The Z′ = 12 superstructure of Λ-cobalt(III) sepulchrate trinitrate governed by C—H⋯O hydrogen bonds

The 12-fold superstructure at T = 95 K is described as a commensurately modulated structure in superspace. Crystal packing in the Z′ = 12 superstructure is determined by short C—H⋯O hydrogen bonds.


Introduction
Macrobicyclic metal cage complexes are templating agents for the synthesis of silicates (Hondow et al., 2012) and zeolites (Garcia et al., 2001). These compounds also serve as catalysts enhancing electrochemical processes (Ritzert et al., 2013), as a photosensitizer for the production of hydrogen from water (Pina et al., 1985) and as reducing agents in the field of bioelectrochemistry (Bernhardt et al., 2006). The crystal structures of these compounds provide useful information because applications of these compounds are correlated to their thermodynamic stability, stereochemistry, size and the nature of coordination inside the cages, and the strong and weak interaction of the cages with the functional groups (Gahan & Harrowfield, 2015).
The compound crystallizes in hexagonal symmetry with space group P6 3 22 at room temperature (phase I) (Dubicki et al., 1980;Schö nleber et al., 2010). The Co(sep) cage and two symmetry-related nitrate groups (nitrate groups A and B) are centred on threefold rotation axes. They have been reported to be connected via N-HÁ Á ÁO hydrogen bonds (Dubiciki et al., 1984). The third nitrate group (nitrate group C) is slightly displaced from the origin, exhibiting a sixfold orientational disorder (Schö nleber et al., 2010).
A phase transition of Co(sep)(NO 3 ) 3 has been found to occur at T 1 = 133 K; spectroscopic methods have indicated that below T 1 the crystals develop a domain structure, as it may appear due to a lowering of its symmetry (Dubiciki et al., 1984). Single-crystal neutron diffraction experiments have revealed satellite reflections below T 1 . Their temperature dependence has indicated two further phase transitions, at T 2 = 107 K and T 3 = 98 K, respectively (Larsen et al., 1988).
We have performed temperature-dependent single-crystal X-ray diffraction studies on Co(sep)(NO 3 ) 3 , which confirmed the existence of different phases at T = 115 K (phase II), 100 K (phase III) and 95 K (phase IV; Dey et al., 2016). The two intermediate phases II and III possess incommensurately modulated crystal structures (Larsen et al., 1988).
The present X-ray diffraction experiments reveal the lowtemperature phase (phase IV) to be a lock-in phase with a 12fold 6a h Â ffiffi ffi 3 p b h Â c h superstructure of the room-temperature hexagonal structure. The phase transition from phase III to phase IV is identified as an incommensurate-to-commensurate transition accompanied by major changes of the modulation wave. Specifically, the disordered nitrate group C becomes fully ordered in phase IV, assuming different orientations at different sites within the 12-fold supercell.
The order as well as the accompanying atomic displacements and molecular distortions are described by modulation functions within the superspace approach ( van Smaalen, 2012;Schö nleber, 2011;Janssen et al., 2007).
The origin of the modulation is discussed in terms of molecular conformations and intermolecular interactions, including the role of hydrogen bonding.

Diffraction experiment and data integration
Single crystals of Co(sep)(NO 3 ) 3 were synthesized by the research team of Alan M. Sargeson (Creaser et al., 1982). The crystals are stable in air at ambient conditions. Single-crystal X-ray diffraction experiments were performed at beamline D3, Hasylab DESY, Hamburg, employing radiation of a wavelength of = 0.50917 Å . The sample was mounted on a four-circle diffractometer in Euler geometry, and diffraction intensities were measured by a MAR-CCD area detector. A data set complete up to a resolution of ðsin =Þ max = 0.838 Å À1 was measured by and ! scans with several exposure times and different offsets of the detector, always maintaining a crystal-to-detector distance of 220 mm and using scans of 1 per image (Table 1). Data processing has been performed with the software EVAL15 (Schreurs et al., 2010). Inspection of the frames revealed that main reflections are surrounded by satellite reflections of first order. Bragg reflections have been indexed using five integers ðh k l m 1 m 2 Þ on a primitive hexagonal lattice and with modulation wavevectors Refinement of the hexagonal orientation matrix and the component of the modulation wavevector resulted in 2 h = 0.16726 (10) = 1 6 + 0.00059 (10), suggesting an incommensurate modulation.
However, diffraction images exhibit diffraction maxima that appear as overlapping Bragg reflections from different domains rather than single peaks. Therefore, we have used an alternative indexing of the diffraction pattern on the Ccentred a h Â ffiffi ffi 3 p b h Â c h orthohexagonal unit cell. In the case of orthorhombic symmetry, each main reflection is composed of three different, nearly coincident Bragg reflections from the three domains, while satellite reflections have contributions from only a single domain (Fig. 2a). With respect to the orthohexagonal unit cell the satellite reflections are indexed by In the case of monoclinic symmetry, each main reflection is composed of six different, nearly coincident Bragg reflections from the six domains; satellite reflections now have contri-butions from two domains (Fig. 2). Each domain of monoclinic symmetry is modulated by a single modulation wavevector with m ' 2 h and 2 ' 0. Refinement with EVAL15 of the orthorhombic lattice parameters and the orientations of the six lattices resulted in a very small orthorhombic lattice distortion together with o ¼ 1 6 À 0:000071 ð26Þ. Further lowering of the symmetry to monoclinic resulted in a lattice distortion given by the angle = 89.9943 (3) and m ¼ 1 6 À 0:000026 ð9Þ. This value is much closer to the commensurate value 1 6 than the value obtained with the hexagonal lattice and it differs from 1 6 by less than three standard uncertainties. The discrepancies can be explained by the fact that the twinned refinement determines the position of the modulation wavevector with respect to the reciprocal lattice in its own domain, whereas the two-dimensional modulation on the hexagonal lattice determines the average satellite position with respect to the average lattice of all domains. A non-zero value for 2 leads to instable refine-ments and a non-significant value for this parameter. Together, we take these refinements as experimental evidence for the commensurability of the modulation in phase IV.
The severe overlap of Bragg reflections from different domains prevents the determination of integrated intensities of individual reflections. Instead, accurate intensities can be obtained for each group of overlapping reflections. Furthermore, available software for absorption correction cannot simultaneously handle twinned and incommensurate data. Therefore, integrated intensities have been determined within the hexagonal setting, employing the two modulation wavevectors from equation (1). Integrated intensities have been obtained for main reflections, ðh k l 0 0Þ and satellite reflections of first order, ðh k l AE1 0Þ, ðh k l 0 AE1Þ and ðh k l AE1 Ç1Þ, employing EVAL15. The absorption correction was determined by SADABS (Sheldrick, 2008). Throughout these calculations, monoclinic point symmetry 2=m (c unique) has been used. This is the minimum symmetry of the diffraction pattern in the case of twin domains of unequal volume fractions. Only for equal volume fractions of the domains can the  Schematic drawing of the diffraction pattern at T = 95 K exhibiting hexagonal to monoclinic sixfold twinning. (a) q 2 , q 1 + q 2 and q 1 belong to the green (1), blue (2) and red (3) orthorhombic or monoclinic domains, respectively. (b) Monoclinic twin domains 4, and 5 and 6 are generated by applying twofold rotation a axes parallel to the twin domains 1, 2 and 3, respectively. The assignment of the q-vectors to the twin domains has been chosen consistent with International Tables for Crystallography, Vols. A and C (Arnold, 2006;Janssen et al., 2006). The reconstructed reciprocal layer hk2 is given as Fig. S1 in the supporting information.   (11), 0.1384 (11) (5, 6) 0.1731 (11), 0.1932 (11) Twin matrices (2) À 1 2 À 3 2 0 1 2 À 1 2 0 0 0 1 (3) À 1 2 3 2 0 À 1 2 À 1 2 0 0 0 1 (4) 1 0 0 0 À 1 0 0 0 À 1 (5) À 1 2 3 2 0 1 2 1 2 0 00 À 1 (6) À 1 2 À 3 2 0 À 1 2 1 2 0 00 À 1 Á min , Á max (e Å À3 ) À0.60, 0.58 point symmetry become higher, e.g. 6=mmm in the case of all volume fractions being equal. After data reduction, the dataset was split into one subset of main reflections (common to all twin domains) and three subsets of satellites reflections (for the three twin domains 1, 2 and 3; Fig. 2a; twin matrices are given in Table 1). The indices were transformed from ðh k l m 1 m 2 Þ to ðh k l mÞ without changing h, k or l, and with m ¼ Àm 2 for the twin domain 1, m ¼ m 1 þ m 2 for twin domain 2 and m ¼ Àm 1 for twin domain 3. The reflection indices were then transformed to the C-centred orthohexagonal setting (Arnold, 2006), using the software JANA2006 (Petricek et al., 2014). The three additional monoclinic twin domains 4, 5 and 6 were described by applying a twofold rotation along a to the domains 1, 2 and 3, respectively. In this way, satellite reflections of each of the three pairs of domains coincide with each other according to: ðh k l mÞ of domain 1 coincides with ðh Àk Àl mÞ of domain 4; main reflections of all six domains coincide. The ratio of the average intensities hIi between main and satellite reflections is approximately 60:1, while the average significance hI=ðIÞi has a ratio of 4:1 between the main and satellite reflections.

Structure solution and refinement
A model for the 12-fold superstructure of phase IV of Co(sep)(NO 3 ) 3 at T = 95 K has been developed within the superspace approach ( van Smaalen, 2012). The basic structure is nearly identical to the crystal structure of phase I, but it has been described on the C-centred orthohexagonal unit cell ( Table 1). Consideration of diffraction symmetry (Table 1) and reflection conditions has led to the space group C2 1 (c-unique) for the basic structure, where the monoclinic unique axis is equal to the hexagonal axis of phase I. This space group is a non-standard setting of P2 1 , No. 4 in International Tables for Crystallography, Vol. A. The superspace group has been found as C2 1 ð 1 2 0Þ0 with 1 ¼ m ¼ 1 6 and 2 ¼ 0. This superspace group is a non-standard setting of P2 1 ð 1 2 0Þ0, No. 4.1.2.1 in Stokes et al. (2011) and van Smaalen et al. (2013).
Formally, charge flipping does not apply to diffraction data from crystals twinned by (pseudo-)merohedry. Nevertheless, SUPERFLIP (Palatinus & Chapuis, 2007) applied to the present data allowed us to determine the positions of the Co atom along with initial values for its modulation parameters. The positions of the other non-H atoms were derived from the atomic positions of phase I (Schö nleber et al., 2010), employing JANA2006 for the application of group-subgroup relations following the reduction of symmetry from P6 3 22 to C222 1 to C2 1 . The low monoclinic symmetry of the pseudohexagonal basic structure is responsible for large correlations between structural parameters. Therefore, restraints on interatomic distances and bond angles of the Co(sep) cage have been introduced in accordance with the crystal structure of phase I (Schö nleber et al., 2010). The nitrate groups have been described as planar molecules with point symmetry 32, leaving the N-O distance as a single refinable parameter. One nitrate molecule is placed in two independent positions corresponding to the nitrate groups A and B. A second nitrate molecule is used for nitrate group C. Each independent position is defined by three translational and three rotational parameters. The modulations of the nitrate groups were initially described by small values for the amplitudes of the first-order harmonic waves for modulation of translations and rotations. Displacement modulations of the other non-H atoms have been described by a single harmonic wave with initially small values for the parameters, except cobalt, for which the parameters obtained by SUPERFLIP have been used. H atoms were added to all ligand N atoms (N lig ), and all ethylene (C en ) and apical (C ap ) C atoms by a riding model, keeping tetrahedral geometries with distances d(N-H) = 0.87 Å and d(C-H) = 0.96 Å . Atomic displacement parameters (ADPs) of H atoms follow from U iso (H) = 1.2 U eq (parent atom). Structure refinements of this (3 + 1)dimensional superspace model have been performed with JANA2006. Employing isotropic ADPs and the incommensurate approximation, the refinement converged at R obs F ðmainÞ ¼ 0:1254 and R obs F ðsatÞ ¼ 0:1564 for main and satellite reflections, respectively.
In the next step, anisotropic ADPs were introduced for the non-H atoms in the Co(sep) cage and TLS parameters (Schomaker & Trueblood, 1968) were applied to the nitrate groups. Refinement resulted in a much improved fit to the main reflections with R obs F ðmainÞ ¼ 0:0425 and R obs F ðsatÞ ¼ 0:1451, and a large reduction of the features in the difference Fourier map, viz Á min =Á max reduced from À2.26/ 10.84 to À1.02/2.19 e Å À3 . Subsequently, first-order harmonic waves have been introduced for the modulation of ADPs of non-H atoms of the Co(sep) cage and for modulation of the TLS parameters of the nitrate groups. Refinement resulted in an improved fit to the satellite reflections with R obs F ðmainÞ ¼ 0:0389 and R obs F ðsatÞ ¼ 0:1052. The next step involved the introduction of first-order harmonic waves for the third-order Gram-Charlier parameters of the Co atom, while the basic third-order Gram-Charlier parameters were constrained to remain zero (Li et al., 2011). The fit to the diffraction data improved again at R obs F ðmainÞ ¼ 0:0376 and R obs F ðsatÞ ¼ 0:1002. More importantly, ADPs of the ten atoms in the Co(sep) cage, which were previously non-positive definite, become positive definite by this procedure.
In the final model constraints of the riding model on the fractional coordinates and modulation parameters of the H atoms attached to the six N lig atoms were replaced by restraints on distances and angles. Restraint parameters are d(N-H) = 0.87 AE 0.02 Å and /(H-N-Co) = /(H-N-C3) = /(H-N-C4) = 109.47 AE 1 . Refinement resulted in an again improved fit, with R obs F ðmainÞ ¼ 0:0373 and R obs F ðsatÞ ¼ 0:0998, and much reduced features in the difference Fourier map (Table 1). The plot of F obs versus F calc shows an excellent match between these quantities (Fig. S2 in the supporting information).
The commensurability of the modulation requires the selection of the correct value of the initial phase, t 0 , of the modulation wave ( van Smaalen, 2012). For the 12-fold superstructure, the modulation wave is sampled at 12 equidi-stant points. Since only first-order satellite reflections have been observed (Fig. 3), this implies that different t 0 as well as the incommensurate model provide fits to the diffraction data of nearly equal quality. Table 2 gives partial R values for three different values of t 0 . We believe that the minor differences in R values are not sufficient to uniquely determine t 0 . Nevertheless, t 0 ¼ 1 48 has slightly higher R values and represents a supercell structure with triclinic symmetry, while t 0 ¼ 0 gives the lowest R values and corresponds to the highest supercell symmetry with space group P2 1 (a model with the same symmetry is obtained for t 0 ¼ 1 24 ). Evidence for lowering the symmetry to triclinic thus is lacking and we have chosen the monoclinic model with t 0 ¼ 0 for further analysis.
The relatively high partial R obs F ðsatÞ value for satellite reflections (Table 2) can be explained by rather weak reflections, as it is expressed by the magnitudes of partial R values for satellite reflections for the averaged standard uncertainty over intensity R ðsatÞ ¼ 0:1510 and for averaging of equivalent reflections R int ðsatÞ ¼ 0:1420. Further evidence for the final structure model has been obtained by establishing that the following variations of the model did not improve the fit to the diffraction data: (i) Treatment of nitrate group A and nitrate group B as different molecules leads to large correlations in the positions of their O atoms without any significant changes in R values.
(ii) The Co(sep) cage was refined without distance and angle restraints and individual atoms were refined for the nitrate groups. This model results in improved statistical parameters of refinement [R obs F ðmainÞ = 0.0335 and R obs F ðsatÞ = 0.0975], but the ADPs of four C atoms are non-positive definite and the geometries of the nitrate groups are outside the physically possible range.
(iii) Since the symmetry is non-centrosymmetric, inversion twinning was introduced for all six twin domains. The refinement resulted in insignificant values of the inversion twin volumes.
(iv) Second-order harmonic waves were added for displacive modulation of the atoms, but the resulting modulation functions showed ripples indicating fitting of the noise in the data.
(v) Isotropic secondary extinction correction resulted in a negative extinction parameter.

Variation of molecular conformations for
The crystal structure of the low-temperature phase (phase IV) of Co(sep)(NO 3 ) 3 is a high-Z 0 structure. Only a few crystal structures feature more independent molecules in the unit cell than the presently observed Z 0 = 12 [for example, the amino acid l-tryptophan with Z 0 = 16 (Gö rbitz et al., 2012); see also the review article by Steed & Steed (2015) and references therein, as well as the high Z 0 structure database by Steed (2016)]. High-Z 0 structures usually suffer from severe correlations between parameters in structure refinements, and restrictions on the parameters beyond symmetry restrictions are necessary. An elegant way of imposing nonsymmetry restrictions is the superspace approach (Schö nleber, 2011; van Smaalen, 2012;Pinheiro & Abakumov, 2015). Parameters are separated into a relatively small subset of atomic coordinates describing the basic structure [one molecule Co(sep) and three nitrate ions] and parameters describing deviations from the basic structure. For Co(sep)(NO 3 ) 3 we have observed satellite reflections in the X-ray diffraction of first order only (Fig. 3), which implies that the superstructure is described by a single harmonic modulation function for each independent parameter of the basic structure; higher harmonics cannot be determined (see the end of x2.2). Deviations from the basic structure are small indeed, as is easily seen by consideration of a plot of the superstructure, showing the 12 crystallographically independent but nearly indistinguishable copies of the molecule (Figs. 4 and 5).
The superspace approach reduces the number of independent parameters dramatically compared with the 12-fold supercell. Nevertheless, the monoclinic superspace group of phase IV does not capture the pseudo-trigonal symmetry of   the Co(sep) molecule, and further restrictions have turned out to be necessary. We have chosen to use rather narrow restraints on bond lengths and bond angles (x2.2). They are justified in hindsight by the good fit to the diffraction data of the thus refined structure model (Tables 1 and 2). Unsurprisingly, the 12 crystallographically independent Co(sep) molecules in the 12-fold supercell feature similar values for each bond length and each bond angle. The variations are most favourably analysed by t-plots ( van Smaalen, 2012), which provide the continuous dependence of each structural parameter on phase t of the modulation wave. Values observed in the 12-fold superstructure with t 0 = 0 are the values t = n/12 for n = 0, . . . , 11. Fig. 6 provides a t-plot of the distances between the Co atom and the 12 C atoms of the same molecule. It shows that these distances (not restrained in the refinement) have but minor variations between the 12 molecules. The (small) elongation of one Co-C bond is compensated for by shortening another Co-C bond, in complete agreement with the behaviour of other modulated compounds. Presently, distances towards the three apical C atoms at the top of the molecule (Nos. 10-12 in Fig. 6) are longer than average simultaneously with the distances towards the three apical C atoms at the bottom of the molecule being shorter than average (Nos. 7-9). This reflects the largest modulation amplitude of Co being along c (Table S1 in the supporting information). Angles within the Co(N lig ) 6 octahedron deviate more from their ideal values than in the structure of phase I (Schö nleber et al., 2010), but their variation with t is again very small (see the supporting information). Bond lengths and bond angles of all 12 independent Co(sep) molecules thus are similar to each other. The average molecule in phase IV has a slightly more distorted geometry than the structure of the molecule within the high-symmetry phase (Schö nleber et al., 2010) as well as in other filled sepulchrate complexes (Bacchi et al., 1993;Bacchi et al., 1996;Gahan & Harrowfield, 2015).  Unit cell of the superstructure projected onto (0 0 1). Atoms with À0.05 < z < 0.45 are shown (one layer; cf. Fig. 5). H atoms are not shown.  Nitrate groups have been restricted to be flat with O-N-O angles of 120 and three equal N-O bond lengths (Fig. 1). Nitrate groups A and B have been described by a common molecule with a refined N-O bond length of 1.237 (6) Å . The N-O bond in nitrate group C is shorter with d(N-O) = 1.160 (7) Å . Major differences between the different copies of the nitrate groups A, B and C are the orientations of these planar molecular anions (Fig. 7). We believe this part of the modulation to be at the origin of the complicated superstructure, as described in the next section.

Competing intermolecular interactions
In phase I, the nitrate groups A and B are parallel to the (a, b)-plane. In the present structure (phase IV), the planes of the 12 nitrate groups A and the 12 nitrate groups B make different angles with the (a, b)-plane, with values between 0 and 5 (Fig.  7). These small rotations are the result of optimizing the interactions between nitrate and sepulchrate moieties (see below). Nitrate group C is highly disordered in phase I (Fig. 5b;Schö nleber et al., 2010). The increased packing density at lower temperatures forces each nitrate group C into a single orientation. Orientations of the 12 crystallographically independent nitrate groups C exhibit a much larger variation than orientations of nitrate groups A and B (Fig. 7), again apparently the result of optimizing intermolecular interactions.
implies that they are weak hydrogen bonds (Jeffrey, 1997), which are hardly affected by the modulation. One would expect the molecules to close in, in order to strengthen the N-HÁ Á ÁO hydrogen bonds. However, this is prevented by actually the shortest interatomic distances between molecules.
Nitrate groups A and B are involved in C-HÁ Á ÁO interactions, which are shorter than the N-HÁ Á ÁO hydrogen bonds (Fig. 9). As short as 2.2 Å , these HÁ Á ÁO distances are at the lower side of the reported C-HÁ Á ÁO hydrogen bonds (Desiraju, 1991;Desiraju et al., 1993;Steiner & Desiraju, 1998;Desiraju & Steiner, 2001;Munshi & Row, 2005). It can thus be conjectured that even closer separations of these atoms would take them onto the repulsion part of the interaction curve, which would be energetically unfavourable. C-HÁ Á ÁO interactions rather than N-HÁ Á ÁO hydrogen bonds thus determine the packing in Co(sep)(NO 3 ) 3 .
The shortest contacts between nitrate group C and the sepulchrate cage are between the O atoms (atoms O9) and H atoms connected to the apical C atoms (atoms H2c41 through to H2c46) (Fig. 10). The range of HÁ Á ÁO distances of $ 2.2-2.5 Å is similar to the distances of the C-HÁ Á ÁO contacts of nitrate groups A and B (Fig. 11). Finally, short intermolecular interatomic distances are found between H atoms attached to apical C atoms on neighbouring sepulchrate molecules (Fig.  12). Again, these contacts prevent a denser packing of the molecules.

Conclusions
The 12-fold superstructure of Ã-cobalt(III) sepulchrate trinitrate at T = 95 K has successfully been described within the superspace approach. The superspace approach effectively removes correlations between crystallographically independent parameters of this high-Z 0 structure with Z 0 = 12.
The origin of the modulation is argued to lie in the avoidance of repulsive interactions rather than hydrogen bonding between neighbouring molecules. The shortest interatomic contacts are C-HÁ Á ÁO weak hydrogen bonds (Figs. 9 and 11) and C-HÁ Á ÁH-C intermolecular H-atom contacts (Fig. 12). Intermolecular N-HÁ Á ÁO hydrogen bonds do exist (Fig. 9), but they are long and weak, apparently prevented from full development by the short intermolecular contacts described above.