Threefold helical assembly via hydroxy hydrogen bonds: the 2:1 co-crystal of bicyclo[3.3.0]octane-endo-3,endo-7-diol and bicyclo[3.3.0]octane-endo-3,exo-7-diol

The structure of bicyclo[3.3.0]octane-endo-3,endo-7-diol and bicyclo[3.3.0]octane-endo-3,exo-7-diol, C8H14O2 form 2:1 co-crystals in the monoclinic P21/n space group rather than undergoing separation by means of fractional recrystallization or column chromatography.

Threefold helical assembly via hydroxy hydrogen bonds: the 2:1 co-crystal of bicyclo[3.3.0]octaneendo-3,endo-7-diol and bicyclo[3.3.0]octane-endo-3,exo-7-diol Reduction of bicyclo[3.3.0]octane-3,7-dione yields a mixture of the endo-3,endo-7-diol and endo-3, exo-7-diol (C 8 H 14 O 2 ) isomers (5 and 6). These form (5) 2 Á(6) co-crystals in the monoclinic P2 1 /n space group (with Z = 6, Z 0 = 1.5) rather than undergoing separation by means of fractional recrystallization or column chromatography. The molecule of 5 occupies a general position, whereas the molecule of 6 is disordered over two orientations across a centre of symmetry with occupancies of 0.463 (2) and 0.037 (2). Individual diol hydroxy groups associate around a pseudo-threefold screw axis by means of hydrogen bonding. The second hydroxy group of each diol behaves in a similar manner, generating a three-dimensional hydrogen-bonded network structure. This hydrogen-bond connectivity is identical to that present in three known helical tubuland diolhydroquinone co-crystals, and the new crystal structure is even more similar to two homologous aliphatic diol co-crystals.

Chemical context
Crystalline binary adducts (Herbstein, 2005) have been classified as clathrates, coordinatoclathrates, clathratocomplexes or complexes (Weber & Josel, 1983). At one end of this structural continuum, clathrates have a dominant host structure, host-guest interactions are less important, and the guests are spatially caged. Complexes, on the other hand, are mutually coordinated and the importance of three-dimensional enclosure is significantly lessened. Hosts may complex with a liquid guest to yield solvates or hydrates. If the two components are both solids of comparable size, however, then the host-guest distinction vanishes. The latter group of complexes are nowadays generally termed co-crystals (Aakerö y & Chopade, 2012).
Research into co-crystals is an area of considerable current significance. Many potentially valuable bioactive molecules have poor aqueous solubility and this restricts their application as pharmaceutical drugs. Combination with a benign partner molecule to produce a co-crystal can result in enhanced properties such as improved drug formulation and greater biological uptake (Almarsson & Zaworotko, 2004). Our knowledge of intermolecular attractive forces often allows a prediction to be made of the complementary partner required for such pharmaceutical co-crystal synthesis (Bis et al., 2006(Bis et al., , 2007. ISSN 2056-9890 A second sub-set of co-crystalline substances comprises unexpected combinations of isomers or structurally related compounds (Kelley et al., 2011). This is not a new phenomenon. Indeed, the first such material now recognised as being a co-crystal was discovered in 1844 by Friedrich Wö hler. This was the 1:1 combination of p-benzoquinone 1 and hydroquinone 2, commonly known as quinhydrone 3 ( Fig. 1) (Karagianni et al., 2018;Sakurai, 1968). These novel co-crystalline materials are generally discovered accidentally as a consequence of preparative organic work going wrong, in particular the very few instances where standard purification techniques fail. It is therefore a rare and unpredictable occurrence.
The present work describes a new example of this phenomenon. Reduction of bicyclo[3.3.0]octane-3,7-dione 4 with lithium aluminium hydride yielded an approximately 2:1 mixture of the diols 5 and 6 (Fig. 2). These isomeric products could not be separated by fractional recrystallization or standard column chromatography using silica or alumina.

Structural commentary
When the mixture of diols 5 and 6 was recrystallized from toluene, thin plate crystals of composition (5) 2 Á(6) were produced in the monoclinic space group P2 1 /n. The molecules of 5 (atoms labelled with suffix A) are in a general position, whereas molecules of 6 are disordered across the centre of inversion in this space group (thus Z = 6, Z 0 = 1.5). There are two sites (atoms labelled with suffixes B and C) of occupancies 0.463 (2) and 0.037 (2), respectively. The minor site C can be described as a position obtained by a twofold rotation about the axis perpendicular to the midpoint of the bond C3B-C7B of the molecule at site B (Fig. 3). However, from here onwards, only the major site B will be used in figures and discussions of intermolecular interactions for the sake of clarity. The bicyclo[3.3.0]octane skeleton comprises two cyclopentane rings fused in a cis-manner. Its basic configuration is a flattened Vshape in solution, with the convex face being termed exo-and the concave face endo-. Reduction of the diketone 4 therefore occurs preferentially on the more exposed exo-face to produce the endo-alcohol configuration. The co-crystal formula indicates that this stereoselectivity is around 5:1 using lithium aluminium hydride in tetrahydrofuran.
The cyclopentane rings, however, have conformational mobility that can contribute to the optimal crystal packing. In 1:1 combination of p-benzoquinone 1 and hydroquinone 2, commonly known as quinhydrone 3

Figure 2
Synthetic route to formation of title compounds 5 and 6

Figure 3
The isomer 5 (molecule A) (upper), the isomer 6 with its major component (molecule B, centre) and minor components (molecule C, lower) showing their crystallographic atom labelling. Displacement ellipsoids are drawn at the 50% probability level and hydrogen atoms are shown as spheres of arbitrary size. particular, envelope conformations may occur with the envelope flap being orientated syn-to either of the exo-or endo-faces. The isomer 5 has one flap syn to each of these ring faces, while 6 has both its flaps syn to the exo-face of the structure (Fig. 3). Ring twisting can also occur but is relatively minor in (5) 2 Á(6). Quantitative descriptions of these conformational effects are summarized by the cyclopentane ring torsion angle values marked on Fig. 4.

Supramolecular features
The isomeric diol molecules are connected by hydroxy hydrogen bonds (Table 1) and a three-dimensional network is formed. Molecules of 5 and 6 form a 2:1 infinite chain with their hydrogen bonds surrounding a pseudo-threefold screw axis along the a-axis direction (Fig. 5). The OÁ Á ÁO distance between molecules of 5 is 2.743 (2) Å , and those between 5 and 6 are 2.629 (12)   The bicyclo[3.3.0]octane ring conformations adopted by the isomers 5 (upper) and 6 (lower) in the structure (5) 2 Á(6). Torsion angles are shown with their e.s.d.s.

Figure 5
The crystal structure of (5) 2 Á(6) projected on the bc plane and looking down the pseudo-threefold screw axes. Colour code: O atoms red, diol 5 green, and diol 6 major component (light and dark blue). Minor component C and all hydrogen atoms are omitted for clarity and the hydroxy hydrogen bonds are indicated as solid black lines.

Figure 6
The crystal structure of (5) 2 Á(6) projected on the ab plane and showing the pseudo-threefold screw axes running horizontally. The alternating zones of isomers 5 and 6 in the crystal should be noted. Colour code is the same as used in Fig. 5. crystal contains alternating zones of 5 and 6 molecules that run along both the a-and c-axis directions (Fig. 6). The only other notable interaction is a C7A-H7AÁ Á ÁO2A weak hydrogen bond [D 3.727 (2), d 2.80 Å ] that links adjacent molecules of 5.
Viewed down a, the isomer 5 is present as two stacked columns of translated diol molecules. It is therefore probable that diol 6 is stacked similarly. This isomer contains no centre of symmetry, but is situated on a crystallographic inversion site. Molecules of 6 therefore appear in Figs. 5 and 6 as a superimposition of two disordered forms across a centre of symmetry.
The hydroxy hydrogen-bonding connectivity present in (5) 2 Á(6) provides a versatile supramolecular network that occurs in at least five other diol co-crystal structures (Fig. 7). Helical tubuland (HT) diols 7-9 employ hydroxy group hydrogen bonding to assemble around threefold screw axes in space group P3 1 21 (Bishop, 2009). This creates tubular voids that enclose guest molecules of many structural types. A notable exception is the phenol family, which instead yields hydrogen-bonded co-crystals. This is achieved by one of the three columns of HT diol molecules being replaced by a column of phenols with concomitant formation of pseudothreefold screw axes. Co-crystals of general formula (HT) 2 Á(2) are produced when hydroquinone 2 is used as the co-former molecule (Ung et al., 1993(Ung et al., , 1994Yue et al., 2002). Fig. 8 compares the threefold and pseudo-threefold screw axes using the example of HT diol 7. These should be compared to the screw axis observed in (5) 2 Á(6) (Fig. 8, right).
The hydrogen-bonding networks of 7, (7) 2 Á(2), and (5) 2 Á(6) are compared in Fig. 9 (upper, centre, and lower). All are viewed looking down the threefold screw axes. Despite the very different shapes and molecular structures of the building blocks 7/5 and 2/6, their hydroxy hydrogen-bonding connectivity is identical. The three networks do, however, differ in their crystallographic symmetry. This is a consequence of the presence, or absence, of chirality.
Structure 7 in chiral space group P3 1 21 contains only one enantiomer (dark green), and the threefold hydroxy hydrogen bonding coincides with the crystallographic 3 1 screw axis. Molecules along b surround a 2 1 screw axis (blue line), but mirror (or glide) symmetry is absent.

Figure 8
Comparison of the threefold screw axis of crystalline 7 (left), and the pseudo-threefold screw axes present in the co-crystals (7) 2 Á(2) (centre) and (5) ecules link the HT diol chains by contributing their hydroxy groups for completion of the pseudo-threefold hydrogenbonded helices running along a.
In contrast, both the diol molecules forming compound (5) 2 Á(6) are achiral, but this present case in space group P2 1 /n reveals a further example of threefold helicity involving different symmetry elements. All the molecules of isomer 5 are identical, but here have been coloured light or dark blue to discriminate those related by mirror symmetry operation. The second diol isomer 6 is shown in yellow and orange.
The hydroxy groups of both isomers associate to produce hydrogen-bonded pseudo-threefold helices down c. Molecules of 5 surround a 2 1 screw axis running along b (green lines), but are not connected by hydrogen bonds. They are also arranged as chains in the c-axis direction and these chains are related by a c-glide (magenta lines). The isomer 6 performs the same roles as hydroquinone did in the previous structure. These bridging molecules are located at the crystallographic inversion centre but lack their own centre of symmetry. Hence there is disorder of isomer 6 that creates a statistical centre of symmetry.

Database survey
The reduction of dione 4 using sodium borohydride or samarium iodide was earlier investigated by Camps et al., (2001). Small amounts of the pure isomers 5 and 6 were isolated, and these compounds were fully characterized by IR, 1 H and 13 C NMR, MS, and combustion analysis. No indication of molecular inclusion was evident. X-ray structure determinations of these pure isomers are unreported. Kelley et al. (2011) have carried out a comprehensive survey titled Failures of fractional recrystallization: ordered co-crystals of isomers and near isomers. This ground-breaking database search revealed 270 X-ray determinations of ordered cocrystals between isomers or closely related compounds. The phenomenon has therefore been demonstrated to be extremely rare. It will occur where the two partner molecules share structural complementarity and near identical solubility. New examples of this phenomenon cannot usually be predicted.
However, we note that cyclohexane-1,4-diol 10 (Loehlin et al., 2008) and cyclodecane-1,6-diol 12 (Ermer et al., 1989) both form 2:1 cis:trans diol co-crystals that are extremely similar to our compound (5) 2 Á(6). These three examples share a simple molecular structure in which two secondary alcohol groups are connected, maintaining net mirror plane symmetry, by means of a cyclic aliphatic linking group. This suggests that other members of this family exist. A probable example is cyclooctane-1,5-diol 11 but, at present, only the X-ray structure of its cis-isomer has been reported (Miller & McPhail, 1979).

Refinement
Crystal data, data collection and structure refinement details are summarized in Table 2. The molecule of 6 (suffix B) is located on a crystallographic inversion centre, which is incompatible with the molecular symmetry of the molecule. The molecule was thus refined as 1:1 disordered across this inversion centre. Close inspection of the difference densities revealed additional disorder, by an approximate twofold rotation perpendicular to the C3-C7 bond, and a second minor disordered moiety was added to the refinement model (suffix C). Bond distances and angles of both disordered moieties were restrained to be similar to that of the ordered molecule of 5 (suffix A) using a SHELXL SAME command (the esd used was 0.02 Å ). U ij components of ADPs of disordered atoms were restrained to be similar for atoms closer to each other than 2.0 Å using a SHELXL SIMU command (the esd used was 0.01 Å 2 ). The atom O1B and the symmetry equivalent (by inversion) of O2B occupy nearly identical positions, and their ADPs were constrained to be identical (SHELXL command EADP). Subject to these conditions, the occupancy rates refined to two times 0.463 (2) (moiety B and its inversion-created counterpart) and two times 0.037 (2) (moiety C and its inversion-created counterpart).
The minor moiety hydroxy atoms (of C) were in addition restrained based on hydrogen-bonding considerations. H2C was restrained to have a distance of 1.90 (2) Å from O2A (at 1 2 + x, 1 2 À y, À 1 2 + z), and H1CA to have a distance of 2.05 (2) Å from O2A (at 1 2 À x, 1 2 + y, 3 2 À z). Most of the H atoms (except for minor disordered component C) could be located in difference maps and the remaining were fixed at stereochemically reasonable positions using appropriate AFIX commands. In the final structural model, all H atoms were treated as riding atoms in geometrically idealized positions, with C-H distances of 0.99 Å (CH 2 ) and 0.84 Å (OH), and with U iso (H) = kU eq (C), where k = 1.5 for OH groups, and 1.2 for all other H atoms.  program(s) used to solve structure: SHELXT2018/2 (Sheldrick, 2015a); program(s) used to refine structure: SHELXL (Sheldrick, 2015b); molecular graphics: OLEX2 (Dolomanov et al., 2009); software used to prepare material for publication: OLEX2 (Dolomanov et al., 2009). Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.