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Acta Cryst. (2010). E66, m661-m662    [ doi:10.1107/S1600536810016995 ]

Di-[mu]2-cyanido-dicyanidobis{2,2'-[ethane-1,2-diylbis(nitrilomethylidyne)]diphenolato}(1,4,8,11-tetraazacyclotetradecane)dichromium(III)nickel(II) methanol disolvate

S. Wang, W. He, X. Ding and W. Huang

Abstract top

In the title compound, [Cr2Ni(C16H14N2O2)2(CN)4(C10H24N4)]·2CH3OH, each [Cr(salen)(CN)2] unit {salen is 2,2'-[ethane-1,2-diylbis(nitrilomethylidyne)]diphenolate} acts as a monodentate ligand through one of its two cyanide groups N bound to a central [Ni(cyclam)]2+ core (cyclam is 1,4,8,11-tetraazacyclotetradecane). Each CrIII ion is coordinated by two N and two O atoms from a salen ligand situated in the equatorial plane with two trans cyanide C atoms, yielding a distorted octahedral coordination geometry. The NiII atom lies on an inversion center and is octahedrally coordinated by a cyclam ligand lying in the equatorial plane and by two cyanide N atoms. The asymmetric unit contains one half of the complex molecule and a methanol solvent molecule. In the crystal structure, the complex molecule is linked to the methanol solvent molecules via O-H...O and N-H...O hydrogen bonds. Individual complex molecules are linked by C-H...N hydrogen bonds, forming chains along b.

Comment top

Cyanide-bridged infinite systems (or Prussian blue analogues) and high-spin clusters have attracted great research interest due to their unique magnetic properties, including high-Tc superconducting magnets and photoinduced magnetization. Among these interesting researches, low-dimensional complexes as well as polynuclear clusters have attracted special attention, because they can be used to investigate the inter-metallic magnetic coupling quantitatively (Lescouëzec et al., 2005).

Recently, a new cyanide-containing building block K[Cr(salen)(CN)2] (salen2- = N,N'- bis(salicyl)ethylenediaminate) with two trans cyanide groups has been exploited to assemble cyanide-bridged low-dimensional complexes (Ni et al., 2008). By using this new building block, we report here the synthesis and crystal structure of the title compound, [Cr(salen)(CN)2]2[Ni(cyclam)].CH3OH.

Complex I consists of a trinuclear cluster and one methanol solvate molecule. As shown in Fig. 1, in this trinuclear cluster, the [Cr(salen)(CN)2] unit acts as a monodentate ligand through one of its two cyanide groups toward a central [Ni(cyclam)]2+ core. The nickel atom is in an axially elongated octahedral environment. Four nitrogen atoms from the cyclam ligand form the equatorial plane. Two cyanide nitrogen atoms occupy the axial positions. The complex are linked with the methanol solvate molecules via O—H···O and N—H···O hydrogen bonds (Fig. 2). The individual complex molecules are linked by C—H···N hydrogen bonds to form chains along b.

Related literature top

For general background to cyanide-bridged low-dimensional complexes and polynuclear clusters, see: Lescouëzec et al. (2005). For a related structure, see: Ni et al. (2008). For synthesis of the complex components, see: Yamada et al. (1969); Bosnich et al. (1965).

Experimental top

K[Cr(salen)(CN)2].H2O was synthesized according to the procedure described in the literature (Yamada et al., 1969). Ni(cyclam)(ClO4)2 was synthesized as described previously (Bosnich et al., (1965).

A solution of K[Cr(salen)(CN)2].H2O (79.6 mg, 0.2 mmol) in methanol (5 ml) was added dropwise to a solution of Ni(cyclam)(ClO4)2 (45.5 mg, 0.1 mmol) in water (3 ml). The mixture was stirred at room temperature for 5 min s and then filtered. Orange block crystals of (I) suitable for X-ray analysis were obtained by slow evaporation of the filtrate.

Refinement top

Aromatic H atoms were placed in calculated positions with C—H = 0.93 Å, and refined in riding mode with Uiso(H) = 1.2Ueq(C).

Computing details top

Data collection: SMART (Bruker, 2007); cell refinement: SAINT (Bruker, 2007); data reduction: SAINT (Bruker, 2007); 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
[Figure 1] Fig. 1. The molecular structure of (I), shown with 50% probability displacement ellipsoids.The unlabeled atoms are derived from the reference atoms by means of the (2-x, -y, 2-z) symmetry transformation.
[Figure 2] Fig. 2. Packing diagram viewed down the c axis, The O—H···O and N—H···O hydrogen bonds are shown as dotted lines.
Di-µ2-cyanido-dicyanidobis{2,2'-[ethane-1,2- diylbis(nitrilomethylidyne)]diphenolato}(1,4,8,11- tetraazacyclotetradecane)dichromium(III)nickel(II) methanol disolvate top
Crystal data top
[Cr2Ni(C16H14N2O2)2(CN)4(C10H24N4)]·2CH4OF(000) = 1112
Mr = 1063.77Dx = 1.477 Mg m−3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 7889 reflections
a = 9.5711 (19) Åθ = 2.2–27.9°
b = 18.936 (4) ŵ = 0.90 mm−1
c = 13.593 (3) ÅT = 100 K
β = 103.93 (3)°Block, orange
V = 2391.1 (9) Å30.25 × 0.15 × 0.09 mm
Z = 2
Data collection top
Bruker SMART CCD area-detector
diffractometer		5363 independent reflections
Radiation source: fine-focus sealed tube5077 reflections with I > 2σ(I)
graphiteRint = 0.0000
Detector resolution: 8.366 pixels mm-1θmax = 27.5°, θmin = 3.2°
φ and ω scansh = 0→12
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)		k = 0→24
Tmin = 0.851, Tmax = 0.922l = −17→17
5363 measured reflections
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)] = 0.054Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.132H-atom parameters constrained
S = 1.16 w = 1/[σ2(Fo2) + (0.0531P)2 + 5.7746P]
where P = (Fo2 + 2Fc2)/3
5363 reflections(Δ/σ)max = 0.001
314 parametersΔρmax = 0.76 e Å−3
0 restraintsΔρmin = −0.76 e Å−3
Crystal data top
[Cr2Ni(C16H14N2O2)2(CN)4(C10H24N4)]·2CH4OV = 2391.1 (9) Å3
Mr = 1063.77Z = 2
Monoclinic, P21/cMo Kα radiation
a = 9.5711 (19) ŵ = 0.90 mm−1
b = 18.936 (4) ÅT = 100 K
c = 13.593 (3) Å0.25 × 0.15 × 0.09 mm
β = 103.93 (3)°
Data collection top
Bruker SMART CCD area-detector
diffractometer		5363 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)		5077 reflections with I > 2σ(I)
Tmin = 0.851, Tmax = 0.922Rint = 0.0000
5363 measured reflectionsθmax = 27.5°
Refinement top
R[F2 > 2σ(F2)] = 0.054H-atom parameters constrained
wR(F2) = 0.132Δρmax = 0.76 e Å−3
S = 1.16Δρmin = −0.76 e Å−3
5363 reflectionsAbsolute structure: ?
314 parametersFlack parameter: ?
0 restraintsRogers parameter: ?
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*/Ueq
O11.2639 (2)0.12757 (10)1.40979 (14)0.0198 (4)
C11.3690 (3)0.10694 (14)1.4854 (2)0.0196 (5)
C21.3393 (3)0.09542 (15)1.5811 (2)0.0238 (6)
H11.24660.10311.58890.029*
C31.4453 (4)0.07288 (16)1.6633 (2)0.0292 (6)
H21.42310.06711.72580.035*
C41.5836 (4)0.05875 (17)1.6546 (2)0.0302 (7)
H31.65320.04241.71000.036*
C51.6166 (3)0.06930 (15)1.5626 (2)0.0249 (6)
H41.70950.06001.55630.030*
C61.5121 (3)0.09400 (14)1.4777 (2)0.0205 (5)
C71.5585 (3)0.10267 (15)1.3849 (2)0.0211 (5)
H51.65030.08711.38400.025*
N11.4815 (2)0.13043 (12)1.30349 (17)0.0181 (4)
Cr11.28346 (4)0.17173 (2)1.28585 (3)0.01505 (12)
C81.3751 (3)0.26188 (15)1.3624 (2)0.0211 (5)
N21.4268 (3)0.31239 (15)1.4018 (2)0.0315 (6)
C91.1978 (3)0.08685 (13)1.19052 (19)0.0150 (5)
N31.1395 (3)0.05280 (14)1.1224 (2)0.0262 (5)
O21.08976 (19)0.21092 (10)1.25226 (14)0.0174 (4)
C101.0208 (3)0.23457 (13)1.1621 (2)0.0171 (5)
C110.8713 (3)0.24589 (14)1.1438 (2)0.0201 (5)
H60.82540.23721.19550.024*
C120.7910 (3)0.26948 (15)1.0515 (2)0.0230 (6)
H70.69240.27601.04200.028*
C130.8559 (3)0.28365 (16)0.9720 (2)0.0263 (6)
H80.80130.29890.90950.032*
C141.0025 (3)0.27454 (15)0.9879 (2)0.0226 (5)
H91.04690.28520.93590.027*
C151.0869 (3)0.24956 (14)1.0807 (2)0.0183 (5)
C161.2394 (3)0.24080 (14)1.0865 (2)0.0205 (5)
H101.27360.25601.03160.025*
N41.3299 (2)0.21365 (12)1.16162 (17)0.0179 (4)
C171.4833 (3)0.20758 (16)1.1619 (2)0.0231 (6)
H111.53740.24631.19970.028*
H121.49560.20891.09320.028*
C181.5359 (3)0.13719 (16)1.2118 (2)0.0222 (5)
H131.50060.09861.16560.027*
H141.64030.13581.22940.027*
Ni11.00000.00001.00000.01755 (13)
C191.2881 (3)−0.00106 (16)0.9439 (2)0.0234 (6)
H151.32930.02851.00190.028*
H161.34130.00730.89260.028*
N51.1361 (2)0.01852 (13)0.90325 (18)0.0207 (5)
H171.1026−0.00780.84650.025*
C201.1149 (3)0.09359 (15)0.8731 (2)0.0240 (6)
H181.14850.10180.81220.029*
H191.16980.12350.92650.029*
C210.9557 (3)0.11151 (16)0.8536 (2)0.0250 (6)
H200.94090.16110.83610.030*
H210.90140.08370.79730.030*
N60.9049 (3)0.09605 (13)0.94632 (17)0.0211 (5)
H220.94180.12980.99310.025*
C220.7465 (3)0.09755 (16)0.9297 (2)0.0239 (6)
H230.70450.06460.87620.029*
H240.71180.14440.90740.029*
C230.6967 (3)0.07874 (16)1.0240 (2)0.0251 (6)
H250.59620.09191.01310.030*
H260.75070.10711.07970.030*
C240.9633 (4)0.04217 (18)0.3659 (3)0.0322 (7)
H271.05370.02350.35900.048*
H280.89670.00410.36490.048*
H290.97730.06720.42890.048*
O30.9074 (2)0.08903 (12)0.28438 (17)0.0290 (5)
H300.96660.12010.28300.044*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0190 (9)0.0243 (9)0.0166 (9)0.0000 (7)0.0051 (7)−0.0010 (7)
C10.0251 (13)0.0169 (12)0.0168 (12)−0.0006 (10)0.0047 (10)−0.0012 (9)
C20.0291 (14)0.0225 (13)0.0217 (13)−0.0005 (11)0.0098 (11)−0.0008 (10)
C30.0450 (18)0.0252 (14)0.0165 (13)−0.0004 (13)0.0057 (12)0.0009 (11)
C40.0352 (16)0.0289 (15)0.0213 (14)−0.0003 (12)−0.0035 (12)0.0014 (11)
C50.0224 (13)0.0236 (13)0.0252 (14)−0.0003 (11)−0.0009 (11)0.0004 (11)
C60.0221 (13)0.0190 (12)0.0187 (12)−0.0047 (10)0.0018 (10)−0.0033 (10)
C70.0165 (12)0.0234 (13)0.0233 (13)0.0001 (10)0.0047 (10)−0.0046 (10)
N10.0161 (10)0.0236 (11)0.0163 (10)−0.0017 (8)0.0073 (8)−0.0038 (8)
Cr10.0139 (2)0.0187 (2)0.0133 (2)−0.00180 (14)0.00477 (15)−0.00241 (14)
C80.0179 (12)0.0277 (14)0.0182 (12)−0.0023 (10)0.0055 (10)−0.0047 (10)
N20.0283 (13)0.0338 (14)0.0339 (14)−0.0063 (11)0.0102 (11)−0.0067 (11)
C90.0132 (10)0.0153 (11)0.0165 (11)−0.0002 (9)0.0035 (9)−0.0035 (9)
N30.0231 (12)0.0284 (13)0.0282 (13)0.0007 (10)0.0083 (10)0.0018 (10)
O20.0157 (8)0.0225 (9)0.0151 (9)−0.0011 (7)0.0056 (7)0.0000 (7)
C100.0179 (12)0.0165 (11)0.0167 (12)−0.0006 (9)0.0038 (9)−0.0032 (9)
C110.0189 (12)0.0195 (12)0.0239 (13)0.0014 (10)0.0091 (10)0.0020 (10)
C120.0171 (12)0.0222 (13)0.0295 (15)0.0033 (10)0.0049 (11)0.0042 (11)
C130.0261 (14)0.0271 (14)0.0253 (14)0.0058 (11)0.0057 (11)0.0074 (11)
C140.0241 (13)0.0227 (13)0.0219 (13)0.0020 (10)0.0071 (11)0.0031 (10)
C150.0194 (12)0.0178 (12)0.0192 (12)0.0003 (9)0.0077 (10)0.0005 (9)
C160.0234 (13)0.0211 (12)0.0203 (13)−0.0021 (10)0.0121 (11)0.0000 (10)
N40.0155 (10)0.0221 (11)0.0188 (11)−0.0031 (8)0.0092 (8)−0.0009 (8)
C170.0155 (12)0.0356 (15)0.0204 (13)−0.0018 (11)0.0084 (10)0.0014 (11)
C180.0185 (12)0.0295 (14)0.0205 (13)0.0013 (10)0.0082 (10)−0.0025 (11)
Ni10.0168 (2)0.0196 (2)0.0167 (2)−0.00043 (17)0.00499 (18)−0.00011 (17)
C190.0179 (13)0.0315 (15)0.0223 (14)0.0001 (10)0.0077 (11)−0.0021 (11)
N50.0202 (11)0.0236 (11)0.0187 (11)−0.0001 (9)0.0053 (9)−0.0027 (9)
C200.0256 (13)0.0237 (13)0.0241 (13)−0.0018 (11)0.0089 (11)0.0020 (11)
C210.0316 (15)0.0248 (14)0.0198 (13)0.0036 (11)0.0087 (11)0.0025 (10)
N60.0221 (11)0.0230 (11)0.0176 (11)0.0009 (9)0.0038 (9)−0.0010 (9)
C220.0224 (13)0.0257 (14)0.0227 (13)0.0042 (11)0.0041 (11)−0.0007 (11)
C230.0218 (13)0.0303 (15)0.0235 (14)0.0040 (11)0.0060 (11)−0.0025 (11)
C240.0296 (15)0.0342 (17)0.0319 (16)−0.0043 (13)0.0059 (13)0.0031 (13)
O30.0240 (10)0.0339 (11)0.0288 (11)−0.0053 (9)0.0058 (9)0.0000 (9)
Geometric parameters (Å, °) top
O1—C11.313 (3)C16—H100.9300
O1—Cr11.930 (2)N4—C171.472 (3)
C1—C21.413 (4)C17—C181.525 (4)
C1—C61.420 (4)C17—H110.9700
C2—C31.384 (4)C17—H120.9700
C2—H10.9300C18—H130.9700
C3—C41.383 (5)C18—H140.9700
C3—H20.9300Ni1—N6i2.086 (2)
C4—C51.376 (5)Ni1—N62.086 (2)
C4—H30.9300Ni1—N5i2.092 (2)
C5—C61.413 (4)Ni1—N52.092 (2)
C5—H40.9300Ni1—N3i2.117 (3)
C6—C71.443 (4)C19—N51.473 (4)
C7—N11.285 (4)C19—C23i1.531 (4)
C7—H50.9300C19—H150.9700
N1—C181.467 (3)C19—H160.9700
N1—Cr12.011 (2)N5—C201.480 (4)
Cr1—O21.9464 (19)N5—H170.9100
Cr1—N42.010 (2)C20—C211.521 (4)
Cr1—C82.080 (3)C20—H180.9700
Cr1—C92.103 (2)C20—H190.9700
C8—N21.148 (4)C21—N61.485 (4)
C9—N31.156 (4)C21—H200.9700
N3—Ni12.117 (3)C21—H210.9700
O2—C101.322 (3)N6—C221.478 (4)
C10—C111.408 (4)N6—H220.9100
C10—C151.429 (4)C22—C231.513 (4)
C11—C121.379 (4)C22—H230.9700
C11—H60.9300C22—H240.9700
C12—C131.396 (4)C23—C19i1.531 (4)
C12—H70.9300C23—H250.9700
C13—C141.378 (4)C23—H260.9700
C13—H80.9300C24—O31.420 (4)
C14—C151.406 (4)C24—H270.9600
C14—H90.9300C24—H280.9600
C15—C161.453 (4)C24—H290.9600
C16—N41.277 (4)O3—H300.8200
C1—O1—Cr1126.52 (18)C18—C17—H12110.3
O1—C1—C2118.7 (3)H11—C17—H12108.6
O1—C1—C6124.3 (2)N1—C18—C17107.9 (2)
C2—C1—C6117.0 (3)N1—C18—H13110.1
C3—C2—C1121.3 (3)C17—C18—H13110.1
C3—C2—H1119.4N1—C18—H14110.1
C1—C2—H1119.4C17—C18—H14110.1
C4—C3—C2121.4 (3)H13—C18—H14108.4
C4—C3—H2119.3N6i—Ni1—N6180.000 (1)
C2—C3—H2119.3N6i—Ni1—N5i85.37 (9)
C5—C4—C3118.9 (3)N6—Ni1—N5i94.63 (9)
C5—C4—H3120.6N6i—Ni1—N594.63 (9)
C3—C4—H3120.6N6—Ni1—N585.37 (9)
C4—C5—C6121.2 (3)N5i—Ni1—N5180.0
C4—C5—H4119.4N6i—Ni1—N3i90.15 (10)
C6—C5—H4119.4N6—Ni1—N3i89.85 (10)
C5—C6—C1120.1 (3)N5i—Ni1—N3i92.54 (10)
C5—C6—C7116.4 (3)N5—Ni1—N3i87.46 (9)
C1—C6—C7123.4 (2)N6i—Ni1—N389.85 (10)
N1—C7—C6124.4 (3)N6—Ni1—N390.15 (10)
N1—C7—H5117.8N5i—Ni1—N387.46 (9)
C6—C7—H5117.8N5—Ni1—N392.54 (10)
C7—N1—C18121.3 (2)N3i—Ni1—N3180.0
C7—N1—Cr1126.18 (19)N5—C19—C23i111.5 (2)
C18—N1—Cr1112.47 (17)N5—C19—H15109.3
O1—Cr1—O294.74 (8)C23i—C19—H15109.3
O1—Cr1—N4172.76 (9)N5—C19—H16109.3
O2—Cr1—N492.47 (9)C23i—C19—H16109.3
O1—Cr1—N190.82 (9)H15—C19—H16108.0
O2—Cr1—N1173.49 (9)C19—N5—C20113.8 (2)
N4—Cr1—N182.02 (10)C19—N5—Ni1115.47 (18)
O1—Cr1—C892.10 (10)C20—N5—Ni1105.70 (17)
O2—Cr1—C893.88 (10)C19—N5—H17107.2
N4—Cr1—C886.81 (10)C20—N5—H17107.2
N1—Cr1—C889.29 (10)Ni1—N5—H17107.2
O1—Cr1—C995.82 (9)N5—C20—C21109.1 (2)
O2—Cr1—C986.51 (9)N5—C20—H18109.9
N4—Cr1—C985.20 (10)C21—C20—H18109.9
N1—Cr1—C989.57 (9)N5—C20—H19109.9
C8—Cr1—C9172.01 (11)C21—C20—H19109.9
N2—C8—Cr1177.7 (3)H18—C20—H19108.3
N3—C9—Cr1164.0 (2)N6—C21—C20109.1 (2)
C9—N3—Ni1170.0 (2)N6—C21—H20109.9
C10—O2—Cr1125.54 (16)C20—C21—H20109.9
O2—C10—C11118.3 (2)N6—C21—H21109.9
O2—C10—C15124.7 (2)C20—C21—H21109.9
C11—C10—C15117.0 (2)H20—C21—H21108.3
C12—C11—C10122.0 (3)C22—N6—C21113.6 (2)
C12—C11—H6119.0C22—N6—Ni1114.53 (18)
C10—C11—H6119.0C21—N6—Ni1105.33 (17)
C11—C12—C13120.8 (3)C22—N6—H22107.7
C11—C12—H7119.6C21—N6—H22107.7
C13—C12—H7119.6Ni1—N6—H22107.7
C14—C13—C12118.7 (3)N6—C22—C23112.8 (2)
C14—C13—H8120.6N6—C22—H23109.0
C12—C13—H8120.6C23—C22—H23109.0
C13—C14—C15121.7 (3)N6—C22—H24109.0
C13—C14—H9119.1C23—C22—H24109.0
C15—C14—H9119.1H23—C22—H24107.8
C14—C15—C10119.7 (2)C22—C23—C19i116.1 (2)
C14—C15—C16116.1 (2)C22—C23—H25108.3
C10—C15—C16124.2 (2)C19i—C23—H25108.3
N4—C16—C15124.6 (2)C22—C23—H26108.3
N4—C16—H10117.7C19i—C23—H26108.3
C15—C16—H10117.7H25—C23—H26107.4
C16—N4—C17121.2 (2)O3—C24—H27109.5
C16—N4—Cr1125.90 (19)O3—C24—H28109.5
C17—N4—Cr1112.89 (17)H27—C24—H28109.5
N4—C17—C18107.0 (2)O3—C24—H29109.5
N4—C17—H11110.3H27—C24—H29109.5
C18—C17—H11110.3H28—C24—H29109.5
N4—C17—H12110.3C24—O3—H30109.5
Symmetry codes: (i) −x+2, −y, −z+2.
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O3—H30···O2ii0.822.182.989 (3)168
N5—H17···O3iii0.912.343.212 (3)161
C17—H12···N2iv0.972.563.467 (4)156
Symmetry codes: (ii) x, y, z−1; (iii) −x+2, −y, −z+1; (iv) x, −y+1/2, z−1/2.
Table 1
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O3—H30···O2i0.822.182.989 (3)168
N5—H17···O3ii0.912.343.212 (3)161
C17—H12···N2iii0.972.563.467 (4)156
Symmetry codes: (i) x, y, z−1; (ii) −x+2, −y, −z+1; (iii) x, −y+1/2, z−1/2.
Acknowledgements top

This work was supported by NY208044, 09KJB150008 and in part by the National Basic Research Program of China (2009CB930601).

references
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