Crystal structure of bis­{N′-[(E)-4-hy­droxy­benzyl­idene]pyridine-4-carbohydrazide-κN1}di­iodidocadmium methanol disolvate

Afkhami, F.A.; Krautscheid, H.; Atioğlu, Z.; Akkurt, M.

doi:10.1107/S2056989016019575

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Volume 73| Part 1| January 2017| Pages 28-30

https://doi.org/10.1107/S2056989016019575

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Crystal structure of bis{N′-[(E)-4-hydroxybenzylidene]pyridine-4-carbohydrazide-κN¹}diiodidocadmium methanol disolvate

Farhad Akbari Afkhami,^a Harald Krautscheid,^b Zeliha Atioğlu ^c and Mehmet Akkurt ^d ^*

^aYoung Researchers and Elite Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran, ^bUniversität Leipzig, Fakultät für Chemie und Mineralogie, Johannisallee 29, D-04103 Leipzig, Germany, ^cİlke Education and Health Foundation, Cappadocia Vocational College, The Medical Imaging Techniques Program, 50420 Mustafapaşa, Ürgüp, Nevşehir, Turkey, and ^dDepartment of Physics, Faculty of Sciences, Erciyes University, 38039 Kayseri, Turkey
^*Correspondence e-mail: akkurt@erciyes.edu.tr

Edited by J. Simpson, University of Otago, New Zealand (Received 30 November 2016; accepted 7 December 2016; online 1 January 2017)

In the title compound, [Cd(C₁₃H₁₁IN₃O₂)₂]·2CH₃OH, which crystallizes with Z = 4 in the space group Pbcn, the Cd^II atom is located on a twofold rotation axis and coordinated by two I⁻ anions and two N atoms from the pyridine rings of the two N′-[(E)-4-hydroxybenzylidene]pyridine-4-carbohydrazide ligands. The geometry around the Cd^II atom is distorted tetrahedral, with bond angles in the range 94.92 (11)–124.29 (2)°. The iodide anions undergo intermolecular hydrogen-bonding contacts with the C—H groups of the organic ligands of an adjacent complex molecule, generating a chain structure along the b axis. Furthermore, an extensive series of O—H⋯O, N—H⋯O and C—H⋯O hydrogen-bonding interactions involving both the complex molecules and the ethanol solvate molecules generate a three-dimensional network.

Keywords: crystal structure; cadmium; hydrazone-based ligand; hydrogen bonding.

CCDC reference: 1521096

1. Chemical context

Hydrazones are organic compounds that incorporate –NH–N=CH– units in their molecules. Hydrazone ligands based on pyridine are among the most important classes of flexible and versatile polydentate ligands and usually act as chelating ligands to metal cations (Afkhami et al., 2016 ), but in some cases they behave as monodentate ligands through the pyridine group alone. The hydrazone-based ligand in the title compound was prepared according to a method reported in the literature (Deng et al., 2005 ). The crystal structure of the ligand and three of its Zn^II metal complexes have been reported previously (Mahmoudi et al., 2016 ). However, the title compound is the first reported crystal structure of a Cd^II complex of the ligand.

2. Structural commentary

The molecular structure of the title compound is shown in Fig. 1. The Cd atom, located on a twofold rotation axis, is coordinated by two Schiff base ligands, acting as monodentate ligands, through the nitrogen atoms of the pyridine rings. The angle between the benzene and pyridine rings is 35.42 (19)°. The Cd—I distance is 2.6909 (5) Å and the Cd—N distance is 2.297 (3) Å. All bonds and angles in the title compound fall within acceptable ranges and are comparable with those reported for related structures of bis{2-[(2,4-dimethylphenyl)iminomethyl]pyridine-κ²N,N′}bis(thiocyanato-κN)cadmium (Malekshahian et al., 2012 ), di-μ-chlorido-bis(chlorido{N-[phenyl(pyridin-2-yl-κN)methylidene]pyridine-2-carbohydrazide-κ²N,O}cadmium) (Akkurt et al., 2014 ) and cis-diaquabis[(E)-4-(2-hydroxybenzyl-ideneamino)benzoato-κ²O,O′]cadmium in which layers are built from strong O—H⋯O hydrogen bonding (Yao et al., 2006 ).

Figure 1
The molecular components of the title compound, showing the atom-numbering scheme. Displacement ellipsoids for non-H atoms are drawn at the 50% probability level [symmetry code: (a) −x, y, −z + $[{1\over 2}]$ ].

3. Supramolecular features

In the crystal, the iodide anions form intermolecular C1—H1⋯I1 hydrogen-bonding contacts with the C—H groups of the pyridine rings of an adjacent complex molecule. This generates a a chain structure along the b axis. In addition, an extensive series of O—H⋯O, N—H⋯O and C—H⋯O hydrogen-bonding interactions, Table 1, involving both the complex molecules and the methanol solvate molecules, generates a three-dimensional network (Figs. 2, 3 and 4).

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N2—H2N⋯O3	0.77 (5)	2.09 (5)	2.849 (4)	174 (4)
O2—H2O⋯O1ⁱⁱ	0.81 (3)	1.89 (4)	2.656 (4)	159 (5)
O3—H3O⋯O2ⁱⁱⁱ	0.80 (3)	2.03 (2)	2.828 (5)	173 (4)
C4—H4⋯O3	0.94	2.58	3.291 (5)	133
C7—H7⋯O3	0.94	2.56	3.327 (5)	140
C1—H1⋯I1^iv	0.94	3.11	3.811 (4)	133
Symmetry codes: (ii) $[x+{\script{1\over 2}}, -y+{\script{3\over 2}}, -z]$ ; (iii) -x+2, -y+1, -z; (iv) $[-x-{\script{1\over 2}}, y+{\script{1\over 2}}, z]$ .

Figure 2
View of the hydrogen bonding and packing of the title compound along the a axis.

Figure 3
View of the hydrogen bonding and packing of the title compound along the b axis.

Figure 4
View of the hydrogen bonding and packing of the title compound along the c axis.

4. Synthesis and crystallization

The title compound was synthesized by the reaction of a methanol solution of the ligand and Cd(NO₃)₂·4H₂O in the presence of excess amount of NaI. The ligand (1 mmol, 0.240 g) and cadmium nitrate (1 mmol, 0.308 g) were placed in the main arm of a branched tube; sodium iodide (2 mmol, 0.300 g) was added to the mixture too. Methanol was carefully added to fill the arms. The tube was sealed and the ligand-containing arm was immersed in an oil bath at 333 K while the branched arm was kept at ambient temperature. After 24 h, suitable single crystals had deposited in the cooler arm which were isolated and air dried.

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2. All C-bound H atoms were idealized (C—H = 0.98–0.99 Å) and refined using the riding-model approximation with U_iso(H) = 1.2 or 1.5 U_eq(C). The N—H and O—H hydrogen atoms were located from difference maps and refined with the restraints N2—H2N = 0.77 (5), O2—H2O = 0.81 (3), O3—H3O = 0.80 (3) Å and with U_iso(H) = 1.2U_eq(N) or U_iso(H) = 1.5U_eq(O).

Table 2
Experimental details

Crystal data
Chemical formula	[Cd(C₁₃H₁₁IN₃O₂)₂]·2CH₄O
M_r	912.79
Crystal system, space group	Orthorhombic, Pbcn
Temperature (K)	213
a, b, c (Å)	8.0245 (4), 13.2482 (9), 30.4540 (19)
V (Å³)	3237.6 (3)
Z	4
Radiation type	Mo Kα
μ (mm⁻¹)	2.63
Crystal size (mm)	0.5 × 0.3 × 0.3

Data collection
Diffractometer	Stoe IPDS1
Absorption correction	Numerical (X-RED32; Stoe & Cie, 2000 )
T_min, T_max	0.337, 0.453
No. of measured, independent and observed [I > 2σ(I)] reflections	3511, 3511, 2542
(sin θ/λ)_max (Å⁻¹)	0.651

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.040, 0.094, 0.88
No. of reflections	3511
No. of parameters	206
No. of restraints	2
H-atom treatment	H atoms treated by a mixture of independent and constrained refinement
Δρ_max, Δρ_min (e Å⁻³)	1.68, −1.47
Computer programs: EXPOSE, CELL, SELECT and INTEGRATE (Stoe & Cie, 2000), SHELXT2014 (Sheldrick, 2015a ), SHELXL2014 (Sheldrick, 2015b ), ORTEP-3 for Windows and WinGX (Farrugia, 2012 ) and PLATON (Spek, 2009 ).

Supporting information

CCDC reference: 1521096

Crystal structure: contains datablocks global, I. DOI: https://doi.org/10.1107/S2056989016019575/sj5516sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989016019575/sj5516Isup2.hkl

checkCIF report

Computing details top

Data collection: EXPOSE (Stoe & Cie, 2000); cell refinement: CELL (Stoe & Cie, 2000); data reduction: SELECT (Stoe & Cie, 2000) and INTEGRATE (Stoe & Cie, 2000); program(s) used to solve structure: SHELXT-2014 (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015b); molecular graphics: ORTEP-3 for Windows (Farrugia, 2012); software used to prepare material for publication: PLATON (Spek, 2009) and WinGX (Farrugia, 2012).

Bis{N'-[(E)-4-hydroxybenzylidene]pyridine-4-carbohydrazide-κN¹}diiodidocadmium methanol disolvate top

Crystal data top

[CdI₂(C₁₃H₁₁N₃O₂)₂]·2CH₄O	F(000) = 1768
M_r = 912.79	D_x = 1.873 Mg m⁻³
Orthorhombic, Pbcn	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2ab	Cell parameters from 428 reflections
a = 8.0245 (4) Å	θ = 2.9–27.6°
b = 13.2482 (9) Å	µ = 2.63 mm⁻¹
c = 30.4540 (19) Å	T = 213 K
V = 3237.6 (3) Å³	Prism, colorless
Z = 4	0.5 × 0.3 × 0.3 mm

Data collection top

Stoe IPDS1 diffractometer	3511 independent reflections
Radiation source: fine-focus sealed tube	2542 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.000
phi scan	θ_max = 27.6°, θ_min = 2.9°
Absorption correction: numerical Stoe XRED32 (Stoe & Cie, 2000)	h = 0→9
T_min = 0.337, T_max = 0.453	k = 0→17
3511 measured reflections	l = 0→39

Refinement top

Refinement on F²	Hydrogen site location: mixed
Least-squares matrix: full	H atoms treated by a mixture of independent and constrained refinement
R[F² > 2σ(F²)] = 0.040	w = 1/[σ²(F_o²) + (0.0655P)²] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.094	(Δ/σ)_max < 0.001
S = 0.88	Δρ_max = 1.68 e Å⁻³
3511 reflections	Δρ_min = −1.47 e Å⁻³
206 parameters	Extinction correction: SHELXL-2014 (Sheldrick, 2015b), Fc^*=kFc[1+0.001XFc²λ³/sin(2θ)]^-1/4
2 restraints	Extinction coefficient: 0.0026 (2)

Special details top

Geometry. Bond distances, angles etc. have been calculated using the rounded fractional coordinates. All su's are estimated from the variances of the (full) variance-covariance matrix. The cell esds are taken into account in the estimation of distances, angles and torsion angles

Refinement. Refinement on F² for ALL reflections except those flagged by the user for potential systematic errors. Weighted R-factors wR and all goodnesses of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The observed criterion of F² > 2sigma(F²) is used only for calculating -R-factor-obs 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
I1	−0.24029 (5)	0.11226 (3)	0.20424 (2)	0.0555 (1)
Cd1	0.00000	0.20717 (2)	0.25000	0.0250 (1)
O1	0.3473 (4)	0.62436 (18)	0.12617 (10)	0.0359 (9)
O2	1.0000 (4)	0.70774 (18)	−0.10066 (9)	0.0310 (8)
N1	0.1497 (5)	0.3244 (2)	0.21085 (10)	0.0284 (10)
N2	0.5039 (5)	0.4973 (2)	0.09734 (10)	0.0263 (9)
N3	0.5712 (5)	0.5598 (2)	0.06532 (10)	0.0269 (10)
C1	0.0746 (6)	0.4087 (3)	0.19639 (12)	0.0295 (11)
C2	0.1550 (5)	0.4791 (3)	0.17078 (12)	0.0280 (11)
C3	0.3166 (5)	0.4612 (2)	0.15733 (12)	0.0247 (10)
O3	0.6488 (4)	0.3011 (2)	0.09399 (12)	0.0431 (11)
C4	0.3962 (6)	0.3747 (3)	0.17287 (13)	0.0302 (11)
C5	0.3096 (6)	0.3093 (3)	0.19927 (13)	0.0319 (13)
C6	0.3943 (5)	0.5354 (2)	0.12611 (12)	0.0262 (10)
C7	0.6539 (5)	0.5138 (3)	0.03593 (12)	0.0265 (10)
C8	0.7372 (5)	0.5675 (3)	−0.00022 (11)	0.0244 (10)
C9	0.7230 (5)	0.6713 (3)	−0.00636 (13)	0.0290 (13)
C10	0.8101 (6)	0.7194 (3)	−0.03945 (13)	0.0293 (13)
C11	0.9119 (5)	0.6642 (2)	−0.06770 (11)	0.0230 (10)
C12	0.9264 (6)	0.5601 (3)	−0.06211 (12)	0.0263 (10)
C13	0.8388 (5)	0.5132 (3)	−0.02870 (12)	0.0268 (13)
C14	0.5662 (7)	0.2065 (3)	0.09320 (17)	0.0450 (16)
H1	−0.03730	0.42000	0.20410	0.0350*
H2	0.10030	0.53890	0.16250	0.0340*
H2N	0.541 (6)	0.444 (4)	0.0984 (14)	0.0320*
H2O	0.967 (7)	0.765 (2)	−0.1033 (17)	0.0460*
H4	0.50760	0.36150	0.16530	0.0360*
H5	0.36440	0.25140	0.20980	0.0380*
H7	0.66220	0.44310	0.03730	0.0320*
H9	0.65340	0.70910	0.01220	0.0350*
H10	0.80070	0.78960	−0.04290	0.0350*
H12	0.99500	0.52210	−0.08090	0.0320*
H13	0.84820	0.44290	−0.02520	0.0320*
H3O	0.748 (3)	0.294 (5)	0.095 (2)	0.0650*
H14A	0.62690	0.15860	0.11120	0.0670*
H14B	0.56100	0.18190	0.06320	0.0670*
H14C	0.45410	0.21430	0.10460	0.0670*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
I1	0.0416 (3)	0.0625 (2)	0.0624 (2)	−0.0191 (2)	0.0021 (2)	−0.0255 (2)
Cd1	0.0250 (2)	0.0179 (2)	0.0320 (2)	0.0000	0.0051 (2)	0.0000
O1	0.041 (2)	0.0198 (12)	0.0469 (16)	0.0042 (12)	0.0127 (14)	0.0091 (11)
O2	0.0326 (17)	0.0217 (11)	0.0386 (13)	0.0017 (13)	0.0098 (13)	0.0098 (10)
N1	0.035 (2)	0.0209 (13)	0.0292 (16)	0.0023 (13)	0.0071 (14)	0.0038 (12)
N2	0.031 (2)	0.0184 (12)	0.0294 (14)	0.0000 (14)	0.0067 (15)	0.0076 (11)
N3	0.027 (2)	0.0232 (13)	0.0306 (16)	−0.0034 (13)	0.0036 (14)	0.0093 (12)
C1	0.027 (2)	0.0294 (18)	0.0321 (19)	0.0061 (16)	0.0084 (16)	0.0039 (14)
C2	0.028 (2)	0.0216 (16)	0.0345 (19)	0.0068 (15)	0.0037 (16)	0.0054 (14)
C3	0.028 (2)	0.0198 (15)	0.0264 (17)	−0.0006 (14)	0.0006 (15)	0.0019 (12)
O3	0.031 (2)	0.0273 (14)	0.071 (2)	0.0040 (13)	0.0092 (16)	0.0070 (14)
C4	0.024 (2)	0.0267 (18)	0.040 (2)	0.0058 (15)	0.0078 (17)	0.0102 (15)
C5	0.034 (3)	0.0256 (18)	0.036 (2)	0.0079 (16)	0.0064 (17)	0.0066 (15)
C6	0.026 (2)	0.0202 (16)	0.0323 (18)	0.0002 (14)	−0.0008 (16)	0.0055 (13)
C7	0.028 (2)	0.0210 (16)	0.0304 (18)	−0.0032 (15)	0.0004 (16)	0.0062 (14)
C8	0.026 (2)	0.0224 (15)	0.0249 (16)	−0.0054 (15)	−0.0014 (15)	0.0041 (13)
C9	0.027 (3)	0.0241 (17)	0.0360 (19)	0.0039 (15)	0.0084 (16)	0.0031 (14)
C10	0.031 (3)	0.0180 (16)	0.039 (2)	0.0031 (15)	0.0057 (17)	0.0062 (14)
C11	0.022 (2)	0.0199 (15)	0.0271 (17)	−0.0009 (14)	−0.0007 (15)	0.0050 (13)
C12	0.032 (2)	0.0184 (15)	0.0285 (17)	0.0034 (15)	0.0018 (16)	0.0005 (13)
C13	0.033 (3)	0.0164 (15)	0.0310 (18)	−0.0025 (15)	−0.0038 (16)	0.0022 (13)
C14	0.044 (3)	0.036 (2)	0.055 (3)	−0.003 (2)	−0.003 (2)	0.003 (2)

Geometric parameters (Å, º) top

I1—Cd1	2.6909 (5)	C8—C13	1.391 (5)
Cd1—I1ⁱ	2.6909 (5)	C8—C9	1.393 (6)
Cd1—N1	2.297 (3)	C9—C10	1.382 (6)
Cd1—N1ⁱ	2.297 (3)	C10—C11	1.394 (5)
O1—C6	1.237 (4)	C11—C12	1.395 (5)
O2—C11	1.357 (4)	C12—C13	1.384 (6)
N1—C1	1.343 (5)	C1—H1	0.9400
N1—C5	1.346 (6)	C2—H2	0.9400
N2—N3	1.389 (4)	O3—H3O	0.80 (3)
N2—C6	1.340 (5)	C4—H4	0.9400
O2—H2O	0.81 (3)	C5—H5	0.9400
N3—C7	1.270 (5)	C7—H7	0.9400
C1—C2	1.376 (6)	C9—H9	0.9400
C2—C3	1.380 (6)	C10—H10	0.9400
N2—H2N	0.77 (5)	C12—H12	0.9400
C3—C4	1.395 (5)	C13—H13	0.9400
C3—C6	1.503 (5)	C14—H14A	0.9700
O3—C14	1.418 (5)	C14—H14B	0.9700
C4—C5	1.371 (6)	C14—H14C	0.9700
C7—C8	1.471 (5)

I1—Cd1—N1	114.95 (8)	O2—C11—C12	117.9 (3)
I1—Cd1—I1ⁱ	124.29 (2)	O2—C11—C10	122.6 (3)
I1—Cd1—N1ⁱ	102.12 (9)	C10—C11—C12	119.5 (3)
I1ⁱ—Cd1—N1	102.12 (9)	C11—C12—C13	119.4 (4)
N1—Cd1—N1ⁱ	94.92 (11)	C8—C13—C12	121.6 (4)
I1ⁱ—Cd1—N1ⁱ	114.95 (8)	N1—C1—H1	119.00
Cd1—N1—C1	119.9 (3)	C2—C1—H1	119.00
Cd1—N1—C5	122.3 (2)	C1—C2—H2	120.00
C1—N1—C5	117.7 (3)	C3—C2—H2	120.00
N3—N2—C6	119.3 (3)	C14—O3—H3O	111 (5)
C11—O2—H2O	108 (4)	C5—C4—H4	121.00
N2—N3—C7	114.3 (3)	C3—C4—H4	120.00
N1—C1—C2	122.6 (4)	N1—C5—H5	119.00
C1—C2—C3	119.5 (4)	C4—C5—H5	119.00
C6—N2—H2N	125 (3)	C8—C7—H7	119.00
N3—N2—H2N	115 (3)	N3—C7—H7	119.00
C2—C3—C4	118.1 (3)	C8—C9—H9	120.00
C2—C3—C6	117.7 (3)	C10—C9—H9	120.00
C4—C3—C6	124.2 (4)	C11—C10—H10	120.00
C3—C4—C5	119.1 (4)	C9—C10—H10	120.00
N1—C5—C4	122.9 (4)	C11—C12—H12	120.00
N2—C6—C3	116.1 (3)	C13—C12—H12	120.00
O1—C6—C3	119.7 (3)	C8—C13—H13	119.00
O1—C6—N2	124.0 (3)	C12—C13—H13	119.00
N3—C7—C8	122.2 (4)	O3—C14—H14A	110.00
C7—C8—C9	122.7 (3)	O3—C14—H14B	109.00
C7—C8—C13	118.9 (4)	O3—C14—H14C	109.00
C9—C8—C13	118.4 (3)	H14A—C14—H14B	110.00
C8—C9—C10	120.8 (4)	H14A—C14—H14C	109.00
C9—C10—C11	120.3 (4)	H14B—C14—H14C	109.00

I1—Cd1—N1—C1	66.6 (3)	C2—C3—C6—O1	27.7 (5)
I1ⁱ—Cd1—N1—C1	−156.1 (3)	C2—C3—C4—C5	2.5 (6)
N1ⁱ—Cd1—N1—C1	−39.2 (3)	C6—C3—C4—C5	−176.2 (4)
I1—Cd1—N1—C5	−109.3 (3)	C2—C3—C6—N2	−147.5 (4)
I1ⁱ—Cd1—N1—C5	28.1 (3)	C4—C3—C6—O1	−153.5 (4)
N1ⁱ—Cd1—N1—C5	144.9 (3)	C3—C4—C5—N1	0.4 (6)
C1—N1—C5—C4	−1.5 (6)	N3—C7—C8—C9	−4.1 (6)
Cd1—N1—C1—C2	−176.4 (3)	N3—C7—C8—C13	173.8 (4)
C5—N1—C1—C2	−0.4 (6)	C7—C8—C9—C10	176.7 (4)
Cd1—N1—C5—C4	174.5 (3)	C13—C8—C9—C10	−1.2 (6)
C6—N2—N3—C7	−170.1 (4)	C7—C8—C13—C12	−177.1 (4)
N3—N2—C6—O1	0.2 (6)	C9—C8—C13—C12	0.9 (6)
N3—N2—C6—C3	175.1 (3)	C8—C9—C10—C11	1.0 (6)
N2—N3—C7—C8	−178.8 (4)	C9—C10—C11—O2	−180.0 (4)
N1—C1—C2—C3	3.3 (6)	C9—C10—C11—C12	−0.5 (6)
C1—C2—C3—C6	174.6 (3)	O2—C11—C12—C13	179.8 (4)
C1—C2—C3—C4	−4.3 (5)	C10—C11—C12—C13	0.3 (6)
C4—C3—C6—N2	31.2 (5)	C11—C12—C13—C8	−0.5 (6)

Symmetry code: (i) −x, y, −z+1/2.

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N2—H2N···O3	0.77 (5)	2.09 (5)	2.849 (4)	174 (4)
O2—H2O···O1ⁱⁱ	0.81 (3)	1.89 (4)	2.656 (4)	159 (5)
O3—H3O···O2ⁱⁱⁱ	0.80 (3)	2.03 (2)	2.828 (5)	173 (4)
C4—H4···O3	0.94	2.58	3.291 (5)	133
C7—H7···O3	0.94	2.56	3.327 (5)	140
C1—H1···I1^iv	0.94	3.11	3.811 (4)	133

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

Acknowledgements

We are grateful to the Young Researchers and Elite Club, Tabriz Branch, Islamic Azad University, for the financial support of this research.

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