L-threo-D-galacto-Octitol: a curious non-classical order–disorder polytype with an 88 Å axis

GalC8 [L-threo-D-galacto-octitol, systematic name (2S,3R,4R,5R,6R,7S)-octane-1,2,3,4,5,6,7,8-octol] crystallizes with a pseudo-tetragonal lattice featuring a long (∼88 Å) c axis. The bulk of the structure possesses P4₃2₁2 (Z′ = 1) pseudo-symmetry, whereby molecules are arranged linearly with eight molecules in a translation period, thus explaining the long c axis. According to this pseudo-symmetry, adjacent molecules are alternately related by 2₁ screw rotations (in 〈100〉 directions) and twofold rotations (in 〈110〉 directions). Due to an asymmetrical hydrogen-bonding network, symmetry is broken in the vicinity of the twofold rotation axes, leading to an overall P2₁ (Z′ = 4) space-group symmetry. The lost symmetry is retained as a twin operation. The structure can be classified as a `non-classical' OD polytype, in the sense that there are nonequivalent layer contacts, yet all members of the polytype family are locally equivalent. The main polytype is not of a maximum degree of order (MDO) and can be described as an alternation of fragments of the two MDO polytypes with P4₃ and P2₁2₁2₁ symmetry, respectively.

1. Introduction

Waste heat management is a key challenge in solving the energy crisis. Whereas thermoelectrics transform heat into electrical energy, phase change materials (PCM) allow for storage and later recuperation of thermal energy. Inagaki & Ishida (2016), using crystal structure prediction, postulated exceptionally high thermal storage densities of up to 450–500 J g⁻¹ for higher-carbon sugar alcohols with even-numbered carbon chain lengths and ideal stereochemical constitution. In particular, the chiral centers should be in 1,3-anti configuration, which allows for two kinds of diastereomers, the manno and galacto type, as exemplified in Scheme 1 for the C8 sugar alcohols (octitols, eight C atoms). The OH groups of the first two adjacent chiral centers are either in anti (manno type, blue arrow) or in syn configuration (galacto type, pink arrow). The remainder of the chain is determined by end-to-end 1,3-anti configuration. In Scheme 1, green arrows indicate the ideal 1,3-anti configuration.

To validate these predictions, we systematically synthesized and conducted structural and partial thermal characterizations of relevant C8 and C10 sugar alcohols of both compound families (Draskovits et al., 2025; Biedermann et al., 2024). So far, the experimental data are in close proximity to the predicted values, with a measured thermal storage density of 381 J g⁻¹ for manno-octitol (Draskovits et al., 2025), for example. This result is remarkable as this is significantly larger than typical storage densities of organic materials, such as paraffins, fatty acids and high-molecular weight alcohols, which are in the range 150–280 J g⁻¹ (Kenisarin, 2014). Only some natural sugar alcohols with outstandingly high values of up to 350 J g⁻¹ (Jadhav et al., 2010; Tomassetti et al., 2022) show comparable storage densities. Consequently, it is of great interest to determine the actual crystal structures and relate them to the predicted structures.

The C6 sugar alcohols galactitol (Berman & Rosenstein, 1968) and mannitol (Berman et al., 1968; Kim et al., 1968; Fronczek et al., 2003) are structurally well characterized. Whereas only one structure of galactitol is known, the polymorphism of mannitol is complex. At least three polymorphs are confirmed (Fronczek et al., 2003). To our knowledge no structures of the corresponding even-length higher-carbon sugar alcohols have been published. The structure of a single linear C10 sugar alcohol is known (Köll et al., 1992); however, it features 1,3-anti mixed with 1,3-syn configuration.

Here we present the structure of the enantiopure C8 galacto-type sugar alcohol, which we will hereafter call GalC8 [systematic name (2S,3R,4R,5R,6R,7S)-octane-1,2,3,4,5,6,7,8-octol]. Due to a large axis and smearing of reflections, data were collected using high-brilliance synchrotron radiation. A pseudo-symmetry analysis to explain the observed structural intricacies will be given. Thereto, we apply a generalization of the order–disorder (OD) theory (Dornberger-Schiff & Grell-Niemann, 1961), which presents an alternative view of crystalline materials, taking into account the short range of interatomic interactions. Members of an OD family are locally equivalent (and thus energetically very similar), but cannot be superimposed by application of a global isometry of Euclidean space. Instead, they have to be related by partial operations mapping distinct overlapping subspaces, usually pairs of layers.

2. Experimental

2.1. Synthesis

GalC8 was synthesized as described in our previous work (Biedermann et al., 2024) from commercially available L-lyxose via indium-mediated acyloxylation and subsequent dihydroxylation of the obtained enitol followed by Mitsunobu reaction. For crystallization, GalC8 (10 mg) was suspended in a methanol/H₂O mixture (4:1, 0.5 ml) in a microwave reaction vial and placed in a Biotage initiator + microwave system. The suspension was heated to 100 °C for 1 min and subsequently allowed to cool down to 70 °C. The vial containing a clear solution was taken out and allowed to slowly cool down to room temperature, leading to crystallization. The colorless crystalline solid was separated via centrifugation, triturated with methanol twice (2 × 1 ml) and pre-dried at 70 °C. Further drying was performed at 40 °C in vacuo (<5 mbar) resulting in 8.5 mg of crystalline GalC8.

2.2. Diffraction

Intensity data of multiple crystals were collected in a dry stream of nitrogen at 170 K on the high-flux P24 beamline of the PETRA III synchrotron facility using 0.560 Å radiation. Two 360° φ-scans with 0.2° frame width were collected. To rule out potential phase transitions, data of a crystal were likewise collected at 300 K. Frames were converted into the ESPERANTO format and processed with CrysAlisPRO (Rigaku Oxford Diffraction, 2022). A correction for absorption effects was performed using the multi-scan approach (ABSPACK). A first solution was obtained from SHELXT (Sheldrick, 2015b) and the correct symmetry was determined as detailed in Results and Discussion. The structure was refined against F² using SHELXL (Sheldrick, 2015a) as a twin by pseudo-merohedry. Integration using two separate twin domains resulted in worse refinements, most likely owing to smearing of reflections. Aliphatic H atoms were placed at calculated positions and thereafter refined as riding on the parent atoms. Hydroxyl H atoms were located from difference Fourier maps and refined using distance restraints with respect to the donor and acceptor O atoms. In some cases, the hydrogen positions were not unambiguous and the hydrogen-bonding network could in fact be disordered as detailed below. More details on data collection and structure refinement are compiled in Table 1.

Table 1
Data collection and refinement details for GalC8

Crystal data
Chemical formula	C8H18O8
Mr	242.22
Crystal system	Monoclinic
Space group	P21
Temperature (K)	170
a, b, c (Å)	4.87027 (10), 4.86819 (12), 87.8394 (16)
β (°)	90.3132 (17)
V (Å^3)	2082.59 (8)
Z, Z′	8, 4
Radiation type	Synchrotron
Wavelength, λ (Å)	0.560
ρcalc (g cm^−3)	1.545
μ (mm^−1)	0.084
Crystal shape, color	Plate, colorless
Crystal size (mm)	0.10 × 0.09 × 0.01
Data collection
Diffractometer	Huber Eulerian cradle
Absorption correction	Multi-scan
Tmin, Tmax	0.653, 1.000
No. of measured, independent and observed [I > 3σ(I)] reflections	34215, 10304, 9099
Rint	0.0770
(Å^−1)	0.812
Refinement
Robs	0.1129
wR(F^2)obs	0.2903
Rall	0.1196
wR(F^2)all	0.2954
Goodness of fit	1.051
No. of parameters	675
No. of restraints	74
Δρmin, Δρmax (e Å^−3)	−0.51, 0.86
Twin operation	4[001]
Twin volume ratio	79:21.0 (5)

3. Results and discussion

3.1. Derivation of the actual and the pseudo-symmetry

Elucidating the actual symmetry of GalC8 was rather difficult and therefore a detailed account of the encountered challenges will be given. In general, navigating different symmetries (up and down group/subgroup chains), including operations such as origin transformations, was performed using the JANA2020 suite (Petříček et al., 2023). Conveniently, JANA2020 automatically transforms symmetry operations, displacement tensors and refinement restraints. Missed symmetry was checked with the ADDSYM routine implemented in PLATON (Spek, 2009).

Intensity measurements using the in-house diffractometer of thin plates of GalC8 suggested a tetragonal symmetry with a highly elongated unit cell (a ≈ 5 Å, c ≈ 88 Å). A structure solution with SHELXT suggested a P4₃ space-group symmetry with Z′ = 2 crystallographically independent molecules. Enantiomorphic space group P4₁ was excluded based on the known absolute configuration of GalC8. However, two terminal O atoms were disordered and refinements were of very poor quality (R₁ > 20%). Implementation of the expected twinning by merohedry (twofold rotation about 〈100〉) did not improve the reliability factors.

To shed light on the matter, intensity data were collected using synchrotron radiation. While performing these experiments, it became clear that the crystals are most likely not tetragonal as they showed typical signs of pseudo-merohedral twinning. Notably, whereas rods with low h and k values showed well resolved reflections, at a larger distance from the origin in reciprocal space, reflections were smeared out along the c* direction (Fig. 1).

Figure 1 Reciprocal space sections at constant (left) h = 0 and (right) h = 4 showing well defined reflections close to the origin and more smeared-out/split reflections at larger h and k values. The reflections expected for a 43 or 41 screw rotation at the (00l)* rod are indicated by white arrows. Other reflections on this rod violate the reflection conditions of these operations.

Moreover, space group P4₃ could be ruled out owing to violation of the reflection conditions on the (00l)* rod (l = 4n, ) (see Fig. 1). Regarding the translationengleiche (possessing the same translation lattice) subgroups, there are precisely two candidates: P4₃ > P112₁ > P1. The intermediate P112₁ can be excluded, as diffusiveness of reflections in c* direction indicates a c vector that is not perfectly normal to the (001) plane. Moreover, the (00l)* rod does not show the absences expected for a 2₁ screw rotation in [001] direction (l = 2n, ). In fact, the disorder did not resolve in P112₁. Therefore, we reduced the symmetry to P1 (Z′ = 8) and implemented the lost point symmetry as twin operations (fourfold rotation about [001]). This resolved the disorder nearly completely and led to an improved, albeit over-parametrized, refinement, which was evident, for example, in unreasonable displacement parameters.

Applied to the triclinic structure, ADDSYM suggested P2₁ symmetry (Z′ = 4), i.e. a twofold screw rotation axis normal to the (pseudo-)tetragonal axis. Combination of such a 2₁ axis with the original 4₃ pseudo-screw rotation gives an P4₃2₁2 (Z′ = 1) pseudo symmetry. Indeed, when manually increasing the symmetry to P4₃2₁2, a structure with only one disordered non-H atom (a terminal O, see above) was obtained. For unknown reasons, we were unable to obtain this symmetry from ADDSYM, even by removal of the atom violating the symmetry. We conclude that reliance on heuristic methods to determine symmetry can be treacherous.

To summarize, GalC8 crystallizes in a structure with actual P2₁ symmetry that can be derived from an idealized structure with P4₃2₁2 symmetry in a translationengleiche symmetry descent of index 4 (P4₃2₁2 P2₁2₁2₁ P12₁1 = P2₁). The intermediate orthorhombic phase can be excluded by the arguments given above: it would not produce diffuseness in the c* directions, but rather in the (a*, b*) plane and is in contradiction with the reflections on (00l)*.

3.2. Crystal structure

Fig. 2 shows the crystal structure of GalC8 viewed along [100]. The molecules are arranged linearly along [001]. There are eight molecules in a translation period, related by the (pseudo-)symmetry of space group P4₃2₁2, indicated by the standard symbols in Fig. 2. In the [100] and [010] directions, all molecules are related by translation, leading to the highly elongated unit cell.

Figure 2 The crystal structure of GalC8 viewed along [100]. C and O atoms are represented by gray and red spheres of arbitrary radius, respectively; H atoms omitted for clarity. Symmetry elements according to the P43212 pseudo-symmetry are indicated using the standard graphical symbols (Hahn & Aroyo, 2016). Elements of the actual symmetry are depicted in red. The 43 axes parallel to the drawing plane and the inclined twofold rotation axes are indicated by symbols used for cubic space groups.

Adjacent molecules in the [001] direction are related in succession by 2₁ ([100] direction), twofold rotation ([110]), 2₁ ([010]), twofold rotation (), etc. Since all these operations invert the orientation of the GalC8 molecules and the atoms were named linearly (C1 → C8 and O1 → O8), O1 connects to O1 (about 2₁ screw rotation axis) and O8 to O8 (about a twofold rotation axis).

The only non-H atoms deviating significantly from P4₃2₁2 symmetry are the O8 atoms (see Fig. 2). In the idealized P4₃2₁2 structure, these atoms are disordered in a 1:1 manner about the twofold axis.

In the actual structure, only the translations and the 2₁ [010] axes remain (red symbols in Fig. 2), which means that there are Z′ = 4 independent molecules in the asymmetric unit, which are named as letters i–l. Along [001], the succession is …lkjiijkl… (see right-hand side of Fig. 2). With respect to O8, the molecules appear as pairs of two conformers (Fig. 3): straight (i, k) and bent (j, l), which would overlap in space group P4₃2₁2. Across the twofold rotation axis one kind of conformer connects to the other via the O8 atoms.

Figure 3 Two distinct conformers of GalC8 illustrated by molecules (top) i and (bottom) j. Note the distinct, fully ordered, positions of the O8 atoms. Ellipsoids are drawn at the 75% probability level. In the actual structure, the molecules have opposite orientation with respect to [001] and have been reoriented here for better comparison.

3.3. Partial symmetry

The P4₃2₁2 pseudo-symmetry in GalC8 applies to parts of the structure but not others. Thus, it is best regarded in terms of partial symmetry. Symmetry operations that map only a subset of Euclidean space, such as layers or other modules, are called partial (symmetry) operations (POs). Each PO has a source and a target, which may or may not coincide. The composition of POs forms a space groupoid (Ito & Sadanaga, 1976). The composition is not closed, since only POs for which the target of the first is the source of the second may be combined. Other than that, the group axioms apply.

An analogous structure, where P2₁/c symmetry is only valid for a subset of Euclidean space is the low-temperature phase vanillyl oxime (Ehrmann et al., 2019). In the high-temperature phase, the P2₁/c symmetry becomes global. In other words, from a symmetry point of view, the phase transition affects only a subset of the crystal space. In GalC8 we did not observe a phase transition to a P4₃2₁2 phase up to 300 K and considering the structural description given below, deem it as highly unlikely.

In OD structures (Dornberger-Schiff & Grell-Niemann, 1961), owing to partial symmetry, there are multiple ways to connect layers, resulting in equivalent pairs of layers. These pairs can be connected to an infinite number of globally nonequivalent polytypes, which are nevertheless all locally equivalent. Even though GalC8 is, strictly speaking, not an OD structure, we will apply the techniques of OD theory and show that it nevertheless has OD character.

The crucial step in an OD interpretation is a choice of layers (or rods), such that there is only small-to-negligible interactions beyond a layer's width. As noted in the previous section, the P4₃2₁2 symmetry applies to all non-H atoms except O8. However, when considering the hydrogen-bonding network (for details see below), different connectivities are also observed for O7 and O6 atoms. Therefore, we will `slice' the molecules at the C5—C6 bond as indicated by dotted lines in Fig. 4.

Figure 4 The two kinds (A and d/b) of layers in GalC8 separated by dotted lines. Atoms as given in Fig. 2. The (idealized) symmetry elements (21 screw rotations) of the A layers are indicated using the standard symbols. Brackets to the right indicate layer n-tuples: individual layers, MERs and fragments of the MDO polytypes.

From a crystal-chemical point of view it may appear surprising to define layers containing pieces of molecules. Yet, an OD argument is purely based on symmetry and the lack of long-range interactions. For a similar case, see Stöger et al. (2013).

Thus, two kinds of layers are obtained. The O5⋯O1O1⋯O5 layers possess p12₁1 and p2₁11 layer-group symmetry (Kopsky & Litvin, 2006), respectively (Fig. 4). In the OD literature, these layers are called nonpolar, because the 2₁ operation exchanges the layer interfaces, i.e. both sides of the layers are related by symmetry. The standard symbol for these kinds of layers is A (Dornberger-Schiff & Grell, 1982).

The O6…O8O8…O6 layers possess only p1 layer symmetry, because the 2 symmetry is broken by the O8 atoms. These layers are called polar, which means that both sides of the layers are not related by layer symmetry and they may, therefore, exist in two orientations with respect to the stacking direction. Depending on this orientation, polar layers are usually designated as d and b (Dornberger-Schiff & Grell, 1982) (note that the letters d and b can be considered as being mirror images of each other).

Thus, GalC8 is an alternating succession of nonpolar A and polar d (or b) layers. Such a structure is formally not of the OD-kind because it violates the condition that equivalent sides of equivalent layers contact to adjacent layers such that the resulting pairs are equivalent (Dornberger-Schiff & Grell-Niemann, 1961). However, the A layer has only one equivalent side that connects to both sides of the d layer resulting in the nonequivalent pairs Ad and Ab.

3.4. Equivalent regions and polytypes

The core argument of OD theory is that all structures of an OD family are locally equivalent, because pairs of layers are equivalent. Parts of the structure that are equivalent in the whole family are called equivalent regions (Grell, 1984). The largest equivalent regions are maximal equivalent regions (MERs). In GalC8, given an A layer, the adjacent layer can either be b or d, which means that A is located at the boundary of a MER. In contrast, given a b layer, to both sides there is only one way of placing the A layer. Thus the MERs are AbA, or the equivalent AdA fragments. The MERs are indicated on the right side of Fig. 4. In such an MER, the orientations of the two A layers to both sides are rotated by 90° about [001], leading to the global tetragonal pseudo-symmetry.

In a classical OD structure, every point in a polytype is covered by two MERs and each MER is at least two layers wide, which means that every point is at least half of a layer inside a MER. It is in that sense that all structures of an OD family are locally equivalent. As can be seen in Fig. 4, in GalC8, some parts (the d/b layers) are covered by only one MER. However, since the MERs are three layers wide, any point is still at least one half A layer inside a MER. Thus, here likewise all members of the structure family are locally equivalent in the same sense as in classical OD structures. We have encountered such a family of structures built of polar and nonpolar layers before [Ca₅Te₄O₁₂(NO₃)₂(H₂O)₂, (Stöger & Weil, 2013)] and named it a non-classical OD family.

All members of the structure family can be constructed by combining MER fragments such that the A layers overlap. Owing to the p12₁1 (or p2₁11) symmetry of the A layers, there are two ways of extending an AbA fragment, as shown in Scheme 2.

Application of a screw rotation generates an AdAdA fragment, where both AdA fragments possess the same orientation with respect to [001] as indicated by red arrows pointing in the same direction. Here stands for a screw rotation operation with counterclockwise rotation about 90° and intrinsic translation . The inverse operation is 4⁺₃: clockwise rotation and translation . The (layer group) symmetry of the fragment is p111, because only the translations of the central A layer map the d layers onto themselves.

The second way is application of the 2₁ screw rotation of the third layer of the AdA fragment, leading to an AdAbA fragment, where the AdA and AbA MERs possess different orientation with respect to [001], as shown by red arrows pointing in opposite directions. The AdAbA fragment possesses p2₁11 or p12₁1 symmetry, because the 2₁ operation maps AdA on AbA and vice versa.

Thus by repeated application of and/or 2₁ operations, an infinite number of polytypes can be constructed. All of them, if only the A layers are considered, possess P4₃2₁2 symmetry, because the positions of the A layers are fixed. Including the d/b layers, the symmetry is reduced. In fact, the obtained structures need not even be periodic in the [001] direction.

The polytypes that cannot be decomposed into fragments of simpler polytypes are said to be of a maximum degree of order (MDO) (Dornberger-Schiff, 1982). There are two GalC8 MDO polytypes:

MDO₁: P4₃, generated by repeated application of  [001], contains only AdAdA or only AbAbA fragments.

MDO₂: P2₁2₁2₁, generated by repeated application of 2₁ 〈100〉, contains only AdAbA and AbAdA fragments.

Note that these were two structure models we considered, but rejected based on the diffraction data (see above), as their symmetries are the maximal translationengleiche subgroups of P4₃2₁2. All other polytypes can be decomposed into five-layer wide fragments of MDO₁ and MDO₂.

In particular, the actually observed polytype with P2₁ symmetry corresponds to alternating fragments of MDO₁ and MDO₂. This is the simplest possible non-MDO polytype. Two (very small) residual peaks in the difference electron density close to O8k and O8l indicate sporadical reversal of the d/b layer at this contact, which suggests the occurrence of other fragments, as is common in structures with OD character.

3.5. Hydrogen bonding

Hydrogen bonds of the type O—H⋯O in alcohols are of comparable strength to those in water (Steiner, 2002). Therefore, the packing of sugar alcohols in the solid state is largely determined by intermolecular hydrogen bonding, which is therefore an essential part of the structure. In GalC8, it plays a crucial role in breaking the idealized symmetry.

As noted in Experimental, assignment of the H-atom position was not always unambiguous and the hydrogen-bonding network might be disordered. From the O—O distances, it is however clear between which O atoms the hydrogen atoms are located. Only the donor and acceptor might be reversed.

We will therefore discuss the hydrogen bonding in terms of non-directed graphs, where nodes represent O atoms and vertices represent hydrogen bonds connecting two O atoms. More precisely, we will use voltage graphs (Eon, 2016), which allow a concise depiction of translationally periodic hydrogen-bonding networks infinitely. All hydrogen bonds in GalC8 are intermolecular. The donor–acceptor distances are compiled in Table 2. They all fall into the moderate-strength category according to the classification of Jeffrey (1997), which corresponds approximately to the hydrogen-bond strength of water.

Table 2
O⋯O distances d of hydrogen-bond connected atoms in GalC8

O⋯H distances are not given, because the positions of the H atoms are not well determined.

Atoms	d (Å)	Atoms	d (Å)
O1i⋯O1i	2.824 (6)	O1k⋯O1j	2.839 (9)
O2i⋯O4i	2.737 (9)	O2k⋯O4k	2.724 (7)
O3i⋯O2i	2.695 (7)	O3k⋯O2k	2.669 (9)
O4i⋯O5i	2.677 (8)	O4k⋯O5k	2.659 (9)
O5i⋯O3i	2.705 (9)	O5k⋯O3k	2.696 (7)
O6i⋯O7i	2.806 (8)	O6k⋯O7k	2.789 (10)
O7i⋯O8i	3.138 (12)	O7k⋯O8k	3.115 (10)
O8i⋯O7j	2.755 (8)	O8k⋯O7l	2.759 (9)
O1j⋯O1k	2.832 (9)	O1l⋯O1l	2.823 (6)
O2j⋯O4j	2.744 (7)	O2l⋯O4l	2.746 (9)
O3j⋯O2j	2.698 (10)	O3l⋯O2l	2.695 (7)
O4j⋯O5j	2.688 (10)	O4l⋯O5l	2.702 (7)
O5j⋯O3j	2.730 (7)	O5l⋯O3l	2.754 (9)
O6j⋯O8j	2.781 (8)	O6l⋯O8l	2.769 (10)
O7j⋯O6j	2.705 (10)	O7l⋯O6l	2.726 (7)
O8j⋯O8i	2.963 (11)	O8l⋯O8k	2.932 (10)

First, let us discuss the hydrogen bonding in the A layers. The O1 atoms of two molecules related by the 2₁ operation form infinite chains in the 〈100〉 directions as shown in Fig. 5 for the i molecules, where the 2₁ operation of the A layer is a global operation of the P2₁ polytype (in the [100] direction the 2₁ operation is not a global operation).

Figure 5 Infinite O1 hydrogen bonding exemplified by the i molecule. H atoms are represented by white spheres, other atoms as given in Fig. 2.

The corresponding graph is

where 2₁ designates the molecule related by the 2₁ operation. The label on an edge is called a voltage and implies that when crossing the edge, a translation is performed with respect to the original node. The arrow head in the middle of the edge does not represent the direction of the hydrogen bond, but rather gives meaning to the voltage. Here, crossing in direction of the arrow means translation along [100] and against the arrow along [100]. Note that the voltages are given for one particular orientation of the A layers. In half of the A layers they are exchanged for 010.

One can also form the quotient graph with respect to all symmetry operations, not only translations (Eon, 2016), though then the situation may become more complex (McColm, 2024). Factoring out the (pseudo-)screw rotation, one obtains the graph

where 2(0, ½, 0) is a twofold screw rotation with intrinsic translation ½b. Passing the edge in the same direction adds a translation component of ½b per loop and thus the quotient graph indeed represents a periodic hydrogen-bonding network.

The O2–O4 atoms are part of a cyclic four-atom network represented by the graph

and shown in Fig. 6. Note that the voltages sum to 000 when taking a full round, which means that the original O atom is reached, as required for a cyclic network.

Figure 6 Cyclic O2—O5 hydrogen bonding exemplified by the i molecule, viewed along [001]. Atoms as given in Fig. 5. H atoms not involved in the cycle have been omitted for clarity.

Then let us turn our attention to the hydrogen bonds in d/b layers, exemplarily shown in Fig. 7. Here, only a single network is observed, described by the graph

The core of the network is a four-atom cycle where all atoms belong to distinct molecules. Molecules obtained by a twofold rotation in the 〈110〉 direction of the P4₃2₁2 pseudo-symmetry are marked by `2'. This twofold rotation symmetry is broken precisely by this hydrogen-bonding network. Additionally an O6 and an O7 atom form a linear side chain. The hydrogen bond of the O7 atom donating into the cycle is distinctly weaker than the others (O7⋯O8 distance ∼3.1 Å, see Table 2).

Figure 7 Hydrogen-bonding network in the d/b layers, exemplified by an i/j pair of molecules, viewed slightly inclined to [100]. Atoms as given in Fig. 5.

The graph in equation (4) clearly shows that the hydrogen-bonding network is incompatible with the pseudo-twofold rotation symmetry as the O6 and O7 atoms are only part in the cycle for one but not the other molecule. Formally, we can say that the permutation that exchanges the atoms supposedly equivalent by pseudo-symmetry is not an automorphism of the graph and therefore the twofold rotation symmetry cannot be realized.

4. Conclusion and outlook

One might assume that a crystal structure with an ≈ 88 Å axis is complex or low in symmetry. GalC8 is not: according to the P4₃2₁2 pseudo-symmetry it is built of only one crystallographically equivalent molecule. The long axis is due to the linear arrangement of the molecules. However, symmetry is broken locally by the hydrogen-bonding network, whereby the lower-symmetry part of the structure may appear in two orientations. Thus an infinite number of locally equivalent arrangements may exist, which, if periodic, all possess a c axis of a multiple of ≈ 88 Å. GalC8 does not adopt the simplest of these polytypes, which means that there is some sort of long-range information transfer during crystal growth.

Clearly, a generalization of space group to partial symmetry is required since it reflects the locality of interatomic interactions. We suggest not considering disjoint subsets (such as layers) as being the objects of the corresponding groupoids, but rather MERs that partially overlap. This overlap expresses the local equivalence of the members of structure families.

The structural elucidation of the remaining long-chain sugar alcohols we have synthesized is in progress and we are looking forward to more interesting surprises.

Supporting information

Computing details

(2S,3R,4R,5R,6R,7S)-1,2,3,4,5,6,7,8-octaneoctol

Crystal data

C8H18O8	F(000) = 1040
Mr = 242.22	Dx = 1.545 Mg m^−3
Monoclinic, P21	Synchrotron radiation, λ = 0.560 Å
a = 4.87027 (10) Å	Cell parameters from 15279 reflections
b = 4.86819 (12) Å	θ = 1.5–26.9°
c = 87.8394 (16) Å	µ = 0.08 mm^−1
β = 90.3132 (17)°	T = 170 K
V = 2082.59 (8) Å^3	Plate, colorless
Z = 8	0.11 × 0.09 × 0.01 mm

Data collection

Huber Eulerian cradle diffractometer	9099 reflections with I > 2σ(I)
φ scans	Rint = 0.077
Absorption correction: multi-scan CrysAlisPro 1.171.42.69a (Rigaku Oxford Diffraction, 2022) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	θmax = 27.0°, θmin = 1.5°
Tmin = 0.653, Tmax = 1.000	h = −7→6
34215 measured reflections	k = −7→4
10304 independent reflections	l = −129→133

Refinement

Refinement on F^2	74 restraints
Least-squares matrix: full	Hydrogen site location: mixed
R[F^2 > 2σ(F^2)] = 0.113	H atoms treated by a mixture of independent and constrained refinement
wR(F^2) = 0.295	w = 1/[σ^2(Fo^2) + (0.1231P)^2 + 8.4901P] where P = (Fo^2 + 2Fc^2)/3
S = 1.05	(Δ/σ)max < 0.001
10304 reflections	Δρmax = 0.86 e Å^−3
674 parameters	Δρmin = −0.51 e Å^−3

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.

Refinement. Refined as a 2-component twin.

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

	x	y	z	Uiso*/Ueq
O1I	0.1465 (12)	0.7965 (18)	0.50063 (7)	0.0424 (17)
H1I	0.04 (2)	0.641 (14)	0.4992 (14)	0.064*
O2I	−0.0386 (11)	0.9160 (15)	0.53062 (6)	0.0348 (13)
H2I	0.027 (9)	1.029 (15)	0.5376 (8)	0.052*
O3I	0.4824 (10)	0.8802 (15)	0.54572 (6)	0.0352 (14)
H3I	0.597 (7)	0.902 (10)	0.5382 (5)	0.053*
O4I	0.0079 (11)	0.3244 (15)	0.55189 (6)	0.0350 (14)
H4I	−0.119 (10)	0.252 (13)	0.5573 (10)	0.053*
O5I	0.5336 (10)	0.2797 (14)	0.56694 (7)	0.0356 (14)
H5I	0.476 (14)	0.121 (11)	0.5631 (6)	0.053*
O6I	0.0179 (12)	0.6614 (17)	0.58783 (6)	0.0405 (15)
H6I	−0.128 (12)	0.60 (2)	0.5930 (11)	0.061*
O7I	0.5245 (11)	0.5337 (17)	0.60258 (7)	0.0422 (16)
H7I	0.421 (13)	0.657 (14)	0.6072 (12)	0.063*
O8I	0.3454 (14)	0.063 (2)	0.62035 (7)	0.056 (2)
H8I	0.29 (2)	0.01 (3)	0.6293 (8)	0.084*
O8J	−0.4435 (12)	0.4955 (16)	0.64105 (7)	0.0419 (15)
H8J	−0.46 (2)	0.405 (17)	0.6326 (6)	0.063*
O7J	0.0865 (12)	0.9911 (16)	0.64787 (6)	0.0399 (15)
H7J	0.09 (2)	1.099 (8)	0.6560 (5)	0.060*
O6J	0.1480 (10)	0.4713 (13)	0.66302 (6)	0.0302 (12)
H6J	0.251 (12)	0.516 (11)	0.6551 (6)	0.045*
O5J	−0.2369 (10)	1.0123 (15)	0.68297 (6)	0.0342 (13)
H5J	−0.376 (15)	0.953 (18)	0.6884 (8)	0.051*
O4J	−0.1996 (10)	0.4939 (15)	0.69781 (6)	0.0332 (13)
H4J	−0.23 (2)	0.379 (7)	0.6904 (6)	0.050*
O3J	0.3649 (11)	0.9608 (16)	0.70453 (6)	0.0371 (14)
H3J	0.325 (14)	1.114 (12)	0.7089 (11)	0.056*
O2J	0.4010 (11)	0.4430 (15)	0.71955 (6)	0.0344 (13)
H2J	0.534 (16)	0.515 (14)	0.7138 (9)	0.052*
O1J	0.2712 (11)	0.6250 (18)	0.74951 (7)	0.0425 (17)
H1J	0.108 (15)	0.53 (3)	0.7503 (13)	0.064*
O1K	0.7722 (11)	0.3271 (16)	0.75042 (7)	0.0392 (15)
H1K	0.609 (15)	0.42 (2)	0.7496 (13)	0.059*
O2K	0.9039 (11)	0.5263 (13)	0.78071 (6)	0.0329 (12)
H2K	1.041 (14)	0.466 (12)	0.7871 (8)	0.049*
O3K	0.8702 (10)	0.0031 (14)	0.79557 (6)	0.0319 (13)
H3K	0.848 (17)	−0.138 (10)	0.7895 (9)	0.048*
O4K	0.3114 (10)	0.4765 (13)	0.80189 (6)	0.0300 (12)
H4K	0.30 (2)	0.579 (6)	0.8099 (4)	0.045*
O5K	0.2715 (11)	−0.0484 (14)	0.81664 (5)	0.0302 (12)
H5K	0.151 (13)	−0.001 (11)	0.8094 (8)	0.045*
O6K	0.6559 (12)	0.4736 (17)	0.83761 (7)	0.0416 (16)
H6K	0.63 (2)	0.637 (12)	0.8418 (12)	0.062*
O7K	0.5410 (12)	−0.0363 (16)	0.85275 (7)	0.0414 (15)
H7K	0.678 (13)	0.056 (16)	0.8577 (12)	0.062*
O8K	0.0689 (16)	0.1411 (18)	0.87035 (8)	0.0518 (18)
H8K	0.05 (3)	0.185 (15)	0.8801 (4)	0.078*
O8L	0.4953 (14)	0.9357 (16)	0.89111 (8)	0.0475 (16)
H8L	0.431 (14)	0.97 (3)	0.8820 (4)	0.071*
O7L	0.9975 (11)	0.4068 (15)	0.89778 (6)	0.0371 (15)
H7L	1.118 (7)	0.37 (2)	0.9048 (6)	0.056*
O6L	0.4847 (11)	0.3474 (16)	0.91285 (6)	0.0373 (15)
H6L	0.528 (14)	0.199 (15)	0.9075 (9)	0.056*
O5L	1.0185 (10)	0.7351 (14)	0.93289 (7)	0.0328 (13)
H5L	0.99 (2)	0.898 (10)	0.9373 (6)	0.049*
O4L	0.5041 (10)	0.6958 (15)	0.94775 (6)	0.0348 (14)
H4L	0.341 (9)	0.664 (17)	0.9444 (10)	0.052*
O3L	0.9741 (10)	0.1419 (14)	0.95453 (6)	0.0312 (12)
H3L	1.145 (6)	0.144 (10)	0.9569 (6)	0.047*
O2L	0.4582 (10)	0.1007 (15)	0.96935 (6)	0.0357 (15)
H2L	0.503 (16)	−0.053 (13)	0.9646 (7)	0.054*
O1L	0.6463 (12)	0.2277 (18)	0.99936 (7)	0.0437 (18)
H1L	0.55 (3)	0.390 (15)	1.0002 (16)	0.066*
C1I	0.3156 (17)	0.754 (2)	0.51384 (7)	0.039 (2)
H1IA	0.4290	0.9198	0.5156	0.047*
H1IB	0.4413	0.5980	0.5120	0.047*
C2I	0.1479 (16)	0.695 (2)	0.52793 (8)	0.036 (2)
H2IA	0.0387	0.5241	0.5261	0.044*
C3I	0.3305 (13)	0.649 (2)	0.54182 (8)	0.0297 (16)
H3IA	0.4623	0.4979	0.5394	0.036*
C4I	0.1649 (14)	0.5601 (19)	0.55581 (8)	0.0300 (16)
H4IA	0.0346	0.7117	0.5584	0.036*
C5I	0.3411 (14)	0.5005 (19)	0.56999 (8)	0.0294 (16)
H5IA	0.4484	0.6698	0.5725	0.035*
C6I	0.1687 (14)	0.421 (2)	0.58401 (9)	0.0348 (19)
H6IA	0.0376	0.2716	0.5811	0.042*
C7I	0.3492 (16)	0.323 (2)	0.59709 (9)	0.039 (2)
H7IA	0.4659	0.1680	0.5933	0.047*
C8I	0.1644 (18)	0.213 (2)	0.60990 (10)	0.040 (2)
H8IA	0.0733	0.3668	0.6153	0.048*
H8IB	0.0214	0.0896	0.6057	0.048*
C8J	−0.2142 (14)	0.666 (2)	0.63802 (9)	0.0331 (17)
H8JA	−0.2573	0.7914	0.6295	0.040*
H8JB	−0.0547	0.5516	0.6351	0.040*
C7J	−0.1470 (15)	0.827 (2)	0.65188 (9)	0.0335 (17)
H7JA	−0.3045	0.9521	0.6542	0.040*
C6J	−0.0807 (13)	0.6577 (19)	0.66594 (8)	0.0264 (14)
H6JA	−0.2455	0.5425	0.6682	0.032*
C5J	−0.0142 (14)	0.8262 (18)	0.68034 (8)	0.0285 (15)
H5JA	0.1547	0.9370	0.6783	0.034*
C4J	0.0437 (13)	0.640 (2)	0.69386 (8)	0.0307 (17)
H4JA	0.1945	0.5082	0.6914	0.037*
C3J	0.1177 (15)	0.806 (2)	0.70823 (8)	0.0306 (16)
H3JA	−0.0349	0.9356	0.7107	0.037*
C2J	0.1775 (13)	0.6241 (19)	0.72208 (9)	0.0293 (16)
H2JA	0.0106	0.5102	0.7241	0.035*
C1J	0.2348 (18)	0.800 (3)	0.73641 (10)	0.045 (2)
H1JA	0.4024	0.9115	0.7349	0.054*
H1JB	0.0792	0.9270	0.7382	0.054*
C1K	0.7346 (17)	0.162 (3)	0.76368 (9)	0.044 (2)
H1KA	0.9009	0.0497	0.7655	0.053*
H1KB	0.5778	0.0363	0.7620	0.053*
C2K	0.6804 (15)	0.340 (2)	0.77766 (9)	0.0336 (18)
H2KA	0.5120	0.4515	0.7756	0.040*
C3K	0.6233 (13)	0.1540 (18)	0.79191 (8)	0.0276 (15)
H3KA	0.4719	0.0221	0.7895	0.033*
C4K	0.5494 (14)	0.317 (2)	0.80592 (9)	0.0320 (17)
H4KA	0.7037	0.4462	0.8082	0.038*
C5K	0.4921 (14)	0.154 (2)	0.81971 (9)	0.0332 (18)
H5KA	0.6625	0.0490	0.8223	0.040*
C6K	0.4156 (14)	0.321 (2)	0.83365 (8)	0.0323 (17)
H6KA	0.2650	0.4522	0.8309	0.039*
C7K	0.3251 (17)	0.147 (2)	0.84737 (9)	0.0357 (18)
H7KA	0.1710	0.0280	0.8437	0.043*
C8K	0.213 (2)	0.320 (3)	0.85989 (10)	0.048 (2)
H8KA	0.3647	0.4154	0.8653	0.058*
H8KB	0.0861	0.4593	0.8557	0.058*
C8L	0.6582 (16)	0.720 (2)	0.88823 (10)	0.038 (2)
H8LA	0.7796	0.7644	0.8796	0.046*
H8LB	0.5433	0.5606	0.8852	0.046*
C7L	0.8365 (14)	0.640 (2)	0.90222 (9)	0.0314 (17)
H7LA	0.9624	0.7965	0.9047	0.038*
C6L	0.6593 (14)	0.581 (2)	0.91574 (8)	0.0323 (18)
H6LA	0.5422	0.7447	0.9179	0.039*
C5L	0.8396 (16)	0.516 (2)	0.93006 (8)	0.037 (2)
H5LA	0.9509	0.3482	0.9280	0.044*
C4L	0.6533 (13)	0.460 (2)	0.94396 (8)	0.0302 (17)
H4LA	0.5217	0.3092	0.9413	0.036*
C3L	0.8239 (14)	0.372 (2)	0.95812 (9)	0.0332 (19)
H3LA	0.9558	0.5231	0.9605	0.040*
C2L	0.6428 (14)	0.329 (2)	0.97197 (8)	0.0307 (17)
H2LA	0.5324	0.4990	0.9737	0.037*
C1L	0.8168 (15)	0.269 (2)	0.98621 (8)	0.038 (2)
H1LA	0.9291	0.1024	0.9845	0.045*
H1LB	0.9433	0.4245	0.9881	0.045*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1I	0.032 (3)	0.069 (5)	0.026 (3)	−0.001 (3)	−0.008 (2)	0.003 (3)
O2I	0.023 (2)	0.048 (4)	0.033 (3)	0.000 (2)	−0.006 (2)	0.000 (3)
O3I	0.017 (2)	0.055 (4)	0.034 (3)	0.004 (2)	−0.0033 (19)	0.000 (3)
O4I	0.025 (2)	0.054 (4)	0.026 (3)	−0.001 (3)	−0.0001 (19)	−0.003 (3)
O5I	0.015 (2)	0.037 (4)	0.055 (4)	0.000 (2)	−0.003 (2)	−0.003 (3)
O6I	0.027 (3)	0.062 (5)	0.032 (3)	0.003 (3)	0.001 (2)	0.001 (3)
O7I	0.026 (2)	0.065 (5)	0.035 (3)	−0.010 (3)	0.000 (2)	−0.006 (3)
O8I	0.042 (3)	0.096 (7)	0.031 (3)	−0.009 (4)	−0.005 (3)	0.012 (4)
O8J	0.034 (3)	0.055 (4)	0.036 (3)	−0.008 (3)	−0.005 (2)	−0.009 (3)
O7J	0.036 (3)	0.054 (4)	0.030 (3)	−0.016 (3)	0.005 (2)	0.001 (3)
O6J	0.020 (2)	0.035 (3)	0.035 (3)	−0.008 (2)	−0.0011 (18)	0.003 (2)
O5J	0.021 (2)	0.054 (4)	0.028 (3)	0.005 (2)	0.0002 (19)	−0.002 (3)
O4J	0.018 (2)	0.046 (4)	0.036 (3)	−0.009 (2)	−0.0022 (19)	−0.004 (3)
O3J	0.023 (2)	0.056 (4)	0.032 (3)	−0.006 (3)	−0.001 (2)	−0.004 (3)
O2J	0.024 (2)	0.044 (4)	0.035 (3)	−0.006 (2)	0.000 (2)	−0.003 (3)
O1J	0.023 (2)	0.070 (5)	0.034 (3)	−0.013 (3)	−0.005 (2)	−0.005 (3)
O1K	0.025 (2)	0.056 (4)	0.037 (3)	0.002 (3)	0.000 (2)	0.002 (3)
O2K	0.026 (2)	0.035 (3)	0.038 (3)	−0.005 (2)	−0.006 (2)	−0.001 (2)
O3K	0.025 (2)	0.038 (3)	0.032 (3)	0.017 (2)	−0.0070 (19)	−0.006 (2)
O4K	0.0173 (19)	0.035 (3)	0.038 (3)	0.004 (2)	−0.0061 (18)	−0.003 (2)
O5K	0.028 (2)	0.044 (4)	0.019 (2)	−0.003 (2)	−0.0041 (18)	0.001 (2)
O6K	0.024 (2)	0.061 (5)	0.040 (3)	−0.010 (3)	0.000 (2)	−0.012 (3)
O7K	0.036 (3)	0.054 (4)	0.034 (3)	0.012 (3)	−0.007 (2)	0.003 (3)
O8K	0.062 (4)	0.053 (5)	0.041 (3)	−0.005 (4)	0.010 (3)	0.000 (3)
O8L	0.046 (3)	0.042 (4)	0.055 (4)	0.013 (3)	−0.005 (3)	0.000 (3)
O7L	0.023 (2)	0.055 (4)	0.033 (3)	0.016 (3)	−0.010 (2)	−0.006 (3)
O6L	0.027 (2)	0.056 (4)	0.028 (3)	−0.004 (3)	−0.009 (2)	0.001 (3)
O5L	0.017 (2)	0.043 (4)	0.038 (3)	0.006 (2)	−0.0041 (19)	−0.005 (3)
O4L	0.019 (2)	0.062 (4)	0.024 (2)	0.007 (3)	−0.0061 (18)	−0.001 (3)
O3L	0.017 (2)	0.043 (4)	0.034 (3)	−0.003 (2)	−0.0095 (18)	0.003 (3)
O2L	0.019 (2)	0.061 (5)	0.027 (3)	−0.002 (2)	−0.0036 (18)	−0.002 (3)
O1L	0.029 (3)	0.078 (6)	0.024 (2)	−0.003 (3)	0.003 (2)	−0.003 (3)
C1I	0.034 (4)	0.070 (7)	0.013 (3)	−0.015 (4)	0.003 (3)	0.004 (3)
C2I	0.029 (3)	0.065 (6)	0.016 (3)	−0.007 (4)	0.005 (2)	0.002 (3)
C3I	0.016 (2)	0.043 (5)	0.031 (3)	−0.001 (3)	0.003 (2)	0.002 (3)
C4I	0.019 (3)	0.046 (5)	0.026 (3)	0.007 (3)	0.001 (2)	0.001 (3)
C5I	0.020 (3)	0.040 (4)	0.028 (3)	−0.018 (3)	−0.002 (2)	0.003 (3)
C6I	0.016 (3)	0.053 (6)	0.036 (4)	0.005 (3)	−0.003 (3)	0.003 (4)
C7I	0.023 (3)	0.060 (6)	0.033 (4)	0.001 (4)	0.004 (3)	0.006 (4)
C8I	0.038 (4)	0.050 (6)	0.034 (4)	−0.016 (4)	−0.005 (3)	0.001 (4)
C8J	0.016 (3)	0.039 (5)	0.044 (4)	−0.009 (3)	−0.007 (3)	0.003 (4)
C7J	0.024 (3)	0.046 (5)	0.031 (4)	−0.002 (3)	0.000 (3)	−0.002 (4)
C6J	0.015 (2)	0.041 (4)	0.024 (3)	−0.006 (3)	−0.003 (2)	0.000 (3)
C5J	0.020 (3)	0.031 (4)	0.035 (4)	0.013 (3)	−0.003 (2)	−0.007 (3)
C4J	0.015 (2)	0.047 (5)	0.030 (3)	−0.013 (3)	−0.005 (2)	−0.004 (3)
C3J	0.024 (3)	0.040 (5)	0.027 (3)	−0.005 (3)	−0.005 (2)	−0.003 (3)
C2J	0.014 (2)	0.037 (4)	0.037 (4)	0.003 (3)	−0.002 (2)	−0.001 (3)
C1J	0.030 (4)	0.069 (7)	0.035 (4)	0.007 (4)	−0.009 (3)	−0.005 (5)
C1K	0.025 (3)	0.072 (7)	0.034 (4)	−0.018 (4)	−0.006 (3)	−0.006 (5)
C2K	0.022 (3)	0.044 (5)	0.035 (4)	0.000 (3)	−0.003 (3)	0.006 (4)
C3K	0.018 (3)	0.037 (4)	0.028 (3)	−0.018 (3)	−0.007 (2)	0.009 (3)
C4K	0.015 (3)	0.044 (5)	0.037 (4)	0.009 (3)	−0.010 (2)	−0.003 (4)
C5K	0.021 (3)	0.046 (5)	0.033 (4)	−0.021 (3)	−0.005 (2)	0.002 (3)
C6K	0.020 (3)	0.051 (5)	0.025 (3)	0.005 (3)	−0.008 (2)	0.001 (3)
C7K	0.032 (4)	0.047 (5)	0.028 (4)	0.010 (4)	−0.001 (3)	0.000 (4)
C8K	0.069 (6)	0.048 (6)	0.027 (4)	0.000 (5)	0.011 (4)	0.000 (4)
C8L	0.024 (3)	0.052 (6)	0.038 (4)	−0.008 (3)	−0.007 (3)	0.014 (4)
C7L	0.020 (3)	0.044 (5)	0.031 (4)	−0.001 (3)	−0.003 (2)	0.010 (3)
C6L	0.015 (3)	0.056 (6)	0.026 (3)	0.001 (3)	−0.004 (2)	0.004 (3)
C5L	0.032 (3)	0.066 (6)	0.014 (3)	0.018 (4)	0.001 (2)	0.002 (3)
C4L	0.017 (2)	0.054 (5)	0.020 (3)	−0.012 (3)	−0.007 (2)	0.002 (3)
C3L	0.016 (3)	0.053 (6)	0.030 (4)	0.006 (3)	−0.008 (2)	−0.004 (3)
C2L	0.019 (3)	0.048 (5)	0.025 (3)	−0.001 (3)	−0.010 (2)	−0.002 (3)
C1L	0.023 (3)	0.073 (7)	0.017 (3)	0.001 (4)	−0.001 (2)	−0.005 (4)

Geometric parameters (Å, º)

O1I—C1I	1.434 (9)	C1I—H1IB	0.9900
O1I—H1I	0.92 (2)	C2I—C3I	1.522 (11)
O2I—C2I	1.429 (12)	C2I—H2IA	1.0000
O2I—H2I	0.884 (19)	C3I—C4I	1.535 (10)
O3I—C3I	1.390 (12)	C3I—H3IA	1.0000
O3I—H3I	0.87 (2)	C4I—C5I	1.536 (10)
O4I—C4I	1.420 (11)	C4I—H4IA	1.0000
O4I—H4I	0.86 (2)	C5I—C6I	1.544 (10)
O5I—C5I	1.452 (11)	C5I—H5IA	1.0000
O5I—H5I	0.89 (2)	C6I—C7I	1.520 (11)
O6I—C6I	1.422 (12)	C6I—H6IA	1.0000
O6I—H6I	0.89 (2)	C7I—C8I	1.541 (12)
O7I—C7I	1.419 (13)	C7I—H7IA	1.0000
O7I—H7I	0.88 (2)	C8I—H8IA	0.9900
O8I—C8I	1.465 (12)	C8I—H8IB	0.9900
O8I—H8I	0.88 (2)	C8J—C7J	1.485 (12)
O8J—C8J	1.418 (10)	C8J—H8JA	0.9900
O8J—H8J	0.87 (2)	C8J—H8JB	0.9900
O7J—C7J	1.434 (11)	C7J—C6J	1.519 (12)
O7J—H7J	0.88 (2)	C7J—H7JA	1.0000
O6J—C6J	1.461 (10)	C6J—C5J	1.540 (11)
O6J—H6J	0.89 (2)	C6J—H6JA	1.0000
O5J—C5J	1.433 (9)	C5J—C4J	1.519 (12)
O5J—H5J	0.88 (2)	C5J—H5JA	1.0000
O4J—C4J	1.426 (9)	C4J—C3J	1.539 (11)
O4J—H4J	0.87 (2)	C4J—H4JA	1.0000
O3J—C3J	1.459 (11)	C3J—C2J	1.530 (12)
O3J—H3J	0.86 (2)	C3J—H3JA	1.0000
O2J—C2J	1.419 (10)	C2J—C1J	1.547 (13)
O2J—H2J	0.89 (2)	C2J—H2JA	1.0000
O1J—C1J	1.442 (13)	C1J—H1JA	0.9900
O1J—H1J	0.915 (18)	C1J—H1JB	0.9900
O1K—C1K	1.427 (12)	C1K—C2K	1.525 (13)
O1K—H1K	0.921 (17)	C1K—H1KA	0.9900
O2K—C2K	1.442 (11)	C1K—H1KB	0.9900
O2K—H2K	0.919 (19)	C2K—C3K	1.570 (11)
O3K—C3K	1.444 (10)	C2K—H2KA	1.0000
O3K—H3K	0.88 (2)	C3K—C4K	1.509 (12)
O4K—C4K	1.438 (9)	C3K—H3KA	1.0000
O4K—H4K	0.87 (2)	C4K—C5K	1.476 (12)
O5K—C5K	1.482 (10)	C4K—H4KA	1.0000
O5K—H5K	0.892 (18)	C5K—C6K	1.518 (12)
O6K—C6K	1.427 (11)	C5K—H5KA	1.0000
O6K—H6K	0.884 (19)	C6K—C7K	1.540 (13)
O7K—C7K	1.457 (11)	C6K—H6KA	1.0000
O7K—H7K	0.91 (2)	C7K—C8K	1.488 (13)
O8K—C8K	1.450 (13)	C7K—H7KA	1.0000
O8K—H8K	0.89 (2)	C8K—H8KA	0.9900
O8L—C8L	1.342 (12)	C8K—H8KB	0.9900
O8L—H8L	0.88 (2)	C8L—C7L	1.550 (11)
O7L—C7L	1.437 (11)	C8L—H8LA	0.9900
O7L—H7L	0.87 (2)	C8L—H8LB	0.9900
O6L—C6L	1.440 (12)	C7L—C6L	1.500 (10)
O6L—H6L	0.89 (2)	C7L—H7LA	1.0000
O5L—C5L	1.397 (13)	C6L—C5L	1.561 (10)
O5L—H5L	0.89 (2)	C6L—H6LA	1.0000
O4L—C4L	1.401 (12)	C5L—C4L	1.551 (10)
O4L—H4L	0.86 (2)	C5L—H5LA	1.0000
O3L—C3L	1.374 (11)	C4L—C3L	1.552 (10)
O3L—H3L	0.85 (2)	C4L—H4LA	1.0000
O2L—C2L	1.447 (12)	C3L—C2L	1.520 (11)
O2L—H2L	0.89 (2)	C3L—H3LA	1.0000
O1L—C1L	1.440 (9)	C2L—C1L	1.536 (10)
O1L—H1L	0.912 (17)	C2L—H2LA	1.0000
C1I—C2I	1.514 (9)	C1L—H1LA	0.9900
C1I—H1IA	0.9900	C1L—H1LB	0.9900
C1I—O1I—H1I	107 (8)	C2J—C3J—C4J	113.1 (8)
C2I—O2I—H2I	111 (4)	O3J—C3J—H3JA	109.6
C3I—O3I—H3I	105 (3)	C2J—C3J—H3JA	109.6
C4I—O4I—H4I	126 (7)	C4J—C3J—H3JA	109.6
C5I—O5I—H5I	121 (5)	O2J—C2J—C3J	112.1 (6)
C6I—O6I—H6I	106 (8)	O2J—C2J—C1J	109.7 (6)
C7I—O7I—H7I	108 (5)	C3J—C2J—C1J	111.1 (8)
C8I—O8I—H8I	120 (7)	O2J—C2J—H2JA	107.9
C8J—O8J—H8J	101 (4)	C3J—C2J—H2JA	107.9
C7J—O7J—H7J	99 (6)	C1J—C2J—H2JA	107.9
C6J—O6J—H6J	115 (4)	O1J—C1J—C2J	110.0 (9)
C5J—O5J—H5J	118 (7)	O1J—C1J—H1JA	109.7
C4J—O4J—H4J	107 (7)	C2J—C1J—H1JA	109.7
C3J—O3J—H3J	99 (6)	O1J—C1J—H1JB	109.7
C2J—O2J—H2J	114 (6)	C2J—C1J—H1JB	109.7
C1J—O1J—H1J	104 (8)	H1JA—C1J—H1JB	108.2
C1K—O1K—H1K	103 (8)	O1K—C1K—C2K	111.3 (9)
C2K—O2K—H2K	117 (6)	O1K—C1K—H1KA	109.4
C3K—O3K—H3K	99 (5)	C2K—C1K—H1KA	109.4
C4K—O4K—H4K	101 (6)	O1K—C1K—H1KB	109.4
C5K—O5K—H5K	116 (5)	C2K—C1K—H1KB	109.4
C6K—O6K—H6K	117 (8)	H1KA—C1K—H1KB	108.0
C7K—O7K—H7K	112 (6)	O2K—C2K—C1K	111.9 (6)
C8K—O8K—H8K	122 (8)	O2K—C2K—C3K	110.6 (6)
C8L—O8L—H8L	101 (6)	C1K—C2K—C3K	110.4 (8)
C7L—O7L—H7L	111 (7)	O2K—C2K—H2KA	108.0
C6L—O6L—H6L	126 (7)	C1K—C2K—H2KA	108.0
C5L—O5L—H5L	130 (8)	C3K—C2K—H2KA	108.0
C4L—O4L—H4L	104 (7)	O3K—C3K—C4K	106.7 (6)
C3L—O3L—H3L	117 (3)	O3K—C3K—C2K	108.6 (6)
C2L—O2L—H2L	125 (7)	C4K—C3K—C2K	113.0 (8)
C1L—O1L—H1L	103 (10)	O3K—C3K—H3KA	109.5
O1I—C1I—C2I	112.3 (7)	C4K—C3K—H3KA	109.5
O1I—C1I—H1IA	109.2	C2K—C3K—H3KA	109.5
C2I—C1I—H1IA	109.2	O4K—C4K—C5K	109.6 (6)
O1I—C1I—H1IB	109.2	O4K—C4K—C3K	106.2 (6)
C2I—C1I—H1IB	109.2	C5K—C4K—C3K	115.7 (8)
H1IA—C1I—H1IB	107.9	O4K—C4K—H4KA	108.4
O2I—C2I—C1I	109.8 (8)	C5K—C4K—H4KA	108.4
O2I—C2I—C3I	110.4 (7)	C3K—C4K—H4KA	108.4
C1I—C2I—C3I	111.6 (6)	C4K—C5K—O5K	110.4 (6)
O2I—C2I—H2IA	108.3	C4K—C5K—C6K	115.0 (8)
C1I—C2I—H2IA	108.3	O5K—C5K—C6K	108.8 (6)
C3I—C2I—H2IA	108.3	C4K—C5K—H5KA	107.5
O3I—C3I—C2I	112.7 (8)	O5K—C5K—H5KA	107.5
O3I—C3I—C4I	108.2 (7)	C6K—C5K—H5KA	107.5
C2I—C3I—C4I	112.1 (6)	O6K—C6K—C5K	105.7 (6)
O3I—C3I—H3IA	107.9	O6K—C6K—C7K	109.4 (6)
C2I—C3I—H3IA	107.9	C5K—C6K—C7K	114.1 (8)
C4I—C3I—H3IA	107.9	O6K—C6K—H6KA	109.2
O4I—C4I—C3I	108.5 (6)	C5K—C6K—H6KA	109.2
O4I—C4I—C5I	110.0 (7)	C7K—C6K—H6KA	109.2
C3I—C4I—C5I	114.1 (6)	O7K—C7K—C8K	111.9 (7)
O4I—C4I—H4IA	108.0	O7K—C7K—C6K	112.5 (7)
C3I—C4I—H4IA	108.0	C8K—C7K—C6K	112.1 (9)
C5I—C4I—H4IA	108.0	O7K—C7K—H7KA	106.6
O5I—C5I—C4I	110.4 (6)	C8K—C7K—H7KA	106.6
O5I—C5I—C6I	108.4 (7)	C6K—C7K—H7KA	106.6
C4I—C5I—C6I	113.0 (6)	O8K—C8K—C7K	108.2 (9)
O5I—C5I—H5IA	108.3	O8K—C8K—H8KA	110.1
C4I—C5I—H5IA	108.3	C7K—C8K—H8KA	110.1
C6I—C5I—H5IA	108.3	O8K—C8K—H8KB	110.1
O6I—C6I—C7I	112.2 (8)	C7K—C8K—H8KB	110.1
O6I—C6I—C5I	105.4 (8)	H8KA—C8K—H8KB	108.4
C7I—C6I—C5I	111.5 (6)	O8L—C8L—C7L	112.0 (8)
O6I—C6I—H6IA	109.2	O8L—C8L—H8LA	109.2
C7I—C6I—H6IA	109.2	C7L—C8L—H8LA	109.2
C5I—C6I—H6IA	109.2	O8L—C8L—H8LB	109.2
O7I—C7I—C6I	111.9 (9)	C7L—C8L—H8LB	109.2
O7I—C7I—C8I	110.8 (7)	H8LA—C8L—H8LB	107.9
C6I—C7I—C8I	108.9 (7)	O7L—C7L—C6L	112.2 (8)
O7I—C7I—H7IA	108.4	O7L—C7L—C8L	106.7 (7)
C6I—C7I—H7IA	108.4	C6L—C7L—C8L	110.7 (6)
C8I—C7I—H7IA	108.4	O7L—C7L—H7LA	109.1
O8I—C8I—C7I	106.2 (7)	C6L—C7L—H7LA	109.1
O8I—C8I—H8IA	110.5	C8L—C7L—H7LA	109.1
C7I—C8I—H8IA	110.5	O6L—C6L—C7L	110.8 (7)
O8I—C8I—H8IB	110.5	O6L—C6L—C5L	108.2 (8)
C7I—C8I—H8IB	110.5	C7L—C6L—C5L	110.7 (6)
H8IA—C8I—H8IB	108.7	O6L—C6L—H6LA	109.0
O8J—C8J—C7J	109.0 (7)	C7L—C6L—H6LA	109.0
O8J—C8J—H8JA	109.9	C5L—C6L—H6LA	109.0
C7J—C8J—H8JA	109.9	O5L—C5L—C4L	111.3 (7)
O8J—C8J—H8JB	109.9	O5L—C5L—C6L	109.8 (8)
C7J—C8J—H8JB	109.9	C4L—C5L—C6L	110.0 (6)
H8JA—C8J—H8JB	108.3	O5L—C5L—H5LA	108.6
O7J—C7J—C8J	105.3 (6)	C4L—C5L—H5LA	108.6
O7J—C7J—C6J	109.7 (6)	C6L—C5L—H5LA	108.6
C8J—C7J—C6J	115.0 (8)	O4L—C4L—C5L	110.3 (8)
O7J—C7J—H7JA	108.9	O4L—C4L—C3L	108.2 (6)
C8J—C7J—H7JA	108.9	C5L—C4L—C3L	111.6 (6)
C6J—C7J—H7JA	108.9	O4L—C4L—H4LA	108.9
O6J—C6J—C7J	110.8 (6)	C5L—C4L—H4LA	108.9
O6J—C6J—C5J	108.5 (5)	C3L—C4L—H4LA	108.9
C7J—C6J—C5J	114.9 (8)	O3L—C3L—C2L	112.6 (8)
O6J—C6J—H6JA	107.5	O3L—C3L—C4L	108.9 (7)
C7J—C6J—H6JA	107.5	C2L—C3L—C4L	111.6 (5)
C5J—C6J—H6JA	107.5	O3L—C3L—H3LA	107.9
O5J—C5J—C4J	112.8 (6)	C2L—C3L—H3LA	107.9
O5J—C5J—C6J	108.2 (6)	C4L—C3L—H3LA	107.9
C4J—C5J—C6J	111.2 (7)	O2L—C2L—C3L	109.9 (7)
O5J—C5J—H5JA	108.1	O2L—C2L—C1L	108.9 (8)
C4J—C5J—H5JA	108.1	C3L—C2L—C1L	111.0 (6)
C6J—C5J—H5JA	108.1	O2L—C2L—H2LA	109.0
O4J—C4J—C5J	109.7 (6)	C3L—C2L—H2LA	109.0
O4J—C4J—C3J	104.6 (6)	C1L—C2L—H2LA	109.0
C5J—C4J—C3J	111.7 (8)	O1L—C1L—C2L	111.2 (6)
O4J—C4J—H4JA	110.2	O1L—C1L—H1LA	109.4
C5J—C4J—H4JA	110.2	C2L—C1L—H1LA	109.4
C3J—C4J—H4JA	110.2	O1L—C1L—H1LB	109.4
O3J—C3J—C2J	108.8 (6)	C2L—C1L—H1LB	109.4
O3J—C3J—C4J	106.2 (6)	H1LA—C1L—H1LB	108.0
O1I—C1I—C2I—O2I	−57.6 (11)	O1K—C1K—C2K—O2K	−59.6 (9)
O1I—C1I—C2I—C3I	179.7 (9)	O1K—C1K—C2K—C3K	176.8 (6)
O2I—C2I—C3I—O3I	−58.9 (8)	O2K—C2K—C3K—O3K	−58.8 (9)
C1I—C2I—C3I—O3I	63.5 (10)	C1K—C2K—C3K—O3K	65.6 (8)
O2I—C2I—C3I—C4I	63.5 (10)	O2K—C2K—C3K—C4K	59.5 (8)
C1I—C2I—C3I—C4I	−174.2 (9)	C1K—C2K—C3K—C4K	−176.2 (6)
O3I—C3I—C4I—O4I	179.7 (6)	O3K—C3K—C4K—O4K	177.3 (6)
C2I—C3I—C4I—O4I	54.8 (10)	C2K—C3K—C4K—O4K	57.9 (8)
O3I—C3I—C4I—C5I	−57.3 (9)	O3K—C3K—C4K—C5K	−60.8 (8)
C2I—C3I—C4I—C5I	177.9 (8)	C2K—C3K—C4K—C5K	179.8 (6)
O4I—C4I—C5I—O5I	61.9 (7)	O4K—C4K—C5K—O5K	64.1 (9)
C3I—C4I—C5I—O5I	−60.3 (9)	C3K—C4K—C5K—O5K	−55.9 (9)
O4I—C4I—C5I—C6I	−59.7 (9)	O4K—C4K—C5K—C6K	−59.4 (9)
C3I—C4I—C5I—C6I	178.1 (8)	C3K—C4K—C5K—C6K	−179.5 (6)
O5I—C5I—C6I—O6I	170.8 (6)	C4K—C5K—C6K—O6K	−66.3 (8)
C4I—C5I—C6I—O6I	−66.5 (9)	O5K—C5K—C6K—O6K	169.4 (7)
O5I—C5I—C6I—C7I	48.8 (10)	C4K—C5K—C6K—C7K	173.5 (6)
C4I—C5I—C6I—C7I	171.5 (8)	O5K—C5K—C6K—C7K	49.1 (9)
O6I—C6I—C7I—O7I	−53.9 (9)	O6K—C6K—C7K—O7K	−56.8 (10)
C5I—C6I—C7I—O7I	64.2 (10)	C5K—C6K—C7K—O7K	61.4 (9)
O6I—C6I—C7I—C8I	69.0 (11)	O6K—C6K—C7K—C8K	70.3 (10)
C5I—C6I—C7I—C8I	−173.0 (8)	C5K—C6K—C7K—C8K	−171.5 (8)
O7I—C7I—C8I—O8I	−69.8 (10)	O7K—C7K—C8K—O8K	−67.5 (11)
C6I—C7I—C8I—O8I	166.7 (9)	C6K—C7K—C8K—O8K	165.1 (8)
O8J—C8J—C7J—O7J	179.6 (7)	O8L—C8L—C7L—O7L	179.3 (7)
O8J—C8J—C7J—C6J	58.7 (9)	O8L—C8L—C7L—C6L	56.9 (11)
O7J—C7J—C6J—O6J	−61.2 (9)	O7L—C7L—C6L—O6L	−56.0 (8)
C8J—C7J—C6J—O6J	57.3 (8)	C8L—C7L—C6L—O6L	63.0 (10)
O7J—C7J—C6J—C5J	62.1 (8)	O7L—C7L—C6L—C5L	64.0 (10)
C8J—C7J—C6J—C5J	−179.4 (6)	C8L—C7L—C6L—C5L	−176.9 (9)
O6J—C6J—C5J—O5J	178.9 (6)	O6L—C6L—C5L—O5L	178.0 (6)
C7J—C6J—C5J—O5J	54.4 (8)	C7L—C6L—C5L—O5L	56.4 (10)
O6J—C6J—C5J—C4J	−56.6 (8)	O6L—C6L—C5L—C4L	−59.3 (9)
C7J—C6J—C5J—C4J	178.9 (6)	C7L—C6L—C5L—C4L	179.1 (9)
O5J—C5J—C4J—O4J	56.0 (9)	O5L—C5L—C4L—O4L	57.5 (8)
C6J—C5J—C4J—O4J	−65.9 (8)	C6L—C5L—C4L—O4L	−64.4 (9)
O5J—C5J—C4J—C3J	−59.6 (8)	O5L—C5L—C4L—C3L	−62.8 (10)
C6J—C5J—C4J—C3J	178.6 (6)	C6L—C5L—C4L—C3L	175.4 (8)
O4J—C4J—C3J—O3J	−179.3 (7)	O4L—C4L—C3L—O3L	−179.3 (7)
C5J—C4J—C3J—O3J	−60.7 (8)	C5L—C4L—C3L—O3L	−57.8 (10)
O4J—C4J—C3J—C2J	61.4 (8)	O4L—C4L—C3L—C2L	55.8 (10)
C5J—C4J—C3J—C2J	−180.0 (6)	C5L—C4L—C3L—C2L	177.3 (8)
O3J—C3J—C2J—O2J	−57.6 (9)	O3L—C3L—C2L—O2L	−57.9 (8)
C4J—C3J—C2J—O2J	60.1 (8)	C4L—C3L—C2L—O2L	64.9 (10)
O3J—C3J—C2J—C1J	65.4 (8)	O3L—C3L—C2L—C1L	62.6 (10)
C4J—C3J—C2J—C1J	−176.8 (6)	C4L—C3L—C2L—C1L	−174.6 (8)
O2J—C2J—C1J—O1J	−59.6 (9)	O2L—C2L—C1L—O1L	−58.8 (10)
C3J—C2J—C1J—O1J	175.9 (6)	C3L—C2L—C1L—O1L	−179.9 (9)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1I—H1I···O1I^i	0.92 (2)	1.92 (2)	2.824 (6)	171 (11)
O2I—H2I···O4I^ii	0.88 (2)	1.91 (2)	2.737 (9)	155 (5)
O3I—H3I···O2I^iii	0.87 (2)	1.90 (2)	2.695 (7)	151 (5)
O4I—H4I···O5I^iv	0.86 (2)	1.90 (2)	2.677 (8)	150 (5)
O5I—H5I···O3I^v	0.89 (2)	1.92 (2)	2.705 (9)	146 (4)
O6I—H6I···O7I^iv	0.89 (2)	1.93 (2)	2.806 (8)	170 (10)
O7I—H7I···O8I^ii	0.88 (2)	2.32 (2)	3.138 (12)	154 (6)
O8I—H8I···O7J^v	0.88 (2)	1.90 (2)	2.755 (8)	164 (9)
O8J—H8J···O8I^iv	0.87 (2)	2.20 (2)	2.963 (11)	146 (5)
O7J—H7J···O6J^ii	0.88 (2)	1.93 (2)	2.705 (10)	145 (4)
O6J—H6J···O8J^iii	0.89 (2)	1.94 (2)	2.781 (8)	158 (6)
O5J—H5J···O3J^iv	0.88 (2)	1.90 (2)	2.730 (7)	156 (6)
O4J—H4J···O5J^v	0.87 (2)	1.90 (2)	2.688 (10)	149 (5)
O3J—H3J···O2J^ii	0.86 (2)	1.89 (2)	2.698 (10)	156 (6)
O2J—H2J···O4J^iii	0.89 (2)	1.92 (2)	2.744 (7)	153 (6)
O1J—H1J···O1K^iv	0.92 (2)	1.92 (2)	2.832 (9)	176 (12)
O1K—H1K···O1J	0.92 (2)	1.92 (2)	2.839 (9)	176 (10)
O2K—H2K···O4K^iii	0.92 (2)	1.84 (2)	2.724 (7)	159 (5)
O3K—H3K···O2K^v	0.88 (2)	1.83 (2)	2.669 (9)	160 (6)
O4K—H4K···O5K^ii	0.87 (2)	1.91 (2)	2.659 (9)	144 (4)
O5K—H5K···O3K^iv	0.89 (2)	1.83 (2)	2.696 (7)	165 (6)
O6K—H6K···O7K^ii	0.88 (2)	1.91 (2)	2.789 (10)	172 (11)
O7K—H7K···O8K^iii	0.91 (2)	2.24 (2)	3.115 (10)	161 (7)
O8K—H8K···O7L^iv	0.89 (2)	1.91 (2)	2.759 (9)	159 (8)
O8L—H8L···O8K^ii	0.88 (2)	2.19 (2)	2.932 (10)	142 (4)
O7L—H7L···O6L^iii	0.87 (2)	1.92 (2)	2.726 (7)	153 (6)
O6L—H6L···O8L^v	0.89 (2)	1.93 (2)	2.769 (10)	156 (5)
O5L—H5L···O3L^ii	0.89 (2)	1.93 (2)	2.754 (9)	153 (6)
O4L—H4L···O5L^iv	0.86 (2)	1.89 (2)	2.702 (7)	156 (6)
O3L—H3L···O2L^iii	0.85 (2)	1.89 (2)	2.695 (7)	157 (6)
O2L—H2L···O4L^v	0.89 (2)	1.92 (2)	2.746 (9)	155 (5)
O1L—H1L···O1L^vi	0.91 (2)	1.91 (2)	2.823 (6)	177 (13)

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