	127.8 (5)	C1—C4—H10	120.2 (12)
C20—C26—C28	125.1 (5)	C9—C4—H10	119.0 (12)
N30—C26—C28	106.8 (4)	C3—C7—H14	118.2 (11)
N31—C28—C26	111.3 (6)	C13—C7—H14	121.9 (11)
N21—C28—N31	128.1 (5)	C13—C9—H15	119.3 (11)
N21—C28—C26	120.3 (4)	C4—C9—H15	120.2 (12)
N30—C35—N31	113.6 (5)	C7—C13—H16	118.4 (13)
H23—C19—H24	109.8 (18)	C9—C13—H16	122.4 (13)
H24—C19—H25	110.1 (17)	C39—C38—C40	121.2 (4)
N17—C19—H23	110.8 (15)	C39—C38—C41	119.2 (4)
N17—C19—H24	108.5 (10)	C40—C38—C41	119.5 (4)
H23—C19—H25	108.2 (18)	O42—C39—N43	121.8 (5)
N17—C19—H25	109.5 (12)	O42—C39—C38	121.6 (5)
N21—C29—H34	108.9 (13)	N43—C39—C38	116.2 (4)
N21—C29—H32	110.5 (10)	C38—C40—C44	120.6 (4)
H32—C29—H34	109.4 (16)	C38—C41—C46	121.2 (4)
H33—C29—H34	110.0 (17)	C40—C44—C50	120.8 (4)
N21—C29—H33	108.1 (12)	C41—C46—C50	118.5 (4)
H32—C29—H33	110.0 (16)	C44—C50—C46	119.4 (4)
N31—C35—H37	124.8 (11)	C38—C40—H45	121.7 (12)
N30—C35—H37	121.5 (12)	C44—C40—H45	117.7 (12)
N54—C55—N58	117.2 (5)	C38—C41—H47	119.4 (11)
O59—C55—N54	121.2 (5)	C46—C41—H47	119.4 (11)
O59—C55—N58	121.0 (6)	C40—C44—H51	117.5 (12)
N54—C57—C63	109.3 (4)	C50—C44—H51	121.7 (12)
O64—C57—N54	121.7 (5)	C41—C46—H52	120.8 (11)
O64—C57—C63	129.0 (6)	C50—C46—H52	120.7 (11)
C57—C63—C65	124.8 (5)	C44—C50—H53	118.3 (12)
N67—C63—C65	105.8 (4)	C46—C50—H53	122.3 (11)
C19—N17—C18—O22	5.3 (11)	C72—N68—C65—N58	174.7 (8)
C20—N17—C18—O22	−178.4 (8)	C72—N68—C65—C63	−4.4 (10)
C19—N17—C18—N21	178.5 (6)	O27—C20—C26—N30	8.2 (15)
C20—N17—C18—N21	−5.3 (12)	O27—C20—C26—C28	−178.8 (9)
C19—N17—C20—C26	180.0 (6)	N17—C20—C26—N30	−177.6 (8)
C18—N17—C20—O27	178.2 (9)	N17—C20—C26—C28	−4.6 (12)
C19—N17—C20—O27	−5.5 (12)	C20—C26—C28—N31	−177.4 (8)
C18—N17—C20—C26	3.7 (12)	N30—C26—C28—N31	−3.2 (10)
C29—N21—C18—O22	−8.6 (11)	C20—C26—C28—N21	7.3 (14)
C28—N21—C18—N17	7.2 (11)	N30—C26—C28—N21	−178.5 (7)
C29—N21—C18—N17	178.1 (6)	N54—C57—C63—C65	4.0 (11)
C28—N21—C18—O22	−179.5 (8)	O64—C57—C63—N67	−1.5 (16)
C18—N21—C28—N31	177.2 (9)	O64—C57—C63—C65	−175.3 (9)
C29—N21—C28—N31	6.6 (13)	N54—C57—C63—N67	177.7 (8)
C18—N21—C28—C26	−8.4 (12)	N67—C63—C65—N58	−175.9 (7)
C29—N21—C28—C26	−179.0 (7)	C57—C63—C65—N58	−0.9 (12)
C26—N30—C35—N31	2.0 (9)	C57—C63—C65—N68	178.3 (8)
C35—N30—C26—C20	174.7 (9)	N67—C63—C65—N68	3.3 (9)
C35—N30—C26—C28	0.7 (9)	C3—C1—C2—O5	−165.8 (6)
C35—N31—C28—N21	179.1 (9)	C3—C1—C2—N6	10.5 (6)
C28—N31—C35—N30	−3.9 (10)	C4—C1—C2—O5	14.1 (7)
C35—N31—C28—C26	4.3 (10)	C4—C1—C2—N6	−169.7 (4)
C56—N54—C55—O59	−1.1 (12)	C2—C1—C3—C7	179.8 (3)
C56—N54—C57—C63	−179.7 (6)	C4—C1—C3—C7	0.0 (5)
C56—N54—C57—O64	−0.4 (12)	C2—C1—C4—C9	−179.9 (3)
C57—N54—C55—N58	−11.5 (13)	C3—C1—C4—C9	0.0 (5)
C55—N54—C57—C63	2.5 (12)	C1—C3—C7—C13	0.0 (5)
C57—N54—C55—O59	176.8 (9)	C1—C4—C9—C13	0.1 (5)
C56—N54—C55—N58	170.6 (6)	C3—C7—C13—C9	0.1 (5)
C55—N54—C57—O64	−178.2 (8)	C4—C9—C13—C7	−0.2 (5)
C55—N58—C65—N68	172.3 (8)	C40—C38—C39—O42	169.0 (6)
C66—N58—C55—O59	−6.2 (12)	C40—C38—C39—N43	−4.0 (7)
C66—N58—C65—C63	−176.1 (6)	C41—C38—C39—O42	−11.1 (7)
C66—N58—C55—N54	−177.9 (6)	C41—C38—C39—N43	175.9 (5)
C55—N58—C65—C63	−8.7 (11)	C39—C38—C40—C44	179.7 (3)
C65—N58—C55—N54	14.2 (11)	C41—C38—C40—C44	−0.2 (5)
C65—N58—C55—O59	−174.1 (8)	C39—C38—C41—C46	−179.8 (3)
C66—N58—C65—N68	4.9 (12)	C40—C38—C41—C46	0.1 (5)
C72—N67—C63—C65	−0.7 (8)	C38—C40—C44—C50	0.2 (5)
C63—N67—C72—N68	−2.1 (9)	C38—C41—C46—C50	0.0 (5)
C72—N67—C63—C57	−175.4 (8)	C40—C44—C50—C46	0.0 (5)
C65—N68—C72—N67	4.0 (10)	C41—C46—C50—C44	0.0 (5)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N6—H11···O64^i	0.985 (18)	2.362 (18)	3.067 (8)	128.0 (14)
N6—H12···N68^ii	0.990 (19)	1.98 (2)	2.961 (7)	172.5 (16)
N30—H36···O42^iii	0.899 (17)	1.975 (17)	2.802 (8)	152.4 (16)
N43—H48···O27^iv	0.984 (19)	2.02 (2)	2.940 (8)	155.2 (18)
N43—H49···O64	0.999 (17)	2.117 (18)	3.102 (9)	168 (3)
N67—H73···O5^v	0.911 (18)	1.923 (17)	2.751 (9)	150.4 (17)

Symmetry codes: (i) −x+1, −y+1, z+1/2; (ii) −y+1, x, z+1/4; (iii) −x+1, −y+2, z+1/2; (iv) −x+1, −y+2, z−1/2; (v) −x+1, −y+1, z−1/2.