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The crystal structure of tris­odium octa­fluoridotantalate, Na3TaF8, has been redetermined using diffractometer data collected at 153 K, resulting in more accurate bond distances and angles than obtained from a previous structure determination based on film data. The structure is built from layers running along [101], which are formed by distorted [TaF8] anti­prisms and [NaF6] recta­ngular bipyramids sharing edges and corners. The individual layers are separated by eight-coordinated Na ions. Two atoms in the asymmetric unit are in special positions: the Ta atom is on a twofold axis in Wyckoff position 4e and one of the Na ions lies on an inversion centre in Wyckoff site 4d.

Supporting information


Crystallographic Information File (CIF)
Contains datablocks I, global


Structure factor file (CIF format)
Contains datablock I

Comment top

As part of our structure investigations of compounds containing Ta–F bonds (Langer et al., 2006; Smrčok et al., 2008; Smrčok et al., 2010), we present a new structure determination providing well determined atomic coordinates essential for future spectral and quantum chemistry studies. The structure of the title compound was reported to be solved in a face-centered pseudo-orthorhombic cell (though the correct monoclinic space group C2/c was recognized) using Patterson and Fourier techniques from the H0L and HK0 projections obtained from the film data, but with no subsequent refinement carried out (Hoard et al., 1954). The coordinates were given for both pseudo-orthorhombic and monoclinic cells, but unfortunately those in the true monoclinic space group are incorrect, as authors did not realise that there are different origins of coordinate systems. Monoclinic coordinates (Hoard et al., 1954) transform approximately to equivalent solution as presented here by transformation of the unit cell -a, -b, a+c with a shift of origin by 1/4, 3/4, 1/2.

The structure of Na3TaF8 can be regarded as consisting of layers built by sharing cornes and/or edges of the [TaF8] antiprisms (Ta1 is at twofold axis in position 4e) and the deformed [NaF6] rectangular bipyramids (Na1 is at 1 in position 4d) (Fig. 1). The Na2 atoms, which like all the F atoms appear in the general positions of the C2/c space group, are sandwiched between the layers and their formal coordination number is eight. The individual Ta—F bond distances in the antiprism (Table 1 and Fig. 2) are longer than those in the monocapped [TaF7] trigonal prisms in K2TaF7 [1.919 (3)–1.976 (2) Å; Torardi & Brixner, 1987], but comparable to the Ta—F bond distances in the [TaF7] prism in K3TaF8 [density functional theory (DFT) data: 1.964–1.995 Å; Smrčok et al., 2010]. The longest Ta—F bond distances involve F1 and F4 shared by the shorter basal edge of the Na1 polyhedron (Fig. 3). Somewhat shorter Ta—F bonds involve F3 atoms, which are shared by the corners of Na1–F bipyramids and [TaF7] antiprism, while the shortest Ta—F bonds involve F2 atoms engaged only in a bond to the interlayer Na2 atom. This variation in the Ta—F bond lentghs is of the same order as in the antiprisms of IF8-, WF82- and ReF82-, but is remarkably smaller than that in XeF82- (Adam et al., 1996). The contact F—F distances within the bases of the antiprism (Fig. 2) are slightly shorter than those separating the atoms of the respective bases, i.e. 2.469 (5) Å [F3—F4 and F3i—F4i; symmetry code: (i) 1-x, y, 3/2-z] or 2.484 (4) Å (F1—F2 and F1i—F2i).

The values of Na—F distances appear on the both sides of the reference value of 2.317 Å reported for NaF (Deshpande, 1961), but the majority of them are longer. Because all of the distances are shorter than sum of the van der Waals radii for Na and F (3.74 Å), they can be considered to be the bond distances. The coordination polyhedron around the hexacoordinate Na1 atom is the distorted rectangular bipyramid with the two sets of Na—F bond distances (Table 1). The polyhedron around the Na2 atom is a highly distorted cube with the span of the Na—F distances larger (0.350 Å) than in the polyhedron around the Na1 atom (0.208 Å).

Related literature top

For related literature, see: Adam et al. (1996); Deshpande (1961); Hoard et al. (1954); Langer et al. (2006); Smrčok et al. (2008, 2010); Torardi & Brixner (1987).

Experimental top

A solution of HF [weight fraction (w) = 5.4 × 10-4, 327.5 ml] was prepared by dilution of concentrated HF (w = 0.40, 0.5 ml) into distilled water. This solution (30 ml) was used as solvent for NaF (0.152 g, 3.62 mmol) and TaF5 (0.25 g, 0.91 mmol). The latter compound was weighted in a dry-box into a hermetically sealed transport ampoule before dissolving it in HF solution. This solution was let to evaporate spontaneously at room temperature for 5 d. When the solid phase had formed in a sufficient amount, it was filtered on a paper filter and washed with acetone and dried under vacuum at 333 K for 30 min. All experiments were carried out using platinum or plastic dishes.

Refinement top

All atoms were refined anisotropically without any restraints.

Computing details top

Data collection: SMART (Bruker, 2003); cell refinement: SAINT (Bruker, 2003); data reduction: SAINT (Bruker, 2003) and SADABS (Sheldrick, 2003); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2009); software used to prepare material for publication: PLATON (Spek, 2009).

Figures top
[Figure 1] Fig. 1. Polyhedral representation of the title structure, viewed along the b axis. The [TaF8] polyhedra are dark (dark green in the electronic version of the paper), the [NaF6] rectangular bipyramids around Na1 atoms are light grey (yellow) and the Na2 atoms are depicted as large spheres.
[Figure 2] Fig. 2. The numbering scheme for the title compound, with atomic displacement ellipsoids drawn at the 50% probability level. Slightly deformed F2/F3/F2i/F3i and F1/F4/F1i/F4i squares form the upper and lower bases of the distorted [TaF8] antiprism. The F···F seprations in the lower and upper base are 2.354 (5)/2.415 (4) and 2.365 (6)/2.406 (3) Å, respectively. [Symmetry code: (i) 1-x, y, 3/2-z.]
[Figure 3] Fig. 3. The layer consisting of [TaF8] antiprisms joined to [NaF6] polyhedra.
trisodium octafluoridotantalate top
Crystal data top
Na3TaF8F(000) = 712
Mr = 401.92Dx = 4.531 Mg m3
Monoclinic, C2/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2ycCell parameters from 2547 reflections
a = 11.5203 (14) Åθ = 4.1–32.3°
b = 5.3453 (6) ŵ = 18.98 mm1
c = 11.1540 (13) ÅT = 153 K
β = 120.919 (2)°Prism, colourless
V = 589.25 (12) Å30.24 × 0.18 × 0.07 mm
Z = 4
Data collection top
Siemens CCD area-detector
1030 independent reflections
Radiation source: fine-focus sealed tube961 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.045
ω scansθmax = 32.9°, θmin = 4.1°
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
h = 1616
Tmin = 0.092, Tmax = 0.350k = 87
4688 measured reflectionsl = 1616
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)] = 0.024 w = 1/[σ2(Fo2) + (0.0288P)2 + 0.1143P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.051(Δ/σ)max < 0.001
S = 1.05Δρmax = 1.93 e Å3
1030 reflectionsΔρmin = 3.00 e Å3
58 parametersExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
0 restraintsExtinction coefficient: 0.0094 (4)
Crystal data top
Na3TaF8V = 589.25 (12) Å3
Mr = 401.92Z = 4
Monoclinic, C2/cMo Kα radiation
a = 11.5203 (14) ŵ = 18.98 mm1
b = 5.3453 (6) ÅT = 153 K
c = 11.1540 (13) Å0.24 × 0.18 × 0.07 mm
β = 120.919 (2)°
Data collection top
Siemens CCD area-detector
1030 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
961 reflections with I > 2σ(I)
Tmin = 0.092, Tmax = 0.350Rint = 0.045
4688 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.02458 parameters
wR(F2) = 0.0510 restraints
S = 1.05Δρmax = 1.93 e Å3
1030 reflectionsΔρmin = 3.00 e Å3
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
Ta10.50000.68650 (4)0.75000.00503 (10)
Na10.75000.25001.00000.0149 (6)
Na20.6346 (2)0.7569 (4)1.1027 (2)0.0110 (4)
F10.5578 (3)0.4657 (5)0.9162 (3)0.0095 (5)
F20.4382 (3)0.8740 (6)0.8603 (3)0.0140 (6)
F30.6553 (3)0.8921 (6)0.8892 (3)0.0145 (6)
F40.6666 (3)0.4915 (5)0.7855 (3)0.0091 (5)
Atomic displacement parameters (Å2) top
Ta10.00306 (13)0.00520 (14)0.00600 (13)0.0000.00174 (9)0.000
Na10.0082 (13)0.0089 (11)0.0173 (13)0.0029 (10)0.0008 (11)0.0021 (10)
Na20.0091 (9)0.0111 (8)0.0128 (8)0.0008 (7)0.0057 (8)0.0010 (7)
F10.0070 (12)0.0109 (12)0.0101 (11)0.0018 (10)0.0040 (10)0.0036 (10)
F20.0125 (14)0.0157 (13)0.0161 (12)0.0037 (11)0.0091 (11)0.0040 (11)
F30.0086 (13)0.0148 (13)0.0151 (12)0.0023 (11)0.0025 (11)0.0044 (11)
F40.0043 (11)0.0129 (13)0.0119 (11)0.0020 (10)0.0053 (10)0.0016 (10)
Geometric parameters (Å, º) top
Ta1—F12.002 (3)Na1—Na23.462 (2)
Ta1—F1i2.002 (3)Na2—F12.375 (3)
Ta1—F2i1.981 (3)Na2—F1v2.428 (3)
Ta1—F21.981 (3)Na2—F22.557 (4)
Ta1—F31.991 (3)Na2—F2vi2.264 (4)
Ta1—F3i1.991 (3)Na2—F32.614 (4)
Ta1—F42.036 (3)Na2—F3iii2.506 (4)
Ta1—F4i2.036 (3)Na2—F4vii2.299 (3)
Na1—F12.231 (3)Na2—F4iii2.382 (3)
Na1—F1ii2.231 (3)Na2—Na1viii3.405 (2)
Na1—F3iii2.234 (3)F1—Na2v2.428 (3)
Na1—F3iv2.234 (3)F2—Na2vi2.263 (4)
Na1—F42.439 (3)F3—Na1viii2.234 (3)
Na1—F4ii2.439 (3)F3—Na2iii2.506 (4)
Na1—Na2iii3.405 (2)F4—Na2ix2.299 (3)
Na1—Na2iv3.405 (2)F4—Na2iii2.382 (3)
Na1—Na2ii3.462 (2)
F2i—Ta1—F2119.21 (18)Na2ii—Na1—Na2180.00 (8)
F2i—Ta1—F374.89 (13)F1ii—Na1—Ta1ii28.85 (7)
F2—Ta1—F372.66 (13)F1—Na1—Ta1ii151.15 (7)
F2i—Ta1—F3i72.66 (13)F3iii—Na1—Ta1ii98.95 (8)
F2—Ta1—F3i74.90 (12)F3iv—Na1—Ta1ii81.05 (8)
F3—Ta1—F3i112.98 (18)F4—Na1—Ta1ii147.99 (6)
F2i—Ta1—F1144.98 (12)F4ii—Na1—Ta1ii32.01 (6)
F2—Ta1—F177.16 (12)Na2iii—Na1—Ta1ii117.50 (3)
F3—Ta1—F182.25 (12)Na2iv—Na1—Ta1ii62.50 (3)
F3i—Ta1—F1141.81 (12)Na2ii—Na1—Ta1ii57.65 (3)
F2i—Ta1—F1i77.16 (12)Na2—Na1—Ta1ii122.35 (3)
F2—Ta1—F1i144.98 (12)F1ii—Na1—Ta1151.15 (7)
F3—Ta1—F1i141.81 (12)F1—Na1—Ta128.85 (7)
F3i—Ta1—F1i82.25 (12)F3iii—Na1—Ta181.05 (8)
F1—Ta1—F1i107.72 (16)F3iv—Na1—Ta198.95 (8)
F2i—Ta1—F477.07 (12)F4—Na1—Ta132.01 (6)
F2—Ta1—F4137.87 (11)F4ii—Na1—Ta1147.99 (6)
F3—Ta1—F475.61 (12)Na2iii—Na1—Ta162.50 (3)
F3i—Ta1—F4144.46 (12)Na2iv—Na1—Ta1117.50 (3)
F1—Ta1—F471.71 (11)Na2ii—Na1—Ta1122.35 (3)
F1i—Ta1—F473.15 (10)Na2—Na1—Ta157.65 (3)
F2i—Ta1—F4i137.87 (11)Ta1ii—Na1—Ta1179.999 (5)
F2—Ta1—F4i77.07 (12)F2vi—Na2—F4vii104.32 (13)
F3—Ta1—F4i144.46 (12)F2vi—Na2—F1136.45 (13)
F3i—Ta1—F4i75.61 (12)F4vii—Na2—F1102.47 (12)
F1—Ta1—F4i73.15 (10)F2vi—Na2—F4iii76.07 (12)
F1i—Ta1—F4i71.71 (11)F4vii—Na2—F4iii100.90 (9)
F4—Ta1—F4i118.43 (16)F1—Na2—F4iii130.82 (13)
F2i—Ta1—Na2i47.69 (9)F2vi—Na2—F1v92.04 (13)
F2—Ta1—Na2i124.20 (9)F4vii—Na2—F1v61.14 (10)
F3—Ta1—Na2i121.98 (10)F1—Na2—F1v71.94 (12)
F3i—Ta1—Na2i49.40 (9)F4iii—Na2—F1v155.75 (13)
F1—Ta1—Na2i150.09 (9)F2vi—Na2—F3iii135.43 (14)
F1i—Ta1—Na2i42.49 (9)F4vii—Na2—F3iii94.17 (12)
F4—Ta1—Na2i96.02 (8)F1—Na2—F3iii75.01 (11)
F4i—Ta1—Na2i90.43 (8)F4iii—Na2—F3iii60.62 (11)
F2i—Ta1—Na2124.20 (9)F1v—Na2—F3iii132.03 (13)
F2—Ta1—Na247.69 (9)F2vi—Na2—F276.70 (12)
F3—Ta1—Na249.40 (10)F4vii—Na2—F2136.98 (13)
F3i—Ta1—Na2121.98 (10)F1—Na2—F260.34 (10)
F1—Ta1—Na242.49 (9)F4iii—Na2—F2120.37 (13)
F1i—Ta1—Na2150.09 (9)F1v—Na2—F275.85 (11)
F4—Ta1—Na290.43 (8)F3iii—Na2—F2115.43 (12)
F4i—Ta1—Na296.02 (8)F2vi—Na2—F398.10 (13)
Na2i—Ta1—Na2167.40 (7)F4vii—Na2—F3156.87 (14)
F2i—Ta1—Na1113.86 (9)F1—Na2—F363.30 (10)
F2—Ta1—Na1104.11 (9)F4iii—Na2—F378.91 (11)
F3—Ta1—Na173.53 (9)F1v—Na2—F3124.24 (11)
F3i—Ta1—Na1172.29 (9)F3iii—Na2—F365.30 (12)
F1—Ta1—Na132.54 (8)F2—Na2—F354.12 (10)
F1i—Ta1—Na195.01 (8)F2vi—Na2—Na1viii68.41 (10)
F4—Ta1—Na139.42 (7)F4vii—Na2—Na1viii146.44 (10)
F4i—Ta1—Na196.70 (7)F1—Na2—Na1viii104.29 (9)
Na2i—Ta1—Na1131.49 (3)F4iii—Na2—Na1viii45.76 (7)
Na2—Ta1—Na158.55 (3)F1v—Na2—Na1viii147.89 (10)
F2i—Ta1—Na1i104.11 (9)F3iii—Na2—Na1viii73.81 (9)
F2—Ta1—Na1i113.86 (9)F2—Na2—Na1viii74.98 (9)
F3—Ta1—Na1i172.29 (9)F3—Na2—Na1viii41.00 (7)
F3i—Ta1—Na1i73.53 (9)F2vi—Na2—Ta1108.26 (10)
F1—Ta1—Na1i95.01 (8)F4vii—Na2—Ta1136.57 (10)
F1i—Ta1—Na1i32.54 (8)F1—Na2—Ta134.70 (7)
F4—Ta1—Na1i96.70 (7)F4iii—Na2—Ta1114.13 (9)
F4i—Ta1—Na1i39.42 (7)F1v—Na2—Ta189.53 (8)
Na2i—Ta1—Na1i58.55 (4)F3iii—Na2—Ta182.26 (8)
Na2—Ta1—Na1i131.49 (4)F2—Na2—Ta134.96 (7)
Na1—Ta1—Na1i100.311 (10)F3—Na2—Ta135.33 (7)
F1ii—Na1—F1180.000 (1)Na1viii—Na2—Ta173.94 (4)
F1ii—Na1—F3iii96.50 (11)F2vi—Na2—Na1169.70 (11)
F1—Na1—F3iii83.50 (11)F4vii—Na2—Na185.85 (9)
F1ii—Na1—F3iv83.50 (10)F1—Na2—Na139.72 (7)
F1—Na1—F3iv96.50 (11)F4iii—Na2—Na1100.70 (9)
F3iii—Na1—F3iv180.0F1v—Na2—Na194.38 (9)
F1ii—Na1—F4119.34 (9)F3iii—Na2—Na140.09 (7)
F1—Na1—F460.66 (9)F2—Na2—Na197.07 (9)
F3iii—Na1—F485.62 (10)F3—Na2—Na171.62 (8)
F3iv—Na1—F494.38 (10)Na1viii—Na2—Na1102.23 (5)
F1ii—Na1—F4ii60.66 (9)Ta1—Na2—Na163.80 (4)
F1—Na1—F4ii119.34 (9)F2vi—Na2—Ta1v101.58 (10)
F3iii—Na1—F4ii94.38 (10)F4vii—Na2—Ta1v30.44 (7)
F3iv—Na1—F4ii85.62 (10)F1—Na2—Ta1v85.15 (9)
F4—Na1—F4ii180.000 (1)F4iii—Na2—Ta1v130.34 (10)
F1ii—Na1—Na2iii93.78 (8)F1v—Na2—Ta1v30.84 (6)
F1—Na1—Na2iii86.22 (8)F3iii—Na2—Ta1v113.78 (10)
F3iii—Na1—Na2iii50.15 (9)F2—Na2—Ta1v106.57 (10)
F3iv—Na1—Na2iii129.85 (9)F3—Na2—Ta1v147.96 (10)
F4—Na1—Na2iii44.38 (7)Na1viii—Na2—Ta1v169.48 (7)
F4ii—Na1—Na2iii135.62 (7)Ta1—Na2—Ta1v113.49 (5)
F1ii—Na1—Na2iv86.22 (8)Na1—Na2—Ta1v87.99 (5)
F1—Na1—Na2iv93.78 (8)Ta1—F1—Na1118.61 (12)
F3iii—Na1—Na2iv129.85 (9)Ta1—F1—Na2102.81 (13)
F3iv—Na1—Na2iv50.15 (9)Na1—F1—Na297.41 (10)
F4—Na1—Na2iv135.62 (7)Ta1—F1—Na2v110.73 (12)
F4ii—Na1—Na2iv44.38 (7)Na1—F1—Na2v116.65 (12)
Na2iii—Na1—Na2iv180.0Na2—F1—Na2v108.06 (12)
F1ii—Na1—Na2ii42.87 (8)Ta1—F2—Na2vi147.08 (17)
F1—Na1—Na2ii137.13 (8)Ta1—F2—Na297.35 (12)
F3iii—Na1—Na2ii133.76 (9)Na2vi—F2—Na2103.30 (12)
F3iv—Na1—Na2ii46.24 (9)Ta1—F3—Na1viii153.10 (16)
F4—Na1—Na2ii96.56 (7)Ta1—F3—Na2iii108.47 (13)
F4ii—Na1—Na2ii83.44 (7)Na1viii—F3—Na2iii93.67 (12)
Na2iii—Na1—Na2ii102.23 (5)Ta1—F3—Na295.27 (13)
Na2iv—Na1—Na2ii77.77 (5)Na1viii—F3—Na288.85 (11)
F1ii—Na1—Na2137.13 (8)Na2iii—F3—Na2114.70 (12)
F1—Na1—Na242.87 (8)Ta1—F4—Na2ix114.67 (12)
F3iii—Na1—Na246.24 (9)Ta1—F4—Na2iii111.69 (13)
F3iv—Na1—Na2133.76 (9)Na2ix—F4—Na2iii117.61 (12)
F4—Na1—Na283.44 (7)Ta1—F4—Na1108.57 (11)
F4ii—Na1—Na296.56 (7)Na2ix—F4—Na1111.53 (12)
Na2iii—Na1—Na277.77 (5)Na2iii—F4—Na189.85 (10)
Na2iv—Na1—Na2102.23 (5)
Symmetry codes: (i) x+1, y, z+3/2; (ii) x+3/2, y+1/2, z+2; (iii) x+3/2, y+3/2, z+2; (iv) x, y1, z; (v) x+1, y+1, z+2; (vi) x+1, y+2, z+2; (vii) x, y+1, z+1/2; (viii) x, y+1, z; (ix) x, y+1, z1/2.

Experimental details

Crystal data
Chemical formulaNa3TaF8
Crystal system, space groupMonoclinic, C2/c
Temperature (K)153
a, b, c (Å)11.5203 (14), 5.3453 (6), 11.1540 (13)
β (°) 120.919 (2)
V3)589.25 (12)
Radiation typeMo Kα
µ (mm1)18.98
Crystal size (mm)0.24 × 0.18 × 0.07
Data collection
DiffractometerSiemens CCD area-detector
Absorption correctionMulti-scan
(SADABS; Sheldrick, 2003)
Tmin, Tmax0.092, 0.350
No. of measured, independent and
observed [I > 2σ(I)] reflections
4688, 1030, 961
(sin θ/λ)max1)0.765
R[F2 > 2σ(F2)], wR(F2), S 0.024, 0.051, 1.05
No. of reflections1030
No. of parameters58
Δρmax, Δρmin (e Å3)1.93, 3.00

Computer programs: SMART (Bruker, 2003), SAINT (Bruker, 2003) and SADABS (Sheldrick, 2003), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), DIAMOND (Brandenburg, 2009), PLATON (Spek, 2009).

Selected bond lengths (Å) top
Ta1—F12.002 (3)Na2—F1ii2.428 (3)
Ta1—F21.981 (3)Na2—F22.557 (4)
Ta1—F31.991 (3)Na2—F2iii2.264 (4)
Ta1—F42.036 (3)Na2—F32.614 (4)
Na1—F12.231 (3)Na2—F3i2.506 (4)
Na1—F3i2.234 (3)Na2—F4iv2.299 (3)
Na1—F42.439 (3)Na2—F4i2.382 (3)
Na2—F12.375 (3)Na2—Na1v3.405 (2)
Symmetry codes: (i) x+3/2, y+3/2, z+2; (ii) x+1, y+1, z+2; (iii) x+1, y+2, z+2; (iv) x, y+1, z+1/2; (v) x, y+1, z.

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