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Acta Cryst. (2008). E64, o1878-o1879    [ doi:10.1107/S1600536808027761 ]

4-Aminopyridinium 4-nitrobenzoate 4-nitrobenzoic acid

C. K. Quah, S. R. Jebas and H.-K. Fun

Abstract top

The asymmetric unit of the title compound, C5H7N2+·C7H4NO4-·C7H5NO4, consists of an aminopyridinium cation, a 4-nitrobenzoate anion and a neutral 4-nitrobenzoic acid molecule. The pyridine ring forms dihedral angles of 64.70 (5)° and 70.37 (5)°, respectively, with the benzene rings of 4-nitrobenzoic acid and 4-nitrobenzoate. In the crystal structure, the cations, anions and the neutral 4-nitrobenzoic acid molecules are linked by O-H...O and N-H...O hydrogen bonds, forming a two-dimensional network parallel to (001). Adjacent networks are cross-linked via C-H...O hydrogen bonds and [pi]-[pi] stacking interactions [centroid-centroid distances 3.6339 (6) and 3.6566 (6) Å].

Comment top

4-Aminopyridine (Fampridine) is used clinically in Lambert-Eaton myasthenic syndrome and multiple sclerosis because by blocking potassium channels, it prolongs the action potentials thereby increasing transmitter release at the neuromuscular junction (Judge et al., 2006; Schwid et al., 1997; Strupp et al., 2004). The crystal structure of 4-aminopyridine has been reported (Chao & Schempp, 1977; Anderson et al., 2005). As an extension of our systematic study of hydrogen bonding patterns of 4-aminopyridine with aromatic carboxylic acids, we report here the crystal structure of the title compound.

The asymmetric unit of the title compound contains one 4-aminopyridinium cation, one 4-nitrobenzoate anion and one 4-nitrobenzoic acid molecule. A proton transfer from the carboxyl group of 4-nitrobenzoic acid to atom N2 of 4-aminopyridine resulted in the formation of ions. This lead to the widening of C8—N2—C12 angle of the pyridine ring to 120.86 (9)°, compared to 115.25 (13)° in the unprotonated 4-aminopyridine (Anderson et al., 2005). This type of protonation is observed in various 4-aminopyridine acid complexes (Bhattacharya et al., 1994; Karle et al., 2003). The bond lengths and angles of the 4-aminopyridne are comparable to the values reported earlier for 4-aminopyridine (Chao & Schempp, 1977; Anderson et al., 2005). The bond lengths and angles of the 4-nitrobenzoic acid is found to be normal(Andrau & White, 2003).

The dihedral angle between the benzene rings of 4-nitrobenzoic acid (C1A-C6A) and 4-nitrobenzoate (C1B-C6B) units is 6.62 (5)°. The pyridine (N2/C8—C12) ring forms dihedral angles of 64.70 (5)° and 70.37 (5)°, respectively, with the C1A-C6A and C1B-C6B rings.

In the crystal structure, the cations, anions and the neutral 4-nitrobenzoic acid molecules are linked to form a two-dimensional network (Fig. 2) parallel to the (0 0 1) by O—H···O and N—H···O hydrogen bonds (Table 1). The adjacent networks are cross-linked via C—H···O hydrogen bonds. The crystal packing is further consolidated by π–π stacking interactions between symmetry-related C1A-C6A (centroid Cg1) and C1B-C6B (centroid Cg2) rings, with Cg1···Cg1i and Cg2···Cg2vii distances of 3.6566 (6) Å and 3.6339 (6) Å, respectively [symmetry codes: (i) 1-x, 2-y, 1-z; (vii) 2-x, 2-y, 2-z].

Related literature top

For the biological activity of 4-aminopyridine, see: Judge et al. (2006); Schwid et al. (1997); Strupp et al. (2004). For related structures, see: Chao & Schempp (1977); Anderson et al. (2005); Andrau & White, (2003); Bhattacharya et al. (1994); Karle et al. (2003).

Experimental top

4-Aminopyridine and 4-nitrobenzoic acid were mixed in equimolar ratio in methanol and warmed in a water bath for 2 h. Colourless single crystals were obtained after a week on slow evaporation.

Refinement top

Atom H1N2 was located from a difference map and was refined with the N-H distance restrained to 0.85 (1) Å. The remaining H atoms were positioned geometrically with C-H = 0.93 Å, N-H = 0.86 Å and O-H = 0.82Å, and refined using a riding model, with Uiso(H) = 1.2Ueq(C,N) and 1.5Ueq(O).

Computing details top

Data collection: APEX2 (Bruker, 2005); cell refinement: APEX2 (Bruker, 2005); data reduction: SAINT (Bruker, 2005); 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, 2003).

Figures top
[Figure 1] Fig. 1. The asymmetric unit of the title compound, showing 50% probability displacement ellipsoids and the atom-numbering scheme.
[Figure 2] Fig. 2. The crystal packing of the title compound, viewed along the a axis. Hydrogen bonds are shown as dashed lines.
(I) top
Crystal data top
C5H7N2+·C7H4NO4−·C7H5NO4Z = 2
Mr = 428.36F(000) = 444
Triclinic, P1Dx = 1.545 Mg m−3
Hall symbol: -P 1Mo Kα radiation, λ = 0.71073 Å
a = 6.4561 (1) ÅCell parameters from 6200 reflections
b = 6.8598 (1) Åθ = 2.2–29.2°
c = 20.9055 (3) ŵ = 0.12 mm−1
α = 85.826 (1)°T = 100 K
β = 87.975 (1)°Block, colourless
γ = 86.188 (1)°0.40 × 0.36 × 0.29 mm
V = 920.92 (2) Å3
Data collection top
Bruker SMART APEXII CCD area-detector
diffractometer		6647 independent reflections
Radiation source: fine-focus sealed tube5169 reflections with I > 2σ(I)
graphiteRint = 0.031
φ and ω scansθmax = 32.5°, θmin = 1.0°
Absorption correction: multi-scan
(SADABS; Bruker, 2005)		h = −9→9
Tmin = 0.952, Tmax = 0.965k = −10→10
24945 measured reflectionsl = −31→31
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)] = 0.044Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.132H atoms treated by a mixture of independent and constrained refinement
S = 1.05 w = 1/[σ2(Fo2) + (0.0736P)2 + 0.1221P]
where P = (Fo2 + 2Fc2)/3
6647 reflections(Δ/σ)max = 0.001
284 parametersΔρmax = 0.43 e Å−3
1 restraintΔρmin = −0.39 e Å−3
Crystal data top
C5H7N2+·C7H4NO4−·C7H5NO4γ = 86.188 (1)°
Mr = 428.36V = 920.92 (2) Å3
Triclinic, P1Z = 2
a = 6.4561 (1) ÅMo Kα radiation
b = 6.8598 (1) ŵ = 0.12 mm−1
c = 20.9055 (3) ÅT = 100 K
α = 85.826 (1)°0.40 × 0.36 × 0.29 mm
β = 87.975 (1)°
Data collection top
Bruker SMART APEXII CCD area-detector
diffractometer		6647 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2005)		5169 reflections with I > 2σ(I)
Tmin = 0.952, Tmax = 0.965Rint = 0.031
24945 measured reflectionsθmax = 32.5°
Refinement top
R[F2 > 2σ(F2)] = 0.044H atoms treated by a mixture of independent and constrained refinement
wR(F2) = 0.132Δρmax = 0.43 e Å−3
S = 1.05Δρmin = −0.39 e Å−3
6647 reflectionsAbsolute structure: ?
284 parametersFlack parameter: ?
1 restraintRogers parameter: ?
Special details top

Experimental. The data was collected with the Oxford Cyrosystem Cobra low-temperature attachment.

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
O1A0.61416 (13)0.64153 (13)0.61139 (4)0.02534 (18)
O1B1.43798 (12)0.64460 (14)1.07244 (4)0.02613 (19)
O2A0.89023 (12)0.63198 (13)0.54960 (4)0.02492 (18)
O2B1.15700 (13)0.66730 (15)1.13139 (4)0.02794 (19)
O3A0.31404 (11)0.97209 (12)0.29069 (4)0.02024 (16)
H1O30.23421.01630.26280.030*
O3B0.89111 (11)0.90736 (11)0.80183 (4)0.01831 (15)
O4A0.02402 (11)0.98398 (11)0.35318 (4)0.01950 (16)
O4B0.59084 (12)0.90329 (13)0.85892 (4)0.02425 (18)
N1A0.70215 (13)0.66162 (13)0.55851 (4)0.01667 (17)
N1B1.24848 (13)0.67136 (13)1.07904 (4)0.01646 (17)
N20.80980 (14)0.30341 (13)0.29153 (4)0.01904 (18)
N30.73597 (13)0.85350 (13)0.20200 (5)0.02020 (18)
H3A0.83540.93090.20220.024*
H3B0.62230.89220.18340.024*
C1A0.24956 (15)0.84572 (14)0.46101 (5)0.01507 (18)
H1AA0.10840.87900.46670.018*
C1B1.11431 (15)0.75402 (14)0.90711 (5)0.01505 (18)
H1BA1.17880.74820.86670.018*
C2A0.36551 (15)0.77640 (14)0.51351 (5)0.01593 (18)
H2AA0.30480.76330.55450.019*
C2B1.22778 (15)0.70459 (14)0.96180 (5)0.01522 (18)
H2BA1.36850.66640.95870.018*
C3B1.12614 (14)0.71350 (14)1.02109 (5)0.01397 (17)
C3A0.57532 (15)0.72731 (14)0.50276 (5)0.01424 (17)
C4A0.67164 (15)0.74110 (15)0.44250 (5)0.01592 (18)
H4AA0.81190.70380.43690.019*
C4B0.91589 (15)0.76542 (14)1.02843 (5)0.01527 (18)
H4BA0.85130.76671.06890.018*
C5A0.55303 (15)0.81214 (15)0.39071 (5)0.01621 (18)
H5AA0.61420.82390.34980.019*
C5B0.80500 (15)0.81538 (14)0.97324 (5)0.01517 (18)
H5BA0.66380.85120.97660.018*
C6A0.34218 (14)0.86598 (14)0.39989 (5)0.01412 (17)
C6B0.90370 (14)0.81237 (14)0.91270 (5)0.01388 (17)
C7A0.21250 (15)0.94696 (14)0.34447 (5)0.01498 (18)
C7B0.78049 (15)0.87820 (14)0.85437 (5)0.01578 (18)
C80.62995 (16)0.35854 (16)0.26207 (5)0.0195 (2)
H8A0.52600.27090.26230.023*
C90.59889 (15)0.54066 (15)0.23204 (5)0.01760 (19)
H9A0.47360.57750.21260.021*
C100.75805 (15)0.67391 (15)0.23052 (5)0.01566 (18)
C110.94501 (15)0.60896 (15)0.26128 (5)0.01670 (19)
H11A1.05380.69140.26110.020*
C120.96496 (16)0.42621 (16)0.29097 (5)0.0186 (2)
H12A1.08770.38490.31130.022*
H1N20.839 (2)0.1892 (15)0.3080 (7)0.029 (4)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O1A0.0250 (4)0.0384 (5)0.0118 (4)−0.0024 (3)−0.0008 (3)0.0048 (3)
O1B0.0158 (3)0.0428 (5)0.0191 (4)0.0041 (3)−0.0028 (3)−0.0013 (3)
O2A0.0172 (3)0.0361 (5)0.0207 (4)0.0016 (3)−0.0036 (3)0.0012 (3)
O2B0.0228 (4)0.0485 (5)0.0115 (4)0.0012 (3)0.0006 (3)0.0003 (3)
O3A0.0183 (3)0.0303 (4)0.0116 (3)−0.0013 (3)−0.0025 (3)0.0027 (3)
O3B0.0174 (3)0.0258 (4)0.0114 (3)−0.0009 (3)−0.0003 (3)0.0006 (3)
O4A0.0158 (3)0.0236 (4)0.0182 (4)0.0011 (3)−0.0016 (3)0.0026 (3)
O4B0.0145 (3)0.0368 (5)0.0198 (4)0.0011 (3)−0.0020 (3)0.0071 (3)
N1A0.0179 (4)0.0178 (4)0.0145 (4)−0.0016 (3)−0.0034 (3)−0.0001 (3)
N1B0.0167 (4)0.0194 (4)0.0131 (4)0.0003 (3)−0.0014 (3)−0.0010 (3)
N20.0213 (4)0.0188 (4)0.0161 (4)0.0014 (3)0.0009 (3)0.0017 (3)
N30.0160 (4)0.0212 (4)0.0224 (5)0.0005 (3)−0.0014 (3)0.0045 (3)
C1A0.0146 (4)0.0166 (4)0.0140 (4)−0.0011 (3)−0.0003 (3)−0.0006 (3)
C1B0.0156 (4)0.0177 (4)0.0114 (4)0.0009 (3)0.0001 (3)−0.0004 (3)
C2A0.0172 (4)0.0180 (4)0.0127 (4)−0.0030 (3)0.0005 (3)−0.0001 (3)
C2B0.0139 (4)0.0175 (4)0.0140 (4)0.0009 (3)−0.0001 (3)−0.0010 (3)
C3B0.0151 (4)0.0154 (4)0.0114 (4)−0.0001 (3)−0.0023 (3)−0.0003 (3)
C3A0.0168 (4)0.0143 (4)0.0118 (4)−0.0017 (3)−0.0030 (3)0.0002 (3)
C4A0.0141 (4)0.0193 (4)0.0143 (4)−0.0007 (3)−0.0005 (3)−0.0013 (3)
C4B0.0158 (4)0.0175 (4)0.0125 (4)−0.0018 (3)0.0009 (3)−0.0007 (3)
C5A0.0163 (4)0.0206 (4)0.0117 (4)−0.0015 (3)0.0000 (3)−0.0013 (3)
C5B0.0131 (4)0.0180 (4)0.0142 (4)−0.0005 (3)−0.0002 (3)0.0001 (3)
C6A0.0154 (4)0.0147 (4)0.0125 (4)−0.0018 (3)−0.0021 (3)−0.0006 (3)
C6B0.0143 (4)0.0151 (4)0.0122 (4)−0.0013 (3)−0.0014 (3)0.0005 (3)
C7A0.0173 (4)0.0153 (4)0.0125 (4)−0.0026 (3)−0.0018 (3)0.0002 (3)
C7B0.0157 (4)0.0167 (4)0.0149 (4)−0.0007 (3)−0.0022 (3)−0.0001 (3)
C80.0175 (4)0.0233 (5)0.0178 (5)−0.0023 (4)0.0008 (4)−0.0016 (4)
C90.0138 (4)0.0231 (5)0.0156 (5)−0.0006 (3)−0.0012 (3)−0.0001 (4)
C100.0144 (4)0.0199 (4)0.0123 (4)0.0012 (3)0.0005 (3)−0.0009 (3)
C110.0151 (4)0.0203 (4)0.0148 (4)−0.0004 (3)−0.0020 (3)−0.0015 (4)
C120.0178 (4)0.0232 (5)0.0143 (5)0.0029 (3)−0.0023 (3)−0.0010 (4)
Geometric parameters (Å, °) top
O1A—N1A1.2278 (12)C2A—H2AA0.93
O1B—N1B1.2294 (11)C2B—C3B1.3851 (14)
O2A—N1A1.2276 (11)C2B—H2BA0.93
O2B—N1B1.2244 (12)C3B—C4B1.3863 (13)
O3A—C7A1.2877 (12)C3A—C4A1.3848 (14)
O3A—H1O30.8200C4A—C5A1.3888 (14)
O3B—C7B1.2993 (12)C4A—H4AA0.93
O4A—C7A1.2362 (12)C4B—C5B1.3890 (14)
O4B—C7B1.2263 (12)C4B—H4BA0.93
N1A—C3A1.4743 (12)C5A—C6A1.3969 (13)
N1B—C3B1.4702 (13)C5A—H5AA0.93
N2—C121.3502 (14)C5B—C6B1.3977 (14)
N2—C81.3523 (14)C5B—H5BA0.93
N2—H1N20.844 (9)C6A—C7A1.5049 (13)
N3—C101.3301 (13)C6B—C7B1.5047 (13)
N3—H3A0.86C8—C91.3626 (15)
N3—H3B0.86C8—H8A0.93
C1A—C2A1.3877 (14)C9—C101.4180 (14)
C1A—C6A1.3930 (14)C9—H9A0.93
C1A—H1AA0.93C10—C111.4180 (13)
C1B—C2B1.3888 (13)C11—C121.3580 (15)
C1B—C6B1.3949 (13)C11—H11A0.93
C1B—H1BA0.93C12—H12A0.93
C2A—C3A1.3884 (13)
C7A—O3A—H1O3109.5C3B—C4B—H4BA121.2
O2A—N1A—O1A123.62 (9)C5B—C4B—H4BA121.2
O2A—N1A—C3A118.18 (9)C4A—C5A—C6A120.21 (9)
O1A—N1A—C3A118.20 (8)C4A—C5A—H5AA119.9
O2B—N1B—O1B123.36 (9)C6A—C5A—H5AA119.9
O2B—N1B—C3B118.43 (8)C4B—C5B—C6B120.61 (9)
O1B—N1B—C3B118.20 (9)C4B—C5B—H5BA119.7
C12—N2—C8120.86 (9)C6B—C5B—H5BA119.7
C12—N2—H1N2115.2 (11)C1A—C6A—C5A119.99 (9)
C8—N2—H1N2123.7 (11)C1A—C6A—C7A119.15 (8)
C10—N3—H3A120.0C5A—C6A—C7A120.86 (9)
C10—N3—H3B120.0C1B—C6B—C5B120.08 (9)
H3A—N3—H3B120.0C1B—C6B—C7B121.02 (9)
C2A—C1A—C6A120.74 (9)C5B—C6B—C7B118.88 (8)
C2A—C1A—H1AA119.6O4A—C7A—O3A125.63 (9)
C6A—C1A—H1AA119.6O4A—C7A—C6A119.65 (9)
C2B—C1B—C6B120.04 (9)O3A—C7A—C6A114.72 (8)
C2B—C1B—H1BA120.0O4B—C7B—O3B125.05 (9)
C6B—C1B—H1BA120.0O4B—C7B—C6B120.18 (9)
C1A—C2A—C3A117.70 (9)O3B—C7B—C6B114.75 (8)
C1A—C2A—H2AA121.2N2—C8—C9120.94 (10)
C3A—C2A—H2AA121.2N2—C8—H8A119.5
C3B—C2B—C1B118.35 (9)C9—C8—H8A119.5
C3B—C2B—H2BA120.8C8—C9—C10119.85 (9)
C1B—C2B—H2BA120.8C8—C9—H9A120.1
C2B—C3B—C4B123.20 (9)C10—C9—H9A120.1
C2B—C3B—N1B118.36 (8)N3—C10—C11120.35 (9)
C4B—C3B—N1B118.42 (9)N3—C10—C9122.38 (9)
C4A—C3A—C2A123.18 (9)C11—C10—C9117.27 (9)
C4A—C3A—N1A118.57 (8)C12—C11—C10119.88 (9)
C2A—C3A—N1A118.23 (9)C12—C11—H11A120.1
C3A—C4A—C5A118.16 (9)C10—C11—H11A120.1
C3A—C4A—H4AA120.9N2—C12—C11121.19 (9)
C5A—C4A—H4AA120.9N2—C12—H12A119.4
C3B—C4B—C5B117.67 (9)C11—C12—H12A119.4
C6A—C1A—C2A—C3A−0.39 (14)C4A—C5A—C6A—C1A−0.97 (14)
C6B—C1B—C2B—C3B0.50 (14)C4A—C5A—C6A—C7A178.78 (9)
C1B—C2B—C3B—C4B1.38 (15)C2B—C1B—C6B—C5B−1.98 (14)
C1B—C2B—C3B—N1B−176.79 (9)C2B—C1B—C6B—C7B176.30 (9)
O2B—N1B—C3B—C2B−175.56 (9)C4B—C5B—C6B—C1B1.65 (14)
O1B—N1B—C3B—C2B5.40 (14)C4B—C5B—C6B—C7B−176.66 (9)
O2B—N1B—C3B—C4B6.18 (14)C1A—C6A—C7A—O4A−4.01 (14)
O1B—N1B—C3B—C4B−172.86 (9)C5A—C6A—C7A—O4A176.24 (9)
C1A—C2A—C3A—C4A−1.18 (15)C1A—C6A—C7A—O3A175.76 (8)
C1A—C2A—C3A—N1A177.40 (8)C5A—C6A—C7A—O3A−3.99 (13)
O2A—N1A—C3A—C4A3.87 (13)C1B—C6B—C7B—O4B170.01 (9)
O1A—N1A—C3A—C4A−176.87 (9)C5B—C6B—C7B—O4B−11.69 (14)
O2A—N1A—C3A—C2A−174.77 (9)C1B—C6B—C7B—O3B−11.13 (13)
O1A—N1A—C3A—C2A4.48 (13)C5B—C6B—C7B—O3B167.17 (9)
C2A—C3A—C4A—C5A1.64 (15)C12—N2—C8—C9−1.21 (16)
N1A—C3A—C4A—C5A−176.93 (8)N2—C8—C9—C101.08 (16)
C2B—C3B—C4B—C5B−1.70 (15)C8—C9—C10—N3−179.88 (10)
N1B—C3B—C4B—C5B176.47 (9)C8—C9—C10—C11−0.23 (15)
C3A—C4A—C5A—C6A−0.53 (14)N3—C10—C11—C12179.16 (10)
C3B—C4B—C5B—C6B0.15 (14)C9—C10—C11—C12−0.50 (15)
C2A—C1A—C6A—C5A1.44 (14)C8—N2—C12—C110.45 (16)
C2A—C1A—C6A—C7A−178.30 (9)C10—C11—C12—N20.41 (16)
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O3A—H1O3···O3Bi0.821.632.4457 (11)170
N3—H3A···O3Bii0.862.142.9977 (12)172
N3—H3B···O4Bi0.862.072.8758 (12)155
N2—H1N2···O4Aiii0.85 (1)1.99 (1)2.7726 (12)153 (1)
C2B—H2BA···O1Biv0.932.523.2187 (13)133
C8—H8A···O3Av0.932.563.4565 (13)161
C12—H12A···O1Avi0.932.553.4427 (13)162
Symmetry codes: (i) −x+1, −y+2, −z+1; (ii) −x+2, −y+2, −z+1; (iii) x+1, y−1, z; (iv) −x+3, −y+1, −z+2; (v) x, y−1, z; (vi) −x+2, −y+1, −z+1.
Table 1
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O3A—H1O3···O3Bi0.821.632.4457 (11)170
N3—H3A···O3Bii0.862.142.9977 (12)172
N3—H3B···O4Bi0.862.072.8758 (12)155
N2—H1N2···O4Aiii0.85 (1)1.99 (1)2.7726 (12)153 (1)
C2B—H2BA···O1Biv0.932.523.2187 (13)133
C8—H8A···O3Av0.932.563.4565 (13)161
C12—H12A···O1Avi0.932.553.4427 (13)162
Symmetry codes: (i) −x+1, −y+2, −z+1; (ii) −x+2, −y+2, −z+1; (iii) x+1, y−1, z; (iv) −x+3, −y+1, −z+2; (v) x, y−1, z; (vi) −x+2, −y+1, −z+1.
Acknowledgements top

HKF and SRJ thank the Malaysian Government and Universiti Sains Malaysia for Science Fund grant No. 305/PFIZIK/613312. SRJ thanks Universiti Sains Malaysia for a post-doctoral research fellowship.

references
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