(S)-3-Acetyl-3-[(R)-1-(4-bromo­phen­yl)-2-nitro­eth­yl]oxolan-2-one

Wang, Y.; Chen, R.; Li, Z.; Xu, D.

doi:10.1107/S1600536811051725

organic compounds

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ISSN: 2056-9890

Volume 68| Part 1| January 2012| Page o110

doi:10.1107/S1600536811051725

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(S)-3-Acetyl-3-[(R)-1-(4-bromophenyl)-2-nitroethyl]oxolan-2-one

Yifeng Wang,^a Ruxiang Chen,^a Zhaobo Li ^b and Danqian Xu ^a ^*

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

(Received 18 November 2011; accepted 1 December 2011; online 14 December 2011)

The title compound, C₁₄H₁₄BrNO₅, has two chiral C atoms. The quaternary C atom in the oxolanone ring has an S configuration, while the adjacent tertiary C atom has an R configuration. The oxolanone ring adopts an envelope conformation, with the flap C atom lying 0.298 (3) Å from the mean plane of the remaining four atoms. In the crystal, molecules are connected into chains along [010] via weak C—H⋯O hydrogen bonds.

Related literature

For general background, see: Li et al. (2009 ), Malerich et al. (2008 ); For related structures, see: Li et al. (2005 ).

Experimental

Crystal data

C₁₄H₁₄BrNO₅
M_r = 356.17
Monoclinic, P 2₁
a = 9.6237 (7) Å
b = 6.6547 (4) Å
c = 12.0503 (8) Å
β = 105.794 (2)°
V = 742.60 (9) Å³
Z = 2
Mo Kα radiation
μ = 2.79 mm⁻¹
T = 296 K
0.43 × 0.27 × 0.22 mm

Data collection

Rigaku R-AXIS RAPID/ZJUG diffractometer
Absorption correction: multi-scan (ABSCOR; Higashi, 1995 ) T_min = 0.301, T_max = 0.542
7336 measured reflections
3272 independent reflections
1893 reflections with I > 2σ(I)
R_int = 0.041

Refinement

R[F² > 2σ(F²)] = 0.033
wR(F²) = 0.104
S = 1.00
3272 reflections
192 parameters
1 restraint
H-atom parameters constrained
Δρ_max = 0.45 e Å⁻³
Δρ_min = −0.45 e Å⁻³
Absolute structure: Flack (1983 ), 1327 Friedel pairs
Flack parameter: 0.014 (14)

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
C11—H11⋯O5ⁱ	0.93	2.58	3.306 (2)	135
C10—H10⋯O3ⁱⁱ	0.93	2.63	3.514 (2)	158
Symmetry codes: (i) x, y-1, z; (ii) $[-x+1, y-{\script{1\over 2}}, -z+1]$ .

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, 1997 ); software used to prepare material for publication: WinGX (Farrugia, 1999 ).

Supporting information

Crystal structure: contains datablocks global, I. DOI: 10.1107/S1600536811051725/pk2367sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536811051725/pk2367Isup2.hkl

Supporting information file. DOI: 10.1107/S1600536811051725/pk2367Isup3.cml

checkCIF report

Comment top

The organocatalytic Michael reaction is often regarded as one of the most efficient and broadly applicable carbon-carbon bond-forming reactions. One of the most studied reactions is the Michael addition of 1,3-dicarbonyl compounds to nitroolefins because the highly functionalized nitro compounds are versatile intermediates in organic synthesis. The title compound, which was readily synthesized by the organocatalytic Michael reaction of 3-acetyldihydrofuran-2(3H)-one to (E)-1-bromo-4-(2-nitrovinyl)benzene, could act as an intermediate in organic and natural product synthesis. In this article, the crystal structure of the title compoud (S)-3-acetyl-3-((R) -1-(4-bromophenyl)-2-nitroethyl)dihydrofuran-2(3H)-one is described (Fig. 1). The structure has two chiral centers. The quaternary carbon in the oxolanone ring of the title compound adopts an S configuration, while the adjacent tertiary carbon atom has R configuration. The oxolanone ring displays an envelope conformation, with the flap carbon atom lying 0.298 (3) Å from the mean plane of the remaining four atoms. In the crystal, molecules are connected into chains along the b axis direction by weak C11—H11···O5ⁱ and C10—H10···O3ⁱⁱ hydrogen bonds [Symmetry code: (i)x, -1 + y, z; (ii) 1 - x, -1/2 + y, 1 - z] (Fig. 2).

Related literature top

For general background [to what?], see: Li et al. (2009), Malerich et al. (2008); For related structures, see: Li et al. (2005).

Experimental top

To a solution of (E)-1-bromo-4-(2-nitrovinyl)benzene (1 mmol) and 3-acetyldihydrofuran-2(3H)-one (1 mmol) in 1,4-dioxane (3 ml) was added 3-((1S)-(6-methoxyquinolin-4-yl) (8-vinylquinuclidin-2-yl)methylamino)-4- ((S)-1-phenylethylamino)cyclobut -3-ene-1,2-dione(0.025 mmol) as catalyst, and the mixture was stirred at room temperature for 12 h (monitored by TLC). Then the solvent was distilled 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.

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, 1997); software used to prepare material for publication: WinGX (Farrugia, 1999).

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. A view showing infinite chains with C11—H11···O5ⁱ and C10—H10···O3ⁱⁱ hydrogen bonds [Symmetry code: (i) x, -1 + y, z; (ii) 1 - x, -1/2 + y, 1 - z].

(S)-3-Acetyl-3-[(R)-1-(4-bromophenyl)-2-nitroethyl]oxolan-2-one top

Crystal data top

C₁₄H₁₄BrNO₅	F(000) = 360
M_r = 356.17	D_x = 1.593 Mg m⁻³
Monoclinic, P2₁	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2yb	Cell parameters from 5006 reflections
a = 9.6237 (7) Å	θ = 3.1–27.4°
b = 6.6547 (4) Å	µ = 2.79 mm⁻¹
c = 12.0503 (8) Å	T = 296 K
β = 105.794 (2)°	Block, colourless
V = 742.60 (9) Å³	0.43 × 0.27 × 0.22 mm
Z = 2

Data collection top

Rigaku R-AXIS RAPID/ZJUG diffractometer	3272 independent reflections
Radiation source: rotating anode	1893 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.041
Detector resolution: 10.00 pixels mm^-1	θ_max = 27.4°, θ_min = 3.2°
ω scans	h = −12→12
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	k = −8→8
T_min = 0.301, T_max = 0.542	l = −15→15
7336 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)] = 0.033	w = 1/[σ²(F_o²) + (0.0212P)² + 0.6532P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.104	(Δ/σ)_max < 0.001
S = 1.00	Δρ_max = 0.45 e Å⁻³
3272 reflections	Δρ_min = −0.45 e Å⁻³
192 parameters	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
1 restraint	Extinction coefficient: 0.013 (2)
Primary atom site location: structure-invariant direct methods	Absolute structure: Flack (1983), 1327 Friedel pairs
Secondary atom site location: difference Fourier map	Absolute structure parameter: 0.014 (14)

Crystal data top

C₁₄H₁₄BrNO₅	V = 742.60 (9) Å³
M_r = 356.17	Z = 2
Monoclinic, P2₁	Mo Kα radiation
a = 9.6237 (7) Å	µ = 2.79 mm⁻¹
b = 6.6547 (4) Å	T = 296 K
c = 12.0503 (8) Å	0.43 × 0.27 × 0.22 mm
β = 105.794 (2)°

Data collection top

Rigaku R-AXIS RAPID/ZJUG diffractometer	3272 independent reflections
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	1893 reflections with I > 2σ(I)
T_min = 0.301, T_max = 0.542	R_int = 0.041
7336 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.033	H-atom parameters constrained
wR(F²) = 0.104	Δρ_max = 0.45 e Å⁻³
S = 1.00	Δρ_min = −0.45 e Å⁻³
3272 reflections	Absolute structure: Flack (1983), 1327 Friedel pairs
192 parameters	Absolute structure parameter: 0.014 (14)
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
Br1	0.01386 (6)	0.39571 (12)	0.91217 (5)	0.0776 (3)
O1	0.6151 (4)	0.8445 (6)	0.9285 (3)	0.0692 (12)
O2	0.5776 (5)	1.1368 (6)	0.8363 (4)	0.0713 (12)
O3	0.6176 (3)	0.9028 (8)	0.5481 (3)	0.0608 (8)
O4	0.2157 (5)	0.9380 (9)	0.4296 (4)	0.0967 (17)
O5	0.1045 (5)	1.0968 (9)	0.5321 (5)	0.121 (2)
N1	0.2123 (6)	1.0229 (7)	0.5175 (4)	0.0647 (12)
C1	0.4009 (5)	0.8284 (6)	0.6525 (4)	0.0429 (11)
H1	0.3954	0.7478	0.5833	0.051*
C2	0.5624 (5)	0.8272 (6)	0.7251 (4)	0.0424 (11)
C3	0.6125 (6)	0.6151 (8)	0.7740 (5)	0.0550 (13)
H3A	0.5456	0.5124	0.7346	0.066*
H3B	0.7080	0.5846	0.7665	0.066*
C4	0.6136 (8)	0.6296 (10)	0.9003 (5)	0.0751 (18)
H4A	0.5284	0.5655	0.9125	0.090*
H4B	0.6985	0.5636	0.9487	0.090*
C5	0.5860 (5)	0.9572 (8)	0.8336 (4)	0.0524 (14)
C6	0.6619 (5)	0.8984 (11)	0.6521 (4)	0.0505 (10)
C7	0.8152 (6)	0.9490 (11)	0.7133 (5)	0.085 (2)
H7A	0.8786	0.8842	0.6752	0.127*
H7B	0.8368	0.9035	0.7917	0.127*
H7C	0.8286	1.0919	0.7121	0.127*
C8	0.3494 (6)	1.0384 (8)	0.6113 (4)	0.0506 (13)
H8A	0.3336	1.1162	0.6749	0.061*
H8B	0.4221	1.1062	0.5829	0.061*
C9	0.2998 (5)	0.7295 (7)	0.7150 (4)	0.0421 (11)
C10	0.2338 (5)	0.5493 (7)	0.6755 (4)	0.0494 (12)
H10	0.2479	0.4934	0.6087	0.059*
C11	0.1475 (5)	0.4496 (7)	0.7317 (4)	0.0528 (13)
H11	0.1046	0.3277	0.7042	0.063*
C12	0.1266 (5)	0.5352 (8)	0.8298 (4)	0.0498 (12)
C13	0.1879 (6)	0.7160 (9)	0.8705 (5)	0.0616 (15)
H13	0.1721	0.7721	0.9367	0.074*
C14	0.2725 (6)	0.8132 (7)	0.8127 (4)	0.0548 (13)
H14	0.3124	0.9373	0.8393	0.066*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Br1	0.0668 (3)	0.1015 (5)	0.0779 (4)	−0.0184 (4)	0.0426 (3)	−0.0001 (4)
O1	0.077 (2)	0.091 (4)	0.0396 (18)	0.004 (2)	0.0162 (17)	0.010 (2)
O2	0.089 (3)	0.052 (3)	0.070 (3)	−0.007 (2)	0.018 (2)	−0.014 (2)
O3	0.073 (2)	0.0688 (19)	0.0500 (18)	−0.006 (3)	0.0329 (16)	0.001 (3)
O4	0.105 (3)	0.120 (5)	0.054 (2)	0.013 (3)	0.002 (2)	−0.020 (3)
O5	0.070 (3)	0.150 (5)	0.124 (4)	0.035 (3)	−0.005 (3)	−0.052 (4)
N1	0.070 (3)	0.059 (3)	0.059 (3)	0.004 (2)	0.008 (3)	−0.001 (2)
C1	0.051 (3)	0.039 (3)	0.043 (2)	0.002 (2)	0.020 (2)	0.001 (2)
C2	0.051 (3)	0.037 (2)	0.045 (2)	0.0014 (19)	0.023 (2)	0.0041 (19)
C3	0.050 (3)	0.052 (3)	0.067 (3)	0.005 (2)	0.024 (3)	0.012 (3)
C4	0.081 (5)	0.073 (4)	0.073 (4)	0.012 (3)	0.024 (4)	0.029 (4)
C5	0.048 (3)	0.065 (4)	0.046 (3)	−0.003 (2)	0.016 (2)	0.003 (2)
C6	0.054 (3)	0.046 (2)	0.057 (3)	−0.003 (3)	0.025 (2)	0.001 (3)
C7	0.062 (3)	0.119 (7)	0.079 (4)	−0.024 (4)	0.028 (3)	0.001 (4)
C8	0.055 (3)	0.042 (3)	0.052 (3)	0.003 (3)	0.010 (3)	−0.001 (2)
C9	0.043 (3)	0.041 (2)	0.046 (3)	0.001 (2)	0.017 (2)	0.000 (2)
C10	0.057 (3)	0.048 (3)	0.049 (3)	−0.007 (2)	0.025 (2)	−0.012 (2)
C11	0.053 (3)	0.053 (3)	0.059 (3)	−0.003 (2)	0.027 (2)	−0.006 (2)
C12	0.039 (3)	0.064 (3)	0.050 (3)	−0.002 (2)	0.019 (2)	0.002 (3)
C13	0.054 (3)	0.083 (4)	0.056 (3)	−0.009 (3)	0.028 (3)	−0.020 (3)
C14	0.062 (3)	0.056 (3)	0.056 (3)	−0.013 (2)	0.033 (3)	−0.021 (2)

Geometric parameters (Å, º) top

Br1—C12	1.900 (5)	C4—H4A	0.9700
O1—C5	1.332 (6)	C4—H4B	0.9700
O1—C4	1.470 (8)	C6—C7	1.497 (7)
O2—C5	1.199 (6)	C7—H7A	0.9600
O3—C6	1.210 (5)	C7—H7B	0.9600
O4—N1	1.208 (6)	C7—H7C	0.9600
O5—N1	1.204 (6)	C8—H8A	0.9700
N1—C8	1.489 (7)	C8—H8B	0.9700
C1—C8	1.521 (6)	C9—C10	1.380 (6)
C1—C9	1.532 (6)	C9—C14	1.391 (6)
C1—C2	1.562 (7)	C10—C11	1.376 (7)
C1—H1	0.9800	C10—H10	0.9300
C2—C5	1.532 (6)	C11—C12	1.375 (7)
C2—C6	1.541 (6)	C11—H11	0.9300
C2—C3	1.555 (6)	C12—C13	1.371 (7)
C3—C4	1.522 (8)	C13—C14	1.369 (7)
C3—H3A	0.9700	C13—H13	0.9300
C3—H3B	0.9700	C14—H14	0.9300

C5—O1—C4	111.3 (4)	O3—C6—C2	120.0 (4)
O5—N1—O4	123.4 (5)	C7—C6—C2	118.1 (4)
O5—N1—C8	118.7 (5)	C6—C7—H7A	109.5
O4—N1—C8	117.9 (5)	C6—C7—H7B	109.5
C8—C1—C9	111.2 (4)	H7A—C7—H7B	109.5
C8—C1—C2	111.9 (4)	C6—C7—H7C	109.5
C9—C1—C2	113.0 (4)	H7A—C7—H7C	109.5
C8—C1—H1	106.8	H7B—C7—H7C	109.5
C9—C1—H1	106.8	N1—C8—C1	109.1 (4)
C2—C1—H1	106.8	N1—C8—H8A	109.9
C5—C2—C6	110.0 (4)	C1—C8—H8A	109.9
C5—C2—C3	103.3 (4)	N1—C8—H8B	109.9
C6—C2—C3	108.6 (4)	C1—C8—H8B	109.9
C5—C2—C1	111.7 (4)	H8A—C8—H8B	108.3
C6—C2—C1	110.9 (4)	C10—C9—C14	117.7 (4)
C3—C2—C1	112.1 (4)	C10—C9—C1	119.9 (4)
C4—C3—C2	103.8 (4)	C14—C9—C1	122.4 (4)
C4—C3—H3A	111.0	C11—C10—C9	122.1 (5)
C2—C3—H3A	111.0	C11—C10—H10	118.9
C4—C3—H3B	111.0	C9—C10—H10	118.9
C2—C3—H3B	111.0	C10—C11—C12	118.2 (5)
H3A—C3—H3B	109.0	C10—C11—H11	120.9
O1—C4—C3	106.8 (4)	C12—C11—H11	120.9
O1—C4—H4A	110.4	C13—C12—C11	121.4 (5)
C3—C4—H4A	110.4	C13—C12—Br1	119.5 (4)
O1—C4—H4B	110.4	C11—C12—Br1	119.0 (4)
C3—C4—H4B	110.4	C14—C13—C12	119.4 (5)
H4A—C4—H4B	108.6	C14—C13—H13	120.3
O2—C5—O1	122.5 (5)	C12—C13—H13	120.3
O2—C5—C2	126.2 (5)	C13—C14—C9	121.1 (5)
O1—C5—C2	111.3 (4)	C13—C14—H14	119.5
O3—C6—C7	121.8 (4)	C9—C14—H14	119.5

C8—C1—C2—C5	60.9 (5)	C5—C2—C6—C7	43.1 (7)
C9—C1—C2—C5	−65.5 (5)	C3—C2—C6—C7	−69.3 (7)
C8—C1—C2—C6	−62.2 (5)	C1—C2—C6—C7	167.1 (5)
C9—C1—C2—C6	171.4 (4)	O5—N1—C8—C1	117.9 (6)
C8—C1—C2—C3	176.3 (4)	O4—N1—C8—C1	−62.9 (7)
C9—C1—C2—C3	49.8 (5)	C9—C1—C8—N1	−68.4 (5)
C5—C2—C3—C4	17.2 (5)	C2—C1—C8—N1	164.2 (4)
C6—C2—C3—C4	133.9 (5)	C8—C1—C9—C10	121.9 (5)
C1—C2—C3—C4	−103.2 (5)	C2—C1—C9—C10	−111.2 (5)
C5—O1—C4—C3	12.5 (7)	C8—C1—C9—C14	−59.0 (6)
C2—C3—C4—O1	−18.2 (6)	C2—C1—C9—C14	67.8 (6)
C4—O1—C5—O2	177.8 (5)	C14—C9—C10—C11	−2.3 (7)
C4—O1—C5—C2	−0.8 (6)	C1—C9—C10—C11	176.8 (5)
C6—C2—C5—O2	54.9 (7)	C9—C10—C11—C12	0.6 (8)
C3—C2—C5—O2	170.7 (5)	C10—C11—C12—C13	0.8 (8)
C1—C2—C5—O2	−68.7 (7)	C10—C11—C12—Br1	−177.7 (4)
C6—C2—C5—O1	−126.5 (4)	C11—C12—C13—C14	−0.4 (8)
C3—C2—C5—O1	−10.8 (5)	Br1—C12—C13—C14	178.1 (4)
C1—C2—C5—O1	109.9 (4)	C12—C13—C14—C9	−1.4 (9)
C5—C2—C6—O3	−140.6 (6)	C10—C9—C14—C13	2.7 (8)
C3—C2—C6—O3	107.0 (7)	C1—C9—C14—C13	−176.4 (5)
C1—C2—C6—O3	−16.5 (8)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C11—H11···O5ⁱ	0.93	2.58	3.306 (2)	135
C10—H10···O3ⁱⁱ	0.93	2.63	3.514 (2)	158

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

Experimental details

Crystal data
Chemical formula	C₁₄H₁₄BrNO₅
M_r	356.17
Crystal system, space group	Monoclinic, P2₁
Temperature (K)	296
a, b, c (Å)	9.6237 (7), 6.6547 (4), 12.0503 (8)
β (°)	105.794 (2)
V (Å³)	742.60 (9)
Z	2
Radiation type	Mo Kα
µ (mm⁻¹)	2.79
Crystal size (mm)	0.43 × 0.27 × 0.22

Data collection
Diffractometer	Rigaku R-AXIS RAPID/ZJUG diffractometer
Absorption correction	Multi-scan (ABSCOR; Higashi, 1995)
T_min, T_max	0.301, 0.542
No. of measured, independent and observed [I > 2σ(I)] reflections	7336, 3272, 1893
R_int	0.041
(sin θ/λ)_max (Å⁻¹)	0.648

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.033, 0.104, 1.00
No. of reflections	3272
No. of parameters	192
No. of restraints	1
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.45, −0.45
Absolute structure	Flack (1983), 1327 Friedel pairs
Absolute structure parameter	0.014 (14)

Computer programs: PROCESS-AUTO (Rigaku, 2006), CrystalStructure (Rigaku, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 1997), WinGX (Farrugia, 1999).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C11—H11···O5ⁱ	0.930	2.580	3.306 (2)	135
C10—H10···O3ⁱⁱ	0.930	2.633	3.514 (2)	158

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

Acknowledgements

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (No. Y4110373) and the Foundation of Zhejiang Education Committee (No. Y201018458). We are also grateful for the help of Professor Jian-Ming Gu of Zhejiang University.

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