(2S,3R)-3-(2-Bromo­phen­yl)-2-nitro-2,3,6,7-tetra­hydro-1-benzo­furan-4(5H)-one

Wang, Y.; Lou, L.; Dong, K.; Xu, D.

doi:10.1107/S1600536813017698

organic compounds

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ISSN: 2056-9890

Volume 69| Part 8| August 2013| Page o1197

doi:10.1107/S1600536813017698

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(2S,3R)-3-(2-Bromophenyl)-2-nitro-2,3,6,7-tetrahydro-1-benzofuran-4(5H)-one

Yifeng Wang,^a Liuliu Lou,^a Kun Dong ^a and Danqian Xu ^a ^*

^aCatalytic Hydrogenation Research Center, Zhejiang University of Technology, Hangzhou 310014, People's Republic of China
^*Correspondence e-mail: chrc@zjut.edu.cn

(Received 17 June 2013; accepted 27 June 2013; online 3 July 2013)

The title compound, C₁₄H₁₂BrNO₄, has two chiral C atoms. The C atom next to the O atom in the dihydrofuran ring has an S configuration, while the adjacent chiral C atom has an R configuration. The cyclohex-2-enone and dihydrofuran rings both adopt envelope conformations, with the flap atoms (middle CH₂ in cyclohex-2-enone and NO₂-substituted C in dihydrofuran) lying 0.612 (3) and 0.295 (2) Å, respectively, from the mean plane of the remaining atoms. The dihedral angle between the mean planes of the furan and benzene rings is 80.0 (3)°. In the crystal, the molecules are linked by C—H⋯O interactions, generating a three-dimensional network.

Related literature

For global background on functionalized 2,3-dihydrofurans, see: Fan et al. (2010 ); Rueping et al. (2010 ). The absolute configuration was assigned by the method of Flack (1983 ).

Experimental

Crystal data

C₁₄H₁₂BrNO₄
M_r = 338.16
Orthorhombic, P 2₁ 2₁ 2₁
a = 7.2162 (8) Å
b = 7.3372 (8) Å
c = 25.9727 (13) Å
V = 1375.2 (2) Å³
Z = 4
Mo Kα radiation
μ = 3.00 mm⁻¹
T = 296 K
0.54 × 0.31 × 0.23 mm

Data collection

Rigaku R-AXIS RAPID/ZJUG diffractometer
Absorption correction: multi-scan (ABSCOR; Higashi, 1995 ) T_min = 0.334, T_max = 0.505
10897 measured reflections
2548 independent reflections
1456 reflections with I > 2σ(I)
R_int = 0.068

Refinement

R[F² > 2σ(F²)] = 0.059
wR(F²) = 0.125
S = 1.00
2548 reflections
182 parameters
H-atom parameters constrained
Δρ_max = 0.51 e Å⁻³
Δρ_min = −0.57 e Å⁻³
Absolute structure: Flack (1983), 1041 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
C1—H1⋯O1ⁱ	0.98	2.51	3.486 (12)	171
C7—H7A⋯O3ⁱⁱ	0.97	2.66	3.403 (12)	134
C7—H7B⋯O3ⁱⁱⁱ	0.97	2.52	3.480 (13)	172
Symmetry codes: (i) x+1, y, z; (ii) $[x-{\script{1\over 2}}, -y+{\script{1\over 2}}, -z+1]$ ; (iii) x, y+1, 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/S1600536813017698/pk2489sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536813017698/pk2489Isup2.hkl

Supporting information file. DOI: 10.1107/S1600536813017698/pk2489Isup3.cml

checkCIF report

Comment top

The highly functionalized 2,3-dihydrofurans are very important compounds that may serve as precursors for the construction of pharmacologically important chemicals. Organocatalytic asymmetric reactions have been used as efficient tools for the synthesis of chiral compounds under mild conditions. The title compound, which was readily synthesized by the organocatalytic Michael-S_N2 reaction of cyclohexane-1,3-dione to (E)-1-bromo-2-(2-bromo-2-nitrovinyl)benzene, could act as an intermediate in organic and natural product synthesis. In this article, the crystal structure of the title compound (2S,3R)-3-(2-bromophenyl)-2-nitro-2,3,6,7- tetrahydrobenzofuran-4(5H)-one is described (Fig. 1). The structure has two chiral centers. The carbon next to the oxygen atom in the dihydrofuran ring has S configuration, while the adjacent chiral carbon atom has R configuration. Both the cyclohex-2-enone ring and dihydrofurane ring adopt envelope conformations, with the flap carbon atom lying 0.612 (3) Å and 0.295 (2) Å respectively on either side of the mean plane of the remaining fused-ring atoms. The dihedral angle between the mean plane of the furan ring and the benzene ring is 80.0 (3)°.

Related literature top

For global background on functionalized 2,3-dihydrofurans, see: Fan et al. (2010); Rueping et al. (2010). The absolute configuration was assigned by the method of Flack (1983).

Experimental top

To a solution of cyclohexane-1,3-dione (1.2 mmol) and (E)-1-bromo-2-(2-bromo-2-nitrovinyl)benzene (1 mmol) in CHCl₃ (3 ml) was added (0.025 mmol) 1-(3,5-bis(trifluoromethyl)phenyl)-3-((S) -(6-methoxyquinolin-4-yl)((2S,4S,8R)-8-vinylquinuclidin-2 -yl)methyl)thiourea as catalyst and DIPEA (0.3 mmol) as the base. The mixture was stirred at room temperature for 12 h (monitored by TLC). Then the solvent was evaporated under vacuum, and the residue was purified by flash column chromatography (silica gel, Hex/AcOEt, v/v, 3:1) giving the title compound. Single crystals were obtained by slow evaporation of a CH₂Cl₂ and iPrOH solution (v/v, 1:1).

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 asymmetric unit of the structure of the title compound. Displacement ellipsoids are drawn at the 50% probability level.
	Fig. 2. The molecular packing of the title compounds.

(2S,3R)-3-(2-Bromophenyl)-2-nitro-2,3,6,7-tetrahydro-1-benzofuran-4(5H)-one top

Crystal data top

C₁₄H₁₂BrNO₄	F(000) = 680
M_r = 338.16	D_x = 1.633 Mg m⁻³
Orthorhombic, P2₁2₁2₁	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2ab	Cell parameters from 6447 reflections
a = 7.2162 (8) Å	θ = 3.1–27.4°
b = 7.3372 (8) Å	µ = 3.00 mm⁻¹
c = 25.9727 (13) Å	T = 296 K
V = 1375.2 (2) Å³	Needle, colorless
Z = 4	0.54 × 0.31 × 0.23 mm

Data collection top

Rigaku R-AXIS RAPID/ZJUG diffractometer	2548 independent reflections
Radiation source: rotating anode	1456 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.068
Detector resolution: 10.00 pixels mm^-1	θ_max = 25.5°, θ_min = 3.1°
ω scans	h = −8→8
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	k = −8→7
T_min = 0.334, T_max = 0.505	l = −31→31
10897 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)] = 0.059	w = 1/[σ²(F_o²) + (0.0081P)² + 2.5658P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.125	(Δ/σ)_max < 0.001
S = 1.00	Δρ_max = 0.51 e Å⁻³
2548 reflections	Δρ_min = −0.57 e Å⁻³
182 parameters	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0117 (17)
Primary atom site location: structure-invariant direct methods	Absolute structure: Flack (1983), 1041 Friedel pairs
Secondary atom site location: difference Fourier map	Absolute structure parameter: 0.03 (2)

Crystal data top

C₁₄H₁₂BrNO₄	V = 1375.2 (2) Å³
M_r = 338.16	Z = 4
Orthorhombic, P2₁2₁2₁	Mo Kα radiation
a = 7.2162 (8) Å	µ = 3.00 mm⁻¹
b = 7.3372 (8) Å	T = 296 K
c = 25.9727 (13) Å	0.54 × 0.31 × 0.23 mm

Data collection top

Rigaku R-AXIS RAPID/ZJUG diffractometer	2548 independent reflections
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	1456 reflections with I > 2σ(I)
T_min = 0.334, T_max = 0.505	R_int = 0.068
10897 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.059	H-atom parameters constrained
wR(F²) = 0.125	Δρ_max = 0.51 e Å⁻³
S = 1.00	Δρ_min = −0.57 e Å⁻³
2548 reflections	Absolute structure: Flack (1983), 1041 Friedel pairs
182 parameters	Absolute structure parameter: 0.03 (2)
0 restraints

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	0.7398 (10)	0.3494 (8)	0.5784 (2)	0.0619 (16)
H1	0.8610	0.3377	0.5952	0.074*
C2	0.5793 (7)	0.3053 (8)	0.6169 (2)	0.0516 (15)
H2	0.5270	0.1847	0.6098	0.062*
C3	0.4449 (7)	0.4531 (9)	0.6016 (2)	0.0492 (14)
C4	0.2478 (9)	0.4690 (8)	0.6141 (2)	0.0569 (14)
C5	0.1536 (9)	0.6322 (9)	0.5902 (2)	0.0660 (19)
H5A	0.0550	0.6715	0.6131	0.079*
H5B	0.0968	0.5944	0.5581	0.079*
C6	0.2792 (9)	0.7952 (8)	0.5794 (2)	0.0677 (18)
H6A	0.3187	0.8488	0.6117	0.081*
H6B	0.2102	0.8867	0.5604	0.081*
C7	0.4499 (9)	0.7389 (9)	0.5482 (2)	0.0660 (18)
H7A	0.4154	0.7167	0.5126	0.079*
H7B	0.5416	0.8355	0.5489	0.079*
C8	0.5265 (8)	0.5737 (9)	0.5708 (2)	0.0506 (15)
C9	0.6438 (8)	0.3183 (8)	0.6723 (2)	0.0532 (15)
C10	0.6320 (9)	0.4785 (10)	0.7000 (3)	0.0721 (19)
H10	0.5734	0.5781	0.6850	0.087*
C11	0.7034 (10)	0.4972 (12)	0.7491 (3)	0.085 (2)
H11	0.6976	0.6076	0.7666	0.102*
C12	0.7845 (11)	0.3438 (16)	0.7712 (3)	0.098 (3)
H12	0.8302	0.3514	0.8046	0.118*
C13	0.7987 (11)	0.1840 (14)	0.7455 (4)	0.096 (3)
H13	0.8524	0.0836	0.7615	0.116*
C14	0.7336 (10)	0.1696 (8)	0.6957 (3)	0.0698 (18)
N1	0.7257 (12)	0.2243 (10)	0.5319 (3)	0.091 (2)
O1	0.1679 (6)	0.3594 (7)	0.64055 (19)	0.0816 (14)
O2	0.7098 (5)	0.5307 (6)	0.56089 (15)	0.0623 (12)
O3	0.7909 (12)	0.0725 (9)	0.5383 (3)	0.147 (3)
O4	0.6648 (14)	0.2703 (15)	0.4940 (3)	0.211 (5)
Br1	0.75326 (16)	−0.05596 (11)	0.66299 (5)	0.1322 (6)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
C1	0.042 (3)	0.072 (4)	0.073 (4)	−0.007 (4)	0.004 (4)	−0.006 (3)
C2	0.046 (3)	0.053 (3)	0.057 (4)	−0.010 (3)	0.002 (3)	−0.004 (3)
C3	0.046 (3)	0.064 (4)	0.037 (3)	−0.008 (3)	−0.001 (3)	−0.002 (3)
C4	0.051 (3)	0.069 (4)	0.051 (3)	−0.004 (4)	−0.005 (3)	−0.003 (3)
C5	0.057 (4)	0.090 (5)	0.051 (4)	0.003 (4)	−0.007 (3)	0.000 (4)
C6	0.067 (5)	0.062 (4)	0.074 (4)	0.004 (4)	−0.013 (4)	0.005 (3)
C7	0.072 (5)	0.068 (4)	0.058 (4)	−0.008 (4)	−0.014 (4)	0.012 (3)
C8	0.050 (3)	0.061 (4)	0.040 (3)	−0.010 (3)	−0.005 (3)	−0.003 (3)
C9	0.045 (3)	0.059 (4)	0.056 (4)	−0.006 (3)	0.001 (3)	0.006 (3)
C10	0.070 (4)	0.087 (5)	0.059 (4)	0.006 (4)	−0.003 (4)	−0.006 (4)
C11	0.082 (5)	0.112 (7)	0.061 (5)	0.004 (5)	−0.009 (4)	−0.012 (4)
C12	0.070 (6)	0.180 (9)	0.044 (4)	−0.010 (6)	−0.014 (4)	0.026 (6)
C13	0.071 (6)	0.123 (7)	0.095 (7)	0.000 (6)	−0.016 (5)	0.036 (6)
C14	0.050 (4)	0.074 (4)	0.085 (5)	0.009 (4)	−0.005 (4)	0.014 (4)
N1	0.098 (5)	0.091 (5)	0.082 (5)	0.002 (5)	0.033 (4)	−0.027 (4)
O1	0.056 (3)	0.104 (4)	0.085 (3)	−0.014 (3)	0.010 (2)	0.022 (3)
O2	0.047 (3)	0.071 (3)	0.068 (3)	−0.009 (2)	0.012 (2)	0.001 (2)
O3	0.195 (8)	0.093 (4)	0.152 (6)	−0.001 (6)	0.066 (6)	−0.038 (4)
O4	0.293 (12)	0.231 (9)	0.108 (6)	0.139 (9)	−0.073 (7)	−0.096 (6)
Br1	0.1192 (8)	0.0727 (5)	0.2046 (12)	0.0255 (6)	−0.0517 (9)	0.0010 (6)

Geometric parameters (Å, º) top

C1—O2	1.423 (7)	C7—C8	1.455 (8)
C1—N1	1.520 (8)	C7—H7A	0.9700
C1—C2	1.563 (8)	C7—H7B	0.9700
C1—H1	0.9800	C8—O2	1.384 (7)
C2—C3	1.507 (8)	C9—C10	1.381 (9)
C2—C9	1.517 (8)	C9—C14	1.407 (8)
C2—H2	0.9800	C10—C11	1.382 (9)
C3—C8	1.332 (8)	C10—H10	0.9300
C3—C4	1.463 (8)	C11—C12	1.393 (11)
C4—O1	1.205 (6)	C11—H11	0.9300
C4—C5	1.510 (8)	C12—C13	1.352 (11)
C5—C6	1.527 (8)	C12—H12	0.9300
C5—H5A	0.9700	C13—C14	1.380 (10)
C5—H5B	0.9700	C13—H13	0.9300
C6—C7	1.531 (9)	C14—Br1	1.866 (7)
C6—H6A	0.9700	N1—O4	1.130 (9)
C6—H6B	0.9700	N1—O3	1.221 (9)

O2—C1—N1	107.4 (5)	C8—C7—H7A	110.0
O2—C1—C2	106.5 (5)	C6—C7—H7A	110.0
N1—C1—C2	109.5 (5)	C8—C7—H7B	110.0
O2—C1—H1	111.1	C6—C7—H7B	110.0
N1—C1—H1	111.1	H7A—C7—H7B	108.4
C2—C1—H1	111.1	C3—C8—O2	112.5 (6)
C3—C2—C9	113.7 (5)	C3—C8—C7	129.0 (6)
C3—C2—C1	99.3 (5)	O2—C8—C7	118.5 (5)
C9—C2—C1	111.5 (5)	C10—C9—C14	117.6 (6)
C3—C2—H2	110.7	C10—C9—C2	121.9 (6)
C9—C2—H2	110.7	C14—C9—C2	120.2 (6)
C1—C2—H2	110.7	C9—C10—C11	122.8 (7)
C8—C3—C4	120.6 (6)	C9—C10—H10	118.6
C8—C3—C2	110.6 (5)	C11—C10—H10	118.6
C4—C3—C2	128.7 (5)	C10—C11—C12	117.2 (7)
O1—C4—C3	122.5 (6)	C10—C11—H11	121.4
O1—C4—C5	123.2 (6)	C12—C11—H11	121.4
C3—C4—C5	114.3 (6)	C13—C12—C11	121.9 (7)
C4—C5—C6	115.4 (5)	C13—C12—H12	119.0
C4—C5—H5A	108.4	C11—C12—H12	119.0
C6—C5—H5A	108.4	C12—C13—C14	120.2 (8)
C4—C5—H5B	108.4	C12—C13—H13	119.9
C6—C5—H5B	108.4	C14—C13—H13	119.9
H5A—C5—H5B	107.5	C13—C14—C9	120.1 (7)
C5—C6—C7	111.4 (5)	C13—C14—Br1	118.0 (6)
C5—C6—H6A	109.4	C9—C14—Br1	121.7 (5)
C7—C6—H6A	109.4	O4—N1—O3	122.7 (9)
C5—C6—H6B	109.4	O4—N1—C1	122.6 (8)
C7—C6—H6B	109.4	O3—N1—C1	114.7 (8)
H6A—C6—H6B	108.0	C8—O2—C1	107.4 (5)
C8—C7—C6	108.5 (5)

O2—C1—C2—C3	17.9 (6)	C1—C2—C9—C10	90.7 (7)
N1—C1—C2—C3	−98.0 (6)	C3—C2—C9—C14	165.2 (5)
O2—C1—C2—C9	−102.2 (6)	C1—C2—C9—C14	−83.6 (7)
N1—C1—C2—C9	142.0 (6)	C14—C9—C10—C11	−0.2 (10)
C9—C2—C3—C8	107.2 (6)	C2—C9—C10—C11	−174.6 (6)
C1—C2—C3—C8	−11.3 (6)	C9—C10—C11—C12	−2.2 (11)
C9—C2—C3—C4	−76.5 (7)	C10—C11—C12—C13	2.0 (13)
C1—C2—C3—C4	165.1 (5)	C11—C12—C13—C14	0.7 (14)
C8—C3—C4—O1	177.6 (6)	C12—C13—C14—C9	−3.2 (12)
C2—C3—C4—O1	1.6 (9)	C12—C13—C14—Br1	−178.8 (7)
C8—C3—C4—C5	−1.4 (8)	C10—C9—C14—C13	3.0 (10)
C2—C3—C4—C5	−177.5 (5)	C2—C9—C14—C13	177.5 (6)
O1—C4—C5—C6	153.7 (6)	C10—C9—C14—Br1	178.4 (5)
C3—C4—C5—C6	−27.3 (7)	C2—C9—C14—Br1	−7.1 (8)
C4—C5—C6—C7	52.2 (7)	O2—C1—N1—O4	−14.4 (12)
C5—C6—C7—C8	−45.7 (7)	C2—C1—N1—O4	101.0 (11)
C4—C3—C8—O2	−176.3 (5)	O2—C1—N1—O3	163.3 (7)
C2—C3—C8—O2	0.4 (7)	C2—C1—N1—O3	−81.4 (9)
C4—C3—C8—C7	4.9 (10)	C3—C8—O2—C1	12.2 (6)
C2—C3—C8—C7	−178.4 (6)	C7—C8—O2—C1	−168.9 (5)
C6—C7—C8—C3	19.8 (9)	N1—C1—O2—C8	98.3 (6)
C6—C7—C8—O2	−158.9 (5)	C2—C1—O2—C8	−19.0 (6)
C3—C2—C9—C10	−20.5 (8)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C1—H1···O1ⁱ	0.98	2.51	3.486 (12)	171
C7—H7A···O3ⁱⁱ	0.97	2.66	3.403 (12)	134
C7—H7B···O3ⁱⁱⁱ	0.97	2.52	3.480 (13)	172

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

Experimental details

Crystal data
Chemical formula	C₁₄H₁₂BrNO₄
M_r	338.16
Crystal system, space group	Orthorhombic, P2₁2₁2₁
Temperature (K)	296
a, b, c (Å)	7.2162 (8), 7.3372 (8), 25.9727 (13)
V (Å³)	1375.2 (2)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	3.00
Crystal size (mm)	0.54 × 0.31 × 0.23

Data collection
Diffractometer	Rigaku R-AXIS RAPID/ZJUG diffractometer
Absorption correction	Multi-scan (ABSCOR; Higashi, 1995)
T_min, T_max	0.334, 0.505
No. of measured, independent and observed [I > 2σ(I)] reflections	10897, 2548, 1456
R_int	0.068
(sin θ/λ)_max (Å⁻¹)	0.606

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.059, 0.125, 1.00
No. of reflections	2548
No. of parameters	182
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.51, −0.57
Absolute structure	Flack (1983), 1041 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
C1—H1···O1ⁱ	0.98	2.51	3.486 (12)	171.2
C7—H7A···O3ⁱⁱ	0.97	2.66	3.403 (12)	134.0
C7—H7B···O3ⁱⁱⁱ	0.97	2.52	3.480 (13)	172.1

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

Acknowledgements

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (No. Y4110373). We are also grateful for the help of Professor Jian-Ming Gu of Zhejiang University.

References

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