(E)-1-(4-Amino­phen­yl)-3-(pyridin-3-yl)prop-2-en-1-one

Chantrapromma, S.; Kobkeatthawin, T.; Chanawanno, K.; Wisitsak, P.; Fun, H.-K.

doi:10.1107/S1600536811023634

organic compounds

CRYSTALLOGRAPHIC
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ISSN: 2056-9890

Volume 67| Part 7| July 2011| Pages o1770-o1771

doi:10.1107/S1600536811023634

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(E)-1-(4-Aminophenyl)-3-(pyridin-3-yl)prop-2-en-1-one

Suchada Chantrapromma,^a ^*‡ Thawanrat Kobkeatthawin,^a Kullapa Chanawanno,^a Pitikan Wisitsak ^b and Hoong-Kun Fun ^c §

^aCrystal Materials Research Unit, Department of Chemistry, Faculty of Science, Prince of Songkla University, Hat-Yai, Songkhla 90112, Thailand, ^bExcellence Center, Mae Fah Luang University, Thasud, Muang, Chaing Rai 57100, Thailand, and ^cX-ray Crystallography Unit, School of Physics, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
^*Correspondence e-mail: suchada.c@psu.ac.th

(Received 13 June 2011; accepted 16 June 2011; online 22 June 2011)

The title chalcone derivative, C₁₄H₁₂N₂O, consists of 4-aminophenyl and pyridine rings bridged by a prop-2-en-1-one unit and exists in a trans configuration with respect to the C=C double bond. The molecule is slightly twisted with a dihedral angle of 29.38 (7)° between the benzene and pyridine rings. The prop-2-en-1-one bridge is nearly planar with an r.m.s. deviation of 0.0384 (1) Å and makes dihedral angles of 15.40 (9) and 16.30 (9)°, respectively, with the benzene and pyridine rings. In the crystal, molecules are linked by N—H⋯N and N—H⋯O hydrogen bonds into a layer parallel to the ab plane. A π–π interaction with a centroid–centroid distance of 3.6946 (10) Å is also observed.

Related literature

For bond-length data, see: Allen et al. (1987 ). For a related structure, see: Horkaew et al. (2010 ). For background to and applications of chalcones, see: Gaber et al. (2008 ); Ávila et al. (2008 ); Mei et al. (2001 ); Ohad et al. (2004 ); Patil et al. (2007 ); Svetlichny et al. (2007 ); Tewtrakul et al. (2003 ); Wu et al. (2006 ); Xu et al. (2005 ). For the stability of the temperature controller used in the data collection, see Cosier & Glazer (1986 ).

Experimental

Crystal data

C₁₄H₁₂N₂O
M_r = 224.26
Orthorhombic, P b c a
a = 12.0046 (12) Å
b = 7.9329 (9) Å
c = 22.925 (3) Å
V = 2183.2 (4) Å³
Z = 8
Mo Kα radiation
μ = 0.09 mm⁻¹
T = 100 K
0.52 × 0.32 × 0.18 mm

Data collection

Bruker APEX DUO CCD area-detector diffractometer
Absorption correction: multi-scan (SADABS; Bruker, 2009 ) T_min = 0.956, T_max = 0.985
12726 measured reflections
3177 independent reflections
2433 reflections with I > 2σ(I)
R_int = 0.043

Refinement

R[F² > 2σ(F²)] = 0.048
wR(F²) = 0.132
S = 1.03
3177 reflections
202 parameters
All H-atom parameters refined
Δρ_max = 0.37 e Å⁻³
Δρ_min = −0.18 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N1—H1N1⋯O1ⁱ	0.88 (2)	2.13 (2)	2.9920 (16)	170 (2)
N1—H2N1⋯N2ⁱⁱ	0.93 (2)	2.26 (2)	3.1471 (17)	161.7 (19)
Symmetry codes: (i) $[-x+2, y-{\script{1\over 2}}, -z+{\script{3\over 2}}]$ ; (ii) $[-x+1, y-{\script{1\over 2}}, -z+{\script{3\over 2}}]$ .

Data collection: APEX2 (Bruker, 2009); cell refinement: SAINT (Bruker, 2009); 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 and PLATON (Spek, 2009 ).

Supporting information

Crystal structure: contains datablocks global, I. DOI: 10.1107/S1600536811023634/is2731sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536811023634/is2731Isup2.hkl

Supporting information file. DOI: 10.1107/S1600536811023634/is2731Isup3.cml

checkCIF report

Comment top

Chalcones are 1,3-diaryl-2-propen-1-ones which can be obtained from both synthetic and natural sources. They have a wide variety of biological activities such as antimalarial (Mei et al., 2001), HIV-1 protease inhibitory (Tewtrakul et al., 2003), antityrosinase (Ohad et al., 2004), antibacterial (Ávila et al., 2008) and antiplasmodial (Wu et al., 2006) properties. Moreover, chalcones have also been studied for non-linear optical (NLO) (Patil et al., 2007) and fluorescent materials (Gaber et al., 2008). These compounds have also been used for sensor, liquid crystal display and fluorescence probe for sensing of DNA or proteins (Svetlichny et al., 2007; Xu et al., 2005). These interesting properties has lead us to synthesize the title compound (I), which contains the amino and pyridine groups in order to study its bioactivity and fluorescent properties. Our results show that (I) was inactive for antibacterial and tyrosinase inhibitory activities. However (I) exhibits weak fluorescence with the maximum emission at 437 nm when was excited at 310 nm. Herein the crystal structure of (I) is reported.

The molecule of the title chalcone derivative (Fig. 1), C₁₄H₁₂N₂O, exists in a E configuration with respect to the C8═C9 ethenyl bond [1.332 (2) Å] and the torsion angle C7–C8–C9–C10 = -176.57 (13)°. The molecule is twisted with a dihedral angle between the phenyl and pyridine rings being 29.38 (7)°. The prop-2-en-1-one unit (C7-C9/O1) is nearly planar [r.m.s. of 0.0384 (1) Å] and the torsion angle O1–C7–C8–C9 being -12.5 (2)°. This middle bridge makes the dihedral angles of 15.40 (9) and 16.30 (9)° with the phenyl and pyridine rings, respectively. The bond distances are of normal values (Allen et al., 1987) and are comparable with the related structure (Horkaew et al., 2010).

In the crystal packing, the molecules are linked by N—H···N and N—H···O hydrogen bonds (Table 1) into sheets parallel to the ab plane (Fig. 2). A π–π interaction with a Cg1···Cg1 distance of 3.6946 (10) Å is observed in the crystal; Cg1 is the centroid of the C10–C14/N1 ring. In addition C···C [3.3505 (19) Å; symmetry code 3/2-x, 1/2+y, z and 3.3776 (19) Å: symmetry code 3/2-x, -1/2+y, z], C···O [3.1312 (18) Å; symmetry code 3/2-x, -1/2+y, z] and N···O [2.9920 (16) Å; symmetry code 2-x,1/2+y,3/2-z] short contacts are also observed.

Related literature top

For bond-length data, see: Allen et al. (1987). For a related structure, see: Horkaew et al. (2010). For background to and applications of chalcones, see: Gaber et al. (2008); Ávila et al. (2008); Mei et al. (2001); Ohad et al. (2004); Patil et al. (2007); Svetlichny et al. (2007); Tewtrakul et al. (2003); Wu et al. (2006); Xu et al. (2005). For the stability of the temperature controller used in the data collection, see Cosier & Glazer (1986).

Experimental top

The title compound was synthesized by condensation of 4-aminoacetophenone (0.40 g, 3 mmol) with 3-pyridinecarboxaldehyde (0.18 ml, 3 mmol) in ethanol (15 ml) in the presence of 10% NaOH (aq) (5 ml). After stirring for 2 hr at room temperature, the resulting yellow solid was collected by filtration, washed with distilled diethyl ether, dried and purified by repeated recrysallization from acetone. Yellow block-shaped single crystals of the title compound suitable for x-ray structure determination were recrystalized from methanol by the slow evaporation of the solvent at room temperature after several days, Mp. 453-454 K.

Computing details top

Data collection: APEX2 (Bruker, 2009); cell refinement: SAINT (Bruker, 2009); data reduction: SAINT (Bruker, 2009); 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) and PLATON (Spek, 2009).

Figures top

	Fig. 1. The molecular structure of the title compound, showing 50% probability displacement ellipsoids and the atom-numbering scheme.
	Fig. 2. The crystal packing of the title compound viewed along the b axis, Hydrogen bonds were shown as dashed lines.

(E)-1-(4-Aminophenyl)-3-(pyridin-3-yl)prop-2-en-1-one top

Crystal data top

C₁₄H₁₂N₂O	D_x = 1.365 Mg m⁻³
M_r = 224.26	Melting point = 453–454 K
Orthorhombic, Pbca	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ac 2ab	Cell parameters from 3177 reflections
a = 12.0046 (12) Å	θ = 2.5–30.0°
b = 7.9329 (9) Å	µ = 0.09 mm⁻¹
c = 22.925 (3) Å	T = 100 K
V = 2183.2 (4) Å³	Block, yellow
Z = 8	0.52 × 0.32 × 0.18 mm
F(000) = 944

Data collection top

Bruker APEX DUO CCD area-detector diffractometer	3177 independent reflections
Radiation source: sealed tube	2433 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.043
ϕ and ω scans	θ_max = 30.0°, θ_min = 2.5°
Absorption correction: multi-scan (SADABS; Bruker, 2009)	h = −16→14
T_min = 0.956, T_max = 0.985	k = −11→10
12726 measured reflections	l = −32→23

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)] = 0.048	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.132	All H-atom parameters refined
S = 1.03	w = 1/[σ²(F_o²) + (0.0702P)² + 0.5761P] where P = (F_o² + 2F_c²)/3
3177 reflections	(Δ/σ)_max = 0.001
202 parameters	Δρ_max = 0.37 e Å⁻³
0 restraints	Δρ_min = −0.18 e Å⁻³

Crystal data top

C₁₄H₁₂N₂O	V = 2183.2 (4) Å³
M_r = 224.26	Z = 8
Orthorhombic, Pbca	Mo Kα radiation
a = 12.0046 (12) Å	µ = 0.09 mm⁻¹
b = 7.9329 (9) Å	T = 100 K
c = 22.925 (3) Å	0.52 × 0.32 × 0.18 mm

Data collection top

Bruker APEX DUO CCD area-detector diffractometer	3177 independent reflections
Absorption correction: multi-scan (SADABS; Bruker, 2009)	2433 reflections with I > 2σ(I)
T_min = 0.956, T_max = 0.985	R_int = 0.043
12726 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.048	0 restraints
wR(F²) = 0.132	All H-atom parameters refined
S = 1.03	Δρ_max = 0.37 e Å⁻³
3177 reflections	Δρ_min = −0.18 e Å⁻³
202 parameters

Special details top

Experimental. The crystal was placed in the cold stream of an Oxford Cryosystems Cobra open-flow nitrogen cryostat (Cosier & Glazer, 1986) operating at 100.0 (1) K.

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds 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 > 2sigma(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
O1	0.87481 (8)	−0.00829 (13)	0.62116 (4)	0.0274 (2)
N1	0.88749 (10)	−0.40307 (16)	0.86417 (5)	0.0262 (3)
H1N1	0.9537 (17)	−0.447 (3)	0.8695 (9)	0.037 (5)*
H2N1	0.8278 (17)	−0.431 (3)	0.8878 (9)	0.043 (5)*
N2	0.34284 (10)	0.06758 (18)	0.57106 (5)	0.0317 (3)
C1	0.82037 (9)	−0.14511 (16)	0.70829 (6)	0.0195 (3)
C2	0.92774 (10)	−0.20798 (16)	0.72041 (6)	0.0210 (3)
H2A	0.9864 (14)	−0.193 (2)	0.6922 (7)	0.023 (4)*
C3	0.95058 (10)	−0.29288 (16)	0.77139 (6)	0.0214 (3)
H3A	1.0254 (14)	−0.340 (2)	0.7786 (7)	0.029 (4)*
C4	0.86642 (10)	−0.31820 (17)	0.81357 (6)	0.0208 (3)
C5	0.75956 (10)	−0.25227 (18)	0.80220 (6)	0.0234 (3)
H5A	0.7024 (17)	−0.265 (3)	0.8321 (9)	0.045 (5)*
C6	0.73797 (10)	−0.16943 (17)	0.75074 (6)	0.0214 (3)
H6A	0.6624 (14)	−0.121 (2)	0.7442 (7)	0.025 (4)*
C7	0.79831 (10)	−0.05897 (16)	0.65285 (6)	0.0205 (3)
C8	0.68037 (10)	−0.03488 (18)	0.63425 (6)	0.0226 (3)
H8A	0.6213 (16)	−0.097 (3)	0.6564 (9)	0.042 (5)*
C9	0.65435 (10)	0.06655 (17)	0.58997 (6)	0.0232 (3)
H9A	0.7163 (14)	0.126 (2)	0.5705 (7)	0.031 (4)*
C10	0.54235 (10)	0.10884 (17)	0.56899 (6)	0.0219 (3)
C11	0.52786 (11)	0.2397 (2)	0.52922 (6)	0.0284 (3)
H11A	0.5968 (15)	0.303 (2)	0.5147 (8)	0.030 (4)*
C12	0.42183 (12)	0.2841 (2)	0.51084 (7)	0.0313 (3)
H12A	0.4105 (16)	0.374 (3)	0.4827 (9)	0.040 (5)*
C13	0.33284 (12)	0.1966 (2)	0.53375 (7)	0.0313 (3)
H13A	0.2553 (16)	0.229 (2)	0.5245 (8)	0.041 (5)*
C14	0.44619 (11)	0.0255 (2)	0.58784 (6)	0.0267 (3)
H14A	0.4500 (15)	−0.070 (3)	0.6168 (8)	0.034 (5)*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O1	0.0178 (4)	0.0354 (6)	0.0292 (5)	−0.0004 (4)	0.0009 (4)	0.0037 (4)
N1	0.0177 (5)	0.0342 (7)	0.0267 (6)	0.0028 (4)	−0.0018 (4)	0.0020 (5)
N2	0.0186 (5)	0.0466 (8)	0.0299 (6)	−0.0020 (5)	−0.0015 (5)	0.0051 (5)
C1	0.0148 (5)	0.0193 (6)	0.0245 (6)	0.0002 (4)	−0.0024 (4)	−0.0034 (5)
C2	0.0143 (5)	0.0216 (6)	0.0271 (6)	−0.0001 (4)	0.0004 (5)	−0.0027 (5)
C3	0.0135 (5)	0.0219 (6)	0.0286 (7)	0.0010 (4)	−0.0020 (4)	−0.0031 (5)
C4	0.0169 (5)	0.0219 (6)	0.0237 (6)	0.0004 (4)	−0.0026 (4)	−0.0043 (5)
C5	0.0156 (5)	0.0296 (7)	0.0248 (6)	0.0029 (5)	0.0011 (5)	−0.0027 (5)
C6	0.0142 (5)	0.0243 (6)	0.0255 (6)	0.0023 (4)	−0.0015 (4)	−0.0051 (5)
C7	0.0158 (5)	0.0210 (6)	0.0246 (6)	0.0004 (4)	−0.0013 (4)	−0.0038 (5)
C8	0.0159 (5)	0.0263 (7)	0.0257 (6)	−0.0015 (5)	−0.0013 (5)	−0.0001 (5)
C9	0.0162 (5)	0.0267 (7)	0.0267 (6)	0.0002 (5)	0.0014 (5)	−0.0009 (5)
C10	0.0186 (6)	0.0265 (7)	0.0205 (6)	0.0019 (4)	−0.0003 (4)	−0.0019 (5)
C11	0.0214 (6)	0.0339 (8)	0.0298 (7)	0.0001 (5)	0.0019 (5)	0.0049 (6)
C12	0.0264 (7)	0.0358 (8)	0.0316 (7)	0.0036 (5)	−0.0038 (6)	0.0071 (6)
C13	0.0210 (6)	0.0440 (9)	0.0290 (7)	0.0039 (6)	−0.0043 (5)	0.0027 (6)
C14	0.0190 (6)	0.0348 (8)	0.0262 (7)	−0.0019 (5)	−0.0015 (5)	0.0039 (6)

Geometric parameters (Å, º) top

O1—C7	1.2381 (16)	C5—H5A	0.97 (2)
N1—C4	1.3649 (18)	C6—H6A	0.996 (17)
N1—H1N1	0.88 (2)	C7—C8	1.4909 (17)
N1—H2N1	0.93 (2)	C8—C9	1.332 (2)
N2—C13	1.339 (2)	C8—H8A	1.00 (2)
N2—C14	1.3410 (17)	C9—C10	1.4668 (17)
C1—C6	1.4011 (18)	C9—H9A	0.986 (18)
C1—C2	1.4097 (16)	C10—C11	1.392 (2)
C1—C7	1.4671 (18)	C10—C14	1.3986 (19)
C2—C3	1.3767 (19)	C11—C12	1.3864 (19)
C2—H2A	0.963 (16)	C11—H11A	1.023 (18)
C3—C4	1.4127 (18)	C12—C13	1.378 (2)
C3—H3A	0.988 (17)	C12—H12A	0.97 (2)
C4—C5	1.4097 (17)	C13—H13A	0.99 (2)
C5—C6	1.3749 (19)	C14—H14A	1.01 (2)

C4—N1—H1N1	118.9 (13)	O1—C7—C8	119.67 (12)
C4—N1—H2N1	118.2 (12)	C1—C7—C8	118.61 (11)
H1N1—N1—H2N1	121.7 (19)	C9—C8—C7	121.19 (12)
C13—N2—C14	117.14 (13)	C9—C8—H8A	121.1 (11)
C6—C1—C2	117.38 (12)	C7—C8—H8A	117.8 (11)
C6—C1—C7	122.58 (11)	C8—C9—C10	127.07 (12)
C2—C1—C7	120.04 (11)	C8—C9—H9A	117.1 (10)
C3—C2—C1	121.50 (12)	C10—C9—H9A	115.8 (10)
C3—C2—H2A	119.0 (10)	C11—C10—C14	116.83 (12)
C1—C2—H2A	119.5 (10)	C11—C10—C9	119.98 (12)
C2—C3—C4	120.55 (11)	C14—C10—C9	123.18 (12)
C2—C3—H3A	120.7 (10)	C12—C11—C10	120.21 (13)
C4—C3—H3A	118.8 (10)	C12—C11—H11A	121.3 (10)
N1—C4—C5	120.58 (12)	C10—C11—H11A	118.5 (10)
N1—C4—C3	121.28 (11)	C13—C12—C11	117.90 (14)
C5—C4—C3	118.13 (12)	C13—C12—H12A	121.0 (12)
C6—C5—C4	120.50 (12)	C11—C12—H12A	121.1 (12)
C6—C5—H5A	121.3 (12)	N2—C13—C12	123.98 (13)
C4—C5—H5A	118.2 (12)	N2—C13—H13A	115.0 (11)
C5—C6—C1	121.92 (11)	C12—C13—H13A	121.0 (11)
C5—C6—H6A	119.0 (10)	N2—C14—C10	123.89 (14)
C1—C6—H6A	119.0 (10)	N2—C14—H14A	114.7 (10)
O1—C7—C1	121.71 (11)	C10—C14—H14A	121.4 (10)

C6—C1—C2—C3	1.23 (18)	O1—C7—C8—C9	−12.5 (2)
C7—C1—C2—C3	−178.45 (12)	C1—C7—C8—C9	168.37 (12)
C1—C2—C3—C4	−0.56 (19)	C7—C8—C9—C10	−176.57 (13)
C2—C3—C4—N1	179.56 (12)	C8—C9—C10—C11	168.40 (14)
C2—C3—C4—C5	−0.85 (19)	C8—C9—C10—C14	−10.3 (2)
N1—C4—C5—C6	−178.84 (13)	C14—C10—C11—C12	1.1 (2)
C3—C4—C5—C6	1.57 (19)	C9—C10—C11—C12	−177.71 (14)
C4—C5—C6—C1	−0.9 (2)	C10—C11—C12—C13	0.9 (2)
C2—C1—C6—C5	−0.50 (19)	C14—N2—C13—C12	1.8 (2)
C7—C1—C6—C5	179.18 (12)	C11—C12—C13—N2	−2.5 (2)
C6—C1—C7—O1	165.18 (12)	C13—N2—C14—C10	0.5 (2)
C2—C1—C7—O1	−15.15 (19)	C11—C10—C14—N2	−1.9 (2)
C6—C1—C7—C8	−15.74 (19)	C9—C10—C14—N2	176.92 (14)
C2—C1—C7—C8	163.92 (12)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1N1···O1ⁱ	0.88 (2)	2.13 (2)	2.9920 (16)	170 (2)
N1—H2N1···N2ⁱⁱ	0.93 (2)	2.26 (2)	3.1471 (17)	161.7 (19)

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

Experimental details

Crystal data
Chemical formula	C₁₄H₁₂N₂O
M_r	224.26
Crystal system, space group	Orthorhombic, Pbca
Temperature (K)	100
a, b, c (Å)	12.0046 (12), 7.9329 (9), 22.925 (3)
V (Å³)	2183.2 (4)
Z	8
Radiation type	Mo Kα
µ (mm⁻¹)	0.09
Crystal size (mm)	0.52 × 0.32 × 0.18

Data collection
Diffractometer	Bruker APEX DUO CCD area-detector diffractometer
Absorption correction	Multi-scan (SADABS; Bruker, 2009)
T_min, T_max	0.956, 0.985
No. of measured, independent and observed [I > 2σ(I)] reflections	12726, 3177, 2433
R_int	0.043
(sin θ/λ)_max (Å⁻¹)	0.703

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.048, 0.132, 1.03
No. of reflections	3177
No. of parameters	202
H-atom treatment	All H-atom parameters refined
Δρ_max, Δρ_min (e Å⁻³)	0.37, −0.18

Computer programs: APEX2 (Bruker, 2009), SAINT (Bruker, 2009), SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2009).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1N1···O1ⁱ	0.88 (2)	2.13 (2)	2.9920 (16)	170 (2)
N1—H2N1···N2ⁱⁱ	0.93 (2)	2.26 (2)	3.1471 (17)	161.7 (19)

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

Footnotes

‡Thomson Reuters ResearcherID: A-5085-2009.

§Thomson Reuters ResearcherID: A-3561-2009. Additional correspondence author, e-mail: hkfun@usm.my.

Acknowledgements

The authors thank the Thailand Research Fund (TRF) for a research grant (RSA 5280033) and the Prince of Songkla University for financial support. The authors also thank Universiti Sains Malaysia for the Research University Grant No. 1001/PFIZIK/811160.

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