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Mol­ecular crystals exhibiting polar symmetry are important paradigms for developing new electrooptical materials. Though accessing bulk polarity still presents a significant challenge, in some cases it may be rationalized as being associated with the specific mol­ecular shapes and symmetries and subtle features of supra­molecular inter­actions. In the crystal structure of 3,5,7-tri­nitro-1-aza­adam­an­tane, C9H12N4O6, the polar symmetry of the mol­ecular arrangement is a result of com­plementary prerequisites, namely the C3v symmetry of the mol­ecules is suited to the generation of polar stacks and the inherent asymmetry of the principal supra­molecular bonding, as is provided by NO2(lone pair)...NO2(π-hole) inter­actions. These bonds arrange the mol­ecules into a trigonal network. In spite of the apparent simplicity, the structure comprises three unique molecules (Z′ = 1 \over 3 + 1 \over 3 + 1 \over 3), two of which are donors and acceptors of three N...O inter­actions and the third being primarily important for weak C—H...O hydrogen bonding. These distinct structural roles agree with the results of Hirshfeld surface analysis. A set of weak C—H...O and C—H...N hydrogen bonds yields three kinds of stacks. The orientation of the stacks is identical and therefore the polarity of each mol­ecule contributes additively to the net dipole moment of the crystal. This suggests a special potential of asymmetric NO2(lone pair)...NO2(π-hole) inter­actions for the supra­molecular synthesis of acentric materials.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S2053229620006762/vp3006sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2053229620006762/vp3006Isup2.hkl
Contains datablock I

CCDC reference: 2004782

Computing details top

Data collection: IPDS (Stoe & Cie, 2000); cell refinement: IPDS (Stoe & Cie, 2000); data reduction: IPDS (Stoe & Cie, 2000); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2018 (Sheldrick, 2015); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: WinGX (Farrugia, 1999).

2,5,7-Trinitro-1-azatricyclo[3.3.1.13.7]decane top
Crystal data top
C9H12N4O6Dx = 1.622 Mg m3
Mr = 272.23Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3Cell parameters from 5172 reflections
a = 12.7917 (14) Åθ = 3.2–29.2°
c = 5.8996 (6) ŵ = 0.14 mm1
V = 836.0 (2) Å3T = 200 K
Z = 3Prism, colorless
F(000) = 4260.22 × 0.20 × 0.17 mm
Data collection top
Stoe Image plate diffraction system IPDS-2T
diffractometer
2451 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tubeRint = 0.038
φ oscillation scansθmax = 29.2°, θmin = 3.2°
Absorption correction: numerical
[X-RED (Stoe & Cie, 2001) and X-SHAPE (Stoe & Cie, 1999)]
h = 1716
Tmin = 0.654, Tmax = 0.792k = 1715
5172 measured reflectionsl = 88
2961 independent reflections
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.032Hydrogen site location: difference Fourier map
wR(F2) = 0.063All H-atom parameters refined
S = 0.92 w = 1/[σ2(Fo2) + (0.033P)2]
where P = (Fo2 + 2Fc2)/3
2961 reflections(Δ/σ)max < 0.001
221 parametersΔρmax = 0.14 e Å3
1 restraintΔρmin = 0.19 e Å3
Special details top

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

Refinement. Refined as a 2-component twin.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
O1A0.2573 (3)0.2891 (2)0.2900 (6)0.0475 (7)
O2A0.3275 (2)0.1737 (3)0.1919 (5)0.0413 (6)
N1A0.0000000.0000000.1998 (7)0.0183 (9)
N2A0.2452 (3)0.1945 (3)0.2164 (4)0.0267 (6)
C1A0.1201 (3)0.0952 (3)0.1220 (5)0.0205 (6)
C2A0.1207 (3)0.0967 (3)0.1406 (5)0.0196 (6)
C3A0.0253 (3)0.1249 (3)0.2281 (5)0.0203 (6)
H1A0.182 (3)0.077 (3)0.183 (5)0.019 (8)*
H2A0.131 (3)0.167 (4)0.173 (6)0.017 (8)*
H3A0.039 (3)0.197 (4)0.180 (5)0.011 (8)*
H4A0.024 (3)0.118 (3)0.396 (6)0.018 (8)*
O1B0.3760 (2)0.3259 (3)0.2319 (5)0.0362 (6)
O2B0.5076 (3)0.4797 (3)0.0412 (6)0.0488 (8)
N1B0.6666670.3333330.5825 (7)0.0224 (10)
N2B0.4789 (3)0.3926 (3)0.1637 (4)0.0259 (6)
C1B0.5760 (3)0.3643 (3)0.5048 (5)0.0241 (6)
C2B0.5754 (3)0.3651 (3)0.2425 (5)0.0178 (6)
C3B0.5402 (3)0.2387 (3)0.1525 (5)0.0183 (6)
H1B0.599 (3)0.443 (4)0.554 (5)0.016 (8)*
H2B0.506 (3)0.312 (3)0.567 (5)0.008 (7)*
H3B0.466 (3)0.182 (3)0.207 (5)0.012 (8)*
H4B0.549 (4)0.243 (3)0.006 (6)0.024 (9)*
O1C0.1491 (3)0.3784 (3)0.2511 (5)0.0462 (7)
O2C0.0360 (3)0.3839 (3)0.5158 (6)0.0521 (9)
N1C0.3333330.6666670.8362 (8)0.0264 (11)
N2C0.1322 (3)0.4261 (2)0.4153 (5)0.0264 (6)
C1C0.2356 (3)0.5486 (3)0.7592 (5)0.0248 (7)
C2C0.2346 (3)0.5470 (3)0.4983 (5)0.0201 (6)
C3C0.3551 (3)0.5649 (3)0.4084 (5)0.0205 (6)
H1C0.160 (4)0.543 (3)0.807 (6)0.025 (9)*
H2C0.245 (4)0.484 (4)0.813 (6)0.024 (9)*
H3C0.347 (3)0.562 (3)0.242 (5)0.010 (8)*
H4C0.370 (3)0.504 (3)0.463 (5)0.014 (7)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O1A0.0353 (15)0.0306 (15)0.0659 (16)0.0084 (12)0.0138 (14)0.0198 (14)
O2A0.0191 (13)0.0453 (16)0.0532 (15)0.0113 (12)0.0059 (11)0.0085 (13)
N1A0.0182 (14)0.0182 (14)0.019 (2)0.0091 (7)0.0000.000
N2A0.0199 (14)0.0239 (14)0.0246 (13)0.0022 (12)0.0032 (10)0.0011 (11)
C1A0.0189 (16)0.0209 (16)0.0188 (13)0.0078 (13)0.0014 (12)0.0020 (12)
C2A0.0191 (15)0.0211 (15)0.0188 (12)0.0102 (13)0.0002 (12)0.0010 (11)
C3A0.0226 (15)0.0201 (16)0.0194 (15)0.0116 (13)0.0018 (11)0.0028 (12)
O1B0.0184 (12)0.0408 (15)0.0510 (15)0.0161 (12)0.0015 (10)0.0020 (12)
O2B0.0373 (17)0.0530 (19)0.0662 (17)0.0300 (15)0.0032 (13)0.0265 (15)
N1B0.0256 (16)0.0256 (16)0.016 (2)0.0128 (8)0.0000.000
N2B0.0243 (15)0.0290 (16)0.0296 (14)0.0173 (12)0.0024 (11)0.0039 (12)
C1B0.0257 (18)0.0283 (17)0.0197 (13)0.0146 (15)0.0058 (12)0.0023 (13)
C2B0.0150 (14)0.0193 (14)0.0208 (13)0.0099 (12)0.0022 (10)0.0019 (11)
C3B0.0164 (15)0.0180 (15)0.0197 (14)0.0079 (12)0.0014 (11)0.0011 (12)
O1C0.0374 (16)0.0329 (15)0.0592 (17)0.0107 (14)0.0005 (13)0.0216 (13)
O2C0.0251 (15)0.0407 (19)0.067 (2)0.0013 (14)0.0101 (13)0.0094 (15)
N1C0.0315 (17)0.0315 (17)0.016 (2)0.0157 (9)0.0000.000
N2C0.0235 (15)0.0186 (14)0.0358 (15)0.0094 (13)0.0017 (12)0.0001 (11)
C1C0.0251 (18)0.0264 (18)0.0221 (15)0.0123 (14)0.0047 (13)0.0051 (12)
C2C0.0171 (16)0.0156 (15)0.0236 (15)0.0052 (12)0.0005 (12)0.0008 (11)
C3C0.0201 (15)0.0191 (15)0.0230 (14)0.0103 (13)0.0018 (12)0.0012 (11)
Geometric parameters (Å, º) top
O1A—N2A1.220 (4)C1B—H1B0.94 (4)
O2A—N2A1.217 (4)C1B—H2B0.89 (3)
N1A—C1Ai1.478 (3)C2B—C3Biv1.523 (4)
N1A—C1Aii1.478 (3)C2B—C3B1.540 (4)
N1A—C1A1.478 (3)C3B—H3B0.92 (3)
N2A—C2A1.519 (4)C3B—H4B0.94 (4)
C1A—C2A1.549 (4)O1C—N2C1.220 (4)
C1A—H1A1.00 (4)O2C—N2C1.222 (4)
C1A—H2A0.91 (4)N1C—C1C1.470 (4)
C2A—C3A1.525 (5)N1C—C1Cv1.470 (4)
C2A—C3Ai1.534 (4)N1C—C1Cvi1.470 (4)
C3A—H3A0.89 (4)N2C—C2C1.524 (4)
C3A—H4A0.99 (3)C1C—C2C1.539 (4)
O1B—N2B1.225 (4)C1C—H1C0.97 (4)
O2B—N2B1.219 (4)C1C—H2C0.95 (4)
N1B—C1Biii1.473 (4)C2C—C3Cv1.532 (4)
N1B—C1Biv1.473 (4)C2C—C3C1.535 (5)
N1B—C1B1.473 (4)C3C—H3C0.99 (3)
N2B—C2B1.517 (4)C3C—H4C0.94 (4)
C1B—C2B1.548 (4)
C1Ai—N1A—C1Aii110.82 (19)N2B—C2B—C3Biv110.2 (2)
C1Ai—N1A—C1A110.82 (19)N2B—C2B—C3B107.1 (2)
C1Aii—N1A—C1A110.82 (19)C3Biv—C2B—C3B111.0 (3)
O2A—N2A—O1A124.4 (3)N2B—C2B—C1B108.4 (2)
O2A—N2A—C2A116.7 (3)C3Biv—C2B—C1B110.3 (2)
O1A—N2A—C2A118.9 (3)C3B—C2B—C1B109.7 (3)
N1A—C1A—C2A108.5 (3)C2Biii—C3B—C2B106.2 (3)
N1A—C1A—H1A108 (2)C2Biii—C3B—H3B109 (2)
C2A—C1A—H1A111.4 (19)C2B—C3B—H3B110 (2)
N1A—C1A—H2A107 (2)C2Biii—C3B—H4B106 (2)
C2A—C1A—H2A109 (2)C2B—C3B—H4B108 (2)
H1A—C1A—H2A112 (3)H3B—C3B—H4B116 (3)
N2A—C2A—C3A109.8 (3)C1C—N1C—C1Cv110.9 (2)
N2A—C2A—C3Ai108.5 (3)C1C—N1C—C1Cvi110.9 (2)
C3A—C2A—C3Ai111.8 (3)C1Cv—N1C—C1Cvi110.9 (2)
N2A—C2A—C1A107.5 (2)O1C—N2C—O2C123.7 (3)
C3A—C2A—C1A110.0 (3)O1C—N2C—C2C119.1 (3)
C3Ai—C2A—C1A109.1 (3)O2C—N2C—C2C117.2 (3)
C2A—C3A—C2Aii106.6 (3)N1C—C1C—C2C108.7 (3)
C2A—C3A—H3A112 (2)N1C—C1C—H1C107 (2)
C2Aii—C3A—H3A111 (2)C2C—C1C—H1C107 (2)
C2A—C3A—H4A107 (2)N1C—C1C—H2C112 (2)
C2Aii—C3A—H4A107.5 (19)C2C—C1C—H2C109 (2)
H3A—C3A—H4A113 (3)H1C—C1C—H2C113 (3)
C1Biii—N1B—C1Biv110.8 (2)N2C—C2C—C3Cv107.1 (2)
C1Biii—N1B—C1B110.8 (2)N2C—C2C—C3C109.2 (3)
C1Biv—N1B—C1B110.8 (2)C3Cv—C2C—C3C111.1 (3)
O2B—N2B—O1B124.0 (3)N2C—C2C—C1C109.4 (3)
O2B—N2B—C2B119.0 (3)C3Cv—C2C—C1C109.8 (2)
O1B—N2B—C2B117.0 (3)C3C—C2C—C1C110.0 (3)
N1B—C1B—C2B108.7 (3)C2Cvi—C3C—C2C106.2 (3)
N1B—C1B—H1B109 (2)C2Cvi—C3C—H3C113 (2)
C2B—C1B—H1B107.5 (19)C2C—C3C—H3C104.9 (18)
N1B—C1B—H2B108 (2)C2Cvi—C3C—H4C109 (2)
C2B—C1B—H2B114.3 (19)C2C—C3C—H4C111 (2)
H1B—C1B—H2B109 (3)H3C—C3C—H4C112 (3)
C1Ai—N1A—C1A—C2A62.2 (3)O1B—N2B—C2B—C1B56.3 (4)
C1Aii—N1A—C1A—C2A61.3 (3)N1B—C1B—C2B—N2B178.0 (2)
O2A—N2A—C2A—C3A168.0 (3)N1B—C1B—C2B—C3Biv61.2 (3)
O1A—N2A—C2A—C3A14.4 (4)N1B—C1B—C2B—C3B61.4 (3)
O2A—N2A—C2A—C3Ai45.5 (4)N2B—C2B—C3B—C2Biii177.4 (2)
O1A—N2A—C2A—C3Ai136.9 (3)C3Biv—C2B—C3B—C2Biii62.2 (4)
O2A—N2A—C2A—C1A72.4 (4)C1B—C2B—C3B—C2Biii60.0 (3)
O1A—N2A—C2A—C1A105.2 (4)C1Cv—N1C—C1C—C2C62.0 (3)
N1A—C1A—C2A—N2A179.6 (2)C1Cvi—N1C—C1C—C2C61.7 (3)
N1A—C1A—C2A—C3A60.9 (3)O1C—N2C—C2C—C3Cv100.4 (3)
N1A—C1A—C2A—C3Ai62.1 (3)O2C—N2C—C2C—C3Cv77.8 (4)
N2A—C2A—C3A—C2Aii178.8 (2)O1C—N2C—C2C—C3C20.1 (4)
C3Ai—C2A—C3A—C2Aii60.7 (4)O2C—N2C—C2C—C3C161.7 (3)
C1A—C2A—C3A—C2Aii60.7 (3)O1C—N2C—C2C—C1C140.6 (3)
C1Biii—N1B—C1B—C2B61.9 (3)O2C—N2C—C2C—C1C41.2 (4)
C1Biv—N1B—C1B—C2B61.4 (3)N1C—C1C—C2C—N2C178.9 (2)
O2B—N2B—C2B—C3Biv1.6 (4)N1C—C1C—C2C—C3Cv61.6 (3)
O1B—N2B—C2B—C3Biv177.1 (3)N1C—C1C—C2C—C3C61.1 (3)
O2B—N2B—C2B—C3B119.2 (3)N2C—C2C—C3C—C2Cvi180.0 (2)
O1B—N2B—C2B—C3B62.0 (3)C3Cv—C2C—C3C—C2Cvi62.0 (4)
O2B—N2B—C2B—C1B122.4 (3)C1C—C2C—C3C—C2Cvi59.9 (3)
Symmetry codes: (i) x+y, x, z; (ii) y, xy, z; (iii) y+1, xy, z; (iv) x+y+1, x+1, z; (v) x+y, x+1, z; (vi) y+1, xy+1, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C1A—H2A···O1C0.90 (4)2.64 (4)3.536 (5)170 (3)
C3A—H4A···N1Avii0.99 (3)2.76 (3)3.678 (5)154 (3)
C1B—H1B···O2Cvi0.94 (4)2.58 (4)3.455 (5)154 (3)
C1B—H2B···O2Aviii0.89 (3)2.51 (3)3.392 (4)170 (2)
C3B—H4B···N1Bvii0.94 (4)2.79 (4)3.664 (5)156 (3)
C1C—H1C···O2B0.98 (4)2.56 (4)3.496 (4)161 (3)
C1C—H2C···O1Aviii0.96 (4)2.64 (4)3.479 (5)147 (3)
C3C—H4C···O1Aviii0.94 (4)2.80 (3)3.574 (4)140 (3)
C3C—H4C···O1B0.94 (4)2.69 (3)3.365 (4)129 (2)
C3C—H3C···N1Cvii0.98 (3)2.79 (3)3.678 (5)150 (3)
Symmetry codes: (vi) y+1, xy+1, z; (vii) x, y, z1; (viii) x, y, z+1.
Calculated interaction energies (kJ mol-1). top
TypeaPathR (Å)EeleEpolEdisErepEtot
Type 1A···B7.72-9.4-2.2-18.713.4-19.7
Type 2A···Bvii8.23-9.3-1.8-10.911.9-13.3
A···C8.27-8.1-1.6-9.16.1-13.9
B···Cvii8.60-7.0-1.1-7.15.3-11.1
Type 3A···Cvii7.70-8.8-2.2-16.59.0-19.7
B···C7.53-8.4-2.9-21.314.4-20.7
Type 4A···Avii5.90-5.7-5.3-32.618.8-26.7
B···Bvii5.90-9.0-5.3-34.620.8-30.8
C···Cvii5.90-11.6-4.0-35.822.0-32.8
Interaction energies were calculated employing the CE-B3LYP/6-31G(d,p) functional/basis set combination. The scale factors used to determine Etot: kele = 1.057, kpol = 0.740, kdis = 0.871 and krep = 0.618 (Mackenzie et al., 2017). Note: (a) for details of the interaction modes, See Fig. 6; R is the distance between the centroids of interacting molecules. [Symmetry code: (vii) x, y, z-1.]
 

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