4-Amino­pyridinium picrate

Ramesh, P.; Akalya, R.; Chandramohan, A.; Ponnuswamy, M.N.

doi:10.1107/S1600536810011050

organic compounds

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Volume 66| Part 4| April 2010| Page o1000

doi:10.1107/S1600536810011050

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4-Aminopyridinium picrate

P. Ramesh,^a R. Akalya,^b A. Chandramohan ^b and M. N. Ponnuswamy ^a ^*

^aCentre of Advanced Study in Crystallography and Biophysics, University of Madras, Guindy Campus, Chennai 600 025, India, and ^bDepartment of Chemistry, Sri Ramakrishna Mission Vidyalaya Arts and Science College, Coimbatore 641 020, India
^*Correspondence e-mail: mnpsy2004@yahoo.com

(Received 12 March 2010; accepted 24 March 2010; online 31 March 2010)

In the title compound, C₅H₇N₂⁺·C₆H₂N₃O₇⁻, the 4-aminopyridinium cation is essentially planar (r.m.s. deviation = 0.002 Å). The three nitro groups in the picrate anion are twisted away from the attached benzene ring [dihedral angles = 24.1 (1), 9.3 (3) and 21.4 (1)°]. In the crystal structure, the ions are linked into a three-dimensional network by N—H⋯O and C—H⋯O hydrogen bonds.

Related literature

For general background to picrate complexes, see: In et al. (1997 ); Zaderenko et al. (1997 ); Ashwell et al. (1995 ); Owen & White (1976 ); Shakir et al. (2009 ).

Experimental

Crystal data

C₅H₇N₂⁺·C₆H₂N₃O₇⁻
M_r = 323.23
Monoclinic, P 2₁ /c
a = 8.5056 (7) Å
b = 11.3338 (9) Å
c = 14.3307 (11) Å
β = 104.162 (5)°
V = 1339.50 (18) Å³
Z = 4
Mo Kα radiation
μ = 0.14 mm⁻¹
T = 293 K
0.22 × 0.19 × 0.16 mm

Data collection

Bruker SMART APEXII area-detector diffractometer
Absorption correction: multi-scan (SADABS; Bruker, 2008 ) T_min = 0.970, T_max = 0.978
12562 measured reflections
3311 independent reflections
2637 reflections with I > 2σ(I)
R_int = 0.026

Refinement

R[F² > 2σ(F²)] = 0.039
wR(F²) = 0.108
S = 1.05
3311 reflections
221 parameters
H atoms treated by a mixture of independent and constrained refinement
Δρ_max = 0.24 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—H1⋯O1ⁱ	0.91 (2)	1.82 (2)	2.6877 (16)	158 (2)
N1—H1⋯O7ⁱ	0.91 (2)	2.34 (2)	2.9359 (19)	122 (2)
N7—H7A⋯O6ⁱⁱ	0.88 (2)	2.30 (3)	3.139 (2)	160 (2)
N7—H7B⋯O5ⁱⁱⁱ	0.88 (2)	2.23 (2)	3.065 (2)	158 (2)
C2—H2⋯O4^iv	0.93	2.47	3.1373 (19)	129
C2—H2⋯O7ⁱ	0.93	2.43	2.9980 (19)	119
Symmetry codes: (i) -x+1, -y, -z; (ii) $[x, -y+{\script{1\over 2}}, z+{\script{1\over 2}}]$ ; (iii) -x+2, -y+1, -z; (iv) $[-x+2, y-{\script{1\over 2}}, -z+{\script{1\over 2}}]$ .

Data collection: APEX2 (Bruker, 2008); cell refinement: SAINT (Bruker, 2008); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 ); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 (Farrugia, 1997 ); software used to prepare material for publication: SHELXL97 and PLATON (Spek, 2009 ).

Supporting information

Crystal structure: contains datablocks global, I. DOI: 10.1107/S1600536810011050/ci5057sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536810011050/ci5057Isup2.hkl

checkCIF report

Comment top

It is well known that picric acid forms charge transfer molecular complexes with a number of aromatic compounds such as aromatic hydrocarbons and amines through electrostatic or hydrogen bonding interactions (In et al., 1997; Zaderenko et al., 1997). The bonding of donor-acceptor picric acid complexes strongly depends on the nature of partners. Some of the picric acid complexes crystallize in centrosymmetric space group though they possess non-linear optical (NLO) properties (Shakir et al., 2009). This is due to the aggregation of the donor and acceptor molecules in a non-centrosymmetric manner which contribute to the bulk susceptibility from intermolecular charge transfer process (Ashwell et al., 1995; Owen & White, 1976).

The 4-aminopyridinium cation is essentially planar (r.m.s. deviation 0.002 Å). In the picrate anion, as a result of deprotanation the C8—O1 distance [1.2392 (16) Å] shows a partial double bond character, and the C8—C9 [1.4568 (17) Å] and C8—C13 [1.4562 (17) Å] distances are longer compared to other aromatic C—C distances. The three nitro groups are twisted out of the attached benzene ring by 24.1 (1)° [N14/O2/O3], 9.3 (3)° [N15/O4/O5] and 21.4 (1)° [N16/O6/O7], which facilitate the interactions between the neighbouring molecules.

The ions are linked through N—H···O and C—H···O hydrogen bonds to form a three-dimensional network as shown in Fig. 2.

Related literature top

For general background to picrate complexes, see: In et al. (1997); Zaderenko et al. (1997); Ashwell et al. (1995); Owen & White (1976); Shakir et al. (2009).

Experimental top

Equimolar solutions of 4-aminopyridine in methanol and picric acid in methanol were mixed together. The solution was stirred well for 1 h and the precipited salt was filtered off. The salt was repeatedly recrystallised from methanol to get single crystals suitable for X-ray analysis.

Computing details top

Data collection: APEX2 (Bruker, 2008); cell refinement: SAINT (Bruker, 2008); data reduction: SAINT (Bruker, 2008); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 (Farrugia, 1997); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008) and PLATON (Spek, 2009).

Figures top

	Fig. 1. The asymmetric unit of the title compound. Displacement ellipsoids are drawn at the 50% probability level.
	Fig. 2. Crystal packing of the title compound. H atoms not involved in hydrogen bonding (dashed lines) have been omitted for clarity.

4-Aminopyridinium picrate top

Crystal data top

C₅H₇N₂⁺·C₆H₂N₃O₇⁻	F(000) = 664
M_r = 323.23	D_x = 1.603 Mg m⁻³
Monoclinic, P2₁/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybc	Cell parameters from 1853 reflections
a = 8.5056 (7) Å	θ = 2.3–28.4°
b = 11.3338 (9) Å	µ = 0.14 mm⁻¹
c = 14.3307 (11) Å	T = 293 K
β = 104.162 (5)°	Block, colourless
V = 1339.50 (18) Å³	0.22 × 0.19 × 0.16 mm
Z = 4

Data collection top

Bruker SMART APEXII area-detector diffractometer	3311 independent reflections
Radiation source: fine-focus sealed tube	2637 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.026
ω and ϕ scans	θ_max = 28.4°, θ_min = 2.3°
Absorption correction: multi-scan (SADABS; Bruker, 2008)	h = −11→11
T_min = 0.970, T_max = 0.978	k = −15→14
12562 measured reflections	l = −18→19

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)] = 0.039	H atoms treated by a mixture of independent and constrained refinement
wR(F²) = 0.108	w = 1/[σ²(F_o²) + (0.0464P)² + 0.3813P] where P = (F_o² + 2F_c²)/3
S = 1.05	(Δ/σ)_max = 0.001
3311 reflections	Δρ_max = 0.24 e Å⁻³
221 parameters	Δρ_min = −0.18 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: 0.022 (2)

Crystal data top

C₅H₇N₂⁺·C₆H₂N₃O₇⁻	V = 1339.50 (18) Å³
M_r = 323.23	Z = 4
Monoclinic, P2₁/c	Mo Kα radiation
a = 8.5056 (7) Å	µ = 0.14 mm⁻¹
b = 11.3338 (9) Å	T = 293 K
c = 14.3307 (11) Å	0.22 × 0.19 × 0.16 mm
β = 104.162 (5)°

Data collection top

Bruker SMART APEXII area-detector diffractometer	3311 independent reflections
Absorption correction: multi-scan (SADABS; Bruker, 2008)	2637 reflections with I > 2σ(I)
T_min = 0.970, T_max = 0.978	R_int = 0.026
12562 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.039	0 restraints
wR(F²) = 0.108	H atoms treated by a mixture of independent and constrained refinement
S = 1.05	Δρ_max = 0.24 e Å⁻³
3311 reflections	Δρ_min = −0.18 e Å⁻³
221 parameters

Special details top

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 > 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
O1	0.87969 (13)	0.03133 (9)	0.06515 (7)	0.0445 (3)
O2	0.97300 (19)	0.02415 (13)	0.25752 (9)	0.0734 (4)
O3	1.20628 (16)	0.09976 (12)	0.31608 (8)	0.0632 (4)
O4	1.35225 (16)	0.45326 (12)	0.18781 (9)	0.0664 (4)
O5	1.23283 (19)	0.50978 (11)	0.04473 (10)	0.0700 (4)
O6	0.92217 (17)	0.22433 (12)	−0.16703 (7)	0.0654 (4)
O7	0.76429 (15)	0.11110 (13)	−0.11519 (8)	0.0686 (4)
N1	0.37289 (15)	0.09339 (12)	0.03722 (9)	0.0441 (3)
H1	0.293 (2)	0.0390 (18)	0.0159 (15)	0.068 (6)*
C2	0.46638 (18)	0.09158 (14)	0.12753 (11)	0.0463 (4)
H2	0.4515	0.0322	0.1694	0.056*
C3	0.58135 (18)	0.17420 (14)	0.15875 (11)	0.0458 (4)
H3	0.6451	0.1710	0.2215	0.055*
C4	0.60534 (17)	0.26532 (13)	0.09690 (10)	0.0396 (3)
C5	0.50530 (19)	0.26449 (15)	0.00273 (11)	0.0481 (4)
H5	0.5164	0.3226	−0.0410	0.058*
C6	0.39262 (19)	0.17818 (15)	−0.02361 (11)	0.0496 (4)
H6	0.3271	0.1781	−0.0859	0.060*
N7	0.71790 (19)	0.34716 (14)	0.12736 (12)	0.0543 (4)
H7A	0.774 (3)	0.347 (2)	0.1874 (18)	0.083 (7)*
H7B	0.721 (3)	0.404 (2)	0.0858 (16)	0.072 (6)*
C8	0.96034 (15)	0.12354 (11)	0.07454 (9)	0.0325 (3)
C9	1.06752 (16)	0.16121 (11)	0.16521 (9)	0.0338 (3)
C10	1.15984 (17)	0.26074 (12)	0.17653 (9)	0.0364 (3)
H10	1.2267	0.2793	0.2364	0.044*
C11	1.15372 (17)	0.33411 (11)	0.09862 (9)	0.0356 (3)
C12	1.05870 (16)	0.30622 (11)	0.00840 (9)	0.0346 (3)
H12	1.0567	0.3554	−0.0438	0.041*
C13	0.96746 (15)	0.20496 (11)	−0.00293 (8)	0.0327 (3)
N14	1.08227 (17)	0.08920 (11)	0.25121 (8)	0.0442 (3)
N15	1.25248 (16)	0.43901 (11)	0.11136 (9)	0.0455 (3)
N16	0.87848 (15)	0.17853 (11)	−0.10042 (8)	0.0400 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O1	0.0511 (6)	0.0403 (6)	0.0398 (5)	−0.0122 (5)	0.0065 (4)	0.0028 (4)
O2	0.1011 (11)	0.0720 (9)	0.0468 (7)	−0.0287 (8)	0.0177 (7)	0.0152 (6)
O3	0.0769 (8)	0.0652 (8)	0.0380 (6)	0.0098 (6)	−0.0041 (6)	0.0119 (5)
O4	0.0691 (8)	0.0613 (8)	0.0600 (7)	−0.0231 (6)	−0.0010 (6)	−0.0163 (6)
O5	0.1005 (11)	0.0484 (7)	0.0610 (8)	−0.0287 (7)	0.0195 (7)	0.0038 (6)
O6	0.0881 (9)	0.0751 (8)	0.0285 (5)	−0.0328 (7)	0.0058 (5)	0.0052 (5)
O7	0.0656 (8)	0.0859 (9)	0.0437 (6)	−0.0384 (7)	−0.0070 (5)	0.0073 (6)
N1	0.0392 (6)	0.0432 (7)	0.0462 (7)	−0.0040 (6)	0.0036 (5)	−0.0038 (5)
C2	0.0447 (8)	0.0427 (8)	0.0476 (8)	−0.0033 (7)	0.0037 (6)	0.0092 (6)
C3	0.0437 (8)	0.0485 (9)	0.0393 (7)	−0.0047 (7)	−0.0010 (6)	0.0064 (6)
C4	0.0370 (7)	0.0388 (7)	0.0434 (7)	0.0002 (6)	0.0103 (6)	−0.0004 (6)
C5	0.0498 (8)	0.0520 (9)	0.0413 (8)	−0.0002 (7)	0.0090 (6)	0.0107 (7)
C6	0.0475 (8)	0.0611 (10)	0.0363 (7)	0.0000 (7)	0.0025 (6)	0.0014 (7)
N7	0.0582 (9)	0.0496 (8)	0.0526 (8)	−0.0150 (7)	0.0087 (7)	0.0019 (7)
C8	0.0353 (6)	0.0326 (6)	0.0303 (6)	0.0013 (5)	0.0090 (5)	−0.0008 (5)
C9	0.0420 (7)	0.0331 (6)	0.0267 (6)	0.0048 (5)	0.0094 (5)	0.0013 (5)
C10	0.0440 (7)	0.0366 (7)	0.0266 (6)	0.0026 (6)	0.0046 (5)	−0.0065 (5)
C11	0.0424 (7)	0.0304 (6)	0.0344 (6)	−0.0039 (5)	0.0103 (5)	−0.0060 (5)
C12	0.0431 (7)	0.0317 (6)	0.0296 (6)	−0.0004 (5)	0.0102 (5)	0.0006 (5)
C13	0.0366 (7)	0.0342 (6)	0.0260 (6)	−0.0004 (5)	0.0053 (5)	−0.0006 (5)
N14	0.0647 (8)	0.0376 (6)	0.0309 (6)	0.0053 (6)	0.0130 (5)	0.0027 (5)
N15	0.0547 (7)	0.0380 (6)	0.0451 (7)	−0.0098 (6)	0.0147 (6)	−0.0108 (5)
N16	0.0461 (7)	0.0396 (6)	0.0306 (5)	−0.0053 (5)	0.0021 (5)	0.0023 (5)

Geometric parameters (Å, º) top

O1—C8	1.2392 (16)	C5—C6	1.357 (2)
O2—N14	1.2069 (18)	C5—H5	0.93
O3—N14	1.2293 (17)	C6—H6	0.93
O4—N15	1.2214 (17)	N7—H7A	0.88 (2)
O5—N15	1.2267 (18)	N7—H7B	0.88 (2)
O6—N16	1.2216 (15)	C8—C13	1.4562 (17)
O7—N16	1.2130 (16)	C8—C9	1.4568 (17)
N1—C6	1.335 (2)	C9—C10	1.3613 (19)
N1—C2	1.3432 (19)	C9—N14	1.4578 (17)
N1—H1	0.91 (2)	C10—C11	1.3829 (19)
C2—C3	1.349 (2)	C10—H10	0.93
C2—H2	0.93	C11—C12	1.3832 (18)
C3—C4	1.408 (2)	C11—N15	1.4413 (17)
C3—H3	0.93	C12—C13	1.3726 (18)
C4—N7	1.328 (2)	C12—H12	0.93
C4—C5	1.408 (2)	C13—N16	1.4481 (16)

C6—N1—C2	120.05 (13)	C10—C9—C8	124.47 (11)
C6—N1—H1	118.0 (13)	C10—C9—N14	115.81 (12)
C2—N1—H1	121.9 (13)	C8—C9—N14	119.71 (12)
N1—C2—C3	121.28 (14)	C9—C10—C11	119.70 (12)
N1—C2—H2	119.4	C9—C10—H10	120.1
C3—C2—H2	119.4	C11—C10—H10	120.1
C2—C3—C4	120.36 (14)	C10—C11—C12	121.01 (12)
C2—C3—H3	119.8	C10—C11—N15	119.22 (12)
C4—C3—H3	119.8	C12—C11—N15	119.74 (12)
N7—C4—C3	120.62 (14)	C13—C12—C11	119.06 (12)
N7—C4—C5	122.52 (15)	C13—C12—H12	120.5
C3—C4—C5	116.85 (13)	C11—C12—H12	120.5
C6—C5—C4	119.43 (14)	C12—C13—N16	115.72 (11)
C6—C5—H5	120.3	C12—C13—C8	124.57 (11)
C4—C5—H5	120.3	N16—C13—C8	119.67 (11)
N1—C6—C5	122.02 (14)	O2—N14—O3	122.46 (13)
N1—C6—H6	119.0	O2—N14—C9	119.79 (13)
C5—C6—H6	119.0	O3—N14—C9	117.73 (13)
C4—N7—H7A	119.8 (16)	O4—N15—O5	122.97 (14)
C4—N7—H7B	115.0 (14)	O4—N15—C11	118.57 (13)
H7A—N7—H7B	125 (2)	O5—N15—C11	118.46 (13)
O1—C8—C13	125.23 (12)	O7—N16—O6	121.00 (12)
O1—C8—C9	123.57 (12)	O7—N16—C13	120.38 (11)
C13—C8—C9	111.14 (11)	O6—N16—C13	118.61 (11)

C6—N1—C2—C3	−0.1 (2)	C11—C12—C13—N16	−176.65 (12)
N1—C2—C3—C4	0.4 (2)	C11—C12—C13—C8	1.1 (2)
C2—C3—C4—N7	179.73 (16)	O1—C8—C13—C12	−179.30 (13)
C2—C3—C4—C5	−0.4 (2)	C9—C8—C13—C12	−2.13 (18)
N7—C4—C5—C6	−179.98 (16)	O1—C8—C13—N16	−1.6 (2)
C3—C4—C5—C6	0.2 (2)	C9—C8—C13—N16	175.54 (11)
C2—N1—C6—C5	−0.2 (2)	C10—C9—N14—O2	155.92 (14)
C4—C5—C6—N1	0.1 (2)	C8—C9—N14—O2	−24.9 (2)
O1—C8—C9—C10	178.44 (13)	C10—C9—N14—O3	−22.44 (18)
C13—C8—C9—C10	1.22 (18)	C8—C9—N14—O3	156.74 (13)
O1—C8—C9—N14	−0.7 (2)	C10—C11—N15—O4	8.1 (2)
C13—C8—C9—N14	−177.89 (11)	C12—C11—N15—O4	−169.71 (13)
C8—C9—C10—C11	0.7 (2)	C10—C11—N15—O5	−172.10 (14)
N14—C9—C10—C11	179.83 (12)	C12—C11—N15—O5	10.1 (2)
C9—C10—C11—C12	−1.9 (2)	C12—C13—N16—O7	−160.64 (14)
C9—C10—C11—N15	−179.76 (12)	C8—C13—N16—O7	21.5 (2)
C10—C11—C12—C13	1.1 (2)	C12—C13—N16—O6	20.26 (19)
N15—C11—C12—C13	178.88 (12)	C8—C13—N16—O6	−157.61 (14)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1···O1ⁱ	0.91 (2)	1.82 (2)	2.6877 (16)	158 (2)
N1—H1···O7ⁱ	0.91 (2)	2.34 (2)	2.9359 (19)	122 (2)
N7—H7A···O6ⁱⁱ	0.88 (2)	2.30 (3)	3.139 (2)	160 (2)
N7—H7B···O5ⁱⁱⁱ	0.88 (2)	2.23 (2)	3.065 (2)	158 (2)
C2—H2···O4^iv	0.93	2.47	3.1373 (19)	129
C2—H2···O7ⁱ	0.93	2.43	2.9980 (19)	119

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

Experimental details

Crystal data
Chemical formula	C₅H₇N₂⁺·C₆H₂N₃O₇⁻
M_r	323.23
Crystal system, space group	Monoclinic, P2₁/c
Temperature (K)	293
a, b, c (Å)	8.5056 (7), 11.3338 (9), 14.3307 (11)
β (°)	104.162 (5)
V (Å³)	1339.50 (18)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	0.14
Crystal size (mm)	0.22 × 0.19 × 0.16

Data collection
Diffractometer	Bruker SMART APEXII area-detector diffractometer
Absorption correction	Multi-scan (SADABS; Bruker, 2008)
T_min, T_max	0.970, 0.978
No. of measured, independent and observed [I > 2σ(I)] reflections	12562, 3311, 2637
R_int	0.026
(sin θ/λ)_max (Å⁻¹)	0.669

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.039, 0.108, 1.05
No. of reflections	3311
No. of parameters	221
H-atom treatment	H atoms treated by a mixture of independent and constrained refinement
Δρ_max, Δρ_min (e Å⁻³)	0.24, −0.18

Computer programs: APEX2 (Bruker, 2008), SAINT (Bruker, 2008), SHELXS97 (Sheldrick, 2008), ORTEP-3 (Farrugia, 1997), SHELXL97 (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—H1···O1ⁱ	0.91 (2)	1.82 (2)	2.6877 (16)	158 (2)
N1—H1···O7ⁱ	0.91 (2)	2.34 (2)	2.9359 (19)	122 (2)
N7—H7A···O6ⁱⁱ	0.88 (2)	2.30 (3)	3.139 (2)	160 (2)
N7—H7B···O5ⁱⁱⁱ	0.88 (2)	2.23 (2)	3.065 (2)	158 (2)
C2—H2···O4^iv	0.93	2.47	3.1373 (19)	129
C2—H2···O7ⁱ	0.93	2.43	2.9980 (19)	119

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

Acknowledgements

The authors wish to thank TBI Consultancy, University of Madras, for the data collection.

References

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