The complex packing pattern of cis-1,2-dimethyl­cyclo­butane-1,2-diol

cis-1,2-Dimethyl­cyclo­butane-1,2-diol, C₆H₁₂O₂, crystallizes with five mol­ecules in the asymmetric unit. Of these, two mol­ecules are the building blocks of columns with a complex hydrogen-bonding pattern in their hydro­philic core. The walls of the columns are formed by the lipophilic parts of the mol­ecules. The remaining three mol­ecules of the asymmetric unit build columns with a less complex hydrogen-bonding system. In terms of co-operativity, the most significant feature is the formation of homodromic rings of six hydroxy functions.

S1. Comment

On crystallization, the polar (hydrophilic) and the apolar (lipophilic) parts of amphiphilic molecules usually segregate into polar and apolar building blocks of the crystal structure, respectively. If the polar and the apolar parts occupy volume fractions of different sizes, only the larger part normally establishes intermolecular contacts in all three dimensions, whereas the smaller part may be restricted to intermolecular contacts in zero (pairs of molecules, clusters) or one dimension (chains, columns).

The diols are a particularly widespread class of compounds which illustrate this principle since, owing to the variety of residues that may be attached to the diol function, the size ratios between the polar and the apolar parts may span an extended range. Moreover, the diols have attracted our interest as they are the parent acids of potentially chelating ligands. Examples of structurally characterized diols which are representative examples in terms of the size ratio between the polar and apolar molecular parts include 1,2-dicyclopentylethane-1,2-diol (Betz et al., 2007) and bi-1,1'-cycloheptyl-1,1'-diol (Betz & Klüfers, 2007), in both of which the diol functions are assembled in hydrogen-bonded chains, and cis- and rac-trans-cyclohexane-1,2-diol (Sillanpää et al., 1984) which exhibit hydrogen-bonded layers. Finite hydrogen-bonding patterns have been found with pinacol, for example, namely eight-membered homodromic rings in tetramers of the diol (Jeffrey & Robbins, 1978).

In the title compound, (I), the apolar part fills, to a similar extent as in pinacol, the major part of the crystal's volume and restricts the polar part to the core of columns with an apolar shell. What makes (I) remarkable is the complexity with which the molecules assemble into the crystal structure; no less than five molecules are found in the asymmetric unit, one of them exhibiting disorder in the apolar part. Fig. 1 shows two of the five independent molecules, while Fig. 2 shows the remaining three molecules. A common feature of all the molecules is the slightly twisted cyclobutane ring, which, together with the methyl substituents, imparts a certain degree of rigidity to the molecules such that the diol torsion angles of all five molecules are within 4° of 30°. One molecule exhibits disorder of the ethylene unit of the cyclobutane ring and of the two methyl substituents (Fig. 3). It should be noted that the two disordered forms are connected by a 180° rotation, which leaves the orientation of the diol function unaltered, so that both disordered forms are compatible with the hydrogen-bonding pattern.

The dimer and the trimer of diols depicted in Figs. 1 and 2 are the building blocks of two different kinds of hydrogen-bonded columns, termed d₂ and d₃, respectively. Although built by the more complex asymmetric building block, the core of the d₃ column has a simpler construction principle in terms of cooperativity; isolated homodromic rings made up of six symmetry-independent hydroxy functions are linked by a diol dimer (Fig. 4). Hence, although the core of a column provides an infinite stack of approximately equidistant hydroxy groups, their O—H vectors do not combine to form an infinite cooperative hydrogen-bonded system. Specifically, infinite cooperativity via intra-diol hydrogen bonding, as found in the related bicycloheptyldiol structure (Betz & Klüfers, 2007), is only weakly, if at all, exhibited both in the d₃ as well as in the d₂ strands (cf. the last three entries in Table 1).

The core of the d₂ columns shows a closely related, but more complex, hydrogen-bonding pattern (Fig. 5). Similar homodromic rings of another six hydroxy functions are again aligned by diol links, but two more hydroxy donors, which bind to two acceptor sites at opposite ring positions, complete the pattern.

For the hydrogen bonds observed in the two different columns, graph-set analysis (Etter et al., 1990; Bernstein et al., 1995) was applied. Each column was analyzed separately because the d₂ and d₃ columns have no linking hydrogen bonds.

The hydrogen bonds in the more basic d₃ column are not crystallographically equivalent, so on the unitary graph level the pattern should be assigned a DDDDDD descriptor. As depicted in Fig. 4, on the binary graph level the descriptor converts to two C₂²(7) chains connected by an R₂²(10) ring. Finally, an R₆⁶(12) [R₃³(9) R₃³(9)] six-level graph set (N₆) [on the ternary level two R₃³(9) rings are found] fits the homodromic rings mentioned above made up of six hydroxy functions. In conclusion, the most important description seems to be that of the second-level graph set, as the unitary graph set provides only finite motifs and the higher levels can be assembled by the patterns of the second level.

The graph-set analysis of the d₂ column results in an R₂²(10)DDD descriptor on the unitary graph level. On the binary graph level the pattern can be depicted by two C₂²(7) chains with opposite cooperativity connected by an R₄²(14) ring (Fig. 5). Finally, on the ternary graph level the homodromic rings mentioned above are found, to which the R₆⁶(12) descriptor can be assigned.

The entire crystal structure is assembled by a pseudohexagonal stacking of both the d₂– and the d₃-type [100] columns in the bc plane (Fig. 6).

Related literature

For related literature, see: Bernstein et al. (1995); Betz & Klüfers (2007); Betz, Herdlicka & Klüfers (2007); Corey et al. (1976); Etter et al. (1990); Jeffrey & Robbins (1978); Sillanpää et al. (1984).

S2. Experimental

The title compound was prepared according to a published procedure (Corey et al., 1976) upon pinacolic coupling of hexane-2,5-dione by means of amalgamated magnesium fillings and titanium tetrachloride in tetrahydrofuran. After an aqueous alkaline workup, extraction with diethyl ether and subsequent distillation yielded the desired product, which had already crystallized in the cooler of the distillation head (m.p. 290 K). Crystals suitable for X-ray analysis were obtained directly from the crystallized reaction product.

S3. Refinement

The C-bonded H atoms were refined as riding on their parent atoms, with C—H distances of 0.98 (methyl) or 0.99 Å (methylene) and with U_iso(H) values of 1.5U_eq(C) for the methyl groups and 1.2U_eq(C) for the methylene groups. The O-bonded H atoms were located in a difference map, and then their positions were optimized geometrically and refined as riding on their parent atoms by using the electron-density-related AFIX 147 instruction of SHELXL97 (Sheldrick, 2008) [O—H = 0.84 Å and U_iso(H) = 1.5U_eq(O)]. The population parameter of the major disordered component in one of the five molecules refined to 0.639 (5), where the sum of the population parameters of the major and minor disordered components was constrained to unity. The C—C distances of the minor disordered component were tied to the corresponding values of the major form by a similarity restraint (the SADI instruction of SHELXL97 with sigma = 0.01).

Computing details

Data collection: Collect (Nonius, 2004); cell refinement: SCALEPACK (Otwinowski & Minor, 1997); data reduction: DENZO and SCALEPACK (Otwinowski & Minor, 1997); program(s) used to solve structure: SIR97 (Altomare et al., 1999); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEPIII (Burnett & Johnson, 1996); software used to prepare material for publication: PLATON (Spek, 2003).

Figures

	Fig. 1. Two of the five symmetry-independent molecules of (I). Displacement ellipsoids are drawn at the 40% probability level.
	Fig. 2. The three remaining independent molecules of (I). Displacement ellipsoids are drawn at the 40% probability level. Only the major component of the disordered molecule 4 (atomic labels X4n) is shown.
	Fig. 3. The disordered molecule 4 (30% ellipsoid probability). Occupancies: diol function fully occupied; major disordered component (dark grey part) 0.639 (5); the minor part is drawn in buff (light grey).
	Fig. 4. Hydrogen bonding in the d3 columns. Vertical axis: [100]; atoms that are not part of a diol function have been omitted. Note the homodromic rings made up of six symmetry-independent hydroxy functions. For graph-set notation, see text. [Symmetry codes: (i) x - 1, y, z; (ii) x + 1, y, z.]
	Fig. 5. Hydrogen bonding in the d2 columns. Vertical axis: [100]; atoms that are not part of a diol function have been omitted. Centrosymmetric homodromic rings made up of three symmetry-independent hydroxy functions are supplemented by O11-hydroxy functions. For graph-set notation, see text. [Symmetry codes: (i) -x + 1, -y, -z + 1; (ii) x + 1, y, z; (iii) -x + 2, -y, -z + 1; (iv) x + 2, y, z; (v) -x + 3, -y, -z + 1.]
	Fig. 6. The pseudohexagonal packing of d2– and d3-type comlumns viewed along [100].

cis-1,2-dimethylcyclobutane-1,2-diol

Crystal data

C6H12O2	Z = 10
Mr = 116.16	F(000) = 640
Triclinic, P1	Dx = 1.125 Mg m^−3
Hall symbol: -P 1	Melting point: 290 K
a = 6.9715 (2) Å	Mo Kα radiation, λ = 0.71073 Å
b = 10.5549 (3) Å	Cell parameters from 19010 reflections
c = 24.8914 (8) Å	θ = 3.1–26.0°
α = 79.614 (2)°	µ = 0.08 mm^−1
β = 88.741 (2)°	T = 200 K
γ = 72.225 (2)°	Needle, colourless
V = 1714.63 (9) Å^3	0.24 × 0.07 × 0.06 mm

Data collection

Nonius KappaCCD diffractometer	4077 reflections with I > 2σ(I)
Radiation source: rotating anode	Rint = 0.039
MONTEL, graded multilayered X-ray optics monochromator	θmax = 26.1°, θmin = 3.2°
phi/ω–scan	h = −8→8
12129 measured reflections	k = −13→13
6647 independent reflections	l = −30→30

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.051	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.139	H-atom parameters constrained
S = 1.03	w = 1/[σ^2(Fo^2) + (0.0594P)^2 + 0.2235P] where P = (Fo^2 + 2Fc^2)/3
6647 reflections	(Δ/σ)max < 0.001
420 parameters	Δρmax = 0.22 e Å^−3
5 restraints	Δρmin = −0.20 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
O11	−0.0498 (2)	0.08109 (15)	0.39561 (6)	0.0567 (4)
H11	0.0392	0.0750	0.4190	0.085*
O12	0.1074 (2)	−0.18891 (15)	0.44390 (5)	0.0454 (4)
H12	0.0071	−0.1517	0.4611	0.068*
C11	0.0328 (3)	−0.0089 (2)	0.35894 (8)	0.0437 (5)
C12	0.0573 (3)	−0.1566 (2)	0.38672 (8)	0.0399 (5)
C13	−0.1617 (3)	−0.1346 (2)	0.36860 (9)	0.0529 (6)
H131	−0.1807	−0.2099	0.3529	0.063*
H132	−0.2610	−0.1095	0.3969	0.063*
C14	−0.1472 (3)	−0.0138 (2)	0.32562 (9)	0.0551 (6)
H141	−0.2663	0.0677	0.3234	0.066*
H142	−0.1124	−0.0361	0.2889	0.066*
C15	0.2083 (4)	0.0240 (3)	0.32985 (10)	0.0658 (7)
H151	0.1678	0.1201	0.3131	0.099*
H152	0.2505	−0.0310	0.3014	0.099*
H153	0.3208	0.0044	0.3561	0.099*
C16	0.2091 (4)	−0.2626 (2)	0.36124 (10)	0.0626 (6)
H161	0.3453	−0.2608	0.3690	0.094*
H162	0.1831	−0.2438	0.3216	0.094*
H163	0.1974	−0.3521	0.3766	0.094*
O21	0.54292 (19)	0.14266 (12)	0.52163 (5)	0.0407 (3)
H21	0.6488	0.1534	0.5327	0.061*
O22	0.20134 (17)	0.11827 (12)	0.48033 (5)	0.0359 (3)
H22	0.3013	0.0481	0.4860	0.054*
C21	0.4220 (3)	0.26654 (18)	0.48928 (7)	0.0352 (4)
C22	0.2656 (3)	0.23127 (18)	0.45597 (7)	0.0348 (4)
C23	0.4162 (3)	0.2125 (2)	0.41002 (8)	0.0445 (5)
H231	0.3553	0.2547	0.3730	0.053*
H232	0.5000	0.1175	0.4111	0.053*
C24	0.5224 (3)	0.2979 (2)	0.43491 (8)	0.0449 (5)
H241	0.6712	0.2604	0.4369	0.054*
H242	0.4787	0.3949	0.4178	0.054*
C25	0.3533 (3)	0.3752 (2)	0.52369 (9)	0.0497 (5)
H251	0.2683	0.3481	0.5526	0.075*
H252	0.2758	0.4603	0.5006	0.075*
H253	0.4711	0.3876	0.5402	0.075*
C26	0.0747 (3)	0.3471 (2)	0.43970 (9)	0.0494 (5)
H261	−0.0045	0.3239	0.4131	0.074*
H262	0.1093	0.4286	0.4233	0.074*
H263	−0.0045	0.3639	0.4721	0.074*
O31	0.45414 (19)	0.62316 (14)	0.22100 (5)	0.0462 (4)
H31	0.5014	0.6808	0.2025	0.069*
O32	0.8316 (2)	0.58909 (14)	0.19051 (6)	0.0499 (4)
H32	0.9510	0.5747	0.1805	0.075*
C31	0.6081 (3)	0.5269 (2)	0.25657 (8)	0.0418 (5)
C32	0.8196 (3)	0.4794 (2)	0.23214 (8)	0.0428 (5)
C33	0.9104 (3)	0.4872 (3)	0.28663 (10)	0.0649 (7)
H331	1.0171	0.5318	0.2825	0.078*
H332	0.9558	0.3993	0.3121	0.078*
C34	0.7035 (3)	0.5796 (3)	0.29950 (9)	0.0611 (6)
H341	0.6615	0.5554	0.3372	0.073*
H342	0.6889	0.6773	0.2901	0.073*
C35	0.5247 (4)	0.4145 (3)	0.28091 (10)	0.0660 (7)
H351	0.4020	0.4513	0.3002	0.099*
H352	0.6250	0.3467	0.3066	0.099*
H353	0.4928	0.3722	0.2517	0.099*
C36	0.8875 (4)	0.3493 (2)	0.21075 (10)	0.0641 (7)
H361	0.8060	0.3574	0.1780	0.096*
H362	0.8710	0.2755	0.2388	0.096*
H363	1.0297	0.3298	0.2015	0.096*
O41	0.2140 (2)	0.54607 (15)	0.15396 (5)	0.0493 (4)
H41	0.2900	0.5752	0.1707	0.074*
O42	0.1483 (2)	0.81383 (16)	0.10175 (6)	0.0543 (4)
H42	0.0546	0.8157	0.1237	0.081*
C41	0.2488 (3)	0.5696 (2)	0.09704 (8)	0.0447 (5)
C42	0.1537 (3)	0.7186 (2)	0.06757 (8)	0.0475 (5)
C43A	0.3563 (6)	0.6948 (4)	0.03588 (15)	0.0599 (12)	0.639 (5)
H431	0.3449	0.6728	−0.0007	0.072*	0.639 (5)
H432	0.4150	0.7700	0.0334	0.072*	0.639 (5)
C44A	0.4657 (9)	0.5686 (6)	0.0798 (4)	0.0542 (16)	0.639 (5)
H441	0.5429	0.4882	0.0647	0.065*	0.639 (5)
H442	0.5463	0.5875	0.1079	0.065*	0.639 (5)
C45A	0.1810 (8)	0.4649 (5)	0.0738 (2)	0.0640 (13)	0.639 (5)
H451	0.0391	0.4759	0.0818	0.096*	0.639 (5)
H452	0.2637	0.3737	0.0905	0.096*	0.639 (5)
H453	0.1966	0.4781	0.0341	0.096*	0.639 (5)
C46A	−0.0382 (8)	0.7598 (6)	0.0368 (2)	0.0751 (15)	0.639 (5)
H461	−0.0688	0.8543	0.0184	0.113*	0.639 (5)
H462	−0.1455	0.7505	0.0618	0.113*	0.639 (5)
H463	−0.0289	0.7021	0.0094	0.113*	0.639 (5)
C43B	0.0852 (11)	0.5353 (8)	0.0658 (3)	0.059 (2)	0.361 (5)
H433	0.0237	0.4721	0.0888	0.071*	0.361 (5)
H434	0.1320	0.5034	0.0314	0.071*	0.361 (5)
C44B	−0.0501 (11)	0.6859 (7)	0.0571 (3)	0.057 (2)	0.361 (5)
H443	−0.1517	0.7068	0.0852	0.068*	0.361 (5)
H444	−0.1105	0.7226	0.0197	0.068*	0.361 (5)
C45B	0.2329 (13)	0.7741 (8)	0.0149 (3)	0.064 (2)	0.361 (5)
H454	0.1385	0.8623	−0.0010	0.096*	0.361 (5)
H455	0.2475	0.7116	−0.0107	0.096*	0.361 (5)
H456	0.3644	0.7846	0.0220	0.096*	0.361 (5)
C46B	0.4607 (16)	0.5151 (12)	0.0878 (8)	0.064 (3)	0.361 (5)
H464	0.4840	0.5341	0.0486	0.096*	0.361 (5)
H465	0.5048	0.4171	0.1009	0.096*	0.361 (5)
H466	0.5374	0.5572	0.1076	0.096*	0.361 (5)
O51	0.4861 (2)	0.84202 (14)	0.14104 (7)	0.0570 (4)
H51	0.3789	0.8369	0.1281	0.085*
O52	0.8345 (2)	0.86116 (14)	0.17234 (7)	0.0553 (4)
H52	0.7913	0.7941	0.1799	0.083*
C51	0.4823 (3)	0.9802 (2)	0.13230 (8)	0.0453 (5)
C52	0.6697 (3)	0.9818 (2)	0.16397 (10)	0.0533 (6)
C53	0.5341 (4)	1.0101 (3)	0.21275 (11)	0.0803 (9)
H531	0.5426	0.9284	0.2405	0.096*
H532	0.5509	1.0838	0.2299	0.096*
C54	0.3493 (3)	1.0539 (3)	0.17356 (10)	0.0708 (8)
H541	0.2411	1.0150	0.1871	0.085*
H542	0.2950	1.1530	0.1612	0.085*
C55	0.4477 (4)	1.0401 (2)	0.07239 (9)	0.0652 (7)
H551	0.5603	0.9923	0.0520	0.098*
H552	0.4383	1.1361	0.0668	0.098*
H553	0.3220	1.0307	0.0593	0.098*
C56	0.7544 (4)	1.0941 (2)	0.14105 (15)	0.0899 (10)
H561	0.8585	1.0960	0.1664	0.135*
H562	0.6464	1.1807	0.1359	0.135*
H563	0.8136	1.0791	0.1058	0.135*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O11	0.0527 (9)	0.0470 (9)	0.0675 (10)	−0.0027 (7)	−0.0114 (8)	−0.0236 (8)
O12	0.0414 (8)	0.0544 (9)	0.0371 (7)	−0.0106 (7)	0.0046 (6)	−0.0076 (6)
C11	0.0481 (12)	0.0428 (12)	0.0399 (11)	−0.0122 (10)	−0.0002 (9)	−0.0094 (9)
C12	0.0419 (11)	0.0421 (11)	0.0363 (11)	−0.0115 (9)	0.0026 (8)	−0.0118 (9)
C13	0.0520 (13)	0.0637 (15)	0.0521 (13)	−0.0256 (12)	−0.0007 (10)	−0.0194 (11)
C14	0.0542 (13)	0.0633 (15)	0.0466 (12)	−0.0134 (12)	−0.0089 (10)	−0.0132 (11)
C15	0.0700 (16)	0.0666 (16)	0.0618 (15)	−0.0326 (14)	0.0030 (12)	0.0059 (12)
C16	0.0739 (16)	0.0512 (14)	0.0579 (14)	−0.0064 (13)	0.0092 (12)	−0.0213 (12)
O21	0.0389 (8)	0.0300 (7)	0.0509 (8)	−0.0080 (6)	−0.0042 (6)	−0.0051 (6)
O22	0.0326 (7)	0.0277 (7)	0.0455 (8)	−0.0089 (6)	0.0043 (6)	−0.0027 (6)
C21	0.0333 (10)	0.0265 (10)	0.0431 (11)	−0.0067 (8)	0.0061 (8)	−0.0048 (8)
C22	0.0344 (10)	0.0269 (10)	0.0410 (11)	−0.0088 (8)	0.0050 (8)	−0.0019 (8)
C23	0.0474 (12)	0.0434 (12)	0.0433 (11)	−0.0158 (10)	0.0096 (9)	−0.0073 (9)
C24	0.0404 (11)	0.0407 (12)	0.0545 (13)	−0.0160 (10)	0.0113 (9)	−0.0059 (10)
C25	0.0582 (13)	0.0330 (11)	0.0593 (13)	−0.0125 (10)	0.0086 (11)	−0.0152 (10)
C26	0.0400 (11)	0.0353 (11)	0.0656 (14)	−0.0073 (9)	−0.0006 (10)	0.0020 (10)
O31	0.0381 (8)	0.0493 (9)	0.0477 (8)	−0.0156 (7)	−0.0038 (6)	0.0050 (7)
O32	0.0416 (8)	0.0400 (8)	0.0642 (10)	−0.0118 (7)	0.0132 (7)	−0.0022 (7)
C31	0.0383 (11)	0.0451 (12)	0.0378 (11)	−0.0102 (9)	−0.0016 (9)	−0.0008 (9)
C32	0.0436 (11)	0.0397 (11)	0.0424 (11)	−0.0106 (9)	0.0035 (9)	−0.0048 (9)
C33	0.0463 (13)	0.0780 (18)	0.0635 (15)	−0.0056 (13)	−0.0116 (11)	−0.0174 (13)
C34	0.0562 (14)	0.0754 (17)	0.0476 (13)	−0.0078 (13)	−0.0048 (11)	−0.0218 (12)
C35	0.0606 (15)	0.0663 (16)	0.0625 (15)	−0.0227 (13)	0.0047 (12)	0.0152 (12)
C36	0.0813 (18)	0.0411 (13)	0.0632 (15)	−0.0108 (12)	0.0159 (13)	−0.0082 (11)
O41	0.0481 (9)	0.0624 (10)	0.0428 (8)	−0.0255 (8)	0.0043 (7)	−0.0084 (7)
O42	0.0637 (10)	0.0589 (10)	0.0538 (9)	−0.0336 (8)	0.0116 (7)	−0.0197 (8)
C41	0.0464 (12)	0.0507 (13)	0.0391 (11)	−0.0158 (10)	0.0038 (9)	−0.0122 (9)
C42	0.0561 (13)	0.0511 (13)	0.0394 (11)	−0.0197 (11)	−0.0027 (10)	−0.0120 (10)
C43A	0.078 (3)	0.060 (3)	0.047 (2)	−0.026 (2)	0.013 (2)	−0.016 (2)
C44A	0.046 (3)	0.065 (4)	0.056 (4)	−0.018 (3)	0.019 (2)	−0.023 (4)
C45A	0.076 (4)	0.055 (3)	0.066 (3)	−0.022 (2)	−0.003 (3)	−0.020 (3)
C46A	0.080 (3)	0.069 (4)	0.072 (3)	−0.013 (3)	−0.030 (3)	−0.016 (3)
C43B	0.072 (6)	0.064 (6)	0.050 (4)	−0.028 (5)	−0.003 (4)	−0.018 (4)
C44B	0.054 (4)	0.072 (6)	0.047 (4)	−0.024 (5)	−0.011 (3)	−0.009 (4)
C45B	0.074 (5)	0.071 (5)	0.046 (4)	−0.022 (4)	0.013 (4)	−0.008 (4)
C46B	0.073 (6)	0.069 (8)	0.055 (7)	−0.025 (6)	0.014 (4)	−0.020 (7)
O51	0.0533 (9)	0.0500 (9)	0.0676 (10)	−0.0262 (8)	−0.0127 (8)	0.0092 (8)
O52	0.0365 (8)	0.0398 (8)	0.0887 (11)	−0.0104 (7)	0.0044 (7)	−0.0117 (8)
C51	0.0453 (12)	0.0446 (12)	0.0447 (12)	−0.0121 (10)	0.0014 (9)	−0.0080 (9)
C52	0.0373 (11)	0.0432 (12)	0.0781 (16)	−0.0058 (10)	−0.0037 (11)	−0.0187 (11)
C53	0.0617 (16)	0.104 (2)	0.0656 (16)	0.0055 (15)	−0.0090 (13)	−0.0439 (16)
C54	0.0469 (14)	0.093 (2)	0.0598 (15)	0.0033 (14)	−0.0007 (11)	−0.0236 (14)
C55	0.0912 (19)	0.0518 (14)	0.0507 (14)	−0.0261 (14)	−0.0050 (13)	0.0037 (11)
C56	0.0672 (17)	0.0422 (15)	0.163 (3)	−0.0189 (14)	−0.0203 (18)	−0.0203 (17)

Geometric parameters (Å, º)

O11—C11	1.422 (2)	C36—H362	0.9800
O11—H11	0.8400	C36—H363	0.9800
O12—C12	1.428 (2)	O41—C41	1.422 (2)
O12—H12	0.8400	O41—H41	0.8400
C11—C15	1.507 (3)	O42—C42	1.421 (2)
C11—C14	1.538 (3)	O42—H42	0.8400
C11—C12	1.547 (3)	C41—C46B	1.443 (10)
C12—C16	1.509 (3)	C41—C45A	1.531 (4)
C12—C13	1.538 (3)	C41—C42	1.556 (3)
C13—C14	1.538 (3)	C41—C43B	1.559 (6)
C13—H131	0.9900	C41—C44A	1.560 (6)
C13—H132	0.9900	C42—C46A	1.462 (5)
C14—H141	0.9900	C42—C45B	1.502 (6)
C14—H142	0.9900	C42—C43A	1.577 (4)
C15—H151	0.9800	C42—C44B	1.598 (7)
C15—H152	0.9800	C43A—C44A	1.564 (7)
C15—H153	0.9800	C43A—H431	0.9900
C16—H161	0.9800	C43A—H432	0.9900
C16—H162	0.9800	C44A—H441	0.9900
C16—H163	0.9800	C44A—H442	0.9900
O21—C21	1.430 (2)	C45A—H451	0.9800
O21—H21	0.8400	C45A—H452	0.9800
O22—C22	1.430 (2)	C45A—H453	0.9800
O22—H22	0.8400	C46A—H461	0.9800
C21—C25	1.509 (3)	C46A—H462	0.9800
C21—C24	1.539 (3)	C46A—H463	0.9800
C21—C22	1.554 (3)	C43B—C44B	1.560 (9)
C22—C26	1.510 (3)	C43B—H433	0.9900
C22—C23	1.534 (3)	C43B—H434	0.9900
C23—C24	1.541 (3)	C44B—H443	0.9900
C23—H231	0.9900	C44B—H444	0.9900
C23—H232	0.9900	C45B—H454	0.9800
C24—H241	0.9900	C45B—H455	0.9800
C24—H242	0.9900	C45B—H456	0.9800
C25—H251	0.9800	C46B—H464	0.9800
C25—H252	0.9800	C46B—H465	0.9800
C25—H253	0.9800	C46B—H466	0.9800
C26—H261	0.9800	O51—C51	1.427 (2)
C26—H262	0.9800	O51—H51	0.8400
C26—H263	0.9800	O52—C52	1.416 (2)
O31—C31	1.421 (2)	O52—H52	0.8400
O31—H31	0.8400	C51—C55	1.505 (3)
O32—C32	1.430 (2)	C51—C54	1.525 (3)
O32—H32	0.8400	C51—C52	1.547 (3)
C31—C35	1.502 (3)	C52—C56	1.500 (3)
C31—C34	1.538 (3)	C52—C53	1.538 (3)
C31—C32	1.554 (3)	C53—C54	1.534 (3)
C32—C36	1.500 (3)	C53—H531	0.9900
C32—C33	1.535 (3)	C53—H532	0.9900
C33—C34	1.539 (3)	C54—H541	0.9900
C33—H331	0.9900	C54—H542	0.9900
C33—H332	0.9900	C55—H551	0.9800
C34—H341	0.9900	C55—H552	0.9800
C34—H342	0.9900	C55—H553	0.9800
C35—H351	0.9800	C56—H561	0.9800
C35—H352	0.9800	C56—H562	0.9800
C35—H353	0.9800	C56—H563	0.9800
C36—H361	0.9800
C11—O11—H11	109.5	C32—C36—H362	109.5
C12—O12—H12	109.5	H361—C36—H362	109.5
O11—C11—C15	111.20 (18)	C32—C36—H363	109.5
O11—C11—C14	106.02 (17)	H361—C36—H363	109.5
C15—C11—C14	119.82 (18)	H362—C36—H363	109.5
O11—C11—C12	110.43 (16)	C41—O41—H41	109.5
C15—C11—C12	119.13 (18)	C42—O42—H42	109.5
C14—C11—C12	87.77 (15)	O41—C41—C46B	110.0 (8)
O12—C12—C16	106.17 (16)	O41—C41—C45A	105.5 (2)
O12—C12—C13	118.13 (16)	O41—C41—C42	114.50 (16)
C16—C12—C13	113.28 (17)	C46B—C41—C42	113.6 (6)
O12—C12—C11	115.76 (15)	C45A—C41—C42	115.0 (2)
C16—C12—C11	114.75 (17)	O41—C41—C43B	108.7 (4)
C13—C12—C11	88.46 (15)	C46B—C41—C43B	121.8 (8)
C14—C13—C12	88.11 (15)	C42—C41—C43B	86.7 (3)
C14—C13—H131	114.0	O41—C41—C44A	117.3 (4)
C12—C13—H131	114.0	C45A—C41—C44A	111.9 (4)
C14—C13—H132	114.0	C42—C41—C44A	92.7 (2)
C12—C13—H132	114.0	O42—C42—C46A	109.0 (3)
H131—C13—H132	111.2	O42—C42—C45B	104.2 (3)
C13—C14—C11	88.77 (15)	O42—C42—C41	112.80 (15)
C13—C14—H141	113.9	C46A—C42—C41	120.7 (3)
C11—C14—H141	113.9	C45B—C42—C41	121.6 (4)
C13—C14—H142	113.9	O42—C42—C43A	108.1 (2)
C11—C14—H142	113.9	C46A—C42—C43A	119.4 (3)
H141—C14—H142	111.1	C41—C42—C43A	84.7 (2)
C11—C15—H151	109.5	O42—C42—C44B	118.2 (3)
C11—C15—H152	109.5	C45B—C42—C44B	111.1 (4)
H151—C15—H152	109.5	C41—C42—C44B	89.5 (3)
C11—C15—H153	109.5	C44A—C43A—C42	91.8 (3)
H151—C15—H153	109.5	C44A—C43A—H431	113.3
H152—C15—H153	109.5	C42—C43A—H431	113.3
C12—C16—H161	109.5	C44A—C43A—H432	113.3
C12—C16—H162	109.5	C42—C43A—H432	113.3
H161—C16—H162	109.5	H431—C43A—H432	110.7
C12—C16—H163	109.5	C41—C44A—C43A	85.0 (3)
H161—C16—H163	109.5	C41—C44A—H441	114.5
H162—C16—H163	109.5	C43A—C44A—H441	114.5
C21—O21—H21	109.5	C41—C44A—H442	114.5
C22—O22—H22	109.5	C43A—C44A—H442	114.5
O21—C21—C25	110.46 (16)	H441—C44A—H442	111.6
O21—C21—C24	110.53 (15)	C41—C45A—H451	109.5
C25—C21—C24	118.80 (16)	C41—C45A—H452	109.5
O21—C21—C22	107.13 (14)	C41—C45A—H453	109.5
C25—C21—C22	120.28 (16)	C42—C46A—H461	109.5
C24—C21—C22	87.44 (14)	C42—C46A—H462	109.5
O22—C22—C26	105.67 (15)	C42—C46A—H463	109.5
O22—C22—C23	118.11 (15)	C41—C43B—C44B	90.8 (4)
C26—C22—C23	113.35 (16)	C41—C43B—H433	113.5
O22—C22—C21	117.01 (14)	C44B—C43B—H433	113.5
C26—C22—C21	114.00 (16)	C41—C43B—H434	113.5
C23—C22—C21	88.51 (14)	C44B—C43B—H434	113.5
C22—C23—C24	88.11 (14)	H433—C43B—H434	110.8
C22—C23—H231	114.0	C43B—C44B—C42	85.2 (4)
C24—C23—H231	114.0	C43B—C44B—H443	114.4
C22—C23—H232	114.0	C42—C44B—H443	114.4
C24—C23—H232	114.0	C43B—C44B—H444	114.4
H231—C23—H232	111.2	C42—C44B—H444	114.4
C21—C24—C23	88.79 (14)	H443—C44B—H444	111.6
C21—C24—H241	113.9	C42—C45B—H454	109.5
C23—C24—H241	113.9	C42—C45B—H455	109.5
C21—C24—H242	113.9	H454—C45B—H455	109.5
C23—C24—H242	113.9	C42—C45B—H456	109.5
H241—C24—H242	111.1	H454—C45B—H456	109.5
C21—C25—H251	109.5	H455—C45B—H456	109.5
C21—C25—H252	109.5	C41—C46B—H464	109.5
H251—C25—H252	109.5	C41—C46B—H465	109.5
C21—C25—H253	109.5	H464—C46B—H465	109.5
H251—C25—H253	109.5	C41—C46B—H466	109.5
H252—C25—H253	109.5	H464—C46B—H466	109.5
C22—C26—H261	109.5	H465—C46B—H466	109.5
C22—C26—H262	109.5	C51—O51—H51	109.5
H261—C26—H262	109.5	C52—O52—H52	109.5
C22—C26—H263	109.5	O51—C51—C55	109.74 (18)
H261—C26—H263	109.5	O51—C51—C54	110.45 (19)
H262—C26—H263	109.5	C55—C51—C54	119.2 (2)
C31—O31—H31	109.5	O51—C51—C52	105.75 (16)
C32—O32—H32	109.5	C55—C51—C52	120.77 (19)
O31—C31—C35	106.68 (16)	C54—C51—C52	88.92 (16)
O31—C31—C34	117.26 (18)	O52—C52—C56	106.39 (18)
C35—C31—C34	113.20 (18)	O52—C52—C53	116.8 (2)
O31—C31—C32	116.27 (16)	C56—C52—C53	113.7 (2)
C35—C31—C32	114.66 (18)	O52—C52—C51	116.81 (17)
C34—C31—C32	88.32 (15)	C56—C52—C51	114.9 (2)
O32—C32—C36	109.99 (17)	C53—C52—C51	87.74 (17)
O32—C32—C33	110.72 (18)	C54—C53—C52	88.91 (18)
C36—C32—C33	119.27 (19)	C54—C53—H531	113.8
O32—C32—C31	106.05 (15)	C52—C53—H531	113.8
C36—C32—C31	120.78 (19)	C54—C53—H532	113.8
C33—C32—C31	87.89 (15)	C52—C53—H532	113.8
C32—C33—C34	88.99 (16)	H531—C53—H532	111.1
C32—C33—H331	113.8	C51—C54—C53	88.66 (17)
C34—C33—H331	113.8	C51—C54—H541	113.9
C32—C33—H332	113.8	C53—C54—H541	113.9
C34—C33—H332	113.8	C51—C54—H542	113.9
H331—C33—H332	111.0	C53—C54—H542	113.9
C31—C34—C33	88.32 (16)	H541—C54—H542	111.1
C31—C34—H341	113.9	C51—C55—H551	109.5
C33—C34—H341	113.9	C51—C55—H552	109.5
C31—C34—H342	113.9	H551—C55—H552	109.5
C33—C34—H342	113.9	C51—C55—H553	109.5
H341—C34—H342	111.1	H551—C55—H553	109.5
C31—C35—H351	109.5	H552—C55—H553	109.5
C31—C35—H352	109.5	C52—C56—H561	109.5
H351—C35—H352	109.5	C52—C56—H562	109.5
C31—C35—H353	109.5	H561—C56—H562	109.5
H351—C35—H353	109.5	C52—C56—H563	109.5
H352—C35—H353	109.5	H561—C56—H563	109.5
C32—C36—H361	109.5	H562—C56—H563	109.5
O11—C11—C12—O12	−34.1 (2)	O41—C41—C42—O42	32.4 (2)
C15—C11—C12—O12	96.4 (2)	C46B—C41—C42—O42	−95.1 (8)
C14—C11—C12—O12	−140.33 (17)	C45A—C41—C42—O42	154.8 (3)
O11—C11—C12—C16	−158.32 (17)	C43B—C41—C42—O42	141.5 (4)
C15—C11—C12—C16	−27.8 (3)	C44A—C41—C42—O42	−89.4 (4)
C14—C11—C12—C16	95.41 (19)	O41—C41—C42—C46A	−98.9 (3)
O11—C11—C12—C13	86.65 (17)	C45A—C41—C42—C46A	23.5 (4)
C15—C11—C12—C13	−142.85 (19)	C44A—C41—C42—C46A	139.3 (5)
C14—C11—C12—C13	−19.62 (16)	O41—C41—C42—C45B	157.2 (4)
O12—C12—C13—C14	138.22 (18)	C46B—C41—C42—C45B	29.7 (9)
C16—C12—C13—C14	−96.8 (2)	C43B—C41—C42—C45B	−93.8 (5)
C11—C12—C13—C14	19.62 (15)	O41—C41—C42—C43A	139.8 (2)
C12—C13—C14—C11	−19.73 (16)	C45A—C41—C42—C43A	−97.7 (3)
O11—C11—C14—C13	−91.00 (18)	C44A—C41—C42—C43A	18.0 (4)
C15—C11—C14—C13	142.3 (2)	O41—C41—C42—C44B	−88.2 (3)
C12—C11—C14—C13	19.62 (16)	C46B—C41—C42—C44B	144.3 (9)
O21—C21—C22—O22	30.4 (2)	C43B—C41—C42—C44B	20.9 (5)
C25—C21—C22—O22	−96.8 (2)	O42—C42—C43A—C44A	94.3 (4)
C24—C21—C22—O22	141.07 (16)	C46A—C42—C43A—C44A	−140.4 (5)
O21—C21—C22—C26	154.34 (16)	C41—C42—C43A—C44A	−18.0 (4)
C25—C21—C22—C26	27.2 (2)	C44B—C42—C43A—C44A	−102.5 (6)
C24—C21—C22—C26	−94.95 (18)	O41—C41—C44A—C43A	−137.6 (3)
O21—C21—C22—C23	−90.68 (15)	C45A—C41—C44A—C43A	100.2 (4)
C25—C21—C22—C23	142.20 (18)	C42—C41—C44A—C43A	−18.2 (4)
C24—C21—C22—C23	20.03 (14)	C42—C43A—C44A—C41	17.9 (4)
O22—C22—C23—C24	−140.08 (16)	O41—C41—C43B—C44B	93.4 (5)
C26—C22—C23—C24	95.59 (18)	C46B—C41—C43B—C44B	−137.3 (8)
C21—C22—C23—C24	−20.01 (14)	C42—C41—C43B—C44B	−21.4 (5)
O21—C21—C24—C23	87.40 (16)	C41—C43B—C44B—C42	20.8 (4)
C25—C21—C24—C23	−143.41 (18)	O42—C42—C44B—C43B	−136.6 (4)
C22—C21—C24—C23	−19.94 (14)	C45B—C42—C44B—C43B	103.1 (5)
C22—C23—C24—C21	20.20 (14)	C41—C42—C44B—C43B	−20.9 (4)
O31—C31—C32—O32	27.9 (2)	O51—C51—C52—O52	26.1 (3)
C35—C31—C32—O32	153.24 (17)	C55—C51—C52—O52	−99.1 (2)
C34—C31—C32—O32	−91.91 (17)	C54—C51—C52—O52	137.1 (2)
O31—C31—C32—C36	−98.0 (2)	O51—C51—C52—C56	151.8 (2)
C35—C31—C32—C36	27.4 (3)	C55—C51—C52—C56	26.7 (3)
C34—C31—C32—C36	142.3 (2)	C54—C51—C52—C56	−97.2 (2)
O31—C31—C32—C33	138.83 (19)	O51—C51—C52—C53	−93.0 (2)
C35—C31—C32—C33	−95.8 (2)	C55—C51—C52—C53	141.9 (2)
C34—C31—C32—C33	19.05 (18)	C54—C51—C52—C53	18.0 (2)
O32—C32—C33—C34	87.3 (2)	O52—C52—C53—C54	−137.0 (2)
C36—C32—C33—C34	−143.5 (2)	C56—C52—C53—C54	98.4 (2)
C31—C32—C33—C34	−19.04 (18)	C51—C52—C53—C54	−17.9 (2)
O31—C31—C34—C33	−137.88 (19)	O51—C51—C54—C53	88.4 (2)
C35—C31—C34—C33	97.2 (2)	C55—C51—C54—C53	−143.2 (2)
C32—C31—C34—C33	−18.99 (17)	C52—C51—C54—C53	−18.0 (2)
C32—C33—C34—C31	19.24 (18)	C52—C53—C54—C51	18.2 (2)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O11—H11···O22	0.84	2.11	2.924 (2)	162
O12—H12···O22^i	0.84	2.03	2.845 (2)	162
O21—H21···O12^ii	0.84	1.97	2.808 (2)	177
O22—H22···O21^ii	0.84	2.01	2.795 (2)	154
O31—H31···O51	0.84	2.05	2.826 (2)	153
O32—H32···O41^iii	0.84	1.89	2.729 (2)	177
O41—H41···O31	0.84	1.94	2.774 (2)	170
O42—H42···O52^iv	0.84	1.93	2.758 (2)	168
O51—H51···O42	0.84	1.85	2.687 (2)	176
O52—H52···O32	0.84	2.06	2.832 (2)	152
O22—H22···O21	0.84	2.46	2.715 (2)	99
O31—H31···O32	0.84	2.24	2.658 (2)	111
O52—H52···O51	0.84	2.23	2.644 (2)	110

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