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

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ISSN: 2056-9890

(5Z)-5-(2-Methyl­benzyl­­idene)-3-phenyl-2-thioxo-1,3-thia­zolidin-4-one

aDepartment of Chemistry, Government College University, Lahore, Pakistan, and bDepartment of Physics, University of Sargodha, Sargodha, Pakistan
*Correspondence e-mail: dmntahir_uos@yahoo.com

(Received 24 October 2009; accepted 24 October 2009; online 31 October 2009)

In the title compound, C17H13NOS2, the heterocyclic ring is oriented at a dihedral angle of 74.43 (5)° with respect to the anilinic benzene ring and at a dihedral angle of 17.31 (9)° with respect to phenyl ring. An intra­molecular C—H⋯S inter­action occurs, resulting in an S(6) ring. In the crystal, the packing is consolidated by C—H⋯π inter­actions and possible very weak aromatic ππ stacking [centroid–centroid separation = 4.025 (1) Å].

Related literature

For related structures, see: Linden et al. (1999[Linden, A., Awad, E. M. A. H. & Heimgartner, H. (1999). Acta Cryst. C55, 1877-1881.]); Shahwar et al. (2009a[Shahwar, D., Tahir, M. N., Raza, M. A. & Iqbal, B. (2009a). Acta Cryst. E65, o2903.],b[Shahwar, D., Tahir, M. N., Raza, M. A., Iqbal, B. & Naz, S. (2009b). Acta Cryst. E65, o2637.],c[Shahwar, D., Tahir, M. N., Raza, M. A., Saddaf, M. & Majeed, S. (2009c). Acta Cryst. E65, o2638.]). For graph-set theory, 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
  • C17H13NOS2

  • Mr = 311.40

  • Monoclinic, P 21 /c

  • a = 9.8317 (4) Å

  • b = 16.6317 (6) Å

  • c = 9.3865 (4) Å

  • β = 93.541 (2)°

  • V = 1531.93 (11) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.35 mm−1

  • T = 296 K

  • 0.40 × 0.30 × 0.18 mm

Data collection
  • Bruker Kappa APEXII CCD diffractometer

  • Absorption correction: multi-scan (SADABS; Bruker, 2005[Bruker (2005). SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]) Tmin = 0.879, Tmax = 0.941

  • 17261 measured reflections

  • 3807 independent reflections

  • 2879 reflections with I > 2σ(I)

  • Rint = 0.028

Refinement
  • R[F2 > 2σ(F2)] = 0.036

  • wR(F2) = 0.104

  • S = 1.01

  • 3807 reflections

  • 191 parameters

  • H-atom parameters constrained

  • Δρmax = 0.24 e Å−3

  • Δρmin = −0.20 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
C16—H16⋯S1 0.93 2.52 3.2197 (19) 133
C17—H17C⋯CgCi 0.96 2.72 3.569 (2) 148
Symmetry code: (i) -x+2, -y+1, -z. CgC is the centroid of C11–C16 benzene ring.

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 (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

The title compound (I, Fig. 1), has been prepared and being reported in continuation of synthesizing various derivatives of rhodanine. In this context we have reported the crystal structure of (II) (5Z)-5-(2-Hydroxybenzylidene)-3-phenyl-2-thioxo-1,3-thiazolidin-4-one (Shahwar et al., 2009a), (III) (5Z)-5-(2-Hydroxybenzylidene)-2-thioxo-1,3-thiazolidin-4-one methanol hemisolvate (Shahwar et al., 2009b) and (IV) (5E)-5-(4-Hydroxy-3-methoxybenzylidene)-2-thioxo-1,3-thiazolidin- 4-one methanol monosolvate (Shahwar et al., 2009c).

The crystal structure of (I) differs from (V) 3-Phenyl-5-(phenylmethylidene)-2-thioxo-1,3-thiazolidin-4-one (Linden et al., 1999) due to attachement of methyl group.

In (I) the heterocyclic ring A (N1/C7/S1/C8/C9), two benzene rings B (C1—C6) and C (C11–C16) are planar with maximum r. m. s. deviations of 0.0047, 0.0074 and 0.0046 Å respectively, from the respective mean square planes. The dihedral angles between A/B, A/C and B/C are 74.43 (5), 17.31 (9) and 59.19 (6)°, respectively. The intramolecular H-bondings of C—H···S (Table 1, Fig. 1) form S(6) ring motif (Bernstein et al., 1995). There exist π···π-interactions between adjacent molecules. The CgA···CgCi and CgC···CgAi [symmetry code: i = 2 - x, 1 - y, 1 - z] have centroid to centroid distance of 4.025 (1) Å, where CgA and CgC are the centroids of rings A and C, respectively. The C–H···π interactions (Table 1) also play role in stabilizing the molecules.

Related literature top

For related structures, see: Linden et al. (1999); Shahwar et al. (2009a,b,c). For graph-set theory, see: Bernstein et al. (1995). CgC is the centroid of C11–C16 benzene ring.

Experimental top

3-Phenyl-2-thioxo-1,3-thiazolidin-4-one (0.419 g, 0.2 mol), 2-Methylbenzaldehyde (0.240 g, 0.2 mol) and K2CO3 (0.553 g, 0.4 mol) were dissolved in 10 ml distilled water at room temperature. The stirring was continued for 24 h and reaction was monitored by TLC. The precipitates were formed during neutalization of the reaction mixture with 5% HCl. The precipitates were filtered off and washed with saturated solution of NaCl. The crude material obtained was recrystalized in ethyl acetate to affoard yellow prisms of (I).

Refinement top

The H-atoms were positioned geometrically (C–H = 0.93–0.96 Å) and refined as riding with Uiso(H) = xUeq(C), where x = 1.5 for methyl and 1.2 for other H atoms.

Structure description top

The title compound (I, Fig. 1), has been prepared and being reported in continuation of synthesizing various derivatives of rhodanine. In this context we have reported the crystal structure of (II) (5Z)-5-(2-Hydroxybenzylidene)-3-phenyl-2-thioxo-1,3-thiazolidin-4-one (Shahwar et al., 2009a), (III) (5Z)-5-(2-Hydroxybenzylidene)-2-thioxo-1,3-thiazolidin-4-one methanol hemisolvate (Shahwar et al., 2009b) and (IV) (5E)-5-(4-Hydroxy-3-methoxybenzylidene)-2-thioxo-1,3-thiazolidin- 4-one methanol monosolvate (Shahwar et al., 2009c).

The crystal structure of (I) differs from (V) 3-Phenyl-5-(phenylmethylidene)-2-thioxo-1,3-thiazolidin-4-one (Linden et al., 1999) due to attachement of methyl group.

In (I) the heterocyclic ring A (N1/C7/S1/C8/C9), two benzene rings B (C1—C6) and C (C11–C16) are planar with maximum r. m. s. deviations of 0.0047, 0.0074 and 0.0046 Å respectively, from the respective mean square planes. The dihedral angles between A/B, A/C and B/C are 74.43 (5), 17.31 (9) and 59.19 (6)°, respectively. The intramolecular H-bondings of C—H···S (Table 1, Fig. 1) form S(6) ring motif (Bernstein et al., 1995). There exist π···π-interactions between adjacent molecules. The CgA···CgCi and CgC···CgAi [symmetry code: i = 2 - x, 1 - y, 1 - z] have centroid to centroid distance of 4.025 (1) Å, where CgA and CgC are the centroids of rings A and C, respectively. The C–H···π interactions (Table 1) also play role in stabilizing the molecules.

For related structures, see: Linden et al. (1999); Shahwar et al. (2009a,b,c). For graph-set theory, see: Bernstein et al. (1995). CgC is the centroid of C11–C16 benzene ring.

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 (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. View of (I) with displacement ellipsoids drawn at the 50% probability level. The dotted line represents the intramolecular H-bond.
(5Z)-5-(2-Methylbenzylidene)-3-phenyl-2-thioxo-1,3-thiazolidin-4-one top
Crystal data top
C17H13NOS2F(000) = 648
Mr = 311.40Dx = 1.350 Mg m3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 3807 reflections
a = 9.8317 (4) Åθ = 2.1–28.3°
b = 16.6317 (6) ŵ = 0.35 mm1
c = 9.3865 (4) ÅT = 296 K
β = 93.541 (2)°Prisms, yellow
V = 1531.93 (11) Å30.40 × 0.30 × 0.18 mm
Z = 4
Data collection top
Bruker Kappa APEXII CCD
diffractometer
3807 independent reflections
Radiation source: fine-focus sealed tube2879 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.028
Detector resolution: 7.40 pixels mm-1θmax = 28.3°, θmin = 2.1°
ω scansh = 1312
Absorption correction: multi-scan
(SADABS; Bruker, 2005)
k = 1322
Tmin = 0.879, Tmax = 0.941l = 129
17261 measured reflections
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.036Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.104H-atom parameters constrained
S = 1.01 w = 1/[σ2(Fo2) + (0.0498P)2 + 0.3691P]
where P = (Fo2 + 2Fc2)/3
3807 reflections(Δ/σ)max < 0.001
191 parametersΔρmax = 0.24 e Å3
0 restraintsΔρmin = 0.20 e Å3
Crystal data top
C17H13NOS2V = 1531.93 (11) Å3
Mr = 311.40Z = 4
Monoclinic, P21/cMo Kα radiation
a = 9.8317 (4) ŵ = 0.35 mm1
b = 16.6317 (6) ÅT = 296 K
c = 9.3865 (4) Å0.40 × 0.30 × 0.18 mm
β = 93.541 (2)°
Data collection top
Bruker Kappa APEXII CCD
diffractometer
3807 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2005)
2879 reflections with I > 2σ(I)
Tmin = 0.879, Tmax = 0.941Rint = 0.028
17261 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0360 restraints
wR(F2) = 0.104H-atom parameters constrained
S = 1.01Δρmax = 0.24 e Å3
3807 reflectionsΔρmin = 0.20 e Å3
191 parameters
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 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
S10.95527 (4)0.36087 (3)0.48338 (4)0.0408 (1)
S20.81145 (5)0.25140 (3)0.66855 (5)0.0544 (2)
O10.62790 (12)0.44603 (8)0.30111 (16)0.0590 (5)
N10.69362 (13)0.35311 (8)0.47353 (15)0.0379 (4)
C10.55749 (16)0.32728 (10)0.49995 (18)0.0409 (5)
C20.47556 (18)0.37600 (11)0.5756 (2)0.0508 (6)
C30.3467 (2)0.34908 (14)0.6034 (3)0.0648 (8)
C40.3022 (2)0.27496 (15)0.5571 (3)0.0686 (8)
C50.3841 (2)0.22789 (15)0.4798 (3)0.0774 (9)
C60.5136 (2)0.25369 (12)0.4493 (3)0.0644 (8)
C70.71757 (16)0.41175 (9)0.37026 (18)0.0400 (5)
C80.86629 (15)0.42329 (9)0.36025 (17)0.0358 (5)
C90.80674 (16)0.32015 (9)0.54449 (17)0.0374 (5)
C100.91369 (16)0.47413 (9)0.26411 (18)0.0390 (5)
C111.05266 (15)0.49045 (10)0.22684 (17)0.0383 (5)
C121.07841 (16)0.55752 (10)0.14107 (17)0.0393 (5)
C131.20990 (18)0.56853 (12)0.0986 (2)0.0522 (6)
C141.31437 (18)0.51669 (14)0.1394 (2)0.0591 (7)
C151.29056 (18)0.45192 (13)0.2249 (2)0.0580 (7)
C161.16070 (17)0.43879 (12)0.2676 (2)0.0509 (6)
C170.96876 (19)0.61723 (10)0.0967 (2)0.0500 (6)
H20.506000.426180.607500.0609*
H30.289760.381610.654100.0777*
H40.216350.256760.578350.0823*
H50.352980.178000.447090.0929*
H60.569160.221850.395890.0773*
H100.847020.503790.212930.0468*
H131.227960.612210.040850.0626*
H141.401330.525610.108910.0709*
H151.361210.417250.253650.0695*
H161.144470.394610.324870.0611*
H17A1.005960.658050.038130.0751*
H17B0.934580.641570.180050.0751*
H17C0.895820.590140.043570.0751*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.0330 (2)0.0478 (2)0.0411 (2)0.0007 (2)0.0014 (2)0.0040 (2)
S20.0639 (3)0.0516 (3)0.0477 (3)0.0025 (2)0.0028 (2)0.0119 (2)
O10.0342 (6)0.0622 (8)0.0804 (10)0.0084 (6)0.0030 (6)0.0248 (7)
N10.0321 (7)0.0371 (7)0.0450 (8)0.0012 (5)0.0062 (5)0.0000 (6)
C10.0342 (8)0.0439 (9)0.0451 (9)0.0024 (7)0.0059 (7)0.0020 (7)
C20.0418 (9)0.0535 (10)0.0578 (11)0.0034 (8)0.0089 (8)0.0037 (9)
C30.0432 (11)0.0808 (15)0.0722 (14)0.0103 (10)0.0183 (10)0.0057 (12)
C40.0382 (10)0.0817 (15)0.0866 (16)0.0095 (10)0.0095 (10)0.0170 (13)
C50.0572 (13)0.0668 (14)0.109 (2)0.0241 (11)0.0110 (13)0.0107 (14)
C60.0501 (11)0.0584 (12)0.0864 (16)0.0107 (9)0.0177 (11)0.0182 (11)
C70.0341 (8)0.0369 (8)0.0495 (9)0.0031 (6)0.0066 (7)0.0013 (7)
C80.0321 (8)0.0346 (8)0.0408 (8)0.0034 (6)0.0023 (6)0.0016 (6)
C90.0396 (8)0.0364 (8)0.0363 (8)0.0013 (6)0.0035 (6)0.0048 (6)
C100.0330 (8)0.0390 (8)0.0451 (9)0.0053 (6)0.0026 (7)0.0011 (7)
C110.0330 (8)0.0445 (8)0.0374 (8)0.0006 (7)0.0025 (6)0.0017 (7)
C120.0378 (8)0.0421 (8)0.0379 (9)0.0053 (7)0.0022 (7)0.0042 (7)
C130.0482 (10)0.0555 (11)0.0535 (11)0.0121 (8)0.0076 (8)0.0006 (9)
C140.0343 (9)0.0815 (14)0.0623 (12)0.0096 (9)0.0106 (8)0.0051 (11)
C150.0336 (9)0.0813 (14)0.0589 (12)0.0108 (9)0.0014 (8)0.0055 (10)
C160.0383 (9)0.0640 (12)0.0508 (10)0.0069 (8)0.0060 (8)0.0122 (9)
C170.0530 (10)0.0416 (9)0.0556 (11)0.0013 (8)0.0043 (8)0.0059 (8)
Geometric parameters (Å, º) top
S1—C81.7476 (16)C12—C131.388 (2)
S1—C91.7389 (16)C12—C171.506 (2)
S2—C91.6306 (16)C13—C141.377 (3)
O1—C71.205 (2)C14—C151.372 (3)
N1—C11.442 (2)C15—C161.379 (2)
N1—C71.405 (2)C2—H20.9300
N1—C91.375 (2)C3—H30.9300
C1—C21.371 (2)C4—H40.9300
C1—C61.373 (3)C5—H50.9300
C2—C31.384 (3)C6—H60.9300
C3—C41.370 (3)C10—H100.9300
C4—C51.364 (3)C13—H130.9300
C5—C61.390 (3)C14—H140.9300
C7—C81.483 (2)C15—H150.9300
C8—C101.341 (2)C16—H160.9300
C10—C111.457 (2)C17—H17A0.9600
C11—C121.408 (2)C17—H17B0.9600
C11—C161.401 (2)C17—H17C0.9600
C8—S1—C993.05 (7)C13—C14—C15120.20 (17)
C1—N1—C7121.49 (13)C14—C15—C16119.26 (18)
C1—N1—C9121.99 (13)C11—C16—C15121.57 (18)
C7—N1—C9116.49 (13)C1—C2—H2121.00
N1—C1—C2119.62 (15)C3—C2—H2121.00
N1—C1—C6118.77 (15)C2—C3—H3120.00
C2—C1—C6121.60 (16)C4—C3—H3120.00
C1—C2—C3118.72 (18)C3—C4—H4120.00
C2—C3—C4120.6 (2)C5—C4—H4120.00
C3—C4—C5119.9 (2)C4—C5—H5120.00
C4—C5—C6120.7 (2)C6—C5—H5120.00
C1—C6—C5118.4 (2)C1—C6—H6121.00
O1—C7—N1123.48 (15)C5—C6—H6121.00
O1—C7—C8126.56 (15)C8—C10—H10115.00
N1—C7—C8109.96 (13)C11—C10—H10115.00
S1—C8—C7109.66 (11)C12—C13—H13119.00
S1—C8—C10129.72 (12)C14—C13—H13119.00
C7—C8—C10120.60 (14)C13—C14—H14120.00
S1—C9—S2121.42 (10)C15—C14—H14120.00
S1—C9—N1110.83 (11)C14—C15—H15120.00
S2—C9—N1127.74 (12)C16—C15—H15120.00
C8—C10—C11130.48 (15)C11—C16—H16119.00
C10—C11—C12119.31 (14)C15—C16—H16119.00
C10—C11—C16121.79 (15)C12—C17—H17A109.00
C12—C11—C16118.82 (14)C12—C17—H17B109.00
C11—C12—C13118.18 (15)C12—C17—H17C109.00
C11—C12—C17122.00 (14)H17A—C17—H17B109.00
C13—C12—C17119.81 (15)H17A—C17—H17C109.00
C12—C13—C14121.96 (18)H17B—C17—H17C109.00
C9—S1—C8—C70.70 (12)C3—C4—C5—C61.1 (4)
C9—S1—C8—C10177.47 (16)C4—C5—C6—C10.6 (4)
C8—S1—C9—S2179.23 (11)O1—C7—C8—S1179.38 (15)
C8—S1—C9—N10.06 (13)O1—C7—C8—C102.3 (3)
C7—N1—C1—C275.8 (2)N1—C7—C8—S11.15 (16)
C7—N1—C1—C6104.8 (2)N1—C7—C8—C10177.21 (14)
C9—N1—C1—C2106.26 (19)S1—C8—C10—C113.5 (3)
C9—N1—C1—C673.2 (2)C7—C8—C10—C11174.47 (16)
C1—N1—C7—O12.6 (2)C8—C10—C11—C12168.06 (17)
C1—N1—C7—C8176.90 (14)C8—C10—C11—C1615.4 (3)
C9—N1—C7—O1179.33 (16)C10—C11—C12—C13175.47 (16)
C9—N1—C7—C81.18 (19)C10—C11—C12—C175.4 (2)
C1—N1—C9—S1177.41 (12)C16—C11—C12—C131.1 (2)
C1—N1—C9—S21.8 (2)C16—C11—C12—C17178.04 (16)
C7—N1—C9—S10.66 (17)C10—C11—C16—C15176.08 (17)
C7—N1—C9—S2179.90 (13)C12—C11—C16—C150.5 (3)
N1—C1—C2—C3178.13 (18)C11—C12—C13—C140.8 (3)
C6—C1—C2—C31.3 (3)C17—C12—C13—C14178.36 (17)
N1—C1—C6—C5177.6 (2)C12—C13—C14—C150.2 (3)
C2—C1—C6—C51.8 (3)C13—C14—C15—C160.9 (3)
C1—C2—C3—C40.5 (3)C14—C15—C16—C110.6 (3)
C2—C3—C4—C51.6 (4)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C16—H16···S10.932.523.2197 (19)133
C17—H17C···CgCi0.962.723.569 (2)148
Symmetry code: (i) x+2, y+1, z.

Experimental details

Crystal data
Chemical formulaC17H13NOS2
Mr311.40
Crystal system, space groupMonoclinic, P21/c
Temperature (K)296
a, b, c (Å)9.8317 (4), 16.6317 (6), 9.3865 (4)
β (°) 93.541 (2)
V3)1531.93 (11)
Z4
Radiation typeMo Kα
µ (mm1)0.35
Crystal size (mm)0.40 × 0.30 × 0.18
Data collection
DiffractometerBruker Kappa APEXII CCD
Absorption correctionMulti-scan
(SADABS; Bruker, 2005)
Tmin, Tmax0.879, 0.941
No. of measured, independent and
observed [I > 2σ(I)] reflections
17261, 3807, 2879
Rint0.028
(sin θ/λ)max1)0.667
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.036, 0.104, 1.01
No. of reflections3807
No. of parameters191
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.24, 0.20

Computer programs: APEX2 (Bruker, 2007), SAINT (Bruker, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 (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
C16—H16···S10.932.523.2197 (19)133
C17—H17C···CgCi0.962.723.569 (2)148
Symmetry code: (i) x+2, y+1, z.
 

Acknowledgements

DS is grateful to Government College University, Lahore, for providing funds under the GCU funded Research Projects Programme.

References

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