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

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ISSN: 2056-9890

Zwitterionic 6-methyl-2-oxo-3-[1-(ureido­iminio)eth­yl]-2H-pyran-4-olate monohydrate

aLaboratoire d'Electrochimie des Matériaux Moléculaires et Complexes, Département de Génie des Procédés, Faculté des Science de l'Ingénieur, Université Farhet Abbes de Setif, DZ-19000 Sétif, Algeria, bUniversité 20 Aout 1955, Skikda, Algeria, cCIMM, CNRS UMR 6200, Faculté des Science, Angers Cedex, France, and dSONAS, EA 921, Université D'Angers, Faculté de Pharmacie, Angers Cedex, France
*Correspondence e-mail: boufas_sihem@yahoo.fr

(Received 5 August 2008; accepted 12 August 2008; online 20 August 2008)

The title compound, C9H11N3O4·H2O, was prepared by the reaction of dehydro­acetic acid and semicarbazide hydro­chloride. It crystallizes in a zwitterionic form with cationic iminium and anionic enolate groups. In the crystal structure, the almost planar mol­ecules are held together by N—H⋯O, O—H⋯O and C—H⋯O hydrogen bonds, some of them involving the water molecules.

Related literature

For related literature, see: Tai et al. (2007[Tai, X.-S., Hao, M.-Y., Yin, J. & Liang, Z.-P. (2007). Acta Cryst. E63, o1725-o1726.]); Zu-Pei Liang et al. (2007[Liang, Z.-P., Li, J., Wang, H.-L. & Wang, H.-Q. (2007). Acta Cryst. E63, o2939.]); Wojciechowski et al. (2003[Wojciechowski, G., Ratajczak-Sitarz, M., Katrusiak, A., Schilf, W., Przybylski, P. & Brzezinski, B. (2003). J. Mol. Struct. 650, 191-199.]); Petek et al. (2006[Petek, H., Albayrak, Ç., Ağar, E. & Kalkan, H. (2006). Acta Cryst. E62, o3685-o3687.]); Huang et al. (2006[Huang, L., Chen, D.-B., Qiu, D. & Zhao, B. (2006). Acta Cryst. E62, o5239-o5240.]); Bernstein et al. (1995[Bernstein, J., Davis, R. E., Shimoni, L. & Chang, N.-L. (1995). Angew. Chem. Int. Ed. Engl. 34, 1555-1573.]); Girija & Begum (2004a[Girija, C. R. & Begum, N. S. (2004a). Acta Cryst. E60, o535-o536.]); Girija et al. (2004b[Girija, C. R., Begum, N. S., Sridhar, M. A., Lokanath, N. K. & Prasad, J. S. (2004b). Acta Cryst. E60, o586-o588.]); Gowda et al. (2007[Gowda, B. T., Foro, S. & Fuess, H. (2007). Acta Cryst. E63, o3087.])..

[Scheme 1]

Experimental

Crystal data
  • C9H11N3O4·H2O

  • Mr = 243.22

  • Monoclinic, P 21 /c

  • a = 7.1731 (4) Å

  • b = 12.6590 (10) Å

  • c = 12.3698 (3) Å

  • β = 104.603 (6)°

  • V = 1086.95 (11) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.12 mm−1

  • T = 173 (2) K

  • 0.35 × 0.05 × 0.02 mm

Data collection
  • Nonius KappaCCD diffractometer

  • Absorption correction: none

  • 11787 measured reflections

  • 2485 independent reflections

  • 1699 reflections with I > 2σ(I)

  • Rint = 0.055

Refinement
  • R[F2 > 2σ(F2)] = 0.048

  • wR(F2) = 0.121

  • S = 1.03

  • 2485 reflections

  • 178 parameters

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

  • Δρmax = 0.33 e Å−3

  • Δρmin = −0.26 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N1—H1A⋯O3i 0.84 (2) 2.18 (2) 3.015 (2) 176.3 (17)
N1—H1B⋯O1Wii 0.87 (2) 2.30 (2) 3.075 (2) 147.9 (19)
N2—H2⋯O1Wii 0.91 (2) 1.98 (2) 2.839 (2) 158 (2)
N3—H3⋯O3 0.98 (2) 1.60 (3) 2.476 (2) 147 (2)
O1W—H11W⋯O4 0.82 (3) 1.99 (3) 2.796 (2) 171 (3)
O1W—H21W⋯O1iii 0.82 (3) 2.00 (3) 2.823 (2) 178.0 (18)
C3—H3B⋯O1 0.96 2.29 2.812 (3) 114
C7—H7⋯O4iv 0.93 2.49 3.294 (2) 145
Symmetry codes: (i) [-x+1, y-{\script{1\over 2}}, -z+{\script{1\over 2}}]; (ii) [x, -y-{\script{1\over 2}}, z+{\script{1\over 2}}]; (iii) -x+2, -y, -z+1; (iv) [-x+1, y+{\script{1\over 2}}, -z+{\script{1\over 2}}].

Data collection: COLLECT (Nonius, 1997[Nonius (1997). COLLECT. Nonius BV, Delft The Netherlands.]); cell refinement: SCALEPACK (Otwinowski & Minor, 1997[Otwinowski, Z. & Minor, W. (1997). Methods in Enzymology, Vol. 276, Macromolecular Crystallography, Part A, edited by C. W. Carter Jr & R. M. Sweet, pp. 307-326. New York: Academic Press.]); data reduction: DENZO (Otwinowski & Minor, 1997[Otwinowski, Z. & Minor, W. (1997). Methods in Enzymology, Vol. 276, Macromolecular Crystallography, Part A, edited by C. W. Carter Jr & R. M. Sweet, pp. 307-326. New York: Academic Press.]) and SCALEPACK; 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 Mercury (Macrae et al., 2006[Macrae, C. F., Edgington, P. R., McCabe, P., Pidcock, E., Shields, G. P., Taylor, R., Towler, M. & van de Streek, J. (2006). J. Appl. Cryst. 39, 453-457.]); software used to prepare material for publication: WinGX (Farrugia, 1999[Farrugia, L. J. (1999). J. Appl. Cryst. 32, 837-838.]) and PARST (Nardelli, 1995[Nardelli, M. (1995). J. Appl. Cryst. 28, 659.]).

Supporting information


Comment top

NLO materials play an important role in the field of fibre optic communications and optical signal processing. In the last two decades, extensive research has shown that organic crystals can exhibit nonlinear optical efficiencies which are two orders of magnitude higher than those of inorganic materials. Semicarbazones of substituted benzaldehydes and acetophenones were reported to be some of the potential organic NLO materials.

In this paper, the structure of the title compound (I), C9H13N3O5 is reported. The asymmetric unit of (I) contains one Dehydroacetic acid semicarbazide molecule and one water molecule (Fig. 1).

It is seen that the structure reported here adopts a zwitterion form, because, among other reasons, its N+—H bond distances [0.98 (3) Å] is comparable with those from similar zwitterions in the literature [1.11 (3) Å; 1.10 (3) Å] (Petek et al., 2006; Wojciechowski et al., 2003).

The bond distances shown in Table 1 indicate that the C2—N3 iminium bond length of 1.303 (2) Å agree with similar bond in related compounds (Girija & Begum, 2004a; Girija et al., 2004b). This distance is slightly longer than a typical C=N bond (1.269 Å); but much shorter than the single carbon-nitrogen (1.409 Å) (Gowda et al. 2007), because of the resonance.

The C8—O3 bond length [1.282 (2) Å] is intermediate between single and double carbon to oxygen bond lengths (1.362 Å, 1.222 Å) the carbon-carbon bond connecting the enol and imine groups exhibit intermediate distances between a single and a double bond, being closer to latter one. C4—C8 = 1.423 (2) Å, C2—C4 = 1.452 (2) Å, indicate the zwitterionic character of the title compound (Wojciechowski et al. 2003). The molecular configuration is determined by the presence of the intramolecular hydrogen bond O-···H—N+ (Table 2).

The main molecule in (I) is essentially planar, with a maximum deviation from the mean plane for the non-hydrogen atoms of 0.022 (2) Å. The iminium atom H3, participates in a strong intramolecular hydrogen bond with the enolate atom, O1 (Table 1), which generates an S(6) ring motif (Bernstein et al. 1995). Similar intramolecular hydrogen bonds were reported in the above-mentioned zwitterionic phenolates (Huang et al. 2006). This six-membered pseudocycle is almost planar, the maximum deviation from the mean plane being 0.012 Å for atom C2. The bond lengths and angles are in usual ranges (E)-1-(4-Hydroxybenzylidene) semicarbazide hemihydrate (Tai et al., 2007) and (E)-1-(4-Methoxybenzylidene) -semicarbazide (Liang et al., 2007).

The crystal structure of (I) is stabilized by N—H···O; O—H···O, and C—H···O hydrogen bonds (Fig. 2 and Table 2).

Related literature top

For related literature, see: Tai et al. (2007); Zu-Pei Liang et al. (2007); Wojciechowski et al. (2003); Petek et al. (2006); Huang et al. (2006); Bernstein et al. (1995); Girija & Begum (2004a); Girija et al. (2004b); Gowda et al. (2007).

Experimental top

A mixture of dehydroacetic acid (0.01 mol) and semicarbazide hydrochloride (0.01 mol), in ethanol (20 ml) was refluxed for 1 h. After cooling, filtration and drying, the compound dehydroacetic acid semicarbazide was obtained. A small quantity of this compound (10 mg) was dissolved in aqueous ethanol (95 / 12 ml), and the solution was then allowed to evaporate at room temperature. Prismatic yellow single crystals of the title compound were formed after 8 days.

Refinement top

The O—H distances of the water molecules were restrained to 0.85 (1) Å, to ensure chemically reasonable geometry, with Uiso fixed at 1.5Ueq(O). The iminium and ammino H atoms was located in a difference Fourier map and were refined isotropically. The methyl H atoms were constrained to an ideal geometry (C—H = 0.96 Å) with Uiso(H) = 1.2Ueq(C), but were allowed to rotate freely about the C—C bonds. H7 atom was placed in a geometrically idealized position (C—H = 0.93 Å) and constrained to ride on its parent atom with Uiso(H) = 1.2Ueq(C).

Computing details top

Data collection: COLLECT (Nonius, 1997); cell refinement: SCALEPACK (Otwinowski & Minor, 1997); data reduction: DENZO and SCALEPACK (Otwinowski & Minor, 1997); 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 Mercury (Macrae et al., 2006); software used to prepare material for publication: WinGX (Farrugia, 1999) and PARST (Nardelli, 1995).

Figures top
[Figure 1] Fig. 1. The molecular structure of (I) showing the atom-labelling scheme. Displacement ellipsoids are drawn at the 50% probability level.
[Figure 2] Fig. 2. The crystal packing of (I), viewed down the b axis. Dashed lines indicate the N—H···O and O—H···O interactions.
6-methyl-2-oxo-3-[1-(ureidoiminio)ethyl]-2H-pyran-4-olate monohydrate top
Crystal data top
C9H11N3O4·H2OF(000) = 512
Mr = 243.22Dx = 1.486 Mg m3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 2841 reflections
a = 7.1731 (4) Åθ = 3.1–25.8°
b = 12.659 (1) ŵ = 0.12 mm1
c = 12.3698 (3) ÅT = 173 K
β = 104.603 (6)°Prism, yellow
V = 1086.95 (11) Å30.35 × 0.05 × 0.02 mm
Z = 4
Data collection top
Nonius KappaCCD
diffractometer
1699 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tubeRint = 0.055
Detector resolution: 9 pixels mm-1θmax = 27.5°, θmin = 2.9°
CCD scansh = 99
11787 measured reflectionsk = 1615
2485 independent reflectionsl = 1516
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)] = 0.048Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.121H atoms treated by a mixture of independent and constrained refinement
S = 1.03 w = 1/[σ2(Fo2) + (0.0289P)2 + 0.445P]
where P = (Fo2 + 2Fc2)/3
2485 reflections(Δ/σ)max < 0.001
178 parametersΔρmax = 0.33 e Å3
0 restraintsΔρmin = 0.26 e Å3
Crystal data top
C9H11N3O4·H2OV = 1086.95 (11) Å3
Mr = 243.22Z = 4
Monoclinic, P21/cMo Kα radiation
a = 7.1731 (4) ŵ = 0.12 mm1
b = 12.659 (1) ÅT = 173 K
c = 12.3698 (3) Å0.35 × 0.05 × 0.02 mm
β = 104.603 (6)°
Data collection top
Nonius KappaCCD
diffractometer
1699 reflections with I > 2σ(I)
11787 measured reflectionsRint = 0.055
2485 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0480 restraints
wR(F2) = 0.121H atoms treated by a mixture of independent and constrained refinement
S = 1.03Δρmax = 0.33 e Å3
2485 reflectionsΔρmin = 0.26 e Å3
178 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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
C10.5343 (3)0.25527 (15)0.37044 (14)0.0287 (4)
C20.7633 (2)0.06094 (14)0.56842 (14)0.0253 (4)
C30.8032 (4)0.11552 (17)0.67854 (16)0.0476 (6)
H3A0.71510.17340.67440.057*
H3B0.78710.06660.73480.057*
H3C0.93290.14180.69740.057*
C40.8087 (2)0.04894 (13)0.55327 (13)0.0240 (4)
C50.9088 (3)0.11044 (14)0.64744 (15)0.0292 (4)
C60.8929 (3)0.26084 (15)0.52451 (15)0.0305 (4)
C70.8054 (3)0.20520 (15)0.43545 (15)0.0316 (4)
H70.77330.23750.36570.038*
C80.7593 (2)0.09564 (14)0.44518 (14)0.0269 (4)
C90.9441 (3)0.37503 (16)0.52619 (18)0.0422 (5)
H9A0.90240.40340.4520.051*
H9B1.08120.38290.55270.051*
H9C0.88170.41230.57490.051*
N10.4877 (3)0.35801 (14)0.36960 (16)0.0397 (4)
N20.6282 (2)0.21693 (12)0.47382 (13)0.0336 (4)
N30.6811 (2)0.11234 (12)0.47752 (12)0.0272 (3)
O10.9689 (2)0.08309 (11)0.74427 (10)0.0424 (4)
O30.6744 (2)0.04451 (10)0.35702 (10)0.0369 (4)
O20.9464 (2)0.21590 (10)0.62831 (10)0.0355 (3)
O40.4983 (2)0.19779 (11)0.28793 (11)0.0414 (4)
O1W0.6521 (3)0.10956 (13)0.12207 (12)0.0470 (4)
H11W0.597 (4)0.131 (2)0.168 (2)0.071*
H21W0.763 (4)0.103 (2)0.160 (2)0.071*
H1A0.440 (3)0.3872 (19)0.308 (2)0.048 (7)*
H1B0.514 (3)0.3924 (17)0.4326 (19)0.037 (6)*
H20.650 (3)0.2591 (18)0.5351 (19)0.042 (6)*
H30.656 (4)0.069 (2)0.410 (2)0.075 (8)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
C10.0301 (9)0.0304 (10)0.0238 (8)0.0033 (7)0.0036 (7)0.0023 (7)
C20.0258 (9)0.0274 (9)0.0222 (8)0.0011 (7)0.0049 (7)0.0004 (7)
C30.0780 (16)0.0371 (12)0.0232 (10)0.0137 (11)0.0043 (10)0.0025 (8)
C40.0260 (9)0.0241 (9)0.0203 (8)0.0006 (7)0.0028 (7)0.0015 (6)
C50.0318 (10)0.0288 (10)0.0254 (9)0.0014 (8)0.0042 (7)0.0023 (7)
C60.0341 (10)0.0264 (9)0.0306 (9)0.0012 (7)0.0073 (8)0.0002 (7)
C70.0379 (11)0.0283 (10)0.0256 (9)0.0005 (8)0.0023 (8)0.0046 (7)
C80.0283 (9)0.0260 (9)0.0237 (9)0.0027 (7)0.0016 (7)0.0001 (7)
C90.0557 (13)0.0270 (10)0.0417 (12)0.0078 (9)0.0082 (10)0.0023 (8)
N10.0568 (12)0.0304 (9)0.0295 (9)0.0110 (8)0.0063 (8)0.0035 (8)
N20.0488 (10)0.0240 (8)0.0243 (8)0.0078 (7)0.0023 (7)0.0014 (6)
N30.0330 (8)0.0230 (8)0.0225 (7)0.0021 (6)0.0016 (6)0.0002 (6)
O10.0586 (9)0.0412 (8)0.0201 (6)0.0112 (7)0.0036 (6)0.0005 (6)
O30.0539 (9)0.0288 (7)0.0204 (6)0.0043 (6)0.0046 (6)0.0014 (5)
O20.0480 (8)0.0284 (7)0.0264 (7)0.0085 (6)0.0024 (6)0.0033 (5)
O40.0562 (9)0.0366 (8)0.0248 (7)0.0108 (7)0.0018 (6)0.0027 (6)
O1W0.0593 (10)0.0501 (10)0.0294 (8)0.0083 (8)0.0068 (7)0.0032 (7)
Geometric parameters (Å, º) top
C1—O41.227 (2)C6—C91.490 (3)
C1—N11.342 (2)C7—C81.438 (3)
C1—N21.375 (2)C7—H70.93
C2—N31.304 (2)C8—O31.282 (2)
C2—C41.452 (2)C9—H9A0.96
C2—C31.489 (2)C9—H9B0.96
C3—H3A0.96C9—H9C0.96
C3—H3B0.96N1—H1A0.84 (3)
C3—H3C0.96N1—H1B0.87 (2)
C4—C81.423 (2)N2—N31.375 (2)
C4—C51.434 (2)N2—H20.91 (2)
C5—O11.217 (2)N3—H30.98 (3)
C5—O21.394 (2)O1W—H11W0.82 (3)
C6—C71.325 (3)O1W—H21W0.82 (3)
C6—O21.368 (2)
O4—C1—N1124.65 (17)C6—C7—H7119.5
O4—C1—N2121.02 (17)C8—C7—H7119.5
N1—C1—N2114.33 (16)O3—C8—C4122.81 (16)
N3—C2—C4115.73 (15)O3—C8—C7119.05 (15)
N3—C2—C3119.87 (17)C4—C8—C7118.13 (15)
C4—C2—C3124.41 (16)C6—C9—H9A109.5
C2—C3—H3A109.5C6—C9—H9B109.5
C2—C3—H3B109.5H9A—C9—H9B109.5
H3A—C3—H3B109.5C6—C9—H9C109.5
C2—C3—H3C109.5H9A—C9—H9C109.5
H3A—C3—H3C109.5H9B—C9—H9C109.5
H3B—C3—H3C109.5C1—N1—H1A118.7 (16)
C8—C4—C5119.53 (16)C1—N1—H1B118.7 (14)
C8—C4—C2120.58 (15)H1A—N1—H1B122 (2)
C5—C4—C2119.87 (15)N3—N2—C1115.93 (15)
O1—C5—O2113.83 (16)N3—N2—H2123.4 (14)
O1—C5—C4128.74 (18)C1—N2—H2120.7 (14)
O2—C5—C4117.43 (15)C2—N3—N2124.75 (15)
C7—C6—O2121.43 (17)C2—N3—H3113.8 (17)
C7—C6—C9126.21 (18)N2—N3—H3121.4 (17)
O2—C6—C9112.36 (16)C6—O2—C5122.49 (14)
C6—C7—C8120.93 (17)H11W—O1W—H21W102 (3)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1A···O3i0.84 (2)2.18 (2)3.015 (2)176.3 (17)
N1—H1B···O1Wii0.87 (2)2.30 (2)3.075 (2)147.9 (19)
N2—H2···O1Wii0.91 (2)1.98 (2)2.839 (2)158 (2)
N3—H3···O30.98 (2)1.60 (3)2.476 (2)147 (2)
O1W—H11W···O40.82 (3)1.99 (3)2.796 (2)171 (3)
O1W—H21W···O1iii0.82 (3)2.00 (3)2.823 (2)178 (2)
C3—H3B···O10.962.292.812 (3)114
C7—H7···O4iv0.932.493.294 (2)145
Symmetry codes: (i) x+1, y1/2, z+1/2; (ii) x, y1/2, z+1/2; (iii) x+2, y, z+1; (iv) x+1, y+1/2, z+1/2.

Experimental details

Crystal data
Chemical formulaC9H11N3O4·H2O
Mr243.22
Crystal system, space groupMonoclinic, P21/c
Temperature (K)173
a, b, c (Å)7.1731 (4), 12.659 (1), 12.3698 (3)
β (°) 104.603 (6)
V3)1086.95 (11)
Z4
Radiation typeMo Kα
µ (mm1)0.12
Crystal size (mm)0.35 × 0.05 × 0.02
Data collection
DiffractometerNonius KappaCCD
diffractometer
Absorption correction
No. of measured, independent and
observed [I > 2σ(I)] reflections
11787, 2485, 1699
Rint0.055
(sin θ/λ)max1)0.650
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.048, 0.121, 1.03
No. of reflections2485
No. of parameters178
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.33, 0.26

Computer programs: COLLECT (Nonius, 1997), DENZO and SCALEPACK (Otwinowski & Minor, 1997), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 1997) and Mercury (Macrae et al., 2006), WinGX (Farrugia, 1999) and PARST (Nardelli, 1995).

Selected bond lengths (Å) top
C2—N31.304 (2)C4—C81.423 (2)
C2—C41.452 (2)C8—O31.282 (2)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1A···O3i0.84 (2)2.18 (2)3.015 (2)176.3 (17)
N1—H1B···O1Wii0.87 (2)2.30 (2)3.075 (2)147.9 (19)
N2—H2···O1Wii0.91 (2)1.98 (2)2.839 (2)158 (2)
N3—H3···O30.98 (2)1.60 (3)2.476 (2)147 (2)
O1W—H11W···O40.82 (3)1.99 (3)2.796 (2)171 (3)
O1W—H21W···O1iii0.82 (3)2.00 (3)2.823 (2)178.0 (18)
C3—H3B···O10.96002.29002.812 (3)114.00
C7—H7···O4iv0.93002.49003.294 (2)145.00
Symmetry codes: (i) x+1, y1/2, z+1/2; (ii) x, y1/2, z+1/2; (iii) x+2, y, z+1; (iv) x+1, y+1/2, z+1/2.
 

Acknowledgements

This work was supported by Université Farhet Abbes de Sétif, Sétif, Algeria.

References

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