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ISSN: 2056-9890

1-Phenyl-2-(1H-1,2,4-triazol-1-yl)ethanone

aZonguldak Karaelmas University, Department of Chemistry, 67100 Zonguldak, Turkey, bSouthampton University, Department of Chemistry, Southampton SO17 1BJ, England, and cHacettepe University, Department of Physics, 06800 Beytepe, Ankara, Turkey
*Correspondence e-mail: merzifon@hacettepe.edu.tr

(Received 18 July 2008; accepted 23 July 2008; online 26 July 2008)

In the mol­ecule of the title compound, C10H9N3O, the triazole and phenyl rings are nearly perpendicular to each other, with a dihedral angle of 88.72 (4)°. In the crystal structure, inter­molecular C—H⋯O and C—H⋯N hydrogen bonds link the mol­ecules. There are C—H⋯π contacts between the 1,2,4-triazole rings, and between the phenyl and 1,2,4-triazole rings, and there is a weak ππ contact between the 1,2,4-triazole and phenyl rings [centroid-to-centroid distance = 4.547 (1) Å].

Related literature

For general background, see: Holla et al. (1996[Holla, B. S., Poojary, K. N., Kalluraya, B. & Gowda, P. V. (1996). Il Farmaco, 51, 793-799.]); Sengupta et al. (1978[Sengupta, A. K., Bajaj, O. P. & Chandra, U. (1978). J. Indian Chem. Soc. 55, 962-964.]); Paulvannan et al. (2001[Paulvannan, K., Hale, R., Sedehi, D. & Chen, T. (2001). Tetrahedron, 57, 9677-9682.]); Sui et al. (1998[Sui, Z. H., Guan, J. H., Hlasta, D. J., Macielag, M. J., Foleno, B. D., Goldschmidt, R. M., Loeloff, M. J., Webb, G. C. & Barrett, J. F. (1998). Bioorg. Med. Chem. Lett. 8, 1929-1934.]); Bodey (1992[Bodey, G. P. (1992). Clin. Infect. Dis. 14, S161-S169.]). For related literature, see: Caira et al. (2004[Caira, M. R., Alkhamis, K. A. & Obaidat, R. M. (2004). J. Pharm. Sci. 93, 601-611.]); Peeters et al. (1996[Peeters, O. M., Blaton, N. M. & De Ranter, C. J. (1996). Acta Cryst. C52, 2225-2229.]); Özel Güven, Tahtacı et al. (2008[Özel Güven, Ö., Tahtacı, H., Coles, S. J. & Hökelek, T. (2008). Acta Cryst. E64, o1254.]); Özel Güven, Erdoğan et al. (2008[Özel Güven, Ö., Erdoğan, T., Coles, S. J. & Hökelek, T. (2008). Acta Cryst. E64, o1358.]). For synthesis, see: Liu et al. (2006[Liu, J., Li, L., Dai, H., Liu, Z. & Fang, J. (2006). J. Organomet. Chem. 691, 2686-2690.]).

[Scheme 1]

Experimental

Crystal data
  • C10H9N3O

  • Mr = 187.20

  • Orthorhombic, P b c a

  • a = 9.3129 (2) Å

  • b = 8.11660 (10) Å

  • c = 24.0475 (4) Å

  • V = 1817.73 (5) Å3

  • Z = 8

  • Mo Kα radiation

  • μ = 0.09 mm−1

  • T = 120 (2) K

  • 0.35 × 0.2 × 0.2 mm

Data collection
  • Bruker Nonius KappaCCD diffractometer

  • Absorption correction: multi-scan (SADABS; Sheldrick, 2007[Sheldrick, G. M. (2007). SADABS. University of Göttingen, Germany.]) Tmin = 0.968, Tmax = 0.972

  • 16799 measured reflections

  • 2077 independent reflections

  • 1736 reflections with I > 2σ(I)

  • Rint = 0.052

Refinement
  • R[F2 > 2σ(F2)] = 0.060

  • wR(F2) = 0.145

  • S = 1.17

  • 2077 reflections

  • 164 parameters

  • All H-atom parameters refined

  • Δρmax = 0.56 e Å−3

  • Δρmin = −0.55 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

Cg1 and Cg2 are the centroids of the rings N1–N3/C1/C2 and C5–C10, respectively.

D—H⋯A D—H H⋯A DA D—H⋯A
C2—H2⋯Oi 0.970 (16) 2.449 (15) 3.2595 (17) 140.9 (12)
C3—H32⋯Oi 0.973 (16) 2.489 (16) 3.2601 (17) 136.1 (13)
C8—H8⋯N3ii 0.97 (2) 2.61 (2) 3.5405 (19) 160.2 (14)
C1—H1⋯Cg2iii 1.001 (17) 2.840 (18) 3.620 (2) 135.20 (13)
C2—H2⋯Cg1iv 0.972 (17) 3.013 (16) 3.829 (2) 142.42 (12)
Symmetry codes: (i) [-x+{\script{1\over 2}}, y+{\script{1\over 2}}, z]; (ii) [x, -y+{\script{1\over 2}}, z-{\script{1\over 2}}]; (iii) -x+1, -y, -z; (iv) [-x+{\script{3\over 2}}, y+{\script{1\over 2}}, z].

Data collection: COLLECT (Nonius, 1998[Nonius (1998). COLLECT. Nonius BV, Delft, The Netherlands.]); cell refinement: 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 COLLECT; data reduction: DENZO and COLLECT; 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

In recent years, among antifungal agents, azole derivatives still have an important place in the class of systemic antifungal drugs. 1,2,4-Triazoles are biologically interesting molecules and their chemistry is receiving considerable attention, due to antihypertensive, antifungal and antibacterial properties (Holla et al., 1996; Sengupta et al., 1978; Paulvannan et al., 2001; Sui et al., 1998). The azole antifungals possessing a triazole ring such as fluconazole (Caira et al., 2004) and itraconazole (Peeters et al., 1996) inhibit the synthesis of sterols in fungi by inhibiting cytochrome P-450-dependent 14α-lanosterol demethylase (P-45014DM) and prevent cytochrome P-450 activity (Bodey, 1992). Recently, we reported the crystal structures of 1,2,4-triazole substituted alcohol (Özel Güven, Tahtacı et al., 2008) and benzimidazole substituted ketone (Özel Güven, Erdoğan et al., 2008). We report herein the crystal structure of the 1,2,4-triazole substituted ketone, (I).

In (I), the bond lengths and angles are generally within normal ranges (Fig. 1). The 1,2,4-triazole and benzene rings, A (N1–N3/C1/C2) and B (C5–C10), are, of course, planar and nearly perpendicular to each other with a dihedral angle of A/B = 88.72 (4)°. Atoms C3 and C4 are -0.028 (2) Å and -0.054 (1) Å away from the ring planes of A and B, respectively. The N1—C3—C4 [112.73 (11)°], C3—C4—C5 [116.93 (11)°], O—C4—C3 [120.73 (12)°] and O—C4—C5 [122.34 (12)°] bond angles are highly different from the corresponding values [111.53 (10)°, 109.94 (10)°, 109.53 (11)° and 110.01 (10)°, respectively] in 1-phenyl-2-(1H-1,2,4-triazol-1-yl)ethanol, (II) (Özel Güven, Tahtacı et al., 2008). In ring A, the nearly equivalent N1—N2—C1 [101.81 (11)°] and C1—N3—C2 [102.23 (11)°] bond angles are narrowed, while highly different N3—C2—N1 [110.53 (13)°] and N3—C1—N2 [115.39 (12)°] bond angles are enlarged, as in (II).

In the crystal structure, intermolecular C—H···O and C—H···N hydrogen bonds (Table 1) link the molecules (Fig. 2), in which they seem to be effective in the stabilization of the structure. The C—H···π contacts (Table 1) between the 1,2,4-triazole and the benzene rings and the 1,2,4-triazole rings and a ππ contact between the 1,2,4-triazole and benzene ring systems Cg2···Cg1i [symmetry code: (i) 1 - x, -y, -z, where Cg1 and Cg2 are centroids of the rings (N1–N3/C1/C2) and (C5–C10), respectively] further stabilize the structure, with centroid–centroid distance of 4.547 (1) Å.

Related literature top

For general background, see: Holla et al. (1996); Sengupta et al. (1978); Paulvannan et al. (2001); Sui et al. (1998); Bodey (1992). For related literature, see: Caira et al. (2004); Peeters et al. (1996); Özel Güven, Tahtacı et al. (2008); Özel Güven, Erdoğan et al. (2008). For synthesis, see: Liu et al. (2006).

Experimental top

The title compound, (I), was synthesized by the reaction of 1H-1,2,4-triazole with 2-bromo-1-phenylethanone (Liu et al., 2006). To a vigorous stirred suspension of 1H-1,2,4-triazole (1105 mg, 16 mmol) and 2-bromo-1-phenylethanone (1990 mg, 10 mmol) in acetone (6 ml) was added triethylamine (2.2 ml) dropwise over a period of 1 h below 273 K, and the reaction mixture was stirred for another 30 min at room temperature. Then the mixture was filtered to remove triethylamine hydrobromide salt, the precipitate was washed with acetone, and the filtrate was evaporated under reduced pressure. The residue was dissolved in chloroform, and washed with water. After evaporation of chloroform, the yellow solid was obtained and crystallized from iso-propanol to obtain the title compound as colorless crystals (yield; 937 mg, 50%).

Refinement top

H atoms were located in difference syntheses and refined isotropically [C—H = 0.954 (18)–1.007 (17) Å, Uiso(H) = 0.030 (4)–0.046 (5) Å2].

Computing details top

Data collection: COLLECT (Nonius, 1998); cell refinement: DENZO (Otwinowski & Minor, 1997) and COLLECT (Nonius, 1998); data reduction: DENZO (Otwinowski & Minor, 1997) and COLLECT (Nonius, 1998); 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 molecular structure of the title molecule with the atom-numbering scheme. Displacement ellipsoids are drawn at the 50% probability level.
[Figure 2] Fig. 2. A packing diagram of (I). Hydrogen bonds are shown as dashed lines.
1-Phenyl-2-(1H-1,2,4-triazol-1-yl)ethanone top
Crystal data top
C10H9N3OF(000) = 784
Mr = 187.20Dx = 1.368 Mg m3
Orthorhombic, PbcaMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ac 2abCell parameters from 2395 reflections
a = 9.3129 (2) Åθ = 2.9–27.5°
b = 8.1166 (1) ŵ = 0.09 mm1
c = 24.0475 (4) ÅT = 120 K
V = 1817.73 (5) Å3Shard, colourless
Z = 80.35 × 0.2 × 0.2 mm
Data collection top
Bruker Nonius KappaCCD
diffractometer
2077 independent reflections
Radiation source: fine-focus sealed tube1736 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.052
Detector resolution: 9.091 pixels mm-1θmax = 27.5°, θmin = 3.4°
ϕ and ω scansh = 1212
Absorption correction: multi-scan
(SADABS; Sheldrick, 2007)
k = 109
Tmin = 0.968, Tmax = 0.972l = 3131
16799 measured reflections
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.060All H-atom parameters refined
wR(F2) = 0.145 w = 1/[σ2(Fo2) + (0.0862P)2 + 0.1878P]
where P = (Fo2 + 2Fc2)/3
S = 1.17(Δ/σ)max < 0.001
2077 reflectionsΔρmax = 0.56 e Å3
164 parametersΔρmin = 0.55 e Å3
0 restraintsExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
Primary atom site location: structure-invariant direct methodsExtinction coefficient: 0.141 (11)
Crystal data top
C10H9N3OV = 1817.73 (5) Å3
Mr = 187.20Z = 8
Orthorhombic, PbcaMo Kα radiation
a = 9.3129 (2) ŵ = 0.09 mm1
b = 8.1166 (1) ÅT = 120 K
c = 24.0475 (4) Å0.35 × 0.2 × 0.2 mm
Data collection top
Bruker Nonius KappaCCD
diffractometer
2077 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 2007)
1736 reflections with I > 2σ(I)
Tmin = 0.968, Tmax = 0.972Rint = 0.052
16799 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0600 restraints
wR(F2) = 0.145All H-atom parameters refined
S = 1.17Δρmax = 0.56 e Å3
2077 reflectionsΔρmin = 0.55 e Å3
164 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
O0.27304 (10)0.10771 (12)0.46535 (4)0.0301 (3)
N10.08642 (12)0.25265 (13)0.53706 (5)0.0237 (3)
N20.04051 (14)0.12395 (15)0.56849 (5)0.0306 (4)
N30.15796 (13)0.31174 (16)0.62134 (5)0.0302 (3)
C10.08629 (16)0.16652 (19)0.61863 (6)0.0302 (4)
H10.0645 (19)0.097 (2)0.6520 (7)0.037 (4)*
C20.15570 (14)0.36160 (18)0.56884 (6)0.0256 (3)
H20.1995 (17)0.460 (2)0.5535 (6)0.030 (4)*
C30.05623 (16)0.25908 (17)0.47805 (5)0.0241 (3)
H310.0374 (19)0.210 (2)0.4711 (6)0.032 (4)*
H320.0550 (18)0.373 (2)0.4655 (7)0.035 (4)*
C40.16946 (13)0.17185 (16)0.44337 (5)0.0229 (3)
C50.14815 (14)0.17126 (16)0.38202 (5)0.0231 (3)
C60.25102 (16)0.09475 (17)0.34846 (6)0.0284 (4)
H60.3339 (19)0.048 (2)0.3658 (7)0.038 (5)*
C70.23147 (18)0.08608 (18)0.29144 (6)0.0333 (4)
H70.3021 (18)0.033 (2)0.2690 (7)0.035 (4)*
C80.11013 (19)0.15544 (19)0.26698 (6)0.0352 (4)
H80.0997 (19)0.151 (2)0.2269 (9)0.046 (5)*
C90.00879 (18)0.23382 (18)0.29988 (6)0.0320 (4)
H90.0794 (18)0.281 (2)0.2837 (7)0.036 (4)*
C100.02666 (15)0.24132 (16)0.35721 (6)0.0263 (4)
H100.0483 (18)0.296 (2)0.3812 (6)0.031 (4)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O0.0267 (5)0.0372 (6)0.0263 (5)0.0052 (4)0.0022 (4)0.0031 (4)
N10.0264 (6)0.0252 (6)0.0194 (6)0.0012 (4)0.0005 (4)0.0005 (4)
N20.0414 (7)0.0283 (6)0.0221 (6)0.0054 (5)0.0016 (5)0.0028 (5)
N30.0340 (7)0.0349 (7)0.0216 (6)0.0024 (5)0.0009 (5)0.0004 (5)
C10.0385 (8)0.0312 (8)0.0208 (7)0.0012 (6)0.0023 (6)0.0016 (5)
C20.0252 (7)0.0295 (7)0.0222 (7)0.0023 (5)0.0005 (5)0.0006 (5)
C30.0259 (7)0.0272 (7)0.0191 (6)0.0006 (5)0.0022 (5)0.0005 (5)
C40.0226 (6)0.0226 (6)0.0235 (7)0.0033 (5)0.0000 (5)0.0016 (5)
C50.0261 (7)0.0221 (7)0.0211 (7)0.0030 (5)0.0002 (5)0.0020 (5)
C60.0323 (7)0.0271 (7)0.0259 (7)0.0009 (6)0.0039 (6)0.0032 (5)
C70.0434 (9)0.0311 (7)0.0256 (7)0.0007 (7)0.0100 (6)0.0008 (6)
C80.0538 (10)0.0320 (8)0.0196 (7)0.0073 (7)0.0006 (6)0.0016 (6)
C90.0397 (8)0.0306 (7)0.0258 (7)0.0030 (6)0.0079 (6)0.0031 (5)
C100.0279 (7)0.0268 (7)0.0242 (7)0.0008 (5)0.0018 (5)0.0006 (5)
Geometric parameters (Å, º) top
O—C41.2170 (16)C4—C51.4884 (17)
N1—N21.3585 (16)C5—C61.398 (2)
N1—C21.3351 (18)C5—C101.3998 (19)
N1—C31.4476 (16)C6—H60.956 (18)
N2—C11.3247 (18)C7—C61.3851 (19)
N3—C11.356 (2)C7—H70.954 (18)
N3—C21.3258 (18)C8—C71.393 (2)
C1—H11.001 (17)C8—C91.386 (2)
C2—H20.972 (17)C8—H80.97 (2)
C3—H310.974 (18)C9—H90.987 (18)
C3—H320.973 (17)C10—C91.390 (2)
C4—C31.5195 (18)C10—H101.007 (17)
C2—N1—N2110.05 (11)C5—C4—C3116.93 (11)
C2—N1—C3129.14 (12)C6—C5—C10119.22 (13)
N2—N1—C3120.80 (11)C6—C5—C4118.82 (12)
C1—N2—N1101.81 (11)C10—C5—C4121.93 (12)
C2—N3—C1102.23 (11)C7—C6—C5120.26 (14)
N2—C1—N3115.39 (12)C7—C6—H6121.1 (10)
N2—C1—H1121.1 (10)C5—C6—H6118.6 (10)
N3—C1—H1123.4 (10)C6—C7—C8120.28 (14)
N3—C2—N1110.53 (13)C6—C7—H7119.5 (10)
N3—C2—H2127.4 (9)C8—C7—H7120.2 (10)
N1—C2—H2122.1 (9)C9—C8—C7119.79 (13)
N1—C3—C4112.73 (11)C9—C8—H8121.0 (11)
N1—C3—H31109.1 (9)C7—C8—H8119.2 (11)
C4—C3—H31109.5 (10)C8—C9—C10120.31 (14)
N1—C3—H32109.9 (10)C8—C9—H9121.3 (10)
C4—C3—H32106.3 (10)C10—C9—H9118.3 (10)
H31—C3—H32109.2 (14)C9—C10—C5120.11 (13)
O—C4—C5122.34 (12)C9—C10—H10120.4 (9)
O—C4—C3120.73 (12)C5—C10—H10119.5 (9)
C2—N1—N2—C10.33 (15)C3—C4—C5—C6178.95 (12)
C3—N1—N2—C1178.72 (12)O—C4—C5—C10178.18 (12)
N2—N1—C2—N30.35 (16)C3—C4—C5—C102.67 (18)
C3—N1—C2—N3178.60 (12)C10—C5—C6—C71.1 (2)
C2—N1—C3—C493.49 (16)C4—C5—C6—C7177.33 (12)
N2—N1—C3—C487.66 (15)C6—C5—C10—C90.3 (2)
N1—N2—C1—N30.21 (17)C4—C5—C10—C9178.08 (12)
C2—N3—C1—N20.01 (17)C8—C7—C6—C50.9 (2)
C1—N3—C2—N10.20 (15)C9—C8—C7—C60.2 (2)
O—C4—C3—N10.91 (18)C7—C8—C9—C101.0 (2)
C5—C4—C3—N1179.92 (11)C5—C10—C9—C80.7 (2)
O—C4—C5—C60.21 (19)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C2—H2···Oi0.970 (16)2.449 (15)3.2595 (17)140.9 (12)
C3—H32···Oi0.973 (16)2.489 (16)3.2601 (17)136.1 (13)
C8—H8···N3ii0.97 (2)2.61 (2)3.5405 (19)160.2 (14)
C1—H1···Cg2iii1.001 (17)2.840 (18)3.620 (2)135.20 (13)
C2—H2···Cg1iv0.972 (17)3.013 (16)3.829 (2)142.42 (12)
Symmetry codes: (i) x+1/2, y+1/2, z; (ii) x, y+1/2, z1/2; (iii) x+1, y, z; (iv) x+3/2, y+1/2, z.

Experimental details

Crystal data
Chemical formulaC10H9N3O
Mr187.20
Crystal system, space groupOrthorhombic, Pbca
Temperature (K)120
a, b, c (Å)9.3129 (2), 8.1166 (1), 24.0475 (4)
V3)1817.73 (5)
Z8
Radiation typeMo Kα
µ (mm1)0.09
Crystal size (mm)0.35 × 0.2 × 0.2
Data collection
DiffractometerBruker Nonius KappaCCD
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 2007)
Tmin, Tmax0.968, 0.972
No. of measured, independent and
observed [I > 2σ(I)] reflections
16799, 2077, 1736
Rint0.052
(sin θ/λ)max1)0.649
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.060, 0.145, 1.17
No. of reflections2077
No. of parameters164
H-atom treatmentAll H-atom parameters refined
Δρmax, Δρmin (e Å3)0.56, 0.55

Computer programs: , DENZO (Otwinowski & Minor, 1997) and COLLECT (Nonius, 1998), 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
C2—H2···Oi0.970 (16)2.449 (15)3.2595 (17)140.9 (12)
C3—H32···Oi0.973 (16)2.489 (16)3.2601 (17)136.1 (13)
C8—H8···N3ii0.97 (2)2.61 (2)3.5405 (19)160.2 (14)
C1—H1···Cg2iii1.001 (17)2.840 (18)3.620 (2)135.20 (13)
C2—H2···Cg1iv0.972 (17)3.013 (16)3.829 (2)142.42 (12)
Symmetry codes: (i) x+1/2, y+1/2, z; (ii) x, y+1/2, z1/2; (iii) x+1, y, z; (iv) x+3/2, y+1/2, z.
 

Acknowledgements

The authors acknowledge the Zonguldak Karaelmas University Research Fund.

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