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

Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890
Volume 69| Part 12| December 2013| Pages m649-m650

Tetra­aqua­bis­­(piperazin-1-ium)cobalt(II) bis­­(sulfate) dihydrate

aLaboratoire de Chimie des Matériaux, Faculté des Sciences de Bizerte, 7021 Zarzouna Bizerte, Tunisia
*Correspondence e-mail: wajda_sta@yahoo.fr

(Received 29 October 2013; accepted 6 November 2013; online 9 November 2013)

In the centrosymmetric title compound, [Co(C4H11N2)2(H2O)4](SO4)2·2H2O, the CoII atom is coordinated in a distorted octa­hedral geometry by four water O atoms and two piperazinium N atoms. These four water O atoms define an equatorial plane with a maximum deviation of 0.0384 (1) Å while the two piperazinium N atoms complete the octa­hedron in the axial positions. Neighboring complex mol­ecules and sulfate anions are connected through an extensive network of N—H⋯O and O—H⋯O hydrogen bonds, which link the different chemical species into layers in the ab plane. Additional Owater—H⋯O hydrogen bonds involving the non-coordinating water mol­ecules and C—H⋯O inter­actions connect these layers into a three-dimensional supra­molecular structure.

Related literature

For metal–sulfate complexes with piperazinium cations, see: Rekik et al. (2005[Rekik, W., Naïli, H., Mhiri, T. & Bataille, T. (2005). Acta Cryst. E61, m629-m631.]); Pan et al. (2003[Pan, J.-X., Yang, G.-Y. & Sun, Y.-Q. (2003). Acta Cryst. E59, m286-m288.]); Sahbani et al. (2011[Sahbani, T., Smirani Sta, W., S. Al-Deyab, S. & Rzaigui, M. (2011). Acta Cryst. E67, m1079.]); Mrinal et al. (2010[Mrinal, S., Supriti, P., Kanak, R., Sandipan, R., Avijit, S., Alok, K. & Debashis, R. (2010). Inorg. Chim. Acta, 363, 3041-3047.]). For the biological activity of piperazines, see: Bogatcheva et al. (2006[Bogatcheva, E., Hanrahan, C., Nikonenko, B., Samala, R., Chen, P., Gearhart, J., Barbosa, F., Einck, L., Nacy, C. A. & Protopopova, M. (2006). J. Med. Chem. 49, 3045-3048.]). For a description of the Cambridge Structural Database, see: Allen (2002[Allen, F. H. (2002). Acta Cryst. B58, 380-388.]).

[Scheme 1]

Experimental

Crystal data
  • [Co(C4H11N2)2(H2O)4](SO4)2·2H2O

  • Mr = 533.46

  • Orthorhombic, P b c a

  • a = 12.187 (2) Å

  • b = 12.980 (2) Å

  • c = 13.437 (2) Å

  • V = 2125.5 (6) Å3

  • Z = 4

  • Ag Kα radiation

  • λ = 0.56085 Å

  • μ = 0.56 mm−1

  • T = 293 K

  • 0.30 × 0.20 × 0.20 mm

Data collection
  • Enraf–Nonius TurboCAD-4 diffractometer

  • 8070 measured reflections

  • 5211 independent reflections

  • 3131 reflections with I > 2σ(I)

  • Rint = 0.023

  • 2 standard reflections every 120 min intensity decay: 5%

Refinement
  • R[F2 > 2σ(F2)] = 0.045

  • wR(F2) = 0.108

  • S = 1.04

  • 5211 reflections

  • 157 parameters

  • 9 restraints

  • H-atom parameters constrained

  • Δρmax = 0.73 e Å−3

  • Δρmin = −0.35 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
O5—H1O5⋯O4i 0.83 (2) 1.96 (2) 2.776 (2) 170 (2)
O5—H2O5⋯O7 0.85 (2) 1.83 (2) 2.672 (2) 178 (2)
O7—H1O7⋯O3ii 0.82 (2) 1.98 (2) 2.797 (2) 169 (2)
O7—H2O7⋯O2 0.82 (2) 1.95 (2) 2.746 (2) 163 (2)
N1—H5⋯O3iii 0.91 2.35 3.240 (2) 166
O6—H1O6⋯O2iv 0.85 (2) 1.85 (2) 2.697 (2) 176 (3)
O6—H2O6⋯O1 0.84 (2) 1.86 (2) 2.686 (2) 168 (2)
N2—H9A⋯O1v 0.90 1.86 2.747 (2) 170
N2—H9B⋯O4ii 0.90 1.85 2.741 (2) 170
C3—H3A⋯O7vi 0.97 2.59 3.326 (3) 133
C4—H4A⋯O4iv 0.97 2.60 3.545 (2) 165
Symmetry codes: (i) [-x+{\script{3\over 2}}, y+{\script{1\over 2}}, z]; (ii) [x, -y+{\script{1\over 2}}, z-{\script{1\over 2}}]; (iii) -x+1, -y+1, -z+1; (iv) [x-{\script{1\over 2}}, -y+{\script{1\over 2}}, -z+1]; (v) [-x+1, y+{\script{1\over 2}}, -z+{\script{1\over 2}}]; (vi) [x-{\script{1\over 2}}, y, -z+{\script{1\over 2}}].

Data collection: CAD-4 EXPRESS (Enraf–Nonius, 1994[Enraf-Nonius (1994). CAD-4 EXPRESS. Enraf-Nonius, Delft, The Netherlands.]); cell refinement: CAD-4 EXPRESS; data reduction: XCAD4 (Harms & Wocadlo, 1995[Harms, K. & Wocadlo, S. (1995). XCAD4. University of Marburg, Germany.]); 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, 2012[Farrugia, L. J. (2012). J. Appl. Cryst. 45, 849-854.]); software used to prepare material for publication: WinGX (Farrugia, 2012[Farrugia, L. J. (2012). J. Appl. Cryst. 45, 849-854.]).

Supporting information


Comment top

In view of the importance of piperazines which are found in biologically active materials across a number of areas of therapeutic importance (Bogatcheva et al., 2006), the structural chemistry of metal salts that include piperazine and its derivatives does not cease to develop and continues to be a subject of research in many laboratories. Among the compounds investigated recently are several metal sulfate salts such as piperazinium hexaaquacobalt (II) disulfate (Pan et al., 2003), piperazinedium hexaaquazinc (II) bis sulfate (Rekik et al., 2005) and homopiperazin-1,4-diium bis-hexaaquacobalt (II) trisulfate (Sahbani et al., 2011), among others. In these structures the cobalt atoms are hexacoordinated by six water molecules, and the piperazinium cations are diprotonated and not metal coordinated. In this report, we would like to present the crystal structure of a sulfate salt of a cobalt-piperazinium complex, [Co(C4H11N2)2(H2O)4](SO4)2.2H2O, in which the metal ion is coordinated to the piperazinium moiety, a coordination mode not reported so far for simple metal sulfates with piperazine as the only other ligand other than water.

The asymmetric unit of the title compound (I) consists of one half cationic complex [Co(C4H11N2)2(H2O)4]4+, an uncoordinated [SO4]2- anion and one uncoordinated water molecule as shown in (Fig.1). The cobalt(II) ion, located on an inversion centre, exhibits a distorted octahedral coordination geometry with Co–O distances ranging from 2.0645 (14) to 2.0887 (13) Å and a Co–N bond distance equal to 2.2003 (14) Å. The O–Co–O and O–Co–N bond angles span the range from 85.72 to 94.28°. The piperazine nitrogen pairs from the monoprotonated cations are coordinated trans to each other, similar as described by Mrinal et al. (2010) for trans-[Ni(NCS)4(PpzH)2], and four oxygen atoms from the water molecules complete the coordination sphere of cobalt atom in the title compound. The piperazinium cation (C4H11N2)+ adopts a chair conformation as evidenced by the mean deviation (±0.0384 Å) from the least square plane defined by the four constituent atoms C1, C2, C3 and C4 and the remaining atoms N1 and N2 displaced from the plane by -0.6523 and 0.6392 Å, respectively. This is the so far only observed conformation for coordinated monoprotonated piperazines (19 entries in the Cambridge structural database with atom coordinates reported, database accessed Nov 2013 (Allen, 2002)).

Neighboring complexes and sulfate anions are connected through an extensive network of N—H···O and O—H···O hydrogen bonds, which link the different chemical species into two-dimensional layers in the ab plane (Fig.2). Additional OW—H···O hydrogen bonds that involve the not coordinated water molecules and C—H···O interactions connect these layers into a three-dimensional supramolecular structure.

Related literature top

For metal–sulfate complexes with piperazinium cations, see: Rekik et al. (2005); Pan et al. (2003); Sahbani et al. (2011); Mrinal et al. (2010). For the biological activity of piperazines, see: Bogatcheva et al. (2006). For a description of the Cambridge Structural Database, see: Allen (2002).

Experimental top

Piperazine (0.17g, 2 mmol) and cobalt acetate (0.24g, 1 mmol) were dissolved in 10 ml of water. The resulting solution was added to an aqueous solution of sulfuric acid (2 mmol, 2 ml). The mixture was stirred for 20 min at room temperature. After slow evaporation of the solvent over several days at ambient temperature, pink single crystals of the title compound suitable for X-ray diffraction formed in the solution. The crystals were filtered off, washed with a small amount of water and dried for 2 h. Yield: (60%, 21.32 mg). M.p. 270°C. Main IR bands (KBr disc, cm -1): [vs = very strong; s = strong; w = weak] 3100 s, 3033 s, 2758 w, 1630 vs, 1467 s, 1342 s, 1225 w, 1040 s, 1080 vs, 963vs, 628 s, 490 s.

Refinement top

All H atoms bonded to C and N atoms were positioned geometrically and treated as riding on their parent atoms, [N–H = 0.89, C–H =0.97 Å with Uiso(H) = 1.2 Ueq(C,N), but those attached to oxygen atom were located in difference density fourier maps. O–H bond distances and distances between two H atoms from each water molecule were restrained to be 0.85 (2) and 1.37 (2) Å, with Uiso(H) = 1.5 Ueq(O).

Computing details top

Data collection: CAD-4 EXPRESS (Enraf–Nonius, 1994); cell refinement: CAD-4 EXPRESS (Enraf–Nonius, 1994); data reduction: XCAD4 (Harms & Wocadlo, 1995); 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, 2012); software used to prepare material for publication: WinGX (Farrugia, 2012).

Figures top
[Figure 1] Fig. 1. ORTEP-3 (Farrugia, 2012) view of [Co(C4H11N2)2(H2O)4](SO4)2.2H2O with atom numbering scheme. Displacement ellipsoids for non-H atoms are drawn at the 30% probability level. Symmetry code: (i) -x+1, -y+1, -z+1.
[Figure 2] Fig. 2. View of a corrugated layer of the title compound along the c axis. Sulfate polyhedra are shown in yellow and cobalt polyhedra in cyan. Hydrogen bonds are denoted by dashed lines.
[Figure 3] Fig. 3. View of the atomic arrangement of the title compound along the b axis.
Tetraaquabis(piperazin-1-ium)cobalt(II) bis(sulfate) dihydrate top
Crystal data top
[Co(C4H11N2)2(H2O)4](SO4)2·2H2OF(000) = 1124
Mr = 533.46Dx = 1.667 Mg m3
Orthorhombic, PbcaAg Kα radiation, λ = 0.56085 Å
Hall symbol: -P 2ac 2abCell parameters from 25 reflections
a = 12.187 (2) Åθ = 9–11°
b = 12.980 (2) ŵ = 0.56 mm1
c = 13.437 (2) ÅT = 293 K
V = 2125.5 (6) Å3Plate, pink
Z = 40.30 × 0.20 × 0.20 mm
Data collection top
Enraf–Nonius TurboCAD-4
diffractometer
Rint = 0.023
Radiation source: fine-focus sealed tubeθmax = 28.0°, θmin = 2.2°
Graphite monochromatorh = 220
non–profiled ω scansk = 221
8070 measured reflectionsl = 322
5211 independent reflections2 standard reflections every 120 min
3131 reflections with I > 2σ(I) intensity decay: 5%
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)] = 0.045Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.108H-atom parameters constrained
S = 1.04 w = 1/[σ2(Fo2) + (0.0459P)2 + 0.2397P]
where P = (Fo2 + 2Fc2)/3
5211 reflections(Δ/σ)max = 0.001
157 parametersΔρmax = 0.73 e Å3
9 restraintsΔρmin = 0.35 e Å3
Crystal data top
[Co(C4H11N2)2(H2O)4](SO4)2·2H2OV = 2125.5 (6) Å3
Mr = 533.46Z = 4
Orthorhombic, PbcaAg Kα radiation, λ = 0.56085 Å
a = 12.187 (2) ŵ = 0.56 mm1
b = 12.980 (2) ÅT = 293 K
c = 13.437 (2) Å0.30 × 0.20 × 0.20 mm
Data collection top
Enraf–Nonius TurboCAD-4
diffractometer
Rint = 0.023
8070 measured reflections2 standard reflections every 120 min
5211 independent reflections intensity decay: 5%
3131 reflections with I > 2σ(I)
Refinement top
R[F2 > 2σ(F2)] = 0.0459 restraints
wR(F2) = 0.108H-atom parameters constrained
S = 1.04Δρmax = 0.73 e Å3
5211 reflectionsΔρmin = 0.35 e Å3
157 parameters
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds 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 > 2sigma(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
Co10.50000.50000.50000.02113 (7)
S0.66158 (3)0.17244 (3)0.58339 (3)0.02297 (8)
N10.48488 (11)0.55679 (11)0.34632 (10)0.0247 (3)
H50.43670.61020.34980.030*
O50.66503 (11)0.46657 (12)0.48732 (11)0.0344 (3)
N20.51689 (12)0.57886 (12)0.13384 (11)0.0290 (3)
H9A0.50150.61150.07640.035*
H9B0.56540.52850.12040.035*
O10.55478 (12)0.18124 (11)0.53281 (12)0.0414 (4)
O40.68095 (11)0.06305 (10)0.60768 (11)0.0363 (3)
O30.65964 (14)0.23468 (12)0.67276 (11)0.0488 (4)
C40.43626 (16)0.48409 (15)0.27435 (13)0.0312 (4)
H4A0.36770.45810.30100.037*
H4B0.48540.42600.26580.037*
O20.74959 (13)0.20647 (14)0.51721 (13)0.0508 (4)
C10.58559 (16)0.60093 (16)0.30341 (13)0.0332 (4)
H1A0.63920.54640.29480.040*
H1B0.61590.65050.34990.040*
C20.56706 (18)0.65320 (15)0.20475 (14)0.0346 (4)
H2A0.51880.71200.21350.041*
H2B0.63640.67780.17840.041*
C30.41497 (16)0.53265 (19)0.17427 (14)0.0375 (4)
H3A0.38780.48080.12850.045*
H3B0.35920.58550.18090.045*
O60.46037 (12)0.35031 (10)0.45571 (11)0.0303 (3)
O70.74564 (16)0.33382 (12)0.35404 (12)0.0458 (4)
H1O50.7166 (17)0.4944 (17)0.5175 (17)0.046 (8)*
H2O50.6900 (18)0.4253 (16)0.4442 (14)0.045 (7)*
H1O70.714 (2)0.320 (2)0.3015 (14)0.065 (9)*
H2O70.745 (2)0.2865 (17)0.3943 (15)0.061 (9)*
H1O60.3931 (12)0.3354 (18)0.4629 (19)0.049 (7)*
H2O60.4975 (17)0.3032 (18)0.4830 (19)0.063 (10)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Co10.02119 (12)0.02247 (13)0.01973 (12)0.00208 (12)0.00085 (12)0.00212 (12)
S0.02149 (16)0.02527 (17)0.02214 (16)0.00342 (15)0.00176 (15)0.00082 (16)
N10.0259 (7)0.0270 (6)0.0212 (6)0.0013 (5)0.0007 (5)0.0003 (5)
O50.0243 (6)0.0392 (7)0.0397 (7)0.0009 (6)0.0004 (6)0.0134 (6)
N20.0308 (8)0.0341 (7)0.0220 (6)0.0027 (6)0.0007 (6)0.0045 (6)
O10.0327 (7)0.0441 (8)0.0474 (8)0.0111 (7)0.0203 (6)0.0123 (7)
O40.0314 (7)0.0282 (6)0.0492 (8)0.0052 (5)0.0058 (6)0.0087 (6)
O30.0609 (10)0.0504 (9)0.0351 (7)0.0137 (8)0.0132 (7)0.0185 (7)
C40.0329 (8)0.0378 (10)0.0228 (7)0.0126 (8)0.0027 (7)0.0021 (7)
O20.0375 (8)0.0530 (9)0.0618 (10)0.0103 (7)0.0192 (8)0.0279 (8)
C10.0326 (9)0.0417 (10)0.0251 (8)0.0134 (8)0.0025 (7)0.0028 (8)
C20.0422 (10)0.0318 (9)0.0297 (8)0.0085 (8)0.0021 (8)0.0068 (8)
C30.0317 (9)0.0535 (11)0.0271 (8)0.0073 (9)0.0071 (8)0.0049 (9)
O60.0314 (6)0.0253 (6)0.0342 (7)0.0010 (5)0.0061 (6)0.0021 (5)
O70.0644 (10)0.0405 (8)0.0324 (7)0.0014 (8)0.0014 (8)0.0016 (7)
Geometric parameters (Å, º) top
Co1—O52.0645 (14)N2—H9A0.9000
Co1—O5i2.0645 (14)N2—H9B0.9000
Co1—O62.0887 (13)C4—C31.508 (2)
Co1—O6i2.0887 (13)C4—H4A0.9700
Co1—N1i2.2003 (14)C4—H4B0.9700
Co1—N12.2003 (14)C1—C21.506 (3)
S—O31.4475 (15)C1—H1A0.9700
S—O21.4615 (15)C1—H1B0.9700
S—O11.4728 (14)C2—H2A0.9700
S—O41.4759 (13)C2—H2B0.9700
N1—C11.472 (2)C3—H3A0.9700
N1—C41.475 (2)C3—H3B0.9700
N1—H50.9100O6—H1O60.848 (15)
O5—H1O50.831 (15)O6—H2O60.845 (16)
O5—H2O50.846 (15)O7—H1O70.824 (16)
N2—C31.483 (2)O7—H2O70.819 (15)
N2—C21.488 (2)
O5—Co1—O5i180.0C2—N2—H9A109.2
O5—Co1—O690.35 (6)C3—N2—H9B109.2
O5i—Co1—O689.65 (6)C2—N2—H9B109.2
O5—Co1—O6i89.65 (6)H9A—N2—H9B107.9
O5i—Co1—O6i90.35 (6)N1—C4—C3112.73 (15)
O6—Co1—O6i180.0N1—C4—H4A109.0
O5—Co1—N1i85.72 (6)C3—C4—H4A109.0
O5i—Co1—N1i94.28 (6)N1—C4—H4B109.0
O6—Co1—N1i88.57 (5)C3—C4—H4B109.0
O6i—Co1—N1i91.43 (5)H4A—C4—H4B107.8
O5—Co1—N194.28 (6)N1—C1—C2113.27 (16)
O5i—Co1—N185.72 (6)N1—C1—H1A108.9
O6—Co1—N191.43 (5)C2—C1—H1A108.9
O6i—Co1—N188.57 (5)N1—C1—H1B108.9
N1i—Co1—N1180.0C2—C1—H1B108.9
O3—S—O2110.37 (11)H1A—C1—H1B107.7
O3—S—O1108.98 (9)N2—C2—C1109.46 (15)
O2—S—O1110.14 (10)N2—C2—H2A109.8
O3—S—O4110.86 (9)C1—C2—H2A109.8
O2—S—O4107.94 (9)N2—C2—H2B109.8
O1—S—O4108.54 (8)C1—C2—H2B109.8
C1—N1—C4109.08 (14)H2A—C2—H2B108.2
C1—N1—Co1115.35 (11)N2—C3—C4110.60 (15)
C4—N1—Co1115.76 (10)N2—C3—H3A109.5
C1—N1—H5105.2C4—C3—H3A109.5
C4—N1—H5105.2N2—C3—H3B109.5
Co1—N1—H5105.2C4—C3—H3B109.5
Co1—O5—H1O5127.2 (16)H3A—C3—H3B108.1
Co1—O5—H2O5122.7 (16)Co1—O6—H1O6113.8 (17)
H1O5—O5—H2O5109.7 (19)Co1—O6—H2O6115.2 (19)
C3—N2—C2111.85 (15)H1O6—O6—H2O6107.6 (19)
C3—N2—H9A109.2H1O7—O7—H2O7114 (2)
Symmetry code: (i) x+1, y+1, z+1.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O5—H1O5···O4ii0.83 (2)1.96 (2)2.776 (2)170 (2)
O5—H2O5···O70.85 (2)1.83 (2)2.672 (2)178 (2)
O7—H1O7···O3iii0.82 (2)1.98 (2)2.797 (2)169 (2)
O7—H2O7···O20.82 (2)1.95 (2)2.746 (2)163 (2)
N1—H5···O3i0.912.353.240 (2)166
O6—H1O6···O2iv0.85 (2)1.85 (2)2.697 (2)176 (3)
O6—H2O6···O10.84 (2)1.86 (2)2.686 (2)168 (2)
N2—H9A···O1v0.901.862.747 (2)170
N2—H9B···O4iii0.901.852.741 (2)170
C3—H3A···O7vi0.972.593.326 (3)133
C4—H4A···O4iv0.972.603.545 (2)165
Symmetry codes: (i) x+1, y+1, z+1; (ii) x+3/2, y+1/2, z; (iii) x, y+1/2, z1/2; (iv) x1/2, y+1/2, z+1; (v) x+1, y+1/2, z+1/2; (vi) x1/2, y, z+1/2.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O5—H1O5···O4i0.83 (2)1.96 (2)2.776 (2)170 (2)
O5—H2O5···O70.85 (2)1.83 (2)2.672 (2)178 (2)
O7—H1O7···O3ii0.82 (2)1.98 (2)2.797 (2)169 (2)
O7—H2O7···O20.82 (2)1.95 (2)2.746 (2)163 (2)
N1—H5···O3iii0.912.353.240 (2)166
O6—H1O6···O2iv0.848 (15)1.851 (16)2.697 (2)176 (3)
O6—H2O6···O10.84 (2)1.86 (2)2.686 (2)168 (2)
N2—H9A···O1v0.901.862.747 (2)170
N2—H9B···O4ii0.901.852.741 (2)170
C3—H3A···O7vi0.972.593.326 (3)133
C4—H4A···O4iv0.972.603.545 (2)165
Symmetry codes: (i) x+3/2, y+1/2, z; (ii) x, y+1/2, z1/2; (iii) x+1, y+1, z+1; (iv) x1/2, y+1/2, z+1; (v) x+1, y+1/2, z+1/2; (vi) x1/2, y, z+1/2.
 

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Volume 69| Part 12| December 2013| Pages m649-m650
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