An azonia derivative of hexahelicene

In 8a-azonia­[6]­helicene hexa­fluoro­phos­phate or 8a-azoniaphenanthro[3,4-c]phen­an­threne hexa­fluoro­phos­phate, C₂₅H₁₆N⁺·PF₆^-, replacement of an outer bridgehead carbon of hexahelicene by a quaternary Nsp² atom results in a geometrical change in the helical structure. The racemic heterohelicene forms homochiral columnar stacks through intermolecular [pi]-[pi] donor-acceptor interactions in the crystalline state.

S1. Comment

Helicenes, a well known representataive of non-planar polycyclic aromatic compounds, have fascinated many chemists since the first synthesis of [6]helicene (Newman et al., 1955) because of their unique helical structure (Laarhoven & Prinsen, 1984). A number of carbohelicenes and heterohelicenes incorporating thiophene, pyrrole, furan and pyridine rings have been synthesized to date and some of their crystal structures were also detemined (Meurer & Vögtle, 1985). Recently, we succeeded in the first synthesis of cationic heterohexahelicenes, azonia[6]helicenes, that possess a quaternary Nsp² atom at a bridgehead position of the outer or inner helix skelton (Arai et al., 1989, 1995). The present study is concerned with the structure of the 8a-azonia[6]helicene hexafluorophosphate salt, (I), which has a quaternary N atom at the outer bridgehead and can be compared with the structure of carbohexahelicene (de Rango et al., 1973). Also, this cationic heterohelicene has π-electron acceptor and donor parts in one molecule and is therefore expected to form a well defind stacked structure in the crystalline state.

Single-crystal X-ray analysis revealed that (I) crystallized as a racemate and the unit cell contains two enantiometric pairs of the cationic heterohelicene and four counter-anions. The molecular geometry of the azonia[6]helicene cation substantially resembles that of carbo[6]helicene and shows common features which are generally found in all other helicenes studied: the aromatic rings deviate significantly from planarity, the inner C≐C bonds are lengthened and the outer bonds are shortened than 1.39 Å (typical aromatic C≐C distance).

However, the salient structural difference from carbo[6]helicene appeared around the N atom. The three N≐C bond lengths of (I) are significantly contracted (ca −0.03 Å) compared with those of the corresponding C≐C bonds in carbo[6]helicene and the bond angles C8—N8a—C9 and C16b—C16c—C16d for (I) are also slightly different from the corresponding angles of carbo[6]helicene (Table 1). From the structural data of the quinolizinium cation (Sato et al., 2001) and azoniafluoranthene (Boubekeur et al., 1989), those differences are considered to be a common feature in azonia aromatic compounds (Arai & Hida, 1992). These subtle changes at the central moiety alters the geometry of the helix of helicene. Table 1 summarizes the angles between the least-square planes of the six-membered rings and the torsion angles of the inner bonds, together with the corresponding values for the carbo[6]helicene taken from the literature (de Rango et al., 1973). These values indicate that 8a-azonia[6]helicene tends to be flattened compared with carbo[6]helicene; the angle between the least-square planes of the two terminal benzene rings of (I) is 49.85 (6)° versus 58.5° in carbo[6]helicene.

On the other hand, inspection of the molecular packing of (I) reveals the formation of a well defined one-dimensional helical columnar structure extending along the b axis (Fig. 2). Each column consists of a single enantiomer and the interstitial regions of the column are occupied by PF₆⁻ anions (Fig. 2, left). The helicene molecules are stacked one above the other in an antiparallel arrangement (Fig. 2, right). The mean interplanar separation between the overlapped naphthalene rings is ca 3.5 Å, which suggests the presence of a face-to-face-type π–π interaction. In addition, attractive electronic interactions between the central π-accepting quinolizinium moiety and the terminal π-donative benzene rings facilitate the above geometrical arrangement and contribute to the stabilization of the columnar stacks. It has been reported that planar acridizinium (benzo[b]quinolizinium) cations in the crystalline state exist exclusively facing each other in an anti-head-to-tail arrangement (Ihmels et al., 1999).

Fig. 3 shows the secondary packing diagram of the helical columns in the crystal, viewed in a projection along the b axis. There are homochiral arrays (of the columns) parallel to the ab plane with periodical inversion of the helicity along the c axis. The packing pattern of racemic (I) differs greatly from that of the carbo- and other hetero-helicenes; most racemic helicenes form racemate crystals in which two antipodes stack either alternately or in an interpenetrative fashion. To the best of our knowledge, one crystalline form of carbo[5]helicene is the only example where similar homochiral arrays are formed in the crystal structure (Kuroda, 1982).

S2. Experimental

Compound (I) was prepared by the photocyclization of 2-stylylnaphtho[1,2-a]quinolizinium hexafluorophosphate similarly to the perchrolate salt as already reported (Arai et al., 1989). Single crystals of (I) were obtained by slow evaporation from an acetonitrile solution (m.p. 508–510 K).

Computing details

Data collection: CrystalClear (Rigaku Corporation, 2000); cell refinement: CrystalClear; data reduction: TEXSAN (Molecular Structure Corporation, 1999); program(s) used to solve structure: SIR92 (Altomare et al., 1994) and DIRDIF94 (Beurskens et al., 1994); program(s) used to refine structure: SHELXL93 (Sheldrick, 1993); molecular graphics: ORTEPIII (Johnson & Burnett, 1996); software used to prepare material for publication: TEXSAN.

Figures

	Fig. 1. The molecular structure of the 8a-azonia[6]helicene in (I), shown with 50% probability displacement ellipsoids for non-H atoms.
	Fig. 2. Two views of the X-ray diagram of one of the enantiomerically pure cylindrical column stacks extending along the b axis. The PF6^− anions have been omitted for clarify in the righthand view.
	Fig. 3. The crystal packing in (I), viewed down the b axis.

8a-Azoniahexahelicene hexafluorophosphate

Crystal data

C25H16N^+·F6P^−	F(000) = 968.00
Mr = 475.37	Dx = 1.619 Mg m^−3
Monoclinic, P21/c	Melting point: 508-510 K K
Hall symbol: -P 2ybc	Mo Kα radiation, λ = 0.7107 Å
a = 9.1026 (7) Å	Cell parameters from 4702 reflections
b = 12.1235 (9) Å	θ = 3.4–27.5°
c = 18.019 (1) Å	µ = 0.21 mm^−1
β = 101.219 (3)°	T = 153 K
V = 1950.5 (2) Å^3	Prism, yellow
Z = 4	0.35 × 0.30 × 0.30 mm

Data collection

Rigaku/MSC Mercury CCD diffractometer	3690 reflections with I > 2σ(I)
Detector resolution: 14.62 pixels mm^-1	Rint = 0.022
ω scans	θmax = 27.5°, θmin = 3.4°
Absorption correction: empirical (using intensity measurements) (Blessing, 1995)	h = −11→11
Tmin = 0.880, Tmax = 0.938	k = −15→15
11700 measured reflections	l = −23→22
4412 independent reflections

Refinement

Refinement on F^2	H-atom parameters not refined
R[F^2 > 2σ(F^2)] = 0.038	w = 1/[σ^2(Fo^2) + (0.0525P)^2 + 0.1568P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.126	(Δ/σ)max = 0.030
S = 0.92	Δρmax = 0.30 e Å^−3
3690 reflections	Δρmin = −0.29 e Å^−3
362 parameters

Special details

Geometry. All e.s.d.'s 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.

Refinement. The structure was solved by direct method and expanded using Fourier techniques. The non-hydrogen atoms were refined anisotropically. Refinement using reflections with F² > 2.0 σ(F²). The weighted R-factor (wR), goodness of fit (S) and R-factor (gt) are based on F, with F set to zero for negative F. The threshold expression of F² > 2.0 σ(F²) is used only for calculating R-factor (gt).

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

	x	y	z	Uiso*/Ueq
P1	0.62476 (4)	0.30363 (3)	0.57999 (2)	0.0271 (1)
F1	0.6241 (1)	0.41089 (8)	0.63146 (6)	0.0473 (3)
F2	0.6708 (1)	0.23051 (8)	0.65472 (5)	0.0424 (3)
F3	0.7970 (1)	0.32397 (9)	0.57845 (6)	0.0459 (3)
F4	0.4517 (1)	0.2840 (1)	0.58107 (6)	0.0542 (3)
F5	0.5789 (1)	0.3760 (1)	0.50539 (6)	0.0514 (3)
F6	0.6262 (2)	0.1952 (1)	0.52970 (6)	0.0577 (3)
N8a	0.6908 (1)	0.0214 (1)	0.77651 (8)	0.0296 (3)
C1	1.0917 (2)	−0.0987 (1)	0.71085 (8)	0.0226 (3)
C2	1.2128 (2)	−0.1454 (1)	0.68750 (8)	0.0264 (3)
C3	1.2111 (2)	−0.1632 (1)	0.61009 (9)	0.0302 (3)
C4	1.0844 (2)	−0.1398 (1)	0.55813 (9)	0.0308 (3)
C4a	0.9559 (2)	−0.0966 (1)	0.58080 (8)	0.0269 (3)
C5	0.8168 (2)	−0.0898 (1)	0.52788 (9)	0.0336 (3)
C6	0.6889 (2)	−0.0660 (1)	0.55097 (9)	0.0349 (4)
C6a	0.6907 (2)	−0.0335 (1)	0.62709 (9)	0.0292 (3)
C7	0.5551 (2)	−0.0155 (1)	0.6531 (1)	0.0358 (4)
C8	0.5567 (2)	0.0024 (1)	0.7259 (1)	0.0356 (4)
C9	0.6849 (2)	0.0366 (1)	0.8523 (1)	0.0361 (4)
C10	0.8092 (2)	0.0571 (1)	0.90359 (9)	0.0350 (4)
C10a	0.9464 (2)	0.0793 (1)	0.87960 (8)	0.0289 (3)
C11	1.0764 (2)	0.1095 (1)	0.93290 (9)	0.0335 (3)
C12	1.2041 (2)	0.1382 (1)	0.91016 (9)	0.0330 (3)
C12a	1.2040 (2)	0.1538 (1)	0.83154 (8)	0.0264 (3)
C13	1.3284 (2)	0.2029 (1)	0.8080 (1)	0.0333 (3)
C14	1.3229 (2)	0.2315 (1)	0.7345 (1)	0.0349 (4)
C15	1.1901 (2)	0.2152 (1)	0.68096 (9)	0.0322 (3)
C16	1.0683 (2)	0.1638 (1)	0.70137 (8)	0.0266 (3)
C16a	1.0747 (2)	0.1281 (1)	0.77628 (8)	0.0228 (3)
C16b	0.9497 (2)	0.0753 (1)	0.80187 (8)	0.0237 (3)
C16c	0.8261 (2)	0.0250 (1)	0.75162 (8)	0.0242 (3)
C16d	0.8275 (2)	−0.0238 (1)	0.67909 (8)	0.0235 (3)
C16e	0.9615 (2)	−0.0694 (1)	0.65812 (8)	0.0224 (3)
H1	1.095	−0.088	0.7619	0.02441*
H2	1.302	−0.168	0.7265	0.03340*
H3	1.301	−0.197	0.5939	0.02925*
H4	1.078	−0.162	0.506	0.05128*
H5	0.818	−0.110	0.475	0.05458*
H6	0.594	−0.075	0.514	0.04470*
H7	0.461	−0.026	0.618	0.04533*
H8	0.473	0.005	0.751	0.04625*
H9	0.584	0.027	0.863	0.03691*
H10	0.803	0.068	0.957	0.04273*
H11	1.067	0.110	0.986	0.05443*
H12	1.292	0.156	0.945	0.03821*
H13	1.417	0.217	0.848	0.03832*
H14	1.405	0.264	0.714	0.04974*
H15	1.183	0.240	0.630	0.03697*
H16	0.977	0.156	0.6626	0.03185*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
P1	0.0257 (2)	0.0329 (2)	0.0237 (2)	−0.0019 (1)	0.0074 (2)	0.0004 (1)
F1	0.0579 (7)	0.0346 (6)	0.0501 (6)	0.0093 (5)	0.0121 (5)	−0.0062 (4)
F2	0.0581 (6)	0.0358 (5)	0.0326 (5)	0.0000 (5)	0.0072 (4)	0.0065 (4)
F3	0.0252 (5)	0.0591 (7)	0.0542 (6)	0.0007 (4)	0.0100 (4)	0.0092 (5)
F4	0.0309 (5)	0.0924 (9)	0.0412 (6)	−0.0153 (5)	0.0121 (4)	0.0047 (6)
F5	0.0388 (6)	0.0784 (8)	0.0371 (6)	0.0047 (5)	0.0074 (4)	0.0257 (5)
F6	0.0787 (9)	0.0556 (7)	0.0427 (6)	−0.0119 (6)	0.0216 (6)	−0.0215 (5)
N8a	0.0252 (6)	0.0250 (6)	0.0414 (7)	0.0009 (5)	0.0130 (5)	0.0032 (5)
C1	0.0242 (6)	0.0220 (6)	0.0216 (6)	−0.0024 (5)	0.0044 (5)	−0.0011 (5)
C2	0.0246 (7)	0.0249 (7)	0.0298 (7)	−0.0027 (5)	0.0055 (5)	−0.0021 (6)
C3	0.0327 (8)	0.0263 (7)	0.0341 (8)	−0.0031 (6)	0.0130 (6)	−0.0048 (6)
C4	0.0411 (8)	0.0274 (7)	0.0252 (7)	−0.0047 (6)	0.0095 (6)	−0.0044 (6)
C4a	0.0336 (7)	0.0220 (7)	0.0240 (7)	−0.0047 (6)	0.0026 (6)	−0.0006 (5)
C5	0.0440 (9)	0.0272 (8)	0.0253 (8)	−0.0027 (6)	−0.0042 (6)	−0.0020 (6)
C6	0.0338 (8)	0.0269 (7)	0.0370 (8)	−0.0020 (6)	−0.0104 (6)	0.0036 (6)
C6a	0.0254 (7)	0.0212 (7)	0.0378 (8)	−0.0026 (5)	−0.0023 (6)	0.0044 (6)
C7	0.0222 (7)	0.0267 (8)	0.055 (1)	−0.0013 (6)	−0.0014 (7)	0.0071 (7)
C8	0.0210 (7)	0.0271 (7)	0.060 (1)	0.0003 (6)	0.0099 (7)	0.0050 (7)
C9	0.0389 (9)	0.0289 (8)	0.0473 (10)	0.0034 (6)	0.0248 (7)	0.0062 (7)
C10	0.0466 (9)	0.0303 (8)	0.0340 (8)	0.0073 (7)	0.0222 (7)	0.0041 (6)
C10a	0.0371 (8)	0.0232 (7)	0.0288 (8)	0.0063 (6)	0.0121 (6)	0.0011 (5)
C11	0.0483 (9)	0.0289 (8)	0.0233 (7)	0.0082 (7)	0.0067 (6)	−0.0016 (6)
C12	0.0379 (8)	0.0276 (7)	0.0295 (8)	0.0061 (6)	−0.0036 (6)	−0.0063 (6)
C12a	0.0265 (7)	0.0210 (6)	0.0305 (7)	0.0041 (5)	0.0028 (5)	−0.0062 (5)
C13	0.0245 (7)	0.0286 (8)	0.0459 (9)	−0.0014 (6)	0.0048 (6)	−0.0120 (7)
C14	0.0298 (7)	0.0279 (8)	0.0505 (10)	−0.0074 (6)	0.0166 (7)	−0.0104 (7)
C15	0.0391 (8)	0.0272 (7)	0.0335 (8)	−0.0077 (6)	0.0153 (7)	−0.0049 (6)
C16	0.0283 (7)	0.0243 (7)	0.0278 (7)	−0.0043 (5)	0.0067 (6)	−0.0039 (5)
C16a	0.0230 (6)	0.0198 (6)	0.0262 (7)	0.0012 (5)	0.0062 (5)	−0.0041 (5)
C16b	0.0254 (7)	0.0204 (6)	0.0262 (7)	0.0041 (5)	0.0070 (5)	0.0016 (5)
C16c	0.0225 (6)	0.0192 (6)	0.0323 (7)	0.0012 (5)	0.0091 (5)	0.0053 (5)
C16d	0.0233 (6)	0.0196 (6)	0.0268 (7)	−0.0019 (5)	0.0026 (5)	0.0033 (5)
C16e	0.0239 (6)	0.0183 (6)	0.0244 (7)	−0.0038 (5)	0.0029 (5)	0.0016 (5)

Geometric parameters (Å, º)

P1—F1	1.598 (1)	C12a—C13	1.416 (2)
P1—F2	1.599 (1)	C12a—C16a	1.420 (2)
P1—F3	1.592 (1)	C13—C14	1.361 (3)
P1—F4	1.597 (1)	C14—C15	1.406 (2)
P1—F5	1.591 (1)	C15—C16	1.382 (2)
P1—F6	1.598 (1)	C16—C16a	1.408 (2)
N8a—C8	1.393 (2)	C16a—C16b	1.456 (2)
N8a—C9	1.390 (2)	C16b—C16c	1.436 (2)
N8a—C16c	1.391 (2)	C16c—C16d	1.437 (2)
C1—C2	1.376 (2)	C16d—C16e	1.455 (2)
C1—C16e	1.412 (2)	C1—H1	0.92
C2—C3	1.408 (2)	C2—H2	1.00
C3—C4	1.366 (2)	C3—H3	1.01
C4—C4a	1.413 (2)	C4—H4	0.96
C4a—C5	1.432 (2)	C5—H5	0.98
C4a—C16e	1.423 (2)	C6—H6	0.99
C5—C6	1.342 (3)	C7—H7	0.97
C6—C6a	1.424 (2)	C8—H8	0.96
C6a—C7	1.420 (2)	C9—H9	0.98
C6a—C16d	1.410 (2)	C10—H10	0.99
C7—C8	1.328 (3)	C11—H11	0.98
C9—C10	1.338 (2)	C12—H12	0.94
C10—C10a	1.424 (3)	C13—H13	0.99
C10a—C11	1.419 (2)	C14—H14	0.98
C10a—C16b	1.408 (2)	C15—H15	0.95
C11—C12	1.351 (3)	C16—H16	0.98
C12—C12a	1.429 (2)
F1···F6	3.196 (2)	C1···C16b	3.104 (2)
F1···C9^i	3.262 (2)	C1···C16	3.191 (2)
F1···C12^ii	3.326 (2)	C2···C4a	2.786 (2)
F1···C12a^ii	3.340 (2)	C2···C8^x	3.556 (2)
F1···C2^ii	3.380 (2)	C3···C16e	2.822 (2)
F1···C1^ii	3.452 (2)	C10···C3^ii	3.402 (2)
F1···C8^i	3.491 (2)	C10a···C3^ii	3.455 (2)
F2···C7	3.162 (2)	C3···C7^x	3.559 (2)
F2···F5	3.190 (1)	C11···C4^ii	3.390 (2)
F2···C16c	3.208 (2)	C4···C5^vii	3.392 (2)
F2···C2^ii	3.209 (2)	C4a···C6a	2.809 (2)
F2···C6a	3.250 (2)	C12···C4a^ii	3.546 (2)
F2···C8	3.300 (2)	C11···C4a^ii	3.579 (2)
F2···N8a	3.335 (2)	C5···C16d	2.823 (2)
F2···C16d	3.390 (2)	C12···C5^ii	3.498 (2)
F2···C1^ii	3.576 (2)	C6···C16e	2.833 (2)
F3···F4	3.189 (1)	C13···C6a^ii	3.419 (2)
F3···C10^iii	3.486 (2)	C7···C16c	2.789 (2)
F3···C16	3.557 (2)	C8···C16d	2.775 (2)
F4···C14^iv	3.269 (2)	C14···C8^ii	3.492 (2)
F4···C15^iv	3.358 (2)	C14···C8^x	3.521 (2)
F4···C12^v	3.571 (2)	C9···C16b	2.777 (2)
F4···C9^i	3.598 (2)	C10···C16c	2.799 (2)
F5···C10^iii	3.149 (2)	C10···C11^xi	3.557 (2)
F5···C9^iii	3.270 (2)	C10a···C12a	2.802 (2)
F5···F5^vi	3.323 (2)	C11···C16a	2.828 (2)
F5···C12^v	3.512 (2)	C12···C16b	2.827 (2)
F6···C3^vii	3.185 (2)	C12a···C15	2.793 (2)
F6···C6	3.228 (2)	C13···C16	2.784 (2)
F6···C6a	3.273 (2)	C14···C16a	2.811 (2)
F6···C6^viii	3.342 (2)	C16···C16b	2.521 (2)
F6···C4^vii	3.393 (2)	C16···C16e	3.042 (2)
F6···C7	3.528 (2)	C16···C16c	3.048 (2)
N8a···C10a	2.771 (2)	C16···C16d	3.130 (2)
N8a···C6a	2.773 (2)	C16a···C16c	2.547 (2)
N8a···C14^ix	3.521 (2)	C16a···C16d	3.161 (2)
C1···C16d	2.530 (2)	C16a···C16e	3.237 (2)
C1···C4	2.785 (2)	C16b···C16d	2.573 (2)
C1···C16a	3.007 (2)	C16b···C16e	3.148 (2)
C1···C16c	3.054 (2)	C16c···C16e	2.545 (2)
F1—P1—F2	89.56 (5)	C12a—C16a—C16b	117.8 (1)
F1—P1—F3	89.94 (6)	C16—C16a—C16b	123.3 (1)
F1—P1—F4	89.95 (7)	C10a—C16b—C16a	118.0 (1)
F1—P1—F5	90.68 (6)	C10a—C16b—C16c	118.5 (1)
F1—P1—F6	179.10 (6)	C16a—C16b—C16c	123.5 (1)
F2—P1—F3	90.15 (6)	N8a—C16c—C16b	116.4 (1)
F2—P1—F4	90.28 (6)	N8a—C16c—C16d	116.4 (1)
F2—P1—F5	179.75 (6)	C16b—C16c—C16d	127.2 (1)
F2—P1—F6	89.53 (6)	C6a—C16d—C16c	118.4 (1)
F3—P1—F4	179.55 (6)	C6a—C16d—C16e	118.2 (1)
F3—P1—F5	89.85 (6)	C16c—C16d—C16e	123.3 (1)
F3—P1—F6	90.04 (7)	C1—C16e—C4a	117.8 (1)
F4—P1—F5	89.72 (6)	C1—C16e—C16d	123.8 (1)
F4—P1—F6	90.08 (7)	C4a—C16e—C16d	118.1 (1)
F5—P1—F6	90.22 (6)	C16e—C1—H1	119.6
C8—N8a—C9	118.0 (1)	C2—C1—H1	119.4
C8—N8a—C16c	120.8 (1)	C1—C2—H2	119.1
C9—N8a—C16c	121.2 (1)	C3—C2—H2	120.2
C2—C1—C16e	121.0 (1)	C2—C3—H3	119.7
C1—C2—C3	120.7 (1)	C4—C3—H3	120.7
C2—C3—C4	119.5 (2)	C3—C4—H4	119.5
C3—C4—C4a	121.0 (1)	C4a—C4—H4	119.1
C4—C4a—C5	120.2 (1)	C4a—C5—H5	117.1
C4—C4a—C16e	119.7 (1)	C6—C5—H5	121.6
C5—C4a—C16e	119.8 (1)	C5—C6—H6	117.9
C4a—C5—C6	121.0 (1)	C6a—C6—H6	121.4
C5—C6—C6a	120.7 (1)	C6a—C7—H7	118.6
C6—C6a—C7	120.8 (1)	C8—C7—H7	120.5
C6—C6a—C16d	120.4 (1)	N8a—C8—H8	111.1
C7—C6a—C16d	118.7 (1)	C7—C8—H8	127.9
C6a—C7—C8	120.5 (1)	N8a—C9—H9	113.4
N8a—C8—C7	120.9 (2)	C10—C9—H9	125.6
N8a—C9—C10	120.9 (2)	C9—C10—H10	120.1
C9—C10—C10a	120.0 (2)	C10a—C10—H10	119.4
C10—C10a—C11	120.5 (1)	C10a—C11—H11	116.7
C10—C10a—C16b	119.0 (1)	C12—C11—H11	122.3
C11—C10a—C16b	120.4 (1)	C11—C12—H12	122.2
C10a—C11—C12	120.9 (2)	C12a—C12—H12	117.5
C11—C12—C12a	120.0 (1)	C12a—C13—H13	116.7
C12—C12a—C13	120.4 (1)	C14—C13—H13	122.1
C12—C12a—C16a	120.4 (1)	C13—C14—H14	125.7
C13—C12a—C16a	119.0 (1)	C15—C14—H14	114.6
C12a—C13—C14	121.2 (1)	C14—C15—H15	120.3
C13—C14—C15	119.7 (2)	C16—C15—H15	119.4
C14—C15—C16	120.5 (1)	C15—C16—H16	117.7
C15—C16—C16a	120.5 (1)	C16a—C16—H16	121.7
C12a—C16a—C16	118.6 (1)
N8a—C9—C10—C10a	9.0 (2)	C8—N8a—C16c—C16b	162.7 (1)
N8a—C16c—C16b—C10a	23.3 (2)	C8—N8a—C16c—C16d	−18.5 (2)
N8a—C16c—C16b—C16a	−153.1 (1)	C8—C7—C6a—C16d	−4.7 (2)
N8a—C16c—C16d—C16e	−153.0 (1)	C9—N8a—C16c—C16b	−17.2 (2)
N8a—C16c—C16d—C6a	23.4 (2)	C9—N8a—C16c—C16d	161.6 (1)
N8a—C8—C7—C6a	10.2 (2)	C9—C10—C10a—C11	175.1 (1)
C1—C2—C3—C4	−4.0 (2)	C9—C10—C10a—C16b	−2.3 (2)
C1—C16e—C4a—C4	−7.0 (2)	C10—C9—N8a—C16c	1.1 (2)
C1—C16e—C4a—C5	167.2 (1)	C10—C10a—C11—C12	−175.3 (1)
C1—C16e—C16d—C6a	−158.3 (1)	C10—C10a—C16b—C16a	162.5 (1)
C1—C16e—C16d—C16c	18.2 (2)	C10—C10a—C16b—C16c	−14.1 (2)
C2—C1—C16e—C4a	4.1 (2)	C10a—C11—C12—C12a	9.0 (2)
C2—C1—C16e—C16d	177.5 (1)	C10a—C16b—C16a—C12a	16.6 (2)
C2—C3—C4—C4a	0.9 (2)	C10a—C16b—C16a—C16	−157.3 (1)
C3—C2—C1—C16e	1.4 (2)	C10a—C16b—C16c—C16d	−155.4 (1)
C3—C4—C4a—C5	−169.5 (1)	C11—C10a—C16b—C16a	−14.9 (2)
C3—C4—C4a—C16e	4.6 (2)	C11—C10a—C16b—C16c	168.5 (1)
C4—C4a—C5—C6	169.2 (1)	C11—C12—C12a—C13	168.4 (1)
C4—C4a—C16e—C16d	179.2 (1)	C11—C12—C12a—C16a	−6.7 (2)
C4a—C5—C6—C6a	7.8 (2)	C12—C11—C10a—C16b	2.0 (2)
C4a—C16e—C16d—C6a	15.1 (2)	C12—C12a—C13—C14	−171.3 (1)
C4a—C16e—C16d—C16c	−168.4 (1)	C12—C12a—C16a—C16	168.0 (1)
C5—C4a—C16e—C16d	−6.7 (2)	C12—C12a—C16a—C16b	−6.2 (2)
C5—C6—C6a—C7	−175.7 (2)	C12a—C13—C14—C15	1.9 (2)
C5—C6—C6a—C16d	1.2 (2)	C12a—C16a—C16—C15	4.9 (2)
C6—C5—C4a—C16e	−4.9 (2)	C12a—C16a—C16b—C16c	−166.9 (1)
C6—C6a—C7—C8	172.3 (2)	C13—C12a—C16a—C16	−7.1 (2)
C6—C6a—C16d—C16c	170.7 (1)	C13—C12a—C16a—C16b	178.6 (1)
C6—C6a—C16d—C16e	−12.7 (2)	C13—C14—C15—C16	−4.2 (2)
C6a—C16d—C16c—C16b	−157.9 (1)	C14—C13—C12a—C16a	3.8 (2)
C7—C6a—C16d—C16c	−12.3 (2)	C14—C15—C16—C16a	0.7 (2)
C7—C6a—C16d—C16e	164.3 (1)	C15—C16—C16a—C16b	178.8 (1)
C7—C8—N8a—C9	−178.3 (1)	C16—C16a—C16b—C16c	19.1 (2)
C7—C8—N8a—C16c	1.8 (2)	C16a—C16b—C16c—C16d	28.2 (2)
C8—N8a—C9—C10	−178.8 (1)	C16b—C16c—C16d—C16e	25.7 (2)

Symmetry codes: (i) −x+1, y+1/2, −z+3/2; (ii) −x+2, y+1/2, −z+3/2; (iii) x, −y+1/2, z−1/2; (iv) x−1, y, z; (v) x−1, −y+1/2, z−1/2; (vi) −x+1, −y+1, −z+1; (vii) −x+2, −y, −z+1; (viii) −x+1, −y, −z+1; (ix) −x+2, y−1/2, −z+3/2; (x) x+1, y, z; (xi) −x+2, −y, −z+2.