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Acta Cryst. (2007). E63, m3051    [ doi:10.1107/S1600536807057753 ]

Poly[[bis([mu]-1,2-bis{[2-(2-pyridyl)-1H-imidazol-1-yl]methyl}benzene)lead(II)] dithiocyanate]

R.-H. Cui and Y.-Q. Lan

Abstract top

The title PbII coordination polymer, {[Pb(C24H20N6)2](SCN)2}n, was obtained by the reaction of Pb(CH3COO)2·3H2O, KSCN and 1,2-bis{[2-(2-pyridyl)-1H-imidazol-1-yl]methyl}benzene (hereafter L). Each L molecule coordinates to two PbII cations through the four aromatic N atoms, thus acting as a bridging bis-bidentate ligand. The PbII cations, which lie on inversion centres, are bridged by four L molecules, forming a two-dimensional (4,4)-sheet. The SCN- anions act as counter-ions and are uncoordinated.

Comment top

In recent years, research into coordination polymers has been expanding rapidly because of their fascinating structural diversity and potential application as functional materials (Batten & Robson, 1998; Moulton & Zaworotko, 2001). As a heavy p-block metal ion, lead(II), with its large radius, flexible coordination environment, and variable stereochemical activity, provides unique opportunities for formation of unusual network topologies with interesting properties (Jack et al., 2004). In the present paper, we report the preparation and crystal structure of a novel two-dimensional coordination polymer, namely [Pb(C24H20N6)2](SCN)2, (I).

As shown in Fig. 1, the PbII cation occupies the inversion centre and is eight-coordinated by eight N atoms from four L molecules. The average Pb—N distances are 2.689 (4), 2.717 (3), 2.750 (3) and 2.805 (3) Å, respectively, which are in the normal Pb—N range (Carcelli et al., 2003). As illustrated in Fig. 2, each L molecule in (I) coordinates to two PbII cations through its four aromatic N atoms, thus acting as a bridging bis(bidentate) ligand. The PbII cations, which lie on the inversion centres, are bridged by four L molecules to form a two-dimensional neutral (4,4)-network (Fig. 3). The (SCN)− anions act as counterions.

Related literature top

For related literature, see: Batten & Robson, (1998); Moulton & Zaworotko, (2001); Jack et al., (2004); Carcelli et al. (2003).

Experimental top

A mixture of Pb(CH3COO)2·3H2O (0.121 g, 0.5 mmol), KSCN(0.097 g, 1 mmol) and L (0.392 g, 1 mmol) in H2O (13 ml) was stirred for 0.5 h. The mixture was then transferred and sealed into an 18 ml Teflon-lined autoclave, which was heated at 150 °C for 60 h. After the mixture was cooled to room temperature, colorless blocks of the title complex were filtered off and dried at ambient temperature in air (yield 62% based on Pb).

Refinement top

All H atoms on C atoms were positioned geometrically and refined as riding atoms, with C—H = 0.93 − 0.97 Å, and Uiso=1.2Ueq (C).

Computing details top

Data collection: SMART (Bruker, 1997); cell refinement: SMART (Bruker, 1997); data reduction: SAINT (Bruker, 1999); program(s) used to solve structure: SHELXS97(Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL-Plus (Sheldrick, 1990); software used to prepare material for publication: SHELXL97 (Sheldrick, 1997).

Figures top
[Figure 1] Fig. 1. A view of the molecule of (I). Displacement ellipsoids are drawn at the 30% probability level. H atoms are omitted for clarity.
[Figure 2] Fig. 2. Ball-stick representation of the two-dimensional structure of (I). All (SCN)− anions are omitted for clarity.
[Figure 3] Fig. 3. View of the (4,4) sheet.
poly[[bis(µ-1,2-bis{[2-(2-pyridyl)-1H-imidazol-1-yl]methyl}benzene)lead(II)] dithiocyanate] top
Crystal data top
[Pb(C24H20N6)2](SCN)2F000 = 2208
Mr = 1108.27Dx = 1.646 Mg m−3
Monoclinic, C2/cMo Kα radiation
λ = 0.71073 Å
Hall symbol: -C 2ycCell parameters from 9825 reflections
a = 23.9560 (8) Åθ = 1.9–28.4º
b = 12.6670 (8) ŵ = 3.92 mm−1
c = 18.3560 (9) ÅT = 293 (2) K
β = 126.593 (1)ºBlock, colorless
V = 4472.2 (4) Å30.36 × 0.31 × 0.28 mm
Z = 4
Data collection top
Bruker APEX CCD area-detector
diffractometer		5253 independent reflections
Radiation source: fine-focus sealed tube4435 reflections with I > 2σ(I)
Monochromator: graphiteRint = 0.043
T = 293(2) Kθmax = 28.4º
ω scansθmin = 1.9º
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)		h = −31→25
Tmin = 0.271, Tmax = 0.333k = −16→16
13428 measured reflectionsl = −24→23
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.034H-atom parameters constrained
wR(F2) = 0.080  w = 1/[σ2(Fo2) + (0.0448P)2]
where P = (Fo2 + 2Fc2)/3
S = 0.99(Δ/σ)max = 0.001
5253 reflectionsΔρmax = 1.02 e Å−3
303 parametersΔρmin = −1.15 e Å−3
Primary atom site location: structure-invariant direct methodsExtinction correction: none
Crystal data top
[Pb(C24H20N6)2](SCN)2V = 4472.2 (4) Å3
Mr = 1108.27Z = 4
Monoclinic, C2/cMo Kα
a = 23.9560 (8) ŵ = 3.92 mm−1
b = 12.6670 (8) ÅT = 293 (2) K
c = 18.3560 (9) Å0.36 × 0.31 × 0.28 mm
β = 126.593 (1)º
Data collection top
Bruker APEX CCD area-detector
diffractometer		5253 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)		4435 reflections with I > 2σ(I)
Tmin = 0.271, Tmax = 0.333Rint = 0.043
13428 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.034303 parameters
wR(F2) = 0.080H-atom parameters constrained
S = 0.99Δρmax = 1.02 e Å−3
5253 reflectionsΔρmin = −1.15 e Å−3
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
xyzUiso*/Ueq
Pb10.00000.369453 (14)0.75000.03277 (8)
S10.23584 (15)0.88594 (17)0.80144 (19)0.1210 (8)
C10.1039 (3)0.6026 (3)0.8718 (3)0.0527 (11)
H10.07000.63910.87130.063*
C20.1559 (3)0.6481 (3)0.8750 (3)0.0510 (11)
H20.16470.72000.87740.061*
C30.1634 (2)0.4757 (3)0.8719 (3)0.0370 (8)
C40.1862 (2)0.3677 (3)0.8724 (2)0.0363 (8)
C50.2552 (3)0.3402 (4)0.9119 (3)0.0494 (10)
H50.28950.39190.93790.059*
C60.2721 (3)0.2370 (4)0.9124 (4)0.0581 (12)
H60.31790.21780.93870.070*
C70.2206 (3)0.1624 (4)0.8734 (3)0.0555 (12)
H70.23050.09170.87220.067*
C80.1535 (3)0.1949 (3)0.8360 (3)0.0484 (11)
H80.11870.14390.81020.058*
C90.2509 (2)0.5851 (3)0.8679 (3)0.0401 (9)
H9A0.24050.64670.83040.048*
H9B0.25460.52500.83830.048*
C100.3202 (2)0.6016 (3)0.9593 (3)0.0338 (8)
C110.3293 (2)0.5842 (3)1.0405 (3)0.0417 (9)
H110.29160.56291.03920.050*
C120.3925 (3)0.5976 (3)1.1220 (3)0.0473 (10)
H120.39770.58461.17560.057*
C130.4494 (2)0.6307 (3)1.1254 (3)0.0461 (10)
H130.49250.64001.18100.055*
C140.4414 (2)0.6498 (3)1.0452 (3)0.0418 (9)
H140.47940.67191.04730.050*
C150.3770 (2)0.6362 (3)0.9617 (2)0.0344 (8)
C160.3669 (2)0.6580 (3)0.8735 (3)0.0406 (9)
H16A0.34250.59890.83270.049*
H16B0.33780.72000.84540.049*
C170.4706 (3)0.5944 (4)0.8856 (3)0.0531 (12)
H170.46350.52240.88680.064*
C180.5209 (3)0.6404 (3)0.8849 (4)0.0606 (13)
H180.55510.60420.88580.073*
C190.4607 (2)0.7666 (3)0.8829 (3)0.0397 (9)
C200.4387 (2)0.8735 (3)0.8845 (3)0.0387 (8)
C210.4112 (3)0.9009 (4)0.9309 (3)0.0506 (11)
H210.40330.84960.96000.061*
C220.3959 (3)1.0061 (4)0.9329 (3)0.0568 (12)
H220.37721.02590.96300.068*
C230.4085 (3)1.0805 (4)0.8903 (3)0.0552 (12)
H230.39901.15140.89130.066*
C240.4356 (3)1.0471 (3)0.8456 (3)0.0479 (10)
H240.44341.09770.81590.057*
C250.1601 (5)0.8640 (6)0.7079 (9)0.110 (4)
N10.4318 (2)0.6750 (3)0.8843 (2)0.0411 (8)
N20.5148 (2)0.7480 (3)0.8825 (3)0.0525 (10)
N30.45138 (19)0.9469 (3)0.8425 (2)0.0406 (8)
N40.1078 (2)0.4945 (3)0.8693 (2)0.0453 (8)
N50.19362 (19)0.5672 (3)0.8739 (2)0.0397 (8)
N60.13584 (19)0.2947 (2)0.8348 (2)0.0395 (7)
N80.1191 (6)0.8507 (9)0.6599 (9)0.182 (6)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Pb10.03127 (11)0.03239 (11)0.04649 (12)0.0000.02959 (9)0.000
S10.1069 (18)0.1023 (15)0.1358 (19)0.0092 (13)0.0626 (16)−0.0211 (12)
C10.052 (3)0.048 (2)0.077 (3)0.000 (2)0.049 (3)−0.013 (2)
C20.053 (3)0.038 (2)0.071 (3)−0.007 (2)0.042 (3)−0.013 (2)
C30.032 (2)0.040 (2)0.045 (2)−0.0058 (17)0.0253 (19)−0.0043 (16)
C40.034 (2)0.041 (2)0.0406 (18)0.0007 (19)0.0257 (16)0.0017 (16)
C50.038 (2)0.049 (2)0.065 (3)−0.001 (2)0.033 (2)−0.001 (2)
C60.050 (3)0.054 (3)0.083 (3)0.012 (2)0.046 (3)0.005 (2)
C70.067 (4)0.043 (2)0.069 (3)0.011 (2)0.047 (3)0.008 (2)
C80.053 (3)0.042 (2)0.054 (2)−0.003 (2)0.033 (2)0.0029 (19)
C90.038 (2)0.044 (2)0.049 (2)−0.0081 (19)0.031 (2)−0.0035 (17)
C100.035 (2)0.0303 (17)0.0433 (19)−0.0031 (16)0.0271 (18)−0.0027 (15)
C110.047 (3)0.041 (2)0.049 (2)−0.0044 (19)0.035 (2)−0.0011 (17)
C120.057 (3)0.048 (2)0.045 (2)0.005 (2)0.034 (2)0.0059 (18)
C130.040 (2)0.052 (2)0.0383 (19)0.005 (2)0.0193 (18)0.0019 (18)
C140.035 (2)0.042 (2)0.051 (2)0.0019 (18)0.0268 (19)0.0051 (17)
C150.035 (2)0.0308 (17)0.0435 (18)−0.0022 (17)0.0267 (17)0.0016 (16)
C160.034 (2)0.048 (2)0.048 (2)−0.0022 (18)0.0284 (19)0.0052 (17)
C170.061 (3)0.040 (2)0.079 (3)0.011 (2)0.053 (3)0.016 (2)
C180.065 (3)0.051 (3)0.096 (4)0.025 (3)0.064 (3)0.024 (2)
C190.041 (2)0.042 (2)0.051 (2)0.0016 (18)0.035 (2)0.0061 (17)
C200.035 (2)0.046 (2)0.0424 (19)0.0030 (19)0.0273 (17)0.0031 (17)
C210.057 (3)0.056 (2)0.060 (3)0.002 (2)0.046 (3)0.003 (2)
C220.065 (3)0.060 (3)0.071 (3)0.006 (3)0.054 (3)−0.004 (2)
C230.061 (3)0.047 (2)0.071 (3)0.002 (2)0.047 (3)−0.008 (2)
C240.053 (3)0.043 (2)0.053 (2)−0.002 (2)0.035 (2)0.0021 (19)
C250.094 (6)0.050 (3)0.237 (13)−0.030 (5)0.125 (8)−0.057 (6)
N10.042 (2)0.0398 (17)0.055 (2)0.0041 (16)0.0366 (18)0.0092 (15)
N20.053 (3)0.049 (2)0.081 (3)0.0086 (18)0.054 (2)0.0153 (18)
N30.042 (2)0.0425 (18)0.0474 (19)−0.0031 (16)0.0318 (17)−0.0024 (14)
N40.044 (2)0.0426 (18)0.067 (2)−0.0085 (16)0.043 (2)−0.0125 (16)
N50.0315 (19)0.0409 (18)0.0497 (19)−0.0052 (15)0.0260 (16)−0.0044 (14)
N60.036 (2)0.0380 (17)0.0478 (19)−0.0002 (15)0.0269 (17)0.0018 (14)
N80.120 (9)0.134 (8)0.213 (12)0.052 (7)0.057 (8)−0.044 (7)
Geometric parameters (Å, °) top
Pb1—N42.689 (4)C11—C121.364 (7)
Pb1—N4i2.689 (4)C11—H110.9300
Pb1—N2ii2.717 (3)C12—C131.392 (7)
Pb1—N2iii2.717 (3)C12—H120.9300
Pb1—N3iii2.750 (3)C13—C141.387 (6)
Pb1—N3ii2.750 (3)C13—H130.9300
Pb1—N62.805 (3)C14—C151.394 (6)
Pb1—N6i2.805 (3)C14—H140.9300
S1—C251.614 (12)C15—C161.512 (5)
C1—C21.343 (7)C16—N11.462 (5)
C1—N41.376 (5)C16—H16A0.9700
C1—H10.9300C16—H16B0.9700
C2—N51.373 (6)C17—C181.347 (7)
C2—H20.9300C17—N11.371 (6)
C3—N41.326 (5)C17—H170.9300
C3—N51.355 (5)C18—N21.368 (5)
C3—C41.472 (5)C18—H180.9300
C4—N61.341 (5)C19—N21.322 (5)
C4—C51.395 (6)C19—N11.359 (5)
C5—C61.367 (6)C19—C201.460 (5)
C5—H50.9300C20—N31.352 (5)
C6—C71.370 (7)C20—C211.396 (5)
C6—H60.9300C21—C221.387 (6)
C7—C81.382 (7)C21—H210.9300
C7—H70.9300C22—C231.368 (7)
C8—N61.329 (5)C22—H220.9300
C8—H80.9300C23—C241.381 (6)
C9—N51.458 (5)C23—H230.9300
C9—C101.515 (6)C24—N31.336 (5)
C9—H9A0.9700C24—H240.9300
C9—H9B0.9700C25—N80.858 (13)
C10—C111.389 (5)N2—Pb1iv2.717 (3)
C10—C151.405 (5)N3—Pb1iv2.750 (3)
N4—Pb1—N4i107.83 (16)C14—C13—H13120.2
N4—Pb1—N2ii127.73 (11)C12—C13—H13120.2
N4i—Pb1—N2ii93.16 (12)C13—C14—C15120.5 (4)
N4—Pb1—N2iii93.16 (12)C13—C14—H14119.8
N4i—Pb1—N2iii127.73 (11)C15—C14—H14119.8
N2ii—Pb1—N2iii111.02 (16)C14—C15—C10119.3 (3)
N4—Pb1—N3iii80.90 (10)C14—C15—C16121.4 (4)
N4i—Pb1—N3iii74.82 (10)C10—C15—C16119.3 (3)
N2ii—Pb1—N3iii151.37 (12)N1—C16—C15113.7 (3)
N2iii—Pb1—N3iii61.71 (10)N1—C16—H16A108.8
N4—Pb1—N3ii74.82 (10)C15—C16—H16A108.8
N4i—Pb1—N3ii80.90 (10)N1—C16—H16B108.8
N2ii—Pb1—N3ii61.71 (10)C15—C16—H16B108.8
N2iii—Pb1—N3ii151.37 (12)H16A—C16—H16B107.7
N3iii—Pb1—N3ii138.22 (14)C18—C17—N1106.2 (4)
C2—C1—N4110.4 (4)C18—C17—H17126.9
C2—C1—H1124.8N1—C17—H17126.9
N4—C1—H1124.8C17—C18—N2110.6 (4)
C1—C2—N5106.3 (4)C17—C18—H18124.7
C1—C2—H2126.8N2—C18—H18124.7
N5—C2—H2126.8N2—C19—N1111.1 (4)
N4—C3—N5110.9 (3)N2—C19—C20122.1 (4)
N4—C3—C4121.9 (3)N1—C19—C20126.8 (4)
N5—C3—C4127.2 (4)N3—C20—C21121.7 (4)
N6—C4—C5121.3 (4)N3—C20—C19114.9 (3)
N6—C4—C3114.9 (4)C21—C20—C19123.3 (4)
C5—C4—C3123.8 (4)C22—C21—C20118.8 (4)
C6—C5—C4119.8 (5)C22—C21—H21120.6
C6—C5—H5120.1C20—C21—H21120.6
C4—C5—H5120.1C23—C22—C21119.7 (4)
C5—C6—C7119.0 (5)C23—C22—H22120.2
C5—C6—H6120.5C21—C22—H22120.2
C7—C6—H6120.5C22—C23—C24118.1 (4)
C6—C7—C8118.3 (4)C22—C23—H23121.0
C6—C7—H7120.9C24—C23—H23121.0
C8—C7—H7120.9N3—C24—C23124.1 (4)
N6—C8—C7123.8 (5)N3—C24—H24117.9
N6—C8—H8118.1C23—C24—H24117.9
C7—C8—H8118.1N8—C25—S1177 (2)
N5—C9—C10113.4 (3)C19—N1—C17106.8 (4)
N5—C9—H9A108.9C19—N1—C16129.5 (4)
C10—C9—H9A108.9C17—N1—C16123.2 (4)
N5—C9—H9B108.9C19—N2—C18105.3 (4)
C10—C9—H9B108.9C19—N2—Pb1iv107.4 (3)
H9A—C9—H9B107.7C18—N2—Pb1iv123.1 (3)
C11—C10—C15119.2 (4)C24—N3—C20117.6 (3)
C11—C10—C9122.3 (4)C24—N3—Pb1iv126.9 (3)
C15—C10—C9118.6 (3)C20—N3—Pb1iv115.4 (2)
C12—C11—C10121.2 (4)C3—N4—C1105.3 (4)
C12—C11—H11119.4C3—N4—Pb1112.4 (2)
C10—C11—H11119.4C1—N4—Pb1124.2 (3)
C11—C12—C13120.3 (4)C3—N5—C2107.0 (4)
C11—C12—H12119.9C3—N5—C9130.0 (3)
C13—C12—H12119.9C2—N5—C9122.8 (3)
C14—C13—C12119.6 (4)C8—N6—C4117.9 (4)
N4—C1—C2—N50.4 (6)C15—C16—N1—C19−103.2 (5)
N4—C3—C4—N625.5 (5)C15—C16—N1—C1786.3 (5)
N5—C3—C4—N6−154.5 (4)N1—C19—N2—C18−0.7 (5)
N4—C3—C4—C5−151.8 (4)C20—C19—N2—C18177.5 (4)
N5—C3—C4—C528.2 (6)N1—C19—N2—Pb1iv132.1 (3)
N6—C4—C5—C60.3 (6)C20—C19—N2—Pb1iv−49.7 (5)
C3—C4—C5—C6177.5 (4)C17—C18—N2—C190.7 (6)
C4—C5—C6—C70.2 (7)C17—C18—N2—Pb1iv−122.6 (4)
C5—C6—C7—C8−0.6 (7)C23—C24—N3—C201.2 (7)
C6—C7—C8—N60.7 (7)C23—C24—N3—Pb1iv177.0 (4)
N5—C9—C10—C119.7 (6)C21—C20—N3—C24−1.1 (6)
N5—C9—C10—C15−170.0 (3)C19—C20—N3—C24−176.8 (4)
C15—C10—C11—C12−1.6 (6)C21—C20—N3—Pb1iv−177.4 (3)
C9—C10—C11—C12178.7 (4)C19—C20—N3—Pb1iv6.9 (5)
C10—C11—C12—C130.9 (7)N5—C3—N4—C1−1.4 (5)
C11—C12—C13—C14−0.1 (6)C4—C3—N4—C1178.6 (4)
C12—C13—C14—C150.1 (6)N5—C3—N4—Pb1136.6 (3)
C13—C14—C15—C10−0.7 (6)C4—C3—N4—Pb1−43.4 (4)
C13—C14—C15—C16179.2 (4)C2—C1—N4—C30.6 (5)
C11—C10—C15—C141.5 (6)C2—C1—N4—Pb1−131.0 (4)
C9—C10—C15—C14−178.8 (4)N4i—Pb1—N4—C3−122.7 (3)
C11—C10—C15—C16−178.4 (3)N2ii—Pb1—N4—C3−13.9 (3)
C9—C10—C15—C161.3 (5)N2iii—Pb1—N4—C3105.9 (3)
C14—C15—C16—N110.4 (5)N3iii—Pb1—N4—C3166.6 (3)
C10—C15—C16—N1−169.7 (3)N3ii—Pb1—N4—C3−47.7 (3)
N1—C17—C18—N2−0.4 (6)N4i—Pb1—N4—C16.1 (3)
N2—C19—C20—N331.1 (6)N2ii—Pb1—N4—C1114.9 (3)
N1—C19—C20—N3−151.0 (4)N2iii—Pb1—N4—C1−125.3 (3)
N2—C19—C20—C21−144.5 (5)N3iii—Pb1—N4—C1−64.7 (3)
N1—C19—C20—C2133.4 (7)N3ii—Pb1—N4—C181.0 (3)
N3—C20—C21—C220.8 (7)N4—C3—N5—C21.6 (5)
C19—C20—C21—C22176.1 (5)C4—C3—N5—C2−178.4 (4)
C20—C21—C22—C23−0.5 (8)N4—C3—N5—C9−173.1 (4)
C21—C22—C23—C240.6 (8)C4—C3—N5—C96.9 (7)
C22—C23—C24—N3−1.0 (8)C1—C2—N5—C3−1.2 (5)
N2—C19—N1—C170.5 (5)C1—C2—N5—C9174.0 (4)
C20—C19—N1—C17−177.6 (4)C10—C9—N5—C3−98.8 (5)
N2—C19—N1—C16−171.2 (4)C10—C9—N5—C287.2 (5)
C20—C19—N1—C1610.7 (7)C7—C8—N6—C4−0.2 (6)
C18—C17—N1—C190.0 (5)C5—C4—N6—C8−0.3 (5)
C18—C17—N1—C16172.3 (4)C3—C4—N6—C8−177.6 (3)
Symmetry codes: (i) −x, y, −z+3/2; (ii) −x+1/2, y−1/2, −z+3/2; (iii) x−1/2, y−1/2, z; (iv) x+1/2, y+1/2, z.
Acknowledgements top

We thank the Science Foundation for Young Teachers of Northeast Normal University (No. 20070309) for support.

references
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