[N′-(3,5-Diiodo-2-oxidobenzyl­idene-κO)-4-methyl­benzohydrazidato-κ2N′,O](methanol-κO)(methano­lato-κO)oxidovanadium(V)

Liu, L.

doi:10.1107/S1600536811010385

metal-organic compounds

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ISSN: 2056-9890

Volume 67| Part 4| April 2011| Page m482

doi:10.1107/S1600536811010385

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[N′-(3,5-Diiodo-2-oxidobenzylidene-κO)-4-methylbenzohydrazidato-κ²N′,O](methanol-κO)(methanolato-κO)oxidovanadium(V)

Lin Liu ^a ^*

^aCollege of Chemistry and Biology Engineering, Yichun University, Yichun 336000, People's Republic of China
^*Correspondence e-mail: liulin_ycu@126.com

(Received 17 March 2011; accepted 19 March 2011; online 26 March 2011)

In the title molecule, [V(C₁₅H₁₀I₂N₂O₂)(CH₃O)O(CH₃OH)], the V^V atom is coordinated by one N and two O atoms from an N′-(3,5-diiodo-2-oxidobenzylidene-κO)-4-methylbenzohydrazidate (L) ligand, one oxide O atom, one methanolate [V—O = 1.761 (3) Å] and one methanol [V—O = 2.383 (4) Å] O atom in a distorted octahedral geometry. In the L ligand, the two benzene rings are nearly parallel, forming a dihedral angle of 2.0 (1)°. In the crystal, intermolecular O—H⋯N hydrogen bonds link pairs of molecules into centrosymmetric dimers which exhibit π–π interactions between the aromatic rings [centroid–centroid distance = 3.677 (5) Å].

Related literature

For background to oxidovanadium complexes, see: Chohan et al. (2010 ); Chohan & Sumrra (2010 ); Sharma et al. (2010 ); Tian et al. (2010 ). For similar oxidovanadium(V) complexes, see: Wang (2011 ); Rajak et al. (2000 ); Mondal et al. (2009 ).

Experimental

Crystal data

[V(C₁₅H₁₀I₂N₂O₂)(CH₃O)O(CH₄O)]
M_r = 634.07
Triclinic, $[P \overline 1]$
a = 7.890 (5) Å
b = 10.030 (6) Å
c = 13.628 (8) Å
α = 81.857 (5)°
β = 84.777 (6)°
γ = 85.286 (5)°
V = 1060.5 (11) Å³
Z = 2
Mo Kα radiation
μ = 3.41 mm⁻¹
T = 298 K
0.17 × 0.13 × 0.12 mm

Data collection

Bruker SMART CCD area-detector diffractometer
Absorption correction: multi-scan (SADABS; Sheldrick, 1996 ) T_min = 0.595, T_max = 0.685
7706 measured reflections
4283 independent reflections
3146 reflections with I > 2σ(I)
R_int = 0.026

Refinement

R[F² > 2σ(F²)] = 0.041
wR(F²) = 0.090
S = 1.02
4283 reflections
250 parameters
1 restraint
H atoms treated by a mixture of independent and constrained refinement
Δρ_max = 1.00 e Å⁻³
Δρ_min = −1.01 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
O4—H4⋯N2ⁱ	0.85 (4)	2.03 (5)	2.858 (5)	168 (8)
Symmetry code: (i) -x, -y, -z+1.

Data collection: SMART (Bruker, 1998 ); cell refinement: SAINT (Bruker, 1998); 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 global, I. DOI: 10.1107/S1600536811010385/cv5063sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536811010385/cv5063Isup2.hkl

checkCIF report

Comment top

Considerable attention has been focused on the synthesis, structures, and biological properties of oxovanadium complexes (Chohan et al., 2010; Chohan & Sumrra, 2010; Sharma et al., 2010; Tian et al., 2010). The present paper reports the crystal structure of the title new oxovanadium complex (I).

In (I) (Fig. 1), [OVL(OCH₃)(CH₃OH)] (H₂L = 3,5-diiodosalicylaldehide (4-methylbenzoyl)hydrazonic acid), the V center is coordinated by one N and two O atoms from L, one oxo O atom, and two O atoms from the methoxy [V—O 1.761 (3) Å] and methanol [V—O 2.383 (4) Å] ligands, respectively, in a distorted octahedral geometry. In the ligand L, two benzene rings are nearly parallel forming a dihedral angle of 2.0 (1)°. The deviation of the V atom from the least-squares plane defined by the three donor atoms of the hydrazone ligand and the methoxy O atom towards the oxo O atom is 0.311 (2) Å. The bond lengths and bond angles related to the V atom are normal and correspond to those observed in the related compounds (Wang, 2011; Rajak et al., 2000; Mondal et al., 2009).

In the crystal structure (Fig. 2), intermolecular O—H···N hydrogen bonds (Table 1) link two molecules into centrosymmetric dimer which exhibits π-π interaction between the aromatic rings [centroid-to-centroid distance of 3.677 (5) Å].

Related literature top

For background to oxidovanadium complexes, see: Chohan et al. (2010); Chohan & Sumrra (2010); Sharma et al. (2010); Tian et al. (2010). For similar oxidovanadium(V) complexes, see: Wang (2011); Rajak et al. (2000); Mondal et al. (2009).

Experimental top

Equimolar quantities (0.1 mmol each) of 3,5-diiodosalicylaldehyde, 4-methylbenzohydrazide, and VOSO₄ were mixed and stirred in methanol for 30 min at reflux. After keeping the filtrate in air for a few days, red block crystals were formed.

Computing details top

Data collection: SMART (Bruker, 1998); cell refinement: SAINT (Bruker, 1998); data reduction: SAINT (Bruker, 1998); 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. Molecular structure of the title complex showing the atomic numbering and 30% probability ellipsoids.
	Fig. 2. A portion of the crystal packing of (I) viewed approximately down the c axis and showing hydrogen-bonded (dashed lines) dimers.

[N'-(3,5-Diiodo-2-oxidobenzylidene-κO)-4-methylbenzohydrazidato- κ²N',O](methanol-κO)(methanolato- κO)oxidovanadium(V) top

Crystal data top

[V(C₁₅H₁₀I₂N₂O₂)(CH₃O)O(CH₄O)]	Z = 2
M_r = 634.07	F(000) = 604
Triclinic, P1	D_x = 1.986 Mg m⁻³
a = 7.890 (5) Å	Mo Kα radiation, λ = 0.71073 Å
b = 10.030 (6) Å	Cell parameters from 2583 reflections
c = 13.628 (8) Å	θ = 2.7–25.0°
α = 81.857 (5)°	µ = 3.41 mm⁻¹
β = 84.777 (6)°	T = 298 K
γ = 85.286 (5)°	Block, red
V = 1060.5 (11) Å³	0.17 × 0.13 × 0.12 mm

Data collection top

Bruker SMART CCD area-detector diffractometer	4283 independent reflections
Radiation source: fine-focus sealed tube	3146 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.026
ω scans	θ_max = 26.5°, θ_min = 2.1°
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	h = −9→9
T_min = 0.595, T_max = 0.685	k = −12→12
7706 measured reflections	l = −17→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)] = 0.041	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.090	H atoms treated by a mixture of independent and constrained refinement
S = 1.02	w = 1/[σ²(F_o²) + (0.03P)² + 1.6979P] where P = (F_o² + 2F_c²)/3
4283 reflections	(Δ/σ)_max < 0.001
250 parameters	Δρ_max = 1.00 e Å⁻³
1 restraint	Δρ_min = −1.01 e Å⁻³

Crystal data top

[V(C₁₅H₁₀I₂N₂O₂)(CH₃O)O(CH₄O)]	γ = 85.286 (5)°
M_r = 634.07	V = 1060.5 (11) Å³
Triclinic, P1	Z = 2
a = 7.890 (5) Å	Mo Kα radiation
b = 10.030 (6) Å	µ = 3.41 mm⁻¹
c = 13.628 (8) Å	T = 298 K
α = 81.857 (5)°	0.17 × 0.13 × 0.12 mm
β = 84.777 (6)°

Data collection top

Bruker SMART CCD area-detector diffractometer	4283 independent reflections
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	3146 reflections with I > 2σ(I)
T_min = 0.595, T_max = 0.685	R_int = 0.026
7706 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.041	1 restraint
wR(F²) = 0.090	H atoms treated by a mixture of independent and constrained refinement
S = 1.02	Δρ_max = 1.00 e Å⁻³
4283 reflections	Δρ_min = −1.01 e Å⁻³
250 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
V1	0.23465 (11)	0.25458 (7)	0.54517 (6)	0.0344 (2)
I1	0.54984 (5)	−0.39607 (4)	0.86399 (3)	0.06551 (15)
I2	0.39530 (6)	0.20017 (4)	0.87434 (3)	0.06716 (16)
N1	0.2307 (5)	0.0559 (4)	0.5077 (3)	0.0311 (9)
N2	0.1714 (5)	0.0473 (4)	0.4152 (3)	0.0346 (9)
O1	0.1488 (5)	0.2762 (3)	0.4147 (2)	0.0423 (8)
O2	0.2580 (5)	0.1637 (3)	0.6730 (2)	0.0428 (8)
O3	0.4296 (4)	0.2723 (3)	0.5122 (3)	0.0497 (9)
O4	−0.0568 (5)	0.2139 (3)	0.5921 (3)	0.0439 (8)
O5	0.1603 (4)	0.4154 (3)	0.5753 (3)	0.0417 (8)
C1	0.3464 (6)	−0.0661 (4)	0.6552 (3)	0.0348 (11)
C2	0.4118 (6)	−0.1917 (5)	0.7000 (4)	0.0379 (11)
H2	0.4156	−0.2667	0.6666	0.046*
C3	0.4699 (6)	−0.2047 (5)	0.7927 (4)	0.0410 (12)
C4	0.4695 (7)	−0.0928 (5)	0.8431 (4)	0.0459 (13)
H4A	0.5129	−0.1016	0.9051	0.055*
C5	0.4040 (6)	0.0303 (5)	0.7998 (4)	0.0394 (12)
C6	0.3362 (6)	0.0472 (5)	0.7069 (3)	0.0344 (11)
C7	0.2817 (6)	−0.0561 (4)	0.5582 (4)	0.0337 (11)
H7	0.2768	−0.1353	0.5307	0.040*
C8	0.1344 (6)	0.1705 (5)	0.3713 (4)	0.0353 (11)
C9	0.0718 (6)	0.1932 (5)	0.2712 (4)	0.0378 (11)
C10	0.0142 (7)	0.3222 (5)	0.2310 (4)	0.0489 (14)
H10	0.0172	0.3939	0.2671	0.059*
C11	−0.0475 (7)	0.3452 (6)	0.1377 (4)	0.0585 (16)
H11	−0.0874	0.4321	0.1128	0.070*
C12	−0.0512 (7)	0.2434 (7)	0.0813 (4)	0.0559 (15)
C13	0.0081 (8)	0.1157 (6)	0.1213 (4)	0.0622 (17)
H13	0.0079	0.0447	0.0842	0.075*
C14	0.0677 (8)	0.0905 (6)	0.2149 (4)	0.0521 (14)
H14	0.1054	0.0031	0.2400	0.062*
C15	−0.1196 (9)	0.2677 (8)	−0.0205 (5)	0.083 (2)
H15A	−0.0267	0.2622	−0.0707	0.125*
H15B	−0.1781	0.3558	−0.0301	0.125*
H15C	−0.1975	0.2006	−0.0252	0.125*
C16	0.2549 (9)	0.5282 (6)	0.5792 (6)	0.076 (2)
H16A	0.3014	0.5199	0.6427	0.114*
H16B	0.1815	0.6094	0.5702	0.114*
H16C	0.3462	0.5318	0.5275	0.114*
C17	−0.1589 (9)	0.2807 (7)	0.6648 (5)	0.075 (2)
H17A	−0.1085	0.2616	0.7273	0.112*
H17B	−0.2716	0.2491	0.6724	0.112*
H17C	−0.1654	0.3763	0.6437	0.112*
H4	−0.087 (10)	0.134 (3)	0.599 (6)	0.088*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
V1	0.0406 (5)	0.0279 (4)	0.0370 (5)	−0.0040 (3)	−0.0089 (4)	−0.0077 (3)
I1	0.0621 (3)	0.0531 (2)	0.0724 (3)	0.00130 (19)	−0.0126 (2)	0.0238 (2)
I2	0.0971 (4)	0.0637 (3)	0.0486 (3)	−0.0046 (2)	−0.0270 (2)	−0.02184 (19)
N1	0.035 (2)	0.032 (2)	0.028 (2)	−0.0051 (16)	−0.0065 (17)	−0.0065 (16)
N2	0.040 (2)	0.036 (2)	0.030 (2)	−0.0071 (17)	−0.0084 (18)	−0.0070 (17)
O1	0.058 (2)	0.0309 (17)	0.040 (2)	−0.0039 (15)	−0.0132 (17)	−0.0030 (14)
O2	0.061 (2)	0.0335 (18)	0.036 (2)	0.0048 (16)	−0.0160 (17)	−0.0096 (14)
O3	0.044 (2)	0.049 (2)	0.060 (2)	−0.0112 (17)	0.0022 (18)	−0.0205 (18)
O4	0.042 (2)	0.044 (2)	0.049 (2)	−0.0068 (17)	−0.0020 (17)	−0.0133 (17)
O5	0.046 (2)	0.0276 (16)	0.054 (2)	−0.0019 (14)	−0.0085 (17)	−0.0089 (15)
C1	0.036 (3)	0.034 (2)	0.034 (3)	−0.008 (2)	−0.007 (2)	0.002 (2)
C2	0.038 (3)	0.036 (3)	0.040 (3)	−0.008 (2)	−0.004 (2)	−0.003 (2)
C3	0.036 (3)	0.041 (3)	0.043 (3)	−0.007 (2)	−0.005 (2)	0.009 (2)
C4	0.046 (3)	0.058 (3)	0.034 (3)	−0.010 (3)	−0.012 (3)	0.003 (2)
C5	0.045 (3)	0.042 (3)	0.034 (3)	−0.008 (2)	−0.010 (2)	−0.006 (2)
C6	0.033 (3)	0.039 (3)	0.032 (3)	−0.009 (2)	−0.002 (2)	−0.006 (2)
C7	0.036 (3)	0.029 (2)	0.038 (3)	−0.005 (2)	−0.005 (2)	−0.006 (2)
C8	0.033 (3)	0.038 (3)	0.035 (3)	−0.008 (2)	−0.003 (2)	0.000 (2)
C9	0.033 (3)	0.048 (3)	0.032 (3)	−0.010 (2)	−0.003 (2)	0.000 (2)
C10	0.050 (3)	0.052 (3)	0.045 (3)	−0.010 (3)	−0.010 (3)	0.000 (3)
C11	0.054 (4)	0.069 (4)	0.050 (4)	−0.011 (3)	−0.016 (3)	0.016 (3)
C12	0.041 (3)	0.089 (5)	0.036 (3)	−0.009 (3)	−0.009 (3)	0.003 (3)
C13	0.076 (5)	0.077 (4)	0.037 (3)	−0.009 (4)	−0.016 (3)	−0.010 (3)
C14	0.065 (4)	0.056 (3)	0.036 (3)	−0.003 (3)	−0.013 (3)	−0.002 (2)
C15	0.075 (5)	0.127 (6)	0.046 (4)	−0.008 (4)	−0.023 (4)	0.008 (4)
C16	0.073 (5)	0.037 (3)	0.122 (6)	−0.015 (3)	−0.007 (4)	−0.021 (3)
C17	0.069 (5)	0.069 (4)	0.087 (5)	−0.008 (3)	0.013 (4)	−0.026 (4)

Geometric parameters (Å, º) top

V1—O3	1.580 (4)	C5—C6	1.402 (6)
V1—O5	1.761 (3)	C7—H7	0.9300
V1—O2	1.865 (3)	C8—C9	1.475 (6)
V1—O1	1.938 (3)	C9—C14	1.372 (7)
V1—N1	2.130 (4)	C9—C10	1.389 (7)
V1—O4	2.383 (4)	C10—C11	1.385 (7)
I1—C3	2.100 (5)	C10—H10	0.9300
I2—C5	2.097 (5)	C11—C12	1.366 (8)
N1—C7	1.286 (6)	C11—H11	0.9300
N1—N2	1.400 (5)	C12—C13	1.381 (8)
N2—C8	1.317 (6)	C12—C15	1.514 (8)
O1—C8	1.302 (5)	C13—C14	1.383 (7)
O2—C6	1.319 (5)	C13—H13	0.9300
O4—C17	1.426 (7)	C14—H14	0.9300
O4—H4	0.85 (4)	C15—H15A	0.9600
O5—C16	1.416 (6)	C15—H15B	0.9600
C1—C2	1.400 (6)	C15—H15C	0.9600
C1—C6	1.413 (6)	C16—H16A	0.9600
C1—C7	1.447 (6)	C16—H16B	0.9600
C2—C3	1.368 (7)	C16—H16C	0.9600
C2—H2	0.9300	C17—H17A	0.9600
C3—C4	1.396 (7)	C17—H17B	0.9600
C4—C5	1.373 (7)	C17—H17C	0.9600
C4—H4A	0.9300

O3—V1—O5	102.77 (17)	N1—C7—C1	123.9 (4)
O3—V1—O2	98.49 (18)	N1—C7—H7	118.1
O5—V1—O2	99.38 (15)	C1—C7—H7	118.1
O3—V1—O1	98.80 (18)	O1—C8—N2	121.8 (4)
O5—V1—O1	96.85 (15)	O1—C8—C9	117.6 (4)
O2—V1—O1	152.99 (14)	N2—C8—C9	120.7 (4)
O3—V1—N1	96.54 (16)	C14—C9—C10	117.8 (5)
O5—V1—N1	159.79 (16)	C14—C9—C8	122.4 (5)
O2—V1—N1	83.42 (14)	C10—C9—C8	119.8 (5)
O1—V1—N1	74.12 (14)	C11—C10—C9	120.7 (5)
O3—V1—O4	176.43 (15)	C11—C10—H10	119.7
O5—V1—O4	80.79 (14)	C9—C10—H10	119.7
O2—V1—O4	81.04 (15)	C12—C11—C10	121.7 (6)
O1—V1—O4	80.42 (14)	C12—C11—H11	119.2
N1—V1—O4	79.89 (13)	C10—C11—H11	119.2
C7—N1—N2	116.4 (4)	C11—C12—C13	117.3 (5)
C7—N1—V1	127.8 (3)	C11—C12—C15	121.9 (6)
N2—N1—V1	115.7 (3)	C13—C12—C15	120.8 (6)
C8—N2—N1	108.5 (4)	C12—C13—C14	121.8 (6)
C8—O1—V1	119.9 (3)	C12—C13—H13	119.1
C6—O2—V1	133.0 (3)	C14—C13—H13	119.1
C17—O4—V1	123.2 (3)	C9—C14—C13	120.7 (5)
C17—O4—H4	107 (5)	C9—C14—H14	119.7
V1—O4—H4	119 (6)	C13—C14—H14	119.7
C16—O5—V1	128.6 (4)	C12—C15—H15A	109.5
C2—C1—C6	119.8 (4)	C12—C15—H15B	109.5
C2—C1—C7	119.1 (4)	H15A—C15—H15B	109.5
C6—C1—C7	120.9 (4)	C12—C15—H15C	109.5
C3—C2—C1	120.4 (4)	H15A—C15—H15C	109.5
C3—C2—H2	119.8	H15B—C15—H15C	109.5
C1—C2—H2	119.8	O5—C16—H16A	109.5
C2—C3—C4	120.8 (5)	O5—C16—H16B	109.5
C2—C3—I1	120.1 (4)	H16A—C16—H16B	109.5
C4—C3—I1	119.0 (4)	O5—C16—H16C	109.5
C5—C4—C3	119.0 (5)	H16A—C16—H16C	109.5
C5—C4—H4A	120.5	H16B—C16—H16C	109.5
C3—C4—H4A	120.5	O4—C17—H17A	109.5
C4—C5—C6	122.2 (4)	O4—C17—H17B	109.5
C4—C5—I2	120.3 (4)	H17A—C17—H17B	109.5
C6—C5—I2	117.5 (3)	O4—C17—H17C	109.5
O2—C6—C5	120.1 (4)	H17A—C17—H17C	109.5
O2—C6—C1	122.1 (4)	H17B—C17—H17C	109.5
C5—C6—C1	117.7 (4)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
O4—H4···N2ⁱ	0.85 (4)	2.03 (5)	2.858 (5)	168 (8)

Symmetry code: (i) −x, −y, −z+1.

Experimental details

Crystal data
Chemical formula	[V(C₁₅H₁₀I₂N₂O₂)(CH₃O)O(CH₄O)]
M_r	634.07
Crystal system, space group	Triclinic, P1
Temperature (K)	298
a, b, c (Å)	7.890 (5), 10.030 (6), 13.628 (8)
α, β, γ (°)	81.857 (5), 84.777 (6), 85.286 (5)
V (Å³)	1060.5 (11)
Z	2
Radiation type	Mo Kα
µ (mm⁻¹)	3.41
Crystal size (mm)	0.17 × 0.13 × 0.12

Data collection
Diffractometer	Bruker SMART CCD area-detector diffractometer
Absorption correction	Multi-scan (SADABS; Sheldrick, 1996)
T_min, T_max	0.595, 0.685
No. of measured, independent and observed [I > 2σ(I)] reflections	7706, 4283, 3146
R_int	0.026
(sin θ/λ)_max (Å⁻¹)	0.628

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.041, 0.090, 1.02
No. of reflections	4283
No. of parameters	250
No. of restraints	1
H-atom treatment	H atoms treated by a mixture of independent and constrained refinement
Δρ_max, Δρ_min (e Å⁻³)	1.00, −1.01

Computer programs: SMART (Bruker, 1998), SAINT (Bruker, 1998), 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
O4—H4···N2ⁱ	0.85 (4)	2.03 (5)	2.858 (5)	168 (8)

Symmetry code: (i) −x, −y, −z+1.

Acknowledgements

This work was supported by Yichun University.

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