organic compounds\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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ISSN: 2056-9890

1-(4-Nitro­phen­yl)-1H-imidazol-3-ium chloride

aSchool of Chemistry & Physics, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa
*Correspondence e-mail: bala@ukzn.ac.za

(Received 19 October 2012; accepted 14 December 2012; online 19 December 2012)

In the title salt, C9H8N3O2+·Cl, the least-squares planes of the imidazolium and benzene rings are almost coplanar, making a dihedral angle of 4.59 (1)°. In the crystal, the chloride anion links the organic mol­ecules through N—H⋯Cl hydrogen bonds, forming chains that run diagonally across the bc face, which compliment strong C—H⋯O hydrogen bonds between neighbouring mol­ecules. These chains are connected to adjacent chains through two weak C—H⋯Cl inter­actions, resulting in hydrogen-bonded sheets extending along the b and c axes. The absolute structure of the title compound was determined using a Flack x parameter of 0.00 (6) and a Hooft y parameter of 0.03 (2).

Related literature

For the synthesis of the title compound, see: Gnanamgari et al. (2009[Gnanamgari, D., Sauer, E. L. O., Schley, N. D., Butler, C., Incarvito, C. D. & Crabtree, R. H. (2009). Organometallics, 28, 321-325.]); Coberan & Peris (2008[Coberan, R. & Peris, E. (2008). Organometallics, 27, 1954-1958.]); Singh et al., (2011[Singh, A. K., Kumar, P., Yadav, M. & Pandey, D. S. (2011). Bull. Chem. Soc. Jpn, 84, 205-210.]). For the structure of imidazole with a bond to phenyl via carbon, see: Gayathri et al. (2010[Gayathri, P., Thiruvalluvar, A., Srinivasan, N., Jayabharathi, J. & Butcher, R. J. (2010). Acta Cryst. E66, o2519.]). For structure of imidazole with a bond to phenyl via nitro­gen, see: Zheng et al. (2011[Zheng, Z., Geng, W.-Q., Wu, Z.-C. & Zhou, H.-P. (2011). Acta Cryst. E67, o524.]). For the structure of nitro­phenyl imidazole as a ligand in a complex, see: Singh et al. (2010[Singh, A. K., Kumar, P., Yadav, M. & Pandey, D. S. (2010). J. Organomet. Chem. 695, 567-573.], 2011[Singh, A. K., Kumar, P., Yadav, M. & Pandey, D. S. (2011). Bull. Chem. Soc. Jpn, 84, 205-210.]). For related structures, see: Ishihara et al. (1992[Ishihara, M., Tonogaki, M., Ohba, S., Saito, Y., Okazaki, M., Katoh, T. & Kamiyama, K. (1992). Acta Cryst. C48, 184-188.]); Scheele et al., (2007[Scheele, U. J., Meyer, F. & Dechert, S. (2007). Tetrahedron Lett. 48, 8366-8370.]). For our related work in this area, see: Ibrahim et al. (2012[Ibrahim, H., Bala, M. D. & Omondi, B. (2012). Acta Cryst. E68, o2305.]).

[Scheme 1]

Experimental

Crystal data
  • C9H8N3O2+·Cl

  • Mr = 225.64

  • Orthorhombic, P n a 21

  • a = 14.6042 (8) Å

  • b = 12.1781 (7) Å

  • c = 5.6070 (3) Å

  • V = 997.21 (10) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.37 mm−1

  • T = 173 K

  • 0.54 × 0.16 × 0.15 mm

Data collection
  • Bruker SMART APEXII CCD diffractometer

  • Absorption correction: multi-scan (SADABS; Bruker, 2008[Bruker (2008). APEX2, SAINT-Plus, XPREP and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA..]) Tmin = 0.524, Tmax = 0.746

  • 20153 measured reflections

  • 2217 independent reflections

  • 2120 reflections with I > 2σ(I)

  • Rint = 0.060

Refinement
  • R[F2 > 2σ(F2)] = 0.029

  • wR(F2) = 0.076

  • S = 1.09

  • 2217 reflections

  • 140 parameters

  • 8 restraints

  • H atoms treated by a mixture of independent and constrained refinement

  • Δρmax = 0.30 e Å−3

  • Δρmin = −0.22 e Å−3

  • Absolute structure: Flack (1983[Flack, H. D. (1983). Acta Cryst. A39, 876-881.]), Hooft et al. (2010[Hooft, R. W. W., Straver, L. H. & Spek, A. L. (2010). J. Appl. Cryst. 43, 665-668.]), Spek (2009[Spek, A. L. (2009). Acta Cryst. D65, 148-155.]); Hooft parameter = 0.03 (2), 856 Bijvoet pairs

  • Flack parameter: 0.00 (6)

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N1—H1⋯Cl1i 0.92 (2) 2.08 (2) 2.9976 (17) 178 (2)
C9—H9⋯Cl1 0.93 2.80 3.5898 (19) 144
C2—H2⋯Cl1ii 0.93 2.52 3.4286 (17) 166
C4—H4⋯O2i 0.93 2.29 3.181 (2) 161
Symmetry codes: (i) [-x+{\script{3\over 2}}, y+{\script{1\over 2}}, z-{\script{3\over 2}}]; (ii) [x-{\script{1\over 2}}, -y+{\script{1\over 2}}, z-1].

Data collection: APEX2 (Bruker, 2008[Bruker (2008). APEX2, SAINT-Plus, XPREP and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA..]); cell refinement: SAINT-Plus (Bruker, 2008[Bruker (2008). APEX2, SAINT-Plus, XPREP and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA..]); data reduction: SAINT-Plus and XPREP (Bruker, 2008[Bruker (2008). APEX2, SAINT-Plus, XPREP and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA..]); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); molecular graphics: ORTEP-3 (Farrugia, 2012[Farrugia, L. J. (2012). J. Appl. Cryst. 45, 849-854.]); software used to prepare material for publication: WinGX (Farrugia, 2012[Farrugia, L. J. (2012). J. Appl. Cryst. 45, 849-854.]).

Supporting information


Comment top

Since the isolation of the first stable free carbene, imidazolium based N-heterocyclic carbene ligands (NHC) ligands have recieved wide interest from researchers because substituted imidazolium salts are major precursors to the NHCs commonly employed in organometallic chemistry and catalysis for the stabilization of metal centers. Recently Gayathri et al., (2010) have reported structural analogues of the title compound with imidazole bond to phenyl via carbon, while Zheng et al., (2011) have reported the structure with imidazole bond to phenyl via nitrogen. For the structure of nitrophenyl imidazole as a ligand in a metal complex, see: (Singh et al., 2010 and 2011). Structures of related compounds were reported by Ishihara et al., (1992), Scheele et al., (2007) and Ibrahim et al., (2012). Hence, the title compound was obtained in an attempt to synthesize an imidazolium salt by the coupling of 2-chloromethylpyridine hydrochloride with p-nitrophenyl imidazole using the method reported by Gnanamgari et al., (2009). Coberan & Peris (2008) and Singh et al., (2011) have also reported synthesis of similar compounds. The grey solid obtained was recrystallized from methanol:ethyl acetate (1:1) solvent system. The planes of the imidazolium and phenyl rings in (I) are almost coplanar. Analysis of the absolute structure using likelihood methods (Hooft et al., 2010) was performed using PLATON (Spek, 2009). The Hooft y-parameter was determined to be 0.03 (2) which corroborated the Flack parameter x = 0.00 (6). These results in conjunction with a correlation coefficient of 0.997 for the Bijvoet normal probability plot indicate that the absolute structure is correctly assigned. In the title compound, C9H8N3O2.Cl, the L.S. planes of the imidazolium (N1—C4) and phenyl (C5—C10) rings are almost coplanar with a dihedral angle of 4.59 (1)°. In the crystal, the chloride atom links the organic molecules through N—H···Cl hydrogen bonds forming chains that run diagonally across the bc face which compliment strong intermolecular C—H···O hydrogen bonds between neighbouring molecules. These chains are connected to adjacent chains through two weak C—H···Cl interactions resulting in hydrogen bonded sheets extending along the b and c axes.

Related literature top

For the synthesis of the title compound, see: Gnanamgari et al. (2009); Coberan & Peris (2008); Singh et al., (2011). For the structure of imidazole with a bond to phenyl via carbon, see: Gayathri et al. (2010). For structure of imidazole with a bond to phenyl via nitrogen, see: Zheng et al. (2011). For the structure of nitrophenyl imidazole as a ligand in a complex, see: Singh et al. (2010, 2011). For related structures, see: Ishihara et al. (1992); Scheele et al., (2007). For our related work in this area, see: Ibrahim et al. (2012).

Experimental top

To a 150 ml round bottom flask containing DMSO (30 ml, MERCK) was added imidazole (0.01 mol, 0.68 g, Fluka AG) and KOH (0.015 mol, 0.84 g, MERCK) then stirred at room temperature for 2 h. This was followed by the dropwise addition of a solution of 1-chloro-4-nitrobenzene (Fluka, 0.01 mol, 1.57 g) in DMSO (5 ml), and refluxed at 100 °C for 24 h. The resulting solution was first chilled and then dilute with distilled water until neutral. The organic component was extracted using CH2Cl2/CHCl3 (1:1, 3 x 20 ml) and then dried with anhydrous MgSO4 and concetrated under vacuum yielding 2.081 g of pure (I). 1H NMR (400 MHz, CDCl3): 8.36(d; 2H) 7.96(s; 1H), 7.57(d; 2H) and 7.25(1H) p.p.m.. 13C NMR (400 MHz, CDCl3): 146.6, 142.3, 135.7, 132.04, 126.1, 121.4 and 117.9 p.p.m.. IR (ATR): 3112(=C—H), 2924(sp3 C—H), 1596(C=N), 1503 and 1370(aromatic NO2), 1049 (C—N medium) and 845 (p-subsituted benzene) cm-1.

Refinement top

Carbon-bound H-atoms were placed in calculated positions [C—H = 0.93 Å for aromatic H atoms; Uiso(H) = 1.2Ueq(C)] and were included in the refinement in the riding model. The nitrogen-bound H atom was located on a difference Fourier map and refined freely with isotropic parameters.

Computing details top

Data collection: APEX2 (Bruker, 2008); cell refinement: SAINT-Plus (Bruker, 2008); data reduction: SAINT-Plus and XPREP (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, 2012); software used to prepare material for publication: WinGX (Farrugia, 2012).

Figures top
[Figure 1] Fig. 1. ORTEP diagram of compound (I). Thermal ellipsoids are represented at the 50% probability level.
[Figure 2] Fig. 2. Packing diagram showing hydrogen bonding interactions in a crystal of (I) viewed along crystallographic c axis.
1-(4-Nitrophenyl)-1H-imidazol-3-ium chloride top
Crystal data top
C9H8N3O2+·ClF(000) = 464
Mr = 225.64Dx = 1.503 Mg m3
Orthorhombic, Pna21Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2c -2nCell parameters from 9896 reflections
a = 14.6042 (8) Åθ = 2.2–28.3°
b = 12.1781 (7) ŵ = 0.37 mm1
c = 5.6070 (3) ÅT = 173 K
V = 997.21 (10) Å3Block, colourless
Z = 40.54 × 0.16 × 0.15 mm
Data collection top
Bruker SMART APEXII CCD
diffractometer
2217 independent reflections
Radiation source: fine-focus sealed tube2120 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.060
ϕ and ω scansθmax = 28.3°, θmin = 2.2°
Absorption correction: multi-scan
(SADABS; Bruker, 2008)
h = 1719
Tmin = 0.524, Tmax = 0.746k = 1616
20153 measured reflectionsl = 76
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.029H atoms treated by a mixture of independent and constrained refinement
wR(F2) = 0.076 w = 1/[σ2(Fo2) + (0.0354P)2 + 0.3302P]
where P = (Fo2 + 2Fc2)/3
S = 1.09(Δ/σ)max < 0.001
2217 reflectionsΔρmax = 0.30 e Å3
140 parametersΔρmin = 0.22 e Å3
8 restraintsAbsolute structure: Flack (1983), Hooft et al. (2010) and Spek (2009); Hooft parameter = 0.03(2), 856 Bijvoet pairs
Primary atom site location: structure-invariant direct methodsAbsolute structure parameter: 0.00 (6)
Crystal data top
C9H8N3O2+·ClV = 997.21 (10) Å3
Mr = 225.64Z = 4
Orthorhombic, Pna21Mo Kα radiation
a = 14.6042 (8) ŵ = 0.37 mm1
b = 12.1781 (7) ÅT = 173 K
c = 5.6070 (3) Å0.54 × 0.16 × 0.15 mm
Data collection top
Bruker SMART APEXII CCD
diffractometer
2217 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2008)
2120 reflections with I > 2σ(I)
Tmin = 0.524, Tmax = 0.746Rint = 0.060
20153 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.029H atoms treated by a mixture of independent and constrained refinement
wR(F2) = 0.076Δρmax = 0.30 e Å3
S = 1.09Δρmin = 0.22 e Å3
2217 reflectionsAbsolute structure: Flack (1983), Hooft et al. (2010) and Spek (2009); Hooft parameter = 0.03(2), 856 Bijvoet pairs
140 parametersAbsolute structure parameter: 0.00 (6)
8 restraints
Special details top

Experimental. Carbon-bound H-atoms were placed in calculated positions [C—H = 0.93 Å for aromatic H atoms; Uiso(H) = 1.2Ueq(C)] and were included in the refinement in the riding model. The nitrogen-bound H atom was located on a difference Fourier map and refined freely with isotropic parameters.

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
xyzUiso*/Ueq
C20.61881 (11)0.39839 (13)0.1020 (3)0.0241 (5)
H20.55560.40680.09180.029*
C40.76184 (13)0.41464 (15)0.2179 (4)0.0308 (5)
H40.81310.43680.30390.037*
C30.76136 (12)0.34674 (15)0.0291 (4)0.0303 (4)
H30.81200.31320.04020.036*
N30.54484 (10)0.08365 (11)0.8199 (3)0.0274 (3)
N20.67050 (9)0.33611 (11)0.0429 (3)0.0210 (3)
N10.67229 (10)0.44554 (12)0.2608 (3)0.0251 (3)
O10.46671 (9)0.09724 (10)0.8910 (3)0.0323 (4)
O20.59895 (10)0.01721 (12)0.9069 (3)0.0406 (4)
H10.6548 (14)0.4898 (17)0.386 (4)0.030 (5)*
Cl10.88518 (2)0.09410 (3)0.84010 (10)0.02647 (12)
C80.57713 (11)0.14961 (13)0.6161 (3)0.0217 (3)
C90.66889 (12)0.14545 (14)0.5571 (4)0.0303 (4)
H90.70930.10220.64430.036*
C100.69939 (11)0.20704 (13)0.3655 (4)0.0300 (4)
H100.76080.20480.32160.036*
C50.63843 (11)0.27213 (12)0.2387 (3)0.0204 (3)
C60.54623 (11)0.27679 (13)0.3038 (4)0.0264 (4)
H60.50580.32120.21960.032*
C70.51553 (11)0.21484 (13)0.4943 (4)0.0260 (4)
H70.45430.21700.53970.031*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
C20.0202 (8)0.0223 (7)0.0297 (13)0.0005 (6)0.0001 (7)0.0027 (7)
C40.0233 (9)0.0369 (9)0.0323 (13)0.0006 (7)0.0030 (8)0.0051 (8)
C30.0172 (8)0.0356 (10)0.0380 (12)0.0008 (7)0.0036 (8)0.0068 (8)
N30.0293 (7)0.0286 (6)0.0242 (9)0.0071 (5)0.0034 (8)0.0010 (6)
N20.0173 (6)0.0196 (6)0.0262 (8)0.0004 (5)0.0005 (6)0.0007 (6)
N10.0247 (7)0.0232 (6)0.0274 (8)0.0002 (5)0.0003 (6)0.0013 (6)
O10.0286 (7)0.0373 (6)0.0311 (9)0.0060 (5)0.0047 (6)0.0014 (6)
O20.0347 (7)0.0438 (8)0.0432 (10)0.0032 (6)0.0100 (6)0.0205 (7)
Cl10.01823 (18)0.02836 (18)0.0328 (2)0.00189 (13)0.00026 (19)0.0061 (2)
C80.0231 (8)0.0202 (7)0.0219 (9)0.0046 (6)0.0016 (7)0.0000 (6)
C90.0231 (8)0.0295 (9)0.0382 (12)0.0013 (7)0.0040 (8)0.0089 (8)
C100.0161 (7)0.0326 (8)0.0415 (12)0.0018 (6)0.0002 (8)0.0085 (9)
C50.0210 (8)0.0190 (6)0.0214 (8)0.0021 (6)0.0001 (6)0.0009 (6)
C60.0202 (7)0.0256 (7)0.0333 (12)0.0044 (6)0.0007 (8)0.0034 (7)
C70.0196 (8)0.0278 (8)0.0307 (10)0.0016 (6)0.0022 (7)0.0005 (7)
Geometric parameters (Å, º) top
C2—N11.316 (2)N1—H10.92 (2)
C2—N21.343 (2)C8—C71.381 (2)
C2—H20.9300C8—C91.381 (2)
C4—C31.343 (3)C9—C101.384 (3)
C4—N11.382 (2)C9—H90.9300
C4—H40.9300C10—C51.388 (2)
C3—N21.393 (2)C10—H100.9300
C3—H30.9300C5—C61.396 (2)
N3—O11.220 (2)C6—C71.382 (3)
N3—O21.232 (2)C6—H60.9300
N3—C81.474 (2)C7—H70.9300
N2—C51.425 (2)
N1—C2—N2108.78 (15)C7—C8—C9122.31 (17)
N1—C2—H2125.6C7—C8—N3119.25 (15)
N2—C2—H2125.6C9—C8—N3118.43 (16)
C3—C4—N1107.45 (16)C8—C9—C10118.58 (16)
C3—C4—H4126.3C8—C9—H9120.7
N1—C4—H4126.3C10—C9—H9120.7
C4—C3—N2106.90 (16)C9—C10—C5120.04 (15)
C4—C3—H3126.5C9—C10—H10120.0
N2—C3—H3126.5C5—C10—H10120.0
O1—N3—O2124.04 (17)C10—C5—C6120.53 (17)
O1—N3—C8118.59 (14)C10—C5—N2119.73 (15)
O2—N3—C8117.37 (15)C6—C5—N2119.73 (15)
C2—N2—C3107.90 (15)C7—C6—C5119.50 (15)
C2—N2—C5126.14 (14)C7—C6—H6120.2
C3—N2—C5125.95 (15)C5—C6—H6120.2
C2—N1—C4108.96 (16)C8—C7—C6119.02 (16)
C2—N1—H1127.3 (13)C8—C7—H7120.5
C4—N1—H1123.7 (13)C6—C7—H7120.5
N1—C4—C3—N20.1 (2)C8—C9—C10—C50.7 (3)
N1—C2—N2—C30.8 (2)C9—C10—C5—C60.4 (3)
N1—C2—N2—C5179.69 (15)C9—C10—C5—N2179.43 (17)
C4—C3—N2—C20.6 (2)C2—N2—C5—C10176.61 (17)
C4—C3—N2—C5179.45 (15)C3—N2—C5—C104.7 (3)
N2—C2—N1—C40.7 (2)C2—N2—C5—C64.4 (3)
C3—C4—N1—C20.4 (2)C3—N2—C5—C6174.27 (17)
O1—N3—C8—C77.6 (2)C10—C5—C6—C70.8 (3)
O2—N3—C8—C7171.90 (17)N2—C5—C6—C7179.81 (15)
O1—N3—C8—C9171.10 (16)C9—C8—C7—C61.1 (3)
O2—N3—C8—C99.4 (2)N3—C8—C7—C6179.81 (16)
C7—C8—C9—C101.5 (3)C5—C6—C7—C80.0 (3)
N3—C8—C9—C10179.81 (16)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1···Cl1i0.92 (2)2.08 (2)2.9976 (17)178 (2)
C9—H9···Cl10.932.803.5898 (19)144
C2—H2···Cl1ii0.932.523.4286 (17)166
C4—H4···O2i0.932.293.181 (2)161
Symmetry codes: (i) x+3/2, y+1/2, z3/2; (ii) x1/2, y+1/2, z1.

Experimental details

Crystal data
Chemical formulaC9H8N3O2+·Cl
Mr225.64
Crystal system, space groupOrthorhombic, Pna21
Temperature (K)173
a, b, c (Å)14.6042 (8), 12.1781 (7), 5.6070 (3)
V3)997.21 (10)
Z4
Radiation typeMo Kα
µ (mm1)0.37
Crystal size (mm)0.54 × 0.16 × 0.15
Data collection
DiffractometerBruker SMART APEXII CCD
diffractometer
Absorption correctionMulti-scan
(SADABS; Bruker, 2008)
Tmin, Tmax0.524, 0.746
No. of measured, independent and
observed [I > 2σ(I)] reflections
20153, 2217, 2120
Rint0.060
(sin θ/λ)max1)0.668
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.029, 0.076, 1.09
No. of reflections2217
No. of parameters140
No. of restraints8
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.30, 0.22
Absolute structureFlack (1983), Hooft et al. (2010) and Spek (2009); Hooft parameter = 0.03(2), 856 Bijvoet pairs
Absolute structure parameter0.00 (6)

Computer programs: APEX2 (Bruker, 2008), SAINT-Plus (Bruker, 2008), SAINT-Plus and XPREP (Bruker, 2008), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 (Farrugia, 2012), WinGX (Farrugia, 2012).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1···Cl1i0.92 (2)2.08 (2)2.9976 (17)178 (2)
C9—H9···Cl10.932.803.5898 (19)144.1
C2—H2···Cl1ii0.932.523.4286 (17)166.1
C4—H4···O2i0.932.293.181 (2)160.6
Symmetry codes: (i) x+3/2, y+1/2, z3/2; (ii) x1/2, y+1/2, z1.
 

Acknowledgements

We thank the NRF and the University of KwaZulu-Natal for financial support.

References

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