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In the title complex, [Zn(C14H13N3O2)2(H2O)4](NO3)2, the Zn atom is located on a center of symmetry. The Zn—O bond distances are 2.0816 (19) and 2.1356 (18) Å, and the Zn—N bond distance is 2.166 (2) Å. The coordination polyhedron is a slightly distorted octa­hedron. The crystal structure is stabilized by O—H(coordinated water)...O(NO3 or carbonyl O) and N—H(imine)...O(NO3) hydrogen bonds, forming a three-dimensional network.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536807057236/rk2055sup1.cif
Contains datablocks I, global

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536807057236/rk2055Isup2.hkl
Contains datablock I

CCDC reference: 672651

Key indicators

  • Single-crystal X-ray study
  • T = 293 K
  • Mean [sigma](C-C) = 0.004 Å
  • R factor = 0.041
  • wR factor = 0.101
  • Data-to-parameter ratio = 15.7

checkCIF/PLATON results

No syntax errors found



Alert level C PLAT029_ALERT_3_C _diffrn_measured_fraction_theta_full Low ....... 0.97 PLAT241_ALERT_2_C Check High Ueq as Compared to Neighbors for O2 PLAT244_ALERT_4_C Low 'Solvent' Ueq as Compared to Neighbors for N4 PLAT250_ALERT_2_C Large U3/U1 Ratio for Average U(i,j) Tensor .... 2.42
Alert level G PLAT199_ALERT_1_G Check the Reported _cell_measurement_temperature 293 K PLAT200_ALERT_1_G Check the Reported _diffrn_ambient_temperature . 293 K PLAT794_ALERT_5_G Check Predicted Bond Valency for Zn1 (2) 1.94
0 ALERT level A = In general: serious problem 0 ALERT level B = Potentially serious problem 4 ALERT level C = Check and explain 3 ALERT level G = General alerts; check 2 ALERT type 1 CIF construction/syntax error, inconsistent or missing data 2 ALERT type 2 Indicator that the structure model may be wrong or deficient 1 ALERT type 3 Indicator that the structure quality may be low 1 ALERT type 4 Improvement, methodology, query or suggestion 1 ALERT type 5 Informative message, check

Comment top

There has been considerable interests in the design and syntheses of transition metal complexes with isonicotinoylhydrazone ligands, owing to that there are multi–dimensional structure or extended multi–dimensional structures in these complexes (Bu et al., 2000; Fu et al., 2007; Ge et al., 2006). As a continued study in these complexes, herein we report the synthesis and crystal structure of complex [Zn(C14H13N3O2)2(H2O)4]·(NO3)2, (I), where C14H13N3O2 is 2–methoxybenzaldehyde isonicotinoylhydrazonate (L).

The complex [Cd(L)2(H2O)4]·(NO3)2 (II) has been reported (Fu et al., 2007). The title complex I (Fig. 1) and the reported complex II form an isomorphous pair. These two complexes show similar molecular configurations and structure parameters. In I, the Zn atom placed on the center of symmetry. The Zn—O bond distances are 2.0816 (19) and 2.1356 (18) Å for Zn1—O6 and Zn1—O7, respectively. This difference between Zn—O(water) bonds in same compound is 0.054 (2) Å. It is normal among the values reported by Quirós et al., 1991; Ryu et al., 2005; Zhu et al., 2003. While the length of 2.166 (2) Å in Zn1—N1 is in agreement with the values reported by Sun et al., 2007 and Uçar et al., 2006. Therefore, the coordination environment of metal centre displays a slightly distorted octahedron (Fig. 1). The dihedral angle between the phenyl and pyridine ring is 21.5 (1)°, which is little bigger than 18.8 (2)° in II.

The crystal structure is stabilized by hydrogen bonds, and confers a three dimensional network as complex II. Every two neighboring complex molecules in complex I are linked by O7—H72···O1iv hydrogen bonds, forming a sheet along bc plane (Fig. 2). And these sheets were connected along a axis into a three dimensional supramolecule via the O6—H61···O3, O6—H62···O(3)iii, O7i—H71i···O4 and N2ii—H21ii···O5 hydrogen bonds (Fig. 3) (symmetry codes: (i) -x + 1, -y, -z + 1; (ii) x + 1/2, -y + 1/2, z - 1/2; (iii) -x, -y, -z + 1; (iv) x - 1/2, -y + 1/2, z - 1/2).

Related literature top

For compounds containing isonicotinoylhydrazone ligands, see: Bu et al. (2000); Fu et al. (2007); Ge et al. (2006); Quirós et al. (1991); Ryu et al. (2005); Sun et al. (2007); Uçar et al. (2006); Zhu et al. (2003).

Experimental top

Ligand L was prepared according Fu et al., 2007. The zinc nitrate hexahydrate (59 mg, 0.2 mmol) and L (51 mg, 0.2 mmol) were mixed and dissolved in 10 ml me thanol. After stirring for an hour, the solution was filtered. Slow evaporation from the solution afforded yellow crystals suitable for X–ray diffraction.

Refinement top

The H atoms in water molecules were located in different Fourier maps, and then allowed to ride on the oxygen atoms with Uiso = 1.5Ueq(O). The other H atoms were placed in idealized positions and treated as riding with d(C—H) = 0.93 Å, Uiso(H) = 1.2Ueq(C) for aromatic, d(C—H) = 0.96 Å, Uiso(H) = 1.5Ueq(C) for methyl and d(N—H) = 0.86 Å, Uiso(H) = 1.2Ueq(N) for the imine group.

Computing details top

Data collection: TEXRAY (Molecular Structure Corporation, 1999); cell refinement: TEXRAY (Molecular Structure Corporation, 1999); data reduction: TEXSAN (Molecular Structure Corporation, 1999); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEX (McArdle, 1995); software used to prepare material for publication: SHELXL97 (Sheldrick, 1997).

Figures top
[Figure 1] Fig. 1. A view of the title complex, showing the atomic numbering scheme. Displacement ellipsoids are drawn at the 30% probability level. H atoms are presented as a spheres of arbitrary radius. Symmetry code: (i), -x + 1, -y, -z + 1.
[Figure 2] Fig. 2. The two–dimentional structure of I in the bc plane. Dashed lines indicate hydrogen bonds. H atoms not involved in hydrogen bonding have been omitted for clarity. Symmetry code: (iv) x - 1/2, -y + 1/2, z - 1/2.
[Figure 3] Fig. 3. The three–dimentional structure of I. Dashed lines indicate hydrogen bonds. H atoms not involved in hydrogen bonding have been omitted for clarity. Symmetry codes: (i) -x + 1, -y, -z + 1; (ii) x + 1/2, -y + 1/2, z - 1/2; (iii) -x, -y, -z + 1; (iv) x - 1/2, -y + 1/2, z - 1/2).
Tetraaquabis(2-methoxybenzaldehyde isonicotinoylhydrazone)zinc dinitrate top
Crystal data top
[Zn(C14H13N3O2)2(H2O)4](NO3)2F(000) = 800
Mr = 772.02Dx = 1.559 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 14941 reflections
a = 7.970 (4) Åθ = 3.1–27.5°
b = 17.647 (9) ŵ = 0.83 mm1
c = 11.838 (4) ÅT = 293 K
β = 99.062 (16)°Prism, yellow
V = 1644.2 (13) Å30.20 × 0.15 × 0.12 mm
Z = 2
Data collection top
Rigaku Weissenberg IP
diffractometer
3665 independent reflections
Radiation source: Fine–focus sealed tube2955 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.053
ϕ–scanθmax = 27.5°, θmin = 3.1°
Absorption correction: empirical
(TEXRAY; Molecular Structure Corporation, 1999)
h = 810
Tmin = 0.853, Tmax = 0.912k = 2222
14941 measured reflectionsl = 1515
Refinement top
Refinement on F2Primary atom site location: Direct
Least-squares matrix: FullSecondary atom site location: Difmap
R[F2 > 2σ(F2)] = 0.041Hydrogen site location: Geom
wR(F2) = 0.101H-atom parameters constrained
S = 1.05 w = 1/[σ2(Fo2) + (0.0413P)2 + 1.115P]
where P = (Fo2 + 2Fc2)/3
3665 reflections(Δ/σ)max < 0.001
233 parametersΔρmax = 0.45 e Å3
0 restraintsΔρmin = 0.49 e Å3
Crystal data top
[Zn(C14H13N3O2)2(H2O)4](NO3)2V = 1644.2 (13) Å3
Mr = 772.02Z = 2
Monoclinic, P21/nMo Kα radiation
a = 7.970 (4) ŵ = 0.83 mm1
b = 17.647 (9) ÅT = 293 K
c = 11.838 (4) Å0.20 × 0.15 × 0.12 mm
β = 99.062 (16)°
Data collection top
Rigaku Weissenberg IP
diffractometer
3665 independent reflections
Absorption correction: empirical
(TEXRAY; Molecular Structure Corporation, 1999)
2955 reflections with I > 2σ(I)
Tmin = 0.853, Tmax = 0.912Rint = 0.053
14941 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0410 restraints
wR(F2) = 0.101H-atom parameters constrained
S = 1.05Δρmax = 0.45 e Å3
3665 reflectionsΔρmin = 0.49 e Å3
233 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 > 2σ(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
Zn10.50000.00000.50000.02783 (11)
N10.5422 (2)0.11807 (10)0.54594 (15)0.0297 (4)
N20.6791 (3)0.39700 (10)0.53791 (16)0.0391 (5)
H210.62150.38490.47280.047*
N30.7507 (3)0.46831 (11)0.55469 (17)0.0407 (5)
N40.1088 (3)0.09550 (13)0.71546 (18)0.0460 (5)
O10.7721 (3)0.36189 (9)0.72069 (14)0.0500 (5)
O20.6753 (4)0.59321 (12)0.27438 (18)0.0836 (9)
O30.0344 (3)0.07244 (13)0.62089 (17)0.0603 (6)
O40.2662 (3)0.09405 (17)0.7342 (2)0.0822 (8)
O50.0287 (3)0.11849 (15)0.78818 (17)0.0775 (8)
O60.2392 (2)0.01951 (10)0.47521 (16)0.0432 (4)
H610.19610.03710.53490.065*
H620.16520.00610.43560.065*
O70.4919 (2)0.02614 (10)0.32308 (14)0.0415 (4)
H710.56980.00620.28890.062*
H720.42240.05050.28060.062*
C10.4726 (3)0.17490 (13)0.47888 (19)0.0368 (5)
H10.39190.16320.41560.044*
C20.5161 (3)0.25000 (13)0.49998 (19)0.0372 (5)
H20.46580.28780.45130.045*
C30.6351 (3)0.26846 (12)0.59417 (18)0.0309 (5)
C40.7015 (3)0.21004 (13)0.66525 (19)0.0360 (5)
H40.77860.22030.73100.043*
C50.6527 (3)0.13666 (12)0.63803 (19)0.0347 (5)
H50.69930.09810.68650.042*
C60.7003 (3)0.34722 (12)0.62393 (18)0.0345 (5)
C70.7243 (4)0.51018 (13)0.4674 (2)0.0429 (6)
H70.65620.49230.40180.051*
C80.7972 (3)0.58583 (13)0.4663 (2)0.0387 (5)
C90.7676 (4)0.62883 (14)0.3661 (2)0.0457 (6)
C100.8338 (4)0.70137 (15)0.3637 (3)0.0544 (7)
H100.81200.73050.29750.065*
C110.9317 (4)0.72970 (16)0.4601 (3)0.0584 (8)
H110.97450.77870.45940.070*
C120.9675 (4)0.68698 (16)0.5574 (3)0.0619 (8)
H121.03730.70630.62120.074*
C130.8998 (4)0.61541 (15)0.5606 (2)0.0494 (7)
H130.92360.58670.62700.059*
C140.6210 (5)0.63421 (19)0.1741 (3)0.0685 (9)
H1410.56160.60100.11710.103*
H1420.71780.65550.14650.103*
H1430.54650.67420.18990.103*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Zn10.0319 (2)0.01876 (17)0.03134 (19)0.00072 (14)0.00039 (13)0.00013 (13)
N10.0360 (11)0.0208 (8)0.0301 (9)0.0031 (7)0.0014 (7)0.0001 (7)
N20.0580 (14)0.0230 (9)0.0320 (10)0.0104 (9)0.0059 (9)0.0001 (7)
N30.0596 (14)0.0224 (9)0.0374 (11)0.0087 (9)0.0005 (9)0.0005 (8)
N40.0534 (15)0.0390 (12)0.0420 (12)0.0053 (10)0.0039 (10)0.0036 (9)
O10.0787 (14)0.0295 (9)0.0347 (9)0.0137 (9)0.0128 (9)0.0005 (7)
O20.144 (3)0.0406 (12)0.0522 (13)0.0262 (14)0.0281 (14)0.0150 (9)
O30.0534 (12)0.0781 (15)0.0476 (11)0.0089 (11)0.0027 (9)0.0230 (10)
O40.0555 (16)0.101 (2)0.0851 (17)0.0147 (14)0.0039 (12)0.0202 (15)
O50.0921 (18)0.0979 (19)0.0391 (11)0.0547 (15)0.0002 (11)0.0087 (11)
O60.0329 (9)0.0440 (10)0.0510 (10)0.0008 (7)0.0014 (7)0.0118 (8)
O70.0533 (11)0.0350 (8)0.0354 (9)0.0093 (8)0.0043 (7)0.0047 (7)
C10.0445 (14)0.0263 (11)0.0348 (12)0.0010 (10)0.0082 (10)0.0009 (9)
C20.0492 (15)0.0234 (10)0.0337 (11)0.0011 (10)0.0097 (10)0.0027 (8)
C30.0403 (13)0.0218 (10)0.0288 (10)0.0016 (9)0.0001 (9)0.0001 (8)
C40.0435 (14)0.0279 (11)0.0322 (11)0.0054 (10)0.0076 (9)0.0012 (8)
C50.0440 (14)0.0239 (10)0.0330 (11)0.0018 (9)0.0032 (9)0.0047 (8)
C60.0470 (14)0.0227 (10)0.0314 (11)0.0046 (9)0.0016 (9)0.0003 (8)
C70.0610 (17)0.0271 (12)0.0371 (13)0.0070 (11)0.0029 (11)0.0009 (9)
C80.0494 (15)0.0249 (11)0.0409 (13)0.0031 (10)0.0040 (10)0.0021 (9)
C90.0620 (18)0.0283 (12)0.0448 (14)0.0049 (11)0.0024 (12)0.0029 (10)
C100.077 (2)0.0312 (13)0.0550 (17)0.0067 (13)0.0116 (14)0.0105 (11)
C110.074 (2)0.0289 (13)0.073 (2)0.0169 (13)0.0128 (16)0.0012 (13)
C120.075 (2)0.0404 (16)0.0641 (19)0.0207 (15)0.0071 (15)0.0045 (13)
C130.0639 (19)0.0334 (13)0.0474 (15)0.0093 (12)0.0025 (13)0.0028 (10)
C140.098 (3)0.0541 (19)0.0482 (17)0.0007 (18)0.0056 (16)0.0134 (14)
Geometric parameters (Å, º) top
Zn1—O6i2.0816 (19)C1—H10.9300
Zn1—O62.0816 (19)C2—C31.384 (3)
Zn1—O72.1356 (18)C2—H20.9300
Zn1—O7i2.1356 (18)C3—C41.382 (3)
Zn1—N1i2.166 (2)C3—C61.506 (3)
Zn1—N12.166 (2)C4—C51.376 (3)
N1—C51.330 (3)C4—H40.9300
N1—C11.343 (3)C5—H50.9300
N2—C61.335 (3)C7—C81.457 (3)
N2—N31.383 (3)C7—H70.9300
N2—H210.8600C8—C131.378 (4)
N3—C71.260 (3)C8—C91.397 (3)
N4—O51.219 (3)C9—C101.386 (4)
N4—O41.240 (3)C10—C111.372 (4)
N4—O31.250 (3)C10—H100.9300
O1—C61.225 (3)C11—C121.368 (4)
O2—C91.365 (3)C11—H110.9300
O2—C141.399 (3)C12—C131.376 (4)
O6—H610.8884C12—H120.9300
O6—H620.8270C13—H130.9300
O7—H710.8673C14—H1410.9600
O7—H720.8106C14—H1420.9600
C1—C21.383 (3)C14—H1430.9600
O6i—Zn1—O6180.0C4—C3—C6117.45 (19)
O6i—Zn1—O792.82 (7)C2—C3—C6124.96 (19)
O6—Zn1—O787.18 (7)C5—C4—C3119.5 (2)
O6i—Zn1—O7i87.18 (7)C5—C4—H4120.3
O6—Zn1—O7i92.82 (7)C3—C4—H4120.3
O7—Zn1—O7i180.0N1—C5—C4123.4 (2)
O6i—Zn1—N1i89.33 (7)N1—C5—H5118.3
O6—Zn1—N1i90.67 (7)C4—C5—H5118.3
O7—Zn1—N1i88.97 (7)O1—C6—N2123.9 (2)
O7i—Zn1—N1i91.03 (7)O1—C6—C3120.5 (2)
O6i—Zn1—N190.67 (7)N2—C6—C3115.54 (19)
O6—Zn1—N189.33 (7)N3—C7—C8122.0 (2)
O7—Zn1—N191.03 (7)N3—C7—H7119.0
O7i—Zn1—N188.97 (7)C8—C7—H7119.0
N1i—Zn1—N1180.00 (9)C13—C8—C9118.8 (2)
C5—N1—C1117.29 (19)C13—C8—C7121.8 (2)
C5—N1—Zn1119.97 (14)C9—C8—C7119.4 (2)
C1—N1—Zn1122.44 (15)O2—C9—C10124.6 (2)
C6—N2—N3119.29 (19)O2—C9—C8115.0 (2)
C6—N2—H21120.4C10—C9—C8120.3 (3)
N3—N2—H21120.4C11—C10—C9119.2 (3)
C7—N3—N2113.8 (2)C11—C10—H10120.4
O5—N4—O4120.5 (2)C9—C10—H10120.4
O5—N4—O3120.9 (3)C12—C11—C10121.0 (3)
O4—N4—O3118.6 (2)C12—C11—H11119.5
C9—O2—C14119.5 (2)C10—C11—H11119.5
Zn1—O6—H61116.6C11—C12—C13119.9 (3)
Zn1—O6—H62126.6C11—C12—H12120.1
H61—O6—H62108.1C13—C12—H12120.1
Zn1—O7—H71117.2C12—C13—C8120.7 (3)
Zn1—O7—H72129.4C12—C13—H13119.6
H71—O7—H72113.3C8—C13—H13119.6
N1—C1—C2122.7 (2)O2—C14—H141109.5
N1—C1—H1118.6O2—C14—H142109.5
C2—C1—H1118.6H141—C14—H142109.5
C1—C2—C3119.4 (2)O2—C14—H143109.5
C1—C2—H2120.3H141—C14—H143109.5
C3—C2—H2120.3H142—C14—H143109.5
C4—C3—C2117.6 (2)
O6i—Zn1—N1—C546.33 (18)C4—C3—C6—O119.0 (4)
O6—Zn1—N1—C5133.67 (18)C2—C3—C6—O1162.2 (3)
O7—Zn1—N1—C5139.16 (18)C4—C3—C6—N2158.8 (2)
O7i—Zn1—N1—C540.84 (18)C2—C3—C6—N220.0 (4)
O6i—Zn1—N1—C1127.22 (19)N2—N3—C7—C8176.6 (2)
O6—Zn1—N1—C152.78 (19)N3—C7—C8—C130.3 (4)
O7—Zn1—N1—C134.38 (19)N3—C7—C8—C9178.2 (3)
O7i—Zn1—N1—C1145.62 (19)C14—O2—C9—C109.4 (5)
C6—N2—N3—C7179.2 (3)C14—O2—C9—C8172.3 (3)
C5—N1—C1—C22.4 (4)C13—C8—C9—O2175.3 (3)
Zn1—N1—C1—C2171.35 (19)C7—C8—C9—O22.6 (4)
N1—C1—C2—C30.5 (4)C13—C8—C9—C103.1 (4)
C1—C2—C3—C41.9 (4)C7—C8—C9—C10179.0 (3)
C1—C2—C3—C6176.8 (2)O2—C9—C10—C11176.8 (3)
C2—C3—C4—C52.4 (4)C8—C9—C10—C111.4 (5)
C6—C3—C4—C5176.5 (2)C9—C10—C11—C121.3 (5)
C1—N1—C5—C41.9 (4)C10—C11—C12—C132.3 (5)
Zn1—N1—C5—C4171.99 (19)C11—C12—C13—C80.5 (5)
C3—C4—C5—N10.5 (4)C9—C8—C13—C122.1 (5)
N3—N2—C6—O14.3 (4)C7—C8—C13—C12179.9 (3)
N3—N2—C6—C3173.4 (2)
Symmetry code: (i) x+1, y, z+1.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O6—H61···O30.891.872.720 (3)159
N2—H21···O5ii0.862.193.022 (3)162
O6—H62···O3iii0.832.002.811 (3)165
O7—H71···O4i0.872.243.014 (3)148
O7—H72···O1iv0.812.012.788 (3)159
Symmetry codes: (i) x+1, y, z+1; (ii) x+1/2, y+1/2, z1/2; (iii) x, y, z+1; (iv) x1/2, y+1/2, z1/2.

Experimental details

Crystal data
Chemical formula[Zn(C14H13N3O2)2(H2O)4](NO3)2
Mr772.02
Crystal system, space groupMonoclinic, P21/n
Temperature (K)293
a, b, c (Å)7.970 (4), 17.647 (9), 11.838 (4)
β (°) 99.062 (16)
V3)1644.2 (13)
Z2
Radiation typeMo Kα
µ (mm1)0.83
Crystal size (mm)0.20 × 0.15 × 0.12
Data collection
DiffractometerRigaku Weissenberg IP
diffractometer
Absorption correctionEmpirical
(TEXRAY; Molecular Structure Corporation, 1999)
Tmin, Tmax0.853, 0.912
No. of measured, independent and
observed [I > 2σ(I)] reflections
14941, 3665, 2955
Rint0.053
(sin θ/λ)max1)0.649
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.041, 0.101, 1.05
No. of reflections3665
No. of parameters233
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.45, 0.49

Computer programs: TEXRAY (Molecular Structure Corporation, 1999), TEXSAN (Molecular Structure Corporation, 1999), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), ORTEX (McArdle, 1995).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O6—H61···O30.891.872.720 (3)159.2
N2—H21···O5i0.862.193.022 (3)161.5
O6—H62···O3ii0.832.002.811 (3)165.0
O7—H71···O4iii0.872.243.014 (3)148.3
O7—H72···O1iv0.812.012.788 (3)159.4
Symmetry codes: (i) x+1/2, y+1/2, z1/2; (ii) x, y, z+1; (iii) x+1, y, z+1; (iv) x1/2, y+1/2, z1/2.
 

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