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ISSN: 2056-9890

N-Benzoyl-4-nitro­benzene­sulfonamide monohydrate

aDepartment of Chemistry, Mangalore University, Mangalagangotri 574 199, Mangalore, India, bInstitute of Materials Science, Darmstadt University of Technology, Petersenstrasse 23, D-64287 Darmstadt, Germany, and cDepartment of Chemistry, University College of Science, Tumkur University, Tumkur 572 102, India
*Correspondence e-mail: gowdabt@yahoo.com

(Received 28 November 2011; accepted 29 November 2011; online 3 December 2011)

In the title compound, C13H10N2O5S·H2O, the dihedral angle between the sulfonyl and benzoyl benzene rings is 83.4 (1)°. In the crystal, the water mol­ecule forms four hydrogen bonds with three different mol­ecules of N-benzoyl-4-nitro­benzene­sulfonamide. One of the H atoms of H2O forms a bifurcated hydrogen bond with a sulfonyl and the carbonyl O atoms. Mol­ecules are linked into a three-dimensional network by N—H⋯O and O—H⋯O hydrogen bonds.

Related literature

For our studies on the effects of substituents on the structures and other aspects of N-(ar­yl)-amides, see: Gowda et al. (2004[Gowda, B. T., Svoboda, I. & Fuess, H. (2004). Z. Naturforsch. Teil A, 59, 845-852.]), on N-(ar­yl)-methane­sulfonamides, see: Jayalakshmi & Gowda (2004[Jayalakshmi, K. L. & Gowda, B. T. (2004). Z. Naturforsch. Teil A, 59, 491-500.]), on N-(ar­yl)-aryl­sulfonamides, see: Gowda et al. (2003[Gowda, B. T., Jyothi, K., Kozisek, J. & Fuess, H. (2003). Z. Naturforsch. Teil A, 58, 656-660.]), on N-(substituted-benzo­yl)-aryl­sulfonamides, see: Suchetan et al. (2011[Suchetan, P. A., Foro, S. & Gowda, B. T. (2011). Acta Cryst. E67, o3515.]) and on N-chloro­aryl­amides, see: Gowda et al. (1996[Gowda, B. T., Dou, S. Q. & Weiss, A. (1996). Z. Naturforsch. Teil A, 51, 627-636.]).

[Scheme 1]

Experimental

Crystal data
  • C13H10N2O5S·H2O

  • Mr = 324.31

  • Monoclinic, P 21 /c

  • a = 22.687 (2) Å

  • b = 5.0673 (4) Å

  • c = 12.755 (1) Å

  • β = 100.04 (1)°

  • V = 1443.9 (2) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.26 mm−1

  • T = 293 K

  • 0.46 × 0.08 × 0.06 mm

Data collection
  • Oxford Diffraction Xcalibur diffractometer with a Sapphire CCD detector

  • Absorption correction: multi-scan (CrysAlis RED; Oxford Diffraction, 2009[Oxford Diffraction (2009). CrysAlis CCD and CrysAlis RED. Oxford Diffraction Ltd, Yarnton, England.]) Tmin = 0.891, Tmax = 0.985

  • 4828 measured reflections

  • 2608 independent reflections

  • 2039 reflections with I > 2σ(I)

  • Rint = 0.021

Refinement
  • R[F2 > 2σ(F2)] = 0.056

  • wR(F2) = 0.110

  • S = 1.26

  • 2608 reflections

  • 208 parameters

  • 3 restraints

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

  • Δρmax = 0.22 e Å−3

  • Δρmin = −0.36 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N1—H1N⋯O6 0.86 (2) 1.92 (2) 2.763 (4) 170 (3)
O6—H61⋯O2i 0.84 (2) 2.14 (2) 2.935 (4) 158 (4)
O6—H62⋯O3ii 0.82 (2) 2.23 (3) 2.919 (4) 142 (4)
O6—H62⋯O1ii 0.82 (2) 2.33 (3) 2.988 (3) 138 (4)
Symmetry codes: (i) x, y-1, z; (ii) [x, -y+{\script{1\over 2}}, z-{\script{1\over 2}}].

Data collection: CrysAlis CCD (Oxford Diffraction, 2009[Oxford Diffraction (2009). CrysAlis CCD and CrysAlis RED. Oxford Diffraction Ltd, Yarnton, England.]); cell refinement: CrysAlis RED (Oxford Diffraction, 2009[Oxford Diffraction (2009). CrysAlis CCD and CrysAlis RED. Oxford Diffraction Ltd, Yarnton, England.]); data reduction: CrysAlis RED; 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: PLATON (Spek, 2009[Spek, A. L. (2009). Acta Cryst. D65, 148-155.]); software used to prepare material for publication: SHELXL97.

Supporting information


Comment top

Diaryl acylsulfonamides are known as potent antitumor agents. As part of our studies on the substituent effects on the structures and other aspects of N-(aryl)-amides (Gowda et al., 2004), N-(aryl)-methanesulfonamides (Jayalakshmi & Gowda, 2004), N-(aryl)-arylsulfonamides (Gowda et al., 2003); N-(substitutedbenzoyl)-arylsulfonamides (Suchetan et al., 2011) and N-chloro-arylsulfonamides (Gowda et al., 1996), in the present work, the crystal structure of N-(benzoyl)- 4-nitrobenzenesulfonamide monohydrate (I) has been determined (Fig.1).

The conformations of the N—H and C=O bonds in the C—SO2—NH—C(O) segment are anti to each other (Fig.1), similar to that observed in N-(benzoyl)-3-nitrobenzenesulfonamide (II)(Suchetan et al., 2011). The molecule is twisted at the S atom with the torsional angle of -72.45 (28)°, compared to the value of -62.80 (17)° in (II).

The dihedral angle between the sulfonyl benzene ring and the —SO2—NH—C—O segment is 78.5 (1)°, compared to the value of 79.2 (1)° in (II). Furthermore, the dihedral angle between the sulfonyl and the benzoyl benzene rings is 83.4 (1)°, compared to the value of 86.7 (1)° in (II).

Further, the crystal structure shows interesting H-bonding. Every water molecule forms four H-bonds with three different molecules of the titile compound. One of the H-atoms of the water molecule forms simultaneous H-bonding with both the sulfonyl and the carbonyl oxygen atoms of the same molecule.

The packing of molecules through N1—H1N···O6, O6—H61···O2, O6—H62···O3 and O6—H62···O1 hydrogen bonds (Table 1) is shown in Fig. 2.

Related literature top

For our studies on the effects of substituents on the structures and other aspects of N-(aryl)-amides, see: Gowda et al. (2004), on N-(aryl)-methanesulfonamides, see: Jayalakshmi & Gowda (2004), on N-(aryl)-arylsulfonamides, see: Gowda et al. (2003), on N-(substituted-benzoyl)-arylsulfonamides, see: Suchetan et al. (2011) and on N-chloroarylamides, see: Gowda et al. (1996).

Experimental top

The title compound was prepared by refluxing a mixture of benzoic acid (0.02 mole), 4-nitrobenzenesulfonamide (0.02 mole) and excess phosphorous oxy chloride for 3 h on a water bath. The resultant mixture was cooled and poured into crushed ice. The solid, N-(benzoyl)-4-nitrobenzenesulfonamide monohydrate, obtained was filtered, washed thoroughly with water and then dissolved in sodium bicarbonate solution. The compound was later reprecipitated by acidifying the filtered solution with dilute HCl. It was filtered, dried and recrystallized.

Rod like colourless single crystals of the title compound used in X-ray diffraction studies were obtained by slow evaporation of an ethanol–tetrahydrofuran solution at room temperature.

Refinement top

The H atoms of the NH group and of the water molecule were located in a difference map and later restrained to N—H = 0.86 (2) Å and O—H = 0.85 (2) Å. The other H atoms were positioned with idealized geometry using a riding model with C—H = 0.93 Å. All H atoms were refined with isotropic displacement parameters set to 1.2 times of the Ueq of the parent atom.

Computing details top

Data collection: CrysAlis CCD (Oxford Diffraction, 2009); cell refinement: CrysAlis RED (Oxford Diffraction, 2009); data reduction: CrysAlis RED (Oxford Diffraction, 2009); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: PLATON (Spek, 2009); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. Molecular structure of the title compound, showing the atom-labelling scheme. Displacement ellipsoids are drawn at the 50% probability level.
[Figure 2] Fig. 2. Molecular packing in the title compound. Hydrogen bonds are shown as dashed lines.
N-Benzoyl-4-nitrobenzenesulfonamide monohydrate top
Crystal data top
C13H10N2O5S·H2OF(000) = 672
Mr = 324.31Dx = 1.492 Mg m3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 1916 reflections
a = 22.687 (2) Åθ = 2.6–27.8°
b = 5.0673 (4) ŵ = 0.26 mm1
c = 12.755 (1) ÅT = 293 K
β = 100.04 (1)°Rod, colourless
V = 1443.9 (2) Å30.46 × 0.08 × 0.06 mm
Z = 4
Data collection top
Oxford Diffraction Xcalibur
diffractometer with a Sapphire CCD detector
2608 independent reflections
Radiation source: fine-focus sealed tube2039 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.021
Rotation method data acquisition using ω and phi scansθmax = 25.4°, θmin = 2.7°
Absorption correction: multi-scan
(CrysAlis RED; Oxford Diffraction, 2009)
h = 2724
Tmin = 0.891, Tmax = 0.985k = 64
4828 measured reflectionsl = 915
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)] = 0.056Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.110H atoms treated by a mixture of independent and constrained refinement
S = 1.26 w = 1/[σ2(Fo2) + (0.0194P)2 + 1.7364P]
where P = (Fo2 + 2Fc2)/3
2608 reflections(Δ/σ)max = 0.005
208 parametersΔρmax = 0.22 e Å3
3 restraintsΔρmin = 0.36 e Å3
Crystal data top
C13H10N2O5S·H2OV = 1443.9 (2) Å3
Mr = 324.31Z = 4
Monoclinic, P21/cMo Kα radiation
a = 22.687 (2) ŵ = 0.26 mm1
b = 5.0673 (4) ÅT = 293 K
c = 12.755 (1) Å0.46 × 0.08 × 0.06 mm
β = 100.04 (1)°
Data collection top
Oxford Diffraction Xcalibur
diffractometer with a Sapphire CCD detector
2608 independent reflections
Absorption correction: multi-scan
(CrysAlis RED; Oxford Diffraction, 2009)
2039 reflections with I > 2σ(I)
Tmin = 0.891, Tmax = 0.985Rint = 0.021
4828 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0563 restraints
wR(F2) = 0.110H atoms treated by a mixture of independent and constrained refinement
S = 1.26Δρmax = 0.22 e Å3
2608 reflectionsΔρmin = 0.36 e Å3
208 parameters
Special details top

Experimental. CrysAlis RED (Oxford Diffraction, 2009) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.

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
C10.16151 (12)0.1882 (6)0.6022 (2)0.0291 (7)
C20.15709 (13)0.1477 (6)0.7078 (2)0.0337 (7)
H20.18200.23930.76120.040*
C30.11581 (13)0.0285 (6)0.7333 (2)0.0351 (8)
H30.11280.05960.80400.042*
C40.07914 (13)0.1576 (6)0.6525 (2)0.0308 (7)
C50.08159 (13)0.1161 (7)0.5468 (2)0.0372 (8)
H50.05550.20360.49380.045*
C60.12353 (13)0.0581 (6)0.5209 (2)0.0364 (8)
H60.12640.08830.45000.044*
C70.31104 (13)0.1086 (6)0.6648 (2)0.0346 (7)
C80.36194 (13)0.0639 (7)0.6498 (3)0.0395 (8)
C90.38346 (15)0.2384 (8)0.7303 (3)0.0534 (10)
H90.36620.24490.79130.064*
C100.43058 (18)0.4035 (9)0.7208 (4)0.0721 (13)
H100.44450.52260.77490.087*
C110.45689 (19)0.3931 (10)0.6324 (5)0.0809 (15)
H110.48860.50520.62630.097*
C120.43649 (18)0.2171 (10)0.5526 (4)0.0776 (14)
H120.45510.20750.49320.093*
C130.38845 (16)0.0536 (9)0.5597 (3)0.0582 (11)
H130.37410.06220.50460.070*
N10.27666 (11)0.2048 (5)0.5716 (2)0.0336 (6)
H1N0.2770 (14)0.123 (6)0.5129 (18)0.040*
N20.03640 (12)0.3529 (5)0.6805 (2)0.0397 (7)
O10.23142 (9)0.5955 (4)0.64774 (16)0.0383 (5)
O20.20107 (10)0.4686 (5)0.45919 (16)0.0421 (6)
O30.30049 (10)0.1645 (5)0.75190 (17)0.0485 (6)
O40.04482 (11)0.4391 (5)0.7715 (2)0.0520 (7)
O50.00594 (11)0.4144 (5)0.61181 (19)0.0587 (7)
O60.26446 (15)0.0825 (6)0.3850 (2)0.0655 (8)
H610.2475 (18)0.227 (5)0.390 (3)0.079*
H620.2696 (19)0.024 (8)0.327 (2)0.079*
S10.21771 (3)0.39587 (16)0.56867 (6)0.0309 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
C10.0273 (15)0.0278 (16)0.0323 (16)0.0009 (13)0.0055 (12)0.0000 (13)
C20.0328 (16)0.0399 (19)0.0276 (15)0.0054 (15)0.0028 (12)0.0072 (15)
C30.0360 (17)0.0417 (19)0.0288 (16)0.0038 (15)0.0095 (13)0.0014 (15)
C40.0294 (15)0.0272 (17)0.0370 (17)0.0008 (13)0.0088 (13)0.0028 (14)
C50.0360 (17)0.0400 (19)0.0336 (17)0.0089 (16)0.0010 (13)0.0071 (16)
C60.0390 (17)0.042 (2)0.0268 (15)0.0023 (16)0.0036 (13)0.0009 (15)
C70.0319 (16)0.0332 (18)0.0385 (18)0.0019 (15)0.0054 (13)0.0020 (16)
C80.0282 (16)0.040 (2)0.049 (2)0.0007 (16)0.0036 (14)0.0099 (17)
C90.039 (2)0.049 (2)0.069 (3)0.0069 (19)0.0023 (18)0.001 (2)
C100.054 (2)0.059 (3)0.096 (4)0.013 (2)0.007 (2)0.001 (3)
C110.048 (2)0.075 (3)0.115 (4)0.022 (3)0.003 (3)0.032 (3)
C120.051 (2)0.100 (4)0.087 (3)0.013 (3)0.023 (2)0.029 (3)
C130.043 (2)0.073 (3)0.060 (2)0.007 (2)0.0139 (18)0.011 (2)
N10.0335 (14)0.0377 (16)0.0303 (14)0.0004 (13)0.0072 (11)0.0041 (12)
N20.0396 (16)0.0376 (17)0.0445 (17)0.0061 (14)0.0149 (13)0.0089 (14)
O10.0449 (12)0.0280 (12)0.0420 (12)0.0012 (11)0.0079 (10)0.0053 (10)
O20.0493 (13)0.0437 (14)0.0325 (12)0.0033 (11)0.0046 (10)0.0116 (11)
O30.0499 (14)0.0608 (17)0.0348 (13)0.0150 (13)0.0077 (10)0.0010 (12)
O40.0555 (15)0.0499 (16)0.0525 (15)0.0081 (13)0.0146 (12)0.0129 (13)
O50.0558 (15)0.0691 (19)0.0517 (15)0.0313 (15)0.0112 (12)0.0165 (14)
O60.113 (2)0.0493 (18)0.0364 (14)0.0145 (17)0.0191 (15)0.0004 (14)
S10.0332 (4)0.0290 (4)0.0304 (4)0.0012 (4)0.0054 (3)0.0021 (4)
Geometric parameters (Å, º) top
C1—C21.383 (4)C9—C101.379 (5)
C1—C61.393 (4)C9—H90.9300
C1—S11.762 (3)C10—C111.366 (6)
C2—C31.373 (4)C10—H100.9300
C2—H20.9300C11—C121.372 (7)
C3—C41.372 (4)C11—H110.9300
C3—H30.9300C12—C131.385 (5)
C4—C51.375 (4)C12—H120.9300
C4—N21.472 (4)C13—H130.9300
C5—C61.380 (4)N1—S11.646 (3)
C5—H50.9300N1—H1N0.856 (17)
C6—H60.9300N2—O51.223 (3)
C7—O31.210 (3)N2—O41.223 (3)
C7—N11.392 (4)O1—S11.424 (2)
C7—C81.487 (4)O2—S11.430 (2)
C8—C91.378 (5)O6—H610.836 (19)
C8—C131.388 (5)O6—H620.822 (19)
C2—C1—C6120.9 (3)C10—C9—H9119.9
C2—C1—S1120.2 (2)C11—C10—C9120.4 (4)
C6—C1—S1118.8 (2)C11—C10—H10119.8
C3—C2—C1119.7 (3)C9—C10—H10119.8
C3—C2—H2120.2C10—C11—C12119.9 (4)
C1—C2—H2120.2C10—C11—H11120.1
C4—C3—C2118.8 (3)C12—C11—H11120.1
C4—C3—H3120.6C11—C12—C13120.5 (4)
C2—C3—H3120.6C11—C12—H12119.7
C3—C4—C5122.7 (3)C13—C12—H12119.7
C3—C4—N2118.5 (3)C12—C13—C8119.4 (4)
C5—C4—N2118.8 (3)C12—C13—H13120.3
C4—C5—C6118.7 (3)C8—C13—H13120.3
C4—C5—H5120.6C7—N1—S1123.9 (2)
C6—C5—H5120.6C7—N1—H1N119 (2)
C5—C6—C1119.1 (3)S1—N1—H1N113 (2)
C5—C6—H6120.4O5—N2—O4124.2 (3)
C1—C6—H6120.4O5—N2—C4117.7 (3)
O3—C7—N1122.1 (3)O4—N2—C4118.0 (3)
O3—C7—C8122.5 (3)H61—O6—H62121 (4)
N1—C7—C8115.4 (3)O1—S1—O2119.78 (14)
C9—C8—C13119.5 (3)O1—S1—N1109.00 (13)
C9—C8—C7117.6 (3)O2—S1—N1104.41 (13)
C13—C8—C7122.9 (3)O1—S1—C1109.29 (13)
C8—C9—C10120.2 (4)O2—S1—C1108.16 (13)
C8—C9—H9119.9N1—S1—C1105.22 (14)
C6—C1—C2—C31.8 (5)C11—C12—C13—C81.7 (7)
S1—C1—C2—C3175.6 (2)C9—C8—C13—C120.6 (6)
C1—C2—C3—C41.0 (5)C7—C8—C13—C12178.7 (3)
C2—C3—C4—C50.7 (5)O3—C7—N1—S11.6 (5)
C2—C3—C4—N2177.9 (3)C8—C7—N1—S1179.2 (2)
C3—C4—C5—C61.5 (5)C3—C4—N2—O5161.0 (3)
N2—C4—C5—C6177.1 (3)C5—C4—N2—O520.3 (4)
C4—C5—C6—C10.7 (5)C3—C4—N2—O417.6 (4)
C2—C1—C6—C50.9 (5)C5—C4—N2—O4161.1 (3)
S1—C1—C6—C5176.4 (2)C7—N1—S1—O144.7 (3)
O3—C7—C8—C924.1 (5)C7—N1—S1—O2173.8 (2)
N1—C7—C8—C9156.8 (3)C7—N1—S1—C172.5 (3)
O3—C7—C8—C13155.3 (3)C2—C1—S1—O130.0 (3)
N1—C7—C8—C1323.9 (5)C6—C1—S1—O1152.6 (2)
C13—C8—C9—C100.7 (5)C2—C1—S1—O2162.0 (2)
C7—C8—C9—C10179.9 (3)C6—C1—S1—O220.7 (3)
C8—C9—C10—C110.9 (6)C2—C1—S1—N186.9 (3)
C9—C10—C11—C120.2 (7)C6—C1—S1—N190.5 (3)
C10—C11—C12—C131.5 (7)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1N···O60.86 (2)1.92 (2)2.763 (4)170 (3)
O6—H61···O2i0.84 (2)2.14 (2)2.935 (4)158 (4)
O6—H62···O3ii0.82 (2)2.23 (3)2.919 (4)142 (4)
O6—H62···O1ii0.82 (2)2.33 (3)2.988 (3)138 (4)
Symmetry codes: (i) x, y1, z; (ii) x, y+1/2, z1/2.

Experimental details

Crystal data
Chemical formulaC13H10N2O5S·H2O
Mr324.31
Crystal system, space groupMonoclinic, P21/c
Temperature (K)293
a, b, c (Å)22.687 (2), 5.0673 (4), 12.755 (1)
β (°) 100.04 (1)
V3)1443.9 (2)
Z4
Radiation typeMo Kα
µ (mm1)0.26
Crystal size (mm)0.46 × 0.08 × 0.06
Data collection
DiffractometerOxford Diffraction Xcalibur
diffractometer with a Sapphire CCD detector
Absorption correctionMulti-scan
(CrysAlis RED; Oxford Diffraction, 2009)
Tmin, Tmax0.891, 0.985
No. of measured, independent and
observed [I > 2σ(I)] reflections
4828, 2608, 2039
Rint0.021
(sin θ/λ)max1)0.602
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.056, 0.110, 1.26
No. of reflections2608
No. of parameters208
No. of restraints3
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.22, 0.36

Computer programs: CrysAlis CCD (Oxford Diffraction, 2009), CrysAlis RED (Oxford Diffraction, 2009), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), PLATON (Spek, 2009).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1N···O60.856 (17)1.916 (19)2.763 (4)170 (3)
O6—H61···O2i0.836 (19)2.14 (2)2.935 (4)158 (4)
O6—H62···O3ii0.822 (19)2.23 (3)2.919 (4)142 (4)
O6—H62···O1ii0.822 (19)2.33 (3)2.988 (3)138 (4)
Symmetry codes: (i) x, y1, z; (ii) x, y+1/2, z1/2.
 

Acknowledgements

BTG thanks the University Grants Commission, Government of India, New Delhi, for a special grant under the UGC–BSR one-time grant to faculty.

References

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