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Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890

1-Phenyl­piperazine-1,4-diium bis­­(hydrogen sulfate)

aLaboratoire de Chimie des Matériaux, Faculté des Sciences de Bizerte, 7021 Zarzouna Bizerte, Tunisia, and bPetrochemical Research Chair, College of Science, King Saud University, Riadh, Saudi Arabia
*Correspondence e-mail: houda.marouani@fsb.rnu.tn

(Received 9 September 2010; accepted 15 September 2010; online 25 September 2010)

In the title compound, C10H16N22+·2HSO4, the S atoms adopt slightly distorted tetra­hedral geometry and the diprotonated piperazine ring adopts a chair conformation. In the crystal, the 1-phenyl­piperazine-1,4-diium cations are anchored between chains formed by the sulfate entities via inter­molecular bifurcated N—H⋯(O,O) and weak C—H⋯O hydrogen bonds. These hydrogen bonds contribute to the cohesion and stability of the network of the crystal structure.

Related literature

For pharmacological properties of phenyl­piperazine, see: Cohen et al. (1982[Cohen, M. R., Hinsch, E., Palkoski, Z., Vergona, R., Urbano, S. & Sztokalo, J. (1982). J. Pharmcol. Exp. Ther. 223, 110-115.]); Conrado et al. (2008[Conrado, D. J., Verli, H., Neves, G., Fraga, C. A., Barreiro, E. J., Rates, S. M. & Dalla-Costa, T. (2008). J. Pharm. Pharmacol. 60, 699-707.]); Neves et al. (2003[Neves, G., Fenner, R., Heckler, A. P., Viana, A. F., Tasso, L., Menegatti, R., Fraga, C. A. M., Barreiro, E. J., Dalla-Costa, T. & Rates, S. M. K. (2003). Braz. J. Med. Biol. Res. 36, 625-629.]). For related structures, see: Ben Gharbia et al. (2005[Ben Gharbia, I., Kefi, R., Rayes, A. & Ben Nasr, C. (2005). Z. Kristallogr. 220, 333-334.]). For a discussion on hydrogen bonding, see: Brown (1976[Brown, I. D. (1976). Acta Cryst. A32, 24-31.]); Blessing (1986[Blessing, R. H. (1986). Acta Cryst. B42, 613-621.]). For structural discussion, see: Arbuckle et al. (2009[Arbuckle, W., Kennedy, A. R. & Morrison, C. A. (2009). Acta Cryst. E65, o1768-o1769.]). For puckering parameters, see: Cremer & Pople (1975[Cremer, D. & Pople, J. A. (1975). J. Am. Chem. Soc. 97, 1354-1358.]).

[Scheme 1]

Experimental

Crystal data
  • C10H16N22+·2HSO4

  • Mr = 358.38

  • Monoclinic, P 21 /c

  • a = 17.535 (6) Å

  • b = 10.996 (2) Å

  • c = 7.631 (2) Å

  • β = 99.86 (2)°

  • V = 1449.7 (7) Å3

  • Z = 4

  • Ag Kα radiation

  • λ = 0.56083 Å

  • μ = 0.22 mm−1

  • T = 293 K

  • 0.5 × 0.4 × 0.1 mm

Data collection
  • Enraf–Nonius CAD-4 diffractometer

  • 8212 measured reflections

  • 7100 independent reflections

  • 4535 reflections with I > 2σ(I)

  • Rint = 0.022

  • 2 standard reflections every 120 min intensity decay: 1%

Refinement
  • R[F2 > 2σ(F2)] = 0.046

  • wR(F2) = 0.127

  • S = 1.03

  • 7100 reflections

  • 201 parameters

  • H-atom parameters constrained

  • Δρmax = 0.43 e Å−3

  • Δρmin = −0.46 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
O1—H1⋯O3i 0.82 1.80 2.6140 (17) 172
O5—H5⋯O7ii 0.82 1.80 2.6066 (18) 169
N1—H1A⋯O2iii 0.90 2.23 2.8636 (19) 128
N1—H1A⋯O3iv 0.90 2.30 3.0279 (19) 138
N1—H1B⋯O3 0.90 2.14 2.9251 (18) 145
N1—H1B⋯O2i 0.90 2.35 2.9892 (18) 128
N2—H2⋯O7 0.91 2.02 2.8216 (16) 146
N2—H2⋯O6ii 0.91 2.32 2.9037 (17) 122
Symmetry codes: (i) [x, -y+{\script{3\over 2}}, z-{\script{1\over 2}}]; (ii) [x, -y+{\script{1\over 2}}, z+{\script{1\over 2}}]; (iii) [-x+2, y-{\script{1\over 2}}, -z+{\script{3\over 2}}]; (iv) -x+2, -y+1, -z+1.

Data collection: CAD-4 EXPRESS (Enraf–Nonius, 1994[Enraf-Nonius (1994). CAD-4 EXPRESS. Enraf-Nonius, Delft, The Netherlands.]); cell refinement: CAD-4 EXPRESS; data reduction: XCAD4 (Harms & Wocadlo, 1995[Harms, K. & Wocadlo, S. (1995). XCAD4. University of Marburg, Germany.]); program(s) used to solve structure: SHELXS86 (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-32 for Windows (Farrugia, 1998[Farrugia, L. J. (1998). ORTEP-32 for Windows. University of Glasgow, Scotland.]); software used to prepare material for publication: WinGX (Farrugia, 1999[Farrugia, L. J. (1999). J. Appl. Cryst. 32, 837-838.]).

Supporting information


Comment top

The phenylpiperazine and its derivatives have been intensively investigated recently owing to their interesting pharmacological, cardiovascular and autonomic properties (Conrado et al., 2008; Cohen et al., 1982; Neves et al., 2003). We report here the preparation and the crystal structure of the title compound, (I).

The asymmetric unit of the title compound (Fig.1) consists of two HSO4- anions and a 1-phenylpiperazine-1,4-diium cation. The interatomic bond lengths and angles of the cation show no significant deviation from those reported in other 1-phenylpiperazinium salts such as [C10H16N2]2ZnCl4 (Ben Gharbia, et al., 2005). In the title compound, the distances S—O are significantly longer than the SO distances as reported in the hydrogen sulfate ion previously (Arbuckle, et al., 2009). The aromatic ring is essentially planar while the diprotonated piperazine ring adopts a chair conformation, with puckering parameters (Cremer & Pople, 1975): Q = 0.5913 (14) Å, θ = 178.61 (15)° and ϕ = 76 (5)°.

The atomic arrangement is characterized by infinite chains built by HSO4- anions. The inorganic chains, extending along the c direction, are located around planes perpendicular to the a axis at x = 0 (for HS1O4-) and x = 1/4, x = 3/4 (for HS2O4-). The hydrogen sulfate groups of the same type are interconnected via strong O—H···O hydrogen bonds (Table 1)[d (O···O) < 2.73 Å] (Brown, 1976; Blessing, 1986). Chains formed by HS1O4 are linked by N1 nitrogen atom of the cation to form layers parallel to the bc plane at x = 0. Two chains of different type are bound between them by the cations through their two nitrogen atoms by means of the N—H···O hydrogen bonds (Fig. 2).

The cations are linked onto the anionic chains, by forming H-bonds with the oxygen atoms with N—H···O distances in the range 2.8216 (16)–3.0279 (19) Å and C—H···O distances in the range 2.949 (2)–3.520 (2) Å. It should be noticed that all the amino hydrogen atoms are involved in bifurcated N—H···(O, O) hydrogen bonding. These hydrogen bonds contribute to the cohesion and stability of the network of the studied crystal structure.

Related literature top

For pharmacological properties of phenylpiperazine, see: Cohen et al. (1982); Conrado et al. (2008); Neves et al. (2003). For related structures, see: Ben Gharbia et al. (2005). For a discussion on hydrogen bonding, see: Brown (1976); Blessing (1986). For structural discussion, see: Arbuckle et al. (2009). For puckering parameters, see: Cremer & Pople (1975).

Experimental top

Single crystals of the title compound were prepared at room temperature from a mixture of an aqueous solution of sulfuric acid (2 mmol), 1-phenylpiperazine (1 mmol), ethanol (10 ml) and water (10 ml). The solution was stirred for 1 h then evaporated slowly at room temperature for several days until the formation of good quality of prismatic single crystals.

Refinement top

All H atoms were fixed geometrically and treated as riding with C—H = 0.93 Å (aromatic) or 0.97 Å (methylene), N—H = 0.90 Å or 0.91 Å and O—H = 0.82 Å with Uiso(H) = 1.2Ueq(C or N) or 1.5Ueq(O).

Computing details top

Data collection: CAD-4 EXPRESS (Enraf–Nonius, 1994); cell refinement: CAD-4 EXPRESS (Enraf–Nonius, 1994); data reduction: XCAD4 (Harms & Wocadlo, 1995); program(s) used to solve structure: SHELXS86 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-32 for Windows (Farrugia, 1998); software used to prepare material for publication: WinGX (Farrugia, 1999).

Figures top
[Figure 1] Fig. 1. An ORTEP view of (I) with the atom-labelling scheme. Displacement ellipsoids are drawn at the 30% probability level. H atoms are represented as small spheres of arbitrary radii.
[Figure 2] Fig. 2. Projection of (I) along the c axis. H atoms non committed in H-bonds are omitted for clarity.
1-Phenylpiperazine-1,4-diium bis(hydrogen sulfate) top
Crystal data top
C10H16N22+·2HSO4F(000) = 752
Mr = 358.38Dx = 1.642 Mg m3
Monoclinic, P21/cAg Kα radiation, λ = 0.56083 Å
Hall symbol: -P 2ybcCell parameters from 25 reflections
a = 17.535 (6) Åθ = 9–11°
b = 10.996 (2) ŵ = 0.22 mm1
c = 7.631 (2) ÅT = 293 K
β = 99.86 (2)°Prism, colorless
V = 1449.7 (7) Å30.5 × 0.4 × 0.1 mm
Z = 4
Data collection top
Enraf–Nonius CAD-4
diffractometer
Rint = 0.022
Radiation source: fine-focus sealed tubeθmax = 28.0°, θmin = 2.4°
Graphite monochromatorh = 329
non–profiled ω scansk = 180
8212 measured reflectionsl = 1212
7100 independent reflections2 standard reflections every 120 min
4535 reflections with I > 2σ(I) intensity decay: 1%
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)] = 0.046Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.127H-atom parameters constrained
S = 1.03 w = 1/[σ2(Fo2) + (0.0603P)2 + 0.1738P]
where P = (Fo2 + 2Fc2)/3
7100 reflections(Δ/σ)max = 0.001
201 parametersΔρmax = 0.43 e Å3
0 restraintsΔρmin = 0.46 e Å3
Crystal data top
C10H16N22+·2HSO4V = 1449.7 (7) Å3
Mr = 358.38Z = 4
Monoclinic, P21/cAg Kα radiation, λ = 0.56083 Å
a = 17.535 (6) ŵ = 0.22 mm1
b = 10.996 (2) ÅT = 293 K
c = 7.631 (2) Å0.5 × 0.4 × 0.1 mm
β = 99.86 (2)°
Data collection top
Enraf–Nonius CAD-4
diffractometer
Rint = 0.022
8212 measured reflections2 standard reflections every 120 min
7100 independent reflections intensity decay: 1%
4535 reflections with I > 2σ(I)
Refinement top
R[F2 > 2σ(F2)] = 0.0460 restraints
wR(F2) = 0.127H-atom parameters constrained
S = 1.03Δρmax = 0.43 e Å3
7100 reflectionsΔρmin = 0.46 e Å3
201 parameters
Special details top

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
S10.958198 (19)0.80824 (3)0.59663 (4)0.02129 (8)
S20.68841 (2)0.18262 (3)0.36929 (5)0.02431 (8)
O70.66990 (8)0.31003 (10)0.32493 (15)0.0332 (2)
O30.97861 (7)0.68051 (10)0.64169 (14)0.0306 (2)
N20.73629 (7)0.53363 (10)0.45259 (15)0.0215 (2)
H20.71630.45790.46070.026*
O20.97180 (7)0.88315 (10)0.75428 (14)0.0295 (2)
N10.89625 (7)0.46159 (12)0.49684 (18)0.0273 (2)
H1A0.93330.40410.51360.033*
H1B0.91940.53420.49130.033*
O11.01876 (7)0.85308 (12)0.48419 (14)0.0355 (3)
H11.00360.83680.37910.053*
O40.88248 (7)0.81856 (12)0.49109 (16)0.0366 (3)
O50.63020 (7)0.13868 (12)0.48817 (15)0.0356 (3)
H50.64380.16390.58980.053*
O60.67139 (8)0.10676 (11)0.21389 (16)0.0371 (3)
C30.79171 (8)0.55729 (14)0.62253 (19)0.0258 (3)
H3A0.76390.55670.72200.031*
H3B0.81520.63680.61730.031*
C20.77975 (9)0.53263 (14)0.29912 (19)0.0266 (3)
H2A0.80230.61220.28760.032*
H2B0.74420.51550.19000.032*
C50.67057 (8)0.61993 (13)0.42348 (19)0.0244 (3)
C10.84293 (8)0.43819 (14)0.3260 (2)0.0284 (3)
H1C0.82030.35780.32840.034*
H1D0.87160.44120.22810.034*
C40.85375 (9)0.46091 (15)0.6493 (2)0.0293 (3)
H4A0.88950.47650.75880.035*
H4B0.83040.38170.65880.035*
O80.76519 (7)0.17042 (14)0.47005 (18)0.0465 (3)
C100.68447 (10)0.74340 (14)0.4204 (3)0.0346 (3)
H100.73480.77350.43840.042*
C60.59670 (9)0.57280 (16)0.3966 (2)0.0347 (3)
H60.58870.48920.39870.042*
C90.62142 (12)0.82154 (17)0.3896 (3)0.0468 (5)
H90.62930.90510.38710.056*
C80.54742 (13)0.7761 (2)0.3629 (3)0.0532 (5)
H80.50550.82910.34220.064*
C70.53462 (10)0.6521 (2)0.3664 (3)0.0489 (5)
H70.48430.62210.34850.059*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.02138 (14)0.02425 (15)0.01794 (14)0.00207 (12)0.00249 (10)0.00047 (11)
S20.02718 (16)0.02462 (15)0.02126 (15)0.00051 (13)0.00451 (12)0.00042 (12)
O70.0483 (7)0.0228 (5)0.0284 (5)0.0016 (5)0.0067 (5)0.0006 (4)
O30.0446 (6)0.0249 (5)0.0219 (5)0.0038 (5)0.0047 (4)0.0000 (4)
N20.0196 (5)0.0189 (5)0.0255 (5)0.0014 (4)0.0029 (4)0.0000 (4)
O20.0372 (6)0.0288 (5)0.0225 (5)0.0006 (4)0.0055 (4)0.0059 (4)
N10.0198 (5)0.0266 (6)0.0352 (6)0.0001 (4)0.0037 (5)0.0005 (5)
O10.0341 (6)0.0512 (7)0.0225 (5)0.0180 (5)0.0087 (4)0.0030 (5)
O40.0250 (5)0.0474 (7)0.0343 (6)0.0012 (5)0.0036 (4)0.0024 (5)
O50.0398 (6)0.0412 (7)0.0275 (5)0.0149 (5)0.0103 (5)0.0031 (5)
O60.0545 (8)0.0298 (5)0.0286 (5)0.0002 (5)0.0116 (5)0.0078 (4)
C30.0247 (6)0.0278 (6)0.0241 (6)0.0011 (5)0.0015 (5)0.0018 (5)
C20.0252 (6)0.0316 (7)0.0234 (6)0.0017 (5)0.0052 (5)0.0003 (5)
C50.0221 (6)0.0232 (6)0.0279 (6)0.0029 (5)0.0040 (5)0.0030 (5)
C10.0243 (6)0.0297 (7)0.0320 (7)0.0002 (6)0.0068 (5)0.0057 (6)
C40.0251 (6)0.0347 (8)0.0273 (7)0.0015 (6)0.0019 (5)0.0049 (6)
O80.0297 (6)0.0652 (9)0.0419 (7)0.0035 (6)0.0015 (5)0.0122 (7)
C100.0301 (8)0.0244 (7)0.0494 (10)0.0011 (6)0.0071 (7)0.0036 (6)
C60.0234 (7)0.0330 (8)0.0467 (9)0.0006 (6)0.0029 (6)0.0045 (7)
C90.0468 (11)0.0280 (8)0.0661 (13)0.0109 (8)0.0110 (10)0.0070 (8)
C80.0408 (10)0.0490 (11)0.0707 (15)0.0220 (9)0.0123 (10)0.0172 (11)
C70.0211 (7)0.0548 (12)0.0698 (14)0.0061 (8)0.0050 (8)0.0140 (11)
Geometric parameters (Å, º) top
S1—O41.4347 (13)C3—H3B0.9700
S1—O21.4438 (11)C2—C11.507 (2)
S1—O31.4754 (11)C2—H2A0.9700
S1—O11.5553 (12)C2—H2B0.9700
S2—O81.4378 (14)C5—C61.377 (2)
S2—O61.4387 (12)C5—C101.380 (2)
S2—O71.4647 (12)C1—H1C0.9700
S2—O51.5542 (12)C1—H1D0.9700
N2—C51.4799 (18)C4—H4A0.9700
N2—C21.5027 (19)C4—H4B0.9700
N2—C31.5041 (18)C10—C91.388 (2)
N2—H20.9100C10—H100.9300
N1—C41.485 (2)C6—C71.383 (2)
N1—C11.491 (2)C6—H60.9300
N1—H1A0.9000C9—C81.373 (3)
N1—H1B0.9000C9—H90.9300
O1—H10.8200C8—C71.383 (3)
O5—H50.8200C8—H80.9300
C3—C41.507 (2)C7—H70.9300
C3—H3A0.9700
O4—S1—O2115.31 (8)C1—C2—H2A109.4
O4—S1—O3111.75 (7)N2—C2—H2B109.4
O2—S1—O3110.49 (7)C1—C2—H2B109.4
O4—S1—O1108.60 (8)H2A—C2—H2B108.0
O2—S1—O1104.35 (7)C6—C5—C10122.13 (15)
O3—S1—O1105.60 (7)C6—C5—N2117.99 (13)
O8—S2—O6115.46 (9)C10—C5—N2119.87 (13)
O8—S2—O7111.29 (8)N1—C1—C2109.67 (12)
O6—S2—O7110.95 (7)N1—C1—H1C109.7
O8—S2—O5107.90 (8)C2—C1—H1C109.7
O6—S2—O5103.68 (7)N1—C1—H1D109.7
O7—S2—O5106.89 (8)C2—C1—H1D109.7
C5—N2—C2111.93 (11)H1C—C1—H1D108.2
C5—N2—C3112.96 (11)N1—C4—C3109.71 (12)
C2—N2—C3109.52 (11)N1—C4—H4A109.7
C5—N2—H2107.4C3—C4—H4A109.7
C2—N2—H2107.4N1—C4—H4B109.7
C3—N2—H2107.4C3—C4—H4B109.7
C4—N1—C1111.13 (12)H4A—C4—H4B108.2
C4—N1—H1A109.4C5—C10—C9118.29 (17)
C1—N1—H1A109.4C5—C10—H10120.9
C4—N1—H1B109.4C9—C10—H10120.9
C1—N1—H1B109.4C5—C6—C7118.74 (17)
H1A—N1—H1B108.0C5—C6—H6120.6
S1—O1—H1109.5C7—C6—H6120.6
S2—O5—H5109.5C8—C9—C10120.33 (18)
N2—C3—C4109.89 (12)C8—C9—H9119.8
N2—C3—H3A109.7C10—C9—H9119.8
C4—C3—H3A109.7C9—C8—C7120.56 (18)
N2—C3—H3B109.7C9—C8—H8119.7
C4—C3—H3B109.7C7—C8—H8119.7
H3A—C3—H3B108.2C8—C7—C6119.95 (18)
N2—C2—C1110.98 (12)C8—C7—H7120.0
N2—C2—H2A109.4C6—C7—H7120.0
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1···O3i0.821.802.6140 (17)172
O5—H5···O7ii0.821.802.6066 (18)169
N1—H1A···O2iii0.902.232.8636 (19)128
N1—H1A···O3iv0.902.303.0279 (19)138
N1—H1B···O30.902.142.9251 (18)145
N1—H1B···O2i0.902.352.9892 (18)128
N2—H2···O70.912.022.8216 (16)146
N2—H2···O6ii0.912.322.9037 (17)122
C1—H1C···O80.972.593.500 (2)156
C1—H1D···O2i0.972.603.113 (2)114
C3—H3A···O6ii0.972.422.949 (2)114
C3—H3B···O40.972.593.513 (2)159
C6—H6···O70.932.553.246 (2)132
C10—H10···O40.932.603.520 (2)170
Symmetry codes: (i) x, y+3/2, z1/2; (ii) x, y+1/2, z+1/2; (iii) x+2, y1/2, z+3/2; (iv) x+2, y+1, z+1.

Experimental details

Crystal data
Chemical formulaC10H16N22+·2HSO4
Mr358.38
Crystal system, space groupMonoclinic, P21/c
Temperature (K)293
a, b, c (Å)17.535 (6), 10.996 (2), 7.631 (2)
β (°) 99.86 (2)
V3)1449.7 (7)
Z4
Radiation typeAg Kα, λ = 0.56083 Å
µ (mm1)0.22
Crystal size (mm)0.5 × 0.4 × 0.1
Data collection
DiffractometerEnraf–Nonius CAD-4
diffractometer
Absorption correction
No. of measured, independent and
observed [I > 2σ(I)] reflections
8212, 7100, 4535
Rint0.022
(sin θ/λ)max1)0.836
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.046, 0.127, 1.03
No. of reflections7100
No. of parameters201
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.43, 0.46

Computer programs: CAD-4 EXPRESS (Enraf–Nonius, 1994), XCAD4 (Harms & Wocadlo, 1995), SHELXS86 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-32 for Windows (Farrugia, 1998), WinGX (Farrugia, 1999).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1···O3i0.821.802.6140 (17)171.8
O5—H5···O7ii0.821.802.6066 (18)169.0
N1—H1A···O2iii0.902.232.8636 (19)127.5
N1—H1A···O3iv0.902.303.0279 (19)138.1
N1—H1B···O30.902.142.9251 (18)145.4
N1—H1B···O2i0.902.352.9892 (18)128.2
N2—H2···O70.912.022.8216 (16)145.8
N2—H2···O6ii0.912.322.9037 (17)121.8
Symmetry codes: (i) x, y+3/2, z1/2; (ii) x, y+1/2, z+1/2; (iii) x+2, y1/2, z+3/2; (iv) x+2, y+1, z+1.
 

Acknowledgements

We would like to acknowledge the support provided by the Secretary of State for Scientific Research and Technology of Tunisia.

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