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Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890
Volume 67| Part 6| June 2011| Pages m654-m655

Bis(2-amino-1,3-benzo­thia­zol-3-ium) tetra­chloridozincate(II)

aLaboratoire de Chimie des Matériaux, Faculté des Sciences de Bizerte, 7021 Zarzouna, Tunisia, bUniverstié Lyon 1, Centre de Diffractométrie Henri Longchambon, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France, and cLaboratoire de Chimie Organometallique de Surface (LCOMS), École Supérieure de Chimie Physique Électronique, 69622 Villeurbanne Cedex, France
*Correspondence e-mail: cherif_bennasr@yahoo.fr

(Received 8 March 2011; accepted 26 April 2011; online 7 May 2011)

The asymmetric unit of the title compound, (C7H7N2S)2[ZnCl4], contains a network of 2-amino­benzothia­zolium cations and tetra­hedral [ZnCl4]2− anions. The crystal packing is influenced by cation-to-anion N—H⋯Cl and C—H⋯Cl hydrogen bonds. The [ZnCl4]2− anions have a distorded tetra­hedral geometry. Inter­molecular ππ stacking inter­actions are present between neighboring benzene rings, thia­zole and benzene rings and neighboring thia­zole rings [centroid–centroid distances = 3.711 (2), 3.554 (1), 3.536 (2) and 3.572 (1) Å].

Related literature

For common applications of organic–inorganic hybrid mat­erials, see: Bringley & Rajeswaran (2006[Bringley, J. F. & Rajeswaran, M. (2006). Acta Cryst. E62, m1304-m1305.]); Pierpont & Jung (1994[Pierpont, C. G. & Jung, O. (1994). J. Am. Chem. Soc. 116, 2229-2230.]); Dai et al. (2002[Dai, J.-C., Wu, X.-T., Fu, Z.-Y., Cui, C.-P., Wu, S.-M., Du, W.-X., Wu, L.-M., Zhang, H.-H. & Sum, Q.-Q. (2002). Inorg. Chem. 41, 1391-1396.]). For the geometry around the zinc atom, see: Harrison (2005[Harrison, W. T. A. (2005). Acta Cryst. E61, m1951-m1952.]). For the weighting scheme used, see: Prince (1982[Prince, E. (1982). Mathematical Techniques in Crystallography and Materials Science. New York: Springer-Verlag]); Watkin (1994[Watkin, D. (1994). Acta Cryst. A50, 411-437.]) and for the extinction correction, see: Larson (1970[Larson, A. C. (1970). Crystallographic Computing, edited by F. R. Ahmed, S. R. Hall & C. P. Huber, pp. 291-294. Copenhagen: Munksgaard.]).

[Scheme 1]

Experimental

Crystal data
  • (C7H7N2S)2[ZnCl4]

  • Mr = 509.61

  • Triclinic, [P \overline 1]

  • a = 7.543 (1) Å

  • b = 7.828 (1) Å

  • c = 17.109 (2) Å

  • α = 94.250 (1)°

  • β = 100.930 (1)°

  • γ = 92.465 (1)°

  • V = 987.5 (2) Å3

  • Z = 2

  • Mo Kα radiation

  • μ = 2.00 mm−1

  • T = 110 K

  • 0.49 × 0.23 × 0.14 mm

Data collection
  • Agilent Xcalibur Atlas Gemini ultra diffractometer

  • Absorption correction: analytical [using a multifaceted crystal model based on expressions derived by Clark & Reid (1995[Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897.]), implemented in CrysAlis PRO (Agilent, 2010[Agilent (2010). CrysAlis PRO. Agilent Technologies Ltd, Yarnton, England.])] Tmin = 0.498, Tmax = 0.771

  • 10196 measured reflections

  • 4685 independent reflections

  • 3630 reflections with I > 2σ(I)

  • Rint = 0.045

Refinement
  • R[F2 > 2σ(F2)] = 0.054

  • wR(F2) = 0.111

  • S = 0.94

  • 4685 reflections

  • 227 parameters

  • H-atom parameters constrained

  • Δρmax = 1.03 e Å−3

  • Δρmin = −1.23 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N8—H81⋯Cl3i 0.88 2.43 3.190 (5) 145
N15—H151⋯Cl3 0.86 2.42 3.235 (5) 157
N15—H152⋯Cl2i 0.86 2.42 3.274 (5) 176
N25—H251⋯Cl5ii 0.86 2.41 3.215 (5) 155
N16—H161⋯Cl4ii 0.86 2.34 3.196 (5) 177
N16—H162⋯Cl2iii 0.86 2.37 3.215 (5) 166
C20—H201⋯Cl2 0.93 2.69 3.473 (6) 142
C22—H221⋯Cl5iv 0.94 2.78 3.701 (5) 167
C11—H111⋯Cl4v 0.93 2.73 3.592 (6) 154
Symmetry codes: (i) x+1, y, z; (ii) -x+1, -y, -z+2; (iii) -x+1, -y+1, -z+2; (iv) x-1, y-1, z; (v) -x+1, -y+1, -z+1.

Data collection: CrysAlis PRO (Agilent, 2010[Agilent (2010). CrysAlis PRO. Agilent Technologies Ltd, Yarnton, England.]); cell refinement: CrysAlis PRO; data reduction: CrysAlis PRO; program(s) used to solve structure: SIR97 (Altomare et al., 1999[Altomare, A., Burla, M. C., Camalli, M., Cascarano, G. L., Giacovazzo, C., Guagliardi, A., Moliterni, A. G. G., Polidori, G. & Spagna, R. (1999). J. Appl. Cryst. 32, 115-119.]); program(s) used to refine structure: CRYSTALS (Betteridge et al., 2003[Betteridge, P. W., Carruthers, J. R., Cooper, R. I., Prout, K. & Watkin, D. J. (2003). J. Appl. Cryst. 36, 1487.]); molecular graphics: DIAMOND (Brandenburg, 2006[Brandenburg, K. (2006). DIAMOND. Crystal Impact GbR, Bonn, Germany.]); software used to prepare material for publication: CRYSTALS.

Supporting information


Comment top

Inorganic-organic hybrid compounds provide a class of materials displaying interesting technological importance (Bringley & Rajeswaran, 2006; Pierpont & Jung, 1994; Dai et al., 2002). We report the crystal structure of one such compound, (C7H7N2S)2[ZnCl4] (I), formed from the reaction of 2-aminobenzothiazole with zinc chloride. As shown in Fig.1, only the nitrogen atom of the thiazole ring of the title compound is protonated, but not that of the amine group. Thus, to ensure charge equilibrium, the structure associates each tetrachlorizincate anion with two (2-aminobenzothiazolium) cations. Fig.2 shows that the atomic arrangement of the title hybrid material can be described as inorganic ZnCl42- units isolated from each other by the organic cations. The different entities are held together by coulombic attraction and multiple hydrogen bonds to form a three dimensional network. The tetraclorozincate anion geometrical features show that the Zn—Cl bond lengths vary between 2.245 (1) and 2.282 (1) Å and the Cl—Zn—Cl angles range from 103.35 (5) to 112.21 (5) °. These values, which are in good agreement with those reported previously, clearly indicate that the [ZnCl4]2- anion has a slightly distorted tetrahedral stereochemistry (Harrison, 2005). Intermolecular π-π stacking interactions are present between neighboring phenyl rings (centroid-centroid distance = 3.711 (2) Å), thiazole-phenyl rings (centroid-centroid distance = 3.554 (1) Å) and thiazole-thiazole rings (centroid-centroid distances = 3.536 (2) and 3.572 (1) Å) (Fig. 3).

Related literature top

For common applications of organic–inorganic hybrid materials, see: Bringley & Rajeswaran (2006); Pierpont & Jung (1994); Dai et al. (2002). For the geometry around the zinc atom, see: Harrison (2005). For the weighting scheme used, see: Prince (1982); Watkin (1994) and for the extinction correction, see: Larson (1970).

Experimental top

A mixture of an aqueous solution of 2-aminobenzothiazole (3 mmol, 0.450 g), zinc chloride (1.5 mmol, 0.297 g) and HCl (10 ml, 0.3 M) in a Petri dish was slowly evaporated at room temperature. Colorless single crystals of the title compound were isolated after several days (yield 58%).

Refinement top

All non hydrogen atoms were refined anisotropically. The H atoms were all located in a difference map. They were initially refined with soft restraints on the bond lengths and angles to regularize their geometry (C—H in the range 0.93–0.98, N—H in the range 0.86–0.89 Å) and Uiso(H) (in the range 1.2–1.5 times Ueq of the parent atom), after which the positions were refined with riding constraints.

Computing details top

Data collection: CrysAlis PRO (Agilent, 2010); cell refinement: CrysAlis PRO (Agilent, 2010); data reduction: CrysAlis PRO (Agilent, 2010); program(s) used to solve structure: SIR97 (Altomare et al., 1999); program(s) used to refine structure: CRYSTALS (Betteridge et al., 2003); molecular graphics: DIAMOND (Brandenburg, 2006); software used to prepare material for publication: CRYSTALS (Betteridge et al., 2003).

Figures top
[Figure 1] Fig. 1. View of (I), showing 50% probability displacement ellipsoids and arbitrary spheres for the H atoms.
[Figure 2] Fig. 2. The crystal packing of the title compound viewed along the a axis. Hydrogen bonds are denoted by dotted lines. ZnCl4 is given in tetrahedral representation.
[Figure 3] Fig. 3. ππ stacking interactions in (C7H7N2S)2[ZnCl4]. The centroids of the rings are indicated by orange spheres.
Bis(2-amino-1,3-benzothiazol-3-ium) tetrachloridozincate(II) top
Crystal data top
(C7H7N2S)2[ZnCl4]Z = 2
Mr = 509.61F(000) = 512
Triclinic, P1Dx = 1.714 Mg m3
Hall symbol: -P 1Mo Kα radiation, λ = 0.7107 Å
a = 7.543 (1) ÅCell parameters from 3221 reflections
b = 7.828 (1) Åθ = 3.4–29.4°
c = 17.109 (2) ŵ = 2.00 mm1
α = 94.250 (1)°T = 110 K
β = 100.930 (1)°Plate, colorless
γ = 92.465 (1)°0.49 × 0.23 × 0.14 mm
V = 987.5 (2) Å3
Data collection top
Agilent Xcalibur Atlas Gemini ultra
diffractometer
4685 independent reflections
Radiation source: Enhance (Mo) X-ray Source3630 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.045
Detector resolution: 10.4685 pixels mm-1θmax = 29.5°, θmin = 3.4°
ω scansh = 99
Absorption correction: analytical
[using a multifaceted crystal model based on expressions derived by Clark & Reid (1995), implemented in CrysAlis PRO (Agilent, 2010)]
k = 1010
Tmin = 0.498, Tmax = 0.771l = 2223
10196 measured reflections
Refinement top
Refinement on F2Hydrogen site location: inferred from neighbouring sites
Least-squares matrix: fullH-atom parameters constrained
R[F2 > 2σ(F2)] = 0.054 Method, part 1, Chebychev polynomial, (Watkin, 1994, Prince, 1982) [weight] = 1.0/[A0*T0(x) + A1*T1(x) ··· + An-1]*Tn-1(x)]
where Ai are the Chebychev coefficients listed below and x = F /Fmax Method = Robust Weighting (Prince, 1982) W = [weight] * [1-(deltaF/6*sigmaF)2]2 Ai are: 0.230E + 04 0.321E + 04 0.179E + 04 528.
wR(F2) = 0.111(Δ/σ)max = 0.001
S = 0.94Δρmax = 1.03 e Å3
4685 reflectionsΔρmin = 1.23 e Å3
227 parametersExtinction correction: Larson (1970), Equation 22
0 restraintsExtinction coefficient: 20 (3)
Primary atom site location: structure-invariant direct methods
Crystal data top
(C7H7N2S)2[ZnCl4]γ = 92.465 (1)°
Mr = 509.61V = 987.5 (2) Å3
Triclinic, P1Z = 2
a = 7.543 (1) ÅMo Kα radiation
b = 7.828 (1) ŵ = 2.00 mm1
c = 17.109 (2) ÅT = 110 K
α = 94.250 (1)°0.49 × 0.23 × 0.14 mm
β = 100.930 (1)°
Data collection top
Agilent Xcalibur Atlas Gemini ultra
diffractometer
4685 independent reflections
Absorption correction: analytical
[using a multifaceted crystal model based on expressions derived by Clark & Reid (1995), implemented in CrysAlis PRO (Agilent, 2010)]
3630 reflections with I > 2σ(I)
Tmin = 0.498, Tmax = 0.771Rint = 0.045
10196 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0540 restraints
wR(F2) = 0.111H-atom parameters constrained
S = 0.94Δρmax = 1.03 e Å3
4685 reflectionsΔρmin = 1.23 e Å3
227 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Zn10.49814 (8)0.31162 (7)0.75071 (4)0.0243
Cl20.29039 (16)0.43801 (16)0.81360 (8)0.0274
Cl30.50293 (17)0.47084 (17)0.64494 (8)0.0312
Cl40.43482 (19)0.03141 (16)0.71252 (8)0.0327
Cl50.76785 (17)0.33826 (17)0.83422 (9)0.0348
S60.80197 (17)0.66813 (17)0.54732 (8)0.0271
C70.9702 (6)0.6161 (6)0.6239 (3)0.0238
N81.1348 (6)0.6629 (5)0.6125 (3)0.0270
C91.1369 (7)0.7391 (6)0.5413 (3)0.0259
C100.9660 (7)0.7508 (6)0.4981 (3)0.0274
C110.9378 (8)0.8213 (7)0.4244 (3)0.0334
C121.0891 (9)0.8761 (7)0.3964 (4)0.0399
C131.2610 (8)0.8636 (7)0.4407 (4)0.0371
C141.2880 (7)0.7940 (7)0.5137 (4)0.0332
N150.9376 (6)0.5413 (6)0.6864 (3)0.0301
N160.4666 (6)0.2078 (6)1.1438 (3)0.0318
C170.3739 (7)0.1401 (6)1.0765 (3)0.0267
S180.33424 (17)0.24680 (16)0.98962 (8)0.0267
C190.2084 (7)0.0651 (7)0.9370 (3)0.0272
C200.1203 (7)0.0453 (7)0.8583 (3)0.0289
C210.0273 (7)0.1091 (7)0.8316 (3)0.0305
C220.0266 (7)0.2424 (6)0.8813 (3)0.0298
C230.1155 (7)0.2224 (6)0.9596 (3)0.0279
C240.2056 (7)0.0673 (6)0.9873 (3)0.0258
N250.2989 (6)0.0203 (5)1.0642 (3)0.0256
H1110.82160.83120.39630.0401*
H1211.07650.92260.34720.0479*
H1311.36140.90090.42050.0452*
H1411.40230.78480.54250.0398*
H2010.12160.13330.82500.0348*
H2110.03540.12540.77960.0368*
H2210.03500.34780.86060.0360*
H2310.11360.31050.99230.0341*
H1521.02680.51600.72180.0362*
H1620.52510.30621.14640.0382*
H1610.49730.14481.18250.0382*
H1510.82750.50820.68810.0364*
H811.23420.63340.64260.0335*
H2510.31110.09041.10140.0316*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Zn10.0209 (3)0.0234 (3)0.0286 (3)0.0006 (2)0.0037 (2)0.0055 (2)
Cl20.0251 (6)0.0269 (6)0.0310 (6)0.0003 (5)0.0074 (5)0.0040 (5)
Cl30.0238 (6)0.0367 (7)0.0359 (7)0.0048 (5)0.0079 (5)0.0140 (5)
Cl40.0414 (7)0.0246 (6)0.0303 (6)0.0007 (5)0.0031 (5)0.0032 (5)
Cl50.0256 (6)0.0321 (7)0.0434 (8)0.0064 (5)0.0049 (5)0.0156 (6)
S60.0210 (6)0.0287 (6)0.0299 (6)0.0014 (5)0.0004 (5)0.0036 (5)
C70.018 (2)0.024 (2)0.031 (3)0.0051 (18)0.0061 (19)0.004 (2)
N80.022 (2)0.025 (2)0.034 (2)0.0004 (16)0.0037 (17)0.0024 (18)
C90.028 (3)0.024 (2)0.028 (2)0.0062 (19)0.009 (2)0.002 (2)
C100.032 (3)0.021 (2)0.028 (3)0.003 (2)0.004 (2)0.003 (2)
C110.045 (3)0.025 (3)0.029 (3)0.001 (2)0.004 (2)0.001 (2)
C120.061 (4)0.026 (3)0.032 (3)0.009 (3)0.013 (3)0.003 (2)
C130.043 (3)0.029 (3)0.044 (3)0.002 (2)0.023 (3)0.004 (2)
C140.026 (3)0.030 (3)0.045 (3)0.001 (2)0.010 (2)0.001 (2)
N150.026 (2)0.035 (2)0.029 (2)0.0015 (18)0.0020 (18)0.0060 (19)
N160.034 (2)0.028 (2)0.032 (2)0.0031 (19)0.0012 (19)0.0066 (19)
C170.023 (2)0.026 (2)0.032 (3)0.0024 (19)0.007 (2)0.006 (2)
S180.0268 (6)0.0231 (6)0.0308 (6)0.0029 (5)0.0068 (5)0.0054 (5)
C190.021 (2)0.029 (3)0.034 (3)0.0000 (19)0.010 (2)0.006 (2)
C200.028 (3)0.027 (3)0.035 (3)0.002 (2)0.011 (2)0.005 (2)
C210.029 (3)0.031 (3)0.030 (3)0.007 (2)0.008 (2)0.002 (2)
C220.029 (3)0.019 (2)0.041 (3)0.0046 (19)0.010 (2)0.004 (2)
C230.028 (3)0.022 (2)0.036 (3)0.0003 (19)0.011 (2)0.004 (2)
C240.022 (2)0.025 (2)0.032 (3)0.0034 (19)0.011 (2)0.003 (2)
N250.028 (2)0.0190 (19)0.031 (2)0.0027 (16)0.0072 (18)0.0060 (17)
Geometric parameters (Å, º) top
Zn1—Cl22.2820 (14)N15—H1520.856
Zn1—Cl32.2770 (14)N15—H1510.865
Zn1—Cl42.2462 (14)N16—C171.292 (7)
Zn1—Cl52.2452 (14)N16—H1620.865
S6—C71.728 (5)N16—H1610.858
S6—C101.750 (5)C17—S181.741 (5)
C7—N81.333 (6)C17—N251.340 (6)
C7—N151.315 (6)S18—C191.762 (5)
N8—C91.397 (6)C19—C201.379 (7)
N8—H810.876C19—C241.398 (7)
C9—C101.369 (7)C20—C211.372 (7)
C9—C141.378 (7)C20—H2010.926
C10—C111.398 (7)C21—C221.394 (7)
C11—C121.383 (8)C21—H2110.922
C11—H1110.926C22—C231.375 (8)
C12—C131.384 (9)C22—H2210.940
C12—H1210.932C23—C241.372 (7)
C13—C141.384 (8)C23—H2310.920
C13—H1310.934C24—N251.385 (7)
C14—H1410.917N25—H2510.865
Cl2—Zn1—Cl3103.35 (5)C7—N15—H152119.0
Cl2—Zn1—Cl4114.50 (5)C7—N15—H151119.2
Cl3—Zn1—Cl4112.21 (6)H152—N15—H151121.4
Cl2—Zn1—Cl5108.54 (6)C17—N16—H162120.4
Cl3—Zn1—Cl5110.34 (5)C17—N16—H161119.8
Cl4—Zn1—Cl5107.81 (6)H162—N16—H161117.3
C7—S6—C1090.0 (2)N16—C17—S18123.7 (4)
S6—C7—N8112.2 (4)N16—C17—N25124.7 (5)
S6—C7—N15123.3 (4)S18—C17—N25111.6 (4)
N8—C7—N15124.5 (5)C17—S18—C1990.6 (2)
C7—N8—C9114.5 (4)S18—C19—C20128.4 (4)
C7—N8—H81123.0S18—C19—C24110.2 (4)
C9—N8—H81121.8C20—C19—C24121.4 (5)
N8—C9—C10111.9 (5)C19—C20—C21117.2 (5)
N8—C9—C14126.5 (5)C19—C20—H201121.4
C10—C9—C14121.6 (5)C21—C20—H201121.4
S6—C10—C9111.4 (4)C20—C21—C22121.5 (5)
S6—C10—C11127.5 (4)C20—C21—H211119.3
C9—C10—C11121.1 (5)C22—C21—H211119.2
C10—C11—C12117.4 (6)C21—C22—C23121.1 (5)
C10—C11—H111120.4C21—C22—H221119.2
C12—C11—H111122.1C23—C22—H221119.7
C11—C12—C13120.8 (6)C22—C23—C24117.9 (5)
C11—C12—H121120.2C22—C23—H231120.7
C13—C12—H121118.9C24—C23—H231121.4
C12—C13—C14121.5 (5)C19—C24—C23120.9 (5)
C12—C13—H131119.5C19—C24—N25112.3 (4)
C14—C13—H131119.0C23—C24—N25126.8 (5)
C13—C14—C9117.5 (5)C24—N25—C17115.3 (4)
C13—C14—H141121.0C24—N25—H251122.4
C9—C14—H141121.5C17—N25—H251122.2
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N8—H81···Cl3i0.882.433.190 (5)145
N15—H151···Cl30.862.423.235 (5)157
N15—H152···Cl2i0.862.423.274 (5)176
N25—H251···Cl5ii0.862.413.215 (5)155
N16—H161···Cl4ii0.862.343.196 (5)177
N16—H162···Cl2iii0.862.373.215 (5)166
C20—H201···Cl20.932.693.473 (6)142
C22—H221···Cl5iv0.942.783.701 (5)167
C11—H111···Cl4v0.932.733.592 (6)154
Symmetry codes: (i) x+1, y, z; (ii) x+1, y, z+2; (iii) x+1, y+1, z+2; (iv) x1, y1, z; (v) x+1, y+1, z+1.

Experimental details

Crystal data
Chemical formula(C7H7N2S)2[ZnCl4]
Mr509.61
Crystal system, space groupTriclinic, P1
Temperature (K)110
a, b, c (Å)7.543 (1), 7.828 (1), 17.109 (2)
α, β, γ (°)94.250 (1), 100.930 (1), 92.465 (1)
V3)987.5 (2)
Z2
Radiation typeMo Kα
µ (mm1)2.00
Crystal size (mm)0.49 × 0.23 × 0.14
Data collection
DiffractometerAgilent Xcalibur Atlas Gemini ultra
diffractometer
Absorption correctionAnalytical
[using a multifaceted crystal model based on expressions derived by Clark & Reid (1995), implemented in CrysAlis PRO (Agilent, 2010)]
Tmin, Tmax0.498, 0.771
No. of measured, independent and
observed [I > 2σ(I)] reflections
10196, 4685, 3630
Rint0.045
(sin θ/λ)max1)0.692
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.054, 0.111, 0.94
No. of reflections4685
No. of parameters227
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)1.03, 1.23

Computer programs: CrysAlis PRO (Agilent, 2010), SIR97 (Altomare et al., 1999), CRYSTALS (Betteridge et al., 2003), DIAMOND (Brandenburg, 2006).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N8—H81···Cl3i0.882.433.190 (5)145
N15—H151···Cl30.862.423.235 (5)157
N15—H152···Cl2i0.862.423.274 (5)176
N25—H251···Cl5ii0.862.413.215 (5)155
N16—H161···Cl4ii0.862.343.196 (5)177
N16—H162···Cl2iii0.862.373.215 (5)166
C20—H201···Cl20.932.693.473 (6)142
C22—H221···Cl5iv0.942.783.701 (5)167
C11—H111···Cl4v0.932.733.592 (6)154
Symmetry codes: (i) x+1, y, z; (ii) x+1, y, z+2; (iii) x+1, y+1, z+2; (iv) x1, y1, z; (v) x+1, 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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Volume 67| Part 6| June 2011| Pages m654-m655
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