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Journal logoCRYSTALLOGRAPHIC
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ISSN: 2056-9890

4,4′-(Anthracene-9,10-di­yl)di­benzoic acid di­methyl­formamide disolvate

aSchool of Food and Biological Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, People's Republic of China, and bCollege of Chemistry and Chemical Engineering, Luoyang Normal University, Luoyang 471022, People's Republic of China
*Correspondence e-mail: lihong@zzuli.edu.cn

(Received 26 March 2009; accepted 22 April 2009; online 7 May 2009)

In the title compound, C28H18O4·2C3H7NO, the dihedral angle between the benzene rings and the anthracene system is 74.05 (12)°. A crystallographic inversion centre is located in the middle of the anthracene unit. The dimethyl­formamide solvent mol­ecules are partially disordered over two positions of approximately equal occupancy [0.529 (6):0.471 (6)]. Inter­molecular O—H⋯O hydrogen bonds with the major occupancy formamide O atom as acceptor result in the formation of 2:1 solvate–complex aggregates, which are alternately linked to shorter solvate units via weak inter­molecular C—H⋯O contacts generated from the rotational disorder of the formamide O atom (minor occupancy component). Weak C—H⋯π inter­actions between the solvent mol­ecules as the donor and the outer anthracene rings support these contacts in the crystal structure for both disorder components.

Related literature

For the structure of 4-(2,5-dihexyl­oxyphen­yl)benzoic acid and the syntheses of related compounds, see: Li et al. (2008[Li, H., Zhang, L., Liu, Y.-Q., Mao, D.-B. & Zhang, W.-Y. (2008). Acta Cryst. E64, o2094.]). For palladium-catalysed Suzuki coupling reactions, see: Xu et al. (2006[Xu, C., Gong, J. F., Yue, S. F., Zhu, Y. & Wu, Y. J. (2006). Dalton Trans. pp. 4730-4739.], 2008[Xu, C., Gong, J. F., Guo, T., Zhang, Y. H. & Wu, Y. J. (2008). J. Mol. Catal. A Chem. 279, 69-76.]); Li et al. (2006[Li, H., Wu, Y. J. & Yan, W. B. (2006). J. Organomet. Chem. 691, 5688-5696.]) and literature cited therein.

[Scheme 1]

Experimental

Crystal data
  • C28H18O4·2C3H7NO

  • Mr = 564.62

  • Triclinic, [P \overline 1]

  • a = 7.3692 (15) Å

  • b = 8.9981 (18) Å

  • c = 12.124 (2) Å

  • α = 71.157 (3)°

  • β = 77.640 (3)°

  • γ = 79.754 (3)°

  • V = 738.0 (3) Å3

  • Z = 1

  • Mo Kα radiation

  • μ = 0.09 mm−1

  • T = 295 K

  • 0.23 × 0.16 × 0.06 mm

Data collection
  • Bruker SMART APEX CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Sheldrick, 1996[Sheldrick, G. M. (1996). SADABS. University of Göttingen, Germany.]) Tmin = 0.980, Tmax = 0.994

  • 5691 measured reflections

  • 2721 independent reflections

  • 1467 reflections with I > 2σ(I)

  • Rint = 0.028

Refinement
  • R[F2 > 2σ(F2)] = 0.053

  • wR(F2) = 0.162

  • S = 1.02

  • 2721 reflections

  • 203 parameters

  • H-atom parameters constrained

  • Δρmax = 0.16 e Å−3

  • Δρmin = −0.20 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
O2—H2D⋯O3i 0.82 1.79 2.603 (4) 170
C5—H5⋯O3′ 0.93 2.63 3.478 (5) 152
C16—H16ACg1 0.96 2.91 3.485 (3) 120
Symmetry code: (i) -x, -y, -z+1. Cg1 is the centroid of the anthracene ring C8,C9,C10,C12A–C14A.

Data collection: APEX2 (Bruker, 2004[Bruker (2004). APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 2004[Bruker (2004). APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); molecular graphics: SHELXTL (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); software used to prepare material for publication: SHELXTL and PLATON (Spek, 2009[Spek, A. L. (2009). Acta Cryst. D65, 148-155.]).

Supporting information


Comment top

Cyclopalladated ferrocenylimine complexs with monophosphino ligands were successfully used as catalysts for Suzuki reactions (Xu et al. 2006; Li et al., 2006; Xu et al. 2008). We have recently reported that the structure of 4-(2,5-dihexyloxyphenyl)benzoic acid was obtained from the Suzuki coupling reaction (Li et al., 2008). The title compound was derived from the Suzuki reaction of 9,10-dibromoanthracene and 4-carboxyphenylboronic acid.

In the title compound (Fig.1), the dihedral angle between benzene rings and anthracene rings is 74.05 (12)°. A crystallographic inversion centre is in the middle of the anthracene unit, and an approximate two-fold pseudo rotation axis is running along the plane of the anthracene unit. The dimethylformamide solvent molecules are partially disordered over two positions, O3 and O3', of approximately equal occupancy, (0.529 (6) and 0.471 (6), respectively. The different intermolecular hydrogen bonding contacts are shown in Fig. 1 (O3' is the acceptor) and Fig. 2 (with O3 as acceptor). The intermolecular O—H···O hydrogen bonds result in the formation of long 2:1 solvate:complex aggregates, (Table 1) which are alternately linked via weak intermolecular C—H···O contacts generated from the rotational disorder of the formamide oxygen atom (0.471 (6) site occupancy). C—H···π interactions support these contacts in the crystal structure foming a one-dimensional supramolecular architecture (Fig. 1 and Fig. 2).

Related literature top

For the structure of 4-(2,5-dihexyloxyphenyl)benzoic acid and the syntheses of related structures, see: Li et al. (2008). For palladium-catalysed Suzuki coupling reactions, see: Xu et al. (2006, 2008); Li et al. (2006) and literature cited therein. Cg1 is the

centroid of the anthracene ring C8, C9, C10, C12A–C14A.

Experimental top

The title compound was obtained from the Suzuki coupling reaction of 9,10-dibromoanthracene and 4-carboxyphenylboronic acid as described in the literature (Li et al., 2008) and recrystallized from dimethylformamide at room temperature to give the desired crystals suitable for single-crystal X-ray diffraction.

Refinement top

H atoms attached to C atoms of the title compound were placed in geometrically idealized positions and treated as riding with C—H distances constrained to 0.93 (aromatic CH), or 0.96 Å (methyl CH3), and constrained to ride on their parent atoms, with Uiso(H) = 1.2Ueq(C) (1.5Ueq for methyl H). The atom-site occupancies for the rotational disordered formamide oxygen atoms O3 and O3' refined to a ratio of 0.53/0.47.

Alert levels A and B for short intermolecular O1···O3' and H2D···H15' contacts with distances of2.50 Å and 2.01 Å may be explained by the difficulties to split the whole solvent molecule due to the pseudo two-fold rotation of the methyl groups around the N1—C15 axis. BUMP instruction or splitting of the whole solvent molecule resulted in unstable refinements. Introduction of shift-limiting restraints (DAMP instruction) resulted in larger R-values without improving the geometries. Therefore the partial disorder refinement (O3, O3', H15, H15') was preferred as a compromise.

Computing details top

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT (Bruker, 2004); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2009).

Figures top
[Figure 1] Fig. 1. The molecular structure of the title compound with displacement ellipsoids at the 30% probability level (suffix A denotes the symmetry code: -x + 1, -y + 1, -z). Weak C—H···π and C—H···O hydrogen bonding contacts are indicated with dashed lines. Cg1 is the centroid of the anthracene ring C8, C9, C10, C12A, C13A, C14A.
[Figure 2] Fig. 2. Partial view of the crystal packing showing the intermolecular O—H···O hydrogen bonds and weak C—H···π interactions. Cg1 is the centroid of the anthracene ring (C8, C9, C10, C12A, C13A, C14A).
4,4'-(Anthracene-9,10-diyl)dibenzoic acid dimethylformamide disolvate top
Crystal data top
C28H18O4·2C3H7NOZ = 1
Mr = 564.62F(000) = 298
Triclinic, P1Dx = 1.270 Mg m3
Hall symbol: -P 1Mo Kα radiation, λ = 0.71073 Å
a = 7.3692 (15) ÅCell parameters from 879 reflections
b = 8.9981 (18) Åθ = 2.9–22.0°
c = 12.124 (2) ŵ = 0.09 mm1
α = 71.157 (3)°T = 295 K
β = 77.640 (3)°Block, colourless
γ = 79.754 (3)°0.23 × 0.16 × 0.06 mm
V = 738.0 (3) Å3
Data collection top
Bruker SMART APEX CCD area-detector
diffractometer
2721 independent reflections
Radiation source: fine-focus sealed tube1467 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.028
ϕ and ω scansθmax = 25.5°, θmin = 2.4°
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
h = 88
Tmin = 0.980, Tmax = 0.994k = 109
5691 measured reflectionsl = 1414
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)] = 0.053Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.162H-atom parameters constrained
S = 1.02 w = 1/[σ2(Fo2) + (0.0732P)2 + 0.04P]
where P = (Fo2 + 2Fc2)/3
2721 reflections(Δ/σ)max < 0.001
203 parametersΔρmax = 0.16 e Å3
0 restraintsΔρmin = 0.20 e Å3
Crystal data top
C28H18O4·2C3H7NOγ = 79.754 (3)°
Mr = 564.62V = 738.0 (3) Å3
Triclinic, P1Z = 1
a = 7.3692 (15) ÅMo Kα radiation
b = 8.9981 (18) ŵ = 0.09 mm1
c = 12.124 (2) ÅT = 295 K
α = 71.157 (3)°0.23 × 0.16 × 0.06 mm
β = 77.640 (3)°
Data collection top
Bruker SMART APEX CCD area-detector
diffractometer
2721 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
1467 reflections with I > 2σ(I)
Tmin = 0.980, Tmax = 0.994Rint = 0.028
5691 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0530 restraints
wR(F2) = 0.162H-atom parameters constrained
S = 1.02Δρmax = 0.16 e Å3
2721 reflectionsΔρmin = 0.20 e Å3
203 parameters
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. 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 (Å2) top
xyzUiso*/UeqOcc. (<1)
C150.5707 (5)0.2790 (4)0.4860 (3)0.0742 (9)0.529 (6)
H150.47710.25950.45360.089*0.529 (6)
O30.5840 (5)0.2039 (5)0.5938 (4)0.0918 (18)0.529 (6)
C15'0.5707 (5)0.2790 (4)0.4860 (3)0.0742 (9)0.471 (6)
H15'0.59440.21410.55980.089*0.471 (6)
O3'0.4309 (7)0.2700 (6)0.4479 (4)0.096 (2)0.471 (6)
N10.6843 (3)0.3826 (3)0.41928 (19)0.0637 (6)
C160.6620 (5)0.4705 (4)0.2994 (3)0.0999 (12)
H16A0.54980.44760.28310.150*
H16B0.76770.44070.24590.150*
H16C0.65350.58160.28950.150*
C170.8377 (4)0.4104 (5)0.4627 (3)0.0945 (11)
H17A0.83750.34500.54290.142*
H17B0.82490.51960.45980.142*
H17C0.95320.38520.41460.142*
O10.1924 (3)0.0937 (3)0.42504 (19)0.1024 (9)
O20.3377 (3)0.0181 (3)0.2730 (2)0.1090 (9)
H2D0.41400.07280.32130.163*
C10.0616 (3)0.0915 (3)0.2520 (2)0.0496 (6)
C20.0651 (4)0.1757 (3)0.1348 (2)0.0638 (8)
H20.15890.16620.09780.077*
C30.0713 (4)0.2746 (3)0.0719 (2)0.0594 (7)
H30.06690.33130.00680.071*
C40.2133 (3)0.2901 (3)0.1243 (2)0.0445 (6)
C50.2169 (3)0.2037 (3)0.2414 (2)0.0525 (7)
H50.31170.21170.27830.063*
C60.0805 (3)0.1053 (3)0.3045 (2)0.0537 (7)
H60.08520.04800.38310.064*
C70.2053 (4)0.0146 (3)0.3219 (3)0.0643 (8)
C80.6573 (4)0.1754 (3)0.1369 (2)0.0640 (8)
H80.66110.08210.15520.077*
C90.5159 (4)0.2148 (3)0.0568 (2)0.0549 (7)
H90.42390.14770.02040.066*
C100.5040 (3)0.3575 (3)0.02629 (19)0.0432 (6)
C110.3592 (3)0.3985 (3)0.05850 (19)0.0419 (6)
C120.3533 (3)0.5398 (3)0.08512 (19)0.0419 (6)
C130.2061 (3)0.5896 (3)0.1681 (2)0.0514 (7)
H130.11100.52590.20590.062*
C140.2008 (4)0.7263 (3)0.1932 (2)0.0620 (8)
H140.10310.75540.24780.074*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
C150.066 (2)0.089 (2)0.066 (2)0.0197 (18)0.0072 (17)0.0164 (19)
O30.082 (3)0.114 (4)0.071 (3)0.054 (3)0.012 (2)0.006 (3)
C15'0.066 (2)0.089 (2)0.066 (2)0.0197 (18)0.0072 (17)0.0164 (19)
O3'0.087 (4)0.120 (4)0.079 (3)0.060 (3)0.015 (3)0.000 (3)
N10.0574 (14)0.0753 (17)0.0547 (14)0.0202 (12)0.0040 (11)0.0113 (12)
C160.088 (2)0.119 (3)0.071 (2)0.022 (2)0.0099 (18)0.004 (2)
C170.079 (2)0.125 (3)0.086 (2)0.045 (2)0.0063 (19)0.028 (2)
O10.0933 (16)0.128 (2)0.0722 (15)0.0639 (15)0.0176 (13)0.0188 (14)
O20.0826 (16)0.137 (2)0.0938 (17)0.0672 (15)0.0245 (14)0.0188 (15)
C10.0454 (14)0.0470 (15)0.0548 (16)0.0134 (12)0.0041 (12)0.0114 (12)
C20.0535 (16)0.0701 (19)0.0652 (18)0.0227 (14)0.0159 (14)0.0045 (15)
C30.0605 (16)0.0624 (18)0.0512 (15)0.0233 (14)0.0133 (13)0.0001 (13)
C40.0460 (14)0.0408 (14)0.0468 (14)0.0098 (11)0.0061 (11)0.0115 (12)
C50.0541 (15)0.0553 (16)0.0474 (15)0.0189 (13)0.0085 (12)0.0077 (13)
C60.0593 (16)0.0519 (16)0.0453 (14)0.0170 (13)0.0041 (12)0.0058 (12)
C70.0506 (17)0.0634 (19)0.074 (2)0.0191 (14)0.0030 (15)0.0121 (16)
C80.085 (2)0.0442 (16)0.0605 (17)0.0144 (14)0.0043 (15)0.0192 (14)
C90.0667 (17)0.0400 (15)0.0549 (16)0.0186 (12)0.0012 (13)0.0107 (12)
C100.0494 (14)0.0359 (14)0.0416 (13)0.0110 (11)0.0061 (11)0.0054 (11)
C110.0453 (13)0.0386 (14)0.0391 (13)0.0119 (10)0.0083 (11)0.0034 (11)
C120.0426 (13)0.0404 (14)0.0404 (13)0.0080 (10)0.0063 (10)0.0074 (11)
C130.0485 (14)0.0494 (16)0.0499 (15)0.0125 (12)0.0041 (12)0.0104 (12)
C140.0724 (18)0.0492 (17)0.0573 (17)0.0080 (14)0.0079 (14)0.0178 (14)
Geometric parameters (Å, º) top
C15—O31.279 (4)C3—H30.9300
C15—N11.314 (4)C4—C51.385 (3)
C15—H150.9300C4—C111.499 (3)
N1—C171.434 (4)C5—C61.389 (3)
N1—C161.441 (3)C5—H50.9300
C16—H16A0.9600C6—H60.9300
C16—H16B0.9600C8—C91.346 (3)
C16—H16C0.9600C8—C14i1.406 (4)
C17—H17A0.9600C8—H80.9300
C17—H17B0.9600C9—C101.430 (3)
C17—H17C0.9600C9—H90.9300
O1—C71.238 (3)C10—C111.403 (3)
O2—C71.255 (3)C10—C12i1.438 (3)
O2—H2D0.8200C11—C121.401 (3)
C1—C61.378 (3)C12—C131.428 (3)
C1—C21.381 (3)C12—C10i1.438 (3)
C1—C71.485 (3)C13—C141.353 (3)
C2—C31.392 (3)C13—H130.9300
C2—H20.9300C14—C8i1.406 (4)
C3—C41.382 (3)C14—H140.9300
O3—C15—N1122.5 (4)C4—C5—C6120.7 (2)
O3—C15—H15118.8C4—C5—H5119.6
N1—C15—H15118.8C6—C5—H5119.6
C15—N1—C17121.0 (3)C1—C6—C5120.8 (2)
C15—N1—C16121.5 (3)C1—C6—H6119.6
C17—N1—C16117.5 (2)C5—C6—H6119.6
N1—C16—H16A109.5O1—C7—O2122.7 (3)
N1—C16—H16B109.5O1—C7—C1119.7 (3)
H16A—C16—H16B109.5O2—C7—C1117.6 (3)
N1—C16—H16C109.5C9—C8—C14i120.8 (3)
H16A—C16—H16C109.5C9—C8—H8119.6
H16B—C16—H16C109.5C14i—C8—H8119.6
N1—C17—H17A109.5C8—C9—C10121.5 (2)
N1—C17—H17B109.5C8—C9—H9119.2
H17A—C17—H17B109.5C10—C9—H9119.2
N1—C17—H17C109.5C11—C10—C9122.0 (2)
H17A—C17—H17C109.5C11—C10—C12i119.9 (2)
H17B—C17—H17C109.5C9—C10—C12i118.1 (2)
C7—O2—H2D109.5C12—C11—C10119.9 (2)
C6—C1—C2118.9 (2)C12—C11—C4119.3 (2)
C6—C1—C7119.4 (2)C10—C11—C4120.8 (2)
C2—C1—C7121.6 (2)C11—C12—C13122.3 (2)
C1—C2—C3120.2 (2)C11—C12—C10i120.2 (2)
C1—C2—H2119.9C13—C12—C10i117.5 (2)
C3—C2—H2119.9C14—C13—C12122.0 (2)
C4—C3—C2121.2 (2)C14—C13—H13119.0
C4—C3—H3119.4C12—C13—H13119.0
C2—C3—H3119.4C13—C14—C8i120.0 (2)
C3—C4—C5118.1 (2)C13—C14—H14120.0
C3—C4—C11121.9 (2)C8i—C14—H14120.0
C5—C4—C11119.9 (2)
O3—C15—N1—C173.6 (5)C8—C9—C10—C11178.9 (2)
O3—C15—N1—C16177.4 (4)C8—C9—C10—C12i0.9 (4)
C6—C1—C2—C31.1 (4)C9—C10—C11—C12179.8 (2)
C7—C1—C2—C3179.7 (2)C12i—C10—C11—C120.4 (4)
C1—C2—C3—C40.5 (4)C9—C10—C11—C42.2 (3)
C2—C3—C4—C50.3 (4)C12i—C10—C11—C4177.6 (2)
C2—C3—C4—C11178.8 (2)C3—C4—C11—C12106.8 (3)
C3—C4—C5—C60.5 (4)C5—C4—C11—C1272.3 (3)
C11—C4—C5—C6178.6 (2)C3—C4—C11—C1075.2 (3)
C2—C1—C6—C50.9 (4)C5—C4—C11—C10105.7 (3)
C7—C1—C6—C5179.9 (2)C10—C11—C12—C13178.1 (2)
C4—C5—C6—C10.1 (4)C4—C11—C12—C133.9 (3)
C6—C1—C7—O12.6 (4)C10—C11—C12—C10i0.4 (4)
C2—C1—C7—O1176.6 (3)C4—C11—C12—C10i177.6 (2)
C6—C1—C7—O2176.5 (3)C11—C12—C13—C14179.8 (2)
C2—C1—C7—O24.3 (4)C10i—C12—C13—C141.3 (4)
C14i—C8—C9—C100.3 (4)C12—C13—C14—C8i0.1 (4)
Symmetry code: (i) x+1, y+1, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O2—H2D···O3ii0.821.792.603 (4)170
C5—H5···O30.932.633.478 (5)152
C16—H16A···Cg10.962.913.485 (3)120
Symmetry code: (ii) x, y, z+1.

Experimental details

Crystal data
Chemical formulaC28H18O4·2C3H7NO
Mr564.62
Crystal system, space groupTriclinic, P1
Temperature (K)295
a, b, c (Å)7.3692 (15), 8.9981 (18), 12.124 (2)
α, β, γ (°)71.157 (3), 77.640 (3), 79.754 (3)
V3)738.0 (3)
Z1
Radiation typeMo Kα
µ (mm1)0.09
Crystal size (mm)0.23 × 0.16 × 0.06
Data collection
DiffractometerBruker SMART APEX CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 1996)
Tmin, Tmax0.980, 0.994
No. of measured, independent and
observed [I > 2σ(I)] reflections
5691, 2721, 1467
Rint0.028
(sin θ/λ)max1)0.606
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.053, 0.162, 1.02
No. of reflections2721
No. of parameters203
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.16, 0.20

Computer programs: APEX2 (Bruker, 2004), SAINT (Bruker, 2004), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2009).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O2—H2D···O3i0.821.792.603 (4)170.2
C5—H5···O3'0.932.633.478 (5)152.2
C16—H16A···Cg10.962.913.485 (3)120
Symmetry code: (i) x, y, z+1.
 

Acknowledgements

This work was supported by the Doctoral Foundation of Zhengzhou University of Light Industry (000420).

References

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