Ab initio X-ray structural characterization of an inclusion compound with a compositionally disordered chiral guest: no prior knowledge of the crystal composition

The crystal structure and absolute configuration of a mol­ecular host/guest/impurity inclusion complex were established unequivocally in spite of our having no prior knowledge of its chemical composition. The host (4R,5R)-4,5-bis­(hy­droxy­diphenyl­meth­yl)-2,2-dimethyl-1,3-dioxolane, (I), displays expected conformational features. The crystal-disordered chiral guest 4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one, (II), is present in the crystal 85.1 (4)% of the time. It shares a common site with 4a-hydro­per­oxy­meth­yl-4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one, (III), present 14.9 (4)% of the time, which is the product of autoxidation of (II). This minor peroxide impurity was isolated, and the results of nuclear magnetic resonance, mass spectrometry, and X-ray fluor­escence studies are consistent with the proposed structure of (III). The complete structure was therefore determined to be (4R,5R)-4,5-bis­(hy­droxy­diphenyl­meth­yl)-2,2-di­methyl-1,3-dioxolane-4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one-4a-hydro­per­oxy­meth­yl-4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one (1/0.85/0.15), C₃₁H₃₀O₄·0.85C₁₀H₁₄O·0.15C₁₀H₁₄O₃, (IV). There are host-host, host-guest, and host-impurity hydrogen-bonding inter­actions of types S and D in the solid state. We believe that the crystals of (IV) were originally prepared to establish the chirality of the guest (II) by means of X-ray diffraction analysis of host/guest crystals obtained in the course of chiral resolution during cocrystallization of (II) with (I). In spite of the absence of `heavy' elements, the absolute configurations of all anomeric centres in the structure are assigned as R based on resonant scattering effects.

S1. Introduction

\ Single-crystal X-ray structural analysis is a definitive analytical technique that, in an `ideal world', requires no prior information about the source or nature of the compound under investigation. For example, Mueller et al. (2006) used X-ray diffraction to establish the structure of an adventitious rhenium(V) complex Re<sub>2</sub>(Cp*)<sub>2</sub>O<sub>2</sub>(µ<sub>2</sub>-O)<sub>2</sub><sup>1</sup> (Cp* is penta­methyl­cyclo­penta­dienyl), whose source proved impossible to determine. A crystalline lilac deposit from a swimming pool was determined to be disodium copper(II) tetra­kis(isocyanurate) hexahydrate [Na<sub>2</sub>Cu(C<sub>3</sub>H<sub>2</sub>N<sub>3</sub>O<sub>3</sub>)<sub>4</sub>·6H<sub>2</sub>O; Hart et al., 1992] and subsequently purposefully synthesized (Falvello et al., 1997). Such examples are rare and, in practice, the crystallographer usually possesses information about the nature of the crystals as well as the synthons and solvents used during the chemical reaction and crystallization. When the structural solution reveals a compound different from the proposed one, typically a large portion of the structure contains correctly assigned elements at the correct positions. The much smaller `unknown' part of the structure is usually the cocrystallized solvent or counter-ion, whose nature and conformation are routinely deduced from the difference Fourier syntheses. Two inter­esting cases of structural analyses that had established the atomic connectivity in compounds of known origin include the bis­(2,3-di­hydro-1,3-diborole) complex [(EtC)₂(EtB)₂CHMe]₂Pt, that took nearly 30 years to produce dark-red single crystals (Wadepohl et al., 2015), and an indaza­lone, that, in the absence of a crystal structure, was believed to be a 2,1-benzisoxazole (Kurth et al., 2005).

With the advent of programs such as Shake-and-Bake (Miller et al., 1994), SUPERFLIP (Palatinus & Chapuis, 2007), SHELXD (Sheldrick, 2010), and SHELXT (Sheldrick, 2015a) that solve structures by performing Fourier transforms in the direct and reciprocal space, prior knowledge of the exact crystal composition has become optional (Feng, 2011). Ab initio structure solution by charge flipping requires no chemical or phase information (Oszlányi & Süto, 2004) and is well suited for ordered, disordered, and modulated structures. The dual-space recycling program SHELXT (Sheldrick, 2015a) takes advantage of the atomistic nature of ordered structures, utilizes the information about the nature of the chemical elements present, and introduces additional elements as necessary. It should be noted that a successful solution of a structure by either of these programs is not a substitute for elemental chemical analysis. Previously, we have had good success with the program SHELXT and were confident that the crystals of the inclusion compound (IV) = (I)·0.85(II)·0.15(III) could be crystallographically characterized (see Scheme). It was believed to be a hydro­carbon, but its origin, formula, and method of crystallization were and still remain unknown. Herein we report the structural and chemical characterization of (4R,5R)-4,5-bis­(hy­droxy­diphenyl­methyl)-2,2-di­methyl-1,3-\ dioxolane–4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one–4a-\ (hydro­per­oxy­methyl)-4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one (1/0.85/0.15), (IV), and propose an explanation for its appearance in the laboratory

1 Mueller et al. (2006) referenced a related Re^V complex [(η⁵-C₅Me₅)Re(O)(µ₂-O)]₂·H₂O, [(VII)·H₂O] (Herrmann et al., 1988), in their pursuit to establish the metal identity of their Re₂(η⁵-C₅Me₅)₂O₂(µ₂-O)₂ complex, (VII). The compositional difference between these two complexes is only the presence of a solvent water molecule in (VII)·H₂O that connects the Re complexes into a one-dimensional chain. Yet an air-stable (VII) and `very oxygen-sensitive' (VII)·H₂O have very different electronic structures and geometries. It is inter­esting to contrast several geometrical parameters in these complexes; the following parameters are reported pairwise for (VII) and (VII)·H₂O: Re···Re separation = 2.724 and 3.14 Å; distance between the bridging O atoms = 3.025 and 2.34 Å; Re—centroid(η⁵-C₅Me₅) = 2.059 and 1.97 Å; Re—O(bridging) = 2.004 and 1.96 Å; Re═O = 1.714 and 1.70 Å. Thus, there is a metal–metal bond in (VII), whereas there appears to be no Re—Re bond in (VII)·H₂O. These facts illustrate how difficult establishing the correct composition and structure might be. A density-functional theory (DFT) study of these systems is underway.

S2. Experimental

S2.1. Synthesis and crystallization

Clear colourless high-quality large centimetre-long parallelepiped-shaped crystals had been stored under air in an Erlenmeyer flask for over 10 years with no visible deterioration. No information about either their synthesis or crystallization was available, when a representative crystal was selected for a single-crystal X-ray structural characterization for the purpose of training a teaching assistant. The crystal composition was initially established crystallographyically and subsequently found to be consistent with its being a cocrystal of the TADDOL (α,α,α',α'-tetra­aryl-2,2-disubstituted 1,3-dioxolane-4,5-di­methanol) host 4,5-bis­(hy­droxy­diphenyl­methyl)-2,2-di­methyl-1,3-dioxolane, (I), with 85.1 (4)% of 4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one, (II), and 14.9 (4)% of 4a-(hydro­per­oxy­methyl)-4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one, (III). It was not possible to identify the student who submitted the crystals; therefore, we can only speculate about their preparation.

TADDOL, (I), is a common chiral catalyst (Seeback et al., 2001) that could have been used in a chiral synthesis leading to the formation of the enone (II), possibly by Robinson annulation or another route. There also is a distinct possibility that the chiral (I) was used as a host cocrystallant for (II), which is an oil, in order to establish its absolute configuration in an undergraduate organic laboratory. An autoxidation of the weak C—H bond at the only chiral center (C32) of enone (II) with ambient air is believed to yield the organic hydro­peroxide (III) that subsequently cocrystallized with (I) and (II) as a minor component. The autoxidation is presumed to have taken place in solution rather than in the solid state. Several data sets on different crystals of (IV) were acquired to confirm that their (II):(III) ratio remains invariant within experimental error. It is noteworthy that all the compounds were stable in the solid state, but the organic hydro­peroxide, (III), once isolated as a waxy solid, degraded into a brown oil within days in air. If (I) was not used to physically separate enanti­omers of (II), another possibility is that the crystals formed serendipitously in the flask used for an organic synthetic procedure and were brought to the laboratory because of their beauty and size, rather than their importance.

S2.2. Chemical analyses

After the crystallographic characterization of (IV), we separated the compounds by physical means and chemically analyzed the pure compounds to further support the identity of each component. About 150 mg of a crystalline sample was subjected to flash-column chromatography on silica gel with a hexanes–ethyl acetate gradient (10% ethyl acetate to 30% ethyl acetate). The separated compounds (I)–(III) were analyzed by ¹H and ¹³C NMR spectroscopy and high-resolution mass spectrometry. The bulk crystalline sample was also analyzed by X-ray fluorescence and the chemical composition of the crystals of solely C, H, and O was supported. The signal at 80.39 p.p.m. in the ¹³C NMR spectrum of impurity (III) is indicative of a C atom bound to an electronegative atom such as oxygen (atom C32). The broad singlet at 7.52 p.p.m. in the ¹H NMR spectrum is due to the hy­droxy H atom. The olefinic C—H signal is shifted downfield to 5.94 p.p.m., whereas the C—H signal of enone (II) is observed at 5.82 p.p.m. (See Supporting information for details of the X-ray fluorescence measurements, and NMR and MS data.)

S2.3. X-ray diffraction analysis and structural refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. There are three chemical moieties in the asymmetric unit. At one site, there is a fully occupied TADDOL host 4,5-bis­(hy­droxy­diphenyl­methyl)-2,2-di­methyl-1,3-dioxolane, (I). At the other site, there is compositional disorder between guest 4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one, (II), present 85.1 (4)% of the time, and impurity 4a-(hydro­per­oxy­methyl)-4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one, (III), observed 14.9 (4)% of the time. Most of the atoms in compounds (II) and (III) have the same coordinates; thus (II) and (III) differ only in the position of one CH₂—CH₂ link and the presence of the hydro­per­oxy group. Soft distance and thermal displacement parameter restraints were applied to the disordered part of the structure in order to achieve a chemically reasonable and computationally stable refinement.

S3. Results and discussion

The original goal of this work was to establish the crystal structure of an unknown, that proved to be compound (IV) (see Scheme), on the basis of X-ray diffraction data alone, as no prior chemical information was available. Due to the high quality of the data, this task proved to be straightforward; compounds (I) and (II) were readily identified and refined. However, two small peaks of electron density (ca 1.02 e Å⁻³) in the difference Fourier map in the vicinity of chiral center C32 in (II) (Fig. 1) suggested the presence of an additional species. These two peaks were tentatively assigned to be C atoms, and their presumed site occupancy was allowed to refine in the next series of least-squares cycles; the site-occupancy factor refined to ~0.20. Refinement with soft thermal displacement parameter restraints on the minor-disorder component was computationally stable; however, the C—C distance of 1.26 (2) Å was too short for a Csp³—Csp³ bond and the origin of this compound was hard to ascertain. An alternative refinement with an ethyl­ene group in place of the ethyl group resulted in a C—C distance of 1.363 (18) Å and an occupancy factor of ~0.21. Neither model was chemically satisfactory. Both models required thermal displacement parameter restraints. An alternative structural model (III) (Fig. 2) involved a hydro­per­oxy group that has the same number of electrons as an ethyl group and whose formation could be explained via autoxidation of (II). A refinement of this presumed structure of (III) as the minor-crystal-disordered component proceeded smoothly to yield the final structure presented herein. No restraints were required for the hydro­per­oxy group. The refined O—O distance of 1.453 (17) Å in (III) is in good agreement with the average CO—OH distance of 1.463 (7) Å obtained by averaging the 101 distances in 82 structures of organic hydro­peroxides listed in the Cambridge Structural Database (CSD, Version 5.36, updated May 2015; Groom & Allen, 2014); it falls well within the range of 1.447–1.463 Å. The C32—O6 distance to the hydro­per­oxy group of 1.560 (11) Å is substanti­ally longer than the average C—O(O) bond of 1.429 (18) Å in 82 related structures, and the difference is statistically significant. Nevertheless, chemical analyses confirmed that the hydro­peroxide (III) is the correct compound, and due to its low site occupancy (Fig. 3), the C32—O6 distance was considered to be acceptable and thereby refined without a restraint.

The C32—O6 bond direction in (III) is different from that of the C32—H32 bond in (II); the O6—C32—H32 angle is 24.5 (5)°. This implies an additional positional disorder of atoms C40 and C41, without which the tetra­hedral geometry of atom C32 in (III) would have been excessively distorted. Indeed, the prolate displacement ellipsoids of atoms C40 and C41, and two small peaks of electron density (ca 0.5 e Å⁻³) in their vicinity substanti­ated this reasoning. The positional disorder of the C40—C41 link over two positions in an 85:15 ratio was refined with distance and anisotropic displacement parameter restraints.

Comparisons of the structure of (IV) with those of previously reported inclusion complexes of (I) will be restricted to two closely related complexes, namely (I):[(R)-6-methylbi­cyclo­[4.4.0]dec-1-ene-3-one], (V), and (I):[(R)-6-methylbi­cyclo­[4.4.0]dec-1-ene-3,7-dione], (VI) (Nassimbeni et al., 1991), that are isomorphous with each other and with (IV).

There are several hydrogen-bonding inter­actions of the O—H···O type in the crystal of (IV) (Table 2). In the major host–guest pair, i.e. (I):(II), there are strong host–host O3—H3···O4 [type S(7) [add reference for graph-set notation?]] and host–guest O4—H4···O5ⁱ [type D(2)] hydrogen bonds. The corresponding values in (V) are very similar to those in (VI), i.e. 2.676 (6)/171° and 2.687 Å/176°, versus 2.661 (6) Å/n/a (the hy­droxy H atom is missing in the structure deposited to the CSD) and 2.694 Å/160°. When (III) is present as the guest, an additional host–guest hydrogen-bonding inter­action, O7—H7···O3 [type D(2)], is formed. It should be noted that the position of atom H7 is less than 2.1 Å away from atom H3 and the H3—O3···H7 angle has an acute value of 78.4°, suggesting a suboptimal steric inter­action between atoms H3 and H7. The positional parameters of H7 are considered to be acceptable due to the absence of hydrogen-bond acceptors other than atom O7 in the vicinity of atom O3.

The absolute configuration of the chiral centres C2, C3, and C32 was unambiguously established via anomalous dispersion effects as R. Whereas the Friedif value (Flack & Shmueli, 2007) that qu­anti­fies the magnitude of the resonant scattering effect for the crystal structure of (IV) is only 28.5, the Flack x = −0.01 (4) and Hooft y = 0.00 (5) parameters are quite conclusive. Had the synthesis of (II) and (III) been intentional, cocrystallization of (II) or (III) with (I) would have been proven to be a good means of optical resolution of the racemic mixture of (II) and its enanti­omer, given the fact that (II) is an oil and (III) is a hard-to-crystallize solid under ambient conditions. The Friedif value for (I), computed as 28.4 is substanti­ally lower than ~80, which is recommended for reliable elucidation of absolute structures (Flack & Bernardinelli, 2008); however, as our results illustrate, this value may be sufficient with high-quality low-temperature data sets.

We believe that the presence of (I) in the crystals of (IV) points to an intentional chiral crystallization of (II), due to the wide use of TADDOLs for such purposes (Seeback et al., 2001). TADDOL (I) has been widely utilized for optical resolution of chiral organic molecules because of its rigid structure and propensity to form hydrogen-bonding inter­actions (Nassimbeni et al., 1991; Seeback et al., 2001); to date, 42 host–guest structures with (I) as the host have been reported to the CSD. The enanti­omeric selectivity of (I) depends on its conformation and the size of the lattice voids accommodating the guest molecules (Báthori & Nassimbeni, 2010). The light-stable compound (I) has been utilized as the host in crystals with the light-sensitive guest tropolone methyl ether (Lavy et al., 2004), and with a number of other compounds, such as ether, enones, pyrazole, pyridine, pyran, and furan derivatives (Groom & Allen, 2014). Additionally, diol (I) was structurally characterized in 1990 (Goldberg et al., 1990) and with a number of typical solvents, such as acetone, di­methyl­formamide, CCl₄, and alcohols (Groom & Allen, 2014).

The structural study reported herein can be summarized as follows: the crystal structure of (IV) was solved ab initio, the compositional disorder was modeled crystallographically, the composition of (II) and (III) was substanti­ated by additional analytical techniques, and a plausible source of the crystals and the synthetic procedure were proposed with a high degree of confidence.

Structure description

\ Single-crystal X-ray structural analysis is a definitive analytical technique that, in an `ideal world', requires no prior information about the source or nature of the compound under investigation. For example, Mueller et al. (2006) used X-ray diffraction to establish the structure of an adventitious rhenium(V) complex Re<sub>2</sub>(Cp*)<sub>2</sub>O<sub>2</sub>(µ<sub>2</sub>-O)<sub>2</sub><sup>1</sup> (Cp* is penta­methyl­cyclo­penta­dienyl), whose source proved impossible to determine. A crystalline lilac deposit from a swimming pool was determined to be disodium copper(II) tetra­kis(isocyanurate) hexahydrate [Na<sub>2</sub>Cu(C<sub>3</sub>H<sub>2</sub>N<sub>3</sub>O<sub>3</sub>)<sub>4</sub>·6H<sub>2</sub>O; Hart et al., 1992] and subsequently purposefully synthesized (Falvello et al., 1997). Such examples are rare and, in practice, the crystallographer usually possesses information about the nature of the crystals as well as the synthons and solvents used during the chemical reaction and crystallization. When the structural solution reveals a compound different from the proposed one, typically a large portion of the structure contains correctly assigned elements at the correct positions. The much smaller `unknown' part of the structure is usually the cocrystallized solvent or counter-ion, whose nature and conformation are routinely deduced from the difference Fourier syntheses. Two inter­esting cases of structural analyses that had established the atomic connectivity in compounds of known origin include the bis­(2,3-di­hydro-1,3-diborole) complex [(EtC)₂(EtB)₂CHMe]₂Pt, that took nearly 30 years to produce dark-red single crystals (Wadepohl et al., 2015), and an indaza­lone, that, in the absence of a crystal structure, was believed to be a 2,1-benzisoxazole (Kurth et al., 2005).

With the advent of programs such as Shake-and-Bake (Miller et al., 1994), SUPERFLIP (Palatinus & Chapuis, 2007), SHELXD (Sheldrick, 2010), and SHELXT (Sheldrick, 2015a) that solve structures by performing Fourier transforms in the direct and reciprocal space, prior knowledge of the exact crystal composition has become optional (Feng, 2011). Ab initio structure solution by charge flipping requires no chemical or phase information (Oszlányi & Süto, 2004) and is well suited for ordered, disordered, and modulated structures. The dual-space recycling program SHELXT (Sheldrick, 2015a) takes advantage of the atomistic nature of ordered structures, utilizes the information about the nature of the chemical elements present, and introduces additional elements as necessary. It should be noted that a successful solution of a structure by either of these programs is not a substitute for elemental chemical analysis. Previously, we have had good success with the program SHELXT and were confident that the crystals of the inclusion compound (IV) = (I)·0.85(II)·0.15(III) could be crystallographically characterized (see Scheme). It was believed to be a hydro­carbon, but its origin, formula, and method of crystallization were and still remain unknown. Herein we report the structural and chemical characterization of (4R,5R)-4,5-bis­(hy­droxy­diphenyl­methyl)-2,2-di­methyl-1,3-\ dioxolane–4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one–4a-\ (hydro­per­oxy­methyl)-4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one (1/0.85/0.15), (IV), and propose an explanation for its appearance in the laboratory

1 Mueller et al. (2006) referenced a related Re^V complex [(η⁵-C₅Me₅)Re(O)(µ₂-O)]₂·H₂O, [(VII)·H₂O] (Herrmann et al., 1988), in their pursuit to establish the metal identity of their Re₂(η⁵-C₅Me₅)₂O₂(µ₂-O)₂ complex, (VII). The compositional difference between these two complexes is only the presence of a solvent water molecule in (VII)·H₂O that connects the Re complexes into a one-dimensional chain. Yet an air-stable (VII) and `very oxygen-sensitive' (VII)·H₂O have very different electronic structures and geometries. It is inter­esting to contrast several geometrical parameters in these complexes; the following parameters are reported pairwise for (VII) and (VII)·H₂O: Re···Re separation = 2.724 and 3.14 Å; distance between the bridging O atoms = 3.025 and 2.34 Å; Re—centroid(η⁵-C₅Me₅) = 2.059 and 1.97 Å; Re—O(bridging) = 2.004 and 1.96 Å; Re═O = 1.714 and 1.70 Å. Thus, there is a metal–metal bond in (VII), whereas there appears to be no Re—Re bond in (VII)·H₂O. These facts illustrate how difficult establishing the correct composition and structure might be. A density-functional theory (DFT) study of these systems is underway.

After the crystallographic characterization of (IV), we separated the compounds by physical means and chemically analyzed the pure compounds to further support the identity of each component. About 150 mg of a crystalline sample was subjected to flash-column chromatography on silica gel with a hexanes–ethyl acetate gradient (10% ethyl acetate to 30% ethyl acetate). The separated compounds (I)–(III) were analyzed by ¹H and ¹³C NMR spectroscopy and high-resolution mass spectrometry. The bulk crystalline sample was also analyzed by X-ray fluorescence and the chemical composition of the crystals of solely C, H, and O was supported. The signal at 80.39 p.p.m. in the ¹³C NMR spectrum of impurity (III) is indicative of a C atom bound to an electronegative atom such as oxygen (atom C32). The broad singlet at 7.52 p.p.m. in the ¹H NMR spectrum is due to the hy­droxy H atom. The olefinic C—H signal is shifted downfield to 5.94 p.p.m., whereas the C—H signal of enone (II) is observed at 5.82 p.p.m. (See Supporting information for details of the X-ray fluorescence measurements, and NMR and MS data.)

The original goal of this work was to establish the crystal structure of an unknown, that proved to be compound (IV) (see Scheme), on the basis of X-ray diffraction data alone, as no prior chemical information was available. Due to the high quality of the data, this task proved to be straightforward; compounds (I) and (II) were readily identified and refined. However, two small peaks of electron density (ca 1.02 e Å⁻³) in the difference Fourier map in the vicinity of chiral center C32 in (II) (Fig. 1) suggested the presence of an additional species. These two peaks were tentatively assigned to be C atoms, and their presumed site occupancy was allowed to refine in the next series of least-squares cycles; the site-occupancy factor refined to ~0.20. Refinement with soft thermal displacement parameter restraints on the minor-disorder component was computationally stable; however, the C—C distance of 1.26 (2) Å was too short for a Csp³—Csp³ bond and the origin of this compound was hard to ascertain. An alternative refinement with an ethyl­ene group in place of the ethyl group resulted in a C—C distance of 1.363 (18) Å and an occupancy factor of ~0.21. Neither model was chemically satisfactory. Both models required thermal displacement parameter restraints. An alternative structural model (III) (Fig. 2) involved a hydro­per­oxy group that has the same number of electrons as an ethyl group and whose formation could be explained via autoxidation of (II). A refinement of this presumed structure of (III) as the minor-crystal-disordered component proceeded smoothly to yield the final structure presented herein. No restraints were required for the hydro­per­oxy group. The refined O—O distance of 1.453 (17) Å in (III) is in good agreement with the average CO—OH distance of 1.463 (7) Å obtained by averaging the 101 distances in 82 structures of organic hydro­peroxides listed in the Cambridge Structural Database (CSD, Version 5.36, updated May 2015; Groom & Allen, 2014); it falls well within the range of 1.447–1.463 Å. The C32—O6 distance to the hydro­per­oxy group of 1.560 (11) Å is substanti­ally longer than the average C—O(O) bond of 1.429 (18) Å in 82 related structures, and the difference is statistically significant. Nevertheless, chemical analyses confirmed that the hydro­peroxide (III) is the correct compound, and due to its low site occupancy (Fig. 3), the C32—O6 distance was considered to be acceptable and thereby refined without a restraint.

The C32—O6 bond direction in (III) is different from that of the C32—H32 bond in (II); the O6—C32—H32 angle is 24.5 (5)°. This implies an additional positional disorder of atoms C40 and C41, without which the tetra­hedral geometry of atom C32 in (III) would have been excessively distorted. Indeed, the prolate displacement ellipsoids of atoms C40 and C41, and two small peaks of electron density (ca 0.5 e Å⁻³) in their vicinity substanti­ated this reasoning. The positional disorder of the C40—C41 link over two positions in an 85:15 ratio was refined with distance and anisotropic displacement parameter restraints.

Comparisons of the structure of (IV) with those of previously reported inclusion complexes of (I) will be restricted to two closely related complexes, namely (I):[(R)-6-methylbi­cyclo­[4.4.0]dec-1-ene-3-one], (V), and (I):[(R)-6-methylbi­cyclo­[4.4.0]dec-1-ene-3,7-dione], (VI) (Nassimbeni et al., 1991), that are isomorphous with each other and with (IV).

There are several hydrogen-bonding inter­actions of the O—H···O type in the crystal of (IV) (Table 2). In the major host–guest pair, i.e. (I):(II), there are strong host–host O3—H3···O4 [type S(7) [add reference for graph-set notation?]] and host–guest O4—H4···O5ⁱ [type D(2)] hydrogen bonds. The corresponding values in (V) are very similar to those in (VI), i.e. 2.676 (6)/171° and 2.687 Å/176°, versus 2.661 (6) Å/n/a (the hy­droxy H atom is missing in the structure deposited to the CSD) and 2.694 Å/160°. When (III) is present as the guest, an additional host–guest hydrogen-bonding inter­action, O7—H7···O3 [type D(2)], is formed. It should be noted that the position of atom H7 is less than 2.1 Å away from atom H3 and the H3—O3···H7 angle has an acute value of 78.4°, suggesting a suboptimal steric inter­action between atoms H3 and H7. The positional parameters of H7 are considered to be acceptable due to the absence of hydrogen-bond acceptors other than atom O7 in the vicinity of atom O3.

The absolute configuration of the chiral centres C2, C3, and C32 was unambiguously established via anomalous dispersion effects as R. Whereas the Friedif value (Flack & Shmueli, 2007) that qu­anti­fies the magnitude of the resonant scattering effect for the crystal structure of (IV) is only 28.5, the Flack x = −0.01 (4) and Hooft y = 0.00 (5) parameters are quite conclusive. Had the synthesis of (II) and (III) been intentional, cocrystallization of (II) or (III) with (I) would have been proven to be a good means of optical resolution of the racemic mixture of (II) and its enanti­omer, given the fact that (II) is an oil and (III) is a hard-to-crystallize solid under ambient conditions. The Friedif value for (I), computed as 28.4 is substanti­ally lower than ~80, which is recommended for reliable elucidation of absolute structures (Flack & Bernardinelli, 2008); however, as our results illustrate, this value may be sufficient with high-quality low-temperature data sets.

We believe that the presence of (I) in the crystals of (IV) points to an intentional chiral crystallization of (II), due to the wide use of TADDOLs for such purposes (Seeback et al., 2001). TADDOL (I) has been widely utilized for optical resolution of chiral organic molecules because of its rigid structure and propensity to form hydrogen-bonding inter­actions (Nassimbeni et al., 1991; Seeback et al., 2001); to date, 42 host–guest structures with (I) as the host have been reported to the CSD. The enanti­omeric selectivity of (I) depends on its conformation and the size of the lattice voids accommodating the guest molecules (Báthori & Nassimbeni, 2010). The light-stable compound (I) has been utilized as the host in crystals with the light-sensitive guest tropolone methyl ether (Lavy et al., 2004), and with a number of other compounds, such as ether, enones, pyrazole, pyridine, pyran, and furan derivatives (Groom & Allen, 2014). Additionally, diol (I) was structurally characterized in 1990 (Goldberg et al., 1990) and with a number of typical solvents, such as acetone, di­methyl­formamide, CCl₄, and alcohols (Groom & Allen, 2014).

The structural study reported herein can be summarized as follows: the crystal structure of (IV) was solved ab initio, the compositional disorder was modeled crystallographically, the composition of (II) and (III) was substanti­ated by additional analytical techniques, and a plausible source of the crystals and the synthetic procedure were proposed with a high degree of confidence.

Synthesis and crystallization

Clear colourless high-quality large centimetre-long parallelepiped-shaped crystals had been stored under air in an Erlenmeyer flask for over 10 years with no visible deterioration. No information about either their synthesis or crystallization was available, when a representative crystal was selected for a single-crystal X-ray structural characterization for the purpose of training a teaching assistant. The crystal composition was initially established crystallographyically and subsequently found to be consistent with its being a cocrystal of the TADDOL (α,α,α',α'-tetra­aryl-2,2-disubstituted 1,3-dioxolane-4,5-di­methanol) host 4,5-bis­(hy­droxy­diphenyl­methyl)-2,2-di­methyl-1,3-dioxolane, (I), with 85.1 (4)% of 4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one, (II), and 14.9 (4)% of 4a-(hydro­per­oxy­methyl)-4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one, (III). It was not possible to identify the student who submitted the crystals; therefore, we can only speculate about their preparation.

TADDOL, (I), is a common chiral catalyst (Seeback et al., 2001) that could have been used in a chiral synthesis leading to the formation of the enone (II), possibly by Robinson annulation or another route. There also is a distinct possibility that the chiral (I) was used as a host cocrystallant for (II), which is an oil, in order to establish its absolute configuration in an undergraduate organic laboratory. An autoxidation of the weak C—H bond at the only chiral center (C32) of enone (II) with ambient air is believed to yield the organic hydro­peroxide (III) that subsequently cocrystallized with (I) and (II) as a minor component. The autoxidation is presumed to have taken place in solution rather than in the solid state. Several data sets on different crystals of (IV) were acquired to confirm that their (II):(III) ratio remains invariant within experimental error. It is noteworthy that all the compounds were stable in the solid state, but the organic hydro­peroxide, (III), once isolated as a waxy solid, degraded into a brown oil within days in air. If (I) was not used to physically separate enanti­omers of (II), another possibility is that the crystals formed serendipitously in the flask used for an organic synthetic procedure and were brought to the laboratory because of their beauty and size, rather than their importance.

Refinement details

Crystal data, data collection and structure refinement details are summarized in Table 1. There are three chemical moieties in the asymmetric unit. At one site, there is a fully occupied TADDOL host 4,5-bis­(hy­droxy­diphenyl­methyl)-2,2-di­methyl-1,3-dioxolane, (I). At the other site, there is compositional disorder between guest 4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one, (II), present 85.1 (4)% of the time, and impurity 4a-(hydro­per­oxy­methyl)-4,4a,5,6,7,8-hexa­hydro­naphthalen-2(3H)-one, (III), observed 14.9 (4)% of the time. Most of the atoms in compounds (II) and (III) have the same coordinates; thus (II) and (III) differ only in the position of one CH₂—CH₂ link and the presence of the hydro­per­oxy group. Soft distance and thermal displacement parameter restraints were applied to the disordered part of the structure in order to achieve a chemically reasonable and computationally stable refinement.

Computing details

Data collection: APEX2 (Bruker, 2014); cell refinement: SAINT-Plus (Bruker, 2014); data reduction: SAINT-Plus (Bruker, 2014); program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXTL2014 (Sheldrick, 2015b); molecular graphics: OLEX2 (Dolomanov et al., 2009); software used to prepare material for publication: SHELXTL2014 (Sheldrick, 2015b).

Figures

	Fig. 1. The molecular structures of (I) and (II), shown with 50% probability displacement ellipsoids. Enone (II) is present 85.1 (4)% of the time. Only H atoms on O and anomeric C atoms are shown. The minor-disorder component (III) has been omitted. [Symmetry code: (i) x + 1, y, z.]
	Fig. 2. The molecular structures off (I) and (III), shown with 50% probability displacement ellipsoids. Hydroperoxide (III) is present 14.9 (4)% of the time. Only H atoms on O and anomeric C atoms are shown. The major-disorder component (II) has been omitted.
	Fig. 3. The molecular structures of (II) and (III), shown with 40% probability displacement ellipsoids. The bonds in enone (II) [85.1 (4)% occupancy] are shown with solid lines, whereas the bonds to the atoms in hydroperoxide (III) [present 14.9 (1)% of the time] that these compounds do not have in common are shown with dashes. Only the H atoms on O and anomeric C atoms are shown.

(4R,5R)-4,5-Bis(hydroxydiphenylmethyl)-2,2-dimethyl-1,3-dioxolane–4,4a,5,6,7,8-hexahydronaphthalen-2(3H)-one–4a-(hydroperoxymethyl)-4,4a,5,6,7,8-hexahydronaphthalen-2(3H)-one (1/0.85/0.15)

Crystal data

C31H30O4·0.85(C10H14O)·0.15(C10H14O3)	Dx = 1.249 Mg m^−3
Mr = 621.56	Cu Kα radiation, λ = 1.54178 Å
Orthorhombic, P212121	Cell parameters from 9920 reflections
a = 9.5183 (5) Å	θ = 3.7–72.9°
b = 9.5950 (7) Å	µ = 0.64 mm^−1
c = 36.207 (4) Å	T = 100 K
V = 3306.7 (5) Å^3	Block, colourless
Z = 4	0.4 × 0.3 × 0.2 mm
F(000) = 1330

Data collection

Bruker SMART APEXII area-detector diffractometer	6592 independent reflections
Radiation source: sealed X-ray tube, Siemens, K FFCU 2K 90	6442 reflections with I > 2σ(I)
Equatorially mounted graphite monochromator	Rint = 0.035
Detector resolution: 7.9 pixels mm^-1	θmax = 73.4°, θmin = 2.4°
0.60° ω and 0.6° φ scans	h = −11→11
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	k = −11→11
Tmin = 0.714, Tmax = 0.754	l = −41→44
50756 measured reflections

Refinement

Refinement on F^2	Hydrogen site location: inferred from neighbouring sites
Least-squares matrix: full	H-atom parameters constrained
R[F^2 > 2σ(F^2)] = 0.035	w = 1/[σ^2(Fo^2) + (0.0471P)^2 + 0.9649P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.088	(Δ/σ)max = 0.001
S = 1.05	Δρmax = 0.28 e Å^−3
6592 reflections	Δρmin = −0.25 e Å^−3
409 parameters	Absolute structure: Flack x determined using 2716 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons et al., 2013)
30 restraints	Absolute structure parameter: 0.00 (5)

Special details

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

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
O1	−0.02369 (14)	0.38554 (13)	0.66881 (3)	0.0179 (3)
O2	0.16594 (14)	0.38359 (14)	0.63014 (4)	0.0190 (3)
O3	−0.14599 (15)	0.72666 (15)	0.63829 (4)	0.0246 (3)
H3	−0.0938	0.7206	0.6196	0.037*
O4	0.01624 (14)	0.67637 (13)	0.57936 (4)	0.0185 (3)
H4	0.0716	0.7402	0.5730	0.028*
C1	0.0895 (2)	0.3011 (2)	0.65631 (5)	0.0189 (4)
C2	−0.04715 (19)	0.4952 (2)	0.64314 (5)	0.0160 (4)
H2	−0.1175	0.4639	0.6244	0.019*
C3	0.09733 (19)	0.51397 (19)	0.62415 (5)	0.0154 (4)
H3A	0.1508	0.5892	0.6371	0.019*
C4	0.0346 (2)	0.1715 (2)	0.63731 (6)	0.0293 (5)
H4A	−0.0314	0.1983	0.6178	0.044*
H4B	−0.0136	0.1124	0.6554	0.044*
H4C	0.1133	0.1199	0.6265	0.044*
C5	0.1825 (2)	0.2687 (3)	0.68916 (6)	0.0313 (5)
H5A	0.2611	0.2100	0.6812	0.047*
H5B	0.1277	0.2193	0.7080	0.047*
H5C	0.2189	0.3557	0.6996	0.047*
C6	−0.10716 (19)	0.62211 (19)	0.66456 (5)	0.0165 (4)
C7	0.00134 (12)	0.67885 (13)	0.69261 (3)	0.0195 (4)
C8	0.03443 (13)	0.60219 (11)	0.72400 (3)	0.0220 (4)
H8	−0.0087	0.5142	0.7281	0.026*
C9	0.13061 (14)	0.65419 (15)	0.74938 (3)	0.0301 (5)
H9	0.1532	0.6018	0.7708	0.036*
C10	0.19371 (13)	0.78286 (15)	0.74338 (4)	0.0386 (6)
H10	0.2594	0.8184	0.7607	0.046*
C11	0.16062 (15)	0.85953 (12)	0.71199 (4)	0.0385 (6)
H11	0.2037	0.9475	0.7079	0.046*
C12	0.06444 (15)	0.80753 (12)	0.68660 (3)	0.0280 (5)
H12	0.0418	0.8599	0.6652	0.034*
C14	−0.33814 (13)	0.48623 (13)	0.66902 (3)	0.0241 (4)
H14	−0.3094	0.4328	0.6483	0.029*
C15	−0.47027 (12)	0.46535 (14)	0.68441 (4)	0.0289 (5)
H15	−0.5318	0.3977	0.6742	0.035*
C16	−0.51232 (10)	0.54345 (15)	0.71480 (4)	0.0277 (5)
H16	−0.6026	0.5292	0.7253	0.033*
C17	−0.42224 (13)	0.64243 (14)	0.72980 (3)	0.0273 (4)
H17	−0.4510	0.6958	0.7506	0.033*
C18	−0.29011 (12)	0.66331 (13)	0.71441 (3)	0.0234 (4)
H18	−0.2285	0.7310	0.7247	0.028*
C13	−0.24806 (10)	0.58521 (14)	0.68403 (3)	0.0180 (4)
C19	0.0921 (2)	0.54668 (19)	0.58206 (5)	0.0167 (4)
C21	0.36275 (13)	0.55617 (15)	0.58562 (3)	0.0258 (4)
H21	0.3585	0.5318	0.6110	0.031*
C20	0.23991 (10)	0.56605 (14)	0.56503 (3)	0.0192 (4)
C25	0.24619 (11)	0.60165 (15)	0.52785 (3)	0.0241 (4)
H25	0.1622	0.6084	0.5138	0.029*
C24	0.37532 (14)	0.62737 (15)	0.51127 (3)	0.0295 (5)
H24	0.3796	0.6517	0.4859	0.035*
C23	0.49817 (11)	0.61748 (16)	0.53186 (4)	0.0314 (5)
H23	0.5864	0.6351	0.5205	0.038*
C22	0.49188 (11)	0.58189 (16)	0.56904 (4)	0.0326 (5)
H22	0.5758	0.5751	0.5831	0.039*
C31	−0.13531 (12)	0.45078 (10)	0.55597 (3)	0.0199 (4)
H31	−0.1800	0.5347	0.5634	0.024*
C30	−0.21370 (10)	0.34447 (13)	0.53999 (4)	0.0236 (4)
H30	−0.3120	0.3558	0.5365	0.028*
C29	−0.14830 (13)	0.22163 (11)	0.52910 (4)	0.0259 (4)
H29	−0.2019	0.1490	0.5182	0.031*
C28	−0.00452 (13)	0.20510 (10)	0.53419 (4)	0.0250 (4)
H28	0.0402	0.1211	0.5267	0.030*
C27	0.07387 (10)	0.31142 (12)	0.55017 (3)	0.0221 (4)
H27	0.1721	0.3001	0.5536	0.027*
C26	0.00848 (12)	0.43426 (10)	0.56106 (3)	0.0178 (4)
O5	−0.83840 (16)	0.89933 (15)	0.55736 (4)	0.0290 (3)
O6	−0.3022 (11)	0.9681 (12)	0.5975 (3)	0.033 (3)	0.149 (4)
O7	−0.3126 (13)	0.8316 (14)	0.5803 (3)	0.040 (3)	0.149 (4)
H7	−0.2876	0.7701	0.5955	0.060*	0.149 (4)
C32	−0.4525 (2)	1.0326 (2)	0.59873 (6)	0.0274 (5)
H32	−0.3747	0.9750	0.5882	0.033*	0.851 (4)
C33	−0.3884 (3)	1.1420 (3)	0.62428 (7)	0.0383 (6)
H33A	−0.4619	1.2100	0.6313	0.046*
H33B	−0.3140	1.1930	0.6108	0.046*
C34	−0.3254 (3)	1.0781 (3)	0.65935 (8)	0.0446 (7)
H34A	−0.2473	1.0148	0.6527	0.054*
H34B	−0.2874	1.1529	0.6753	0.054*
C35	−0.4387 (3)	0.9969 (3)	0.68029 (6)	0.0361 (5)
H35A	−0.3980	0.9562	0.7030	0.043*
H35B	−0.5155	1.0608	0.6876	0.043*
C36	−0.4970 (2)	0.8811 (2)	0.65582 (6)	0.0300 (5)
H36A	−0.4221	0.8119	0.6510	0.036*
H36B	−0.5743	0.8331	0.6690	0.036*
C37	−0.5509 (2)	0.9369 (2)	0.61966 (5)	0.0240 (4)
C38	−0.6771 (2)	0.9007 (2)	0.60643 (6)	0.0231 (4)
H38	−0.7387	0.8492	0.6219	0.028*
C39	−0.7241 (2)	0.9366 (2)	0.56952 (6)	0.0245 (4)
C40	−0.6206 (3)	1.0102 (3)	0.54461 (7)	0.0302 (7)	0.851 (4)
H40A	−0.6723	1.0643	0.5257	0.036*	0.851 (4)
H40B	−0.5618	0.9404	0.5317	0.036*	0.851 (4)
C41	−0.5274 (3)	1.1075 (3)	0.56677 (8)	0.0331 (7)	0.851 (4)
H41A	−0.5852	1.1843	0.5769	0.040*	0.851 (4)
H41B	−0.4561	1.1490	0.5502	0.040*	0.851 (4)
C41A	−0.4917 (15)	1.040 (2)	0.5589 (3)	0.038 (4)	0.149 (4)
H41C	−0.4714	0.9503	0.5463	0.045*	0.149 (4)
H41D	−0.4397	1.1152	0.5463	0.045*	0.149 (4)
C40A	−0.6470 (15)	1.0691 (15)	0.5590 (6)	0.037 (4)	0.149 (4)
H40C	−0.6774	1.1005	0.5342	0.045*	0.149 (4)
H40D	−0.6686	1.1438	0.5770	0.045*	0.149 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0185 (6)	0.0177 (6)	0.0175 (6)	0.0010 (5)	0.0050 (5)	0.0033 (5)
O2	0.0184 (6)	0.0187 (6)	0.0200 (6)	0.0029 (5)	0.0057 (5)	0.0050 (5)
O3	0.0275 (7)	0.0253 (7)	0.0210 (7)	0.0092 (6)	0.0083 (6)	0.0089 (6)
O4	0.0205 (7)	0.0150 (6)	0.0201 (6)	−0.0006 (5)	0.0054 (5)	0.0021 (5)
C1	0.0164 (9)	0.0196 (9)	0.0205 (9)	0.0008 (7)	0.0045 (7)	0.0046 (7)
C2	0.0148 (8)	0.0197 (9)	0.0136 (8)	−0.0025 (7)	0.0014 (7)	0.0017 (7)
C3	0.0133 (8)	0.0155 (8)	0.0174 (9)	0.0000 (7)	0.0018 (7)	−0.0008 (7)
C4	0.0319 (11)	0.0200 (10)	0.0359 (12)	−0.0025 (9)	0.0105 (9)	−0.0016 (8)
C5	0.0205 (10)	0.0451 (13)	0.0283 (11)	0.0025 (9)	0.0020 (8)	0.0153 (10)
C6	0.0173 (8)	0.0182 (9)	0.0141 (8)	0.0019 (7)	0.0025 (7)	0.0025 (7)
C7	0.0168 (9)	0.0206 (9)	0.0210 (9)	−0.0004 (7)	0.0070 (7)	−0.0050 (7)
C8	0.0182 (9)	0.0268 (10)	0.0210 (9)	0.0003 (8)	0.0022 (7)	−0.0061 (8)
C9	0.0187 (9)	0.0439 (13)	0.0276 (11)	0.0066 (9)	−0.0014 (8)	−0.0131 (10)
C10	0.0196 (10)	0.0486 (15)	0.0475 (14)	−0.0017 (10)	0.0005 (10)	−0.0320 (13)
C11	0.0286 (12)	0.0293 (12)	0.0576 (16)	−0.0100 (10)	0.0136 (11)	−0.0217 (11)
C12	0.0274 (11)	0.0201 (10)	0.0364 (11)	−0.0013 (8)	0.0118 (9)	−0.0079 (9)
C14	0.0203 (9)	0.0285 (10)	0.0233 (10)	0.0002 (8)	0.0046 (8)	−0.0029 (8)
C15	0.0212 (10)	0.0346 (12)	0.0307 (11)	−0.0037 (9)	0.0029 (8)	−0.0012 (9)
C16	0.0171 (9)	0.0405 (12)	0.0256 (10)	0.0038 (9)	0.0062 (8)	0.0065 (9)
C17	0.0241 (10)	0.0400 (12)	0.0179 (9)	0.0051 (9)	0.0057 (8)	−0.0006 (9)
C18	0.0212 (10)	0.0310 (11)	0.0180 (9)	0.0016 (8)	0.0006 (7)	0.0006 (8)
C13	0.0155 (8)	0.0226 (9)	0.0158 (8)	0.0036 (7)	0.0014 (7)	0.0048 (7)
C19	0.0187 (9)	0.0153 (8)	0.0161 (8)	−0.0006 (7)	0.0029 (7)	0.0013 (7)
C21	0.0218 (10)	0.0272 (10)	0.0285 (11)	0.0009 (8)	0.0071 (8)	0.0047 (8)
C20	0.0216 (9)	0.0145 (8)	0.0216 (9)	−0.0021 (7)	0.0075 (7)	−0.0025 (7)
C25	0.0295 (10)	0.0210 (10)	0.0220 (9)	−0.0035 (8)	0.0065 (8)	−0.0035 (8)
C24	0.0386 (12)	0.0236 (10)	0.0263 (10)	−0.0033 (9)	0.0163 (9)	−0.0014 (8)
C23	0.0275 (11)	0.0245 (10)	0.0421 (12)	−0.0026 (9)	0.0203 (10)	0.0005 (9)
C22	0.0206 (10)	0.0335 (12)	0.0438 (13)	0.0015 (9)	0.0076 (9)	0.0061 (10)
C31	0.0240 (10)	0.0206 (9)	0.0151 (8)	−0.0009 (8)	0.0006 (7)	0.0011 (7)
C30	0.0236 (10)	0.0284 (11)	0.0188 (9)	−0.0041 (8)	−0.0025 (7)	0.0020 (8)
C29	0.0349 (11)	0.0228 (10)	0.0199 (10)	−0.0100 (9)	−0.0022 (9)	−0.0015 (8)
C28	0.0352 (11)	0.0194 (9)	0.0204 (9)	−0.0010 (9)	0.0031 (8)	−0.0016 (7)
C27	0.0246 (10)	0.0228 (9)	0.0190 (9)	−0.0016 (8)	0.0040 (7)	0.0002 (8)
C26	0.0231 (9)	0.0187 (9)	0.0116 (8)	−0.0037 (7)	0.0026 (7)	0.0020 (7)
O5	0.0274 (7)	0.0218 (7)	0.0379 (8)	−0.0051 (6)	−0.0082 (6)	0.0072 (6)
O6	0.021 (5)	0.040 (6)	0.039 (6)	0.002 (4)	0.002 (4)	0.001 (5)
O7	0.042 (7)	0.050 (7)	0.028 (6)	−0.001 (5)	0.009 (5)	−0.011 (5)
C32	0.0260 (10)	0.0315 (11)	0.0248 (10)	−0.0078 (9)	0.0002 (8)	−0.0010 (9)
C33	0.0439 (14)	0.0330 (12)	0.0379 (13)	−0.0118 (11)	−0.0121 (11)	0.0014 (10)
C34	0.0488 (15)	0.0448 (15)	0.0402 (14)	−0.0116 (13)	−0.0216 (12)	−0.0002 (12)
C35	0.0454 (14)	0.0391 (13)	0.0236 (11)	0.0060 (11)	−0.0114 (10)	−0.0013 (10)
C36	0.0313 (11)	0.0318 (11)	0.0267 (11)	0.0024 (10)	−0.0001 (9)	0.0054 (9)
C37	0.0276 (10)	0.0244 (10)	0.0199 (9)	−0.0015 (8)	0.0034 (8)	−0.0020 (8)
C38	0.0252 (9)	0.0227 (9)	0.0214 (9)	−0.0041 (8)	0.0056 (8)	0.0006 (8)
C39	0.0265 (10)	0.0162 (9)	0.0308 (11)	−0.0027 (8)	−0.0010 (8)	0.0036 (8)
C40	0.0414 (16)	0.0342 (16)	0.0150 (12)	−0.0170 (13)	−0.0037 (11)	0.0059 (11)
C41	0.0393 (16)	0.0365 (17)	0.0235 (14)	−0.0228 (14)	−0.0063 (12)	0.0083 (12)
C41A	0.044 (7)	0.046 (10)	0.023 (5)	−0.021 (7)	0.016 (6)	−0.008 (7)
C40A	0.046 (7)	0.033 (8)	0.034 (9)	−0.008 (6)	−0.012 (6)	0.011 (7)

Geometric parameters (Å, º)

O1—C1	1.422 (2)	C24—H24	0.9500
O1—C2	1.421 (2)	C24—C23	1.3900
O2—C1	1.433 (2)	C23—H23	0.9500
O2—C3	1.428 (2)	C23—C22	1.3900
O3—H3	0.8400	C22—H22	0.9500
O3—C6	1.431 (2)	C31—H31	0.9500
O4—H4	0.8400	C31—C30	1.3900
O4—C19	1.442 (2)	C31—C26	1.3900
C1—C4	1.514 (3)	C30—H30	0.9500
C1—C5	1.515 (3)	C30—C29	1.3900
C2—H2	1.0000	C29—H29	0.9500
C2—C3	1.548 (2)	C29—C28	1.3900
C2—C6	1.553 (3)	C28—H28	0.9500
C3—H3A	1.0000	C28—C27	1.3900
C3—C19	1.557 (3)	C27—H27	0.9500
C4—H4A	0.9800	C27—C26	1.3900
C4—H4B	0.9800	O5—C39	1.227 (3)
C4—H4C	0.9800	O6—O7	1.453 (17)
C5—H5A	0.9800	O6—C32	1.560 (11)
C5—H5B	0.9800	O7—H7	0.8400
C5—H5C	0.9800	C32—H32	1.0000
C6—C7	1.547 (2)	C32—C33	1.527 (3)
C6—C13	1.5559 (19)	C32—C37	1.514 (3)
C7—C8	1.3900	C32—C41	1.537 (3)
C7—C12	1.3900	C32—C41A	1.491 (11)
C8—H8	0.9500	C33—H33A	0.9900
C8—C9	1.3900	C33—H33B	0.9900
C9—H9	0.9500	C33—C34	1.532 (3)
C9—C10	1.3900	C34—H34A	0.9900
C10—H10	0.9500	C34—H34B	0.9900
C10—C11	1.3900	C34—C35	1.531 (4)
C11—H11	0.9500	C35—H35A	0.9900
C11—C12	1.3900	C35—H35B	0.9900
C12—H12	0.9500	C35—C36	1.526 (3)
C14—H14	0.9500	C36—H36A	0.9900
C14—C15	1.3900	C36—H36B	0.9900
C14—C13	1.3900	C36—C37	1.504 (3)
C15—H15	0.9500	C37—C38	1.339 (3)
C15—C16	1.3900	C38—H38	0.9500
C16—H16	0.9500	C38—C39	1.451 (3)
C16—C17	1.3900	C39—C40	1.511 (3)
C17—H17	0.9500	C39—C40A	1.516 (11)
C17—C18	1.3900	C40—H40A	0.9900
C18—H18	0.9500	C40—H40B	0.9900
C18—C13	1.3900	C40—C41	1.518 (4)
C19—C20	1.547 (2)	C41—H41A	0.9900
C19—C26	1.541 (2)	C41—H41B	0.9900
C21—H21	0.9500	C41A—H41C	0.9900
C21—C20	1.3900	C41A—H41D	0.9900
C21—C22	1.3900	C41A—C40A	1.505 (13)
C20—C25	1.3900	C40A—H40C	0.9900
C25—H25	0.9500	C40A—H40D	0.9900
C25—C24	1.3900
C2—O1—C1	109.43 (13)	C24—C23—C22	120.0
C3—O2—C1	110.61 (14)	C22—C23—H23	120.0
C6—O3—H3	109.5	C21—C22—H22	120.0
C19—O4—H4	109.5	C23—C22—C21	120.0
O1—C1—O2	106.28 (14)	C23—C22—H22	120.0
O1—C1—C4	110.58 (16)	C30—C31—H31	120.0
O1—C1—C5	108.06 (16)	C30—C31—C26	120.0
O2—C1—C4	109.16 (16)	C26—C31—H31	120.0
O2—C1—C5	109.61 (16)	C31—C30—H30	120.0
C4—C1—C5	112.92 (18)	C29—C30—C31	120.0
O1—C2—H2	109.1	C29—C30—H30	120.0
O1—C2—C3	103.72 (14)	C30—C29—H29	120.0
O1—C2—C6	108.16 (14)	C30—C29—C28	120.0
C3—C2—H2	109.1	C28—C29—H29	120.0
C3—C2—C6	117.19 (15)	C29—C28—H28	120.0
C6—C2—H2	109.1	C27—C28—C29	120.0
O2—C3—C2	103.69 (14)	C27—C28—H28	120.0
O2—C3—H3A	109.2	C28—C27—H27	120.0
O2—C3—C19	109.87 (14)	C28—C27—C26	120.0
C2—C3—H3A	109.2	C26—C27—H27	120.0
C2—C3—C19	115.47 (15)	C31—C26—C19	119.62 (10)
C19—C3—H3A	109.2	C27—C26—C19	120.13 (10)
C1—C4—H4A	109.5	C27—C26—C31	120.0
C1—C4—H4B	109.5	O7—O6—C32	107.8 (8)
C1—C4—H4C	109.5	O6—O7—H7	109.5
H4A—C4—H4B	109.5	C33—C32—O6	85.6 (5)
H4A—C4—H4C	109.5	C33—C32—H32	108.3
H4B—C4—H4C	109.5	C33—C32—C41	108.7 (2)
C1—C5—H5A	109.5	C37—C32—O6	109.9 (4)
C1—C5—H5B	109.5	C37—C32—H32	108.3
C1—C5—H5C	109.5	C37—C32—C33	111.15 (18)
H5A—C5—H5B	109.5	C37—C32—C41	111.95 (19)
H5A—C5—H5C	109.5	C41—C32—H32	108.3
H5B—C5—H5C	109.5	C41A—C32—O6	102.8 (8)
O3—C6—C2	108.24 (14)	C41A—C32—C33	130.9 (8)
O3—C6—C7	111.22 (14)	C41A—C32—C37	110.9 (7)
O3—C6—C13	103.77 (13)	C32—C33—H33A	109.1
C2—C6—C13	111.39 (14)	C32—C33—H33B	109.1
C7—C6—C2	110.99 (14)	C32—C33—C34	112.6 (2)
C7—C6—C13	110.98 (13)	H33A—C33—H33B	107.8
C8—C7—C6	120.11 (10)	C34—C33—H33A	109.1
C8—C7—C12	120.0	C34—C33—H33B	109.1
C12—C7—C6	119.89 (10)	C33—C34—H34A	109.7
C7—C8—H8	120.0	C33—C34—H34B	109.7
C7—C8—C9	120.0	H34A—C34—H34B	108.2
C9—C8—H8	120.0	C35—C34—C33	109.8 (2)
C8—C9—H9	120.0	C35—C34—H34A	109.7
C10—C9—C8	120.0	C35—C34—H34B	109.7
C10—C9—H9	120.0	C34—C35—H35A	109.7
C9—C10—H10	120.0	C34—C35—H35B	109.7
C11—C10—C9	120.0	H35A—C35—H35B	108.2
C11—C10—H10	120.0	C36—C35—C34	109.8 (2)
C10—C11—H11	120.0	C36—C35—H35A	109.7
C12—C11—C10	120.0	C36—C35—H35B	109.7
C12—C11—H11	120.0	C35—C36—H36A	109.3
C7—C12—H12	120.0	C35—C36—H36B	109.3
C11—C12—C7	120.0	H36A—C36—H36B	107.9
C11—C12—H12	120.0	C37—C36—C35	111.73 (19)
C15—C14—H14	120.0	C37—C36—H36A	109.3
C15—C14—C13	120.0	C37—C36—H36B	109.3
C13—C14—H14	120.0	C36—C37—C32	116.12 (19)
C14—C15—H15	120.0	C38—C37—C32	122.19 (19)
C14—C15—C16	120.0	C38—C37—C36	121.67 (19)
C16—C15—H15	120.0	C37—C38—H38	118.5
C15—C16—H16	120.0	C37—C38—C39	123.00 (19)
C15—C16—C17	120.0	C39—C38—H38	118.5
C17—C16—H16	120.0	O5—C39—C38	122.32 (19)
C16—C17—H17	120.0	O5—C39—C40	120.0 (2)
C18—C17—C16	120.0	O5—C39—C40A	125.7 (6)
C18—C17—H17	120.0	C38—C39—C40	117.39 (19)
C17—C18—H18	120.0	C38—C39—C40A	106.3 (7)
C17—C18—C13	120.0	C39—C40—H40A	109.5
C13—C18—H18	120.0	C39—C40—H40B	109.5
C14—C13—C6	120.68 (10)	C39—C40—C41	110.7 (2)
C18—C13—C6	118.95 (10)	H40A—C40—H40B	108.1
C18—C13—C14	120.0	C41—C40—H40A	109.5
O4—C19—C3	104.84 (14)	C41—C40—H40B	109.5
O4—C19—C20	108.95 (13)	C32—C41—H41A	109.1
O4—C19—C26	108.16 (14)	C32—C41—H41B	109.1
C20—C19—C3	112.68 (14)	C40—C41—C32	112.4 (2)
C26—C19—C3	110.99 (14)	C40—C41—H41A	109.1
C26—C19—C20	110.92 (13)	C40—C41—H41B	109.1
C20—C21—H21	120.0	H41A—C41—H41B	107.9
C20—C21—C22	120.0	C32—C41A—H41C	110.8
C22—C21—H21	120.0	C32—C41A—H41D	110.8
C21—C20—C19	122.87 (10)	C32—C41A—C40A	104.6 (11)
C21—C20—C25	120.0	H41C—C41A—H41D	108.9
C25—C20—C19	117.04 (10)	C40A—C41A—H41C	110.8
C20—C25—H25	120.0	C40A—C41A—H41D	110.8
C24—C25—C20	120.0	C39—C40A—H40C	110.0
C24—C25—H25	120.0	C39—C40A—H40D	110.0
C25—C24—H24	120.0	C41A—C40A—C39	108.6 (12)
C25—C24—C23	120.0	C41A—C40A—H40C	110.0
C23—C24—H24	120.0	C41A—C40A—H40D	110.0
C24—C23—H23	120.0	H40C—C40A—H40D	108.4
O1—C2—C3—O2	21.91 (17)	C13—C6—C7—C8	53.96 (16)
O1—C2—C3—C19	142.14 (15)	C13—C6—C7—C12	−125.23 (12)
O1—C2—C6—O3	−173.43 (14)	C13—C14—C15—C16	0.0
O1—C2—C6—C7	64.26 (17)	C19—C20—C25—C24	176.83 (13)
O1—C2—C6—C13	−59.96 (18)	C21—C20—C25—C24	0.0
O2—C3—C19—O4	177.70 (13)	C20—C19—C26—C31	−143.43 (11)
O2—C3—C19—C20	−63.95 (18)	C20—C19—C26—C27	42.29 (16)
O2—C3—C19—C26	61.15 (18)	C20—C21—C22—C23	0.0
O3—C6—C7—C8	168.95 (10)	C20—C25—C24—C23	0.0
O3—C6—C7—C12	−10.24 (17)	C25—C24—C23—C22	0.0
O3—C6—C13—C14	85.78 (15)	C24—C23—C22—C21	0.0
O3—C6—C13—C18	−87.20 (14)	C22—C21—C20—C19	−176.63 (14)
O4—C19—C20—C21	115.36 (13)	C22—C21—C20—C25	0.0
O4—C19—C20—C25	−61.36 (16)	C31—C30—C29—C28	0.0
O4—C19—C26—C31	−24.00 (16)	C30—C31—C26—C19	−174.29 (13)
O4—C19—C26—C27	161.72 (10)	C30—C31—C26—C27	0.0
C1—O1—C2—C3	−25.52 (18)	C30—C29—C28—C27	0.0
C1—O1—C2—C6	−150.63 (14)	C29—C28—C27—C26	0.0
C1—O2—C3—C2	−11.07 (18)	C28—C27—C26—C19	174.26 (13)
C1—O2—C3—C19	−135.03 (15)	C28—C27—C26—C31	0.0
C2—O1—C1—O2	19.26 (19)	C26—C19—C20—C21	−125.69 (12)
C2—O1—C1—C4	−99.09 (18)	C26—C19—C20—C25	57.59 (15)
C2—O1—C1—C5	136.85 (16)	C26—C31—C30—C29	0.0
C2—C3—C19—O4	60.90 (19)	O5—C39—C40—C41	151.4 (3)
C2—C3—C19—C20	179.25 (14)	O5—C39—C40A—C41A	−144.8 (9)
C2—C3—C19—C26	−55.65 (19)	O6—C32—C33—C34	−59.7 (5)
C2—C6—C7—C8	−70.48 (16)	O6—C32—C37—C36	46.6 (5)
C2—C6—C7—C12	110.33 (13)	O6—C32—C37—C38	−131.7 (5)
C2—C6—C13—C14	−30.46 (17)	O6—C32—C41A—C40A	167.1 (11)
C2—C6—C13—C18	156.56 (11)	O7—O6—C32—C33	168.6 (8)
C3—O2—C1—O1	−4.02 (19)	O7—O6—C32—C37	57.7 (9)
C3—O2—C1—C4	115.27 (17)	O7—O6—C32—C41A	−60.4 (12)
C3—O2—C1—C5	−120.57 (18)	C32—C33—C34—C35	−58.0 (3)
C3—C2—C6—O3	69.88 (19)	C32—C37—C38—C39	7.1 (3)
C3—C2—C6—C7	−52.43 (19)	C32—C41A—C40A—C39	−74.8 (17)
C3—C2—C6—C13	−176.65 (14)	C33—C32—C37—C36	−46.4 (3)
C3—C19—C20—C21	−0.55 (19)	C33—C32—C37—C38	135.4 (2)
C3—C19—C20—C25	−177.28 (11)	C33—C32—C41—C40	−167.5 (3)
C3—C19—C26—C31	90.49 (14)	C33—C32—C41A—C40A	−97.7 (12)
C3—C19—C26—C27	−83.79 (15)	C33—C34—C35—C36	59.7 (3)
C6—C2—C3—O2	140.99 (15)	C34—C35—C36—C37	−55.3 (3)
C6—C2—C3—C19	−98.78 (19)	C35—C36—C37—C32	49.8 (3)
C6—C7—C8—C9	−179.19 (13)	C35—C36—C37—C38	−131.9 (2)
C6—C7—C12—C11	179.19 (13)	C36—C37—C38—C39	−171.1 (2)
C7—C6—C13—C14	−154.68 (10)	C37—C32—C33—C34	50.0 (3)
C7—C6—C13—C18	32.34 (16)	C37—C32—C41—C40	−44.4 (4)
C7—C8—C9—C10	0.0	C37—C32—C41A—C40A	49.7 (14)
C8—C7—C12—C11	0.0	C37—C38—C39—O5	177.8 (2)
C8—C9—C10—C11	0.0	C37—C38—C39—C40	3.9 (3)
C9—C10—C11—C12	0.0	C37—C38—C39—C40A	−27.4 (8)
C10—C11—C12—C7	0.0	C38—C39—C40—C41	−34.6 (4)
C12—C7—C8—C9	0.0	C38—C39—C40A—C41A	61.5 (14)
C14—C15—C16—C17	0.0	C39—C40—C41—C32	54.6 (4)
C15—C14—C13—C6	−172.91 (13)	C41—C32—C33—C34	173.6 (2)
C15—C14—C13—C18	0.0	C41—C32—C37—C36	−168.1 (2)
C15—C16—C17—C18	0.0	C41—C32—C37—C38	13.6 (3)
C16—C17—C18—C13	0.0	C41A—C32—C33—C34	−162.7 (8)
C17—C18—C13—C6	173.04 (13)	C41A—C32—C37—C36	159.6 (8)
C17—C18—C13—C14	0.0	C41A—C32—C37—C38	−18.7 (9)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O3—H3···O4	0.84	1.85	2.6777 (19)	171
O4—H4···O5^i	0.84	1.84	2.6693 (19)	169
O7—H7···O3	0.84	2.10	2.818 (13)	144

Symmetry code: (i) x+1, y, z.