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ISSN: 2056-9890

4-(4-Fluoro­phen­yl)-2-oxo-1,2,5,6-tetra­hydro­benzo[h]quinoline-3-carbo­nitrile

aDepartment of Public Health, Xuzhou Medical College, Xuzhou 221000, People's Republic of China, and bCollege of Chemistry and Chemical Engineering, Xuzhou Normal University, Xuzhou 221116, People's Republic of China
*Correspondence e-mail: yanshu126@126.com

(Received 8 May 2009; accepted 13 May 2009; online 20 May 2009)

In the mol­ecule of the title compound, C20H13FN2O, the fluoro­phenyl ring is oriented at a dihedral angle of 72.76 (3)° with respect to the fused benzene ring. In the crystal structure, inter­molecular N—H⋯O, C—H⋯O and C—H⋯F inter­actions link the mol­ecules into chains. ππ contacts between the quinoline and benzene rings [centroid–centroid distance = 3.918 (3) Å] may further stabilize the structure. A weak C—H⋯π inter­action is also present. The O atom and two of the CH2 groups of the quinoline ring system are disordered over two positions. The O atom was refined with occupancies of 0.489 (17) and 0.511 (17), while C and H atoms were refined with occupancies of 0.435 (13) and 0.565 (13).

Related literature

For general background to substituted six-membered lactams, see: Daly (1998[Daly, J. W. (1998). J. Nat. Prod. 61, 162-172.]); Plunkett (1994[Plunkett, A. O. (1994). Nat. Prod. Rep. 11, 581-590.]); Robertson et al. (1986[Robertson, D. W., Beedle, E. E., Swartzendruber, J. K., Jones, N. D., Elzey, T. K., Kauffman, R. F., Wilson, H. & Hayes, J. S. (1986). J. Med. Chem. 29, 635-640.]). For bond-length data, see: Allen et al. (1987[Allen, F. H., Kennard, O., Watson, D. G., Brammer, L., Orpen, A. G. & Taylor, R. (1987). J. Chem. Soc. Perkin Trans. 2, pp. S1-19.]).

[Scheme 1]

Experimental

Crystal data
  • C20H13FN2O

  • Mr = 316.32

  • Triclinic, [P \overline 1]

  • a = 8.116 (10) Å

  • b = 9.278 (12) Å

  • c = 11.263 (14) Å

  • α = 98.674 (19)°

  • β = 105.095 (17)°

  • γ = 104.846 (18)°

  • V = 769.7 (16) Å3

  • Z = 2

  • Mo Kα radiation

  • μ = 0.09 mm−1

  • T = 298 K

  • 0.48 × 0.35 × 0.33 mm

Data collection
  • Bruker SMART CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Sheldrick, 1996[Sheldrick, G. M. (1996). SADABS. University of Göttingen, Germany.]) Tmin = 0.956, Tmax = 0.970

  • 3950 measured reflections

  • 2656 independent reflections

  • 1399 reflections with I > 2σ(I)

  • Rint = 0.020

Refinement
  • R[F2 > 2σ(F2)] = 0.048

  • wR(F2) = 0.144

  • S = 1.00

  • 2656 reflections

  • 240 parameters

  • H-atom parameters constrained

  • Δρmax = 0.15 e Å−3

  • Δρmin = −0.17 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N1—H1⋯O1i 0.86 2.08 2.883 (3) 155
C7—H7⋯O1i 0.93 2.35 3.223 (3) 157
C12—H12B⋯O1ii 0.97 2.21 2.863 (3) 124
C13—H13B⋯F1iii 0.97 2.42 3.270 (3) 147
C15—H15⋯Cg3iv 0.93 2.90 3.671 (3) 141
Symmetry codes: (i) -x, -y, -z+1; (ii) x+1, y, z; (iii) -x+1, -y+1, -z; (iv) -x+1, -y+1, -z+1.

Data collection: SMART (Bruker, 1998[Bruker (1998). SMART and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 1998[Bruker (1998). SMART and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; 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: ORTEP-3 for Windows (Farrugia, 1997[Farrugia, L. J. (1997). J. Appl. Cryst. 30, 565.]); software used to prepare material for publication: SHELXL97 and PLATON (Spek, 2009[Spek, A. L. (2009). Acta Cryst. D65, 148-155.]).

Supporting information


Comment top

Substituted six-membered lactams have attracted the attention of synthetic organic chemists for many years because these structural features are found in a wide variety of naturally occurring alkaloids (Daly, 1998; Plunkett, 1994). Since compounds with these scaffolds have been shown to exhibit significant pharmacological properties, medicinal chemists often incorporate these motifs in the design of novel biologically active molecules. For example, compounds Arnrinone 1 and Milrinone 2 are the cardiotonic drugs (Robertson et al., 1986) and that have been found to display effective activities on therapy of miocardial infarction. Development of a general and efficient synthetic strategy to synthesize those compounds is still desired. We report herein the crystal structure of the title compound.

In the molecule of the title compound (Fig. 1), the bond lengths (Allen et al., 1987) and angles are within normal ranges. Rings A (N1/C1-C5), C (C6-C11) and D (C14-C19) are, of course, planar and they are oriented at dihedral angles of A/C = 3.57 (3), A/D = 76.11 (3) and C/D = 72.76 (3) °. Ring B (C4-C6/C11-C13) is not planar, and adopts twisted conformation.

In the crystal structure, intermolecular N-H···O, C-H···O and C-H···F interactions (Table 1) link the molecules into chains (Fig. 2), in which they may be effective in the stabilization of the structure. The π···π contact between the quinoline and the benzene rings, Cg1—Cg3i [symmetry code: (i) 1 - x, -y, 1 - z, where Cg1 and Cg3 are centroids of the rings A (N1/C1-C5) and C (C6-C11), respectively] may further stabilize the structure, with centroid-centroid distance of 3.918 (3) Å. There also exists a weak C-H···π interaction (Table 1).

Related literature top

For general background to substituted six-membered lactams, see: Daly (1998); Plunkett (1994); Robertson et al. (1986). For bond-length data, see: Allen et al. (1987).

Experimental top

The title compound was prepared by the reaction of 3,4-dihydronaphthalen-1(2H) -one (2 mmol), aromatic aldehydes (2 mmol), malononitrile (3 mmol) and NaOH (2 mmol) under solvent-free conditions using heating method.

Refinement top

The O1, C12, C13, H12A, H12B, H13A and H13B atoms were disordered. During the refinement process, the disordered C and H atoms were refined with occupancies of 0.435 (13) and 0.565 (13), while O atom was refined with occupancies of 0.489 (17) and 0.511 (17). H atoms were positioned geometrically with N-H = 0.86 Å (for NH) and C-H = 0.93 and 0.97 Å, for aromatic and methylene H atoms, respectively, and constrained to ride on their parent atoms, with Uiso(H) = 1.2Ueq(C,N).

Computing details top

Data collection: SMART (Bruker, 1998); cell refinement: SAINT (Bruker, 1998); data reduction: SAINT (Bruker, 1998); 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: SHELXL97 (Sheldrick, 2008) and PLATON (Spek, 2009).

Figures top
[Figure 1] Fig. 1. The molecular structure of the title molecule, with the atom-numbering scheme. Displacement ellipsoids are drawn at the 30% probability level.
[Figure 2] Fig. 2. A partial packing diagram of the title compound. Hydrogen bonds are shown as dashed lines.
4-(4-Fluorophenyl)-2-oxo-1,2,5,6-tetrahydrobenzo[h]quinoline-3- carbonitrile top
Crystal data top
C20H13FN2OZ = 2
Mr = 316.32F(000) = 328
Triclinic, P1Dx = 1.365 Mg m3
Hall symbol: -P 1Melting point > 598 K
a = 8.116 (10) ÅMo Kα radiation, λ = 0.71073 Å
b = 9.278 (12) ÅCell parameters from 929 reflections
c = 11.263 (14) Åθ = 2.3–25.4°
α = 98.674 (19)°µ = 0.09 mm1
β = 105.095 (17)°T = 298 K
γ = 104.846 (18)°Block, colourless
V = 769.7 (16) Å30.48 × 0.35 × 0.33 mm
Data collection top
Bruker SMART CCD area-detector
diffractometer
2656 independent reflections
Radiation source: fine-focus sealed tube1399 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.020
ϕ and ω scansθmax = 25.0°, θmin = 2.3°
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
h = 99
Tmin = 0.956, Tmax = 0.970k = 118
3950 measured reflectionsl = 913
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)] = 0.048H-atom parameters constrained
wR(F2) = 0.144 w = 1/[σ2(Fo2) + (0.0683P)2]
where P = (Fo2 + 2Fc2)/3
S = 1.00(Δ/σ)max < 0.001
2656 reflectionsΔρmax = 0.15 e Å3
240 parametersΔρmin = 0.17 e Å3
Primary atom site location: structure-invariant direct methods
Crystal data top
C20H13FN2Oγ = 104.846 (18)°
Mr = 316.32V = 769.7 (16) Å3
Triclinic, P1Z = 2
a = 8.116 (10) ÅMo Kα radiation
b = 9.278 (12) ŵ = 0.09 mm1
c = 11.263 (14) ÅT = 298 K
α = 98.674 (19)°0.48 × 0.35 × 0.33 mm
β = 105.095 (17)°
Data collection top
Bruker SMART CCD area-detector
diffractometer
2656 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
1399 reflections with I > 2σ(I)
Tmin = 0.956, Tmax = 0.970Rint = 0.020
3950 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.048240 parameters
wR(F2) = 0.144H-atom parameters constrained
S = 1.00Δρmax = 0.15 e Å3
2656 reflectionsΔρmin = 0.17 e Å3
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*/UeqOcc. (<1)
F10.2899 (2)0.4261 (2)0.18711 (16)0.1127 (7)
N10.2029 (3)0.1315 (2)0.45914 (18)0.0580 (6)
H10.19260.09480.52350.070*
N20.2136 (3)0.1660 (3)0.0916 (2)0.0781 (7)
O10.101 (3)0.0761 (19)0.3875 (16)0.063 (2)0.489 (17)
O1'0.100 (2)0.0203 (19)0.3604 (16)0.063 (2)0.511 (17)
C10.0482 (3)0.1170 (3)0.3667 (2)0.0589 (7)
C20.0742 (3)0.1847 (3)0.2646 (2)0.0474 (6)
C30.2423 (3)0.2493 (3)0.2576 (2)0.0449 (6)
C40.3947 (3)0.2594 (3)0.3564 (2)0.0514 (7)
C50.3716 (3)0.1991 (3)0.4576 (2)0.0441 (6)
C60.5250 (3)0.2014 (3)0.5626 (2)0.0472 (6)
C70.5053 (4)0.1393 (3)0.6645 (2)0.0611 (7)
H70.39080.09750.66940.073*
C80.6514 (4)0.1387 (3)0.7579 (2)0.0673 (8)
H80.63540.09730.82590.081*
C90.8191 (4)0.1978 (3)0.7521 (3)0.0705 (8)
H90.91810.19540.81490.085*
C100.8420 (4)0.2613 (4)0.6529 (3)0.0817 (9)
H100.95750.30210.64960.098*
C110.6977 (4)0.2660 (3)0.5580 (2)0.0652 (8)
C120.7151 (13)0.2943 (16)0.4310 (10)0.060 (2)0.435 (13)
H12A0.83450.36110.44290.072*0.435 (13)
H12B0.69640.19790.37400.072*0.435 (13)
C130.5770 (13)0.3675 (14)0.3755 (13)0.061 (3)0.435 (13)
H13A0.59550.46400.43230.073*0.435 (13)
H13B0.58720.38800.29530.073*0.435 (13)
C12'0.7237 (10)0.3759 (13)0.4687 (7)0.069 (2)0.565 (13)
H12C0.70970.47290.50270.083*0.565 (13)
H12D0.84320.39540.46080.083*0.565 (13)
C13'0.5852 (10)0.3014 (12)0.3417 (7)0.059 (2)0.565 (13)
H13C0.60680.20950.30460.071*0.565 (13)
H13D0.59360.37100.28580.071*0.565 (13)
C140.2601 (3)0.3026 (3)0.1417 (2)0.0493 (6)
C150.2276 (4)0.4341 (3)0.1176 (3)0.0681 (8)
H150.19760.49560.17640.082*
C160.2388 (4)0.4774 (4)0.0065 (3)0.0769 (9)
H160.21650.56710.00980.092*
C170.2827 (4)0.3865 (4)0.0771 (3)0.0729 (9)
C180.3162 (4)0.2565 (4)0.0566 (3)0.0858 (10)
H180.34560.19570.11630.103*
C190.3064 (4)0.2146 (4)0.0539 (3)0.0769 (9)
H190.33140.12560.06960.092*
C200.0853 (4)0.1739 (3)0.1674 (2)0.0561 (7)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
F10.0932 (13)0.1675 (19)0.0723 (12)0.0028 (12)0.0250 (10)0.0801 (12)
N10.0489 (13)0.0912 (17)0.0447 (12)0.0206 (12)0.0199 (11)0.0405 (12)
N20.0698 (17)0.100 (2)0.0663 (16)0.0261 (15)0.0106 (14)0.0435 (15)
O10.0480 (12)0.100 (8)0.058 (6)0.025 (5)0.027 (3)0.044 (5)
O1'0.0480 (12)0.100 (8)0.058 (6)0.025 (5)0.027 (3)0.044 (5)
C10.0495 (16)0.088 (2)0.0505 (16)0.0231 (15)0.0207 (14)0.0367 (15)
C20.0511 (15)0.0574 (16)0.0420 (14)0.0187 (13)0.0187 (12)0.0256 (12)
C30.0535 (15)0.0467 (15)0.0418 (14)0.0153 (12)0.0212 (12)0.0207 (12)
C40.0509 (15)0.0569 (16)0.0503 (15)0.0113 (13)0.0198 (13)0.0266 (13)
C50.0461 (14)0.0482 (15)0.0414 (14)0.0141 (12)0.0164 (12)0.0163 (12)
C60.0485 (15)0.0505 (16)0.0426 (14)0.0140 (13)0.0143 (12)0.0131 (12)
C70.0549 (17)0.078 (2)0.0479 (16)0.0119 (14)0.0124 (13)0.0282 (14)
C80.072 (2)0.068 (2)0.0521 (17)0.0144 (16)0.0056 (16)0.0245 (15)
C90.064 (2)0.080 (2)0.0585 (19)0.0225 (17)0.0024 (15)0.0179 (16)
C100.0517 (18)0.114 (3)0.080 (2)0.0235 (18)0.0158 (16)0.037 (2)
C110.0536 (17)0.085 (2)0.0588 (17)0.0193 (15)0.0158 (14)0.0276 (16)
C120.043 (4)0.072 (6)0.068 (5)0.015 (5)0.020 (4)0.026 (4)
C130.065 (5)0.062 (6)0.057 (5)0.012 (4)0.024 (4)0.024 (4)
C12'0.055 (3)0.079 (5)0.071 (4)0.010 (4)0.021 (3)0.029 (4)
C13'0.049 (3)0.071 (5)0.062 (5)0.010 (4)0.024 (3)0.032 (4)
C140.0499 (15)0.0571 (16)0.0440 (15)0.0110 (13)0.0178 (12)0.0253 (13)
C150.084 (2)0.0655 (19)0.0653 (19)0.0249 (16)0.0280 (16)0.0360 (15)
C160.077 (2)0.075 (2)0.079 (2)0.0134 (17)0.0159 (18)0.0533 (18)
C170.0537 (18)0.108 (3)0.0502 (18)0.0009 (18)0.0128 (14)0.0486 (19)
C180.104 (3)0.112 (3)0.064 (2)0.038 (2)0.0474 (19)0.041 (2)
C190.112 (3)0.086 (2)0.0628 (19)0.046 (2)0.0480 (19)0.0436 (17)
C200.0602 (18)0.0676 (18)0.0495 (17)0.0195 (15)0.0222 (15)0.0318 (14)
Geometric parameters (Å, º) top
F1—C171.356 (3)C10—C111.381 (4)
N1—C51.358 (3)C10—H100.9300
N1—C11.367 (3)C11—C121.528 (9)
N1—H10.8600C11—C12'1.550 (8)
N2—C201.139 (3)C12—C131.505 (14)
O1—C11.267 (18)C12—H12A0.9700
O1'—C11.279 (18)C12—H12B0.9700
C1—C21.428 (3)C13—H13A0.9700
C2—C31.370 (3)C13—H13B0.9700
C2—C201.431 (4)C12'—C13'1.501 (12)
C3—C41.404 (3)C12'—H12C0.9700
C3—C141.491 (3)C12'—H12D0.9700
C4—C51.377 (3)C13'—H13C0.9700
C4—C131.499 (10)C13'—H13D0.9700
C4—C13'1.553 (8)C14—C151.363 (4)
C5—C61.470 (3)C14—C191.376 (4)
C6—C71.387 (3)C15—C161.389 (4)
C6—C111.394 (4)C15—H150.9300
C7—C81.367 (4)C16—C171.347 (4)
C7—H70.9300C16—H160.9300
C8—C91.354 (4)C17—C181.342 (4)
C8—H80.9300C18—C191.375 (4)
C9—C101.371 (4)C18—H180.9300
C9—H90.9300C19—H190.9300
C5—N1—C1125.3 (2)C13—C12—H12A109.9
C5—N1—H1117.4C11—C12—H12A109.9
C1—N1—H1117.4C13—C12—H12B109.9
O1—C1—N1119.7 (9)C11—C12—H12B109.9
O1'—C1—N1120.2 (8)H12A—C12—H12B108.3
O1—C1—C2124.0 (9)C4—C13—C12108.2 (9)
O1'—C1—C2123.2 (8)C4—C13—H13A110.1
N1—C1—C2114.7 (2)C12—C13—H13A110.1
C3—C2—C1121.7 (2)C4—C13—H13B110.1
C3—C2—C20122.2 (2)C12—C13—H13B110.1
C1—C2—C20116.0 (2)H13A—C13—H13B108.4
C2—C3—C4120.1 (2)C13'—C12'—C11108.2 (7)
C2—C3—C14119.1 (2)C13'—C12'—H12C110.1
C4—C3—C14120.8 (2)C11—C12'—H12C110.1
C5—C4—C3118.8 (2)C13'—C12'—H12D110.1
C5—C4—C13116.3 (5)C11—C12'—H12D110.1
C3—C4—C13122.8 (5)H12C—C12'—H12D108.4
C5—C4—C13'118.0 (4)C12'—C13'—C4109.8 (7)
C3—C4—C13'121.8 (4)C12'—C13'—H13C109.7
N1—C5—C4119.4 (2)C4—C13'—H13C109.7
N1—C5—C6118.8 (2)C12'—C13'—H13D109.7
C4—C5—C6121.8 (2)C4—C13'—H13D109.7
C7—C6—C11118.7 (2)H13C—C13'—H13D108.2
C7—C6—C5122.9 (2)C15—C14—C19118.4 (2)
C11—C6—C5118.4 (2)C15—C14—C3122.3 (2)
C8—C7—C6121.1 (3)C19—C14—C3119.2 (2)
C8—C7—H7119.5C14—C15—C16120.9 (3)
C6—C7—H7119.5C14—C15—H15119.5
C9—C8—C7120.4 (3)C16—C15—H15119.5
C9—C8—H8119.8C17—C16—C15118.4 (3)
C7—C8—H8119.8C17—C16—H16120.8
C8—C9—C10119.5 (3)C15—C16—H16120.8
C8—C9—H9120.2C18—C17—C16122.5 (3)
C10—C9—H9120.2C18—C17—F1118.7 (3)
C9—C10—C11121.6 (3)C16—C17—F1118.8 (3)
C9—C10—H10119.2C17—C18—C19118.9 (3)
C11—C10—H10119.2C17—C18—H18120.5
C10—C11—C6118.7 (3)C19—C18—H18120.5
C10—C11—C12121.7 (4)C18—C19—C14120.9 (3)
C6—C11—C12117.1 (4)C18—C19—H19119.6
C10—C11—C12'120.9 (4)C14—C19—H19119.6
C6—C11—C12'118.5 (4)N2—C20—C2178.8 (3)
C13—C12—C11108.8 (9)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1···O1i0.862.082.883 (3)155
C7—H7···O1i0.932.353.223 (3)157
C12—H12B···O1ii0.972.212.863 (3)124
C13—H13B···F1iii0.972.423.270 (3)147
C15—H15···Cg3iv0.932.903.671 (3)141
Symmetry codes: (i) x, y, z+1; (ii) x+1, y, z; (iii) x+1, y+1, z; (iv) x+1, y+1, z+1.

Experimental details

Crystal data
Chemical formulaC20H13FN2O
Mr316.32
Crystal system, space groupTriclinic, P1
Temperature (K)298
a, b, c (Å)8.116 (10), 9.278 (12), 11.263 (14)
α, β, γ (°)98.674 (19), 105.095 (17), 104.846 (18)
V3)769.7 (16)
Z2
Radiation typeMo Kα
µ (mm1)0.09
Crystal size (mm)0.48 × 0.35 × 0.33
Data collection
DiffractometerBruker SMART CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 1996)
Tmin, Tmax0.956, 0.970
No. of measured, independent and
observed [I > 2σ(I)] reflections
3950, 2656, 1399
Rint0.020
(sin θ/λ)max1)0.595
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.048, 0.144, 1.00
No. of reflections2656
No. of parameters240
No. of restraints?
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.15, 0.17

Computer programs: SMART (Bruker, 1998), SAINT (Bruker, 1998), SHELXS97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 1997), SHELXL97 (Sheldrick, 2008) and PLATON (Spek, 2009).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1···O1i0.862.082.883 (3)155
C7—H7···O1i0.932.353.223 (3)157
C12—H12B···O1ii0.972.212.863 (3)124
C13—H13B···F1iii0.972.423.270 (3)147
C15—H15···Cg3iv0.932.903.671 (3)141
Symmetry codes: (i) x, y, z+1; (ii) x+1, y, z; (iii) x+1, y+1, z; (iv) x+1, y+1, z+1.
 

Acknowledgements

The authors thank the National Natural Science Foundation of China (grant No. 30872143) and the Foundation of Xuzhou Medical College (grant No. 08 K J50) for financial support.

References

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