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ISSN: 2056-9890

3-[(Methyl­carbamo­yl)amino]-1H-isoindolium chloride

aUniversity of the Punjab, Institute of Chemistry, Lahore 54590, Pakistan, bUniversity of Sargodha, Department of Chemistry, Sargodha, Pakistan, cUniversity of Sargodha, Department of Physics, Sargodha, Pakistan, and dUniversity of the Punjab, Institute of Chemistry, Lahore-54590, Pakistan
*Correspondence e-mail: dmntahir_uos@yahoo.com

(Received 16 December 2008; accepted 29 January 2009; online 4 February 2009)

The title compound, C10H12N3O+·Cl, is a derivative of o-phthaldehyde and methyl­thio­urea. The mol­ecules form dimers through intra- and inter­molecular N—H⋯O hydrogen bonds. The dimers are further linked into chains through one C—H⋯Cl and two N—H⋯Cl hydrogen bonds.

Related literature

For applications of iminium salts, see: Page et al. (2008[Page, P. C. B., Parker, P., Rassias, G. A., Buckley, B. R. & Bethell, D. (2008). Adv. Synth. Catal. 350, 1867-1874.]); Skalkos et al. (1994[Skalkos, D., Hampton, J. A., Keck, R. W., Wagoner, M. & Selman, S. H. (1994). Photochem. Photobiol. 59, 175-181.]) Tariq et al. (2008[Tariq, M. I., Siddiqui, H. L., Hussain, I. & Afzal, S. (2008). J. Chem. Soc. Pak. 30, 472-475.]). For the formation of derivatives of o-phthaldehyde with different ureas, see: Maliha, Tariq, Tahir, Hussain & Ali (2009[Maliha, B., Tariq, M. I., Tahir, M. N., Hussain, I. & Ali, M. (2009). Acta Cryst. E65, o41.]); Maliha, Tariq, Tahir, Hussain & Siddiqui (2009[Maliha, B., Tariq, M. I., Tahir, M. N., Hussain, I. & Siddiqui, H. L. (2009). Acta Cryst. E65, o42-o43.]); Maliha et al. (2008[Maliha, B., Tariq, M. I., Tahir, M. N., Hussain, I. & Siddiqui, H. L. (2008). Acta Cryst. E64, o786.]). For a related structure, see: Arfan et al. (2008[Arfan, M., Tahir, M. N., Khan, R. & Iqbal, M. S. (2008). Acta Cryst. E64, o1505.]).

[Scheme 1]

Experimental

Crystal data
  • C10H12N3O+·Cl

  • Mr = 225.68

  • Triclinic, [P \overline 1]

  • a = 7.1171 (5) Å

  • b = 7.7900 (6) Å

  • c = 10.3033 (8) Å

  • α = 89.484 (3)°

  • β = 69.997 (2)°

  • γ = 74.613 (4)°

  • V = 515.43 (7) Å3

  • Z = 2

  • Mo Kα radiation

  • μ = 0.35 mm−1

  • T = 296 (2) K

  • 0.30 × 0.10 × 0.06 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 = 0.982, Tmax = 0.989

  • 8853 measured reflections

  • 2369 independent reflections

  • 2210 reflections with I > 2σ(I)

  • Rint = 0.020

Refinement
  • R[F2 > 2σ(F2)] = 0.032

  • wR(F2) = 0.101

  • S = 1.01

  • 2369 reflections

  • 146 parameters

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

  • Δρmax = 0.69 e Å−3

  • Δρmin = −0.22 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N1—H1N⋯O1 0.81 (2) 2.22 (2) 2.7097 (16) 119.9 (18)
N1—H1N⋯O1i 0.81 (2) 2.15 (2) 2.8760 (17) 150 (2)
N2—H2N⋯Cl1ii 0.90 (2) 2.23 (2) 3.0969 (13) 160.5 (18)
N3—H3N⋯Cl1ii 0.86 (2) 2.40 (2) 3.2082 (13) 157.0 (17)
C1—H1B⋯Cl1iii 0.97 2.74 3.6755 (16) 162
Symmetry codes: (i) -x+1, -y, -z+1; (ii) -x, -y+1, -z+1; (iii) x+1, y, 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, 2003[Spek, A. L. (2003). J. Appl. Cryst. 36, 7-13.]); 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

Iminium salts are a class of organic compounds acting as reactive intermediates. These are being extensively synthesized and further reacted in an efficient and convenient manner for the preparation of multidrug-resistance reversal agents and pesticides and for metal complexation to form new photosensitizers (Page et al., 2008; Skalkos et al., 1994; Tariq et al., 2008). The present paper relates to the continuation of our studies regarding the formation of derivatives of O-phthaldehyde with different ureas (Maliha et al., 2008; Maliha, Tariq, Tahir, Hussain & Ali, 2009; Maliha, Tariq, Tahir, Hussain & Siddiqui, 2009).

The molecule of the title compound (I; Fig 1), is almost planar. It has three N—H bonds in the asymmetric unit. The N—H of the pyrrole ring forms an intramolecular as well as an intermolecular N–H···O H-bond. The title compound forms a dimer (Fig 2) with a central four membered O···H···O···H unit. The other two N–H groups in the methyl urea moiety are involved in intermolecular H-bonding with the Cl-. The Cl- also forms H-bonds with the methylene group of the pyrrole ring. Consequently, the chlorine anion makes three H-bonds. Similar Cl- bonding behavior has been reported by Arfan et al. (2008). No strong π interactions are observed.

Related literature top

For related literature regarding applications of iminium salts, see: Page et al. (2008); Skalkos et al. (1994) Tariq et al. (2008). For related literature regarding the formation of derivatives of O-phthaldehyde with different ureas, see: Maliha, Tariq, Tahir, Hussain & Ali (2009); Maliha, Tariq, Tahir, Hussain & Siddiqui (2009); Maliha et al. (2008). For a related structure, see: Arfan et al. (2008).

Experimental top

O-phthaldehyde (200 mmol), methylthiourea (200 mmol) and a few drops of 2M HCl were mixed and ground in mortar and pestle. The product obtained was washed sequentially with hexane, ether, ethanol and water. The precipitate was dried and recrystallized from a mixture of methanol:acetone (9:1), by slow evaporation at room temperature.

Computing details top

Data collection: APEX2 (Bruker, 2007); cell refinement: APEX2 (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, 2003); software used to prepare material for publication: WinGX (Farrugia, 1999) and PLATON (Spek, 2003).

Figures top
[Figure 1] Fig. 1. The title compound (I) with displacement ellipsoids drawn at 50% probability level. Intramolecular H-bonds are indicated by broken lines.
[Figure 2] Fig. 2. The packing of I (PLATON: Spek, 2003) showing the dimers and H-bonds to the chlorine anion. H-bonds are indicated by broken lines.
3-[(Methylcarbamoyl)amino]-1H-isoindolium chloride top
Crystal data top
C10H12N3O+·ClZ = 2
Mr = 225.68F(000) = 236
Triclinic, P1Dx = 1.454 Mg m3
Hall symbol: -P 1Mo Kα radiation, λ = 0.71073 Å
a = 7.1171 (5) ÅCell parameters from 2369 reflections
b = 7.7900 (6) Åθ = 3.1–27.5°
c = 10.3033 (8) ŵ = 0.35 mm1
α = 89.484 (3)°T = 296 K
β = 69.997 (2)°Needle, light yellow
γ = 74.613 (4)°0.30 × 0.10 × 0.06 mm
V = 515.43 (7) Å3
Data collection top
Bruker Kappa APEXII CCD
diffractometer
2369 independent reflections
Radiation source: fine-focus sealed tube2210 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.020
Detector resolution: 7.50 pixels mm-1θmax = 27.5°, θmin = 3.1°
ω scansh = 99
Absorption correction: multi-scan
(SADABS; Bruker, 2005)
k = 1010
Tmin = 0.982, Tmax = 0.989l = 1313
8853 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)] = 0.032Hydrogen site location: mixed
wR(F2) = 0.101H atoms treated by a mixture of independent and constrained refinement
S = 1.01 w = 1/[σ2(Fo2) + (0.0646P)2 + 0.2853P]
where P = (Fo2 + 2Fc2)/3
2369 reflections(Δ/σ)max < 0.001
146 parametersΔρmax = 0.69 e Å3
0 restraintsΔρmin = 0.22 e Å3
Crystal data top
C10H12N3O+·Clγ = 74.613 (4)°
Mr = 225.68V = 515.43 (7) Å3
Triclinic, P1Z = 2
a = 7.1171 (5) ÅMo Kα radiation
b = 7.7900 (6) ŵ = 0.35 mm1
c = 10.3033 (8) ÅT = 296 K
α = 89.484 (3)°0.30 × 0.10 × 0.06 mm
β = 69.997 (2)°
Data collection top
Bruker Kappa APEXII CCD
diffractometer
2369 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2005)
2210 reflections with I > 2σ(I)
Tmin = 0.982, Tmax = 0.989Rint = 0.020
8853 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0320 restraints
wR(F2) = 0.101H atoms treated by a mixture of independent and constrained refinement
S = 1.01Δρmax = 0.69 e Å3
2369 reflectionsΔρmin = 0.22 e Å3
146 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 esds 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
O10.29475 (16)0.09740 (13)0.60677 (11)0.0195 (3)
N10.46180 (18)0.25619 (17)0.37719 (12)0.0161 (3)
N20.19866 (18)0.40058 (16)0.58681 (12)0.0155 (3)
N30.05849 (19)0.28726 (17)0.79177 (13)0.0177 (3)
C10.5740 (2)0.29979 (19)0.23859 (15)0.0175 (4)
C20.4836 (2)0.49861 (19)0.24873 (15)0.0165 (4)
C30.5278 (2)0.6215 (2)0.15233 (15)0.0201 (4)
C40.4209 (2)0.8007 (2)0.19298 (17)0.0222 (4)
C50.2750 (2)0.8576 (2)0.32626 (17)0.0214 (4)
C60.2298 (2)0.73562 (19)0.42329 (15)0.0183 (4)
C70.3359 (2)0.55629 (19)0.38103 (14)0.0149 (4)
C80.3263 (2)0.39698 (18)0.45638 (14)0.0147 (3)
C90.1900 (2)0.24711 (19)0.66151 (14)0.0155 (3)
C100.0312 (3)0.1475 (2)0.88541 (15)0.0218 (4)
Cl10.11104 (5)0.28646 (4)0.19897 (3)0.0186 (1)
H1A0.547290.239970.167350.0210*
H1B0.722870.267950.219410.0210*
H1N0.487 (3)0.156 (3)0.401 (2)0.0194*
H2N0.113 (3)0.507 (3)0.631 (2)0.0186*
H30.625470.585100.063600.0242*
H3N0.007 (3)0.397 (3)0.819 (2)0.0212*
H40.447290.885010.129760.0266*
H50.207290.978640.350360.0256*
H60.133170.772120.512340.0220*
H10A0.012120.049820.839960.0327*
H10B0.088890.194480.967220.0327*
H10C0.152380.106080.910810.0327*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0212 (5)0.0138 (5)0.0177 (5)0.0003 (4)0.0033 (4)0.0024 (4)
N10.0167 (5)0.0144 (6)0.0145 (6)0.0019 (4)0.0039 (4)0.0029 (4)
N20.0166 (5)0.0126 (6)0.0143 (6)0.0020 (4)0.0032 (4)0.0016 (4)
N30.0208 (6)0.0145 (6)0.0145 (6)0.0031 (5)0.0036 (5)0.0021 (4)
C10.0162 (6)0.0182 (7)0.0149 (6)0.0030 (5)0.0029 (5)0.0021 (5)
C20.0146 (6)0.0192 (7)0.0165 (7)0.0058 (5)0.0057 (5)0.0024 (5)
C30.0193 (7)0.0251 (8)0.0169 (7)0.0097 (6)0.0049 (5)0.0049 (6)
C40.0251 (7)0.0221 (8)0.0249 (7)0.0130 (6)0.0111 (6)0.0101 (6)
C50.0245 (7)0.0158 (7)0.0264 (8)0.0074 (6)0.0109 (6)0.0047 (6)
C60.0181 (6)0.0176 (7)0.0200 (7)0.0053 (5)0.0074 (5)0.0016 (5)
C70.0142 (6)0.0160 (6)0.0164 (7)0.0055 (5)0.0067 (5)0.0037 (5)
C80.0140 (6)0.0156 (6)0.0158 (6)0.0040 (5)0.0071 (5)0.0018 (5)
C90.0160 (6)0.0156 (6)0.0155 (6)0.0048 (5)0.0062 (5)0.0033 (5)
C100.0280 (7)0.0197 (7)0.0156 (7)0.0068 (6)0.0050 (6)0.0060 (5)
Cl10.0195 (2)0.0144 (2)0.0192 (2)0.0041 (1)0.0040 (1)0.0002 (1)
Geometric parameters (Å, º) top
O1—C91.2234 (17)C4—C51.397 (2)
N1—C11.4654 (19)C5—C61.390 (2)
N1—C81.3096 (19)C6—C71.392 (2)
N2—C81.3356 (18)C7—C81.463 (2)
N2—C91.4197 (19)C1—H1A0.9700
N3—C91.3296 (19)C1—H1B0.9700
N3—C101.456 (2)C3—H30.9300
N1—H1N0.81 (2)C4—H40.9300
N2—H2N0.90 (2)C5—H50.9300
N3—H3N0.86 (2)C6—H60.9300
C1—C21.501 (2)C10—H10A0.9600
C2—C31.390 (2)C10—H10B0.9600
C2—C71.395 (2)C10—H10C0.9600
C3—C41.390 (2)
Cl1···C13.4838 (16)C8···C7vii3.457 (2)
Cl1···C23.6463 (16)C9···C3vii3.539 (2)
Cl1···C5i3.6252 (16)C9···C6ii3.358 (2)
Cl1···N2ii3.0969 (13)C9···C4vii3.513 (2)
Cl1···N3ii3.2082 (13)C9···C5ii3.575 (2)
Cl1···H5i2.9100C10···C4ii3.500 (3)
Cl1···H1A2.9300C10···C5ii3.579 (3)
Cl1···H1Biii2.7400C10···C10ix3.283 (2)
Cl1···H2Nii2.23 (2)C1···H10Bx2.9400
Cl1···H3iv3.0500C5···H10Aii3.0400
Cl1···H3Nii2.40 (2)C6···H2N2.82 (2)
Cl1···H6ii2.9900C9···H1N2.75 (2)
Cl1···H10Av3.0400C10···H10Bix3.0600
O1···O1vi2.9982 (16)C10···H10Cix3.0700
O1···N1vi2.8760 (17)H1A···Cl12.9300
O1···N12.7097 (16)H1B···Cl1xi2.7400
O1···H1Nvi2.15 (2)H1B···H10Bx2.4700
O1···H10A2.6500H1N···O1vi2.15 (2)
O1···H1N2.22 (2)H1N···C92.75 (2)
N1···O12.7097 (16)H1N···O12.22 (2)
N1···O1vi2.8760 (17)H2N···H62.4000
N2···Cl1ii3.0969 (13)H2N···H3N2.11 (3)
N3···C5ii3.436 (2)H2N···C62.82 (2)
N3···C3vii3.433 (2)H2N···Cl1ii2.23 (2)
N3···Cl1ii3.2082 (13)H3···Cl1iv3.0500
N2···H62.9400H3N···H2N2.11 (3)
C1···Cl13.4838 (16)H3N···Cl1ii2.40 (2)
C2···Cl13.6463 (16)H5···Cl1viii2.9100
C3···N3vii3.433 (2)H6···H2N2.4000
C3···C9vii3.539 (2)H6···N22.9400
C4···C9vii3.513 (2)H6···Cl1ii2.9900
C4···C10ii3.500 (3)H10A···O12.6500
C5···N3ii3.436 (2)H10A···Cl1v3.0400
C5···C9ii3.575 (2)H10A···C5ii3.0400
C5···C10ii3.579 (3)H10B···C10ix3.0600
C5···Cl1viii3.6252 (16)H10B···H1Bxii2.4700
C6···C9ii3.358 (2)H10B···C1xii2.9400
C7···C8vii3.457 (2)H10C···C10ix3.0700
C1—N1—C8112.52 (12)N2—C9—N3112.47 (12)
C8—N2—C9124.09 (12)O1—C9—N2121.32 (12)
C9—N3—C10120.48 (13)O1—C9—N3126.20 (13)
C8—N1—H1N125.2 (14)N1—C1—H1A111.00
C1—N1—H1N122.2 (14)N1—C1—H1B111.00
C8—N2—H2N118.4 (13)C2—C1—H1A111.00
C9—N2—H2N117.5 (13)C2—C1—H1B111.00
C10—N3—H3N121.3 (13)H1A—C1—H1B109.00
C9—N3—H3N118.2 (13)C2—C3—H3121.00
N1—C1—C2101.98 (12)C4—C3—H3121.00
C1—C2—C3130.68 (13)C3—C4—H4119.00
C3—C2—C7120.12 (13)C5—C4—H4119.00
C1—C2—C7109.19 (12)C4—C5—H5120.00
C2—C3—C4117.74 (14)C6—C5—H5120.00
C3—C4—C5121.78 (14)C5—C6—H6122.00
C4—C5—C6120.86 (14)C7—C6—H6122.00
C5—C6—C7116.91 (13)N3—C10—H10A109.00
C2—C7—C8106.74 (12)N3—C10—H10B109.00
C2—C7—C6122.59 (13)N3—C10—H10C109.00
C6—C7—C8130.66 (13)H10A—C10—H10B109.00
N1—C8—C7109.54 (12)H10A—C10—H10C109.00
N1—C8—N2126.82 (13)H10B—C10—H10C109.00
N2—C8—C7123.63 (12)
C8—N1—C1—C21.26 (17)C1—C2—C7—C6177.86 (14)
C1—N1—C8—C71.95 (18)C1—C2—C7—C81.00 (17)
C1—N1—C8—N2178.99 (15)C3—C2—C7—C61.0 (2)
C9—N2—C8—N10.2 (3)C3—C2—C7—C8179.83 (14)
C8—N2—C9—N3176.55 (15)C2—C3—C4—C50.6 (2)
C9—N2—C8—C7179.15 (14)C3—C4—C5—C60.6 (2)
C8—N2—C9—O13.7 (2)C4—C5—C6—C70.1 (2)
C10—N3—C9—O11.4 (3)C5—C6—C7—C8179.48 (16)
C10—N3—C9—N2178.92 (15)C5—C6—C7—C20.9 (2)
N1—C1—C2—C3178.61 (16)C2—C7—C8—N11.83 (18)
N1—C1—C2—C70.06 (17)C6—C7—C8—N1176.90 (16)
C1—C2—C3—C4178.36 (16)C6—C7—C8—N22.2 (3)
C7—C2—C3—C40.2 (2)C2—C7—C8—N2179.07 (15)
Symmetry codes: (i) x, y1, z; (ii) x, y+1, z+1; (iii) x1, y, z; (iv) x+1, y+1, z; (v) x, y, z+1; (vi) x+1, y, z+1; (vii) x+1, y+1, z+1; (viii) x, y+1, z; (ix) x, y, z+2; (x) x+1, y, z1; (xi) x+1, y, z; (xii) x1, y, z+1.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1N···O10.81 (2)2.22 (2)2.7097 (16)119.9 (18)
N1—H1N···O1vi0.81 (2)2.15 (2)2.8760 (17)150 (2)
N2—H2N···Cl1ii0.90 (2)2.23 (2)3.0969 (13)160.5 (18)
N3—H3N···Cl1ii0.86 (2)2.40 (2)3.2082 (13)157.0 (17)
C1—H1B···Cl1xi0.97002.74003.6755 (16)162.00
Symmetry codes: (ii) x, y+1, z+1; (vi) x+1, y, z+1; (xi) x+1, y, z.

Experimental details

Crystal data
Chemical formulaC10H12N3O+·Cl
Mr225.68
Crystal system, space groupTriclinic, P1
Temperature (K)296
a, b, c (Å)7.1171 (5), 7.7900 (6), 10.3033 (8)
α, β, γ (°)89.484 (3), 69.997 (2), 74.613 (4)
V3)515.43 (7)
Z2
Radiation typeMo Kα
µ (mm1)0.35
Crystal size (mm)0.30 × 0.10 × 0.06
Data collection
DiffractometerBruker Kappa APEXII CCD
diffractometer
Absorption correctionMulti-scan
(SADABS; Bruker, 2005)
Tmin, Tmax0.982, 0.989
No. of measured, independent and
observed [I > 2σ(I)] reflections
8853, 2369, 2210
Rint0.020
(sin θ/λ)max1)0.651
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.032, 0.101, 1.01
No. of reflections2369
No. of parameters146
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.69, 0.22

Computer programs: APEX2 (Bruker, 2007), SAINT (Bruker, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 1997) and PLATON (Spek, 2003), WinGX (Farrugia, 1999) and PLATON (Spek, 2003).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1N···O10.81 (2)2.22 (2)2.7097 (16)119.9 (18)
N1—H1N···O1i0.81 (2)2.15 (2)2.8760 (17)150 (2)
N2—H2N···Cl1ii0.90 (2)2.23 (2)3.0969 (13)160.5 (18)
N3—H3N···Cl1ii0.86 (2)2.40 (2)3.2082 (13)157.0 (17)
C1—H1B···Cl1iii0.97002.74003.6755 (16)162.00
Symmetry codes: (i) x+1, y, z+1; (ii) x, y+1, z+1; (iii) x+1, y, z.
 

Acknowledgements

The authors acknowledge the Higher Education Commission, Islamabad, and the University of the Punjab, Lahore, Pakistan, for funding the research.

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