Phenyl 3-meth­oxy-4-phen­oxy­benzoate

Zhou, J.; Zheng, S.; Chen, G.; Wang, W.; Du, Z.

doi:10.1107/S1600536811033678

organic compounds

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ISSN: 2056-9890

Volume 67| Part 9| September 2011| Page o2393

doi:10.1107/S1600536811033678

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Phenyl 3-methoxy-4-phenoxybenzoate

Jing Zhou,^a Shuai Zheng,^a Gang Chen,^a Wenjing Wang ^a and Zhenting Du ^a ^*

^aCollege of Science, Northwest A&F University, Yangling, Shaanxi 712100, People's Republic of China
^*Correspondence e-mail: duzt@nwsuaf.edu.cn

(Received 8 July 2011; accepted 18 August 2011; online 27 August 2011)

In the title molecule, C₂₀H₁₆O₄, the two outermost phenyl rings form dihedral angles of 79.80 (7) and 69.35 (7)° with the central benzene ring. In the crystal structure, weak intermolecular C—H⋯O interactions link the molecules into ribbons propagating along [1 $[\overline{1}]$ 0].

Related literature

For the general synthesis of derivatives of diphenylethers, see: Paul & Gupta (2004 ). For related structures, see: Chen et al. (2006 ); Petek et al. (2005 ); Chantrapromma et al.(2001 ); Nakamura et al. (1983 ); Gopal et al. (1980 ). For applications of diphenylether derivatives, see: Dey & Desiraju (2005 ); Wang et al. (2005 ).

Experimental

Crystal data

C₂₀H₁₆O₄
M_r = 320.33
Monoclinic, C 2/c
a = 11.0261 (10) Å
b = 11.9624 (11) Å
c = 24.961 (2) Å
β = 97.842 (1)°
V = 3261.5 (5) Å³
Z = 8
Mo Kα radiation
μ = 0.09 mm⁻¹
T = 298 K
0.49 × 0.42 × 0.40 mm

Data collection

Bruker SMART APEXII CCD area-detector diffractometer
Absorption correction: multi-scan (SADABS; Bruker, 2009 ) T_min = 0.957, T_max = 0.965
7972 measured reflections
2878 independent reflections
1785 reflections with I > 2σ(I)
R_int = 0.040

Refinement

R[F² > 2σ(F²)] = 0.041
wR(F²) = 0.118
S = 1.05
2878 reflections
219 parameters
H-atom parameters constrained
Δρ_max = 0.16 e Å⁻³
Δρ_min = −0.17 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
C8—H8C⋯O2ⁱ	0.96	2.52	3.408 (4)	153
C14—H14⋯O2ⁱⁱ	0.93	2.53	3.446 (3)	167
C20—H20⋯O3ⁱⁱ	0.93	2.60	3.468 (3)	155
Symmetry codes: (i) $[-x+{\script{1\over 2}}, -y+{\script{3\over 2}}, -z+1]$ ; (ii) -x+1, -y+1, -z+1.

Data collection: APEX2 (Bruker, 2009); cell refinement: SAINT (Bruker, 2009); data reduction: SAINT; 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.

Supporting information

Crystal structure: contains datablocks I, global. DOI: 10.1107/S1600536811033678/cv5133sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536811033678/cv5133Isup2.hkl

Supporting information file. DOI: 10.1107/S1600536811033678/cv5133Isup3.cml

checkCIF report

Comment top

4,4'-Dicarboxydiphenyl ether was widely used in polymer frameworks which show potential applications in microelectronics, nonlinear optics, porous materials and catalysis (Dey & Desiraju, 2005; Wang et al., 2005). The title compound (I) was obtained as unexpected product in the cyclization of diazonium salt to dibenzofuran. Accidently, in our pursuing new methodology of synthesis of dibenzofuran the diazonium salt was heated without any catalyst. In order to determine the structure of a new compound, it was characterized by single-crystal X-ray analysis.

In (I) (Fig. 1) all bond lengths and angles are normal and correspond to those observed in the related compounds (Chen et al., 2006; Petek et al., 2005; Chantrapromma et al., 2001; Nakamura et al., 1983; Gopal et al., 1980). Two utmost phenyl rings form the dihedral angles of 79.80 (7) and 69.35 (7)°, respectively, with the central benzene ring. In the crystal structure, weak intermolecular C—H···O interactions (Table 1) link molecules into ribbons propagated in [110].

Related literature top

For the general synthesis of derivatives of diphenylethers, see: Paul & Gupta (2004). For related structures, see: Chen et al. (2006); Petek et al. (2005); Chantrapromma et al.(2001); Nakamura et al. (1983); Gopal et al. (1980). For applications of diphenylether derivatives, see: Dey & Desiraju (2005); Wang et al. (2005). [Please provide details of H-atom treatment for the _publ_section_exptl_refinement section]

Experimental top

A solution of 2-(2-methoxy-4-(phenoxycarbonyl)phenoxy)benzenediazonium tetrafluroborate (0.868 g, 2 mmol) in ethanol (30 ml) was refluxed for 1 h. Then the solvent was evaporated and the residue was purified through column chromatography. The compound was dissolved in hexane, and white square crystals were obtained by slow evaporation of the solvent over one week.

Computing details top

Data collection: APEX2 (Bruker, 2009); cell refinement: APEX2 (Bruker, 2009); data reduction: SAINT (Bruker, 2009); 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).

Figures top

Fig. 1. The molecular structure of (I). Displacement ellipsoids are drawn at the 30% probability level.

Phenyl 3-methoxy-4-phenoxybenzoate top

Crystal data top

C₂₀H₁₆O₄	D_x = 1.305 Mg m⁻³
M_r = 320.33	Melting point: 383 K
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
a = 11.0261 (10) Å	Cell parameters from 2372 reflections
b = 11.9624 (11) Å	θ = 2.5–27.3°
c = 24.961 (2) Å	µ = 0.09 mm⁻¹
β = 97.842 (1)°	T = 298 K
V = 3261.5 (5) Å³	Block, white
Z = 8	0.49 × 0.42 × 0.40 mm
F(000) = 1344

Data collection top

Bruker SMART APEXII CCD area-detector diffractometer	2878 independent reflections
Radiation source: fine-focus sealed tube	1785 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.040
ϕ and ω scans	θ_max = 25.0°, θ_min = 2.5°
Absorption correction: multi-scan (SADABS; Bruker, 2009)	h = −12→13
T_min = 0.957, T_max = 0.965	k = −14→8
7972 measured reflections	l = −29→29

Refinement top

Refinement on F²	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F² > 2σ(F²)] = 0.041	H-atom parameters constrained
wR(F²) = 0.118	w = 1/[σ²(F_o²) + (0.0413P)² + 1.7982P] where P = (F_o² + 2F_c²)/3
S = 1.05	(Δ/σ)_max < 0.001
2878 reflections	Δρ_max = 0.16 e Å⁻³
219 parameters	Δρ_min = −0.17 e Å⁻³
0 restraints	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.0053 (4)

Crystal data top

C₂₀H₁₆O₄	V = 3261.5 (5) Å³
M_r = 320.33	Z = 8
Monoclinic, C2/c	Mo Kα radiation
a = 11.0261 (10) Å	µ = 0.09 mm⁻¹
b = 11.9624 (11) Å	T = 298 K
c = 24.961 (2) Å	0.49 × 0.42 × 0.40 mm
β = 97.842 (1)°

Data collection top

Bruker SMART APEXII CCD area-detector diffractometer	2878 independent reflections
Absorption correction: multi-scan (SADABS; Bruker, 2009)	1785 reflections with I > 2σ(I)
T_min = 0.957, T_max = 0.965	R_int = 0.040
7972 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.041	0 restraints
wR(F²) = 0.118	H-atom parameters constrained
S = 1.05	Δρ_max = 0.16 e Å⁻³
2878 reflections	Δρ_min = −0.17 e Å⁻³
219 parameters

Special details top

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 (Å²) top

	x	y	z	U_iso*/U_eq
O1	0.20235 (14)	0.40188 (12)	0.47155 (6)	0.0542 (5)
O2	0.22859 (15)	0.58572 (13)	0.46169 (6)	0.0617 (5)
O3	0.55526 (13)	0.68666 (12)	0.61835 (6)	0.0510 (4)
O4	0.59538 (14)	0.50787 (12)	0.67467 (5)	0.0562 (5)
C1	0.25750 (19)	0.50110 (18)	0.48580 (8)	0.0416 (5)
C2	0.35069 (17)	0.49359 (16)	0.53388 (7)	0.0365 (5)
C3	0.40974 (17)	0.59252 (17)	0.55134 (7)	0.0383 (5)
H3	0.3923	0.6579	0.5316	0.046*
C4	0.49363 (17)	0.59433 (16)	0.59748 (8)	0.0362 (5)
C5	0.51873 (18)	0.49544 (17)	0.62679 (7)	0.0393 (5)
C6	0.4624 (2)	0.39727 (18)	0.60920 (8)	0.0484 (6)
H6	0.4809	0.3316	0.6285	0.058*
C7	0.37782 (19)	0.39605 (18)	0.56250 (8)	0.0454 (6)
H7	0.3396	0.3296	0.5506	0.054*
C8	0.5401 (3)	0.7870 (2)	0.58760 (11)	0.0768 (9)
H8A	0.5629	0.7742	0.5524	0.115*
H8B	0.5911	0.8444	0.6056	0.115*
H8C	0.4560	0.8101	0.5841	0.115*
C9	0.6653 (2)	0.41886 (18)	0.69837 (8)	0.0459 (6)
C10	0.6668 (2)	0.4066 (2)	0.75311 (9)	0.0601 (7)
H10	0.6174	0.4510	0.7718	0.072*
C11	0.7429 (3)	0.3271 (3)	0.77982 (10)	0.0760 (9)
H11	0.7440	0.3173	0.8169	0.091*
C12	0.8166 (2)	0.2624 (2)	0.75287 (12)	0.0739 (9)
H12	0.8679	0.2094	0.7714	0.089*
C13	0.8145 (2)	0.2764 (2)	0.69818 (11)	0.0663 (7)
H13	0.8648	0.2329	0.6796	0.080*
C14	0.7378 (2)	0.3548 (2)	0.67055 (9)	0.0566 (7)
H14	0.7357	0.3638	0.6334	0.068*
C15	0.1108 (2)	0.40450 (17)	0.42591 (8)	0.0436 (6)
C16	−0.0096 (2)	0.40588 (19)	0.43430 (9)	0.0548 (6)
H16	−0.0307	0.4064	0.4691	0.066*
C17	−0.0987 (2)	0.4065 (2)	0.38964 (10)	0.0623 (7)
H17	−0.1809	0.4077	0.3944	0.075*
C18	−0.0671 (2)	0.4055 (2)	0.33860 (10)	0.0606 (7)
H18	−0.1276	0.4068	0.3088	0.073*
C19	0.0534 (2)	0.4024 (2)	0.33141 (9)	0.0620 (7)
H19	0.0747	0.4013	0.2966	0.074*
C20	0.1434 (2)	0.40105 (19)	0.37542 (9)	0.0539 (6)
H20	0.2255	0.3978	0.3706	0.065*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O1	0.0618 (10)	0.0448 (9)	0.0481 (9)	−0.0063 (8)	−0.0211 (8)	0.0062 (7)
O2	0.0733 (11)	0.0466 (10)	0.0555 (10)	−0.0032 (8)	−0.0256 (8)	0.0097 (8)
O3	0.0550 (9)	0.0386 (9)	0.0528 (9)	−0.0041 (7)	−0.0163 (7)	0.0042 (7)
O4	0.0706 (11)	0.0496 (10)	0.0405 (8)	0.0025 (8)	−0.0208 (8)	0.0034 (7)
C1	0.0434 (12)	0.0420 (13)	0.0374 (12)	−0.0009 (11)	−0.0016 (10)	0.0005 (10)
C2	0.0368 (11)	0.0383 (12)	0.0328 (10)	0.0004 (9)	−0.0008 (9)	0.0020 (9)
C3	0.0383 (11)	0.0392 (12)	0.0361 (11)	0.0030 (10)	0.0000 (9)	0.0093 (9)
C4	0.0348 (11)	0.0366 (12)	0.0359 (11)	0.0007 (9)	−0.0001 (9)	−0.0001 (9)
C5	0.0412 (12)	0.0430 (13)	0.0309 (10)	0.0019 (10)	−0.0053 (9)	0.0030 (9)
C6	0.0592 (14)	0.0394 (13)	0.0423 (12)	0.0007 (11)	−0.0086 (11)	0.0114 (10)
C7	0.0496 (13)	0.0397 (13)	0.0434 (12)	−0.0039 (10)	−0.0061 (10)	0.0018 (10)
C8	0.0853 (19)	0.0437 (15)	0.089 (2)	−0.0156 (14)	−0.0321 (16)	0.0169 (14)
C9	0.0454 (13)	0.0466 (13)	0.0403 (12)	−0.0045 (11)	−0.0131 (10)	0.0126 (11)
C10	0.0530 (14)	0.0817 (18)	0.0419 (13)	−0.0012 (13)	−0.0065 (11)	0.0126 (13)
C11	0.0707 (19)	0.104 (2)	0.0473 (15)	−0.0006 (18)	−0.0142 (14)	0.0313 (16)
C12	0.0597 (17)	0.078 (2)	0.0744 (19)	0.0020 (15)	−0.0244 (15)	0.0286 (16)
C13	0.0544 (15)	0.0668 (17)	0.0740 (18)	0.0055 (13)	−0.0047 (13)	0.0088 (14)
C14	0.0622 (16)	0.0592 (15)	0.0452 (13)	−0.0011 (13)	−0.0039 (12)	0.0090 (12)
C15	0.0481 (14)	0.0376 (12)	0.0405 (12)	−0.0027 (10)	−0.0108 (10)	0.0020 (10)
C16	0.0587 (16)	0.0583 (15)	0.0466 (13)	−0.0017 (12)	0.0044 (11)	−0.0078 (11)
C17	0.0422 (13)	0.0724 (18)	0.0694 (17)	0.0012 (12)	−0.0025 (12)	−0.0132 (14)
C18	0.0569 (16)	0.0643 (17)	0.0534 (15)	−0.0035 (13)	−0.0183 (12)	−0.0025 (12)
C19	0.0620 (17)	0.0809 (19)	0.0408 (13)	−0.0123 (14)	−0.0015 (11)	0.0036 (12)
C20	0.0456 (13)	0.0633 (16)	0.0514 (14)	−0.0077 (12)	0.0010 (11)	0.0023 (12)

Geometric parameters (Å, º) top

O1—C1	1.359 (2)	C9—C10	1.372 (3)
O1—C15	1.415 (2)	C10—C11	1.379 (3)
O2—C1	1.198 (2)	C10—H10	0.9300
O3—C4	1.362 (2)	C11—C12	1.364 (4)
O3—C8	1.422 (3)	C11—H11	0.9300
O4—C5	1.375 (2)	C12—C13	1.372 (4)
O4—C9	1.398 (2)	C12—H12	0.9300
C1—C2	1.472 (3)	C13—C14	1.383 (3)
C2—C7	1.379 (3)	C13—H13	0.9300
C2—C3	1.392 (3)	C14—H14	0.9300
C3—C4	1.375 (3)	C15—C20	1.358 (3)
C3—H3	0.9300	C15—C16	1.372 (3)
C4—C5	1.399 (3)	C16—C17	1.382 (3)
C5—C6	1.372 (3)	C16—H16	0.9300
C6—C7	1.390 (3)	C17—C18	1.366 (3)
C6—H6	0.9300	C17—H17	0.9300
C7—H7	0.9300	C18—C19	1.365 (3)
C8—H8A	0.9600	C18—H18	0.9300
C8—H8B	0.9600	C19—C20	1.377 (3)
C8—H8C	0.9600	C19—H19	0.9300
C9—C14	1.363 (3)	C20—H20	0.9300

C1—O1—C15	115.84 (15)	C9—C10—C11	118.6 (3)
C4—O3—C8	117.53 (15)	C9—C10—H10	120.7
C5—O4—C9	121.60 (16)	C11—C10—H10	120.7
O2—C1—O1	121.84 (18)	C12—C11—C10	121.1 (2)
O2—C1—C2	124.68 (19)	C12—C11—H11	119.4
O1—C1—C2	113.44 (18)	C10—C11—H11	119.4
C7—C2—C3	119.86 (17)	C11—C12—C13	119.4 (2)
C7—C2—C1	123.48 (19)	C11—C12—H12	120.3
C3—C2—C1	116.62 (17)	C13—C12—H12	120.3
C4—C3—C2	120.53 (18)	C12—C13—C14	120.4 (3)
C4—C3—H3	119.7	C12—C13—H13	119.8
C2—C3—H3	119.7	C14—C13—H13	119.8
O3—C4—C3	125.18 (17)	C9—C14—C13	119.2 (2)
O3—C4—C5	115.66 (16)	C9—C14—H14	120.4
C3—C4—C5	119.15 (18)	C13—C14—H14	120.4
C6—C5—O4	124.64 (18)	C20—C15—C16	121.75 (19)
C6—C5—C4	120.53 (17)	C20—C15—O1	119.8 (2)
O4—C5—C4	114.69 (17)	C16—C15—O1	118.42 (19)
C5—C6—C7	119.99 (19)	C15—C16—C17	118.3 (2)
C5—C6—H6	120.0	C15—C16—H16	120.9
C7—C6—H6	120.0	C17—C16—H16	120.9
C2—C7—C6	119.91 (19)	C18—C17—C16	120.6 (2)
C2—C7—H7	120.0	C18—C17—H17	119.7
C6—C7—H7	120.0	C16—C17—H17	119.7
O3—C8—H8A	109.5	C19—C18—C17	120.0 (2)
O3—C8—H8B	109.5	C19—C18—H18	120.0
H8A—C8—H8B	109.5	C17—C18—H18	120.0
O3—C8—H8C	109.5	C18—C19—C20	120.3 (2)
H8A—C8—H8C	109.5	C18—C19—H19	119.9
H8B—C8—H8C	109.5	C20—C19—H19	119.9
C14—C9—C10	121.3 (2)	C15—C20—C19	119.1 (2)
C14—C9—O4	122.70 (19)	C15—C20—H20	120.4
C10—C9—O4	115.7 (2)	C19—C20—H20	120.4

C15—O1—C1—O2	1.3 (3)	C5—C6—C7—C2	0.1 (3)
C15—O1—C1—C2	179.29 (18)	C5—O4—C9—C14	50.8 (3)
O2—C1—C2—C7	176.6 (2)	C5—O4—C9—C10	−135.7 (2)
O1—C1—C2—C7	−1.3 (3)	C14—C9—C10—C11	−0.4 (3)
O2—C1—C2—C3	−1.1 (3)	O4—C9—C10—C11	−174.1 (2)
O1—C1—C2—C3	−179.05 (17)	C9—C10—C11—C12	0.7 (4)
C7—C2—C3—C4	−1.1 (3)	C10—C11—C12—C13	−0.4 (4)
C1—C2—C3—C4	176.72 (19)	C11—C12—C13—C14	−0.3 (4)
C8—O3—C4—C3	−5.9 (3)	C10—C9—C14—C13	−0.3 (3)
C8—O3—C4—C5	175.0 (2)	O4—C9—C14—C13	172.91 (19)
C2—C3—C4—O3	−179.20 (19)	C12—C13—C14—C9	0.6 (4)
C2—C3—C4—C5	−0.2 (3)	C1—O1—C15—C20	81.7 (2)
C9—O4—C5—C6	28.7 (3)	C1—O1—C15—C16	−100.9 (2)
C9—O4—C5—C4	−155.67 (19)	C20—C15—C16—C17	−1.6 (3)
O3—C4—C5—C6	−179.50 (19)	O1—C15—C16—C17	−178.9 (2)
C3—C4—C5—C6	1.4 (3)	C15—C16—C17—C18	0.2 (4)
O3—C4—C5—O4	4.6 (3)	C16—C17—C18—C19	0.8 (4)
C3—C4—C5—O4	−174.49 (18)	C17—C18—C19—C20	−0.4 (4)
O4—C5—C6—C7	174.1 (2)	C16—C15—C20—C19	2.0 (3)
C4—C5—C6—C7	−1.3 (3)	O1—C15—C20—C19	179.3 (2)
C3—C2—C7—C6	1.1 (3)	C18—C19—C20—C15	−1.0 (4)
C1—C2—C7—C6	−176.5 (2)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C8—H8C···O2ⁱ	0.96	2.52	3.408 (4)	153
C14—H14···O2ⁱⁱ	0.93	2.53	3.446 (3)	167
C20—H20···O3ⁱⁱ	0.93	2.60	3.468 (3)	155

Symmetry codes: (i) −x+1/2, −y+3/2, −z+1; (ii) −x+1, −y+1, −z+1.

Experimental details

Crystal data
Chemical formula	C₂₀H₁₆O₄
M_r	320.33
Crystal system, space group	Monoclinic, C2/c
Temperature (K)	298
a, b, c (Å)	11.0261 (10), 11.9624 (11), 24.961 (2)
β (°)	97.842 (1)
V (Å³)	3261.5 (5)
Z	8
Radiation type	Mo Kα
µ (mm⁻¹)	0.09
Crystal size (mm)	0.49 × 0.42 × 0.40

Data collection
Diffractometer	Bruker SMART APEXII CCD area-detector diffractometer
Absorption correction	Multi-scan (SADABS; Bruker, 2009)
T_min, T_max	0.957, 0.965
No. of measured, independent and observed [I > 2σ(I)] reflections	7972, 2878, 1785
R_int	0.040
(sin θ/λ)_max (Å⁻¹)	0.595

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.041, 0.118, 1.05
No. of reflections	2878
No. of parameters	219
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.16, −0.17

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

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C8—H8C···O2ⁱ	0.96	2.52	3.408 (4)	153
C14—H14···O2ⁱⁱ	0.93	2.53	3.446 (3)	167
C20—H20···O3ⁱⁱ	0.93	2.60	3.468 (3)	155

Symmetry codes: (i) −x+1/2, −y+3/2, −z+1; (ii) −x+1, −y+1, −z+1.

Acknowledgements

Financial support from the Fundamental Research Funds for the Central Universities in NWSUAF (grant No. QN2009048) and from the National Natural Science Foundation of China (grant No. 20802058) is greatly appreciated.

References

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