N2,N2,N5,N5-Tetra­kis(2-chloro­ethyl)-3,4-dimethyl­thio­phene-2,5-dicarboxamide

Tang, Y.-D.; Geng, R.-X.; Zhou, C.-H.

doi:10.1107/S1600536809052374

organic compounds

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ISSN: 2056-9890

Volume 66| Part 1| January 2010| Page o100

doi:10.1107/S1600536809052374

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N²,N²,N⁵,N⁵-Tetrakis(2-chloroethyl)-3,4-dimethylthiophene-2,5-dicarboxamide

Yi-Dan Tang,^a Rong-Xia Geng ^a and Cheng-He Zhou ^a ^*

^aSchool of Chemistry and Chemical Engineering, Southwest University, Chongqing 400715, People's Republic of China
^*Correspondence e-mail: zhouch@swu.edu.cn

(Received 4 December 2009; accepted 5 December 2009; online 12 December 2009)

In the title compound, C₁₆H₂₂Cl₄N₂O₂S, the two imide groups adopt a trans arrangement relative to the central thienyl ring, so the four terminal 2-chloroethyl arms adopt different orientations. In the crystal, molecules are linked by weak C—H⋯Cl and C—H⋯O hydrogen bonds into a three-dimensional network.

Related literature

For general background to nitrogen mustard agents as antitumor dugs, see: Zhuang et al. (2008 ). For the synthesis, see: Luo et al. (2007 ). For a related structure, see: Dong et al. (2006 ).

Experimental

Crystal data

C₁₆H₂₂Cl₄N₂O₂S
M_r = 448.22
Monoclinic, P 2₁ /c
a = 7.9238 (4) Å
b = 21.1712 (11) Å
c = 12.6186 (7) Å
β = 99.2380 (10)°
V = 2089.39 (19) Å³
Z = 4
Mo Kα radiation
μ = 0.68 mm⁻¹
T = 298 K
0.25 × 0.22 × 0.20 mm

Data collection

Bruker APEXII area-detector diffractometer
Absorption correction: multi-scan (SADABS; Sheldrick, 1996 ) T_min = 0.849, T_max = 0.876
13412 measured reflections
4008 independent reflections
3342 reflections with I > 2σ(I)
R_int = 0.018

Refinement

R[F² > 2σ(F²)] = 0.042
wR(F²) = 0.126
S = 1.04
4008 reflections
228 parameters
H-atom parameters constrained
Δρ_max = 0.88 e Å⁻³
Δρ_min = −0.63 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
C14—H14B⋯O2ⁱ	0.97	2.45	3.257 (3)	141
C14—H14A⋯Cl1ⁱⁱ	0.97	2.80	3.632 (3)	145
C6—H6B⋯O1ⁱⁱⁱ	0.96	2.54	3.474 (3)	166
C5—H5B⋯O1^iv	0.96	2.54	3.477 (3)	165
Symmetry codes: (i) $[x, -y+{\script{1\over 2}}, z-{\script{1\over 2}}]$ ; (ii) x-1, y, z-1; (iii) -x+1, -y, -z+1; (iv) x+1, y, z.

Data collection: APEX2 (Bruker, 2004 ); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT; 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: APEX2 (Bruker, 2004) and publCIF (Westrip, 2009 ).

Supporting information

Crystal structure: contains datablocks I, global. DOI: 10.1107/S1600536809052374/ng2703sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536809052374/ng2703Isup2.hkl

checkCIF report

Comment top

Nitrogen mustard agents are one of the most important antitumor dugs, and have been widely used for the treatment of solid neoplastic and leukemia tumor for many years. The incorporation of amido and/or conjugated moiety into nitrogen mustards often helps to decrease the toxicity and improve the target affinity due to the dispersion of N atom electron atmosphere density (Zhuang et al., 2008). Herein, in order to find new antitumor dugs, we have successfully synthesized the title compound (I) by an acylation reaction of bis(2-chloroethyl)amine wiht 3,4-dimethylthiophene-2,5-dicarbonyl dichloride (Luo et al., 2007) and fully characterized by single-crystal X-ray diffraction.

The molecular structure of the title compound is shown in Fig. 1. Single crystal analysis revealed that two imide groups of the title compound adopt trans-conformation arrangement (Dong et al., 2006) compared with the central thiophene ring, so the four terminal 2-chloroethyl arms are oriented in the different orientation. As indicated in Fig. 2, in the solid state, these moleculers are bonded together with Cl···H—C hydrogen bonds into an H-bonding-driven three-dimensional network, corresponding O(7)···H(3 A), O(7)···O(3), and O(7)···H(3 A)—O(3) data are 2.33 Å, 3.19 Å and 145.1°, respectively.

Related literature top

For general background to nitrogen mustard agents as antitumor dugs, see: Zhuang et al. (2008). For the synthesis, see: Luo et al. (2007). For a related structure, see: Dong et al. (2006).

Experimental top

The title compound (I) was gained by amidation of 3,4-dimethylthiophene-2,5-dicarbonyl dichloride (1 mmol) with bis(2-chloroethyl)amine (2 mmol) according to literature (Luo et al., 2007). A crystal of (I) suitable for X-ray analysis was grown from a mixture solution of ethyl acetate and petroleum ether by slow evaporation at room temperature.

Computing details top

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT (Bruker, 2004); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXLTL (Sheldrick, 2008); software used to prepare material for publication: APEX2 (Bruker, 2004) and publCIF (Westrip, 2009).

Figures top

	Fig. 1. The molecular structure of the title compound, showing the atom-numbering scheme. Displacement ellipsoids are drawn at the 50% probability level.
	Fig. 2. Packing diagram.

N²,N²,N⁵,N⁵-Tetrakis(2-chloroethyl)-3,4- dimethylthiophene-2,5-dicarboxamide top

Crystal data top

C₁₆H₂₂Cl₄N₂O₂S	F(000) = 928
M_r = 448.22	D_x = 1.425 Mg m⁻³
Monoclinic, P2₁/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybc	Cell parameters from 7657 reflections
a = 7.9238 (4) Å	θ = 1.0–28.3°
b = 21.1712 (11) Å	µ = 0.68 mm⁻¹
c = 12.6186 (7) Å	T = 298 K
β = 99.238 (1)°	Block, white
V = 2089.39 (19) Å³	0.25 × 0.22 × 0.20 mm
Z = 4

Data collection top

Bruker APEXII area-detector diffractometer	4008 independent reflections
Radiation source: fine-focus sealed tube	3342 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.018
ϕ and ω scan	θ_max = 26.0°, θ_min = 1.9°
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	h = −9→9
T_min = 0.849, T_max = 0.876	k = −26→26
13412 measured reflections	l = −15→15

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.042	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.126	H-atom parameters constrained
S = 1.04	w = 1/[σ²(F_o²) + (0.0694P)² + 1.0128P] where P = (F_o² + 2F_c²)/3
4008 reflections	(Δ/σ)_max < 0.001
228 parameters	Δρ_max = 0.88 e Å⁻³
0 restraints	Δρ_min = −0.63 e Å⁻³

Crystal data top

C₁₆H₂₂Cl₄N₂O₂S	V = 2089.39 (19) Å³
M_r = 448.22	Z = 4
Monoclinic, P2₁/c	Mo Kα radiation
a = 7.9238 (4) Å	µ = 0.68 mm⁻¹
b = 21.1712 (11) Å	T = 298 K
c = 12.6186 (7) Å	0.25 × 0.22 × 0.20 mm
β = 99.238 (1)°

Data collection top

Bruker APEXII area-detector diffractometer	4008 independent reflections
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	3342 reflections with I > 2σ(I)
T_min = 0.849, T_max = 0.876	R_int = 0.018
13412 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.042	0 restraints
wR(F²) = 0.126	H-atom parameters constrained
S = 1.04	Δρ_max = 0.88 e Å⁻³
4008 reflections	Δρ_min = −0.63 e Å⁻³
228 parameters

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

	x	y	z	U_iso*/U_eq
C1	0.6440 (3)	0.16192 (11)	0.56639 (16)	0.0422 (5)
C2	0.4663 (3)	0.10478 (11)	0.41970 (16)	0.0443 (5)
C3	0.7314 (3)	0.11337 (11)	0.52879 (16)	0.0443 (5)
C4	0.6267 (3)	0.07973 (11)	0.44327 (16)	0.0452 (5)
C5	0.9129 (3)	0.09640 (14)	0.5718 (2)	0.0604 (7)
H5A	0.9596	0.1267	0.6251	0.091*
H5B	0.9788	0.0965	0.5142	0.091*
H5C	0.9166	0.0551	0.6034	0.091*
C6	0.6887 (4)	0.02243 (13)	0.3905 (2)	0.0622 (7)
H6A	0.5947	0.0033	0.3441	0.093*
H6B	0.7362	−0.0073	0.4445	0.093*
H6C	0.7749	0.0348	0.3491	0.093*
C7	0.3109 (3)	0.08236 (11)	0.34627 (17)	0.0458 (5)
C8	0.7126 (3)	0.21071 (11)	0.64859 (17)	0.0422 (5)
C9	0.6710 (3)	0.13373 (12)	0.79073 (18)	0.0500 (6)
H9A	0.7502	0.1203	0.8534	0.060*
H9B	0.6717	0.1022	0.7350	0.060*
C10	0.4939 (4)	0.13895 (13)	0.8188 (2)	0.0643 (7)
H10A	0.4128	0.1483	0.7547	0.077*
H10B	0.4904	0.1732	0.8694	0.077*
C11	0.7869 (4)	0.24259 (14)	0.8346 (2)	0.0575 (6)
H11A	0.7587	0.2291	0.9031	0.069*
H11B	0.7269	0.2819	0.8152	0.069*
C12	0.9744 (4)	0.25440 (18)	0.8472 (3)	0.0832 (10)
H12A	1.0070	0.2838	0.9059	0.100*
H12B	1.0009	0.2738	0.7822	0.100*
C13	0.4527 (3)	0.10073 (11)	0.18708 (17)	0.0459 (5)
H13A	0.4924	0.0670	0.1451	0.055*
H13B	0.5478	0.1132	0.2414	0.055*
C14	0.4016 (3)	0.15598 (12)	0.11482 (18)	0.0504 (6)
H14A	0.3109	0.1434	0.0577	0.060*
H14B	0.4985	0.1696	0.0824	0.060*
C15	0.1637 (3)	0.05019 (11)	0.17242 (19)	0.0497 (6)
H15A	0.1273	0.0125	0.2063	0.060*
H15B	0.1937	0.0379	0.1038	0.060*
C16	0.0165 (3)	0.09661 (13)	0.1536 (2)	0.0577 (6)
H16A	0.0514	0.1342	0.1190	0.069*
H16B	−0.0148	0.1089	0.2219	0.069*
Cl1	1.09507 (11)	0.18434 (6)	0.87299 (8)	0.0971 (3)
Cl2	0.43645 (12)	0.06673 (3)	0.87659 (6)	0.0720 (2)
Cl3	−0.16257 (10)	0.06186 (4)	0.07135 (7)	0.0781 (3)
Cl4	0.32971 (10)	0.22004 (3)	0.18815 (6)	0.0651 (2)
N1	0.3156 (2)	0.07637 (9)	0.24030 (14)	0.0420 (4)
N2	0.7258 (2)	0.19471 (9)	0.75320 (14)	0.0434 (4)
O1	0.1805 (3)	0.06964 (11)	0.38336 (14)	0.0699 (6)
O2	0.7529 (3)	0.26329 (8)	0.62021 (14)	0.0593 (5)
S1	0.43739 (8)	0.16811 (3)	0.50083 (4)	0.04896 (18)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
C1	0.0423 (12)	0.0513 (12)	0.0326 (10)	0.0084 (9)	0.0052 (8)	0.0022 (9)
C2	0.0492 (13)	0.0534 (13)	0.0302 (10)	0.0059 (10)	0.0066 (9)	−0.0019 (9)
C3	0.0471 (13)	0.0543 (13)	0.0321 (10)	0.0109 (10)	0.0082 (9)	0.0025 (9)
C4	0.0547 (14)	0.0508 (12)	0.0307 (10)	0.0123 (10)	0.0089 (9)	0.0026 (9)
C5	0.0496 (15)	0.0781 (18)	0.0526 (14)	0.0201 (13)	0.0054 (11)	−0.0018 (13)
C6	0.0777 (19)	0.0630 (16)	0.0451 (13)	0.0261 (14)	0.0073 (12)	−0.0057 (11)
C7	0.0508 (14)	0.0507 (12)	0.0361 (11)	0.0023 (10)	0.0072 (10)	0.0025 (9)
C8	0.0369 (12)	0.0505 (12)	0.0390 (11)	0.0072 (9)	0.0058 (9)	0.0011 (9)
C9	0.0589 (15)	0.0538 (13)	0.0373 (11)	0.0106 (11)	0.0077 (10)	0.0037 (10)
C10	0.0720 (19)	0.0531 (14)	0.0737 (17)	0.0027 (13)	0.0295 (14)	0.0103 (13)
C11	0.0556 (16)	0.0686 (16)	0.0464 (13)	0.0011 (12)	0.0026 (11)	−0.0132 (12)
C12	0.068 (2)	0.096 (2)	0.079 (2)	−0.0103 (17)	−0.0062 (16)	−0.0104 (18)
C13	0.0453 (13)	0.0577 (13)	0.0357 (11)	0.0011 (10)	0.0093 (9)	−0.0033 (9)
C14	0.0542 (15)	0.0603 (14)	0.0376 (11)	−0.0078 (11)	0.0100 (10)	−0.0009 (10)
C15	0.0568 (15)	0.0478 (12)	0.0435 (12)	−0.0091 (11)	0.0049 (10)	−0.0084 (10)
C16	0.0510 (15)	0.0590 (15)	0.0592 (15)	−0.0086 (12)	−0.0024 (11)	−0.0083 (12)
Cl1	0.0548 (5)	0.1416 (9)	0.0898 (6)	0.0198 (5)	−0.0041 (4)	0.0276 (6)
Cl2	0.1030 (6)	0.0533 (4)	0.0654 (4)	−0.0134 (3)	0.0309 (4)	−0.0015 (3)
Cl3	0.0515 (4)	0.1027 (6)	0.0773 (5)	−0.0200 (4)	0.0019 (3)	−0.0212 (4)
Cl4	0.0750 (5)	0.0475 (3)	0.0758 (5)	−0.0069 (3)	0.0213 (4)	−0.0027 (3)
N1	0.0468 (11)	0.0451 (10)	0.0340 (9)	−0.0025 (8)	0.0056 (8)	−0.0029 (7)
N2	0.0432 (11)	0.0517 (10)	0.0346 (9)	0.0023 (8)	0.0037 (7)	−0.0030 (8)
O1	0.0591 (12)	0.1096 (17)	0.0431 (9)	−0.0159 (11)	0.0148 (8)	0.0033 (10)
O2	0.0674 (12)	0.0544 (10)	0.0566 (10)	−0.0052 (8)	0.0112 (9)	0.0066 (8)
S1	0.0447 (3)	0.0604 (4)	0.0402 (3)	0.0135 (3)	0.0020 (2)	−0.0095 (2)

Geometric parameters (Å, º) top

C1—C3	1.366 (3)	C10—H10A	0.9700
C1—C8	1.502 (3)	C10—H10B	0.9700
C1—S1	1.717 (2)	C11—N2	1.468 (3)
C2—C4	1.365 (3)	C11—C12	1.490 (4)
C2—C7	1.494 (3)	C11—H11A	0.9700
C2—S1	1.724 (2)	C11—H11B	0.9700
C3—C4	1.440 (3)	C12—Cl1	1.766 (4)
C3—C5	1.497 (3)	C12—H12A	0.9700
C4—C6	1.504 (3)	C12—H12B	0.9700
C5—H5A	0.9600	C13—N1	1.460 (3)
C5—H5B	0.9600	C13—C14	1.498 (3)
C5—H5C	0.9600	C13—H13A	0.9700
C6—H6A	0.9600	C13—H13B	0.9700
C6—H6B	0.9600	C14—Cl4	1.786 (3)
C6—H6C	0.9600	C14—H14A	0.9700
C7—O1	1.231 (3)	C14—H14B	0.9700
C7—N1	1.350 (3)	C15—N1	1.469 (3)
C8—O2	1.227 (3)	C15—C16	1.514 (4)
C8—N2	1.350 (3)	C15—H15A	0.9700
C9—N2	1.465 (3)	C15—H15B	0.9700
C9—C10	1.505 (4)	C16—Cl3	1.777 (3)
C9—H9A	0.9700	C16—H16A	0.9700
C9—H9B	0.9700	C16—H16B	0.9700
C10—Cl2	1.784 (3)

C3—C1—C8	127.6 (2)	N2—C11—H11A	108.8
C3—C1—S1	112.81 (17)	C12—C11—H11A	108.8
C8—C1—S1	119.44 (16)	N2—C11—H11B	108.8
C4—C2—C7	131.1 (2)	C12—C11—H11B	108.8
C4—C2—S1	112.36 (17)	H11A—C11—H11B	107.7
C7—C2—S1	116.12 (17)	C11—C12—Cl1	112.3 (3)
C1—C3—C4	111.6 (2)	C11—C12—H12A	109.1
C1—C3—C5	124.5 (2)	Cl1—C12—H12A	109.1
C4—C3—C5	123.9 (2)	C11—C12—H12B	109.1
C2—C4—C3	112.1 (2)	Cl1—C12—H12B	109.1
C2—C4—C6	125.2 (2)	H12A—C12—H12B	107.9
C3—C4—C6	122.7 (2)	N1—C13—C14	114.0 (2)
C3—C5—H5A	109.5	N1—C13—H13A	108.7
C3—C5—H5B	109.5	C14—C13—H13A	108.7
H5A—C5—H5B	109.5	N1—C13—H13B	108.7
C3—C5—H5C	109.5	C14—C13—H13B	108.7
H5A—C5—H5C	109.5	H13A—C13—H13B	107.6
H5B—C5—H5C	109.5	C13—C14—Cl4	110.80 (15)
C4—C6—H6A	109.5	C13—C14—H14A	109.5
C4—C6—H6B	109.5	Cl4—C14—H14A	109.5
H6A—C6—H6B	109.5	C13—C14—H14B	109.5
C4—C6—H6C	109.5	Cl4—C14—H14B	109.5
H6A—C6—H6C	109.5	H14A—C14—H14B	108.1
H6B—C6—H6C	109.5	N1—C15—C16	112.64 (19)
O1—C7—N1	121.0 (2)	N1—C15—H15A	109.1
O1—C7—C2	119.5 (2)	C16—C15—H15A	109.1
N1—C7—C2	119.6 (2)	N1—C15—H15B	109.1
O2—C8—N2	122.0 (2)	C16—C15—H15B	109.1
O2—C8—C1	120.3 (2)	H15A—C15—H15B	107.8
N2—C8—C1	117.7 (2)	C15—C16—Cl3	110.22 (18)
N2—C9—C10	110.34 (19)	C15—C16—H16A	109.6
N2—C9—H9A	109.6	Cl3—C16—H16A	109.6
C10—C9—H9A	109.6	C15—C16—H16B	109.6
N2—C9—H9B	109.6	Cl3—C16—H16B	109.6
C10—C9—H9B	109.6	H16A—C16—H16B	108.1
H9A—C9—H9B	108.1	C7—N1—C13	124.28 (19)
C9—C10—Cl2	110.00 (19)	C7—N1—C15	117.58 (19)
C9—C10—H10A	109.7	C13—N1—C15	117.75 (17)
Cl2—C10—H10A	109.7	C8—N2—C9	123.80 (19)
C9—C10—H10B	109.7	C8—N2—C11	118.4 (2)
Cl2—C10—H10B	109.7	C9—N2—C11	117.63 (19)
H10A—C10—H10B	108.2	C1—S1—C2	91.11 (11)
N2—C11—C12	113.7 (2)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C14—H14B···O2ⁱ	0.97	2.45	3.257 (3)	141
C14—H14A···Cl1ⁱⁱ	0.97	2.80	3.632 (3)	145
C6—H6B···O1ⁱⁱⁱ	0.96	2.54	3.474 (3)	166
C5—H5B···O1^iv	0.96	2.54	3.477 (3)	165

Symmetry codes: (i) x, −y+1/2, z−1/2; (ii) x−1, y, z−1; (iii) −x+1, −y, −z+1; (iv) x+1, y, z.

Experimental details

Crystal data
Chemical formula	C₁₆H₂₂Cl₄N₂O₂S
M_r	448.22
Crystal system, space group	Monoclinic, P2₁/c
Temperature (K)	298
a, b, c (Å)	7.9238 (4), 21.1712 (11), 12.6186 (7)
β (°)	99.238 (1)
V (Å³)	2089.39 (19)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	0.68
Crystal size (mm)	0.25 × 0.22 × 0.20

Data collection
Diffractometer	Bruker APEXII area-detector diffractometer
Absorption correction	Multi-scan (SADABS; Sheldrick, 1996)
T_min, T_max	0.849, 0.876
No. of measured, independent and observed [I > 2σ(I)] reflections	13412, 4008, 3342
R_int	0.018
(sin θ/λ)_max (Å⁻¹)	0.617

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.042, 0.126, 1.04
No. of reflections	4008
No. of parameters	228
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.88, −0.63

Computer programs: , SAINT (Bruker, 2004), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), SHELXLTL (Sheldrick, 2008), APEX2 (Bruker, 2004) and publCIF (Westrip, 2009).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C14—H14B···O2ⁱ	0.97	2.45	3.257 (3)	140.5
C14—H14A···Cl1ⁱⁱ	0.97	2.80	3.632 (3)	144.6
C6—H6B···O1ⁱⁱⁱ	0.96	2.54	3.474 (3)	165.5
C5—H5B···O1^iv	0.96	2.54	3.477 (3)	165.1

Symmetry codes: (i) x, −y+1/2, z−1/2; (ii) x−1, y, z−1; (iii) −x+1, −y, −z+1; (iv) x+1, y, z.

Acknowledgements

The authors thank the Southwest University (grant Nos. SWUB2006018, XSGX0602 and SWUF2007023) and the Natural Science Foundation of Chongqing (grant Nos. 2007BB5369, 2006BB4341) for financial support.

References

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