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

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ISSN: 2056-9890

9-{4-[(E)-2-(4,6-Di­methyl-1,3,5-triazin-2-yl)ethen­yl]phen­yl}-9H-carbazole

aDepartment of Chemical Engineering, Shandong Institute of Light Industry, Jinan 250353, Shandong Province, People's Republic of China, bSchool of Materials Science and Engineering, Institute of Power Source and Ecomaterials Science, Hebei University of Technology, Tianjin 300130, People's Republic of China, and cDepartment of Chemistry, University of Malaya, 50603 Kuala Lumpur, Malaysia
*Correspondence e-mail: yuezhicui@163.com

(Received 22 July 2009; accepted 30 July 2009; online 8 August 2009)

In the crystal structure of the title compound, C25H20N4, the triazinyl ring is nearly coplanar with the planar (r.m.s. deviation = 0.028 Å) phenyl­ethenyl unit, the twist being only 5.8 (2)°; however, the planar carbazolyl unit (r.m.s. deviation = 0.008 Å) is twisted by 47.8 (1)° with respect to the phenyl­ethenyl unit. The nonplanar nature of the mol­ecule explains the phenomenon of light emission at short wavelengths in the solid state but at long wavelengths in solution.

Related literature

For background literature on donor–π-acceptor chromophores, see: Cui et al. (2003[Cui, Y. Z., Fang, Q., Lei, H., Xue, G. & Yu, W. T. (2003). Chem. Phys. Lett. 377, 507-511.], 2004[Cui, Y. Z., Fang, Q., Huang, Z. L., Xue, G., Xu, G. B. & Yu, W. T. (2004). J. Mater. Chem. 14, 2443-2449.]); Kannan et al. (2004[Kannan, R., He, G. S., Lin, T. C., Prasad, P. N., Vaia, R. A. & Tan, L. S. (2004). Chem. Mater. 16, 185-194.]); Maury & Bozec (2005[Maury, O. & Bozec, H. L. (2005). Acc. Chem. Res. 38, 691-704.]); Zhong et al. (2008[Zhong, H. L., Xu, E. J., Zeng, D. L., Du, J. P., Sun, J., Ren, S. J., Jiang, B. & Fang, Q. (2008). Org. Lett. 10, 709-712.]).

[Scheme 1]

Experimental

Crystal data
  • C25H20N4

  • Mr = 376.45

  • Orthorhombic, P 21 21 21

  • a = 8.0415 (8) Å

  • b = 15.716 (2) Å

  • c = 16.098 (1) Å

  • V = 2034.4 (3) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.07 mm−1

  • T = 293 K

  • 0.42 × 0.28 × 0.16 mm

Data collection
  • Siemens P4 four-circle diffractometer

  • Absorption correction: ψ scan (North et al., 1968[North, A. C. T., Phillips, D. C. & Mathews, F. S. (1968). Acta Cryst. A24, 351-359.]) Tmin = 0.901, Tmax = 0.988

  • 2991 measured reflections

  • 2291 independent reflections

  • 1288 reflections with I > 2σ(I)

  • Rint = 0.026

  • 3 standard reflections every 97 reflections intensity decay: 1%

Refinement
  • R[F2 > 2σ(F2)] = 0.055

  • wR(F2) = 0.160

  • S = 1.00

  • 2291 reflections

  • 265 parameters

  • H-atom parameters constrained

  • Δρmax = 0.26 e Å−3

  • Δρmin = −0.30 e Å−3

Data collection: XSCANS (Siemens, 1996[Siemens (1996). XSCANS. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: XSCANS; data reduction: XSCANS; 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: X-SEED (Barbour, 2001[Barbour, L. J. (2001). J. Supramol. Chem. 1, 189-191.]); software used to prepare material for publication: publCIF (Westrip, 2009[Westrip, S. P. (2009). publCIF. In preparation.]).

Supporting information


Comment top

s-Triazine, which has a conjugated structure is commonly derivatized in the design of chromophores that display specific physical properties (Cui et al., 2003; Maury et al., 2005; Zhong et al., 2008), particularly two-photon absorption (Cui et al., 2004; Kannan et al., 2004). The title compound (Fig. 1, Scheme 1) exemplifies a donor-π-acceptor compound with a carbazolyl donor and an s-triazinyl acceptor. It emits blue light in solid state and yellow-green light in solution. However, this property is unusual as most compounds show a bathochromic shift of fluorescence in solid state relative to their emission in solution.

An intramolecular charge transfer (ICT) axis runs from atom N2 to atom N4. The phenylethenyl unit is almost coplanar with the triazinyl ring. However, the carbazolyl unit is severely twisted with respect to the phenylethenyl and triazinyl units, so that conjugation is poor. Accordingly, such a poorly-conjugated molecule can only emit at a short wavelength (in the solid state) whereas in solution, the molecule is probably freed from strain and can achieve planarity. Consequently, it emits at longer wavelengths. The molecules are packed such that the axes of one half the number molecules are aligned in one direction whereas those of the other half are aligned approximately perpendicular to it (Fig. 2).

Related literature top

For background literature on donor–π-acceptor chromophores, see: Cui et al. (2003, 2004); Kannan et al. (2004); Maury & Bozec (2005); Zhong et al. (2008).

Experimental top

4-N-Carbazolylbenzaldehyde (2.03 g, 7.5 mmol) in methanol (30 ml) was added to 2,4,6-trimethyl-s-triazine (1.85 g, 15 mmol) and potassium hydroxide (0.5 g) in methanol (50 ml). The mixture was heated for 24 h. The solvent was removed and the residue was purified by column chromatography on silica gel by using benzene/ethanol (10/1) as eluent. Crystals were obtained by recrystallization from a benzene/ethanol solution of the compound.

Refinement top

Due to the absence of anomalous scatterers, 1509 Friedel pairs were merged. Hydrogen atoms were geometrically fixed and allowed to ride on their parent atoms, with C–H 0.93–0.96 Å and Uiso(H) set to 1.2–1.5Ueq(C).

Computing details top

Data collection: XSCANS (Siemens, 1996); cell refinement: XSCANS (Siemens, 1996); data reduction: XSCANS (Siemens, 1996); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: X-SEED (Barbour, 2001); software used to prepare material for publication: publCIF (Westrip, 2009).

Figures top
[Figure 1] Fig. 1. Anisotropic displacement ellipsoid plot (Barbour, 2001) of C25H20N4 with displacement ellipsoids are drawn at the 50% probability level.
[Figure 2] Fig. 2. Anisotropic displacement ellipsoid plot (Barbour, 2001) depicting the alignment of four molecules in the unit cell.
9-{4-[(E)-2-(4,6-Dimethyl-1,3,5-triazin-2-yl)ethenyl]phenyl}-9H- carbazole top
Crystal data top
C25H20N4F(000) = 792
Mr = 376.45Dx = 1.229 Mg m3
Orthorhombic, P212121Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2abCell parameters from 40 reflections
a = 8.0415 (8) Åθ = 4.6–12.4°
b = 15.716 (2) ŵ = 0.07 mm1
c = 16.098 (1) ÅT = 293 K
V = 2034.4 (3) Å3Prism, pale green
Z = 40.42 × 0.28 × 0.16 mm
Data collection top
Siemens P4 four-circle
diffractometer
1288 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tubeRint = 0.026
Graphite monochromatorθmax = 26.0°, θmin = 1.8°
ω scansh = 19
Absorption correction: ψ scan
(North et al., 1968)
k = 191
Tmin = 0.901, Tmax = 0.988l = 191
2991 measured reflections3 standard reflections every 97 reflections
2291 independent reflections intensity decay: 1%
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)] = 0.055H-atom parameters constrained
wR(F2) = 0.160 w = 1/[σ2(Fo2) + (0.0785P)2]
where P = (Fo2 + 2Fc2)/3
S = 1.00(Δ/σ)max = 0.001
2291 reflectionsΔρmax = 0.26 e Å3
265 parametersΔρmin = 0.30 e Å3
0 restraintsExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
Primary atom site location: structure-invariant direct methodsExtinction coefficient: 0.063 (5)
Crystal data top
C25H20N4V = 2034.4 (3) Å3
Mr = 376.45Z = 4
Orthorhombic, P212121Mo Kα radiation
a = 8.0415 (8) ŵ = 0.07 mm1
b = 15.716 (2) ÅT = 293 K
c = 16.098 (1) Å0.42 × 0.28 × 0.16 mm
Data collection top
Siemens P4 four-circle
diffractometer
1288 reflections with I > 2σ(I)
Absorption correction: ψ scan
(North et al., 1968)
Rint = 0.026
Tmin = 0.901, Tmax = 0.9883 standard reflections every 97 reflections
2991 measured reflections intensity decay: 1%
2291 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0550 restraints
wR(F2) = 0.160H-atom parameters constrained
S = 1.00Δρmax = 0.26 e Å3
2291 reflectionsΔρmin = 0.30 e Å3
265 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
N10.3440 (7)0.5461 (3)0.7650 (3)0.0774 (15)
N20.2899 (6)0.4809 (2)0.6348 (2)0.0627 (12)
N30.4255 (6)0.4024 (3)0.7419 (3)0.0659 (12)
N40.3597 (5)0.0613 (2)0.3022 (2)0.0511 (11)
C10.2848 (8)0.5466 (3)0.6880 (4)0.0732 (17)
C20.4126 (8)0.4724 (4)0.7893 (3)0.0727 (17)
C30.3621 (7)0.4108 (3)0.6658 (3)0.0584 (14)
C40.2098 (9)0.6278 (3)0.6563 (4)0.091 (2)
H4A0.12030.64480.69210.137*
H4B0.16800.61900.60110.137*
H4C0.29320.67150.65540.137*
C50.4801 (8)0.4663 (4)0.8757 (3)0.097 (2)
H5A0.49460.40760.89030.146*
H5B0.40360.49250.91370.146*
H5C0.58530.49500.87850.146*
C60.3767 (7)0.3359 (3)0.6121 (3)0.0563 (13)
H60.42720.28750.63370.068*
C70.3217 (7)0.3333 (3)0.5341 (3)0.0539 (12)
H70.27040.38230.51440.065*
C80.3331 (7)0.2616 (3)0.4757 (3)0.0498 (12)
C90.2847 (7)0.2736 (3)0.3941 (3)0.0545 (13)
H90.24750.32690.37710.065*
C100.2910 (7)0.2076 (3)0.3373 (3)0.0544 (13)
H100.25590.21660.28300.065*
C110.3490 (6)0.1284 (3)0.3607 (3)0.0471 (12)
C120.3989 (7)0.1159 (3)0.4417 (3)0.0537 (12)
H120.43890.06300.45810.064*
C130.3898 (7)0.1816 (3)0.4988 (3)0.0563 (13)
H130.42230.17200.55340.068*
C140.4250 (6)0.0677 (3)0.2221 (3)0.0503 (12)
C150.5018 (7)0.1357 (3)0.1836 (3)0.0630 (14)
H150.51470.18750.21080.076*
C160.5584 (7)0.1243 (4)0.1036 (3)0.0700 (15)
H160.61040.16930.07660.084*
C170.5401 (7)0.0476 (4)0.0625 (3)0.0712 (16)
H170.57850.04190.00830.085*
C180.4658 (6)0.0198 (4)0.1013 (3)0.0636 (15)
H180.45390.07130.07350.076*
C190.4080 (6)0.0115 (3)0.1823 (3)0.0521 (12)
C200.3274 (6)0.0680 (3)0.2402 (3)0.0520 (12)
C210.2764 (7)0.1526 (3)0.2366 (3)0.0662 (15)
H210.29460.18440.18880.079*
C220.2003 (8)0.1884 (3)0.3032 (3)0.0733 (16)
H220.16610.24480.30060.088*
C230.1725 (7)0.1418 (3)0.3754 (3)0.0688 (15)
H230.12020.16750.42040.083*
C240.2220 (7)0.0573 (3)0.3811 (3)0.0624 (14)
H240.20280.02600.42910.075*
C250.3004 (6)0.0213 (3)0.3137 (3)0.0520 (12)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
N10.088 (4)0.069 (3)0.075 (3)0.020 (3)0.025 (3)0.033 (3)
N20.075 (3)0.049 (2)0.065 (2)0.009 (2)0.021 (3)0.010 (2)
N30.077 (3)0.064 (3)0.056 (2)0.019 (3)0.017 (3)0.019 (2)
N40.064 (3)0.044 (2)0.045 (2)0.002 (2)0.001 (2)0.0078 (17)
C10.081 (4)0.057 (3)0.081 (4)0.021 (3)0.031 (4)0.025 (3)
C20.075 (4)0.083 (4)0.060 (3)0.030 (4)0.023 (3)0.023 (3)
C30.067 (4)0.055 (3)0.053 (3)0.015 (3)0.017 (3)0.013 (2)
C40.108 (5)0.053 (3)0.114 (5)0.003 (3)0.038 (5)0.016 (3)
C50.099 (5)0.126 (5)0.066 (4)0.037 (4)0.013 (4)0.041 (4)
C60.072 (4)0.047 (3)0.050 (3)0.008 (3)0.011 (3)0.009 (2)
C70.065 (3)0.043 (2)0.053 (3)0.005 (3)0.008 (3)0.004 (2)
C80.060 (3)0.041 (2)0.049 (3)0.005 (2)0.004 (3)0.007 (2)
C90.071 (4)0.040 (2)0.052 (3)0.006 (3)0.001 (3)0.005 (2)
C100.071 (3)0.047 (3)0.046 (2)0.004 (3)0.002 (3)0.005 (2)
C110.056 (3)0.043 (2)0.043 (2)0.000 (2)0.001 (2)0.008 (2)
C120.071 (3)0.042 (2)0.048 (3)0.004 (3)0.006 (3)0.006 (2)
C130.074 (4)0.051 (3)0.043 (2)0.001 (3)0.004 (3)0.007 (2)
C140.052 (3)0.054 (3)0.044 (3)0.006 (3)0.000 (2)0.006 (2)
C150.074 (4)0.063 (3)0.051 (3)0.003 (3)0.002 (3)0.006 (3)
C160.077 (4)0.084 (4)0.049 (3)0.005 (4)0.007 (3)0.001 (3)
C170.074 (4)0.094 (4)0.045 (3)0.007 (4)0.003 (3)0.006 (3)
C180.064 (4)0.076 (3)0.050 (3)0.011 (3)0.006 (3)0.026 (3)
C190.051 (3)0.057 (3)0.048 (3)0.008 (3)0.007 (2)0.010 (2)
C200.053 (3)0.047 (3)0.056 (3)0.006 (2)0.009 (3)0.012 (2)
C210.072 (4)0.054 (3)0.072 (3)0.004 (3)0.011 (3)0.019 (3)
C220.091 (4)0.047 (3)0.082 (4)0.001 (3)0.005 (4)0.007 (3)
C230.078 (4)0.057 (3)0.072 (3)0.004 (3)0.008 (3)0.003 (3)
C240.073 (4)0.049 (3)0.065 (3)0.003 (3)0.007 (3)0.008 (2)
C250.057 (3)0.044 (2)0.055 (3)0.004 (2)0.005 (3)0.004 (2)
Geometric parameters (Å, º) top
N1—C11.328 (7)C10—H100.9300
N1—C21.342 (7)C11—C121.378 (6)
N2—C11.341 (5)C12—C131.384 (6)
N2—C31.341 (6)C12—H120.9300
N3—C31.333 (6)C13—H130.9300
N3—C21.342 (6)C14—C151.382 (6)
N4—C251.396 (6)C14—C191.406 (6)
N4—C141.396 (5)C15—C161.378 (6)
N4—C111.416 (5)C15—H150.9300
C1—C41.500 (7)C16—C171.382 (7)
C2—C51.496 (8)C16—H160.9300
C3—C61.465 (6)C17—C181.367 (7)
C4—H4A0.9600C17—H170.9300
C4—H4B0.9600C18—C191.391 (6)
C4—H4C0.9600C18—H180.9300
C5—H5A0.9600C19—C201.441 (6)
C5—H5B0.9600C20—C211.393 (6)
C5—H5C0.9600C20—C251.408 (6)
C6—C71.332 (6)C21—C221.357 (7)
C6—H60.9300C21—H210.9300
C7—C81.471 (5)C22—C231.392 (7)
C7—H70.9300C22—H220.9300
C8—C91.383 (6)C23—C241.389 (6)
C8—C131.388 (6)C23—H230.9300
C9—C101.383 (6)C24—C251.377 (6)
C9—H90.9300C24—H240.9300
C10—C111.382 (6)
C1—N1—C2115.1 (4)C10—C11—N4120.6 (4)
C1—N2—C3114.1 (4)C11—C12—C13120.4 (4)
C3—N3—C2114.3 (5)C11—C12—H12119.8
C25—N4—C14108.5 (4)C13—C12—H12119.8
C25—N4—C11125.8 (4)C12—C13—C8121.0 (4)
C14—N4—C11125.7 (4)C12—C13—H13119.5
N1—C1—N2125.4 (5)C8—C13—H13119.5
N1—C1—C4117.8 (5)C15—C14—N4129.6 (4)
N2—C1—C4116.7 (5)C15—C14—C19121.6 (4)
N3—C2—N1125.0 (5)N4—C14—C19108.8 (4)
N3—C2—C5116.6 (6)C16—C15—C14117.8 (5)
N1—C2—C5118.3 (5)C16—C15—H15121.1
N3—C3—N2126.1 (4)C14—C15—H15121.1
N3—C3—C6115.6 (5)C15—C16—C17121.8 (5)
N2—C3—C6118.4 (4)C15—C16—H16119.1
C1—C4—H4A109.5C17—C16—H16119.1
C1—C4—H4B109.5C18—C17—C16120.2 (5)
H4A—C4—H4B109.5C18—C17—H17119.9
C1—C4—H4C109.5C16—C17—H17119.9
H4A—C4—H4C109.5C17—C18—C19120.1 (5)
H4B—C4—H4C109.5C17—C18—H18120.0
C2—C5—H5A109.5C19—C18—H18120.0
C2—C5—H5B109.5C18—C19—C14118.6 (5)
H5A—C5—H5B109.5C18—C19—C20134.3 (5)
C2—C5—H5C109.5C14—C19—C20107.1 (4)
H5A—C5—H5C109.5C21—C20—C25119.1 (5)
H5B—C5—H5C109.5C21—C20—C19133.9 (5)
C7—C6—C3123.6 (5)C25—C20—C19107.0 (4)
C7—C6—H6118.2C22—C21—C20119.7 (5)
C3—C6—H6118.2C22—C21—H21120.1
C6—C7—C8127.3 (5)C20—C21—H21120.1
C6—C7—H7116.4C21—C22—C23121.0 (5)
C8—C7—H7116.4C21—C22—H22119.5
C9—C8—C13118.1 (4)C23—C22—H22119.5
C9—C8—C7119.0 (4)C24—C23—C22120.8 (5)
C13—C8—C7122.9 (4)C24—C23—H23119.6
C8—C9—C10121.0 (4)C22—C23—H23119.6
C8—C9—H9119.5C25—C24—C23118.2 (5)
C10—C9—H9119.5C25—C24—H24120.9
C9—C10—C11120.5 (4)C23—C24—H24120.9
C9—C10—H10119.8C24—C25—N4130.0 (4)
C11—C10—H10119.8C24—C25—C20121.2 (4)
C12—C11—C10119.0 (4)N4—C25—C20108.7 (4)
C12—C11—N4120.3 (4)
C2—N1—C1—N20.5 (9)C25—N4—C14—C190.3 (5)
C2—N1—C1—C4178.7 (5)C11—N4—C14—C19177.8 (4)
C3—N2—C1—N10.1 (8)N4—C14—C15—C16178.7 (5)
C3—N2—C1—C4178.3 (5)C19—C14—C15—C161.4 (8)
C3—N3—C2—N10.4 (8)C14—C15—C16—C170.0 (8)
C3—N3—C2—C5179.4 (5)C15—C16—C17—C180.7 (9)
C1—N1—C2—N30.7 (9)C16—C17—C18—C190.1 (8)
C1—N1—C2—C5179.2 (5)C17—C18—C19—C141.2 (7)
C2—N3—C3—N20.0 (8)C17—C18—C19—C20179.4 (5)
C2—N3—C3—C6179.0 (4)C15—C14—C19—C181.9 (7)
C1—N2—C3—N30.1 (8)N4—C14—C19—C18179.8 (4)
C1—N2—C3—C6178.9 (5)C15—C14—C19—C20178.5 (5)
N3—C3—C6—C7179.4 (5)N4—C14—C19—C200.6 (5)
N2—C3—C6—C70.3 (8)C18—C19—C20—C210.2 (10)
C3—C6—C7—C8179.2 (5)C14—C19—C20—C21179.3 (5)
C6—C7—C8—C9173.2 (5)C18—C19—C20—C25179.7 (5)
C6—C7—C8—C137.1 (8)C14—C19—C20—C250.8 (5)
C13—C8—C9—C100.7 (8)C25—C20—C21—C220.7 (8)
C7—C8—C9—C10179.1 (5)C19—C20—C21—C22179.3 (6)
C8—C9—C10—C111.3 (8)C20—C21—C22—C230.2 (9)
C9—C10—C11—C120.7 (8)C21—C22—C23—C240.1 (9)
C9—C10—C11—N4178.3 (5)C22—C23—C24—C250.5 (8)
C25—N4—C11—C1249.7 (7)C23—C24—C25—N4178.9 (5)
C14—N4—C11—C12133.2 (5)C23—C24—C25—C201.1 (8)
C25—N4—C11—C10131.3 (5)C14—N4—C25—C24178.2 (5)
C14—N4—C11—C1045.8 (7)C11—N4—C25—C240.7 (8)
C10—C11—C12—C130.5 (8)C14—N4—C25—C200.2 (5)
N4—C11—C12—C13179.5 (5)C11—N4—C25—C20177.3 (4)
C11—C12—C13—C81.0 (8)C21—C20—C25—C241.2 (7)
C9—C8—C13—C120.4 (8)C19—C20—C25—C24178.8 (4)
C7—C8—C13—C12179.8 (5)C21—C20—C25—N4179.4 (5)
C25—N4—C14—C15177.9 (5)C19—C20—C25—N40.6 (5)
C11—N4—C14—C154.6 (8)

Experimental details

Crystal data
Chemical formulaC25H20N4
Mr376.45
Crystal system, space groupOrthorhombic, P212121
Temperature (K)293
a, b, c (Å)8.0415 (8), 15.716 (2), 16.098 (1)
V3)2034.4 (3)
Z4
Radiation typeMo Kα
µ (mm1)0.07
Crystal size (mm)0.42 × 0.28 × 0.16
Data collection
DiffractometerSiemens P4 four-circle
diffractometer
Absorption correctionψ scan
(North et al., 1968)
Tmin, Tmax0.901, 0.988
No. of measured, independent and
observed [I > 2σ(I)] reflections
2991, 2291, 1288
Rint0.026
(sin θ/λ)max1)0.617
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.055, 0.160, 1.00
No. of reflections2291
No. of parameters265
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.26, 0.30

Computer programs: XSCANS (Siemens, 1996), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), X-SEED (Barbour, 2001), publCIF (Westrip, 2009).

 

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 20676074) and the Foundation for Excellent Middle/Young Scientists of Shandong Province (grant No. 2005BS11011).

References

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