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ISSN: 2056-9890

Bis(4-fluoro­anilinium) sulfate

aX-ray Crystallography Unit, School of Physics, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia, and bDepartment of Chemistry, Mangalore University, Karnataka, India
*Correspondence e-mail: hkfun@usm.my

(Received 11 August 2011; accepted 16 August 2011; online 27 August 2011)

In the crystal of the title molecular salt, 2C6H7FN+·SO42−, the cations and anions are linked by N—H⋯O and C—H⋯O hydrogen bonds into sheets parallel to the ab plane. The crystal studied was found to be a racemic twin with a 0.50 (10):0.50 (10) domain ratio.

Related literature

For related literature on phase transition dielectric materials, see: Fu et al. (2007[Fu, D.-W., Song, Y.-M., Wang, G.-X., Ye, Q., Xiong, R.-G., Akutagawa, T., Nakamura, T., Chan, P. W. H. & Huang, S. P. D. (2007). J. Am. Chem. Soc. 129, 5346-5347.], 2008[Fu, D.-W., Zhang, W. & Xiong, R.-G. (2008). Cryst. Growth Des. 8, 3461-3464.], 2009[Fu, D.-W., Ge, J.-Z., Dai, J., Ye, H.-Y. & Qu, Z.-R. (2009). Inorg. Chem. Commun. 12, 994-997.]); Fu & Xiong (2008[Fu, D.-W. & Xiong, R.-G. (2008). Dalton Trans. pp. 3946-3948.]). For hydrogen bonding studies, see: Zimmerman & Corbin (2000[Zimmerman, S. C. & Corbin, P. S. (2000). Struct. Bond. 96, 63-94.]); Brunsveld et al. (2001[Brunsveld, L., Folmer, B. J. B., Meijer, E. W. & Sijbesma, R. P. (2001). Chem. Rev. 101, 4071-4097.]); Desiraju (2002[Desiraju, G. R. (2002). Acc. Chem. Res. 35, 565-573.]); Steiner (2002[Steiner, T. (2002). Angew. Chem. Int. Ed. 41, 48-76.]); Desiraju & Steiner (1999[Desiraju, G. R. & Steiner, T. (1999). The Weak Hydrogen Bond in Structural Chemistry and Biology, p. 507. New York: Oxford University Press.]); Boutobba et al. (2010[Boutobba, Z., Direm, A. & Benali-Cherif, N. (2010). Acta Cryst. E66, o595-o596.]). For reference bond-length data, see: Allen et al. (1987[Allen, F. H., Kennard, O., Watson, D. G., Brammer, L., Orpen, A. G. & Taylor, R. (1987). J. Chem. Soc. Perkin Trans. 2, pp. S1-19.]). For a related crystal structure, see: Boutobba et al. (2010[Boutobba, Z., Direm, A. & Benali-Cherif, N. (2010). Acta Cryst. E66, o595-o596.])

[Scheme 1]

Experimental

Crystal data
  • 2C6H7FN+·SO42−

  • Mr = 320.31

  • Orthorhombic, P 21 21 21

  • a = 6.2907 (5) Å

  • b = 7.4155 (6) Å

  • c = 30.168 (3) Å

  • V = 1407.3 (2) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.27 mm−1

  • T = 296 K

  • 0.58 × 0.12 × 0.07 mm

Data collection
  • Bruker SMART APEXII DUO CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Bruker, 2009[Bruker (2009). SADABS, APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]) Tmin = 0.859, Tmax = 0.982

  • 31062 measured reflections

  • 4292 independent reflections

  • 3503 reflections with I > 2σ(I)

  • Rint = 0.044

Refinement
  • R[F2 > 2σ(F2)] = 0.038

  • wR(F2) = 0.103

  • S = 0.98

  • 4292 reflections

  • 191 parameters

  • H-atom parameters constrained

  • Δρmax = 0.18 e Å−3

  • Δρmin = −0.39 e Å−3

  • Absolute structure: Flack (1983[Flack, H. D. (1983). Acta Cryst. A39, 876-881.]), 1794 Friedel pairs

  • Flack parameter: 0.50 (10)

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N1—H3N1⋯O3 0.97 2.09 2.887 (3) 138
N2—H2N2⋯O3 0.85 1.90 2.741 (3) 168
N1—H1N1⋯O1i 0.86 1.92 2.761 (2) 162
N1—H2N1⋯O3ii 0.82 2.25 2.967 (2) 146
N1—H2N1⋯O4ii 0.82 2.55 3.151 (3) 131
N1—H3N1⋯O2iii 0.97 2.24 2.925 (2) 126
N2—H1N2⋯O4iv 0.94 1.78 2.7121 (18) 170
N2—H3N2⋯O2v 0.99 1.72 2.702 (2) 170
C11—H11A⋯O4iii 0.93 2.53 3.374 (3) 151
Symmetry codes: (i) x, y+1, z; (ii) [x-{\script{1\over 2}}, -y+{\script{3\over 2}}, -z]; (iii) [x+{\script{1\over 2}}, -y+{\script{3\over 2}}, -z]; (iv) [x+{\script{1\over 2}}, -y+{\script{1\over 2}}, -z]; (v) x+1, y, z.

Data collection: APEX2 (Bruker, 2009[Bruker (2009). SADABS, APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 2009[Bruker (2009). SADABS, APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; program(s) used to solve structure: SHELXTL (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL and PLATON (Spek, 2009[Spek, A. L. (2009). Acta Cryst. D65, 148-155.]).

Supporting information


Comment top

Amine salts have attracted much attention as phase transition dielectric materials for their application in memory storage (Fu et al. 2007; Fu & Xiong 2008; Fu et al. 2008; Fu et al. 2009). Hydrogen bonding is one of the most versatile non-covalent forces in supramolecular chemistry and crystal engineering (Zimmerman & Corbin, 2000; Brunsveld et al., 2001; Desiraju, 2002). Therefore, in the past decades assessment of discrete hydrogen bonding patterns has received great attention (Steiner, 2002; Desiraju & Steiner, 1999; Boutobba et al., 2010) because of their widespread occurrence in biological systems.

The asymmetric unit of the title compound (Fig 1), contains two crystallographically independent 4-fluoroanilinium cations and a sulfate anion. The bond lengths (Allen et al., 1987) and angles are within normal ranges and comparable to those in a closely related crystal structure (Boutobba et al., 2010).

The cations and anions are linked via intermolecular N1—H3N1···O3 and N2—H2N2···O3 hydrogen bonds (Table 1). In the crystal packing (Fig. 2), the intermolecular N1—H1N1···O1, N1—H2N1···O3, N1—H2N1···O4, N1—H3N1···O2, N2—H1N2···O4, N2—H3N2···O2 and C11—H11A···O4 hydrogen bonds (Table 1) link the molecules into sheets parallel to the ab plane.

Related literature top

For related literature on phase transition dielectric materials, see: Fu et al. (2007, 2008, 2009); Fu & Xiong (2008). For hydrogen bonding studies, see: Zimmerman & Corbin (2000); Brunsveld et al. (2001); Desiraju (2002); Steiner (2002); Desiraju & Steiner (1999); Boutobba et al. (2010). For reference bond-length data, see: Allen et al. (1987). For a related crystal structure, see: Boutobba et al. (2010)

Experimental top

To a solution of 4-fluoroaniline (10 mmol) in absolute ethanol was added sulfuric acid (5 drops) and the mixture refluxed for 4 h. After cooling the mixture to room temperature, a white solid appeared. This crude product was recrystallized from dimethylformamide to afford the desired product. M.p: 151–153°C.

Refinement top

N-bound H atoms were located from a difference Fourier map, fixed at their found location and refined using a riding model with Uiso(H) = 1.5Ueq(N) [N–H = 0.8198 to 0.9875 Å]. The remaining H atoms were positioned geometrically [C–H = 0.93 Å] and refined using a riding model with Uiso(H) = 1.2 Ueq(C). The studied crystal is an inversion twin, the refined ratio of twin components being 0.50 (10): 0.50 (10).

Computing details top

Data collection: APEX2 (Bruker, 2009); cell refinement: SAINT (Bruker, 2009); data reduction: SAINT (Bruker, 2009); program(s) used to solve structure: SHELXTL (Sheldrick, 2008); program(s) used to refine structure: SHELXTL (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2009).

Figures top
[Figure 1] Fig. 1. The molecular structure of the title compound with atom labels with 30% probability displacement ellipsoids. Hydrogen atoms are shown as spheres of arbitrary radius.
[Figure 2] Fig. 2. The crystal packing of the title compound. Dashed lines represent hydrogen bonds. H atoms not involved in the hydrogen bond interactions have been omitted for clarity.
Bis(4-fluoroanilinium) sulfate top
Crystal data top
2C6H7FN+·SO42F(000) = 664
Mr = 320.31Dx = 1.512 Mg m3
Orthorhombic, P212121Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2abCell parameters from 5694 reflections
a = 6.2907 (5) Åθ = 2.7–27.5°
b = 7.4155 (6) ŵ = 0.27 mm1
c = 30.168 (3) ÅT = 296 K
V = 1407.3 (2) Å3Needle, colourless
Z = 40.58 × 0.12 × 0.07 mm
Data collection top
Bruker SMART APEXII DUO CCD area-detector
diffractometer
4292 independent reflections
Radiation source: fine-focus sealed tube3503 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.044
ϕ and ω scansθmax = 30.6°, θmin = 2.7°
Absorption correction: multi-scan
(SADABS; Bruker, 2009)
h = 88
Tmin = 0.859, Tmax = 0.982k = 1010
31062 measured reflectionsl = 4343
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)] = 0.038H-atom parameters constrained
wR(F2) = 0.103 w = 1/[σ2(Fo2) + (0.0492P)2 + 0.377P]
where P = (Fo2 + 2Fc2)/3
S = 0.98(Δ/σ)max < 0.001
4292 reflectionsΔρmax = 0.18 e Å3
191 parametersΔρmin = 0.39 e Å3
0 restraintsAbsolute structure: Flack (1983), 1794 Friedel pairs
Primary atom site location: structure-invariant direct methodsAbsolute structure parameter: 0.50 (10)
Crystal data top
2C6H7FN+·SO42V = 1407.3 (2) Å3
Mr = 320.31Z = 4
Orthorhombic, P212121Mo Kα radiation
a = 6.2907 (5) ŵ = 0.27 mm1
b = 7.4155 (6) ÅT = 296 K
c = 30.168 (3) Å0.58 × 0.12 × 0.07 mm
Data collection top
Bruker SMART APEXII DUO CCD area-detector
diffractometer
4292 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2009)
3503 reflections with I > 2σ(I)
Tmin = 0.859, Tmax = 0.982Rint = 0.044
31062 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.038H-atom parameters constrained
wR(F2) = 0.103Δρmax = 0.18 e Å3
S = 0.98Δρmin = 0.39 e Å3
4292 reflectionsAbsolute structure: Flack (1983), 1794 Friedel pairs
191 parametersAbsolute structure parameter: 0.50 (10)
0 restraints
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
S10.00432 (8)0.47390 (4)0.013801 (11)0.02691 (9)
F10.5089 (5)0.3730 (3)0.25139 (4)0.1033 (6)
F20.0181 (4)0.8372 (3)0.22704 (4)0.1096 (7)
O10.0040 (3)0.29560 (14)0.03416 (4)0.0452 (3)
O20.2002 (2)0.5713 (2)0.02606 (5)0.0372 (3)
O30.1801 (2)0.5795 (2)0.02941 (5)0.0381 (4)
O40.0060 (3)0.45980 (17)0.03476 (4)0.0470 (3)
N10.0142 (3)0.92624 (16)0.04544 (4)0.0309 (3)
H1N10.01251.03690.03840.046*
H2N10.12520.89820.03300.046*
H3N10.09350.85140.03150.046*
N20.4960 (3)0.37944 (17)0.06828 (4)0.0332 (3)
H1N20.51630.26390.05630.050*
H2N20.38560.42880.05730.050*
H3N20.60380.46050.05530.050*
C10.3283 (3)0.4459 (4)0.13955 (7)0.0492 (5)
H1A0.21150.49260.12450.059*
C20.3318 (4)0.4435 (4)0.18574 (7)0.0639 (7)
H2A0.21790.48810.20200.077*
C30.5047 (5)0.3749 (3)0.20625 (6)0.0634 (6)
C40.6765 (5)0.3079 (4)0.18406 (8)0.0646 (7)
H4A0.79230.26110.19940.077*
C50.6742 (4)0.3113 (3)0.13811 (7)0.0487 (5)
H5A0.79010.26860.12210.058*
C60.4990 (4)0.37857 (19)0.11639 (5)0.0326 (3)
C70.1933 (3)0.8307 (3)0.11348 (6)0.0434 (5)
H7A0.31130.79820.09670.052*
C80.1934 (4)0.8076 (4)0.15908 (7)0.0583 (6)
H8A0.31010.75750.17340.070*
C90.0178 (5)0.8602 (4)0.18240 (6)0.0636 (7)
C100.1576 (4)0.9328 (4)0.16300 (8)0.0671 (7)
H10A0.27390.96770.18000.081*
C110.1593 (4)0.9536 (3)0.11737 (7)0.0496 (5)
H11A0.27781.00150.10320.059*
C120.0157 (3)0.9027 (2)0.09331 (5)0.0317 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.02748 (16)0.02319 (15)0.03006 (16)0.0005 (2)0.0004 (2)0.00064 (11)
F10.1150 (14)0.1674 (18)0.0274 (6)0.006 (2)0.0039 (9)0.0034 (8)
F20.1171 (15)0.1814 (19)0.0301 (6)0.013 (2)0.0030 (10)0.0157 (9)
O10.0549 (8)0.0257 (5)0.0550 (7)0.0033 (10)0.0022 (10)0.0096 (5)
O20.0269 (6)0.0333 (9)0.0515 (8)0.0032 (6)0.0029 (6)0.0008 (7)
O30.0295 (6)0.0324 (9)0.0524 (8)0.0017 (6)0.0039 (6)0.0042 (7)
O40.0639 (8)0.0467 (7)0.0303 (6)0.0010 (14)0.0026 (8)0.0026 (5)
N10.0369 (7)0.0261 (5)0.0298 (6)0.0007 (9)0.0015 (7)0.0008 (4)
N20.0321 (6)0.0393 (6)0.0283 (6)0.0015 (10)0.0003 (9)0.0001 (4)
C10.0423 (10)0.0681 (15)0.0373 (10)0.0054 (11)0.0034 (8)0.0018 (10)
C20.0595 (14)0.095 (2)0.0372 (11)0.0064 (16)0.0121 (10)0.0068 (13)
C30.0767 (16)0.0857 (16)0.0279 (8)0.008 (2)0.0039 (15)0.0008 (8)
C40.0707 (17)0.0807 (19)0.0424 (12)0.0137 (15)0.0198 (11)0.0016 (12)
C50.0482 (12)0.0584 (14)0.0394 (10)0.0137 (11)0.0061 (9)0.0058 (10)
C60.0364 (8)0.0336 (7)0.0279 (6)0.0029 (12)0.0022 (10)0.0012 (5)
C70.0436 (11)0.0487 (12)0.0380 (10)0.0036 (10)0.0068 (8)0.0001 (9)
C80.0661 (16)0.0679 (16)0.0409 (11)0.0040 (14)0.0180 (11)0.0081 (11)
C90.0770 (18)0.0866 (16)0.0272 (8)0.010 (2)0.0032 (13)0.0061 (9)
C100.0642 (15)0.097 (2)0.0400 (11)0.0012 (16)0.0178 (11)0.0017 (14)
C110.0458 (11)0.0629 (14)0.0399 (10)0.0086 (11)0.0051 (9)0.0039 (10)
C120.0372 (9)0.0281 (6)0.0298 (7)0.0017 (10)0.0002 (9)0.0012 (5)
Geometric parameters (Å, º) top
S1—O11.4579 (11)C2—C31.350 (4)
S1—O41.4700 (11)C2—H2A0.9300
S1—O21.4755 (14)C3—C41.365 (4)
S1—O31.4767 (14)C4—C51.387 (3)
F1—C31.362 (2)C4—H4A0.9300
F2—C91.357 (2)C5—C61.376 (3)
N1—C121.4548 (19)C5—H5A0.9300
N1—H1N10.8644C7—C121.379 (3)
N1—H2N10.8198C7—C81.386 (3)
N1—H3N10.9724C7—H7A0.9300
N2—C61.4513 (17)C8—C91.366 (4)
N2—H1N20.9393C8—H8A0.9300
N2—H2N20.8524C9—C101.360 (4)
N2—H3N20.9875C10—C111.385 (3)
C1—C61.376 (3)C10—H10A0.9300
C1—C21.394 (3)C11—C121.371 (3)
C1—H1A0.9300C11—H11A0.9300
O1—S1—O4110.81 (7)C3—C4—C5118.4 (2)
O1—S1—O2109.84 (10)C3—C4—H4A120.8
O4—S1—O2108.76 (10)C5—C4—H4A120.8
O1—S1—O3110.21 (10)C6—C5—C4119.4 (2)
O4—S1—O3108.71 (10)C6—C5—H5A120.3
O2—S1—O3108.45 (7)C4—C5—H5A120.3
C12—N1—H1N1111.1C1—C6—C5121.03 (16)
C12—N1—H2N1114.8C1—C6—N2119.73 (19)
H1N1—N1—H2N1107.0C5—C6—N2119.24 (19)
C12—N1—H3N1111.5C12—C7—C8119.1 (2)
H1N1—N1—H3N1107.5C12—C7—H7A120.5
H2N1—N1—H3N1104.5C8—C7—H7A120.5
C6—N2—H1N2112.3C9—C8—C7118.4 (2)
C6—N2—H2N2113.7C9—C8—H8A120.8
H1N2—N2—H2N2110.6C7—C8—H8A120.8
C6—N2—H3N2113.0F2—C9—C10118.5 (3)
H1N2—N2—H3N2108.0F2—C9—C8118.3 (3)
H2N2—N2—H3N298.3C10—C9—C8123.19 (19)
C6—C1—C2119.4 (2)C9—C10—C11118.5 (2)
C6—C1—H1A120.3C9—C10—H10A120.7
C2—C1—H1A120.3C11—C10—H10A120.7
C3—C2—C1118.4 (2)C12—C11—C10119.3 (2)
C3—C2—H2A120.8C12—C11—H11A120.4
C1—C2—H2A120.8C10—C11—H11A120.4
C2—C3—F1118.5 (3)C11—C12—C7121.54 (17)
C2—C3—C4123.4 (2)C11—C12—N1119.15 (19)
F1—C3—C4118.1 (3)C7—C12—N1119.31 (18)
C6—C1—C2—C30.2 (4)C12—C7—C8—C91.1 (4)
C1—C2—C3—F1179.8 (2)C7—C8—C9—F2179.9 (2)
C1—C2—C3—C40.1 (5)C7—C8—C9—C100.5 (4)
C2—C3—C4—C50.4 (5)F2—C9—C10—C11179.0 (3)
F1—C3—C4—C5179.3 (2)C8—C9—C10—C110.4 (5)
C3—C4—C5—C61.1 (4)C9—C10—C11—C120.8 (4)
C2—C1—C6—C50.9 (4)C10—C11—C12—C70.2 (4)
C2—C1—C6—N2179.6 (2)C10—C11—C12—N1179.4 (2)
C4—C5—C6—C11.4 (4)C8—C7—C12—C110.8 (3)
C4—C5—C6—N2179.1 (2)C8—C7—C12—N1179.62 (19)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H3N1···O30.972.092.887 (3)138
N2—H2N2···O30.851.902.741 (3)168
N1—H1N1···O1i0.861.922.761 (2)162
N1—H2N1···O3ii0.822.252.967 (2)146
N1—H2N1···O4ii0.822.553.151 (3)131
N1—H3N1···O2iii0.972.242.925 (2)126
N2—H1N2···O4iv0.941.782.7121 (18)170
N2—H3N2···O2v0.991.722.702 (2)170
C11—H11A···O4iii0.932.533.374 (3)151
Symmetry codes: (i) x, y+1, z; (ii) x1/2, y+3/2, z; (iii) x+1/2, y+3/2, z; (iv) x+1/2, y+1/2, z; (v) x+1, y, z.

Experimental details

Crystal data
Chemical formula2C6H7FN+·SO42
Mr320.31
Crystal system, space groupOrthorhombic, P212121
Temperature (K)296
a, b, c (Å)6.2907 (5), 7.4155 (6), 30.168 (3)
V3)1407.3 (2)
Z4
Radiation typeMo Kα
µ (mm1)0.27
Crystal size (mm)0.58 × 0.12 × 0.07
Data collection
DiffractometerBruker SMART APEXII DUO CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Bruker, 2009)
Tmin, Tmax0.859, 0.982
No. of measured, independent and
observed [I > 2σ(I)] reflections
31062, 4292, 3503
Rint0.044
(sin θ/λ)max1)0.716
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.038, 0.103, 0.98
No. of reflections4292
No. of parameters191
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.18, 0.39
Absolute structureFlack (1983), 1794 Friedel pairs
Absolute structure parameter0.50 (10)

Computer programs: APEX2 (Bruker, 2009), SAINT (Bruker, 2009), SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2009).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H3N1···O30.972.092.887 (3)138
N2—H2N2···O30.851.902.741 (3)168
N1—H1N1···O1i0.861.922.761 (2)162
N1—H2N1···O3ii0.822.252.967 (2)145.9
N1—H2N1···O4ii0.822.553.151 (3)131.4
N1—H3N1···O2iii0.972.242.925 (2)126.4
N2—H1N2···O4iv0.941.782.7121 (18)170
N2—H3N2···O2v0.991.722.702 (2)170
C11—H11A···O4iii0.932.533.374 (3)150.8
Symmetry codes: (i) x, y+1, z; (ii) x1/2, y+3/2, z; (iii) x+1/2, y+3/2, z; (iv) x+1/2, y+1/2, z; (v) x+1, y, z.
 

Footnotes

Thomson Reuters ResearcherID: A-3561-2009.

Acknowledgements

The authors thank Universiti Sains Malaysia (USM) for the Research University Grant (1001/PFIZIK/811160). SA thanks the Malaysian Government and USM for the award of a research scholarship.

References

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