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Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890
Volume 68| Part 5| May 2012| Page o1488

Cyano­methyl 4-(4-methyl­benzene­sulfonamido)­benzoate

aDepartment of Chemistry, GC University, Lahore 54000, Pakistan, and bDepartment of Physics, Faculty of Sciences, Erciyes University, 38039 Kayseri, Turkey
*Correspondence e-mail: gmustafa884@yahoo.com, akkurt@erciyes.edu.tr

(Received 10 April 2012; accepted 18 April 2012; online 21 April 2012)

The title mol­ecule, C16H14N2O4S, adopts an L-shaped conformation, with the central C—S—N—C torsion angle being −69.1 (3)°. The two benzene rings form a dihedral angle of 89.94 (15)°. The mol­ecular conformation may be influenced by a weak intra­molecular C—H⋯O hydrogen bond which generates an S(6) ring motif. In the crystal, mol­ecules are linked by N—H⋯O and weak C—H⋯O hydrogen bonds, forming chains propagating along the b axis. Weak C—H⋯N hydrogen bonds connect the chains into a two-dimensional network parallel to (011). The crystal studied was an inversion twin, the ratio of components being 0.7 (1):0.3 (1).

Related literature

For related structures, see: Mustafa et al. (2010[Mustafa, G., Akkurt, M., Khan, I. U., Naseem, R. & Sajjad, B. (2010). Acta Cryst. E66, o1768.], 2011[Mustafa, G., Khan, I. U., Zia-ur-Rehman, M., Sharif, S. & Arshad, M. N. (2011). Acta Cryst. E67, o1018.], 2012a[Mustafa, G., Khan, I. U., Khan, F. M. & Akkurt, M. (2012a). Acta Cryst. E68, o1305.],b[Mustafa, G., Muhmood, T., Khan, I. U. & Akkurt, M. (2012b). Acta Cryst. E68, o1388.]); Khan et al. (2011[Khan, I. U., Mustafa, G. & Akkurt, M. (2011). Acta Cryst. E67, o1857.]). For standard bond-length data, see: Allen et al. (1987[Allen, F. H., Kennard, O., Watson, D. G., Brammer, L., Orpen, A. G. & Taylor, R. (1987). J. Chem. Soc. Perkin Trans. 2, pp. S1-19.]). For hydrogen bond motifs, see: Bernstein et al. (1995[Bernstein, J., Davis, R. E., Shimoni, L. & Chang, N.-L. (1995). Angew. Chem. Int. Ed. Engl. 34, 1555-1573.]).

[Scheme 1]

Experimental

Crystal data
  • C16H14N2O4S

  • Mr = 330.36

  • Monoclinic, P 21

  • a = 5.9360 (3) Å

  • b = 8.1992 (4) Å

  • c = 15.9068 (8) Å

  • β = 91.222 (3)°

  • V = 774.02 (7) Å3

  • Z = 2

  • Mo Kα radiation

  • μ = 0.23 mm−1

  • T = 296 K

  • 0.28 × 0.23 × 0.19 mm

Data collection
  • Bruker APEXII CCD diffractometer

  • 6266 measured reflections

  • 3077 independent reflections

  • 2306 reflections with I > 2σ(I)

  • Rint = 0.027

Refinement
  • R[F2 > 2σ(F2)] = 0.046

  • wR(F2) = 0.106

  • S = 1.01

  • 3077 reflections

  • 210 parameters

  • 1 restraint

  • H-atom parameters constrained

  • Δρmax = 0.20 e Å−3

  • Δρmin = −0.25 e Å−3

  • Absolute structure: Flack (1983[Flack, H. D. (1983). Acta Cryst. A39, 876-881.]), 1248 Freidel pairs

  • Flack parameter: 0.30 (10)

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N1—H1⋯O3i 0.86 2.21 2.904 (3) 138
C1—H1A⋯O2ii 0.96 2.58 3.446 (5) 150
C9—H9⋯O2 0.93 2.38 3.025 (4) 126
C10—H10⋯O1iii 0.93 2.51 3.431 (4) 172
C12—H12⋯N2iv 0.93 2.62 3.426 (6) 146
Symmetry codes: (i) x, y+1, z; (ii) [-x+1, y+{\script{1\over 2}}, -z+1]; (iii) x, y-1, z; (iv) [-x-1, y+{\script{1\over 2}}, -z].

Data collection: APEX2 (Bruker, 2007[Bruker (2007). APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 2007[Bruker (2007). APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; 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 for Windows (Farrugia, 1997[Farrugia, L. J. (1997). J. Appl. Cryst. 30, 565.]) and PLATON (Spek, 2009[Spek, A. L. (2009). Acta Cryst. D65, 148-155.]); software used to prepare material for publication: WinGX (Farrugia, 1999[Farrugia, L. J. (1999). J. Appl. Cryst. 32, 837-838.]) and PLATON.

Supporting information


Comment top

As part of our ongoing studies of sulfonamides with potential biological properties (Mustafa et al., 2010, 2011, 2012a,b; Khan et al., 2011), the crystal structure of the title compound (I) has been determined.

The molecular structure of (I) (Fig. 1), has a L-shaped conformation, with the central C5—S1—N1—C8 torsion angle being -69.1 (3)°. The two benzene rings (C2—C7) and (C8—C13) are nearly perpendicular to each other, with a dihedral angle of 89.94 (15)°. All the bond lengths (Allen et al., 1987) and angles are normal (Mustafa et al., 2010; 2011, 2012a,b; Khan et al., 2011).

The title molecule exhibits an S(6) motif (Bernstein et al., 1995) formed by a weak intramolecular C—H···O hydrogen bond interaction (Table 1). In the crystal, molecules are linked by N—H···O and weak C—H···O hydrogen bonds forming chains propagating along the b axis. Weak intermolecular C—H···N hydrogen bonds connect the chains into a two dimensional netwok (Table 1, Fig. 2).

Related literature top

For related structures, see: Mustafa et al. (2010, 2011, 2012a,b); Khan et al. (2011). For standard bond-length data, see: Allen et al. (1987). For hydrogen bond motifs, see: Bernstein et al. (1995).

Experimental top

To an aquious solution of p-amino benzoic acid (1.0 g, 7.3 mmol), sodium carbonate (1 N) was added to adjust the pH to 8. Then p-toluenesulfonyl chloride (1.80 g, 9.48 mmol) was added and the mixture was stirred at room temperature keeping the pH of the mixture at 8.0 with occasional addition of sodium carbonate solution. Progress and completion of the reaction was confirmed by TLC and conversion of the suspension into a clear solution. After 2 h, whole mixture was poured into a beaker and the pH was adjusted to 2.0 by 1 N HCl. Pprecipitates were produced which were filtered and washed with distilled water.

The prepared sulfonamide (4-(Toluene-4-sulfonylamino)-benzoic acid) (1.0 g, 3.43 mmol), DMF (10 ml) and n-hexane washed sodium hydride (0.25 g, 10.31 mmol) were stirred at room temperature for 40 min followed by the addition of chloroacetonitrile (0.34 g, 4.46 mmol). The whole reaction mixture was stirred at 353 K till the completion of the reaction and poured into crushed ice in a beaker. The pH of the mixture was adjusted to 4.0 with 1 N HCl. Precipitates were produced, filtered and washed twice with distilled water. Crystals suitable for X-ray diffraction were grown from a chloroform solution of the title compound.

Refinement top

All H atoms were positioned with idealized geometry and were refined using a riding model with Uiso(H) = 1.2 or 1.5Ueq(C) [N—H = 0.86 Å, C—H = 0.93, 0.96 or 0.97 Å]. One reflection (0 0 2) was omitted from the refinement. The crystal studied is an inversion twin with the refined BASF ratio of 0.70 (10)/0.30 (10).

Computing details top

Data collection: APEX2 (Bruker, 2007); cell refinement: SAINT (Bruker, 2007); data reduction: SAINT (Bruker, 2007); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997) and PLATON (Spek, 2009); software used to prepare material for publication: WinGX (Farrugia, 1999) and PLATON (Spek, 2009).

Figures top
[Figure 1] Fig. 1. The molecular structure of (I) with displacement ellipsoids for non-H atoms drawn at the 30% probability level.
[Figure 2] Fig. 2. View of the packing and hydrogen-bonding interactions in (I) The hydrogen atoms not involved in the hydrogen bonds have been omitted.
Cyanomethyl 4-(4-methylbenzenesulfonamido)benzoate top
Crystal data top
C16H14N2O4SF(000) = 344
Mr = 330.36Dx = 1.418 Mg m3
Monoclinic, P21Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ybCell parameters from 2045 reflections
a = 5.9360 (3) Åθ = 2.6–24.7°
b = 8.1992 (4) ŵ = 0.23 mm1
c = 15.9068 (8) ÅT = 296 K
β = 91.222 (3)°Block, yellow
V = 774.02 (7) Å30.28 × 0.23 × 0.19 mm
Z = 2
Data collection top
Bruker APEXII CCD
diffractometer
2306 reflections with I > 2σ(I)
Radiation source: sealed tubeRint = 0.027
Graphite monochromatorθmax = 27.1°, θmin = 1.3°
ϕ and ω scansh = 77
6266 measured reflectionsk = 810
3077 independent reflectionsl = 2015
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)] = 0.046H-atom parameters constrained
wR(F2) = 0.106 w = 1/[σ2(Fo2) + (0.0538P)2 + 0.0338P]
where P = (Fo2 + 2Fc2)/3
S = 1.01(Δ/σ)max < 0.001
3077 reflectionsΔρmax = 0.20 e Å3
210 parametersΔρmin = 0.25 e Å3
1 restraintAbsolute structure: Flack (1983), 1248 Freidel pairs
Primary atom site location: structure-invariant direct methodsAbsolute structure parameter: 0.30 (10)
Crystal data top
C16H14N2O4SV = 774.02 (7) Å3
Mr = 330.36Z = 2
Monoclinic, P21Mo Kα radiation
a = 5.9360 (3) ŵ = 0.23 mm1
b = 8.1992 (4) ÅT = 296 K
c = 15.9068 (8) Å0.28 × 0.23 × 0.19 mm
β = 91.222 (3)°
Data collection top
Bruker APEXII CCD
diffractometer
2306 reflections with I > 2σ(I)
6266 measured reflectionsRint = 0.027
3077 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.046H-atom parameters constrained
wR(F2) = 0.106Δρmax = 0.20 e Å3
S = 1.01Δρmin = 0.25 e Å3
3077 reflectionsAbsolute structure: Flack (1983), 1248 Freidel pairs
210 parametersAbsolute structure parameter: 0.30 (10)
1 restraint
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 e.s.d.'s 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 > σ(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
xyzUiso*/Ueq
S10.58175 (11)0.32017 (11)0.30134 (5)0.0453 (2)
O10.6354 (4)0.4862 (3)0.28356 (14)0.0570 (8)
O20.7581 (3)0.2041 (3)0.31249 (15)0.0597 (9)
O30.1129 (4)0.4816 (3)0.16303 (18)0.0630 (10)
O40.1469 (4)0.3362 (3)0.09421 (15)0.0576 (8)
N10.4185 (4)0.2648 (3)0.22249 (17)0.0505 (9)
N20.6118 (7)0.3907 (7)0.0148 (3)0.1056 (19)
C10.0250 (6)0.3400 (6)0.6140 (2)0.0774 (14)
C20.1617 (5)0.3314 (5)0.53585 (18)0.0512 (10)
C30.3637 (6)0.2464 (4)0.5345 (2)0.0595 (12)
C40.4901 (5)0.2381 (4)0.4627 (2)0.0515 (11)
C50.4149 (4)0.3166 (4)0.39131 (16)0.0400 (8)
C60.2138 (5)0.4021 (4)0.3910 (2)0.0487 (11)
C70.0899 (5)0.4073 (4)0.4624 (2)0.0542 (11)
C80.3266 (5)0.1077 (4)0.20785 (18)0.0422 (10)
C90.4346 (5)0.0359 (4)0.2306 (2)0.0538 (11)
C100.3380 (4)0.1827 (5)0.20995 (18)0.0508 (9)
C110.1348 (4)0.1913 (5)0.16607 (16)0.0416 (8)
C120.0272 (5)0.0468 (4)0.1442 (2)0.0466 (11)
C130.1211 (5)0.0997 (4)0.1656 (2)0.0484 (11)
C140.0402 (5)0.3518 (4)0.1432 (2)0.0481 (11)
C150.2527 (6)0.4841 (4)0.0670 (2)0.0621 (12)
C160.4543 (8)0.4347 (5)0.0209 (3)0.0704 (17)
H10.385200.338800.186000.0610*
H1A0.024300.450000.634600.1160*
H1B0.089900.269400.656100.1160*
H1C0.126700.306100.601200.1160*
H30.415100.193800.583100.0710*
H40.624700.180000.462700.0620*
H60.163400.455600.342500.0590*
H70.046300.463400.461600.0650*
H90.572100.032700.259600.0640*
H100.410800.278700.225800.0610*
H120.109800.049800.114800.0560*
H130.045600.195600.151500.0580*
H15A0.290800.551200.114900.0740*
H15B0.153600.545700.031100.0740*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.0447 (3)0.0424 (4)0.0486 (4)0.0002 (4)0.0010 (3)0.0054 (4)
O10.0656 (14)0.0481 (15)0.0572 (15)0.0175 (12)0.0007 (11)0.0017 (11)
O20.0456 (12)0.0650 (16)0.0684 (17)0.0109 (12)0.0035 (12)0.0136 (13)
O30.0728 (17)0.0376 (14)0.078 (2)0.0009 (12)0.0101 (15)0.0073 (13)
O40.0626 (13)0.0432 (13)0.0662 (16)0.0060 (11)0.0166 (11)0.0016 (12)
N10.0686 (16)0.0394 (17)0.0430 (16)0.0007 (12)0.0077 (13)0.0001 (11)
N20.080 (3)0.147 (4)0.089 (3)0.016 (3)0.017 (2)0.030 (3)
C10.081 (2)0.087 (3)0.065 (2)0.032 (3)0.0211 (18)0.016 (3)
C20.0556 (16)0.0490 (19)0.0493 (18)0.0153 (19)0.0056 (13)0.012 (2)
C30.069 (2)0.060 (2)0.049 (2)0.0071 (17)0.0092 (17)0.0152 (16)
C40.0490 (16)0.0492 (19)0.056 (2)0.0085 (15)0.0042 (16)0.0071 (16)
C50.0401 (12)0.0322 (13)0.0473 (15)0.0002 (17)0.0056 (11)0.0017 (18)
C60.0481 (17)0.0507 (18)0.047 (2)0.0090 (16)0.0053 (15)0.0056 (15)
C70.0441 (16)0.0535 (19)0.065 (2)0.0053 (16)0.0008 (16)0.0030 (18)
C80.0480 (16)0.0437 (19)0.0352 (17)0.0022 (15)0.0048 (13)0.0013 (14)
C90.0486 (17)0.051 (2)0.061 (2)0.0068 (16)0.0147 (16)0.0020 (17)
C100.0517 (14)0.0448 (17)0.0554 (18)0.011 (2)0.0074 (13)0.002 (2)
C110.0458 (12)0.0407 (16)0.0383 (15)0.0018 (18)0.0024 (11)0.0028 (17)
C120.0435 (17)0.047 (2)0.049 (2)0.0035 (15)0.0040 (15)0.0004 (16)
C130.0458 (17)0.044 (2)0.055 (2)0.0056 (16)0.0082 (17)0.0011 (18)
C140.0471 (17)0.048 (2)0.049 (2)0.0018 (17)0.0003 (16)0.0013 (18)
C150.072 (2)0.057 (2)0.057 (2)0.0181 (19)0.0040 (19)0.0070 (18)
C160.066 (3)0.095 (3)0.050 (3)0.018 (2)0.0030 (19)0.015 (2)
Geometric parameters (Å, º) top
S1—O11.428 (3)C9—C101.370 (5)
S1—O21.423 (2)C10—C111.382 (3)
S1—N11.633 (3)C11—C121.387 (5)
S1—C51.758 (3)C11—C141.473 (5)
O3—C141.189 (4)C12—C131.364 (5)
O4—C141.349 (4)C15—C161.448 (6)
O4—C151.429 (4)C1—H1A0.9600
N1—C81.416 (4)C1—H1B0.9600
N2—C161.142 (7)C1—H1C0.9600
N1—H10.8600C3—H30.9300
C1—C21.501 (4)C4—H40.9300
C2—C71.383 (4)C6—H60.9300
C2—C31.388 (5)C7—H70.9300
C3—C41.382 (5)C9—H90.9300
C4—C51.372 (4)C10—H100.9300
C5—C61.384 (4)C12—H120.9300
C6—C71.367 (4)C13—H130.9300
C8—C91.385 (5)C15—H15A0.9700
C8—C131.382 (4)C15—H15B0.9700
O1—S1—O2119.72 (14)O3—C14—O4121.9 (3)
O1—S1—N1104.13 (14)O4—C14—C11111.3 (3)
O1—S1—C5108.00 (15)O4—C15—C16105.6 (3)
O2—S1—N1109.43 (14)N2—C16—C15177.8 (5)
O2—S1—C5108.25 (14)C2—C1—H1A109.00
N1—S1—C5106.57 (13)C2—C1—H1B109.00
C14—O4—C15116.5 (3)C2—C1—H1C109.00
S1—N1—C8126.8 (2)H1A—C1—H1B109.00
S1—N1—H1117.00H1A—C1—H1C109.00
C8—N1—H1117.00H1B—C1—H1C110.00
C3—C2—C7117.6 (3)C2—C3—H3119.00
C1—C2—C3121.3 (3)C4—C3—H3119.00
C1—C2—C7121.1 (3)C3—C4—H4120.00
C2—C3—C4121.5 (3)C5—C4—H4120.00
C3—C4—C5119.2 (3)C5—C6—H6120.00
S1—C5—C6119.3 (2)C7—C6—H6120.00
S1—C5—C4120.2 (2)C2—C7—H7119.00
C4—C5—C6120.4 (3)C6—C7—H7119.00
C5—C6—C7119.5 (3)C8—C9—H9120.00
C2—C7—C6121.8 (3)C10—C9—H9120.00
C9—C8—C13119.1 (3)C9—C10—H10119.00
N1—C8—C13117.1 (3)C11—C10—H10119.00
N1—C8—C9123.8 (3)C11—C12—H12120.00
C8—C9—C10119.7 (3)C13—C12—H12120.00
C9—C10—C11121.5 (3)C8—C13—H13120.00
C12—C11—C14122.0 (2)C12—C13—H13119.00
C10—C11—C12118.4 (3)O4—C15—H15A111.00
C10—C11—C14119.6 (3)O4—C15—H15B111.00
C11—C12—C13120.4 (3)C16—C15—H15A111.00
C8—C13—C12121.0 (3)C16—C15—H15B111.00
O3—C14—C11126.9 (3)H15A—C15—H15B109.00
O1—S1—N1—C8176.9 (2)C3—C4—C5—C60.5 (5)
O2—S1—N1—C847.8 (3)C3—C4—C5—S1175.5 (3)
C5—S1—N1—C869.1 (3)C4—C5—C6—C70.2 (5)
O1—S1—C5—C4118.0 (3)S1—C5—C6—C7176.3 (2)
O2—S1—C5—C413.0 (3)C5—C6—C7—C21.1 (5)
N1—S1—C5—C4130.6 (3)N1—C8—C13—C12175.8 (3)
O1—S1—C5—C658.1 (3)C9—C8—C13—C121.8 (5)
O2—S1—C5—C6171.0 (2)N1—C8—C9—C10176.6 (3)
N1—S1—C5—C653.3 (3)C13—C8—C9—C100.9 (4)
C15—O4—C14—C11179.3 (2)C8—C9—C10—C110.5 (4)
C14—O4—C15—C16176.3 (3)C9—C10—C11—C121.0 (4)
C15—O4—C14—O30.3 (4)C9—C10—C11—C14178.3 (3)
S1—N1—C8—C932.5 (4)C10—C11—C14—O4174.3 (2)
S1—N1—C8—C13150.0 (2)C12—C11—C14—O3175.5 (3)
C1—C2—C7—C6179.3 (3)C12—C11—C14—O45.0 (4)
C1—C2—C3—C4180.0 (3)C10—C11—C14—O35.2 (5)
C3—C2—C7—C61.1 (5)C10—C11—C12—C130.1 (4)
C7—C2—C3—C40.3 (5)C14—C11—C12—C13179.2 (3)
C2—C3—C4—C50.5 (5)C11—C12—C13—C81.3 (5)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1···O3i0.862.212.904 (3)138
C1—H1A···O2ii0.962.583.446 (5)150
C9—H9···O20.932.383.025 (4)126
C10—H10···O1iii0.932.513.431 (4)172
C12—H12···N2iv0.932.623.426 (6)146
Symmetry codes: (i) x, y+1, z; (ii) x+1, y+1/2, z+1; (iii) x, y1, z; (iv) x1, y+1/2, z.

Experimental details

Crystal data
Chemical formulaC16H14N2O4S
Mr330.36
Crystal system, space groupMonoclinic, P21
Temperature (K)296
a, b, c (Å)5.9360 (3), 8.1992 (4), 15.9068 (8)
β (°) 91.222 (3)
V3)774.02 (7)
Z2
Radiation typeMo Kα
µ (mm1)0.23
Crystal size (mm)0.28 × 0.23 × 0.19
Data collection
DiffractometerBruker APEXII CCD
diffractometer
Absorption correction
No. of measured, independent and
observed [I > 2σ(I)] reflections
6266, 3077, 2306
Rint0.027
(sin θ/λ)max1)0.641
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.046, 0.106, 1.01
No. of reflections3077
No. of parameters210
No. of restraints1
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.20, 0.25
Absolute structureFlack (1983), 1248 Freidel pairs
Absolute structure parameter0.30 (10)

Computer programs: APEX2 (Bruker, 2007), SAINT (Bruker, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 1997) and PLATON (Spek, 2009), WinGX (Farrugia, 1999) and PLATON (Spek, 2009).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1···O3i0.862.212.904 (3)138
C1—H1A···O2ii0.962.583.446 (5)150
C9—H9···O20.932.383.025 (4)126
C10—H10···O1iii0.932.513.431 (4)172
C12—H12···N2iv0.932.623.426 (6)146
Symmetry codes: (i) x, y+1, z; (ii) x+1, y+1/2, z+1; (iii) x, y1, z; (iv) x1, y+1/2, z.
 

Acknowledgements

The authors are grateful to Mr Muhammad Shafiq for his assistance and the Higher Education Commission (HEC), Pakistan, for financial support.

References

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Volume 68| Part 5| May 2012| Page o1488
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