metal-organic compounds\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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catena-Poly[[(nitrato-κ2O,O′)silver(I)]-μ-N,N′-bis­­(3-pyridyl­methyl­­idene)benzene-1,4-di­amine]

aDepartment of Physics, Daqing Normal University, Daqing, 163712, People's Republic of China
*Correspondence e-mail: yonghaoliu1980@163.com

(Received 13 June 2010; accepted 1 July 2010; online 7 July 2010)

In the title compound, [Ag(NO3)(C18H14N4)]n, the AgI atom is coordinated by two N atoms from two N,N′-bis­(3-pyridyl­methyl­idene)benzene-1,4-diamine (bpbd) mol­ecules and two O atoms from a bidentate nitrate anion. The bpbd mol­ecules bridge the Ag atoms into a chain. Two adjacent chains are further connected by Ag⋯Ag inter­actions [3.1631 (8) Å], forming a double-chain structure. A ππ inter­action [centroid–centroid distance = 3.758 (3) Å] occurs between the double chains. Inter­chain C—H⋯O hydrogen bonds are observed.

Related literature

For general background to metal–organic frameworks with bipyridine-type ligands, see: Biradha et al. (2006[Biradha, K., Sarkar, M. & Rajput, L. (2006). Chem. Commun. pp. 4169-4171.]); Cunha-Silva et al. (2006[Cunha-Silva, L., Westcot, A., Whitford, N. & Hardie, M. J. (2006). Cryst. Growth Des. 6, 726-733.]); Lu et al. (2002[Lu, C.-Z., Wu, C.-D., Zhuang, H.-H. & Huang, J.-S. (2002). Chem. Mater. 14, 2649-2653.]); Ye et al. (2004[Ye, K.-Q., Kong, J.-F., Jiang, S.-M. & Wang, Y. (2004). J. Mol. Sci. 20, 1-5.]).

[Scheme 1]

Experimental

Crystal data
  • [Ag(NO3)(C18H14N4)]

  • Mr = 456.21

  • Triclinic, [P \overline 1]

  • a = 9.2148 (18) Å

  • b = 9.771 (2) Å

  • c = 10.800 (2) Å

  • α = 81.51 (3)°

  • β = 74.27 (3)°

  • γ = 66.52 (3)°

  • V = 857.6 (4) Å3

  • Z = 2

  • Mo Kα radiation

  • μ = 1.21 mm−1

  • T = 293 K

  • 0.31 × 0.30 × 0.08 mm

Data collection
  • Rigaku R-AXIS RAPID diffractometer

  • Absorption correction: multi-scan (ABSCOR; Higashi, 1995[Higashi, T. (1995). ABSCOR. Rigaku Corporation, Tokyo, Japan.]) Tmin = 0.705, Tmax = 0.908

  • 8493 measured reflections

  • 3891 independent reflections

  • 3163 reflections with I > 2σ(I)

  • Rint = 0.019

Refinement
  • R[F2 > 2σ(F2)] = 0.032

  • wR(F2) = 0.094

  • S = 1.10

  • 3891 reflections

  • 244 parameters

  • H-atom parameters constrained

  • Δρmax = 0.72 e Å−3

  • Δρmin = −0.29 e Å−3

Table 1
Selected bond lengths (Å)

Ag1—N1 2.162 (2)
Ag1—N4i 2.163 (2)
Ag1—O2 2.731 (3)
Ag1—O3 2.704 (3)
Symmetry code: (i) x+2, y-1, z-1.

Table 2
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
C1—H1A⋯O3ii 0.93 2.50 3.276 (4) 141
C16—H16A⋯O2iii 0.93 2.44 3.280 (4) 151
Symmetry codes: (ii) -x+3, -y, -z+1; (iii) -x+1, -y+2, -z+2.

Data collection: RAPID-AUTO (Rigaku, 1998[Rigaku (1998). RAPID-AUTO. Rigaku Corporation, Tokyo, Japan.]); cell refinement: RAPID-AUTO; data reduction: RAPID-AUTO; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); molecular graphics: DIAMOND (Brandenburg, 1999[Brandenburg, K. (1999). DIAMOND. Crystal Impact GbR, Bonn, Germany.]); software used to prepare material for publication: SHELXL97.

Supporting information


Comment top

Bipyridine-type ligands have been extensively investigated in recent years, owing to their simple structures, readily availabilities and more predictable formation of network structures (Biradha et al., 2006; Cunha-Silva et al., 2006; Lu et al., 2002). Moreover, when introducing double Schiff-base, a great deal of metal–organic frameworks with unusual network patterns and novel properties can be achieved due to the specific geometry including the different relative orientation of N-donors and the zigzag conformation of the space moiety between the two terminal coordination groups (Ye et al., 2004).

Herein, we choose 3,3'-bipyridine-type Schiff-base as an organic linking ligand. In this simple compound, NC—H group can act as a hydrogen bonding donor and the pyridyl N atom as an acceptor. In the title complex, the ligand takes a bidentate bridging coordination fashion and links two AgI centers with two pyridyl N atoms (Fig. 1), forming a zigzag chain, with Ag—N distances being 2.162 (2) and 2.163 (2) Å (Table 1). The two neighboring Ag atoms exhibit an Ag···Ag interaction, with a distance of 3.1631 (8) Å. The Ag atoms are also coordinated by distant nitrate O atoms [Ag—O = 2.731 (3) and 2.704 (3) Å], leading to a deviation from linearity [N—Ag—N = 159.44 (9)°]. Two adjacent chains are connected by the Ag···Ag interactions into a double-chain structure (Fig. 2). A ππ interaction [centroid–centroid distance = 3.758 (3) Å] occurs between the double-chains. Interchain C—H···O hydrogen bonds are observed (Table 2).

Related literature top

For general background to metal–organic frameworks with bipyridine-type ligands, see: Biradha et al. (2006); Cunha-Silva et al. (2006); Lu et al. (2002); Ye et al. (2004).

Experimental top

The ligand L was prepared according to the previous method (Ye et al., 2004). 1,4-Diaminobenzene (2.14 mg, 10 mmol) was dissolved in methanol (20 ml), followed by addition of 3-pyridinecarboxaldehyde (4.24 mg, 40 mmol). The mixture was stirred at room temperature for 2 h and filtered. The resulting yellow crystalline solid was washed with methanol several times and dried in air. A solution of AgNO3 (33.9 mg, 0.2 mmol) in acetonitrile (10 ml) was slowly layered onto a solution of L (117 mg, 0.625 mmol) in methylene chloride (10 ml). Diffusion between the two phases over a week produced colorless crystals.

Refinement top

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

Structure description top

Bipyridine-type ligands have been extensively investigated in recent years, owing to their simple structures, readily availabilities and more predictable formation of network structures (Biradha et al., 2006; Cunha-Silva et al., 2006; Lu et al., 2002). Moreover, when introducing double Schiff-base, a great deal of metal–organic frameworks with unusual network patterns and novel properties can be achieved due to the specific geometry including the different relative orientation of N-donors and the zigzag conformation of the space moiety between the two terminal coordination groups (Ye et al., 2004).

Herein, we choose 3,3'-bipyridine-type Schiff-base as an organic linking ligand. In this simple compound, NC—H group can act as a hydrogen bonding donor and the pyridyl N atom as an acceptor. In the title complex, the ligand takes a bidentate bridging coordination fashion and links two AgI centers with two pyridyl N atoms (Fig. 1), forming a zigzag chain, with Ag—N distances being 2.162 (2) and 2.163 (2) Å (Table 1). The two neighboring Ag atoms exhibit an Ag···Ag interaction, with a distance of 3.1631 (8) Å. The Ag atoms are also coordinated by distant nitrate O atoms [Ag—O = 2.731 (3) and 2.704 (3) Å], leading to a deviation from linearity [N—Ag—N = 159.44 (9)°]. Two adjacent chains are connected by the Ag···Ag interactions into a double-chain structure (Fig. 2). A ππ interaction [centroid–centroid distance = 3.758 (3) Å] occurs between the double-chains. Interchain C—H···O hydrogen bonds are observed (Table 2).

For general background to metal–organic frameworks with bipyridine-type ligands, see: Biradha et al. (2006); Cunha-Silva et al. (2006); Lu et al. (2002); Ye et al. (2004).

Computing details top

Data collection: RAPID-AUTO (Rigaku, 1998); cell refinement: RAPID-AUTO (Rigaku, 1998); data reduction: RAPID-AUTO (Rigaku, 1998); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. The asymmetric unit of the title compound with displacement ellipsoids shown at the 50% probability level. [Symmetry codes: (i) 2+x, -1+y, -1+z; (ii) -2+x, 1+y, 1+z.]
[Figure 2] Fig. 2. A view of the double-chain structure in the title compound.
catena-Poly[[(nitrato-κ2O,O')silver(I)]-µ- N,N'-bis(3-pyridylmethylidene)benzene-1,4-diamine] top
Crystal data top
[Ag(NO3)(C18H14N4)]Z = 2
Mr = 456.21F(000) = 456
Triclinic, P1Dx = 1.767 Mg m3
Hall symbol: -P 1Mo Kα radiation, λ = 0.71073 Å
a = 9.2148 (18) ÅCell parameters from 3891 reflections
b = 9.771 (2) Åθ = 3.1–27.5°
c = 10.800 (2) ŵ = 1.21 mm1
α = 81.51 (3)°T = 293 K
β = 74.27 (3)°Block, colorless
γ = 66.52 (3)°0.31 × 0.30 × 0.08 mm
V = 857.6 (4) Å3
Data collection top
Rigaku R-AXIS RAPID
diffractometer
3891 independent reflections
Radiation source: fine-focus sealed tube3163 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.019
Detector resolution: 10 pixels mm-1θmax = 27.5°, θmin = 3.1°
ω scansh = 1111
Absorption correction: multi-scan
(ABSCOR; Higashi, 1995)
k = 1212
Tmin = 0.705, Tmax = 0.908l = 1314
8493 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)] = 0.032Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.094H-atom parameters constrained
S = 1.10 w = 1/[σ2(Fo2) + (0.059P)2]
where P = (Fo2 + 2Fc2)/3
3891 reflections(Δ/σ)max = 0.002
244 parametersΔρmax = 0.72 e Å3
0 restraintsΔρmin = 0.29 e Å3
Crystal data top
[Ag(NO3)(C18H14N4)]γ = 66.52 (3)°
Mr = 456.21V = 857.6 (4) Å3
Triclinic, P1Z = 2
a = 9.2148 (18) ÅMo Kα radiation
b = 9.771 (2) ŵ = 1.21 mm1
c = 10.800 (2) ÅT = 293 K
α = 81.51 (3)°0.31 × 0.30 × 0.08 mm
β = 74.27 (3)°
Data collection top
Rigaku R-AXIS RAPID
diffractometer
3891 independent reflections
Absorption correction: multi-scan
(ABSCOR; Higashi, 1995)
3163 reflections with I > 2σ(I)
Tmin = 0.705, Tmax = 0.908Rint = 0.019
8493 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0320 restraints
wR(F2) = 0.094H-atom parameters constrained
S = 1.10Δρmax = 0.72 e Å3
3891 reflectionsΔρmin = 0.29 e Å3
244 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ag11.45799 (2)0.37548 (2)0.45603 (2)0.05309 (11)
N11.2254 (3)0.3738 (2)0.5682 (2)0.0379 (5)
N20.6797 (3)0.6198 (2)0.8049 (2)0.0394 (5)
N30.1476 (3)1.1322 (2)1.0027 (2)0.0451 (5)
N40.3549 (3)1.3921 (2)1.2898 (2)0.0409 (5)
N51.7214 (3)0.1260 (3)0.5841 (3)0.0519 (6)
O11.8206 (4)0.0262 (4)0.6349 (3)0.0910 (9)
O21.6959 (3)0.2598 (3)0.5904 (3)0.0794 (8)
O31.6440 (4)0.0949 (3)0.5224 (3)0.0686 (7)
C11.2039 (3)0.2446 (3)0.5801 (3)0.0447 (6)
H1A1.29150.16010.54620.054*
C21.0576 (4)0.2313 (3)0.6405 (3)0.0530 (7)
H2A1.04570.14050.64370.064*
C30.9290 (3)0.3543 (3)0.6960 (3)0.0468 (6)
H3A0.83020.34700.73940.056*
C40.9491 (3)0.4889 (3)0.6862 (2)0.0338 (5)
C51.0982 (3)0.4942 (3)0.6205 (2)0.0358 (5)
H5A1.11130.58500.61190.043*
C60.8148 (3)0.6244 (3)0.7420 (2)0.0373 (5)
H6A0.82990.71450.73060.045*
C70.5498 (3)0.7521 (3)0.8539 (2)0.0356 (5)
C80.4388 (3)0.7368 (3)0.9655 (3)0.0426 (6)
H8A0.45280.64241.00460.051*
C90.3077 (3)0.8597 (3)1.0195 (3)0.0464 (7)
H9A0.23640.84811.09600.056*
C100.2824 (3)1.0000 (3)0.9596 (2)0.0379 (5)
C110.3917 (4)1.0142 (3)0.8472 (3)0.0492 (7)
H11A0.37571.10810.80650.059*
C120.5248 (3)0.8915 (3)0.7937 (3)0.0475 (7)
H12A0.59680.90310.71760.057*
C130.0370 (3)1.1306 (3)1.0983 (3)0.0421 (6)
H13A0.04341.04121.14490.051*
C140.1040 (3)1.2686 (3)1.1388 (2)0.0372 (5)
C150.2228 (3)1.2683 (3)1.2502 (3)0.0405 (6)
H15A0.21081.17951.29920.049*
C160.3680 (3)1.5191 (3)1.2194 (3)0.0432 (6)
H16A0.45791.60511.24640.052*
C170.2541 (3)1.5289 (3)1.1081 (3)0.0456 (6)
H17A0.26651.61971.06220.055*
C180.1215 (3)1.4008 (3)1.0666 (3)0.0408 (6)
H18A0.04471.40360.99090.049*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ag10.03204 (13)0.06102 (16)0.05624 (16)0.01785 (10)0.01587 (10)0.02131 (11)
N10.0264 (10)0.0419 (10)0.0382 (11)0.0094 (9)0.0035 (8)0.0110 (9)
N20.0282 (10)0.0374 (10)0.0411 (11)0.0048 (8)0.0019 (9)0.0082 (9)
N30.0340 (11)0.0366 (10)0.0471 (12)0.0048 (9)0.0079 (10)0.0068 (10)
N40.0270 (10)0.0442 (11)0.0430 (12)0.0088 (9)0.0045 (9)0.0137 (10)
N50.0433 (13)0.0540 (14)0.0494 (14)0.0170 (12)0.0032 (11)0.0059 (12)
O10.0671 (18)0.092 (2)0.106 (2)0.0279 (16)0.0287 (17)0.0307 (18)
O20.0651 (16)0.0626 (14)0.111 (2)0.0149 (12)0.0198 (16)0.0331 (14)
O30.0859 (19)0.0556 (12)0.0735 (16)0.0326 (13)0.0263 (14)0.0020 (12)
C10.0350 (13)0.0367 (12)0.0483 (15)0.0050 (11)0.0031 (11)0.0087 (11)
C20.0443 (16)0.0356 (12)0.067 (2)0.0132 (12)0.0051 (14)0.0053 (13)
C30.0344 (13)0.0434 (13)0.0524 (16)0.0143 (11)0.0057 (12)0.0025 (12)
C40.0253 (11)0.0378 (11)0.0317 (11)0.0066 (9)0.0010 (9)0.0074 (10)
C50.0282 (11)0.0388 (12)0.0369 (12)0.0109 (10)0.0007 (10)0.0091 (10)
C60.0268 (11)0.0417 (12)0.0390 (13)0.0084 (10)0.0023 (10)0.0123 (11)
C70.0240 (11)0.0386 (12)0.0380 (12)0.0080 (9)0.0003 (10)0.0071 (10)
C80.0297 (12)0.0362 (12)0.0475 (15)0.0064 (10)0.0032 (11)0.0002 (11)
C90.0316 (13)0.0423 (13)0.0453 (15)0.0056 (11)0.0096 (11)0.0022 (12)
C100.0283 (12)0.0352 (11)0.0406 (13)0.0074 (10)0.0033 (10)0.0073 (10)
C110.0411 (14)0.0357 (12)0.0488 (16)0.0065 (11)0.0100 (12)0.0018 (12)
C120.0365 (14)0.0432 (13)0.0432 (14)0.0090 (11)0.0132 (11)0.0034 (12)
C130.0336 (13)0.0327 (11)0.0468 (14)0.0070 (10)0.0049 (11)0.0053 (11)
C140.0269 (11)0.0363 (11)0.0413 (13)0.0084 (10)0.0016 (10)0.0091 (10)
C150.0324 (12)0.0390 (12)0.0420 (13)0.0117 (10)0.0026 (11)0.0044 (11)
C160.0290 (12)0.0416 (13)0.0487 (15)0.0033 (10)0.0023 (11)0.0127 (12)
C170.0398 (14)0.0408 (13)0.0461 (15)0.0073 (11)0.0069 (12)0.0004 (12)
C180.0319 (12)0.0431 (13)0.0391 (13)0.0113 (11)0.0022 (10)0.0052 (11)
Geometric parameters (Å, º) top
Ag1—N12.162 (2)C4—C61.474 (3)
Ag1—N4i2.163 (2)C5—H5A0.9300
Ag1—O22.731 (3)C6—H6A0.9300
Ag1—O32.704 (3)C7—C121.378 (4)
Ag1—Ag1ii3.1631 (8)C7—C81.386 (3)
N1—C11.337 (4)C8—C91.382 (3)
N1—C51.347 (3)C8—H8A0.9300
N2—C61.261 (3)C9—C101.385 (4)
N2—C71.417 (3)C9—H9A0.9300
N3—C131.242 (3)C10—C111.381 (4)
N3—C101.419 (3)C11—C121.388 (4)
N4—C161.336 (4)C11—H11A0.9300
N4—C151.351 (3)C12—H12A0.9300
N5—O11.221 (4)C13—C141.472 (3)
N5—O31.240 (4)C13—H13A0.9300
N5—O21.242 (4)C14—C181.382 (4)
C1—C21.378 (4)C14—C151.390 (3)
C1—H1A0.9300C15—H15A0.9300
C2—C31.379 (4)C16—C171.385 (4)
C2—H2A0.9300C16—H16A0.9300
C3—C41.385 (4)C17—C181.382 (4)
C3—H3A0.9300C17—H17A0.9300
C4—C51.382 (3)C18—H18A0.9300
N1—Ag1—N4i159.44 (9)C12—C7—C8119.2 (2)
N1—Ag1—Ag1ii111.41 (6)C12—C7—N2123.7 (2)
N4i—Ag1—Ag1ii79.97 (7)C8—C7—N2117.0 (2)
N1—Ag1—O2112.93 (10)C9—C8—C7121.0 (2)
N1—Ag1—O397.63 (10)C9—C8—H8A119.5
N4i—Ag1—O287.07 (9)C7—C8—H8A119.5
N4i—Ag1—O392.98 (9)C8—C9—C10120.0 (2)
C1—N1—C5117.7 (2)C8—C9—H9A120.0
C1—N1—Ag1117.05 (16)C10—C9—H9A120.0
C5—N1—Ag1125.13 (18)C11—C10—C9118.7 (2)
C6—N2—C7120.2 (2)C11—C10—N3116.5 (2)
C13—N3—C10121.8 (2)C9—C10—N3124.8 (2)
C16—N4—C15117.8 (2)C10—C11—C12121.4 (3)
C16—N4—Ag1iii122.67 (17)C10—C11—H11A119.3
C15—N4—Ag1iii119.45 (18)C12—C11—H11A119.3
O1—N5—O3119.9 (3)C7—C12—C11119.6 (2)
O1—N5—O2122.2 (3)C7—C12—H12A120.2
O3—N5—O2117.9 (3)C11—C12—H12A120.2
N1—C1—C2122.8 (2)N3—C13—C14120.8 (2)
N1—C1—H1A118.6N3—C13—H13A119.6
C2—C1—H1A118.6C14—C13—H13A119.6
C1—C2—C3119.1 (3)C18—C14—C15118.7 (2)
C1—C2—H2A120.5C18—C14—C13120.7 (2)
C3—C2—H2A120.5C15—C14—C13120.7 (2)
C2—C3—C4119.1 (3)N4—C15—C14122.5 (2)
C2—C3—H3A120.5N4—C15—H15A118.8
C4—C3—H3A120.5C14—C15—H15A118.8
C5—C4—C3118.3 (2)N4—C16—C17123.2 (2)
C5—C4—C6120.4 (2)N4—C16—H16A118.4
C3—C4—C6121.3 (2)C17—C16—H16A118.4
N1—C5—C4123.0 (2)C18—C17—C16118.5 (3)
N1—C5—H5A118.5C18—C17—H17A120.7
C4—C5—H5A118.5C16—C17—H17A120.7
N2—C6—C4120.9 (2)C14—C18—C17119.3 (2)
N2—C6—H6A119.6C14—C18—H18A120.3
C4—C6—H6A119.6C17—C18—H18A120.3
Symmetry codes: (i) x+2, y1, z1; (ii) x+3, y+1, z+1; (iii) x2, y+1, z+1.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C1—H1A···O3iv0.932.503.276 (4)141
C16—H16A···O2v0.932.443.280 (4)151
Symmetry codes: (iv) x+3, y, z+1; (v) x+1, y+2, z+2.

Experimental details

Crystal data
Chemical formula[Ag(NO3)(C18H14N4)]
Mr456.21
Crystal system, space groupTriclinic, P1
Temperature (K)293
a, b, c (Å)9.2148 (18), 9.771 (2), 10.800 (2)
α, β, γ (°)81.51 (3), 74.27 (3), 66.52 (3)
V3)857.6 (4)
Z2
Radiation typeMo Kα
µ (mm1)1.21
Crystal size (mm)0.31 × 0.30 × 0.08
Data collection
DiffractometerRigaku R-AXIS RAPID
Absorption correctionMulti-scan
(ABSCOR; Higashi, 1995)
Tmin, Tmax0.705, 0.908
No. of measured, independent and
observed [I > 2σ(I)] reflections
8493, 3891, 3163
Rint0.019
(sin θ/λ)max1)0.649
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.032, 0.094, 1.10
No. of reflections3891
No. of parameters244
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.72, 0.29

Computer programs: RAPID-AUTO (Rigaku, 1998), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), DIAMOND (Brandenburg, 1999).

Selected bond lengths (Å) top
Ag1—N12.162 (2)Ag1—O22.731 (3)
Ag1—N4i2.163 (2)Ag1—O32.704 (3)
Symmetry code: (i) x+2, y1, z1.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C1—H1A···O3ii0.932.503.276 (4)141
C16—H16A···O2iii0.932.443.280 (4)151
Symmetry codes: (ii) x+3, y, z+1; (iii) x+1, y+2, z+2.
 

Acknowledgements

The authors thank the Natural Science Foundation of Heilongjiang Province (grant No. A200506), the Scientific Research Fund of Heilongjiang Provincial Education Department (grant No. 11553006) and the Doctoral Start-up Fund of Daqing Normal University (grant No. 08ZB02) for supporting this work.

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