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Acta Cryst. (2011). E67, m837-m838    [ doi:10.1107/S1600536811019209 ]

Poly[dimethylammonium [aquadi-[mu]2-oxalato-yttriate(III)] trihydrate]

Y.-K. Lv, L.-H. Gan, L. Xu, H.-W. Zheng and C. Liu

Abstract top

The title complex, {(C2H8N)[Y(C2O4)2(H2O)]·3H2O}n, was obtained accidentally under hydrothermal conditions. The YIII atom is chelated by four oxalate ligands and one water molecule resulting in a distorted tricapped trigonal-prismatic geometry. Each oxalate ligand bridges two YIII atoms, thus generating a three-dimensional network with cavities in which the ammonium cations and lattice water molecules reside. Various O-H...O and N-H...O hydrogen-bonding interactions stabilize the crystal structure. The title complex is isotypic with the Eu and Dy analogues.

Comment top

Rational design and synthesis of metal-organic polymers have attracted much attention in the field of supramolecular chemistry and crystal engineering (Lv et al., 2010; 2011). Oxalate, which usually represent one of the products of the degradation of some organic compounds, is one of the simplest multidentate organic ligands potentially able to bridge metal ions in a bidentate chelating manner (Deguenon et al., 1990). Herein, we report the synthesis and structure of a novel yttrium(III) complex, (C2H8N)[Y(C2O4)2(H2O)].3H2O, (I).

Complex (I) is isotypic with its Eu(III) (Yang et al., 2005) and Dy(III) (Ye & Lin, 2010) analogues. As shown in Fig. 1, the YIII atom is chelated by four oxalate ligands and one water molecule resulting in a distorted tricapped trigonal-prismatic coordination environment. The Y—O bond lengths fall in the range of 2.374 (2)-2.459 (2) Å, which is in agreement with comparable values reported elsewhere (Platel et al., 2009; Gao & Cui, 2008). Each oxalate ligand bridges two YIII atoms, thus generating a three-dimensional network with cavities where the ammonium cations and lattice water molecules reside (Fig. 2). Furthermore, there are various hydrogen-bonding interactions (N—H···O and O—H···O), involving the lattice water molecules and the cations, which give rise to a tightly held network structure.

Related literature top

For general background to the rational design and synthesis of metal-organic polymers, see: Lv et al. (2010, 2011). For related structures, see: Platel et al. (2009); Gao & Cui, (2008); Deguenon et al. (1990). The structure of the isotypic EuIII compound was reported by Yang et al. (2005), and that of the DyIII compound by Ye & Lin (2010). For decomposition products obtained under hydrothermal conditions, see: Song et al. (2004).

Experimental top

A mixture of D-saccharic acid potassium salt (0.248 g, 1.0 mmol), Y(NO3)3.6H2O (0.191 g, 0.5 mmol) and N,N-dimethylformamide (20 ml) was stirred and heated at 373 K for 1 hour. The resulted colorless solution was kept at 293 K. Colorless block-shaped crystals of the title compound suitable for X-ray crystallographic study were obtained via slow evaporation within 2 weeks.

It is most likely that the oxalate ligands in this complex originates from the decomposition of the potassium salt of D-saccharic acid, and the protonated dimethylamine cations compensating the negative charge of the anionic network are believed to result from decomposition of the N,N-dimethylformamide solvent (Song et al., 2004; Ye & Lin, 2010).

Refinement top

The hydrogen atoms attached to carbon and nitrogen atoms were positioned geometrically, while those attached to oxygen atom were located from difference Fourier maps. H atoms attached to C atoms were refined using a riding model with C—H = 0.96 Å and Uiso(H) = 1.2Ueq(C); H atoms attached to N atoms were refined with N—H = 0.90 Å and Uiso(H) = 1.2Ueq(N); H atoms attached to O atoms were refined without distance restraints and with Uiso(H) = 1.2Ueq(O).

Computing details top

Data collection: APEX2 (Bruker, 2006); cell refinement: SAINT (Bruker, 2006); data reduction: SAINT (Bruker, 2006); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg & Putz, 2004); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. An expanded vioew of the asymmetric unit of (I), showing the coordination of the YIII atom, and the presence of the lattice water molecules and the ammonium cation. All hydrogen atoms were omitted for clarity. [Symmetry codes: (i) -x + 1, y + 1/2, -z + 1/2; (ii) -x + 1, -y + 2, -z + 1; (iii) -x + 2, -y + 2, -z + 1.]
[Figure 2] Fig. 2. View of the three-dimensional framework of (I). All hydrogen atoms are omitted for clarity. Hydrogen bonding between donator and acceptor atoms is indicated by dashed lines.
Poly[dimethylammonium [aquadi-µ2-oxalato-yttriate(III)] trihydrate] top
Crystal data top
(C2H8N)[Y(C2O4)2(H2O)]·3H2OF(000) = 776
Mr = 383.11Dx = 1.905 Mg m−3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 2287 reflections
a = 9.6008 (1) Åθ = 2.0–28.0°
b = 11.5422 (2) ŵ = 4.43 mm−1
c = 14.2886 (2) ÅT = 293 K
β = 122.460 (1)°Block, colourless
V = 1336.00 (3) Å30.31 × 0.20 × 0.19 mm
Z = 4
Data collection top
Bruker APEXII area-detector
diffractometer		3040 independent reflections
Radiation source: fine-focus sealed tube2384 reflections with I > 2σ(I)
graphiteRint = 0.044
ω scansθmax = 27.5°, θmin = 2.9°
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)		h = −12→12
Tmin = 0.36, Tmax = 0.43k = −14→14
11935 measured reflectionsl = −18→18
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)] = 0.033Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.082H atoms treated by a mixture of independent and constrained refinement
S = 1.00 w = 1/[σ2(Fo2) + (0.0359P)2 + 1.2217P]
where P = (Fo2 + 2Fc2)/3
3040 reflections(Δ/σ)max = 0.001
207 parametersΔρmax = 0.70 e Å−3
13 restraintsΔρmin = −0.58 e Å−3
Crystal data top
(C2H8N)[Y(C2O4)2(H2O)]·3H2OV = 1336.00 (3) Å3
Mr = 383.11Z = 4
Monoclinic, P21/cMo Kα radiation
a = 9.6008 (1) ŵ = 4.43 mm−1
b = 11.5422 (2) ÅT = 293 K
c = 14.2886 (2) Å0.31 × 0.20 × 0.19 mm
β = 122.460 (1)°
Data collection top
Bruker APEXII area-detector
diffractometer		3040 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)		2384 reflections with I > 2σ(I)
Tmin = 0.36, Tmax = 0.43Rint = 0.044
11935 measured reflectionsθmax = 27.5°
Refinement top
R[F2 > 2σ(F2)] = 0.033H atoms treated by a mixture of independent and constrained refinement
wR(F2) = 0.082Δρmax = 0.70 e Å−3
S = 1.00Δρmin = −0.58 e Å−3
3040 reflectionsAbsolute structure: ?
207 parametersFlack parameter: ?
13 restraintsRogers parameter: ?
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
xyzUiso*/Ueq
Y10.61770 (3)0.98846 (2)0.33257 (2)0.01817 (10)
O10.7049 (3)0.78990 (17)0.34286 (19)0.0270 (5)
O20.6167 (3)0.60733 (18)0.2950 (2)0.0304 (6)
O30.3054 (3)0.68334 (17)0.17013 (18)0.0231 (5)
O40.3959 (3)0.86535 (17)0.20743 (19)0.0259 (5)
O60.5198 (3)0.88268 (18)0.4319 (2)0.0293 (5)
O70.5387 (3)1.11238 (19)0.4367 (2)0.0320 (6)
O80.8892 (3)0.99123 (17)0.35640 (19)0.0245 (5)
O90.8389 (3)0.98964 (18)0.52152 (19)0.0278 (5)
O1W0.6044 (3)0.9808 (2)0.1578 (2)0.0348 (6)
H1WA0.617 (5)1.039 (2)0.129 (3)0.042*
H1WB0.568 (4)0.931 (2)0.122 (3)0.042*
O2W1.3774 (5)0.8468 (3)0.9672 (3)0.0649 (10)
H2WA1.386 (6)0.785 (3)0.946 (4)0.078*
H2WB1.293 (4)0.850 (4)0.965 (5)0.078*
O3W0.8383 (7)0.5082 (4)0.5055 (4)0.1038 (17)
H3WA0.857 (10)0.539 (5)0.457 (5)0.125*
H3WB0.889 (8)0.444 (3)0.512 (6)0.125*
O4W1.0523 (5)0.7844 (3)0.9661 (3)0.0861 (13)
H4WA0.959 (3)0.758 (5)0.936 (4)0.103*
H4WB1.103 (6)0.758 (5)1.030 (2)0.103*
N10.9245 (4)0.6326 (3)0.6962 (3)0.0585 (11)
H1A0.89280.60070.73940.070*
H1B0.88080.58950.63410.070*
C10.5960 (4)0.7148 (2)0.2919 (3)0.0222 (7)
C20.4163 (4)0.7587 (2)0.2166 (3)0.0195 (6)
C30.4947 (4)0.9335 (3)0.4984 (3)0.0243 (7)
C41.0151 (4)1.0005 (2)0.4524 (3)0.0202 (6)
C51.0993 (6)0.6253 (6)0.7531 (5)0.0864 (19)
H5A1.13140.54590.75670.104*
H5B1.14760.65530.82690.104*
H5C1.13700.66990.71410.104*
C60.8547 (8)0.7488 (5)0.6652 (5)0.0897 (19)
H6A0.73650.74420.62540.108*
H6B0.88720.78410.61900.108*
H6C0.89440.79460.73090.108*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Y10.01775 (15)0.01434 (15)0.01968 (16)−0.00007 (11)0.00824 (12)−0.00024 (11)
O10.0193 (12)0.0194 (11)0.0322 (14)−0.0013 (8)0.0071 (11)−0.0044 (9)
O20.0264 (12)0.0173 (11)0.0332 (14)0.0029 (9)0.0066 (11)−0.0002 (9)
O30.0203 (11)0.0193 (10)0.0265 (13)−0.0017 (8)0.0105 (10)−0.0016 (9)
O40.0232 (12)0.0170 (10)0.0285 (13)0.0016 (8)0.0079 (10)0.0003 (9)
O60.0347 (13)0.0252 (12)0.0331 (15)−0.0039 (9)0.0216 (12)−0.0047 (10)
O70.0424 (14)0.0252 (12)0.0402 (16)0.0045 (10)0.0301 (13)0.0060 (10)
O80.0195 (10)0.0307 (12)0.0205 (11)0.0009 (9)0.0088 (9)−0.0019 (9)
O90.0209 (11)0.0368 (13)0.0265 (12)−0.0014 (9)0.0132 (10)−0.0004 (10)
O1W0.0408 (14)0.0346 (14)0.0265 (14)−0.0076 (12)0.0165 (12)−0.0043 (11)
O2W0.080 (3)0.0390 (17)0.069 (2)0.0025 (16)0.036 (2)0.0072 (16)
O3W0.112 (4)0.095 (3)0.061 (3)0.031 (3)0.017 (3)−0.013 (2)
O4W0.070 (3)0.061 (2)0.069 (3)−0.0094 (19)−0.001 (2)0.0154 (19)
N10.045 (2)0.071 (3)0.058 (3)−0.0039 (18)0.027 (2)0.022 (2)
C10.0233 (16)0.0187 (15)0.0242 (17)0.0003 (11)0.0124 (14)−0.0014 (12)
C20.0236 (17)0.0206 (15)0.0165 (16)−0.0012 (11)0.0121 (14)−0.0026 (12)
C30.0184 (14)0.0272 (17)0.0257 (17)−0.0012 (12)0.0108 (13)−0.0008 (13)
C40.0205 (14)0.0145 (14)0.0222 (16)0.0004 (11)0.0092 (13)−0.0013 (12)
C50.046 (3)0.144 (6)0.066 (4)−0.004 (3)0.028 (3)0.027 (4)
C60.110 (5)0.073 (4)0.103 (5)0.024 (3)0.068 (4)0.029 (3)
Geometric parameters (Å, °) top
Y1—O3i2.374 (2)O2W—H2WA0.805 (19)
Y1—O92.376 (2)O2W—H2WB0.794 (19)
Y1—O42.380 (2)O3W—H3WA0.88 (2)
Y1—O62.413 (2)O3W—H3WB0.86 (2)
Y1—O12.417 (2)O4W—H4WA0.82 (2)
Y1—O2i2.422 (2)O4W—H4WB0.83 (2)
Y1—O1W2.432 (3)N1—C51.421 (6)
Y1—O82.441 (2)N1—C61.458 (6)
Y1—O72.459 (2)N1—H1A0.9000
O1—C11.247 (3)N1—H1B0.9000
O2—C11.254 (3)C1—C21.548 (4)
O2—Y1ii2.422 (2)C3—O7iii1.250 (4)
O3—C21.254 (3)C3—C3iii1.536 (6)
O3—Y1ii2.374 (2)C4—O9iv1.248 (4)
O4—C21.243 (3)C4—C4iv1.535 (6)
O6—C31.246 (4)C5—H5A0.9600
O7—C3iii1.250 (4)C5—H5B0.9600
O8—C41.255 (4)C5—H5C0.9600
O9—C4iv1.248 (4)C6—H6A0.9600
O1W—H1WA0.828 (18)C6—H6B0.9600
O1W—H1WB0.720 (17)C6—H6C0.9600
O3i—Y1—O985.24 (7)C3—O6—Y1120.4 (2)
O3i—Y1—O4135.57 (7)C3iii—O7—Y1119.2 (2)
O9—Y1—O4138.66 (8)C4—O8—Y1118.9 (2)
O3i—Y1—O6135.37 (8)C4iv—O9—Y1121.0 (2)
O9—Y1—O674.17 (8)Y1—O1W—H1WA122 (3)
O4—Y1—O670.48 (8)Y1—O1W—H1WB119 (3)
O3i—Y1—O1143.01 (7)H1WA—O1W—H1WB117 (3)
O9—Y1—O182.37 (7)H2WA—O2W—H2WB110 (3)
O4—Y1—O167.70 (7)H3WA—O3W—H3WB95 (7)
O6—Y1—O173.50 (8)H4WA—O4W—H4WB106 (3)
O3i—Y1—O2i67.82 (7)C5—N1—C6115.9 (5)
O9—Y1—O2i139.01 (8)C5—N1—H1A108.3
O4—Y1—O2i71.18 (7)C6—N1—H1A108.3
O6—Y1—O2i103.39 (8)C5—N1—H1B108.3
O1—Y1—O2i137.25 (7)C6—N1—H1B108.3
O3i—Y1—O1W82.13 (8)H1A—N1—H1B107.4
O9—Y1—O1W133.57 (8)O1—C1—O2126.8 (3)
O4—Y1—O1W70.99 (8)O1—C1—C2116.8 (2)
O6—Y1—O1W139.75 (8)O2—C1—C2116.4 (3)
O1—Y1—O1W81.59 (8)O4—C2—O3126.2 (3)
O2i—Y1—O1W74.46 (9)O4—C2—C1116.8 (3)
O3i—Y1—O870.84 (7)O3—C2—C1117.0 (3)
O9—Y1—O866.75 (7)O6—C3—O7iii126.7 (3)
O4—Y1—O8124.78 (8)O6—C3—C3iii117.1 (4)
O6—Y1—O8130.44 (8)O7iii—C3—C3iii116.2 (4)
O1—Y1—O872.24 (7)O9iv—C4—O8127.1 (3)
O2i—Y1—O8126.06 (8)O9iv—C4—C4iv116.9 (3)
O1W—Y1—O866.89 (8)O8—C4—C4iv116.0 (3)
O3i—Y1—O770.02 (7)N1—C5—H5A109.5
O9—Y1—O771.75 (8)N1—C5—H5B109.5
O4—Y1—O7111.09 (8)H5A—C5—H5B109.5
O6—Y1—O766.06 (8)N1—C5—H5C109.5
O1—Y1—O7136.38 (8)H5A—C5—H5C109.5
O2i—Y1—O770.27 (8)H5B—C5—H5C109.5
O1W—Y1—O7141.16 (8)N1—C6—H6A109.5
O8—Y1—O7124.12 (8)N1—C6—H6B109.5
C1—O1—Y1117.95 (18)H6A—C6—H6B109.5
C1—O2—Y1ii117.94 (19)N1—C6—H6C109.5
C2—O3—Y1ii118.85 (19)H6A—C6—H6C109.5
C2—O4—Y1119.03 (19)H6B—C6—H6C109.5
O3i—Y1—O1—C1−146.8 (2)O3i—Y1—O8—C487.9 (2)
O9—Y1—O1—C1141.7 (2)O9—Y1—O8—C4−5.14 (19)
O4—Y1—O1—C1−9.2 (2)O4—Y1—O8—C4−139.29 (19)
O6—Y1—O1—C166.0 (2)O6—Y1—O8—C4−46.0 (2)
O2i—Y1—O1—C1−26.0 (3)O1—Y1—O8—C4−94.3 (2)
O1W—Y1—O1—C1−82.0 (2)O2i—Y1—O8—C4129.6 (2)
O8—Y1—O1—C1−150.3 (3)O1W—Y1—O8—C4177.4 (2)
O7—Y1—O1—C188.5 (3)O7—Y1—O8—C440.2 (2)
O3i—Y1—O4—C2156.4 (2)O3i—Y1—O9—C4iv−65.9 (2)
O9—Y1—O4—C2−35.0 (3)O4—Y1—O9—C4iv122.1 (2)
O6—Y1—O4—C2−67.7 (2)O6—Y1—O9—C4iv154.1 (2)
O1—Y1—O4—C211.9 (2)O1—Y1—O9—C4iv79.1 (2)
O2i—Y1—O4—C2179.9 (3)O2i—Y1—O9—C4iv−113.6 (2)
O1W—Y1—O4—C2100.4 (2)O1W—Y1—O9—C4iv8.5 (3)
O8—Y1—O4—C258.5 (3)O8—Y1—O9—C4iv5.23 (19)
O7—Y1—O4—C2−121.0 (2)O7—Y1—O9—C4iv−136.5 (2)
O3i—Y1—O6—C32.2 (3)Y1—O1—C1—O2−173.7 (3)
O9—Y1—O6—C368.0 (2)Y1—O1—C1—C26.4 (4)
O4—Y1—O6—C3−133.8 (3)Y1ii—O2—C1—O1−172.3 (3)
O1—Y1—O6—C3154.5 (3)Y1ii—O2—C1—C27.6 (4)
O2i—Y1—O6—C3−69.7 (2)Y1—O4—C2—O3167.4 (2)
O1W—Y1—O6—C3−151.3 (2)Y1—O4—C2—C1−13.2 (4)
O8—Y1—O6—C3106.6 (2)Y1ii—O3—C2—O4165.7 (3)
O7—Y1—O6—C3−8.7 (2)Y1ii—O3—C2—C1−13.8 (4)
O3i—Y1—O7—C3iii−163.4 (3)O1—C1—C2—O44.4 (4)
O9—Y1—O7—C3iii−71.8 (2)O2—C1—C2—O4−175.5 (3)
O4—Y1—O7—C3iii64.3 (3)O1—C1—C2—O3−176.1 (3)
O6—Y1—O7—C3iii8.5 (2)O2—C1—C2—O34.0 (4)
O1—Y1—O7—C3iii−15.1 (3)Y1—O6—C3—O7iii−171.9 (3)
O2i—Y1—O7—C3iii123.9 (3)Y1—O6—C3—C3iii8.3 (5)
O1W—Y1—O7—C3iii149.8 (2)Y1—O8—C4—O9iv−175.3 (2)
O8—Y1—O7—C3iii−115.3 (2)Y1—O8—C4—C4iv4.7 (4)
Symmetry codes: (i) −x+1, y+1/2, −z+1/2; (ii) −x+1, y−1/2, −z+1/2; (iii) −x+1, −y+2, −z+1; (iv) −x+2, −y+2, −z+1.
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O1W—H1WA···O2Wiv0.83 (2)1.93 (2)2.742 (4)167 (4)
O1W—H1WB···O2Wv0.72 (2)2.20 (2)2.861 (4)152 (4)
O2W—H2WA···O6vi0.81 (2)2.38 (2)3.143 (4)158 (5)
O2W—H2WA···O7vii0.81 (2)2.45 (5)2.944 (4)121 (5)
O2W—H2WB···O3Wviii0.79 (2)2.38 (3)2.963 (7)131 (4)
O2W—H2WB···O4W0.79 (2)2.44 (3)3.194 (6)159 (5)
O3W—H3WA···O20.88 (2)2.36 (7)2.830 (5)114 (6)
O3W—H3WB···O4Wvii0.86 (2)1.90 (3)2.735 (6)161 (6)
O4W—H4WA···O1ix0.82 (2)2.13 (2)2.943 (4)172 (5)
O4W—H4WB···O3x0.83 (2)2.08 (3)2.857 (4)155 (6)
N1—H1A···O8ix0.902.002.869 (4)163
N1—H1A···O1Wix0.902.543.107 (4)122
N1—H1B···O3W0.901.902.784 (6)166
Symmetry codes: (iv) −x+2, −y+2, −z+1; (v) x−1, y, z−1; (vi) x+1, −y+3/2, z+1/2; (vii) −x+2, y−1/2, −z+3/2; (viii) −x+2, y+1/2, −z+3/2; (ix) x, −y+3/2, z+1/2; (x) x+1, y, z+1.
Table 1
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O1W—H1WA···O2Wi0.83 (2)1.93 (2)2.742 (4)167 (4)
O1W—H1WB···O2Wii0.72 (2)2.20 (2)2.861 (4)152 (4)
O2W—H2WA···O6iii0.81 (2)2.38 (2)3.143 (4)158 (5)
O2W—H2WA···O7iv0.81 (2)2.45 (5)2.944 (4)121 (5)
O2W—H2WB···O3Wv0.79 (2)2.38 (3)2.963 (7)131 (4)
O2W—H2WB···O4W0.79 (2)2.44 (3)3.194 (6)159 (5)
O3W—H3WA···O20.88 (2)2.36 (7)2.830 (5)114 (6)
O3W—H3WB···O4Wiv0.86 (2)1.90 (3)2.735 (6)161 (6)
O4W—H4WA···O1vi0.82 (2)2.13 (2)2.943 (4)172 (5)
O4W—H4WB···O3vii0.83 (2)2.08 (3)2.857 (4)155 (6)
N1—H1A···O8vi0.902.002.869 (4)163
N1—H1A···O1Wvi0.902.543.107 (4)122
N1—H1B···O3W0.901.902.784 (6)166
Symmetry codes: (i) −x+2, −y+2, −z+1; (ii) x−1, y, z−1; (iii) x+1, −y+3/2, z+1/2; (iv) −x+2, y−1/2, −z+3/2; (v) −x+2, y+1/2, −z+3/2; (vi) x, −y+3/2, z+1/2; (vii) x+1, y, z+1.
references
References top

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