(2S,4R)-2-[(1R)-1-(4-Bromo­phen­yl)-2-nitro­eth­yl]-4-ethyl­cyclo­hexa­none

Zhang, C.-X.; Zhang, Y.-P.; Xia, A.-B.

doi:10.1107/S1600536813001426

organic compounds

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ISSN: 2056-9890

Volume 69| Part 2| February 2013| Page o263

doi:10.1107/S1600536813001426

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(2S,4R)-2-[(1R)-1-(4-Bromophenyl)-2-nitroethyl]-4-ethylcyclohexanone

Chi-Xiao Zhang,^a Yan-Peng Zhang ^a and Ai-Bao Xia ^a ^*

^aState Key Laboratory Breeding Base of Green Chemistry-Synthesis Technology, Zhejiang University of Technology, Hangzhou 310014, People's Republic of China
^*Correspondence e-mail: xiaaibao@zjut.edu.cn

(Received 27 December 2012; accepted 15 January 2013; online 19 January 2013)

The crystal structure of the title compound, C₁₆H₂₀BrNO₃, contains three chiral centers in the configuration 1R,2S,6R. The cyclohexane ring is in a chair conformation. In the crystal, molecules are linked by weak C—H⋯O interactions, forming chains along the a-axis direction.

Related literature

For related compounds, see: Hayashi et al. (2005 ); Li et al. (2009 ); Xia et al. (2009 ); Wu et al. (2011 ). For asymmetric Michael addition reactions, see: Luo et al. (2007 ). For enantioselective organocatalytic Michael additions, see: Peelen et al. (2005 ); Ma et al. (2008 ).

Experimental

Crystal data

C₁₆H₂₀BrNO₃
M_r = 354.24
Monoclinic, P 2₁
a = 5.6434 (4) Å
b = 9.2179 (6) Å
c = 16.5472 (9) Å
β = 101.782 (3)°
V = 842.65 (9) Å³
Z = 2
Mo Kα radiation
μ = 2.45 mm⁻¹
T = 296 K
0.52 × 0.31 × 0.18 mm

Data collection

Rigaku R-AXIS RAPID/ZJUG diffractometer
Absorption correction: multi-scan (ABSCOR; Higashi, 1995 ) T_min = 0.279, T_max = 0.644
7234 measured reflections
3277 independent reflections
1619 reflections with I > 2σ(I)
R_int = 0.071

Refinement

R[F² > 2σ(F²)] = 0.056
wR(F²) = 0.175
S = 1.00
3277 reflections
191 parameters
1 restraint
H-atom parameters constrained
Δρ_max = 0.35 e Å⁻³
Δρ_min = −0.29 e Å⁻³
Absolute structure: Flack (1983 ), 1259 Friedel pairs
Flack parameter: 0.03 (2)

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
C11—H11⋯O3ⁱ	0.93	2.56	3.478 (9)	169
C16—H16B⋯O3ⁱ	0.97	2.58	3.500 (8)	158
Symmetry code: (i) x+1, y, z.

Data collection: PROCESS-AUTO (Rigaku, 2006 ); cell refinement: PROCESS-AUTO; data reduction: CrystalStructure (Rigaku, 2007 ); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 ); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 2012 ); software used to prepare material for publication: WinGX (Farrugia, 2012).

Supporting information

Crystal structure: contains datablocks global, I. DOI: 10.1107/S1600536813001426/zq2194sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536813001426/zq2194Isup2.hkl

Supporting information file. DOI: 10.1107/S1600536813001426/zq2194Isup3.cml

checkCIF report

Comment top

The Michael reaction (e.g. Luo et al., 2007; Ma et al., 2008; Peelen et al., 2005) of a carbon nucleophile with a nitroalkene is one useful synthetic method for the preparation of nitroalkanes, which are versatile synthetic intermediates owing to the various possible transformations of the nitro group into other useful functional groups (Hayashi et al., 2005). The title compound was obtained from the Michael addition of 4-ethylcyclohexanone to 1-(4-bromophenyl)-2-nitroethene in our laboratory. For related structures, see: Li et al. (2009); Xia et al. (2009); Wu et al. (2011).

The title compound is shown in Fig. 1.The cyclohexyl ring adopts a chair conformation. The plane of the phenyl ring and the least-square plane of the cyclohexyl moiety enclose an angle of 70.00 (3)° while the plane through the nitro group and the adjacent C16 atom encloses an angle of 63.26 (3)° with the phenyl ring. In the crystal, molecules are linked by weak C—H···O interactions forming chains along the a axis (Table 1).

Related literature top

For related compounds, see: Hayashi et al. (2005); Li et al. (2009); Xia et al. (2009); Wu et al. (2011). For asymmetric Michael addition reactions, see: Luo et al. (2007). For enantioselective organocatalytic Michael additions, see: Peelen et al. (2005); Ma et al. (2008).

Experimental top

An isopropyl ether (0.5 mL) solution of 1-(4-bromophenyl)-2-nitroethene (0.6 mmol) and 4-ethylcyclohexanone (1.2 mmol) was stirred with the (S)-2-(pyrrolidin-2-ylmethylthio)pyridine (0.12 mmol) as catalyst and benzoic acid (0.12 mmol) as cocatalyst at room temperature. After completion of the reaction, the mixture was extracted with ethyl acetate. Solvents were removed under vacuum and the residue was purified by column chromatography on silica gel (eluent: petroleum ether-ether). Suitable crystals were obtained by slow evaporation of an ether solution.

Computing details top

Data collection: PROCESS-AUTO (Rigaku, 2006); cell refinement: PROCESS-AUTO (Rigaku, 2006); data reduction: CrystalStructure (Rigaku, 2007); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 2012); software used to prepare material for publication: WinGX (Farrugia, 2012).

Figures top

Fig. 1. The molecular structure of the title compound with the atomic labeling scheme. Displacement ellipsoids are drawn at the 50% probability level.

(2S,4R)-2-[(1R)-1-(4-Bromophenyl)-2-nitroethyl]- 4-ethylcyclohexanone top

Crystal data top

C₁₆H₂₀BrNO₃	F(000) = 364
M_r = 354.24	D_x = 1.396 Mg m⁻³
Monoclinic, P2₁	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2yb	Cell parameters from 4682 reflections
a = 5.6434 (4) Å	θ = 3.4–27.4°
b = 9.2179 (6) Å	µ = 2.45 mm⁻¹
c = 16.5472 (9) Å	T = 296 K
β = 101.782 (3)°	Platelet, colourless
V = 842.65 (9) Å³	0.52 × 0.31 × 0.18 mm
Z = 2

Data collection top

Rigaku R-AXIS RAPID/ZJUG diffractometer	3277 independent reflections
Radiation source: rotating anode	1619 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.071
Detector resolution: 10.00 pixels mm^-1	θ_max = 26.0°, θ_min = 3.4°
ω scans	h = −6→6
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	k = −11→11
T_min = 0.279, T_max = 0.644	l = −20→20
7234 measured reflections

Refinement top

Refinement on F²	Hydrogen site location: inferred from neighbouring sites
Least-squares matrix: full	H-atom parameters constrained
R[F² > 2σ(F²)] = 0.056	w = 1/[σ²(F_o²) + (0.0605P)² + 0.3P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.175	(Δ/σ)_max < 0.001
S = 1.00	Δρ_max = 0.35 e Å⁻³
3277 reflections	Δρ_min = −0.29 e Å⁻³
191 parameters	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
1 restraint	Extinction coefficient: 0.072 (8)
Primary atom site location: structure-invariant direct methods	Absolute structure: Flack (1983), 1259 Friedel pairs
Secondary atom site location: difference Fourier map	Absolute structure parameter: 0.03 (2)

Crystal data top

C₁₆H₂₀BrNO₃	V = 842.65 (9) Å³
M_r = 354.24	Z = 2
Monoclinic, P2₁	Mo Kα radiation
a = 5.6434 (4) Å	µ = 2.45 mm⁻¹
b = 9.2179 (6) Å	T = 296 K
c = 16.5472 (9) Å	0.52 × 0.31 × 0.18 mm
β = 101.782 (3)°

Data collection top

Rigaku R-AXIS RAPID/ZJUG diffractometer	3277 independent reflections
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	1619 reflections with I > 2σ(I)
T_min = 0.279, T_max = 0.644	R_int = 0.071
7234 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.056	H-atom parameters constrained
wR(F²) = 0.175	Δρ_max = 0.35 e Å⁻³
S = 1.00	Δρ_min = −0.29 e Å⁻³
3277 reflections	Absolute structure: Flack (1983), 1259 Friedel pairs
191 parameters	Absolute structure parameter: 0.03 (2)
1 restraint

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
C1	0.2312 (11)	0.2884 (7)	0.1770 (4)	0.0563 (15)
H1	0.0766	0.3379	0.1754	0.068*
C2	0.4174 (11)	0.4066 (6)	0.1660 (4)	0.0541 (15)
H2	0.5499	0.3592	0.1461	0.065*
C3	0.3093 (14)	0.5225 (7)	0.1030 (4)	0.0712 (19)
C4	0.4813 (15)	0.6373 (10)	0.0880 (5)	0.091 (3)
H4A	0.3957	0.7096	0.0504	0.109*
H4B	0.6060	0.5948	0.0629	0.109*
C5	0.5974 (14)	0.7093 (9)	0.1702 (5)	0.090 (2)
H5A	0.7190	0.7778	0.1605	0.108*
H5B	0.4742	0.7634	0.1905	0.108*
C6	0.7146 (11)	0.6025 (7)	0.2361 (5)	0.0672 (18)
H6	0.8446	0.5533	0.2156	0.081*
C7	0.5264 (10)	0.4859 (8)	0.2467 (3)	0.0582 (14)
H7A	0.6031	0.4153	0.2872	0.070*
H7B	0.3969	0.5317	0.2679	0.070*
C8	0.8263 (14)	0.6704 (9)	0.3179 (5)	0.089 (2)
H8A	0.8867	0.5934	0.3565	0.107*
H8B	0.6999	0.7206	0.3387	0.107*
C9	1.0317 (16)	0.7769 (10)	0.3167 (7)	0.110 (3)
H9A	1.0904	0.8137	0.3714	0.165*
H9B	0.9736	0.8558	0.2802	0.165*
H9C	1.1607	0.7282	0.2978	0.165*
C10	0.2948 (10)	0.2114 (7)	0.2592 (4)	0.0522 (14)
C11	0.4955 (12)	0.1193 (7)	0.2768 (4)	0.0646 (17)
H11	0.5875	0.1042	0.2369	0.078*
C12	0.5606 (13)	0.0500 (7)	0.3524 (5)	0.075 (2)
H12	0.6965	−0.0094	0.3637	0.090*
C13	0.4189 (15)	0.0708 (8)	0.4112 (5)	0.076 (2)
C14	0.2187 (14)	0.1583 (8)	0.3947 (4)	0.0708 (19)
H14	0.1244	0.1714	0.4341	0.085*
C15	0.1579 (11)	0.2267 (8)	0.3194 (4)	0.0622 (17)
H15	0.0206	0.2851	0.3085	0.075*
C16	0.1937 (11)	0.1852 (7)	0.1032 (4)	0.0616 (17)
H16A	0.1394	0.2399	0.0527	0.074*
H16B	0.3464	0.1395	0.1001	0.074*
N1	0.0135 (12)	0.0724 (7)	0.1101 (4)	0.0700 (16)
O1	0.0953 (10)	0.5240 (6)	0.0704 (3)	0.0925 (19)
O2	0.0723 (11)	−0.0541 (7)	0.1111 (4)	0.1028 (18)
O3	−0.1912 (9)	0.1117 (7)	0.1163 (3)	0.0939 (17)
Br1	0.5073 (2)	−0.02467 (17)	0.51442 (5)	0.1269 (6)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
C1	0.058 (3)	0.059 (3)	0.054 (4)	−0.002 (3)	0.015 (3)	−0.004 (3)
C2	0.053 (3)	0.055 (3)	0.056 (3)	−0.005 (3)	0.015 (3)	0.006 (3)
C3	0.089 (5)	0.074 (5)	0.053 (4)	−0.003 (4)	0.019 (3)	0.010 (3)
C4	0.096 (5)	0.099 (6)	0.074 (5)	−0.021 (5)	0.007 (4)	0.028 (4)
C5	0.084 (5)	0.071 (5)	0.120 (7)	−0.004 (4)	0.028 (5)	0.035 (5)
C6	0.058 (4)	0.052 (4)	0.091 (5)	−0.004 (3)	0.012 (4)	−0.001 (4)
C7	0.063 (3)	0.050 (3)	0.059 (3)	0.002 (3)	0.008 (3)	−0.005 (4)
C8	0.084 (5)	0.076 (5)	0.105 (6)	−0.013 (4)	0.013 (4)	−0.015 (4)
C9	0.087 (5)	0.092 (6)	0.153 (10)	−0.022 (5)	0.030 (6)	−0.035 (6)
C10	0.050 (3)	0.050 (3)	0.056 (4)	0.002 (3)	0.009 (3)	0.005 (3)
C11	0.072 (4)	0.067 (4)	0.059 (4)	0.004 (4)	0.023 (3)	0.010 (3)
C12	0.069 (4)	0.061 (4)	0.089 (5)	0.005 (3)	0.000 (4)	−0.002 (4)
C13	0.094 (5)	0.069 (4)	0.063 (4)	−0.006 (4)	0.011 (4)	−0.015 (4)
C14	0.085 (5)	0.083 (5)	0.047 (4)	0.001 (4)	0.020 (3)	−0.003 (3)
C15	0.062 (4)	0.066 (4)	0.062 (4)	0.001 (4)	0.019 (3)	0.002 (3)
C16	0.060 (3)	0.074 (5)	0.051 (3)	−0.011 (3)	0.012 (3)	−0.008 (4)
N1	0.077 (4)	0.078 (5)	0.053 (3)	−0.015 (4)	0.009 (3)	−0.001 (3)
O1	0.081 (3)	0.111 (5)	0.077 (3)	0.000 (3)	−0.003 (3)	0.031 (3)
O2	0.107 (4)	0.067 (4)	0.128 (5)	−0.012 (3)	0.007 (3)	0.016 (3)
O3	0.063 (3)	0.127 (5)	0.097 (4)	−0.028 (3)	0.030 (3)	−0.031 (3)
Br1	0.1788 (11)	0.1258 (9)	0.0677 (6)	0.0169 (8)	0.0050 (5)	0.0258 (7)

Geometric parameters (Å, º) top

C1—C10	1.511 (8)	C8—H8A	0.9700
C1—C16	1.528 (8)	C8—H8B	0.9700
C1—C2	1.550 (8)	C9—H9A	0.9600
C1—H1	0.9800	C9—H9B	0.9600
C2—C3	1.530 (8)	C9—H9C	0.9600
C2—C7	1.535 (8)	C10—C15	1.387 (8)
C2—H2	0.9800	C10—C11	1.398 (8)
C3—O1	1.218 (8)	C11—C12	1.386 (9)
C3—C4	1.490 (10)	C11—H11	0.9300
C4—C5	1.536 (12)	C12—C13	1.392 (11)
C4—H4A	0.9700	C12—H12	0.9300
C4—H4B	0.9700	C13—C14	1.370 (10)
C5—C6	1.517 (10)	C13—Br1	1.896 (8)
C5—H5A	0.9700	C14—C15	1.376 (9)
C5—H5B	0.9700	C14—H14	0.9300
C6—C8	1.506 (10)	C15—H15	0.9300
C6—C7	1.546 (9)	C16—N1	1.475 (9)
C6—H6	0.9800	C16—H16A	0.9700
C7—H7A	0.9700	C16—H16B	0.9700
C7—H7B	0.9700	N1—O2	1.212 (9)
C8—C9	1.522 (11)	N1—O3	1.235 (7)

C10—C1—C16	113.3 (5)	C6—C8—C9	115.9 (8)
C10—C1—C2	113.2 (5)	C6—C8—H8A	108.3
C16—C1—C2	109.3 (5)	C9—C8—H8A	108.3
C10—C1—H1	106.9	C6—C8—H8B	108.3
C16—C1—H1	106.9	C9—C8—H8B	108.3
C2—C1—H1	106.9	H8A—C8—H8B	107.4
C3—C2—C7	107.1 (5)	C8—C9—H9A	109.5
C3—C2—C1	112.7 (5)	C8—C9—H9B	109.5
C7—C2—C1	113.2 (5)	H9A—C9—H9B	109.5
C3—C2—H2	107.9	C8—C9—H9C	109.5
C7—C2—H2	107.9	H9A—C9—H9C	109.5
C1—C2—H2	107.9	H9B—C9—H9C	109.5
O1—C3—C4	122.6 (6)	C15—C10—C11	117.3 (6)
O1—C3—C2	122.0 (6)	C15—C10—C1	122.3 (5)
C4—C3—C2	115.3 (6)	C11—C10—C1	120.4 (5)
C3—C4—C5	109.5 (6)	C12—C11—C10	121.5 (6)
C3—C4—H4A	109.8	C12—C11—H11	119.2
C5—C4—H4A	109.8	C10—C11—H11	119.2
C3—C4—H4B	109.8	C11—C12—C13	118.9 (7)
C5—C4—H4B	109.8	C11—C12—H12	120.6
H4A—C4—H4B	108.2	C13—C12—H12	120.6
C6—C5—C4	113.7 (7)	C14—C13—C12	120.7 (7)
C6—C5—H5A	108.8	C14—C13—Br1	120.5 (6)
C4—C5—H5A	108.8	C12—C13—Br1	118.8 (6)
C6—C5—H5B	108.8	C15—C14—C13	119.6 (7)
C4—C5—H5B	108.8	C15—C14—H14	120.2
H5A—C5—H5B	107.7	C13—C14—H14	120.2
C8—C6—C5	114.6 (6)	C14—C15—C10	122.1 (6)
C8—C6—C7	111.0 (6)	C14—C15—H15	119.0
C5—C6—C7	108.9 (5)	C10—C15—H15	119.0
C8—C6—H6	107.3	N1—C16—C1	111.2 (5)
C5—C6—H6	107.3	N1—C16—H16A	109.4
C7—C6—H6	107.3	C1—C16—H16A	109.4
C2—C7—C6	113.3 (5)	N1—C16—H16B	109.4
C2—C7—H7A	108.9	C1—C16—H16B	109.4
C6—C7—H7A	108.9	H16A—C16—H16B	108.0
C2—C7—H7B	108.9	O2—N1—O3	122.6 (7)
C6—C7—H7B	108.9	O2—N1—C16	119.2 (7)
H7A—C7—H7B	107.7	O3—N1—C16	118.1 (6)

C10—C1—C2—C3	−156.6 (5)	C16—C1—C10—C15	−122.7 (7)
C16—C1—C2—C3	76.1 (6)	C2—C1—C10—C15	112.1 (7)
C10—C1—C2—C7	−34.9 (7)	C16—C1—C10—C11	56.5 (8)
C16—C1—C2—C7	−162.2 (5)	C2—C1—C10—C11	−68.7 (8)
C7—C2—C3—O1	−120.3 (7)	C15—C10—C11—C12	−2.2 (9)
C1—C2—C3—O1	4.8 (9)	C1—C10—C11—C12	178.6 (6)
C7—C2—C3—C4	56.5 (8)	C10—C11—C12—C13	1.3 (10)
C1—C2—C3—C4	−178.4 (6)	C11—C12—C13—C14	0.0 (11)
O1—C3—C4—C5	121.3 (8)	C11—C12—C13—Br1	179.8 (5)
C2—C3—C4—C5	−55.4 (9)	C12—C13—C14—C15	−0.3 (11)
C3—C4—C5—C6	53.7 (9)	Br1—C13—C14—C15	179.9 (6)
C4—C5—C6—C8	−179.0 (6)	C13—C14—C15—C10	−0.7 (11)
C4—C5—C6—C7	−54.0 (8)	C11—C10—C15—C14	1.9 (10)
C3—C2—C7—C6	−56.0 (7)	C1—C10—C15—C14	−178.9 (6)
C1—C2—C7—C6	179.2 (5)	C10—C1—C16—N1	54.0 (7)
C8—C6—C7—C2	−176.6 (5)	C2—C1—C16—N1	−178.8 (5)
C5—C6—C7—C2	56.3 (8)	C1—C16—N1—O2	−120.9 (8)
C5—C6—C8—C9	−61.7 (9)	C1—C16—N1—O3	57.6 (7)
C7—C6—C8—C9	174.4 (7)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C11—H11···O3ⁱ	0.93	2.56	3.478 (9)	169
C16—H16B···O3ⁱ	0.97	2.58	3.500 (8)	158

Symmetry code: (i) x+1, y, z.

Experimental details

Crystal data
Chemical formula	C₁₆H₂₀BrNO₃
M_r	354.24
Crystal system, space group	Monoclinic, P2₁
Temperature (K)	296
a, b, c (Å)	5.6434 (4), 9.2179 (6), 16.5472 (9)
β (°)	101.782 (3)
V (Å³)	842.65 (9)
Z	2
Radiation type	Mo Kα
µ (mm⁻¹)	2.45
Crystal size (mm)	0.52 × 0.31 × 0.18

Data collection
Diffractometer	Rigaku R-AXIS RAPID/ZJUG diffractometer
Absorption correction	Multi-scan (ABSCOR; Higashi, 1995)
T_min, T_max	0.279, 0.644
No. of measured, independent and observed [I > 2σ(I)] reflections	7234, 3277, 1619
R_int	0.071
(sin θ/λ)_max (Å⁻¹)	0.617

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.056, 0.175, 1.00
No. of reflections	3277
No. of parameters	191
No. of restraints	1
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.35, −0.29
Absolute structure	Flack (1983), 1259 Friedel pairs
Absolute structure parameter	0.03 (2)

Computer programs: PROCESS-AUTO (Rigaku, 2006), CrystalStructure (Rigaku, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 2012), WinGX (Farrugia, 2012).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C11—H11···O3ⁱ	0.93	2.56	3.478 (9)	168.7
C16—H16B···O3ⁱ	0.97	2.58	3.500 (8)	158.2

Symmetry code: (i) x+1, y, z.

Acknowledgements

The authors thank Professor Jian-Ming Gu of Zhejiang University for his help.

References

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