Ethyl 2-amino-6-benzyl-4,5,6,7-tetra­hydro­thieno[2,3-c]pyridine-3-carboxyl­ate

Meng, S.-M.; Wang, K.-W.; Xie, H.; Fan, Y.-Q.; Guo, Y.

doi:10.1107/S1600536810051986

organic compounds

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ISSN: 2056-9890

Volume 67| Part 1| January 2011| Page o226

https://doi.org/10.1107/S1600536810051986

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Ethyl 2-amino-6-benzyl-4,5,6,7-tetrahydrothieno[2,3-c]pyridine-3-carboxylate

Shuang-Ming Meng,^a Ke-Wei Wang,^a Hai Xie,^a Yue-Qin Fan ^a and Yong Guo ^a ^*

^aCollege of Chemistry and Chemical Engineering, Shanxi Datong University, Datong 037009, People's Republic of China
^*Correspondence e-mail: ybsymsm@126.com

(Received 7 December 2010; accepted 11 December 2010; online 24 December 2010)

In the title compound, C₁₇H₂₀N₂O₂S, the tetrahydropyridine ring adopts an envelope conformation with the N atom at the flap position; the phenyl ring makes a dihedral angle of 81.06 (10)° with the thiophene ring. The amino group links with the carbonyl O atom via intramolecular N—H⋯O hydrogen bonding, forming a six-membered ring. In the crystal, intermolecular N—H⋯O hydrogen bonds link the molecules into infinite chains running along the b axis.

Related literature

For the biological activity of thiophene and its derivatives, see: Kidwai & Mishra (2003 ); Amr et al. (2006 ); Sherif (1996 ).

Experimental

Crystal data

C₁₇H₂₀N₂O₂S
M_r = 316.41
Monoclinic, P 2₁ /n
a = 12.197 (3) Å
b = 9.936 (3) Å
c = 13.775 (4) Å
β = 103.430 (4)°
V = 1623.8 (8) Å³
Z = 4
Mo Kα radiation
μ = 0.21 mm⁻¹
T = 293 K
0.25 × 0.19 × 0.14 mm

Data collection

Bruker SMART APEX CCD diffractometer
Absorption correction: multi-scan (SADABS; Bruker, 1999 ) T_min = 0.953, T_max = 0.977
8867 measured reflections
2875 independent reflections
2122 reflections with I > 2σ(I)
R_int = 0.030

Refinement

R[F² > 2σ(F²)] = 0.042
wR(F²) = 0.107
S = 1.04
2875 reflections
205 parameters
3 restraints
H atoms treated by a mixture of independent and constrained refinement
Δρ_max = 0.20 e Å⁻³
Δρ_min = −0.17 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N2—H1N⋯O1ⁱ	0.81 (2)	2.17 (2)	2.972 (2)	171 (2)
N2—H2N⋯O1	0.81 (1)	2.17 (2)	2.777 (2)	132 (2)
Symmetry code: (i) $[-x+{\script{3\over 2}}, y+{\script{1\over 2}}, -z+{\script{3\over 2}}]$ .

Data collection: SMART (Bruker, 1999); cell refinement: SAINT (Bruker, 1999); data reduction: SAINT; program(s) used to solve structure: SHELXTL (Sheldrick, 2008); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.

Supporting information

Crystal structure: contains datablocks global, I. DOI: https://doi.org/10.1107/S1600536810051986/xu5117sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S1600536810051986/xu5117Isup2.hkl

checkCIF report

Comment top

As part of an investigation of the thiophene and it's derivatives systems due to their diverse biological activities (Kidwai et al., 2003; Amr et al., 2006; Sherif et al., 1996), we present here the crystal structure of the title compound, (I).

In the crystal structure of title compound (Fig.1), all bond lengths and bond angles have standard dimensions.

The fragments (C8 to C12) of piperidine nearly planar (mean deviation from plane within 0.0632 (1) Å) while the the six-membered piperidine ring exhibits half-chair conformation. The amino group are hydrogen bonded to the carbonyl O atom of another molecule (Table 1), forming a one-dimensional supramolecular structure (Fig. 2). In addition, there are intramolecular N—H···O hydrogen-bonding interactions in the crystal.

Related literature top

For the biological activity of thiophene and its derivatives, see: Kidwai & Mishra (2003); Amr et al. (2006); Sherif (1996).

Experimental top

To the solution containing the ethyl 2-cyanoacetate (10 mmol, 1.06 ml), 1-benzylpiperidin-4-one (10 mmol, 1.80 ml) and powdered sulfur (12 mmol, 0.38 g) in DMF (6 ml), was under stirring triethylamine (1.20 ml) dropwise added. When the reaction was finished (TLC monitoring) the mixture was filtered with charcoal and poured into crushed ice. The formed crystals were filtered off and washed with water. The products were crystallized from ethanol.

Structure description top

In the crystal structure of title compound (Fig.1), all bond lengths and bond angles have standard dimensions.

For the biological activity of thiophene and its derivatives, see: Kidwai & Mishra (2003); Amr et al. (2006); Sherif (1996).

Computing details top

Data collection: SMART (Bruker, 1999); cell refinement: SAINT (Bruker, 1999); data reduction: SAINT (Bruker, 1999); program(s) used to solve structure: SHELXTL (Sheldrick, 2008); program(s) used to refine structure: SHELXTL (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures top

	Fig. 1. Molecular structure of the title compound. Displacement ellipsoids are drawn at the 30% probabilitylevel.
	Fig. 2. View of the one-dimensional supra-molecular chain of the title compound formed by hydrogen bonding (dashed lines). H atoms of C omitted for clarity.

Ethyl 2-amino-6-benzyl-4,5,6,7-tetrahydrothieno[2,3-c]pyridine-3-carboxylate top

Crystal data top

C₁₇H₂₀N₂O₂S	F(000) = 672
M_r = 316.41	D_x = 1.294 Mg m⁻³
Monoclinic, P2₁/n	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yn	Cell parameters from 2875 reflections
a = 12.197 (3) Å	θ = 2.2–25.1°
b = 9.936 (3) Å	µ = 0.21 mm⁻¹
c = 13.775 (4) Å	T = 293 K
β = 103.430 (4)°	Block, yellow
V = 1623.8 (8) Å³	0.25 × 0.19 × 0.14 mm
Z = 4

Data collection top

Bruker SMART APEX CCD diffractometer	2875 independent reflections
Radiation source: fine-focus sealed tube	2122 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.030
ω scans	θ_max = 25.1°, θ_min = 2.0°
Absorption correction: multi-scan (SADABS; Bruker, 1999)	h = −14→14
T_min = 0.953, T_max = 0.977	k = −10→11
8867 measured reflections	l = −16→14

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) = 0.107	H atoms treated by a mixture of independent and constrained refinement
S = 1.04	w = 1/[σ²(F_o²) + (0.0533P)² + 0.2035P] where P = (F_o² + 2F_c²)/3
2875 reflections	(Δ/σ)_max < 0.001
205 parameters	Δρ_max = 0.20 e Å⁻³
3 restraints	Δρ_min = −0.17 e Å⁻³

Crystal data top

C₁₇H₂₀N₂O₂S	V = 1623.8 (8) Å³
M_r = 316.41	Z = 4
Monoclinic, P2₁/n	Mo Kα radiation
a = 12.197 (3) Å	µ = 0.21 mm⁻¹
b = 9.936 (3) Å	T = 293 K
c = 13.775 (4) Å	0.25 × 0.19 × 0.14 mm
β = 103.430 (4)°

Data collection top

Bruker SMART APEX CCD diffractometer	2875 independent reflections
Absorption correction: multi-scan (SADABS; Bruker, 1999)	2122 reflections with I > 2σ(I)
T_min = 0.953, T_max = 0.977	R_int = 0.030
8867 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.042	3 restraints
wR(F²) = 0.107	H atoms treated by a mixture of independent and constrained refinement
S = 1.04	Δρ_max = 0.20 e Å⁻³
2875 reflections	Δρ_min = −0.17 e Å⁻³
205 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	0.15299 (16)	0.6448 (2)	0.47716 (17)	0.0480 (5)
H1	0.1593	0.6354	0.4115	0.058*
C2	0.14619 (18)	0.7720 (2)	0.51559 (19)	0.0583 (6)
H2	0.1477	0.8472	0.4757	0.070*
C3	0.13735 (19)	0.7877 (2)	0.6113 (2)	0.0610 (6)
H3	0.1325	0.8734	0.6370	0.073*
C4	0.1356 (2)	0.6766 (3)	0.67014 (19)	0.0630 (6)
H4	0.1300	0.6873	0.7359	0.076*
C5	0.14210 (18)	0.5487 (2)	0.63200 (17)	0.0539 (6)
H5	0.1408	0.4740	0.6724	0.065*
C6	0.15054 (15)	0.5310 (2)	0.53451 (16)	0.0416 (5)
C7	0.15136 (17)	0.3930 (2)	0.48984 (17)	0.0503 (6)
H7A	0.0800	0.3494	0.4889	0.060*
H7B	0.1577	0.4022	0.4212	0.060*
C8	0.23336 (17)	0.17339 (19)	0.49528 (17)	0.0480 (5)
H8A	0.2476	0.1822	0.4292	0.058*
H8B	0.1571	0.1401	0.4878	0.058*
C9	0.31573 (15)	0.07232 (19)	0.55515 (16)	0.0441 (5)
H9A	0.2875	0.0412	0.6115	0.053*
H9B	0.3216	−0.0049	0.5136	0.053*
C10	0.43028 (15)	0.13375 (19)	0.59228 (14)	0.0372 (5)
C11	0.44382 (15)	0.26693 (19)	0.58452 (15)	0.0409 (5)
C12	0.35245 (15)	0.36571 (19)	0.54262 (17)	0.0471 (5)
H12A	0.3633	0.4473	0.5824	0.057*
H12B	0.3552	0.3890	0.4748	0.057*
C13	0.53359 (15)	0.06514 (18)	0.64255 (14)	0.0371 (4)
C14	0.62303 (15)	0.15380 (19)	0.66948 (15)	0.0405 (5)
C15	0.54785 (16)	−0.07575 (19)	0.66775 (14)	0.0400 (5)
C16	0.45439 (19)	−0.28970 (19)	0.65815 (19)	0.0562 (6)
H16A	0.5239	−0.3251	0.6456	0.067*
H16B	0.3921	−0.3307	0.6106	0.067*
C17	0.4472 (2)	−0.3267 (2)	0.7607 (2)	0.0746 (8)
H17A	0.4497	−0.4229	0.7676	0.112*
H17B	0.3777	−0.2935	0.7730	0.112*
H17C	0.5095	−0.2877	0.8080	0.112*
O1	0.63729 (11)	−0.12830 (13)	0.70893 (11)	0.0503 (4)
O2	0.45118 (11)	−0.14512 (13)	0.64303 (12)	0.0540 (4)
S1	0.58197 (4)	0.31782 (5)	0.63602 (5)	0.0502 (2)
N1	0.24303 (12)	0.30618 (15)	0.54336 (13)	0.0417 (4)
N2	0.73186 (14)	0.12651 (18)	0.71338 (16)	0.0544 (5)
H1N	0.7738 (18)	0.1883 (17)	0.7340 (17)	0.065*
H2N	0.7441 (19)	0.0488 (15)	0.7300 (17)	0.065*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
C1	0.0413 (11)	0.0530 (14)	0.0484 (13)	−0.0033 (10)	0.0078 (10)	0.0019 (10)
C2	0.0566 (14)	0.0454 (14)	0.0690 (17)	−0.0080 (11)	0.0066 (12)	0.0068 (12)
C3	0.0595 (15)	0.0463 (14)	0.0756 (19)	−0.0028 (11)	0.0125 (13)	−0.0119 (12)
C4	0.0689 (16)	0.0696 (17)	0.0550 (15)	0.0006 (13)	0.0232 (12)	−0.0077 (13)
C5	0.0573 (14)	0.0506 (14)	0.0553 (15)	0.0017 (11)	0.0157 (11)	0.0094 (11)
C6	0.0290 (10)	0.0431 (12)	0.0510 (13)	0.0035 (8)	0.0058 (9)	0.0013 (10)
C7	0.0397 (11)	0.0476 (13)	0.0586 (14)	0.0062 (10)	0.0012 (10)	−0.0040 (10)
C8	0.0384 (11)	0.0411 (12)	0.0595 (14)	−0.0027 (9)	0.0009 (10)	−0.0071 (10)
C9	0.0378 (11)	0.0329 (11)	0.0592 (14)	−0.0022 (8)	0.0063 (10)	−0.0038 (9)
C10	0.0346 (10)	0.0327 (10)	0.0445 (12)	−0.0012 (8)	0.0100 (9)	−0.0014 (8)
C11	0.0332 (10)	0.0334 (11)	0.0561 (13)	−0.0011 (8)	0.0100 (9)	0.0031 (9)
C12	0.0373 (11)	0.0359 (11)	0.0667 (15)	0.0017 (9)	0.0090 (10)	0.0065 (10)
C13	0.0356 (10)	0.0296 (10)	0.0459 (12)	−0.0007 (8)	0.0090 (9)	−0.0015 (8)
C14	0.0355 (10)	0.0358 (11)	0.0495 (13)	0.0015 (8)	0.0087 (9)	0.0003 (9)
C15	0.0387 (11)	0.0353 (11)	0.0456 (12)	−0.0004 (9)	0.0088 (9)	−0.0041 (9)
C16	0.0553 (14)	0.0261 (11)	0.0791 (18)	−0.0048 (9)	−0.0010 (12)	−0.0014 (10)
C17	0.0791 (18)	0.0546 (15)	0.083 (2)	−0.0141 (13)	0.0051 (15)	0.0115 (14)
O1	0.0399 (8)	0.0375 (8)	0.0689 (10)	0.0062 (6)	0.0032 (7)	0.0037 (7)
O2	0.0413 (8)	0.0291 (8)	0.0841 (11)	−0.0039 (6)	−0.0006 (7)	0.0050 (7)
S1	0.0357 (3)	0.0324 (3)	0.0794 (4)	−0.0055 (2)	0.0068 (3)	0.0047 (3)
N1	0.0319 (8)	0.0328 (9)	0.0576 (11)	0.0020 (7)	0.0048 (8)	−0.0008 (8)
N2	0.0363 (10)	0.0392 (10)	0.0810 (15)	−0.0036 (8)	−0.0002 (9)	0.0014 (10)

Geometric parameters (Å, º) top

C1—C2	1.380 (3)	C10—C11	1.341 (3)
C1—C6	1.383 (3)	C10—C13	1.458 (3)
C1—H1	0.9300	C11—C12	1.497 (3)
C2—C3	1.357 (3)	C11—S1	1.7445 (19)
C2—H2	0.9300	C12—N1	1.462 (2)
C3—C4	1.372 (3)	C12—H12A	0.9700
C3—H3	0.9300	C12—H12B	0.9700
C4—C5	1.384 (3)	C13—C14	1.384 (3)
C4—H4	0.9300	C13—C15	1.443 (3)
C5—C6	1.382 (3)	C14—N2	1.352 (2)
C5—H5	0.9300	C14—S1	1.736 (2)
C6—C7	1.505 (3)	C15—O1	1.224 (2)
C7—N1	1.468 (2)	C15—O2	1.340 (2)
C7—H7A	0.9700	C16—O2	1.451 (2)
C7—H7B	0.9700	C16—C17	1.482 (3)
C8—N1	1.469 (2)	C16—H16A	0.9700
C8—C9	1.521 (3)	C16—H16B	0.9700
C8—H8A	0.9700	C17—H17A	0.9600
C8—H8B	0.9700	C17—H17B	0.9600
C9—C10	1.501 (3)	C17—H17C	0.9600
C9—H9A	0.9700	N2—H1N	0.807 (15)
C9—H9B	0.9700	N2—H2N	0.809 (14)

C2—C1—C6	121.2 (2)	C10—C11—C12	125.70 (17)
C2—C1—H1	119.4	C10—C11—S1	112.26 (14)
C6—C1—H1	119.4	C12—C11—S1	121.95 (14)
C3—C2—C1	120.2 (2)	N1—C12—C11	109.34 (16)
C3—C2—H2	119.9	N1—C12—H12A	109.8
C1—C2—H2	119.9	C11—C12—H12A	109.8
C2—C3—C4	119.8 (2)	N1—C12—H12B	109.8
C2—C3—H3	120.1	C11—C12—H12B	109.8
C4—C3—H3	120.1	H12A—C12—H12B	108.3
C3—C4—C5	120.3 (2)	C14—C13—C15	120.63 (17)
C3—C4—H4	119.9	C14—C13—C10	111.72 (17)
C5—C4—H4	119.9	C15—C13—C10	127.61 (17)
C6—C5—C4	120.6 (2)	N2—C14—C13	128.54 (18)
C6—C5—H5	119.7	N2—C14—S1	119.99 (15)
C4—C5—H5	119.7	C13—C14—S1	111.45 (14)
C5—C6—C1	117.87 (19)	O1—C15—O2	122.38 (18)
C5—C6—C7	121.5 (2)	O1—C15—C13	124.76 (18)
C1—C6—C7	120.6 (2)	O2—C15—C13	112.84 (16)
N1—C7—C6	114.01 (16)	O2—C16—C17	112.14 (19)
N1—C7—H7A	108.8	O2—C16—H16A	109.2
C6—C7—H7A	108.8	C17—C16—H16A	109.2
N1—C7—H7B	108.8	O2—C16—H16B	109.2
C6—C7—H7B	108.8	C17—C16—H16B	109.2
H7A—C7—H7B	107.6	H16A—C16—H16B	107.9
N1—C8—C9	112.02 (16)	C16—C17—H17A	109.5
N1—C8—H8A	109.2	C16—C17—H17B	109.5
C9—C8—H8A	109.2	H17A—C17—H17B	109.5
N1—C8—H8B	109.2	C16—C17—H17C	109.5
C9—C8—H8B	109.2	H17A—C17—H17C	109.5
H8A—C8—H8B	107.9	H17B—C17—H17C	109.5
C10—C9—C8	111.19 (16)	C15—O2—C16	118.70 (15)
C10—C9—H9A	109.4	C14—S1—C11	91.59 (9)
C8—C9—H9A	109.4	C12—N1—C7	110.42 (15)
C10—C9—H9B	109.4	C12—N1—C8	109.76 (16)
C8—C9—H9B	109.4	C7—N1—C8	109.22 (15)
H9A—C9—H9B	108.0	C14—N2—H1N	118.7 (16)
C11—C10—C13	112.98 (16)	C14—N2—H2N	114.6 (16)
C11—C10—C9	119.74 (17)	H1N—N2—H2N	124 (2)
C13—C10—C9	127.21 (17)

C6—C1—C2—C3	0.3 (3)	C9—C10—C13—C15	−0.3 (3)
C1—C2—C3—C4	0.2 (4)	C15—C13—C14—N2	5.0 (3)
C2—C3—C4—C5	−0.4 (4)	C10—C13—C14—N2	−177.1 (2)
C3—C4—C5—C6	0.1 (4)	C15—C13—C14—S1	−176.97 (15)
C4—C5—C6—C1	0.4 (3)	C10—C13—C14—S1	0.9 (2)
C4—C5—C6—C7	−176.62 (19)	C14—C13—C15—O1	−3.6 (3)
C2—C1—C6—C5	−0.6 (3)	C10—C13—C15—O1	178.95 (19)
C2—C1—C6—C7	176.49 (19)	C14—C13—C15—O2	175.16 (18)
C5—C6—C7—N1	−58.6 (3)	C10—C13—C15—O2	−2.3 (3)
C1—C6—C7—N1	124.5 (2)	O1—C15—O2—C16	−5.2 (3)
N1—C8—C9—C10	−43.7 (2)	C13—C15—O2—C16	176.01 (18)
C8—C9—C10—C11	10.4 (3)	C17—C16—O2—C15	86.3 (2)
C8—C9—C10—C13	−172.76 (19)	N2—C14—S1—C11	177.73 (18)
C13—C10—C11—C12	−175.99 (19)	C13—C14—S1—C11	−0.45 (17)
C9—C10—C11—C12	1.2 (3)	C10—C11—S1—C14	−0.11 (17)
C13—C10—C11—S1	0.6 (2)	C12—C11—S1—C14	176.65 (18)
C9—C10—C11—S1	177.86 (15)	C11—C12—N1—C7	−171.98 (17)
C10—C11—C12—N1	19.4 (3)	C11—C12—N1—C8	−51.5 (2)
S1—C11—C12—N1	−156.87 (15)	C6—C7—N1—C12	−61.0 (2)
C11—C10—C13—C14	−1.0 (3)	C6—C7—N1—C8	178.23 (18)
C9—C10—C13—C14	−177.97 (19)	C9—C8—N1—C12	66.7 (2)
C11—C10—C13—C15	176.68 (19)	C9—C8—N1—C7	−172.09 (18)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N2—H1N···O1ⁱ	0.81 (2)	2.17 (2)	2.972 (2)	171 (2)
N2—H2N···O1	0.81 (1)	2.17 (2)	2.777 (2)	132 (2)

Symmetry code: (i) −x+3/2, y+1/2, −z+3/2.

Experimental details

Crystal data
Chemical formula	C₁₇H₂₀N₂O₂S
M_r	316.41
Crystal system, space group	Monoclinic, P2₁/n
Temperature (K)	293
a, b, c (Å)	12.197 (3), 9.936 (3), 13.775 (4)
β (°)	103.430 (4)
V (Å³)	1623.8 (8)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	0.21
Crystal size (mm)	0.25 × 0.19 × 0.14

Data collection
Diffractometer	Bruker SMART APEX CCD
Absorption correction	Multi-scan (SADABS; Bruker, 1999)
T_min, T_max	0.953, 0.977
No. of measured, independent and observed [I > 2σ(I)] reflections	8867, 2875, 2122
R_int	0.030
(sin θ/λ)_max (Å⁻¹)	0.597

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.042, 0.107, 1.04
No. of reflections	2875
No. of parameters	205
No. of restraints	3
H-atom treatment	H atoms treated by a mixture of independent and constrained refinement
Δρ_max, Δρ_min (e Å⁻³)	0.20, −0.17

Computer programs: SMART (Bruker, 1999), SAINT (Bruker, 1999), SHELXTL (Sheldrick, 2008).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N2—H1N···O1ⁱ	0.807 (15)	2.172 (15)	2.972 (2)	171 (2)
N2—H2N···O1	0.809 (14)	2.169 (18)	2.777 (2)	132 (2)

Symmetry code: (i) −x+3/2, y+1/2, −z+3/2.

Acknowledgements

We thank the Natural Science Foundation of Shanxi Province, China (No. 2010011018) for supporting this work.

References

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