4-(2-Azaniumyl­eth­yl)piperazin-1-ium bis(perchlorate)

Reisi, M.R.; Saleh Salga, M.; Khaledi, H.; Mohd Ali, H.

doi:10.1107/S1600536811033976

organic compounds

CRYSTALLOGRAPHIC
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ISSN: 2056-9890

Volume 67| Part 9| September 2011| Page o2400

doi:10.1107/S1600536811033976

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4-(2-Azaniumylethyl)piperazin-1-ium bis(perchlorate)

Mohammad Reza Reisi,^a Muhammad Saleh Salga,^b Hamid Khaledi ^b ^* and Hapipah Mohd Ali ^b

^aChemistry Department, Isfahan University, 81646-73441 Isfahan, Iran, and ^bDepartment of Chemistry, University of Malaya, 50603 Kuala Lumpur, Malaysia
^*Correspondence e-mail: khaledi@siswa.um.edu.my

(Received 12 August 2011; accepted 19 August 2011; online 27 August 2011)

In the title compound, C₆H₁₇N₃²⁺·2ClO₄⁻, the piperazine ring adopts a chair conformation with the ethylammonium fragment occupying an equatorial position. In the crystal, the dications and perchlorate anions are linked through N—H⋯O hydrogen bonding and weak C—H⋯O hydrogen bonding into a three-dimensional supramolecular network.

Related literature

For the structures of related salts of the 4-(2-ammonioethyl)piperazin-1-ium cation, see: Guerfel et al. (1999 ); Srinivasan et al. (2008 , 2009 ).

Experimental

Crystal data

C₆H₁₇N₃²⁺·2ClO₄⁻
M_r = 330.13
Monoclinic, P 2₁ /n
a = 7.5218 (1) Å
b = 11.4371 (2) Å
c = 15.2239 (2) Å
β = 97.437 (1)°
V = 1298.66 (3) Å³
Z = 4
Mo Kα radiation
μ = 0.54 mm⁻¹
T = 100 K
0.28 × 0.17 × 0.06 mm

Data collection

Bruker APEXII CCD diffractometer
Absorption correction: multi-scan (SADABS; Sheldrick, 1996 ) T_min = 0.863, T_max = 0.968
8644 measured reflections
2969 independent reflections
2671 reflections with I > 2σ(I)
R_int = 0.023

Refinement

R[F² > 2σ(F²)] = 0.030
wR(F²) = 0.080
S = 1.05
2969 reflections
187 parameters
5 restraints
H atoms treated by a mixture of independent and constrained refinement
Δρ_max = 0.27 e Å⁻³
Δρ_min = −0.59 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N1—H1C⋯O4ⁱ	0.90 (2)	2.16 (2)	2.9298 (19)	143 (2)
N1—H1D⋯O3ⁱⁱ	0.88 (2)	2.09 (2)	2.964 (2)	168 (2)
N3—H3C⋯O6ⁱ	0.89 (2)	2.38 (2)	3.0741 (19)	135 (2)
N3—H3C⋯O4	0.89 (2)	2.39 (2)	3.0225 (19)	128 (2)
N3—H3D⋯O1ⁱⁱⁱ	0.89 (2)	2.12 (2)	2.9875 (18)	163 (2)
N3—H3E⋯O8^iv	0.88 (2)	2.14 (2)	2.9025 (19)	145 (2)
N3—H3E⋯O3	0.88 (2)	2.52 (2)	3.0724 (19)	122 (2)
C1—H1B⋯O7^v	0.99	2.56	3.407 (2)	143
C3—H3A⋯O8ⁱⁱⁱ	0.99	2.56	3.226 (2)	124
C5—H5A⋯O5^vi	0.99	2.58	3.436 (2)	145
C5—H5B⋯O2ⁱⁱⁱ	0.99	2.46	3.452 (2)	178
Symmetry codes: (i) -x+1, -y+1, -z+1; (ii) $[x-{\script{1\over 2}}, -y+{\script{1\over 2}}, z-{\script{1\over 2}}]$ ; (iii) x-1, y, z; (iv) $[x-{\script{1\over 2}}, -y+{\script{1\over 2}}, z+{\script{1\over 2}}]$ ; (v) $[-x+{\script{3\over 2}}, y-{\script{1\over 2}}, -z+{\script{1\over 2}}]$ ; (vi) $[-x+{\script{1\over 2}}, y-{\script{1\over 2}}, -z+{\script{1\over 2}}]$ .

Data collection: APEX2 (Bruker, 2007 ); cell refinement: SAINT (Bruker, 2007); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 ); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: X-SEED (Barbour, 2001 ); software used to prepare material for publication: SHELXL97 and publCIF (Westrip, 2010 ).

Supporting information

Crystal structure: contains datablocks I, global. DOI: 10.1107/S1600536811033976/xu5296sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536811033976/xu5296Isup2.hkl

Supporting information file. DOI: 10.1107/S1600536811033976/xu5296Isup3.cml

checkCIF report

Comment top

The crystals of the title compound were obtained unexpectedly during an attempt to prepare a tin(IV) complex of 1-(2-aminoethyl)piperazine in the presence of sodium perchlorate. The organic molecule is doubly protonated at its primary and secondary N atoms, while the tertiary N atom, N2, remains unprotonated. Similar to the structures of some other 1-(2-ammoniumethyl)piperazinium salts (Guerfel et al., 1999; Srinivasan et al., 2008, 2009), the piperazine ring adopts a chair conformation with the ethylammonium group occupying an equatorial position. In the crystal, the dicationic organic moieties and perchlorate anions are linked through N—H···O and C—H···O interactions (Table 1) into a three-dimensional supra-molecular network.

Related literature top

For the structures of related salts of the 4-(2-ammonioethyl)piperazin-1-ium cation, see: Guerfel et al. (1999); Srinivasan et al. (2008, 2009).

Experimental top

A mixture of 4-(2-aminoethyl)piperazine (0.26 g, 2 mmol) and Bu₂SnCl₂ (0.6 g, 2 mmol) in methanol (50 ml) was refluxed for 2 h. NaClO₄ (0.56 g, 4 mmol) was then added and the precipitated sodium chloride was filtered off. The filtrate was evaporated and the obtained solid was recrystallized from ethanol at room temperature to give the colorless crystals of the title compound.

Computing details top

Data collection: APEX2 (Bruker, 2007); cell refinement: SAINT (Bruker, 2007); data reduction: SAINT (Bruker, 2007); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: X-SEED (Barbour, 2001); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008) and publCIF (Westrip, 2010).

Figures top

Fig. 1. Molecular structure of the title compound with thermal ellipsoids at the 50% probability level. H atoms are drawn as spheres of arbitrary radius.

4-(2-Azaniumylethyl)piperazin-1-ium bis(perchlorate) top

Crystal data top

C₆H₁₇N₃²⁺·2ClO₄⁻	F(000) = 688
M_r = 330.13	D_x = 1.688 Mg m⁻³
Monoclinic, P2₁/n	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yn	Cell parameters from 4052 reflections
a = 7.5218 (1) Å	θ = 2.2–30.5°
b = 11.4371 (2) Å	µ = 0.54 mm⁻¹
c = 15.2239 (2) Å	T = 100 K
β = 97.437 (1)°	Blade, colourless
V = 1298.66 (3) Å³	0.28 × 0.17 × 0.06 mm
Z = 4

Data collection top

Bruker APEXII CCD diffractometer	2969 independent reflections
Radiation source: fine-focus sealed tube	2671 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.023
ϕ and ω scans	θ_max = 27.5°, θ_min = 2.2°
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	h = −9→9
T_min = 0.863, T_max = 0.968	k = −14→12
8644 measured reflections	l = −19→18

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.030	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.080	H atoms treated by a mixture of independent and constrained refinement
S = 1.05	w = 1/[σ²(F_o²) + (0.0388P)² + 0.8608P] where P = (F_o² + 2F_c²)/3
2969 reflections	(Δ/σ)_max = 0.001
187 parameters	Δρ_max = 0.27 e Å⁻³
5 restraints	Δρ_min = −0.59 e Å⁻³

Crystal data top

C₆H₁₇N₃²⁺·2ClO₄⁻	V = 1298.66 (3) Å³
M_r = 330.13	Z = 4
Monoclinic, P2₁/n	Mo Kα radiation
a = 7.5218 (1) Å	µ = 0.54 mm⁻¹
b = 11.4371 (2) Å	T = 100 K
c = 15.2239 (2) Å	0.28 × 0.17 × 0.06 mm
β = 97.437 (1)°

Data collection top

Bruker APEXII CCD diffractometer	2969 independent reflections
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	2671 reflections with I > 2σ(I)
T_min = 0.863, T_max = 0.968	R_int = 0.023
8644 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.030	5 restraints
wR(F²) = 0.080	H atoms treated by a mixture of independent and constrained refinement
S = 1.05	Δρ_max = 0.27 e Å⁻³
2969 reflections	Δρ_min = −0.59 e Å⁻³
187 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

	x	y	z	U_iso*/U_eq
N1	0.3280 (2)	0.44351 (13)	0.34193 (10)	0.0188 (3)
H1C	0.390 (3)	0.5105 (15)	0.3389 (14)	0.023*
H1D	0.268 (3)	0.4345 (19)	0.2884 (11)	0.023*
N2	0.22434 (17)	0.25008 (12)	0.44167 (9)	0.0137 (3)
N3	0.26916 (19)	0.16033 (12)	0.61553 (9)	0.0138 (3)
H3C	0.308 (3)	0.2308 (14)	0.6010 (13)	0.017*
H3D	0.161 (2)	0.1729 (17)	0.6323 (13)	0.017*
H3E	0.340 (2)	0.1314 (17)	0.6606 (11)	0.017*
C1	0.4538 (2)	0.34346 (15)	0.36621 (12)	0.0212 (4)
H1A	0.5295	0.3604	0.4229	0.025*
H1B	0.5334	0.3327	0.3199	0.025*
C2	0.3466 (2)	0.23325 (15)	0.37506 (11)	0.0182 (3)
H2A	0.2769	0.2137	0.3173	0.022*
H2B	0.4289	0.1674	0.3928	0.022*
C3	0.1959 (2)	0.45727 (15)	0.40696 (12)	0.0186 (3)
H3A	0.1099	0.5205	0.3873	0.022*
H3B	0.2595	0.4787	0.4658	0.022*
C4	0.0963 (2)	0.34326 (15)	0.41350 (12)	0.0190 (3)
H4A	0.0095	0.3513	0.4568	0.023*
H4B	0.0289	0.3235	0.3552	0.023*
C5	0.1375 (2)	0.13996 (15)	0.46127 (11)	0.0165 (3)
H5A	0.1257	0.0886	0.4085	0.020*
H5B	0.0160	0.1559	0.4768	0.020*
C6	0.2498 (2)	0.08004 (14)	0.53790 (11)	0.0158 (3)
H6A	0.1911	0.0065	0.5529	0.019*
H6B	0.3694	0.0606	0.5214	0.019*
Cl1	0.72577 (5)	0.21252 (3)	0.61138 (3)	0.01391 (10)
O1	0.90644 (15)	0.24485 (11)	0.64617 (9)	0.0220 (3)
O2	0.71413 (18)	0.18723 (12)	0.51861 (8)	0.0263 (3)
O3	0.67246 (17)	0.10996 (11)	0.65736 (9)	0.0241 (3)
O4	0.60538 (16)	0.30697 (11)	0.62494 (10)	0.0246 (3)
Cl2	0.74537 (5)	0.57603 (3)	0.26377 (2)	0.01355 (10)
O5	0.59033 (15)	0.51100 (11)	0.22387 (8)	0.0188 (3)
O6	0.75093 (17)	0.57359 (11)	0.35894 (8)	0.0200 (3)
O7	0.73342 (17)	0.69479 (10)	0.23263 (8)	0.0204 (3)
O8	0.90557 (15)	0.52178 (11)	0.23899 (8)	0.0202 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
N1	0.0269 (8)	0.0140 (7)	0.0159 (7)	−0.0024 (6)	0.0044 (6)	0.0008 (6)
N2	0.0141 (6)	0.0131 (7)	0.0144 (7)	−0.0002 (5)	0.0034 (5)	0.0015 (5)
N3	0.0150 (6)	0.0119 (7)	0.0147 (7)	−0.0003 (5)	0.0026 (5)	0.0003 (5)
C1	0.0235 (9)	0.0174 (9)	0.0246 (9)	0.0005 (7)	0.0107 (7)	0.0029 (7)
C2	0.0227 (8)	0.0158 (8)	0.0178 (8)	−0.0002 (6)	0.0090 (6)	0.0002 (6)
C3	0.0193 (8)	0.0171 (8)	0.0195 (8)	0.0022 (6)	0.0030 (6)	0.0004 (7)
C4	0.0151 (8)	0.0187 (9)	0.0227 (9)	0.0016 (6)	0.0009 (6)	0.0016 (7)
C5	0.0175 (8)	0.0162 (8)	0.0158 (8)	−0.0044 (6)	0.0027 (6)	−0.0009 (6)
C6	0.0190 (8)	0.0125 (8)	0.0164 (8)	−0.0014 (6)	0.0046 (6)	−0.0026 (6)
Cl1	0.01169 (18)	0.01297 (19)	0.0174 (2)	−0.00018 (13)	0.00309 (13)	−0.00125 (14)
O1	0.0125 (6)	0.0229 (7)	0.0300 (7)	−0.0028 (5)	0.0010 (5)	−0.0039 (5)
O2	0.0263 (7)	0.0354 (8)	0.0176 (7)	−0.0007 (6)	0.0045 (5)	−0.0055 (6)
O3	0.0219 (6)	0.0207 (7)	0.0290 (7)	−0.0045 (5)	0.0012 (5)	0.0090 (5)
O4	0.0155 (6)	0.0157 (6)	0.0437 (8)	0.0021 (5)	0.0076 (5)	−0.0067 (6)
Cl2	0.01502 (19)	0.01298 (19)	0.01291 (19)	0.00041 (13)	0.00284 (13)	−0.00077 (13)
O5	0.0160 (6)	0.0196 (6)	0.0206 (6)	−0.0037 (5)	0.0016 (5)	−0.0013 (5)
O6	0.0283 (7)	0.0194 (6)	0.0128 (6)	0.0033 (5)	0.0045 (5)	−0.0001 (5)
O7	0.0274 (7)	0.0134 (6)	0.0207 (6)	−0.0012 (5)	0.0038 (5)	0.0031 (5)
O8	0.0164 (6)	0.0227 (7)	0.0223 (7)	0.0022 (5)	0.0056 (5)	−0.0069 (5)

Geometric parameters (Å, º) top

N1—C3	1.499 (2)	C3—H3A	0.9900
N1—C1	1.500 (2)	C3—H3B	0.9900
N1—H1C	0.902 (15)	C4—H4A	0.9900
N1—H1D	0.884 (15)	C4—H4B	0.9900
N2—C4	1.463 (2)	C5—C6	1.513 (2)
N2—C5	1.467 (2)	C5—H5A	0.9900
N2—C2	1.467 (2)	C5—H5B	0.9900
N3—C6	1.489 (2)	C6—H6A	0.9900
N3—H3C	0.894 (15)	C6—H6B	0.9900
N3—H3D	0.894 (15)	Cl1—O2	1.4331 (13)
N3—H3E	0.878 (15)	Cl1—O1	1.4414 (12)
C1—C2	1.512 (2)	Cl1—O4	1.4416 (12)
C1—H1A	0.9900	Cl1—O3	1.4489 (13)
C1—H1B	0.9900	Cl2—O7	1.4376 (12)
C2—H2A	0.9900	Cl2—O6	1.4444 (12)
C2—H2B	0.9900	Cl2—O8	1.4481 (12)
C3—C4	1.513 (2)	Cl2—O5	1.4487 (12)

C3—N1—C1	111.60 (13)	H3A—C3—H3B	108.3
C3—N1—H1C	109.7 (13)	N2—C4—C3	109.53 (13)
C1—N1—H1C	110.3 (13)	N2—C4—H4A	109.8
C3—N1—H1D	108.6 (14)	C3—C4—H4A	109.8
C1—N1—H1D	111.6 (14)	N2—C4—H4B	109.8
H1C—N1—H1D	104.8 (19)	C3—C4—H4B	109.8
C4—N2—C5	113.04 (13)	H4A—C4—H4B	108.2
C4—N2—C2	109.92 (13)	N2—C5—C6	109.07 (13)
C5—N2—C2	111.30 (13)	N2—C5—H5A	109.9
C6—N3—H3C	111.2 (13)	C6—C5—H5A	109.9
C6—N3—H3D	109.1 (13)	N2—C5—H5B	109.9
H3C—N3—H3D	105.1 (18)	C6—C5—H5B	109.9
C6—N3—H3E	112.0 (13)	H5A—C5—H5B	108.3
H3C—N3—H3E	110.4 (18)	N3—C6—C5	108.67 (13)
H3D—N3—H3E	108.8 (18)	N3—C6—H6A	110.0
N1—C1—C2	109.35 (14)	C5—C6—H6A	110.0
N1—C1—H1A	109.8	N3—C6—H6B	110.0
C2—C1—H1A	109.8	C5—C6—H6B	110.0
N1—C1—H1B	109.8	H6A—C6—H6B	108.3
C2—C1—H1B	109.8	O2—Cl1—O1	110.39 (8)
H1A—C1—H1B	108.3	O2—Cl1—O4	109.44 (8)
N2—C2—C1	109.97 (14)	O1—Cl1—O4	109.57 (8)
N2—C2—H2A	109.7	O2—Cl1—O3	109.10 (8)
C1—C2—H2A	109.7	O1—Cl1—O3	109.69 (8)
N2—C2—H2B	109.7	O4—Cl1—O3	108.62 (8)
C1—C2—H2B	109.7	O7—Cl2—O6	109.97 (7)
H2A—C2—H2B	108.2	O7—Cl2—O8	109.73 (8)
N1—C3—C4	109.21 (14)	O6—Cl2—O8	109.63 (7)
N1—C3—H3A	109.8	O7—Cl2—O5	109.52 (7)
C4—C3—H3A	109.8	O6—Cl2—O5	109.14 (7)
N1—C3—H3B	109.8	O8—Cl2—O5	108.82 (7)
C4—C3—H3B	109.8

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1C···O4ⁱ	0.90 (2)	2.16 (2)	2.9298 (19)	143 (2)
N1—H1D···O3ⁱⁱ	0.88 (2)	2.09 (2)	2.964 (2)	168 (2)
N3—H3C···O6ⁱ	0.89 (2)	2.38 (2)	3.0741 (19)	135 (2)
N3—H3C···O4	0.89 (2)	2.39 (2)	3.0225 (19)	128 (2)
N3—H3D···O1ⁱⁱⁱ	0.89 (2)	2.12 (2)	2.9875 (18)	163 (2)
N3—H3E···O8^iv	0.88 (2)	2.14 (2)	2.9025 (19)	145 (2)
N3—H3E···O3	0.88 (2)	2.52 (2)	3.0724 (19)	122 (2)
C1—H1B···O7^v	0.99	2.56	3.407 (2)	143
C3—H3A···O8ⁱⁱⁱ	0.99	2.56	3.226 (2)	124
C5—H5A···O5^vi	0.99	2.58	3.436 (2)	145
C5—H5B···O2ⁱⁱⁱ	0.99	2.46	3.452 (2)	178

Symmetry codes: (i) −x+1, −y+1, −z+1; (ii) x−1/2, −y+1/2, z−1/2; (iii) x−1, y, z; (iv) x−1/2, −y+1/2, z+1/2; (v) −x+3/2, y−1/2, −z+1/2; (vi) −x+1/2, y−1/2, −z+1/2.

Experimental details

Crystal data
Chemical formula	C₆H₁₇N₃²⁺·2ClO₄⁻
M_r	330.13
Crystal system, space group	Monoclinic, P2₁/n
Temperature (K)	100
a, b, c (Å)	7.5218 (1), 11.4371 (2), 15.2239 (2)
β (°)	97.437 (1)
V (Å³)	1298.66 (3)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	0.54
Crystal size (mm)	0.28 × 0.17 × 0.06

Data collection
Diffractometer	Bruker APEXII CCD diffractometer
Absorption correction	Multi-scan (SADABS; Sheldrick, 1996)
T_min, T_max	0.863, 0.968
No. of measured, independent and observed [I > 2σ(I)] reflections	8644, 2969, 2671
R_int	0.023
(sin θ/λ)_max (Å⁻¹)	0.650

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.030, 0.080, 1.05
No. of reflections	2969
No. of parameters	187
No. of restraints	5
H-atom treatment	H atoms treated by a mixture of independent and constrained refinement
Δρ_max, Δρ_min (e Å⁻³)	0.27, −0.59

Computer programs: APEX2 (Bruker, 2007), SAINT (Bruker, 2007), SHELXS97 (Sheldrick, 2008), X-SEED (Barbour, 2001), SHELXL97 (Sheldrick, 2008) and publCIF (Westrip, 2010).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1C···O4ⁱ	0.902 (15)	2.158 (18)	2.9298 (19)	143.1 (18)
N1—H1D···O3ⁱⁱ	0.884 (15)	2.094 (16)	2.964 (2)	167.8 (19)
N3—H3C···O6ⁱ	0.894 (15)	2.375 (18)	3.0741 (19)	135.2 (16)
N3—H3C···O4	0.894 (15)	2.387 (18)	3.0225 (19)	128.2 (16)
N3—H3D···O1ⁱⁱⁱ	0.894 (15)	2.121 (16)	2.9875 (18)	163.0 (18)
N3—H3E···O8^iv	0.878 (15)	2.141 (17)	2.9025 (19)	144.7 (18)
N3—H3E···O3	0.878 (15)	2.517 (18)	3.0724 (19)	121.9 (16)
C1—H1B···O7^v	0.99	2.56	3.407 (2)	143.1
C3—H3A···O8ⁱⁱⁱ	0.99	2.56	3.226 (2)	124.4
C5—H5A···O5^vi	0.99	2.58	3.436 (2)	145.1
C5—H5B···O2ⁱⁱⁱ	0.99	2.46	3.452 (2)	177.5

Symmetry codes: (i) −x+1, −y+1, −z+1; (ii) x−1/2, −y+1/2, z−1/2; (iii) x−1, y, z; (iv) x−1/2, −y+1/2, z+1/2; (v) −x+3/2, y−1/2, −z+1/2; (vi) −x+1/2, y−1/2, −z+1/2.

Acknowledgements

The authors thank the University of Malaya for funding this study (PPP grant No. PS359/2009C).

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