rac-9-Ethyl-12a-hydroxy­tetra­deca­hydro­triphenyl­ene-1,5(2H,4bH)-dione: stabilization of a new isomer of a functionalized perhydro­triphenyl­ene through a tandem Michael addition-aldol reaction

The title compound, C₂₀H₃₀O₃, is a new functionalized perhydro­triphenyl­ene derivative formed via a tandem Michael addition-aldol reaction. The structural study reveals that the system of fused rings approximates a C₂ point symmetry, with trans-cis-cis ring junctions, while highly symmetric all-trans perhydro­triphenyl­ene, previously characterized, approximates a D₃ symmetry. The perhydro­triphenyl­ene nucleus of the title compound corresponds to the third stable stereo­isomer isolated for this polycyclic system. Considering that the C_s isomer was obtained recently through a similar tandem reaction, a general strategy is proposed which may help to obtain other stable stereoisomers of perhydro­triphenyl­ene.

S1. Comment

Perhydrotriphenylene (C₁₈H₃₆, abbreviated PHTP hereinafter) has a complex stereochemistry. There are six enantiomeric pairs and four meso-forms, as determined by Farina & Audisio (1970a). These authors were able to resolve into antipodes the highly symmetrical isomer belonging to the D₃ point group, in which all rings have a chair conformation and all fused-ring junctions have a trans configuration (Farina & Audisio, 1970b). Following Farina's nomenclature, the D₃ isomer may be described as anti-trans-anti-trans-anti-trans, shortened ATATAT. Descriptors trans apply to endo C—C bonds of the central ring (bonds shared by two cycles), while anti descriptors are for C—C exo bonds.

Racemic D₃-PHTP has been characterized crystallographically (Harlow & Desiraju, 1990). This isomer generally forms inclusion compounds with small organic molecules (König et al., 1997). In most cases, crystallographic studies of PHTP clathrates are severely complicated due to a tendency to disorder, with diffraction patterns including incommensurate satellites (Weber et al., 2001; Bürgi et al., 2005). For these reasons, very few PHTP derivatives have been characterized in the solid state. On the other hand, to the best of our knowledge, the possibility of stabilizing other isomers of PHTP has not been addressed, neither through accurate ab initio calculations nor by crystallizing such isomers.

The matter may be probed, at least partially, through the synthesis of PHTP derivatives, provided that the starting materials do not include fused rings. With the exception of the above-mentioned naked D₃-PHTP, only one guest-free PHTP derivative has been characterized crystallographically to date, namely 9-benzyl-12a-hydroxytetradecahydrotriphenylene- 1,5(2H,4bH)dione. This derivative was synthesized (Blake et al., 2007) through an original triple cascade reaction involving two Michael additions followed by an intramolecular aldol reaction. The main difficulty for their X-ray study was due to the very small size of the single crystals available (0.08 × 0.01 × 0.01 mm).

During our work on the copper-catalyzed conjugate addition of Et₂Zn to enones in the presence of chiral phosphoramidites (Feringa, 2000), we found that 2-cyclohexen-1-one, (3), behaves as expected, affording 3-ethylcyclohexanone, (4), but a by-product, the title compound, rac-(I), was also produced in a low 6% yield (see Scheme 1 and Experimental). Analytical data indicated that (I) is the 9-ethyl analogue of Blake and co-workers' functionalized PHTP. In fact, these authors also detected (I) in their oligomeric mixture, but were unable to isolate it as a pure crystalline solid. We surmise that the formation of rac-(I) under our conditions occurred by trapping the enolate of 3-ethylcyclohexanone with 2-cyclohexen-1-one, which afforded the enolate of trans-3-ethyl-2-(3-hydroxycyclohex-2-enyl)cyclohexanone. This step was followed by a Michael addition reaction with another equivalent of 2-cyclohexen-1-one, and finally the ring closure proceeded by an aldol reaction, leading to a functionalized-PHTP enolate. Protonation finally afforded the title alcohol, rac-(I).

The molecular strcture of compound (I) is illustrated in Fig. 1. The relative stereochemistry at the six chiral C atoms of the central A ring is 1aRS,4aRS,5aSR,8aRS,9aRS,12aSR. This configuration corresponds to ring junctions trans-cis-cis for A/C, A/B and A/D, respectively (Scheme 2 and Fig. 1). All the exo central C—C bonds are anti. All six-membered rings have chair conformations, with small deviations from ideal geometry, which can be attributed to polycyclic strain [θ puckering parameters (Cremer & Pople, 1975) 177.67 (16), 5.31 (18), 176.33 (17) and 1.36 (17)° for rings A, B, C and D, respectively]. Assuming ideal chair conformations for rings A–D, the PHTP core structure of rac-(I) corresponds to the rac-ATACAC isomer in Farina's nomenclature, and belongs to point group C₂.

Interestingly, Blake et al. isolated a third isomer for the core PHTP structure, namely meso-STACAT, which includes a syn C8a—C9a exo bond and a trans C9a—C12a A/D ring junction (Scheme 2). The central A ring has a twist-boat conformation (θ = 89.9° and ϕ = 146.3°) as does ring B (θ = 85.9° and ϕ = 153.6°). The other peripheral rings have distorted chair conformations (ring C, θ = 167.5°; ring D, θ = 169.4°). The PHTP nucleus of this isomer approximates a C_s symmetry, assuming ideal boat and chair conformations. However, considering departures from ideal geometry, the actual symmetry is rather C₁ and the molecule is not a true meso form.

As discussed above, a reasonable assumption is that both C₂ and C_s isomers are produced following identical routes. The stabilization of different isomers should then be related to the nature of the functional group at C9 rather than to the reaction conditions. If the proposed tandem mechanism is correct, the differentiation takes place during the first Michael addition, forming the C8a—C9a bond. In the case of 3-benzylcyclohexanone enolate addition, a syn–exo C—C bond is formed. The benzyl group is then equatorial, avoiding 1,3-diaxial interactions. With the ethyl analogue, the opposite enolate enantiomer is more favourably added, leading to an axially oriented ethyl group. The second Michael addition, forming the C4a—C5a bond and the final ring closure, is identical regardless of the substituent at C9. In both cases, it seems that the aldol reaction, forming the C1a—C12a bond, is assisted by the formation of a weak intramolecular hydrogen bond involving the hydroxy and carbonyl functional groups at C12a and C1, respectively. Other non-covalent interactions seem to have very little influence on the observed structure. For (I), the crystal packing features centrosymmetric dimers formed through weak C═O···H hydrogen bonds (Table 1). NMR data (COSY and HSQC) are consistent with the configuration observed in the solid state. We thus consider that the stereochemistry of (I) is induced by the Zn catalyst formed in situ, and not by intermolecular interactions in the solid state.

In conclusion, we propose that the MiMiRC tandem reaction (Mi = Michael addition; RC = ring closure) may be extended to libraries of substituted enones, allowing new stereoisomers of PHTP derivatives to be stabilized. By using suitable easily removable functional groups, new pure or racemic PHTP stereoisomers would then be achievable.

S2. Experimental

(1S,2S)-trans-N,N'-Bis[1-(S)-phenylethyl]-1,2-diaminocyclohexane, (S,S,S,S)-(1) (18 mg, 2.2 mol%) (Anaya de Parrodi et al., 1998), diethylaniline (13 ml, 32 mol%), CDCl₃ (0.5 ml) and PCl₃ (4.6 M solution in CH₂Cl₂, 12 µl, 2.3 mol%) were placed with vigorous stirring in a NMR tube and the reaction was followed by ³¹P NMR. After 5 min, the chlorodiazaphospholidine was formed in situ. Immediately after phenol or naphthol were added to the reaction mixture with vigorous stirring, ³¹P NMR spectra were recorded, showing that the chiral phosphoramidites ligands (S,S,S,S)-(2a) or (S,S,S,S)-(2b) were produced. Phosphoramidites (S,S,S,S)-(2a) or (S,S,S,S)-(2b) were added direct from the NMR tube, without purification, to a solution of Cu(OAc)₂ (7.7 mg, 1.7 mol%) in toluene (3 ml). The solution was stirred under N₂ at 298 K for 30 min and then cooled to 273 K. Et₂Zn (1.0 M solution in hexane, 3.8 ml, 3.8 mmol, 1.5 equivalents) and 2-cyclohexen-1-one, (3) (0.24 ml, 2.5 mmol, 1 equivalent), were added to the reaction mixture. After 5 h at 273 K, the reaction was quenched with aqueous NH₄Cl and the mixture was extracted with CH₂Cl₂ (2 × 20 ml). The organic phases were combined, dried over Na₂SO₄, filtered and concentrated. The crude product was purified by column chromatography on deactivated silica gel (Et₃N/SiO₂, 2.5% v/v) with hexane as eluent, affording rac-3-ethylcyclohexanone, (4) (47 mg, 15%), a mixture of non-isolated oligomers, and rac-(I) as colourless crystals (48 mg, 6%), which were recrystallized from hexane–CH₂Cl₂ (10:1 v/v). Analytical data for rac-(I) are available in the archived CIF.

S3. Refinement

Hydroxyl H atom H3 was located in a difference Fourier map and refined freely, with O—H = 0.82 (2) Å. The remaining H atoms were included in calculated positions and treated as riding atoms, with C—H = 0.96–0.98 Å, and with U_iso(H) = 1.2 or 1.5U_eq(C).

Computing details

Data collection: XSCANS (Siemens, 1996); cell refinement: XSCANS (Siemens, 1996); data reduction: XSCANS (Siemens, 1996); program(s) used to solve structure: SHELXTL-Plus (Sheldrick, 2008); program(s) used to refine structure: SHELXTL-Plus (Sheldrick, 2008); molecular graphics: SHELXTL-Plus (Sheldrick, 2008); software used to prepare material for publication: SHELXTL-Plus (Sheldrick, 2008).

Figures

Fig. 1. The molecular structure of compound (I), showing the atom-numbering scheme. Displacement ellipsoids are drawn at the 40% probability level and H atoms are shown as small spheres of arbitrary radii. The intramolecular hydrogen bond is indicated as a dotted line (see also Table 1).

rac-9-Ethyl-12a-hydroxytetradecahydrotriphenylene- 1,5(2H,4bH)-dione

Crystal data

C20H30O3	Z = 2
Mr = 318.44	F(000) = 348
Triclinic, P1	Dx = 1.232 Mg m^−3
Hall symbol: -P 1	Melting point = 457–459 K
a = 8.6898 (10) Å	Mo Kα radiation, λ = 0.71073 Å
b = 9.2312 (12) Å	Cell parameters from 60 reflections
c = 12.3633 (14) Å	θ = 4.7–15.2°
α = 72.377 (11)°	µ = 0.08 mm^−1
β = 73.574 (10)°	T = 298 K
γ = 67.681 (9)°	Prism, colourless
V = 858.41 (18) Å^3	0.60 × 0.44 × 0.18 mm

Data collection

Bruker P4 diffractometer	Rint = 0.019
Radiation source: fine-focus sealed tube	θmax = 27.5°, θmin = 2.5°
Graphite monochromator	h = −10→3
2θ/ω scans	k = −11→11
6729 measured reflections	l = −16→16
3878 independent reflections	3 standard reflections every 97 reflections
2728 reflections with I > 2σ(I)	intensity decay: 1%

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)] = 0.042	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.119	H atoms treated by a mixture of independent and constrained refinement
S = 1.05	w = 1/[σ^2(Fo^2) + (0.0445P)^2 + 0.1781P] where P = (Fo^2 + 2Fc^2)/3
3878 reflections	(Δ/σ)max = 0.001
213 parameters	Δρmax = 0.21 e Å^−3
0 restraints	Δρmin = −0.16 e Å^−3
0 constraints

Special details

Experimental. Analytical data: m.p. 457–459 K; ¹H NMR (200 MHz, CDCl₃, δ, p.p.m.): 0.92 (t, 3H, ³J = 7 Hz), 1.25–1.44 (m, 5H), 1.60–2.00 (m, 11H), 2.04–2.38 (m, 8H), 2.45 (d, 1H, ³J = 6 Hz), 2.67–2.73 (m, 1H), 4.02 (d, 1H, ³J = 3 Hz); ¹³C NMR (50 MHz, CDCl₃, δ, p.p.m.): 14.3 (CH3), 17.4 (CH2), 22.9 (CH2), 25.1 (CH2), 27.9 (CH2), 28.4 (CH2), 28.5 (CH2), 32.3 (CH2), 33.3 (CH2), 36.7 (CH), 37.4 (CH), 43.6 (CH2), 43.7 (CH2), 47.1 (CH), 47.6 (CH), 53.9 (CH), 61.2 (CH) 73.1 (C), 211.5 (CO), 215.7 (CO); IR (Film, cm^-1) 3491.1, 2918.7, 2862.2, 1687.9; HRMS-FAB⁺ m/z found: 319.2275 [(MH)⁺; calculated 319.2273 for C₂₀H₃₁O₃].

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

	x	y	z	Uiso*/Ueq
C1a	0.24345 (17)	−0.02153 (16)	0.86487 (11)	0.0369 (3)
H1aA	0.1628	−0.0804	0.8839	0.044*
C1	0.31055 (18)	−0.05948 (17)	0.97485 (11)	0.0410 (3)
C2	0.4083 (2)	−0.23276 (18)	1.01700 (14)	0.0524 (4)
H2A	0.3311	−0.2950	1.0456	0.063*
H2B	0.4581	−0.2418	1.0808	0.063*
C3	0.5478 (2)	−0.30162 (18)	0.92217 (15)	0.0545 (4)
H3B	0.6352	−0.2518	0.9023	0.065*
H3C	0.5987	−0.4161	0.9499	0.065*
C4	0.4770 (2)	−0.27226 (17)	0.81575 (14)	0.0535 (4)
H4A	0.3973	−0.3307	0.8346	0.064*
H4B	0.5687	−0.3139	0.7556	0.064*
C4a	0.38682 (18)	−0.09280 (16)	0.76924 (12)	0.0401 (3)
H4aA	0.3340	−0.0855	0.7066	0.048*
C5a	0.50498 (17)	0.00984 (15)	0.71971 (11)	0.0355 (3)
H5aA	0.5614	−0.0001	0.7812	0.043*
C5	0.64169 (18)	−0.04443 (17)	0.61816 (12)	0.0432 (3)
C6	0.7674 (2)	0.0458 (2)	0.57005 (14)	0.0554 (4)
H6A	0.8462	0.0068	0.5039	0.067*
H6B	0.8314	0.0283	0.6282	0.067*
C7	0.6740 (2)	0.22420 (19)	0.53362 (13)	0.0517 (4)
H7A	0.7538	0.2833	0.5098	0.062*
H7B	0.6232	0.2429	0.4681	0.062*
C8	0.5367 (2)	0.28454 (18)	0.63266 (13)	0.0482 (4)
H8A	0.4770	0.3975	0.6066	0.058*
H8B	0.5890	0.2739	0.6955	0.058*
C8a	0.40885 (16)	0.19169 (15)	0.67741 (10)	0.0345 (3)
H8aA	0.3600	0.2019	0.6120	0.041*
C9a	0.26086 (16)	0.26114 (15)	0.77206 (10)	0.0329 (3)
H9aA	0.3112	0.2573	0.8349	0.039*
C9	0.16102 (18)	0.43964 (16)	0.72735 (11)	0.0394 (3)
H9A	0.2465	0.4902	0.6807	0.047*
C10	0.0514 (2)	0.45491 (19)	0.64449 (13)	0.0497 (4)
H10A	−0.0165	0.5665	0.6231	0.060*
H10B	0.1245	0.4225	0.5746	0.060*
C11	−0.0654 (2)	0.3530 (2)	0.69696 (14)	0.0543 (4)
H11A	−0.1274	0.3620	0.6398	0.065*
H11B	−0.1470	0.3926	0.7620	0.065*
C12	0.03526 (19)	0.17706 (18)	0.73761 (13)	0.0472 (4)
H12A	0.1087	0.1348	0.6713	0.057*
H12B	−0.0425	0.1159	0.7738	0.057*
C12a	0.14246 (16)	0.15644 (15)	0.82361 (10)	0.0355 (3)
C13	0.0632 (2)	0.53367 (18)	0.82315 (13)	0.0511 (4)
H13A	−0.0401	0.5071	0.8595	0.061*
H13B	0.1316	0.5006	0.8817	0.061*
C14	0.0184 (3)	0.71386 (19)	0.77799 (17)	0.0670 (5)
H14A	−0.0418	0.7667	0.8408	0.101*
H14B	−0.0518	0.7477	0.7215	0.101*
H14C	0.1202	0.7412	0.7431	0.101*
O1	0.28530 (15)	0.04040 (13)	1.02878 (9)	0.0538 (3)
O2	0.64498 (15)	−0.14713 (14)	0.57434 (9)	0.0596 (3)
O3	0.01867 (13)	0.21168 (12)	0.92094 (9)	0.0449 (3)
H3	0.075 (3)	0.194 (3)	0.9697 (18)	0.082 (7)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C1a	0.0333 (7)	0.0390 (7)	0.0383 (7)	−0.0191 (6)	0.0014 (6)	−0.0063 (5)
C1	0.0353 (7)	0.0462 (8)	0.0365 (7)	−0.0174 (6)	0.0009 (6)	−0.0039 (6)
C2	0.0508 (9)	0.0482 (8)	0.0505 (8)	−0.0156 (7)	−0.0112 (7)	0.0008 (7)
C3	0.0444 (9)	0.0376 (8)	0.0682 (10)	−0.0110 (7)	−0.0043 (8)	−0.0022 (7)
C4	0.0565 (10)	0.0378 (7)	0.0623 (10)	−0.0186 (7)	0.0031 (8)	−0.0145 (7)
C4a	0.0412 (8)	0.0401 (7)	0.0411 (7)	−0.0174 (6)	−0.0016 (6)	−0.0122 (6)
C5a	0.0337 (7)	0.0395 (7)	0.0324 (6)	−0.0130 (6)	−0.0007 (5)	−0.0101 (5)
C5	0.0360 (8)	0.0478 (8)	0.0387 (7)	−0.0075 (6)	−0.0031 (6)	−0.0110 (6)
C6	0.0363 (8)	0.0673 (10)	0.0527 (9)	−0.0161 (7)	0.0091 (7)	−0.0162 (8)
C7	0.0434 (8)	0.0646 (10)	0.0423 (8)	−0.0272 (8)	0.0074 (7)	−0.0071 (7)
C8	0.0451 (8)	0.0481 (8)	0.0478 (8)	−0.0238 (7)	0.0072 (7)	−0.0091 (6)
C8a	0.0334 (7)	0.0392 (7)	0.0297 (6)	−0.0154 (6)	0.0007 (5)	−0.0074 (5)
C9a	0.0326 (7)	0.0368 (6)	0.0288 (6)	−0.0141 (5)	−0.0009 (5)	−0.0072 (5)
C9	0.0387 (7)	0.0381 (7)	0.0366 (7)	−0.0138 (6)	−0.0005 (6)	−0.0058 (5)
C10	0.0515 (9)	0.0488 (8)	0.0423 (8)	−0.0127 (7)	−0.0122 (7)	−0.0022 (6)
C11	0.0458 (9)	0.0629 (10)	0.0545 (9)	−0.0165 (8)	−0.0197 (7)	−0.0050 (7)
C12	0.0409 (8)	0.0542 (9)	0.0510 (8)	−0.0220 (7)	−0.0098 (7)	−0.0081 (7)
C12a	0.0299 (7)	0.0415 (7)	0.0317 (6)	−0.0141 (6)	0.0018 (5)	−0.0072 (5)
C13	0.0514 (9)	0.0460 (8)	0.0485 (8)	−0.0094 (7)	−0.0021 (7)	−0.0152 (7)
C14	0.0693 (12)	0.0490 (9)	0.0761 (12)	−0.0119 (9)	−0.0037 (10)	−0.0229 (8)
O1	0.0608 (7)	0.0562 (6)	0.0421 (6)	−0.0144 (5)	−0.0102 (5)	−0.0131 (5)
O2	0.0622 (7)	0.0631 (7)	0.0526 (6)	−0.0159 (6)	0.0028 (5)	−0.0299 (5)
O3	0.0342 (5)	0.0514 (6)	0.0390 (5)	−0.0135 (5)	0.0055 (4)	−0.0077 (4)

Geometric parameters (Å, º)

C1a—C1	1.5220 (19)	C8—C8a	1.5371 (19)
C1a—C12a	1.5427 (18)	C8—H8A	0.9700
C1a—C4a	1.5486 (18)	C8—H8B	0.9700
C1a—H1aA	0.9800	C8a—C9a	1.5527 (17)
C1—O1	1.2160 (17)	C8a—H8aA	0.9800
C1—C2	1.505 (2)	C9a—C9	1.5516 (17)
C2—C3	1.520 (2)	C9a—C12a	1.5526 (17)
C2—H2A	0.9700	C9a—H9aA	0.9800
C2—H2B	0.9700	C9—C10	1.529 (2)
C3—C4	1.516 (2)	C9—C13	1.5399 (19)
C3—H3B	0.9700	C9—H9A	0.9800
C3—H3C	0.9700	C10—C11	1.523 (2)
C4—H4A	0.9700	C10—H10A	0.9700
C4—H4B	0.9700	C10—H10B	0.9700
C4a—C5a	1.5359 (18)	C11—C12	1.527 (2)
C4a—C4	1.543 (2)	C11—H11A	0.9700
C4a—H4aA	0.9800	C11—H11B	0.9700
C5a—C5	1.5244 (18)	C12—C12a	1.529 (2)
C5a—C8a	1.5620 (18)	C12—H12A	0.9700
C5a—H5aA	0.9800	C12—H12B	0.9700
C5—O2	1.2143 (17)	C12a—O3	1.4450 (15)
C5—C6	1.505 (2)	C13—C14	1.516 (2)
C6—C7	1.522 (2)	C13—H13A	0.9700
C6—H6A	0.9700	C13—H13B	0.9700
C6—H6B	0.9700	C14—H14A	0.9600
C7—C8	1.522 (2)	C14—H14B	0.9600
C7—H7A	0.9700	C14—H14C	0.9600
C7—H7B	0.9700	O3—H3	0.82 (2)
C1—C1a—C12a	114.97 (11)	C8a—C8—H8B	109.2
C1—C1a—C4a	110.45 (11)	H8A—C8—H8B	107.9
C12a—C1a—C4a	113.36 (10)	C8—C8a—C9a	112.40 (11)
C1—C1a—H1aA	105.7	C8—C8a—C5a	109.11 (11)
C12a—C1a—H1aA	105.7	C9a—C8a—C5a	112.35 (10)
C4a—C1a—H1aA	105.7	C8—C8a—H8aA	107.6
O1—C1—C2	120.64 (14)	C9a—C8a—H8aA	107.6
O1—C1—C1a	123.57 (13)	C5a—C8a—H8aA	107.6
C2—C1—C1a	115.77 (13)	C9—C9a—C12a	111.77 (11)
C1—C2—C3	112.04 (12)	C9—C9a—C8a	111.93 (10)
C1—C2—H2A	109.2	C12a—C9a—C8a	111.41 (10)
C3—C2—H2A	109.2	C9—C9a—H9aA	107.1
C1—C2—H2B	109.2	C12a—C9a—H9aA	107.1
C3—C2—H2B	109.2	C8a—C9a—H9aA	107.1
H2A—C2—H2B	107.9	C10—C9—C13	113.33 (12)
C4—C3—C2	110.52 (13)	C10—C9—C9a	110.94 (11)
C4—C3—H3B	109.5	C13—C9—C9a	114.29 (11)
C2—C3—H3B	109.5	C10—C9—H9A	105.8
C4—C3—H3C	109.5	C13—C9—H9A	105.8
C2—C3—H3C	109.5	C9a—C9—H9A	105.8
H3B—C3—H3C	108.1	C11—C10—C9	112.58 (12)
C3—C4—C4a	112.74 (12)	C11—C10—H10A	109.1
C3—C4—H4A	109.0	C9—C10—H10A	109.1
C4a—C4—H4A	109.0	C11—C10—H10B	109.1
C3—C4—H4B	109.0	C9—C10—H10B	109.1
C4a—C4—H4B	109.0	H10A—C10—H10B	107.8
H4A—C4—H4B	107.8	C10—C11—C12	111.00 (13)
C5a—C4a—C4	114.38 (12)	C10—C11—H11A	109.4
C5a—C4a—C1a	109.54 (10)	C12—C11—H11A	109.4
C4—C4a—C1a	110.21 (11)	C10—C11—H11B	109.4
C5a—C4a—H4aA	107.5	C12—C11—H11B	109.4
C4—C4a—H4aA	107.5	H11A—C11—H11B	108.0
C1a—C4a—H4aA	107.5	C11—C12—C12a	111.74 (12)
C5—C5a—C4a	112.83 (11)	C11—C12—H12A	109.3
C5—C5a—C8a	107.06 (10)	C12a—C12—H12A	109.3
C4a—C5a—C8a	113.03 (11)	C11—C12—H12B	109.3
C5—C5a—H5aA	107.9	C12a—C12—H12B	109.3
C4a—C5a—H5aA	107.9	H12A—C12—H12B	107.9
C8a—C5a—H5aA	107.9	O3—C12a—C12	103.79 (11)
O2—C5—C6	121.63 (13)	O3—C12a—C1a	108.39 (10)
O2—C5—C5a	122.93 (14)	C12—C12a—C1a	111.59 (11)
C6—C5—C5a	115.32 (12)	O3—C12a—C9a	110.31 (10)
C5—C6—C7	109.57 (13)	C12—C12a—C9a	111.07 (11)
C5—C6—H6A	109.8	C1a—C12a—C9a	111.38 (10)
C7—C6—H6A	109.8	C14—C13—C9	112.72 (13)
C5—C6—H6B	109.8	C14—C13—H13A	109.0
C7—C6—H6B	109.8	C9—C13—H13A	109.0
H6A—C6—H6B	108.2	C14—C13—H13B	109.0
C8—C7—C6	110.78 (12)	C9—C13—H13B	109.0
C8—C7—H7A	109.5	H13A—C13—H13B	107.8
C6—C7—H7A	109.5	C13—C14—H14A	109.5
C8—C7—H7B	109.5	C13—C14—H14B	109.5
C6—C7—H7B	109.5	H14A—C14—H14B	109.5
H7A—C7—H7B	108.1	C13—C14—H14C	109.5
C7—C8—C8a	112.19 (12)	H14A—C14—H14C	109.5
C7—C8—H8A	109.2	H14B—C14—H14C	109.5
C8a—C8—H8A	109.2	C12a—O3—H3	104.2 (15)
C7—C8—H8B	109.2
C12a—C1a—C1—O1	1.35 (19)	C4a—C5a—C8a—C9a	53.13 (14)
C4a—C1a—C1—O1	131.18 (14)	C8—C8a—C9a—C9	59.13 (15)
C12a—C1a—C1—C2	179.54 (11)	C5a—C8a—C9a—C9	−177.33 (11)
C4a—C1a—C1—C2	−50.62 (15)	C8—C8a—C9a—C12a	−174.89 (11)
O1—C1—C2—C3	−130.50 (15)	C5a—C8a—C9a—C12a	−51.36 (14)
C1a—C1—C2—C3	51.24 (18)	C12a—C9a—C9—C10	−52.52 (14)
C1—C2—C3—C4	−52.43 (18)	C8a—C9a—C9—C10	73.26 (14)
C1—C1a—C4a—C5a	−75.14 (13)	C12a—C9a—C9—C13	77.12 (15)
C12a—C1a—C4a—C5a	55.54 (15)	C8a—C9a—C9—C13	−157.11 (12)
C1—C1a—C4a—C4	51.54 (15)	C13—C9—C10—C11	−76.11 (16)
C12a—C1a—C4a—C4	−177.78 (12)	C9a—C9—C10—C11	54.03 (16)
C2—C3—C4—C4a	56.80 (17)	C9—C10—C11—C12	−55.92 (18)
C5a—C4a—C4—C3	67.15 (16)	C10—C11—C12—C12a	56.32 (17)
C1a—C4a—C4—C3	−56.78 (17)	C11—C12—C12a—O3	63.25 (14)
C4—C4a—C5a—C5	60.37 (16)	C11—C12—C12a—C1a	179.77 (11)
C1a—C4a—C5a—C5	−175.35 (11)	C11—C12—C12a—C9a	−55.28 (15)
C4—C4a—C5a—C8a	−177.98 (11)	C1—C1a—C12a—O3	−48.79 (14)
C1a—C4a—C5a—C8a	−53.69 (14)	C4a—C1a—C12a—O3	−177.18 (11)
C4a—C5a—C5—O2	7.1 (2)	C1—C1a—C12a—C12	−162.48 (11)
C8a—C5a—C5—O2	−117.90 (15)	C4a—C1a—C12a—C12	69.13 (14)
C4a—C5a—C5—C6	−176.77 (12)	C1—C1a—C12a—C9a	72.75 (13)
C8a—C5a—C5—C6	58.26 (16)	C4a—C1a—C12a—C9a	−55.64 (15)
O2—C5—C6—C7	119.32 (16)	C9—C9a—C12a—O3	−61.09 (13)
C5a—C5—C6—C7	−56.89 (17)	C8a—C9a—C12a—O3	172.85 (10)
C5—C6—C7—C8	53.52 (18)	C9—C9a—C12a—C12	53.44 (14)
C6—C7—C8—C8a	−57.22 (18)	C8a—C9a—C12a—C12	−72.62 (14)
C7—C8—C8a—C9a	−175.63 (12)	C9—C9a—C12a—C1a	178.50 (10)
C7—C8—C8a—C5a	59.05 (16)	C8a—C9a—C12a—C1a	52.44 (14)
C5—C5a—C8a—C8	−56.67 (14)	C10—C9—C13—C14	−71.18 (18)
C4a—C5a—C8a—C8	178.48 (11)	C9a—C9—C13—C14	160.39 (14)
C5—C5a—C8a—C9a	177.98 (11)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O3—H3···O1	0.82 (2)	2.01 (2)	2.7081 (16)	143 (2)
C8a—H8aA···O2^i	0.98	2.52	3.4381 (18)	156

Symmetry code: (i) −x+1, −y, −z+1.