1,5-Bis(2-meth­oxy­benzyl­idene)thio­carbonohydrazide methanol monosolvate

Yu, J.; Tang, S.; Zeng, J.; Yan, Z.

doi:10.1107/S1600536813016954

organic compounds

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ISSN: 2056-9890

Volume 69| Part 7| July 2013| Page o1147

https://doi.org/10.1107/S1600536813016954

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1,5-Bis(2-methoxybenzylidene)thiocarbonohydrazide methanol monosolvate

Jianfeng Yu,^a Shiming Tang,^a Jingbin Zeng ^a and Zifeng Yan ^b ^*

^aDepartment of Chemistry, College of Science, China University of Petroleum, Qingdao 266555, People's Republic of China, and ^bSate Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao 266555, People's Republic of China
^*Correspondence e-mail: zfyancat@163.com

(Received 20 May 2013; accepted 19 June 2013; online 22 June 2013)

The title compound, C₁₇H₁₈N₄O₂S·CH₃OH, was synthesized by the condensation reaction of o-methoxybenzaldehyde with thiocarbohydrazide in methanol. The two benzene rings are inclined each to other at 31.7 (1)°. Intermolecular N—H⋯O and bifurcated O—H⋯N(S) hydrogen bonds link two thiocarbonohydrazide and two solvent molecules into a centrosymmetric unit. These units, related by translation along the b axis, are further aggregated into columns through N—H⋯S hydrogen bonds.

Related literature

For biological activities of thiocarbohydrazides, see: Liang (2003 ); Bacchi et al. (2005 ). For the crystal structures of related compounds, see: Fang et al. (2006 ); Feng et al. (2011 ); Zhao (2011 ).

Experimental

Crystal data

C₁₇H₁₈N₄O₂S·CH₄O
M_r = 374.46
Triclinic, $[P \overline 1]$
a = 7.7223 (15) Å
b = 10.232 (2) Å
c = 12.648 (3) Å
α = 85.938 (3)°
β = 80.796 (3)°
γ = 79.550 (3)°
V = 969.3 (3) Å³
Z = 2
Mo Kα radiation
μ = 0.19 mm⁻¹
T = 296 K
0.25 × 0.21 × 0.18 mm

Data collection

Bruker SMART APEX CCD area-detector diffractometer
Absorption correction: multi-scan (SADABS; Bruker, 2007 ) T_min = 0.954, T_max = 0.966
4769 measured reflections
3324 independent reflections
2766 reflections with I > 2σ(I)
R_int = 0.024

Refinement

R[F² > 2σ(F²)] = 0.049
wR(F²) = 0.171
S = 1.01
3324 reflections
240 parameters
H-atom parameters constrained
Δρ_max = 0.20 e Å⁻³
Δρ_min = −0.21 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
O3—H3⋯S1ⁱ	0.82	2.80	3.534 (2)	150
O3—H3⋯N4ⁱ	0.82	2.36	3.028 (3)	139
N3—H3A⋯O3	0.86	2.38	3.126 (3)	145
N1—H1⋯S1ⁱⁱ	0.86	2.57	3.4184 (19)	169
Symmetry codes: (i) -x+1, -y+1, -z; (ii) -x+1, -y+2, -z.

Data collection: SMART (Bruker, 2007); cell refinement: SAINT (Bruker, 2007); 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: SHELXTL.

Supporting information

Crystal structure: contains datablocks I, global. DOI: https://doi.org/10.1107/S1600536813016954/cv5415sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S1600536813016954/cv5415Isup2.hkl

Supporting information file. DOI: https://doi.org/10.1107/S1600536813016954/cv5415Isup3.cml

checkCIF report

Comment top

Schiff bases of thiocarbohydrazide are impotant organic intermediates owing to their biological activities (Liang, 2003; Bacchi et al., 2005). In a continuation of structural study of Schiff bases of thiocarbohydrazide (Fang et al., 2006; Feng et al., 2011; Zhao, 2011), we present here the title compound (I).

In (I) (Fig. 1), the bond lengths and angles are normal and correspond to those observed in 1,5-bis[(1E)-(2-methoxyphenyl)methylene]- thiocarbonohydrazide ethanol solvate (Fang, et al., 2006), N'',N'''-bis(1-phenylethylidene)thiocarbonohydrazide (Feng et al., 2011) and N'',N'''-bis(4-methoxybenzylidene)thiocarbonohydrazide methanol solvate (Zhao, 2011).

In the crystal, the benzene ring C3—C8 and the benzene ring C11—C16 are inclined each to other at 31.7 (1)°. In the crystal, intermolecular N—H···O and bifurcated O—H···N(S) hydrogen bonds (Table 1) link two M and two solvent molecules into centrosymmetric unit. These units related by translation along the b axis are futher aggregated into columns through the N—H···S hydrogen bonds (Table 1).

Related literature top

For biological activities of thiocarbohydrazides, see: Liang (2003); Bacchi et al. (2005). For the crystal structures of related compounds, see: Fang et al. (2006); Feng et al. (2011); Zhao (2011).

Experimental top

A 50 ml flask was charged with a magnetic stir bar, o-methoxybenzaldehyde (1 mmol), thiocarbohydrazide (0.5 mmol) in 20 ml me thanol.After stirring 3 h at 373 K, the resulting mixture was cooled to room temperature, and recrystalized from methanol, and afforded the title compound as a crystalline solid.

Structure description top

For biological activities of thiocarbohydrazides, see: Liang (2003); Bacchi et al. (2005). For the crystal structures of related compounds, see: Fang et al. (2006); Feng et al. (2011); Zhao (2011).

Computing details top

Data collection: SMART (Bruker, 2007); cell refinement: SAINT (Bruker, 2007); data reduction: SAINT (Bruker, 2007); 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: SHELXTL (Sheldrick, 2008).

Figures top

Fig. 1. The molecular structure of (I) showing the atomic numbering and 30% probability displacement ellipsoids.

1,5-Bis(2-methoxybenzylidene)thiocarbonohydrazide methanol monosolvate top

Crystal data top

C₁₇H₁₈N₄O₂S·CH₄O	Z = 2
M_r = 374.46	F(000) = 396
Triclinic, P1	D_x = 1.283 Mg m⁻³
a = 7.7223 (15) Å	Mo Kα radiation, λ = 0.71073 Å
b = 10.232 (2) Å	Cell parameters from 2955 reflections
c = 12.648 (3) Å	θ = 3.0–28.1°
α = 85.938 (3)°	µ = 0.19 mm⁻¹
β = 80.796 (3)°	T = 296 K
γ = 79.550 (3)°	Block, colourless
V = 969.3 (3) Å³	0.25 × 0.21 × 0.18 mm

Data collection top

Bruker SMART APEX CCD area-detector diffractometer	3324 independent reflections
Radiation source: fine-focus sealed tube	2766 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.024
phi and ω scans	θ_max = 25.0°, θ_min = 1.6°
Absorption correction: multi-scan (SADABS; Bruker, 2007)	h = −8→9
T_min = 0.954, T_max = 0.966	k = −9→12
4769 measured reflections	l = −15→13

Refinement top

Refinement on F²	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F² > 2σ(F²)] = 0.049	H-atom parameters constrained
wR(F²) = 0.171	w = 1/[σ²(F_o²) + (0.1P)² + 0.3851P] where P = (F_o² + 2F_c²)/3
S = 1.01	(Δ/σ)_max = 0.010
3324 reflections	Δρ_max = 0.20 e Å⁻³
240 parameters	Δρ_min = −0.21 e Å⁻³
0 restraints	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.038 (7)

Crystal data top

C₁₇H₁₈N₄O₂S·CH₄O	γ = 79.550 (3)°
M_r = 374.46	V = 969.3 (3) Å³
Triclinic, P1	Z = 2
a = 7.7223 (15) Å	Mo Kα radiation
b = 10.232 (2) Å	µ = 0.19 mm⁻¹
c = 12.648 (3) Å	T = 296 K
α = 85.938 (3)°	0.25 × 0.21 × 0.18 mm
β = 80.796 (3)°

Data collection top

Bruker SMART APEX CCD area-detector diffractometer	3324 independent reflections
Absorption correction: multi-scan (SADABS; Bruker, 2007)	2766 reflections with I > 2σ(I)
T_min = 0.954, T_max = 0.966	R_int = 0.024
4769 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.049	0 restraints
wR(F²) = 0.171	H-atom parameters constrained
S = 1.01	Δρ_max = 0.20 e Å⁻³
3324 reflections	Δρ_min = −0.21 e Å⁻³
240 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
N1	0.4120 (3)	0.85311 (18)	0.10378 (15)	0.0503 (5)
H1	0.4497	0.9278	0.0942	0.060*
N2	0.3689 (3)	0.80149 (19)	0.20555 (15)	0.0524 (5)
N3	0.3445 (2)	0.66888 (17)	0.04305 (15)	0.0476 (5)
H3A	0.3322	0.6395	0.1087	0.057*
N4	0.3114 (2)	0.59365 (18)	−0.03557 (15)	0.0480 (5)
O1	0.2688 (4)	1.0468 (2)	0.44226 (17)	0.1014 (9)
O2	0.1142 (3)	0.27193 (17)	0.08315 (18)	0.0739 (6)
S1	0.43309 (9)	0.85466 (6)	−0.10545 (5)	0.0567 (3)
C1	0.3953 (3)	0.7867 (2)	0.01844 (18)	0.0438 (5)
C2	0.3709 (3)	0.8750 (3)	0.28184 (19)	0.0574 (6)
H2	0.3972	0.9601	0.2666	0.069*
C3	0.3324 (4)	0.8276 (3)	0.3932 (2)	0.0644 (7)
C4	0.3466 (6)	0.6932 (3)	0.4199 (3)	0.0963 (11)
H4	0.3800	0.6319	0.3662	0.116*
C5	0.3117 (8)	0.6491 (4)	0.5254 (3)	0.144 (2)
H5	0.3207	0.5585	0.5428	0.173*
C6	0.2634 (8)	0.7397 (5)	0.6049 (3)	0.137 (2)
H6	0.2389	0.7098	0.6760	0.164*
C7	0.2510 (6)	0.8722 (4)	0.5809 (3)	0.1038 (12)
H7	0.2214	0.9324	0.6354	0.125*
C8	0.2826 (4)	0.9174 (3)	0.4751 (2)	0.0720 (7)
C9	0.2107 (7)	1.1424 (4)	0.5220 (3)	0.1161 (15)
H9A	0.0990	1.1274	0.5620	0.174*
H9B	0.1962	1.2301	0.4885	0.174*
H9C	0.2977	1.1346	0.5695	0.174*
C10	0.2413 (3)	0.4934 (2)	0.0006 (2)	0.0487 (5)
H10	0.2192	0.4771	0.0744	0.058*
C11	0.1943 (3)	0.4031 (2)	−0.0700 (2)	0.0543 (6)
C12	0.2091 (4)	0.4269 (3)	−0.1782 (2)	0.0731 (8)
H12	0.2533	0.5019	−0.2087	0.088*
C13	0.1593 (5)	0.3415 (4)	−0.2435 (3)	0.0937 (11)
H13	0.1698	0.3585	−0.3173	0.112*
C14	0.0940 (4)	0.2309 (4)	−0.1973 (3)	0.0958 (12)
H14	0.0581	0.1741	−0.2404	0.115*
C15	0.0809 (4)	0.2032 (3)	−0.0901 (3)	0.0804 (9)
H15	0.0392	0.1268	−0.0607	0.097*
C16	0.1297 (3)	0.2888 (2)	−0.0246 (3)	0.0600 (7)
C17	0.0616 (5)	0.1520 (3)	0.1332 (4)	0.0952 (11)
H17A	−0.0618	0.1534	0.1290	0.143*
H17B	0.0787	0.1458	0.2070	0.143*
H17C	0.1326	0.0766	0.0970	0.143*
O3	0.3985 (3)	0.4521 (2)	0.22744 (16)	0.0803 (6)
H3	0.4610	0.4009	0.1842	0.121*
C18	0.2837 (6)	0.3838 (4)	0.2970 (3)	0.1132 (14)
H18A	0.3517	0.3184	0.3393	0.170*
H18B	0.2173	0.3406	0.2563	0.170*
H18C	0.2031	0.4454	0.3434	0.170*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
N1	0.0627 (11)	0.0401 (10)	0.0515 (11)	−0.0201 (8)	−0.0034 (8)	−0.0085 (8)
N2	0.0588 (11)	0.0468 (10)	0.0529 (11)	−0.0149 (9)	−0.0028 (8)	−0.0086 (9)
N3	0.0554 (10)	0.0389 (9)	0.0514 (10)	−0.0155 (8)	−0.0049 (8)	−0.0098 (8)
N4	0.0496 (10)	0.0398 (9)	0.0569 (11)	−0.0113 (8)	−0.0059 (8)	−0.0129 (8)
O1	0.172 (2)	0.0723 (14)	0.0597 (12)	−0.0446 (15)	0.0175 (13)	−0.0220 (10)
O2	0.0782 (12)	0.0486 (10)	0.1034 (16)	−0.0266 (9)	−0.0268 (11)	0.0098 (10)
S1	0.0740 (4)	0.0492 (4)	0.0532 (4)	−0.0275 (3)	−0.0076 (3)	−0.0062 (3)
C1	0.0403 (10)	0.0361 (10)	0.0555 (12)	−0.0073 (8)	−0.0049 (9)	−0.0098 (9)
C2	0.0680 (14)	0.0541 (13)	0.0526 (13)	−0.0203 (11)	−0.0022 (11)	−0.0106 (11)
C3	0.0760 (16)	0.0634 (16)	0.0527 (14)	−0.0142 (13)	−0.0024 (12)	−0.0053 (12)
C4	0.140 (3)	0.0634 (18)	0.0710 (19)	−0.0009 (19)	0.0064 (19)	−0.0020 (15)
C5	0.235 (6)	0.077 (2)	0.085 (3)	0.015 (3)	0.022 (3)	0.022 (2)
C6	0.212 (5)	0.102 (3)	0.066 (2)	0.021 (3)	0.007 (3)	0.017 (2)
C7	0.146 (3)	0.101 (3)	0.0549 (17)	−0.007 (2)	−0.0002 (19)	−0.0093 (17)
C8	0.0876 (19)	0.0748 (18)	0.0527 (14)	−0.0158 (15)	−0.0034 (13)	−0.0082 (13)
C9	0.188 (4)	0.087 (2)	0.074 (2)	−0.047 (3)	0.019 (2)	−0.0335 (19)
C10	0.0453 (11)	0.0381 (11)	0.0653 (14)	−0.0105 (9)	−0.0103 (10)	−0.0080 (10)
C11	0.0439 (11)	0.0452 (12)	0.0758 (16)	−0.0115 (9)	−0.0040 (10)	−0.0185 (11)
C12	0.0740 (17)	0.0731 (18)	0.0786 (19)	−0.0300 (14)	−0.0008 (14)	−0.0262 (15)
C13	0.098 (2)	0.109 (3)	0.083 (2)	−0.042 (2)	0.0038 (17)	−0.044 (2)
C14	0.085 (2)	0.095 (2)	0.118 (3)	−0.0436 (19)	0.0095 (19)	−0.062 (2)
C15	0.0646 (16)	0.0599 (16)	0.122 (3)	−0.0255 (13)	0.0028 (16)	−0.0369 (17)
C16	0.0412 (11)	0.0383 (12)	0.102 (2)	−0.0056 (9)	−0.0084 (12)	−0.0193 (12)
C17	0.082 (2)	0.0633 (18)	0.148 (3)	−0.0364 (16)	−0.026 (2)	0.026 (2)
O3	0.1011 (15)	0.0707 (13)	0.0658 (12)	−0.0183 (11)	0.0032 (10)	−0.0064 (10)
C18	0.152 (4)	0.103 (3)	0.084 (2)	−0.050 (3)	0.014 (2)	0.000 (2)

Geometric parameters (Å, º) top

N1—C1	1.351 (3)	C7—H7	0.9300
N1—N2	1.370 (3)	C9—H9A	0.9600
N1—H1	0.8600	C9—H9B	0.9600
N2—C2	1.268 (3)	C9—H9C	0.9600
N3—C1	1.335 (3)	C10—C11	1.458 (3)
N3—N4	1.381 (2)	C10—H10	0.9300
N3—H3A	0.8600	C11—C12	1.363 (4)
N4—C10	1.269 (3)	C11—C16	1.404 (3)
O1—C8	1.350 (4)	C12—C13	1.386 (4)
O1—C9	1.419 (4)	C12—H12	0.9300
O2—C16	1.350 (4)	C13—C14	1.377 (5)
O2—C17	1.435 (3)	C13—H13	0.9300
S1—C1	1.672 (2)	C14—C15	1.356 (5)
C2—C3	1.459 (4)	C14—H14	0.9300
C2—H2	0.9300	C15—C16	1.385 (4)
C3—C4	1.382 (4)	C15—H15	0.9300
C3—C8	1.395 (4)	C17—H17A	0.9600
C4—C5	1.379 (5)	C17—H17B	0.9600
C4—H4	0.9300	C17—H17C	0.9600
C5—C6	1.378 (6)	O3—C18	1.391 (4)
C5—H5	0.9300	O3—H3	0.8200
C6—C7	1.358 (6)	C18—H18A	0.9600
C6—H6	0.9300	C18—H18B	0.9600
C7—C8	1.383 (4)	C18—H18C	0.9600

C1—N1—N2	119.98 (18)	O1—C9—H9C	109.5
C1—N1—H1	120.0	H9A—C9—H9C	109.5
N2—N1—H1	120.0	H9B—C9—H9C	109.5
C2—N2—N1	116.55 (19)	N4—C10—C11	122.0 (2)
C1—N3—N4	120.89 (19)	N4—C10—H10	119.0
C1—N3—H3A	119.6	C11—C10—H10	119.0
N4—N3—H3A	119.6	C12—C11—C16	119.1 (2)
C10—N4—N3	113.93 (19)	C12—C11—C10	122.2 (2)
C8—O1—C9	117.2 (3)	C16—C11—C10	118.7 (2)
C16—O2—C17	118.8 (3)	C11—C12—C13	121.2 (3)
N3—C1—N1	114.5 (2)	C11—C12—H12	119.4
N3—C1—S1	125.35 (17)	C13—C12—H12	119.4
N1—C1—S1	120.10 (16)	C14—C13—C12	118.8 (4)
N2—C2—C3	120.8 (2)	C14—C13—H13	120.6
N2—C2—H2	119.6	C12—C13—H13	120.6
C3—C2—H2	119.6	C15—C14—C13	121.4 (3)
C4—C3—C8	118.6 (3)	C15—C14—H14	119.3
C4—C3—C2	120.9 (3)	C13—C14—H14	119.3
C8—C3—C2	120.5 (2)	C14—C15—C16	119.9 (3)
C5—C4—C3	120.5 (3)	C14—C15—H15	120.0
C5—C4—H4	119.7	C16—C15—H15	120.0
C3—C4—H4	119.7	O2—C16—C15	123.9 (3)
C6—C5—C4	119.7 (4)	O2—C16—C11	116.5 (2)
C6—C5—H5	120.1	C15—C16—C11	119.5 (3)
C4—C5—H5	120.1	O2—C17—H17A	109.5
C7—C6—C5	120.8 (4)	O2—C17—H17B	109.5
C7—C6—H6	119.6	H17A—C17—H17B	109.5
C5—C6—H6	119.6	O2—C17—H17C	109.5
C6—C7—C8	119.8 (3)	H17A—C17—H17C	109.5
C6—C7—H7	120.1	H17B—C17—H17C	109.5
C8—C7—H7	120.1	C18—O3—H3	109.5
O1—C8—C7	124.6 (3)	O3—C18—H18A	109.5
O1—C8—C3	115.0 (2)	O3—C18—H18B	109.5
C7—C8—C3	120.4 (3)	H18A—C18—H18B	109.5
O1—C9—H9A	109.5	O3—C18—H18C	109.5
O1—C9—H9B	109.5	H18A—C18—H18C	109.5
H9A—C9—H9B	109.5	H18B—C18—H18C	109.5

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
O3—H3···S1ⁱ	0.82	2.80	3.534 (2)	150
O3—H3···N4ⁱ	0.82	2.36	3.028 (3)	139
N3—H3A···O3	0.86	2.38	3.126 (3)	145
N1—H1···S1ⁱⁱ	0.86	2.57	3.4184 (19)	169
N3—H3A···N2	0.86	2.21	2.591 (3)	106

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

Experimental details

Crystal data
Chemical formula	C₁₇H₁₈N₄O₂S·CH₄O
M_r	374.46
Crystal system, space group	Triclinic, P1
Temperature (K)	296
a, b, c (Å)	7.7223 (15), 10.232 (2), 12.648 (3)
α, β, γ (°)	85.938 (3), 80.796 (3), 79.550 (3)
V (Å³)	969.3 (3)
Z	2
Radiation type	Mo Kα
µ (mm⁻¹)	0.19
Crystal size (mm)	0.25 × 0.21 × 0.18

Data collection
Diffractometer	Bruker SMART APEX CCD area-detector
Absorption correction	Multi-scan (SADABS; Bruker, 2007)
T_min, T_max	0.954, 0.966
No. of measured, independent and observed [I > 2σ(I)] reflections	4769, 3324, 2766
R_int	0.024
(sin θ/λ)_max (Å⁻¹)	0.596

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.049, 0.171, 1.01
No. of reflections	3324
No. of parameters	240
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.20, −0.21

Computer programs: SMART (Bruker, 2007), SAINT (Bruker, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), SHELXTL (Sheldrick, 2008).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
O3—H3···S1ⁱ	0.82	2.80	3.534 (2)	150.4
O3—H3···N4ⁱ	0.82	2.36	3.028 (3)	138.6
N3—H3A···O3	0.86	2.38	3.126 (3)	145.2
N1—H1···S1ⁱⁱ	0.86	2.57	3.4184 (19)	168.7
N3—H3A···N2	0.86	2.21	2.591 (3)	106.4

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

Acknowledgements

The authors gratefully acknowledge the financial support of the Fundamental Research Funds for the Central Universities (grant No. 12CX04091A).

References

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