()-3-Ethyl-2-methyl-4-oxo­cyclo­hexane­carboxyl­ic acid: catemeric hydrogen bonding in a cyclic δ-keto acid

In the title compound, C₁₀H₁₆O₃, the two mol­ecules of the asymmetric unit form acid-to-ketone hydrogen-bonded chains. The two species differ only very slightly and are related by a pseudo-center, so that the apparent translational relationship among the units of the hydrogen-bonded chain is actually a pseudo-translation, with the mol­ecules alternating in type. Two counterdirectional pairs of chains proceed through each cell [O...O = 2.743 (2) and 2.683 (2) Å, and O—H...O = 171 (3) and 157 (3)°]. Three intermolecular C—H...O close contacts were found, involving all three O atoms of one of the mol­ecules.

S1. Comment

Our study of the crystallography of solid ketocarboxylic acids explores the molecular characteristics that control their five known hydrogen-bonding modes. The generality of carboxyl dimerization frequently declines when other functional groups are present, and we have extensively documented this case for keto acids. Specifically, we find that the acid-to-ketone catemer mode becomes dominant whenever centrosymmetry is precluded (chiral non-racemates) and when low conformational flexibility restricts the acid's ability to find centrosymmetric crystallization modes of suitably low energy. Among the many acid-to-ketone catemers that we have observed, several exist for simple cyclohexanone and cyclopentanone acids (Barcon et al., 1998, 2002; Lalancette & Thompson, 2003). The strong occurrence of catemers in such systems may at first seem surprising because of the perceived conformational flexibility of their rings. However, this flexibility is entirely a solution phenomenon, absent in the solid, and even in solution the set of available conformations is typically quite restricted.

Fig. 1 shows the two molecules of the asymmetric unit for (I), designated (IA) and (IB), which differ only very slightly. The substituents all lie on the same molecular face, so that at least one substituent must be axial in any chair arrangement. The observed conformation for both species, the one expected in terms of cyclohexane-based equatorial/axial ΔG° preferences for these groups (Hirsch, 1967), actually has even less strain than those values suggest, since the ketone site lacks an axial H atom. Once the requirement of staggering the substituents on the exocyclic bonds at atoms C2 and C3 is met, just two significant options remain for bond rotation. Of the three staggered conformations about the C3—C8 bond, only two are feasible, since the one positioning the C8—C9 bond parallel to C2—C7 is equivalent to a 1,3-diaxial interaction. The conformation actually chosen for both species places atom C9 in an anti rather than a syn relationship to the ketone C=O bond. The remaining conformational option, carboxyl rotation, has the carboxyl plane coinciding closely with the C1—C6 bond [O2—C10—C1—C6 = 1.7 (3)° for (IA) and 0.5 (3)° for (IB)]. The dihedral angle between the ketone (O1/C3–C5) and the carboxyl (O2/O3/C10/C1) planes is 47.98 (11)° for (IA) and 48.70 (11)° for (IB).

These slight angular variations are typical of the differences between molecules (IA) and (IB); the molecules are superimposable (with an inversion of one of them), with no paired atoms deviating from one another by more than 0.063 Å. The largest variation in torsion angle between (IA) and (IB) is 4.0 (3)°, for C4—C3—C8—C9. Because the apparent pseudocenter relating (IA) and (IB) lies at what might imaginably be a special position (1/2, 1/2, 3/4), we attempted solutions with half the c cell dimension and Z=2. However, all such trials either resisted solution or led to dramatically worse refinements.

The partial averaging of carboxyl C—O bond lengths and C—C—O angles by disorder, often seen in acids, is unique to the paired hydrogen-bonding mode, whose geometry permits transposition of the two carboxyl O atoms. In non-dimeric acid modes, no significant averaging occurs. For (IA), the C—O bond lengths are 1.198 (2) and 1.327 (2) Å, with C—C—O angles of 125.03 (19) and 112.00 (18)°; for (IB), the lengths are 1.193 (2) and 1.318 (2) Å, with C—C—O angles of 125.39 (18) and 112.01 (16)°. Our own survey of 56 keto acid structures that are not acid dimers gives average values of 1.20 (1) and 1.32 (2) Å, and 124.5 (14) and 112.7 (17)°, for these lengths and angles, in accordance with the typical values [1.21 and 1.31 Å, and 123 and 112°] cited for highly ordered dimeric carboxyls (Borthwick, 1980).

Fig. 2 illustrates the packing of the cell and the hydrogen-bonding arrangement, which involves aggregation in the acid-to-ketone catemeric hydrogen-bonding mode. The combination of the true center at 0, ¹/₂, ¹/₂ and the pseudocenter presents each molecule with a partner of the opposite type for hydrogen-bonding. The result is chains in which (IA) and (IB) alternate, and in which the O···O distances and O—H···O angles differ depending on type (Table 2). Because of the tilt of (IA) and (IB) within the chosen cell, every hydrogen bond involves a partner either one cell away in the (positive) c direction and one away (negative) in a, or vice versa, and thus the chains are also tilted with respect to the chosen cell. Each asymmetric unit generates a counterdirectional pair of hydrogen-bonding chains, and by centrosymmetry about ¹/₂, ¹/₂, ¹/₂, two such pairs of hydrogen-bonding chains proceed through each cell.

The variations in intermolecular connections cited above for (IA) and (IB) are significantly larger than any of their internal differences, and emphasize that the two molecules are significantly different and that no Z=2 solution is possible. Another assessment of the notion of a pseudocenter at ¹/₂, ¹/₂, ³/₄ can be achieved by a symmetry-based superposition of the two halves of the asymmetric unit, which shows that the distances for correlated atom pairs range from 0.117 (3) Å (for O3) to 1.132 (3) Å (for O1). An additional demonstration lies in the measurably different orientations of (IA) and (IB) within the cell; the dihedral angle for the average (non-H atom) plane of (IA) relative to the average plane for all the non-H atoms shown in Fig. 2 is 26.98 (5)°, but this angle is 28.09 (5)° for (IB). This differential tilt of the two species generates markedly different angles for the hydrogen bonding beyond the O···O distances and O—H···O angles noted above.

We characterize the geometry of H bonding to carbonyls using a combination of the H···O=C angle and the H···O=C—C torsion angle. These describe the approach of the H atom to the O atom in terms of its deviation from, respectively, C=O axiality (ideal = 120°) and planarity with the carbonyl (ideal = 0°). For hydrogen bonds from (IA) to (IB), the H···O=C and H···O=C—C angles are 142.8 (9) and −70.1 (14)°; for the alternative type, from (IB) to (IA), they are, respectively, 138.0 (9) and −42.4 (14)°.

Three intermolecular C—H···O close contacts exist for the system, involving all three O atoms in (IB) and lying within the 2.7 Å range we normally employ for non-bonded H···O packing interactions (Steiner, 1997), viz. 2.68 Å from O1A to H3A, 2.66 Å from O2A to H5B, and 2.60 Å from O3A to H73A. Using compiled data for a large number of C—H···O contacts, Steiner & Desiraju (1998) find significant statistical directionality even as far out as 3.0 Å, and conclude that these are legitimately viewed as `weak hydrogen bonds', with a greater contribution to packing forces than simple van der Waals attractions.

The solid-state (KBr) IR spectrum of (I) has C=O absorptions at 1730 (COOH) and 1691 cm⁻¹ (ketone). This peak separation conforms to the shifts seen typically in catemers, where hydrogen bonding is absent from the acid C=O but present in the ketone. In CHCl₃ solution, these absorptions converge to a single peak at 1709 cm⁻¹, consistent with dimerically hydrogen-bonded carboxyl and a normal ketone.

S2. Experimental

A technical grade (described as >60% pure) of 4-carbethoxy-2-ethyl-3-methyl-2-cyclohexene-1-one (2-ethyl-Hagemann's ester) was purchased from Acros Organics/Fisher Scientific, Springfield, NJ, USA. Hydrogenation in 95% ethanol with a 5% Pd/C catalyst led to a concentrated liquid product that was directly saponified without purification. After distillation in a short-path apparatus, the product crystallized on refrigeration. Crystals of (I) suitable for X-ray analysis (m.p. 376 K) were obtained from ethyl acetate.

S3. Refinement

All H atoms for (I) were found in electron density difference maps and were refinable (R=0.048 and wR=0.136 for 332 parameters), but C-bound H atoms were placed in calculated positions (0.97 Å for methylene H atoms, 0.98 Å for methine H atoms and 0.96 Å for methyl H atoms) and allowed to refine as riding on their respective C atoms; their displacement parameters were fixed at 120% of those of their respective C atoms, except for the methyl H atoms, whose displacement parameters were fixed at 150% of those of their respective C atoms. The hydroxyl H atoms were allowed to refine completely.

Computing details

Data collection: XSCANS (Siemens, 1996); cell refinement: XSCANS; data reduction: XSCANS; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997a); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997a); molecular graphics: SHELXP97 (Sheldrick, 1997a); software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. The asymmetric unit for (I), with numbering shown only for the (IA) species. The apparent centrosymmetry is due to a pseudocenter at 1/2, 1/2, 3/4. Displacement ellipsoids are shown at the 30% probability level.
	Fig. 2. A partial packing diagram with extra molecules, illustrating the two hydrogen-bonded catemers. For clarity, all C-bound H atoms have been omitted and molecules of type (IB) are differentiated by open bonds. Displacement ellipsoids are set at the 20% probability level.

(±)-3-Ethyl-2-methyl-4-oxocyclohexanecarboxylic acid

Crystal data

C10H16O3	Z = 4
Mr = 184.23	F(000) = 400
Triclinic, P1	Dx = 1.219 Mg m^−3
Hall symbol: -P 1	Melting point: 376 K
a = 5.5739 (12) Å	Mo Kα radiation, λ = 0.71073 Å
b = 12.814 (3) Å	Cell parameters from 36 reflections
c = 14.396 (3) Å	θ = 1.7–8.9°
α = 80.425 (14)°	µ = 0.09 mm^−1
β = 85.53 (2)°	T = 296 K
γ = 82.67 (2)°	Trapezoidal block, colourless
V = 1003.9 (4) Å^3	0.50 × 0.36 × 0.20 mm

Data collection

Siemens P4 diffractometer	2587 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.025
Graphite monochromator	θmax = 25.1°, θmin = 1.6°
2θ/θ scans	h = −1→6
Absorption correction: numerical Sheldrick (1997)	k = −15→15
Tmin = 0.962, Tmax = 0.982	l = −17→17
4736 measured reflections	3 standard reflections every 97 reflections
3556 independent reflections	intensity decay: variation <2%

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F^2 > 2σ(F^2)] = 0.048	H atoms treated by a mixture of independent and constrained refinement
wR(F^2) = 0.133	w = 1/[σ^2(Fo^2) + (0.0519P)^2 + 0.3545P] where P = (Fo^2 + 2Fc^2)/3
S = 1.02	(Δ/σ)max < 0.001
3556 reflections	Δρmax = 0.20 e Å^−3
244 parameters	Δρmin = −0.16 e Å^−3
0 restraints	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.024 (3)

Special details

Experimental. 'crystal mounted on glass fiber using cyanoacrylate cement'

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.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq
O1	−0.1032 (3)	0.76596 (14)	0.97307 (11)	0.0693 (5)
O2	0.3582 (3)	0.62351 (14)	0.61493 (11)	0.0661 (5)
O3	0.6454 (3)	0.72226 (14)	0.63338 (12)	0.0638 (5)
H3C	0.689 (5)	0.713 (2)	0.576 (2)	0.089 (9)*
O1A	1.1683 (3)	0.30886 (14)	0.54323 (11)	0.0673 (5)
O2A	0.5939 (3)	0.38549 (15)	0.90124 (11)	0.0748 (6)
O3A	0.3455 (3)	0.28282 (15)	0.86003 (11)	0.0653 (5)
H3D	0.291 (5)	0.280 (2)	0.918 (2)	0.089 (9)*
C1	0.3789 (3)	0.67917 (15)	0.76584 (13)	0.0371 (4)
H1	0.5167	0.6468	0.8032	0.045*
C2	0.3247 (3)	0.79592 (14)	0.78220 (12)	0.0358 (4)
H2	0.4715	0.8305	0.7624	0.043*
C3	0.2722 (3)	0.79885 (15)	0.88911 (12)	0.0379 (4)
H3	0.4186	0.7643	0.9201	0.046*
C4	0.0721 (4)	0.73110 (17)	0.92687 (13)	0.0448 (5)
C5	0.1016 (4)	0.61980 (17)	0.90570 (15)	0.0537 (6)
H5A	−0.0484	0.5888	0.9237	0.064*
H5B	0.2274	0.5774	0.9431	0.064*
C6	0.1681 (4)	0.61569 (16)	0.80092 (14)	0.0466 (5)
H6A	0.2117	0.5422	0.7919	0.056*
H6B	0.0288	0.6445	0.7645	0.056*
C7	0.1208 (4)	0.85732 (17)	0.72333 (14)	0.0538 (6)
H7A	0.0937	0.9294	0.7355	0.081*
H7B	−0.0248	0.8240	0.7399	0.081*
H7C	0.1652	0.8571	0.6576	0.081*
C8	0.2248 (4)	0.91063 (17)	0.91547 (14)	0.0516 (6)
H8A	0.0742	0.9455	0.8896	0.062*
H8B	0.2040	0.9044	0.9836	0.062*
C9	0.4240 (5)	0.98048 (19)	0.88093 (18)	0.0680 (7)
H9A	0.3807	1.0493	0.8995	0.102*
H9B	0.4446	0.9882	0.8134	0.102*
H9C	0.5728	0.9481	0.9081	0.102*
C10	0.4543 (4)	0.67122 (16)	0.66359 (14)	0.0422 (5)
C1A	0.6222 (3)	0.35140 (14)	0.74084 (12)	0.0334 (4)
H1A	0.4899	0.3862	0.7015	0.040*
C2A	0.6992 (3)	0.24070 (14)	0.71172 (12)	0.0339 (4)
H2A	0.5561	0.2022	0.7199	0.041*
C3A	0.7838 (4)	0.25465 (16)	0.60548 (12)	0.0410 (5)
H3A	0.6429	0.2892	0.5708	0.049*
C4A	0.9743 (4)	0.33089 (17)	0.58496 (13)	0.0458 (5)
C5A	0.9140 (4)	0.43568 (17)	0.61828 (15)	0.0529 (6)
H51A	0.7893	0.4785	0.5806	0.063*
H52A	1.0566	0.4732	0.6097	0.063*
C6A	0.8252 (4)	0.42206 (15)	0.72231 (14)	0.0425 (5)
H61A	0.9587	0.3906	0.7610	0.051*
H62A	0.7675	0.4913	0.7396	0.051*
C7A	0.8924 (4)	0.17515 (16)	0.77360 (14)	0.0476 (5)
H71A	0.9351	0.1071	0.7534	0.071*
H72A	0.8302	0.1650	0.8381	0.071*
H73A	1.0334	0.2121	0.7682	0.071*
C8A	0.8627 (4)	0.14994 (19)	0.56777 (16)	0.0588 (6)
H81A	0.9121	0.1661	0.5013	0.071*
H82A	1.0028	0.1134	0.6004	0.071*
C9A	0.6679 (5)	0.0754 (2)	0.5790 (2)	0.0811 (8)
H91A	0.7304	0.0116	0.5542	0.122*
H92A	0.5302	0.1099	0.5451	0.122*
H93A	0.6199	0.0576	0.6446	0.122*
C10A	0.5245 (3)	0.34263 (15)	0.84264 (13)	0.0390 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0606 (10)	0.0811 (12)	0.0576 (10)	−0.0064 (9)	0.0315 (8)	−0.0036 (8)
O2	0.0747 (12)	0.0839 (12)	0.0482 (9)	−0.0212 (10)	0.0031 (8)	−0.0293 (9)
O3	0.0585 (10)	0.0922 (13)	0.0473 (9)	−0.0239 (9)	0.0220 (8)	−0.0307 (9)
O1A	0.0505 (10)	0.0943 (13)	0.0514 (9)	−0.0023 (9)	0.0231 (8)	−0.0119 (8)
O2A	0.0939 (14)	0.1028 (14)	0.0400 (9)	−0.0429 (11)	0.0094 (9)	−0.0293 (9)
O3A	0.0604 (11)	0.1029 (14)	0.0403 (9)	−0.0389 (10)	0.0226 (8)	−0.0226 (9)
C1	0.0359 (10)	0.0409 (10)	0.0338 (10)	−0.0006 (8)	−0.0005 (8)	−0.0074 (8)
C2	0.0376 (10)	0.0410 (10)	0.0285 (9)	−0.0084 (8)	0.0078 (8)	−0.0061 (8)
C3	0.0382 (10)	0.0460 (11)	0.0284 (9)	−0.0050 (8)	0.0037 (8)	−0.0053 (8)
C4	0.0448 (12)	0.0582 (13)	0.0269 (9)	−0.0055 (10)	0.0066 (9)	0.0022 (9)
C5	0.0601 (14)	0.0525 (13)	0.0464 (12)	−0.0218 (11)	0.0073 (10)	0.0046 (10)
C6	0.0523 (13)	0.0417 (11)	0.0466 (12)	−0.0130 (10)	0.0019 (10)	−0.0055 (9)
C7	0.0720 (16)	0.0485 (12)	0.0374 (11)	0.0073 (11)	−0.0075 (10)	−0.0050 (9)
C8	0.0646 (15)	0.0545 (13)	0.0362 (11)	−0.0044 (11)	0.0054 (10)	−0.0149 (9)
C9	0.0889 (19)	0.0535 (14)	0.0675 (16)	−0.0205 (13)	−0.0013 (14)	−0.0188 (12)
C10	0.0436 (11)	0.0437 (11)	0.0388 (11)	0.0004 (9)	0.0037 (9)	−0.0116 (9)
C1A	0.0318 (9)	0.0391 (10)	0.0282 (9)	−0.0026 (8)	0.0013 (7)	−0.0049 (7)
C2A	0.0345 (10)	0.0401 (10)	0.0280 (9)	−0.0082 (8)	0.0048 (7)	−0.0077 (7)
C3A	0.0400 (11)	0.0547 (12)	0.0272 (9)	0.0019 (9)	−0.0002 (8)	−0.0101 (8)
C4A	0.0425 (12)	0.0632 (13)	0.0253 (9)	−0.0006 (10)	0.0090 (9)	0.0021 (9)
C5A	0.0539 (13)	0.0492 (12)	0.0503 (13)	−0.0113 (10)	0.0145 (10)	0.0032 (10)
C6A	0.0442 (11)	0.0366 (10)	0.0458 (11)	−0.0066 (9)	0.0049 (9)	−0.0059 (8)
C7A	0.0621 (14)	0.0424 (11)	0.0362 (10)	0.0023 (10)	−0.0047 (10)	−0.0056 (8)
C8A	0.0651 (15)	0.0703 (15)	0.0430 (12)	0.0048 (12)	−0.0009 (11)	−0.0251 (11)
C9A	0.097 (2)	0.0715 (17)	0.087 (2)	−0.0091 (16)	−0.0101 (17)	−0.0446 (15)
C10A	0.0382 (11)	0.0465 (11)	0.0316 (10)	−0.0025 (9)	0.0029 (8)	−0.0082 (8)

Geometric parameters (Å, º)

O1—C4	1.218 (2)	C8—H8B	0.9700
O2—C10	1.198 (2)	C9—H9A	0.9600
O3—C10	1.327 (2)	C9—H9B	0.9600
O3—H3C	0.87 (3)	C9—H9C	0.9600
O1A—C4A	1.220 (2)	C1A—C10A	1.515 (2)
O2A—C10A	1.193 (2)	C1A—C6A	1.518 (3)
O3A—C10A	1.318 (2)	C1A—C2A	1.545 (2)
O3A—H3D	0.86 (3)	C1A—H1A	0.9800
C1—C10	1.515 (3)	C2A—C7A	1.526 (3)
C1—C6	1.521 (3)	C2A—C3A	1.553 (2)
C1—C2	1.541 (3)	C2A—H2A	0.9800
C1—H1	0.9800	C3A—C4A	1.513 (3)
C2—C7	1.526 (3)	C3A—C8A	1.531 (3)
C2—C3	1.550 (2)	C3A—H3A	0.9800
C2—H2	0.9800	C4A—C5A	1.490 (3)
C3—C4	1.513 (3)	C5A—C6A	1.529 (3)
C3—C8	1.528 (3)	C5A—H51A	0.9700
C3—H3	0.9800	C5A—H52A	0.9700
C4—C5	1.494 (3)	C6A—H61A	0.9700
C5—C6	1.533 (3)	C6A—H62A	0.9700
C5—H5A	0.9700	C7A—H71A	0.9600
C5—H5B	0.9700	C7A—H72A	0.9600
C6—H6A	0.9700	C7A—H73A	0.9600
C6—H6B	0.9700	C8A—C9A	1.518 (4)
C7—H7A	0.9600	C8A—H81A	0.9700
C7—H7B	0.9600	C8A—H82A	0.9700
C7—H7C	0.9600	C9A—H91A	0.9600
C8—C9	1.517 (3)	C9A—H92A	0.9600
C8—H8A	0.9700	C9A—H93A	0.9600
C10—O3—H3C	109.5 (19)	O3—C10—C1	112.00 (18)
C10A—O3A—H3D	110.3 (19)	C10A—C1A—C6A	110.96 (15)
C10—C1—C6	111.41 (16)	C10A—C1A—C2A	111.76 (14)
C10—C1—C2	111.86 (15)	C6A—C1A—C2A	112.25 (15)
C6—C1—C2	111.94 (15)	C10A—C1A—H1A	107.2
C10—C1—H1	107.1	C6A—C1A—H1A	107.2
C6—C1—H1	107.1	C2A—C1A—H1A	107.2
C2—C1—H1	107.1	C7A—C2A—C1A	111.99 (15)
C7—C2—C1	112.30 (16)	C7A—C2A—C3A	111.97 (15)
C7—C2—C3	112.31 (16)	C1A—C2A—C3A	109.38 (14)
C1—C2—C3	109.37 (14)	C7A—C2A—H2A	107.8
C7—C2—H2	107.5	C1A—C2A—H2A	107.8
C1—C2—H2	107.5	C3A—C2A—H2A	107.8
C3—C2—H2	107.5	C4A—C3A—C8A	112.55 (17)
C4—C3—C8	112.56 (16)	C4A—C3A—C2A	110.31 (15)
C4—C3—C2	109.76 (15)	C8A—C3A—C2A	114.34 (17)
C8—C3—C2	114.69 (15)	C4A—C3A—H3A	106.3
C4—C3—H3	106.4	C8A—C3A—H3A	106.3
C8—C3—H3	106.4	C2A—C3A—H3A	106.3
C2—C3—H3	106.4	O1A—C4A—C5A	120.9 (2)
O1—C4—C5	121.9 (2)	O1A—C4A—C3A	122.4 (2)
O1—C4—C3	121.2 (2)	C5A—C4A—C3A	116.71 (16)
C5—C4—C3	116.91 (17)	C4A—C5A—C6A	111.52 (16)
C4—C5—C6	112.04 (16)	C4A—C5A—H51A	109.3
C4—C5—H5A	109.2	C6A—C5A—H51A	109.3
C6—C5—H5A	109.2	C4A—C5A—H52A	109.3
C4—C5—H5B	109.2	C6A—C5A—H52A	109.3
C6—C5—H5B	109.2	H51A—C5A—H52A	108.0
H5A—C5—H5B	107.9	C1A—C6A—C5A	110.81 (17)
C1—C6—C5	110.94 (17)	C1A—C6A—H61A	109.5
C1—C6—H6A	109.5	C5A—C6A—H61A	109.5
C5—C6—H6A	109.5	C1A—C6A—H62A	109.5
C1—C6—H6B	109.5	C5A—C6A—H62A	109.5
C5—C6—H6B	109.5	H61A—C6A—H62A	108.1
H6A—C6—H6B	108.0	C2A—C7A—H71A	109.5
C2—C7—H7A	109.5	C2A—C7A—H72A	109.5
C2—C7—H7B	109.5	H71A—C7A—H72A	109.5
H7A—C7—H7B	109.5	C2A—C7A—H73A	109.5
C2—C7—H7C	109.5	H71A—C7A—H73A	109.5
H7A—C7—H7C	109.5	H72A—C7A—H73A	109.5
H7B—C7—H7C	109.5	C9A—C8A—C3A	114.16 (19)
C9—C8—C3	114.31 (18)	C9A—C8A—H81A	108.7
C9—C8—H8A	108.7	C3A—C8A—H81A	108.7
C3—C8—H8A	108.7	C9A—C8A—H82A	108.7
C9—C8—H8B	108.7	C3A—C8A—H82A	108.7
C3—C8—H8B	108.7	H81A—C8A—H82A	107.6
H8A—C8—H8B	107.6	C8A—C9A—H91A	109.5
C8—C9—H9A	109.5	C8A—C9A—H92A	109.5
C8—C9—H9B	109.5	H91A—C9A—H92A	109.5
H9A—C9—H9B	109.5	C8A—C9A—H93A	109.5
C8—C9—H9C	109.5	H91A—C9A—H93A	109.5
H9A—C9—H9C	109.5	H92A—C9A—H93A	109.5
H9B—C9—H9C	109.5	O2A—C10A—O3A	122.58 (18)
O2—C10—O3	122.97 (19)	O2A—C10A—C1A	125.39 (18)
O2—C10—C1	125.03 (19)	O3A—C10A—C1A	112.01 (16)
C10—C1—C2—C7	59.9 (2)	C10A—C1A—C2A—C7A	−58.5 (2)
C6—C1—C2—C7	−66.0 (2)	C6A—C1A—C2A—C7A	66.9 (2)
C10—C1—C2—C3	−174.77 (16)	C10A—C1A—C2A—C3A	176.79 (15)
C6—C1—C2—C3	59.4 (2)	C6A—C1A—C2A—C3A	−57.8 (2)
C7—C2—C3—C4	71.0 (2)	C7A—C2A—C3A—C4A	−72.2 (2)
C1—C2—C3—C4	−54.3 (2)	C1A—C2A—C3A—C4A	52.6 (2)
C7—C2—C3—C8	−56.8 (2)	C7A—C2A—C3A—C8A	55.9 (2)
C1—C2—C3—C8	177.80 (17)	C1A—C2A—C3A—C8A	−179.40 (17)
C8—C3—C4—O1	−0.2 (3)	C8A—C3A—C4A—O1A	−0.4 (3)
C2—C3—C4—O1	−129.2 (2)	C2A—C3A—C4A—O1A	128.6 (2)
C8—C3—C4—C5	−179.53 (18)	C8A—C3A—C4A—C5A	179.58 (18)
C2—C3—C4—C5	51.4 (2)	C2A—C3A—C4A—C5A	−51.4 (2)
O1—C4—C5—C6	131.6 (2)	O1A—C4A—C5A—C6A	−129.4 (2)
C3—C4—C5—C6	−49.1 (3)	C3A—C4A—C5A—C6A	50.7 (3)
C10—C1—C6—C5	177.20 (17)	C10A—C1A—C6A—C5A	−176.89 (16)
C2—C1—C6—C5	−56.7 (2)	C2A—C1A—C6A—C5A	57.3 (2)
C4—C5—C6—C1	49.7 (2)	C4A—C5A—C6A—C1A	−51.7 (2)
C4—C3—C8—C9	178.64 (18)	C4A—C3A—C8A—C9A	−174.7 (2)
C2—C3—C8—C9	−54.9 (3)	C2A—C3A—C8A—C9A	58.4 (3)
C6—C1—C10—O2	1.7 (3)	C6A—C1A—C10A—O2A	0.5 (3)
C2—C1—C10—O2	−124.4 (2)	C2A—C1A—C10A—O2A	126.6 (2)
C6—C1—C10—O3	−177.10 (17)	C6A—C1A—C10A—O3A	179.09 (17)
C2—C1—C10—O3	56.8 (2)	C2A—C1A—C10A—O3A	−54.8 (2)