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The novel title compound, poly­[octa-[mu]-aqua-octa­aqua-[mu]-decavanadato-hexalithium], contains [V10O28]6- polyanions with 2/m symmetry linked by centrosymmetric [Li6(H2O)16]6+ cation chains. The [V10O28]6- polyanions form a two-dimensional network with [Li6(H2O)16]6+ chains via O-polyanion-Li-chain coordination, with Li-O bond lengths in the range 2.007 (5)-2.016 (5) Å. The hexalithium hexadecahydrate chain is composed of a centrosymmetric pair of LiO6 octahedra and four distorted LiO4 tetrahedra. Hydro­gen bonds occur between the polyanion and the Li-based chains, and within the Li-based chains.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270105013181/ta1489sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270105013181/ta1489Isup2.hkl
Contains datablock I

Comment top

Recently polyoxometalates have received extensive attention because of their varied applications in many fields, such as clinical chemistry, catalysis, medicine, solid-state devices and materials science (Kozhevnikov, 1998; Müller, 1998; Rhule et al., 1998; Toshihiro, 1998). Polyoxovanadate clusters, an important class of polyoxometalates, have been studied deeply because of their fascinating structure and potential applications (Zhang & Chen, 2003). In this work, orange single crystals of hexalithium hexadecahydrate decavanadate, [Li6(H2O)16V10O28]n, (I), have been synthesized and their structure determined.

Compound (I) contains [V10O28]6− polyanions with 2/m symmetry and centrosymmetric [Li6(H2O)16]6+ cation chains (Fig. 1). The decavanadate anion, presenting a cage-like structure, is composed of ten [VO6] octahedra combined via shared edges and shared corners. Six octahedra are arranged in a (2 × 3) equatorial plane sharing edges with one another; the other four octahedra are distributed above and below the equatorial plane, connected by shared sloping edges with the central six octahedra. According to the coordinative conditions, the O atoms in the polyanion can be classified into four types, viz. eight terminal O atoms (O3, O9, O6 and symmetry-related atoms) lying on the outer corners, with V—O distances of 1.595 (2)–1.607 (2) Å; fourteen double-bridging O atoms (O4, O8, O2 and O1) with V—O distances of 1.694 (1)–1.882 (1) Å; four triply bridging O atoms (O7) lying on the surface of the [V10O28]6− cluster, with V—O distances of 1.898 (1)–2.019 (1) Å; and two six-coordinate O atoms (O5) in the centers of the [OV6] octahedra with V—O distances of 2.126 (1)–2.308 (1) Å. The bond lengths and angles of the [V10O28]6− anion show a similar trend to those found in the literature (Kamenar et al., 1996; Choi & Chang, 2003).

The hexalithium hexadecahydrate chain is composed of a centrosymmetric pair of edge-shared octahedra (Li3) extended from the symmetry center by an edge-shared tetrahedron (Li2) linked to a corner-shared tetrahedron (Li1). In the octahedra, the lengths of the Li—O bonds are in the range 2.072 (6)–2.195 (4) Å, the cis-O—Li—O angles are in the range 83.9 (2)–93.33 (5)° and the angles of trans-O—Li—O are in the range of 175.4 (3)–177.2 (2)°. In the tetrahedra, one oxygen is from the [V10O28]6− ion with Li—O lengths of 2.007 (5)–2.016 (5) Å, and three O atoms are from water molecules with Li—O lengths of 1.954 (4)–2.144 (6) Å, and O—L—O angles of 94.0 (2)–149.8 (5)°.

In the ab plane, [V10O28]6− clusters are linked through [Li6(H2O)16]6+ chains to form an extended two-dimensional array (Fig. 2). Atom Li2 in the [Li6(H2O)16]6+ chain is bonded to an axial terminal O atom (O1) of a neighboring [V10O28]6− anion, and atom Li1 is bonded to atom O6 of another [V10O28]6− anion.

Hydrogen-bonds occur between the polyanion and Li-based chain, and within the Li-based chain in the compound. The water molecules, except the two water molecules containing O15, form hydrogen bonds with O atoms of the decavanadate group; there are also OW—H···OW hydrogen-bond interactions. All of the O atoms on the surface of the decavanadate anion form hydrogen bonds with water except atoms O1, O3, O6 and O9. Atom O3 participates in no hydrogen-bond interactions. Hydrogen-bonds with a distance less than 2.95 Å are listed in Table 1.

TGA results show that the weight loss of the crystal is around 22.0% in the range 343–583 K. This is compatible with the content of water (22.4 wt%) resulting from the theoretical calculation in the molecular formula.

Experimental top

The compound was prepared by hydrothermal treatment of NH4VO3 and LiOH (in a 1:0.6 molar ratio) acidified to pH 4.5. The reaction mixture was heated for 10 h at 393 K·The filtrate was kept at room temperature and orange single crystals formed after 15 d.

Refinement top

The coordinates of all H atoms were determined from a difference Fourier map. H atoms were included in the final cycles of refinement in a riding model, with O—H = 0.8013–0.9510 Å and Uiso(H) = 1.2Ueq(carrier atom).

Computing details top

Data collection: PROCESS-AUTO (Rigaku Corporation, 2002); cell refinement: PROCESS-AUTO; data reduction: CrystalStructure (Rigaku/MSC, 2004); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: CRYSTALS (Watkin et al., 1996); molecular graphics: WinGX (Farrugia, 1999); software used to prepare material for publication: CrystalStructure.

Figures top
[Figure 1] Fig. 1. The structure of Li6(H2O)16V10O28, with 40% probability displacement ellipsoids, showing the labeling of the atoms.
[Figure 2] Fig. 2. Two-dimensional layered structure packing diagram for [Li6(H2O)16V10O28]n.
poly[octa-µ-aqua-ocataqua-µ-decavanadato-hexalithium] top
Crystal data top
Li6(H2O)16V10O28F(000) = 1264.00
Mr = 1287.29Dx = 2.546 Mg m3
Orthorhombic, PnnmMo Kα radiation, λ = 0.7107 Å
Hall symbol: -P 2 2nCell parameters from 16740 reflections
a = 17.6164 (2) Åθ = 2.3–27.5°
b = 10.3189 (1) ŵ = 2.79 mm1
c = 9.2348 (3) ÅT = 273 K
V = 1678.72 (6) Å3Block, orange
Z = 20.39 × 0.31 × 0.26 mm
Data collection top
Rigaku R-AXIS RAPID
diffractometer
1611 reflections with F2 > 2σ(F2)
Detector resolution: 10.00 pixels mm-1Rint = 0.021
ω scansθmax = 27.5°
Absorption correction: multi-scan
(Higashi, 1995)
h = 2222
Tmin = 0.391, Tmax = 0.484k = 1313
16609 measured reflectionsl = 1111
2044 independent reflections
Refinement top
Refinement on F25 restraints
R[F2 > 2σ(F2)] = 0.021H-atom parameters constrained
wR(F2) = 0.072 w = 1/[0.001Fo2 + σ(Fo2)]/(4Fo2)
S = 1.03(Δ/σ)max < 0.001
1611 reflectionsΔρmax = 0.33 e Å3
160 parametersΔρmin = 0.42 e Å3
Crystal data top
Li6(H2O)16V10O28V = 1678.72 (6) Å3
Mr = 1287.29Z = 2
Orthorhombic, PnnmMo Kα radiation
a = 17.6164 (2) ŵ = 2.79 mm1
b = 10.3189 (1) ÅT = 273 K
c = 9.2348 (3) Å0.39 × 0.31 × 0.26 mm
Data collection top
Rigaku R-AXIS RAPID
diffractometer
2044 independent reflections
Absorption correction: multi-scan
(Higashi, 1995)
1611 reflections with F2 > 2σ(F2)
Tmin = 0.391, Tmax = 0.484Rint = 0.021
16609 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0215 restraints
wR(F2) = 0.072H-atom parameters constrained
S = 1.03Δρmax = 0.33 e Å3
1611 reflectionsΔρmin = 0.42 e Å3
160 parameters
Special details top

Geometry. ENTER SPECIAL DETAILS OF THE MOLECULAR GEOMETRY

Refinement. Refinement using reflections with F2 > 2.0 σ(F2). The weighted R-factor (wR) and goodness of fit (S) are based on F2. R-factor (gt) are based on F. The threshold expression of F2 > 2.0 σ(F2) is used only for calculating R-factor (gt).

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
V10.64709 (2)0.66201 (3)0.66489 (4)0.0141 (1)
V20.64143 (2)0.40100 (4)0.50000.0112 (1)
V30.50000.50000.67800 (5)0.0101 (1)
V40.49439 (2)0.23635 (4)0.50000.0127 (1)
O10.6977 (1)0.7148 (2)0.50000.0163 (5)
O20.57373 (7)0.7932 (1)0.6463 (1)0.0153 (3)
O30.69740 (8)0.7153 (1)0.7960 (2)0.0226 (4)
O40.68548 (8)0.4927 (1)0.6455 (1)0.0151 (3)
O50.5645 (1)0.5704 (1)0.50000.0113 (4)
O60.6876 (1)0.2667 (2)0.50000.0175 (5)
O70.55641 (7)0.3483 (1)0.6343 (1)0.0114 (3)
O80.43484 (7)0.4295 (1)0.7875 (1)0.0152 (3)
O90.5469 (1)0.1105 (2)0.50000.0204 (5)
O100.68872 (9)1.0026 (1)0.6689 (2)0.0232 (4)
O110.8336 (1)0.9689 (2)0.50000 (1)0.0230 (5)
O120.86619 (8)0.7062 (1)0.6573 (1)0.0213 (4)
O131.0207 (1)0.7409 (2)0.50000 (1)0.0313 (6)
O140.8557 (1)0.4521 (2)0.50000 (1)0.0340 (7)
O151.00000 (1)0.50000 (1)0.6672 (2)0.0251 (6)
Li10.7345 (3)1.0895 (5)0.50000.029 (1)
Li20.8057 (3)0.7794 (5)0.50000.024 (1)
Li30.9343 (3)0.6014 (5)0.50000.029 (1)
H10.65810.94710.65240.028*
H20.72890.97810.72340.029*
H30.85740.99380.57610.028*
H40.84790.65010.71160.026*
H50.88630.75830.71240.026*
H61.03750.79610.57600.039*
H70.80670.44890.50000.041*
H80.88460.38950.50000.041*
H91.02400.56000.72830.031*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
V10.0120 (2)0.0153 (2)0.0150 (2)0.0024 (1)0.0019 (1)0.0020 (1)
V20.0083 (2)0.0110 (3)0.0144 (3)0.0008 (1)0.00000.0000
V30.0097 (2)0.0114 (2)0.0092 (2)0.0002 (1)0.00000.0000
V40.0112 (2)0.0096 (2)0.0173 (3)0.0004 (2)0.00000.0000
O10.0116 (9)0.0142 (9)0.023 (1)0.0020 (7)0.00000.0000
O20.0133 (6)0.0134 (6)0.0192 (7)0.0017 (5)0.0005 (5)0.0038 (5)
O30.0178 (7)0.0260 (7)0.0239 (8)0.0032 (6)0.0055 (6)0.0068 (7)
O40.0120 (6)0.0147 (6)0.0186 (7)0.0002 (5)0.0035 (5)0.0001 (5)
O50.0097 (8)0.0110 (8)0.0132 (9)0.0004 (7)0.00000.0000
O60.015 (1)0.015 (1)0.022 (1)0.0038 (8)0.00000.0000
O70.0107 (6)0.0115 (6)0.0121 (6)0.0003 (5)0.0008 (5)0.0017 (5)
O80.0147 (6)0.0183 (6)0.0127 (6)0.0007 (5)0.0024 (5)0.0007 (5)
O90.017 (1)0.0133 (9)0.031 (1)0.0008 (7)0.00000.0000
O100.0226 (7)0.0224 (8)0.0246 (9)0.0036 (6)0.0026 (6)0.0008 (6)
O110.024 (1)0.025 (1)0.020 (1)0.0021 (9)0.00000.0000
O120.0247 (7)0.0222 (7)0.0170 (7)0.0072 (6)0.0008 (6)0.0005 (6)
O130.042 (1)0.026 (1)0.026 (1)0.014 (1)0.00000.0000
O140.029 (1)0.033 (1)0.040 (2)0.006 (1)0.00000.0000
O150.027 (1)0.027 (1)0.022 (1)0.0026 (9)0.00000.0000
Li10.033 (3)0.024 (3)0.029 (3)0.007 (2)0.00000.0000
Li20.023 (3)0.024 (2)0.023 (2)0.005 (2)0.00000.0000
Li30.029 (3)0.029 (3)0.029 (3)0.002 (2)0.00000.0000
Geometric parameters (Å, º) top
V1—O11.846 (1)O14—Li32.072 (6)
V1—O21.880 (1)O14—Li3ii2.072 (6)
V1—O31.598 (1)O15—Li32.195 (4)
V1—O41.882 (1)O15—Li3ii2.195 (4)
V1—O52.308 (1)Li1—O6v2.007 (5)
V1—O8i2.063 (1)Li1—O10ii1.971 (4)
V2—O41.817 (1)Li1—O112.144 (6)
V2—O4ii1.817 (1)Li1—O11ii2.144 (6)
V2—O52.212 (2)Li2—O112.016 (5)
V2—O61.607 (2)Li2—O11ii2.016 (5)
V2—O72.019 (1)Li2—O12ii1.954 (4)
V2—O7ii2.019 (1)Li3—O12ii2.173 (4)
V3—O52.126 (1)Li3—O132.094 (6)
V3—O5i2.126 (1)Li3—O13ii2.094 (6)
V3—O71.898 (1)Li3—O142.072 (6)
V3—O7i1.898 (1)Li3—O14ii2.072 (6)
V3—O81.694 (1)Li3—O152.195 (4)
V3—O8i1.694 (1)Li3—O15ii2.195 (4)
V4—O2i1.833 (1)O10—H10.8013
V4—O2iii1.833 (1)O10—H20.9045
V4—O5i2.248 (2)O11—H30.8579
V4—O72.016 (1)O11—H3ii0.8579
V4—O7ii2.016 (1)O12—H40.8305
V4—O91.595 (2)O12—H50.8197
O1—V1ii1.846 (1)O13—H60.9510
O1—Li22.016 (5)O13—H6ii0.9510
O2—V4i1.833 (1)O14—H70.8638
O5—V1ii2.308 (1)O14—H7ii0.8638
O5—V3iii2.126 (1)O14—H80.8229
O5—V4i2.248 (2)O14—H8ii0.8229
O6—Li1iv2.007 (5)O15—H90.9385
O8—V1i2.063 (1)H3—O110.8579
O10—Li11.971 (4)H3—O11ii0.8579
O11—Li12.144 (6)H6—O130.9510
O11—Li1ii2.144 (6)H6—O13ii0.9510
O11—Li22.016 (5)H7—O140.8638
O11—Li2ii2.016 (5)H7—O14ii0.8638
O12—Li21.954 (4)H8—O140.8229
O12—Li32.173 (4)H8—O14ii0.8229
O13—Li32.094 (6)H9—O150.9385
O13—Li3ii2.094 (6)
V1—O1—V1ii111.11 (9)V3—O8—V1i110.05 (7)
O2—V1—O192.51 (7)O7—V4—O2i89.81 (5)
O3—V1—O1104.82 (7)O7ii—V4—O2i154.64 (6)
O4—V1—O191.27 (7)O9—V4—O2i104.14 (6)
O5—V1—O183.16 (6)V4—O2i—V1i113.42 (7)
O8i—V1—O1157.70 (6)O5i—V4—O2i81.12 (5)
V1—O1—Li2123.57 (5)O2iii—V4—O2i95.00 (6)
V1—O2—V4i113.42 (7)O7—V4—O2iii154.64 (6)
O3—V1—O2101.68 (7)O7ii—V4—O2iii89.81 (5)
O4—V1—O2155.11 (6)O9—V4—O2iii104.14 (6)
O5—V1—O278.55 (6)O5i—V4—O2iii81.12 (5)
O8i—V1—O284.19 (5)V4—O2iii—V1iii113.42 (7)
O4—V1—O3101.10 (7)V4—O5i—V3iii93.24 (5)
O5—V1—O3171.97 (6)O7—V4—O5i75.04 (5)
O8i—V1—O397.44 (7)O7ii—V4—O5i75.04 (5)
V1—O4—V2113.60 (7)O9—V4—O5i172.01 (8)
O5—V1—O477.49 (6)V4—O5i—V1i85.85 (5)
O8i—V1—O483.04 (5)V4—O5i—V2i169.70 (9)
V1—O5—V1ii82.54 (6)V4—O5i—V1iii85.85 (5)
V1—O5—V286.41 (5)O7ii—V4—O775.90 (5)
V1—O5—V388.10 (1)O9—V4—O798.75 (7)
V1—O5—V4i85.85 (5)V4—O7ii—V3iii108.64 (6)
O8i—V1—O574.56 (5)O9—V4—O7ii98.75 (7)
V1—O5—V3iii170.63 (6)O1—V1ii—O2ii92.51 (7)
V1—O8i—V3110.05 (7)O1—V1ii—O4ii91.27 (7)
O4ii—V2—O495.35 (6)O1—V1ii—O583.16 (6)
O5—V2—O481.39 (5)Li2—O1—V1ii123.57 (5)
O6—V2—O4103.45 (6)O1—V1ii—O8iii157.70 (6)
O7—V2—O490.17 (6)O1—V1ii—O3ii104.82 (7)
O7ii—V2—O4155.66 (6)O1—Li2—O11123.4 (3)
V2—O4ii—V1ii113.60 (7)O1—Li2—O12112.8 (2)
O5—V2—O4ii81.39 (5)O1—Li2—O12ii112.8 (2)
O6—V2—O4ii103.45 (6)O2—V4i—O2ii95.00 (6)
O7—V2—O4ii155.66 (6)O2—V4i—O581.12 (5)
O7ii—V2—O4ii90.17 (6)O2—V4i—O7i89.81 (5)
V2—O5—V1ii86.41 (5)O2—V4i—O7iii154.64 (6)
V2—O5—V393.29 (5)O2—V4i—O9i104.14 (6)
V2—O5—V4i169.70 (9)V4i—O5—V1ii85.85 (5)
V2—O5—V3iii93.29 (5)O5—V1ii—O2ii78.55 (6)
O6—V2—O5172.64 (8)O5—V1ii—O4ii77.49 (6)
O7—V2—O576.02 (5)V3iii—O5—V1ii88.10 (1)
O7ii—V2—O576.02 (5)O5—V1ii—O8iii74.56 (5)
O7—V2—O698.24 (6)O5—V1ii—O3ii171.97 (6)
O7ii—V2—O698.24 (6)V4i—O5—V3iii93.24 (5)
V2—O6—Li1iv173.9 (2)O5—V3iii—O7ii80.65 (6)
V2—O7—V3107.27 (6)O5—V3iii—O8iii87.29 (6)
V2—O7—V4100.29 (6)O5—V3iii—O5i78.73 (5)
O7ii—V2—O775.78 (5)O5—V3iii—O7iii80.42 (6)
V2—O7ii—V3iii107.27 (6)O5—V3iii—O8ii166.03 (6)
V2—O7ii—V4100.29 (6)O5—V4i—O2ii81.12 (5)
V3—O5—V1ii170.63 (6)O5—V4i—O7i75.04 (5)
V3—O5—V4i93.24 (5)O5—V4i—O7iii75.04 (5)
O7i—V3—O580.42 (6)O5—V4i—O9i172.01 (8)
O8i—V3—O587.29 (6)O8—V1i—O2i84.19 (5)
V3—O5—V3iii101.27 (7)O8—V1i—O4i83.04 (5)
O7—V3—O580.65 (6)O8—V1i—O5i74.56 (5)
O5i—V3—O578.73 (5)O8—V1i—O1i157.70 (6)
O8—V3—O5166.03 (6)O8—V1i—O3i97.44 (7)
O7i—V3—O5i80.65 (6)O10—Li1—O10ii104.6 (3)
O8i—V3—O5i166.03 (6)O10—Li1—O1194.0 (2)
V3—O5i—V3iii101.27 (7)O10—Li1—O6v104.3 (2)
V3—O5i—V493.24 (5)Li2—O11—Li1111.4 (2)
O7—V3—O5i80.42 (6)O11—Li1—O10ii94.0 (2)
V3—O5i—V1i88.10 (1)O11—Li1—O6v149.8 (3)
V3—O5i—V2i93.29 (5)O11—Li2—O12104.0 (2)
O8—V3—O5i87.29 (6)O12—Li2—O12ii96.1 (2)
V3—O5i—V1iii170.63 (6)Li3—O12—Li289.8 (2)
O7i—V3—O7155.43 (6)O12—Li3—O12ii83.9 (2)
O8i—V3—O797.26 (5)O12—Li3—O1490.0 (2)
V3—O7—V4108.64 (6)O12—Li3—O1393.4 (2)
O8—V3—O797.33 (5)O12—Li3—O1593.33 (5)
V3—O7i—V4i108.64 (6)O13—Li3—O14175.4 (3)
O8i—V3—O7i97.33 (5)O13—Li3—O1586.8 (2)
V3—O7i—V2i107.27 (6)O14—Li3—O1589.9 (2)
O8—V3—O7i97.26 (6)O15—Li3—O15ii89.4 (2)
O8i—V3—O8106.68 (7)O15ii—Li3—O12ii93.33 (5)
Symmetry codes: (i) x+1, y+1, z; (ii) x, y, z+1; (iii) x+1, y+1, z+1; (iv) x, y1, z; (v) x, y+1, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O10—H2···O4vi0.901.942.804 (2)159
O11—H3···O8vii0.852.012.851 (2)163
O12—H4···O10viii0.831.982.815 (2)174
O12—H5···O7vi0.821.972.777 (2)167
O13—H6···O8vi0.951.922.872 (2)171
O14—H8···O13ix0.822.142.952 (3)167
O10—H1···O20.792.182.969 (2)170
O14—H7···O40.862.563.312 (3)146
O15—H9···O2vii0.942.103.034 (2)175
Symmetry codes: (vi) x+3/2, y+1/2, z+3/2; (vii) x+1/2, y+3/2, z+3/2; (viii) x+3/2, y1/2, z+3/2; (ix) x+2, y+1, z.

Experimental details

Crystal data
Chemical formulaLi6(H2O)16V10O28
Mr1287.29
Crystal system, space groupOrthorhombic, Pnnm
Temperature (K)273
a, b, c (Å)17.6164 (2), 10.3189 (1), 9.2348 (3)
V3)1678.72 (6)
Z2
Radiation typeMo Kα
µ (mm1)2.79
Crystal size (mm)0.39 × 0.31 × 0.26
Data collection
DiffractometerRigaku R-AXIS RAPID
diffractometer
Absorption correctionMulti-scan
(Higashi, 1995)
Tmin, Tmax0.391, 0.484
No. of measured, independent and
observed [F2 > 2σ(F2)] reflections
16609, 2044, 1611
Rint0.021
(sin θ/λ)max1)0.649
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.021, 0.072, 1.03
No. of reflections1611
No. of parameters160
No. of restraints5
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.33, 0.42

Computer programs: PROCESS-AUTO (Rigaku Corporation, 2002), PROCESS-AUTO, CrystalStructure (Rigaku/MSC, 2004), SHELXS97 (Sheldrick, 1997), CRYSTALS (Watkin et al., 1996), WinGX (Farrugia, 1999), CrystalStructure.

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O10—H2···O4i0.901.942.804 (2)159
O11—H3···O8ii0.852.012.851 (2)163
O12—H4···O10iii0.831.982.815 (2)174
O12—H5···O7i0.821.972.777 (2)167
O13—H6···O8i0.951.922.872 (2)171
O14—H8···O13iv0.822.142.952 (3)167
O10—H1···O20.792.182.969 (2)170
O14—H7···O40.862.563.312 (3)146
O15—H9···O2ii0.942.103.034 (2)175
Symmetry codes: (i) x+3/2, y+1/2, z+3/2; (ii) x+1/2, y+3/2, z+3/2; (iii) x+3/2, y1/2, z+3/2; (iv) x+2, y+1, z.
 

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