Hexalithium hexadecahydrate decavanadate, [Li₆(H₂O)₁₆V₁₀O₂₈]_n

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.

S1. Comment

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.

S2. Experimental

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.

S3. Refinement

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 U_iso(H) = 1.2U_eq(carrier atom).

Computing details

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

	Fig. 1. The structure of Li6(H2O)16V10O28, with 40% probability displacement ellipsoids, showing the labeling of the atoms.
	Fig. 2. Two-dimensional layered structure packing diagram for [Li6(H2O)16V10O28]n.

poly[octa-µ-aqua-ocataqua-µ-decavanadato-hexalithium]

Crystal data

Li6(H2O)16V10O28	F(000) = 1264.00
Mr = 1287.29	Dx = 2.546 Mg m^−3
Orthorhombic, Pnnm	Mo Kα radiation, λ = 0.7107 Å
Hall symbol: -P 2 2n	Cell parameters from 16740 reflections
a = 17.6164 (2) Å	θ = 2.3–27.5°
b = 10.3189 (1) Å	µ = 2.79 mm^−1
c = 9.2348 (3) Å	T = 273 K
V = 1678.72 (6) Å^3	Block, orange
Z = 2	0.39 × 0.31 × 0.26 mm

Data collection

Rigaku R-AXIS RAPID diffractometer	1611 reflections with F^2 > 2σ(F^2)
Detector resolution: 10.00 pixels mm^-1	Rint = 0.021
ω scans	θmax = 27.5°
Absorption correction: multi-scan (Higashi, 1995)	h = −22→22
Tmin = 0.391, Tmax = 0.484	k = −13→13
16609 measured reflections	l = −11→11
2044 independent reflections

Refinement

Refinement on F^2	5 restraints
R[F^2 > 2σ(F^2)] = 0.021	H-atom parameters constrained
wR(F^2) = 0.072	w = 1/[0.001Fo^2 + σ(Fo^2)]/(4Fo^2)
S = 1.03	(Δ/σ)max < 0.001
1611 reflections	Δρmax = 0.33 e Å^−3
160 parameters	Δρmin = −0.42 e Å^−3

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
V1	0.64709 (2)	0.66201 (3)	0.66489 (4)	0.0141 (1)
V2	0.64143 (2)	0.40100 (4)	0.5000	0.0112 (1)
V3	0.5000	0.5000	0.67800 (5)	0.0101 (1)
V4	0.49439 (2)	0.23635 (4)	0.5000	0.0127 (1)
O1	0.6977 (1)	0.7148 (2)	0.5000	0.0163 (5)
O2	0.57373 (7)	0.7932 (1)	0.6463 (1)	0.0153 (3)
O3	0.69740 (8)	0.7153 (1)	0.7960 (2)	0.0226 (4)
O4	0.68548 (8)	0.4927 (1)	0.6455 (1)	0.0151 (3)
O5	0.5645 (1)	0.5704 (1)	0.5000	0.0113 (4)
O6	0.6876 (1)	0.2667 (2)	0.5000	0.0175 (5)
O7	0.55641 (7)	0.3483 (1)	0.6343 (1)	0.0114 (3)
O8	0.43484 (7)	0.4295 (1)	0.7875 (1)	0.0152 (3)
O9	0.5469 (1)	0.1105 (2)	0.5000	0.0204 (5)
O10	0.68872 (9)	1.0026 (1)	0.6689 (2)	0.0232 (4)
O11	0.8336 (1)	0.9689 (2)	0.50000 (1)	0.0230 (5)
O12	0.86619 (8)	0.7062 (1)	0.6573 (1)	0.0213 (4)
O13	1.0207 (1)	0.7409 (2)	0.50000 (1)	0.0313 (6)
O14	0.8557 (1)	0.4521 (2)	0.50000 (1)	0.0340 (7)
O15	1.00000 (1)	0.50000 (1)	0.6672 (2)	0.0251 (6)
Li1	0.7345 (3)	1.0895 (5)	0.5000	0.029 (1)
Li2	0.8057 (3)	0.7794 (5)	0.5000	0.024 (1)
Li3	0.9343 (3)	0.6014 (5)	0.5000	0.029 (1)
H1	0.6581	0.9471	0.6524	0.028*
H2	0.7289	0.9781	0.7234	0.029*
H3	0.8574	0.9938	0.5761	0.028*
H4	0.8479	0.6501	0.7116	0.026*
H5	0.8863	0.7583	0.7124	0.026*
H6	1.0375	0.7961	0.5760	0.039*
H7	0.8067	0.4489	0.5000	0.041*
H8	0.8846	0.3895	0.5000	0.041*
H9	1.0240	0.5600	0.7283	0.031*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
V1	0.0120 (2)	0.0153 (2)	0.0150 (2)	−0.0024 (1)	−0.0019 (1)	−0.0020 (1)
V2	0.0083 (2)	0.0110 (3)	0.0144 (3)	0.0008 (1)	0.0000	0.0000
V3	0.0097 (2)	0.0114 (2)	0.0092 (2)	−0.0002 (1)	0.0000	0.0000
V4	0.0112 (2)	0.0096 (2)	0.0173 (3)	−0.0004 (2)	0.0000	0.0000
O1	0.0116 (9)	0.0142 (9)	0.023 (1)	−0.0020 (7)	0.0000	0.0000
O2	0.0133 (6)	0.0134 (6)	0.0192 (7)	−0.0017 (5)	−0.0005 (5)	−0.0038 (5)
O3	0.0178 (7)	0.0260 (7)	0.0239 (8)	−0.0032 (6)	−0.0055 (6)	−0.0068 (7)
O4	0.0120 (6)	0.0147 (6)	0.0186 (7)	0.0002 (5)	−0.0035 (5)	−0.0001 (5)
O5	0.0097 (8)	0.0110 (8)	0.0132 (9)	0.0004 (7)	0.0000	0.0000
O6	0.015 (1)	0.015 (1)	0.022 (1)	0.0038 (8)	0.0000	0.0000
O7	0.0107 (6)	0.0115 (6)	0.0121 (6)	0.0003 (5)	−0.0008 (5)	0.0017 (5)
O8	0.0147 (6)	0.0183 (6)	0.0127 (6)	−0.0007 (5)	0.0024 (5)	0.0007 (5)
O9	0.017 (1)	0.0133 (9)	0.031 (1)	0.0008 (7)	0.0000	0.0000
O10	0.0226 (7)	0.0224 (8)	0.0246 (9)	−0.0036 (6)	−0.0026 (6)	−0.0008 (6)
O11	0.024 (1)	0.025 (1)	0.020 (1)	−0.0021 (9)	0.0000	0.0000
O12	0.0247 (7)	0.0222 (7)	0.0170 (7)	−0.0072 (6)	−0.0008 (6)	−0.0005 (6)
O13	0.042 (1)	0.026 (1)	0.026 (1)	−0.014 (1)	0.0000	0.0000
O14	0.029 (1)	0.033 (1)	0.040 (2)	−0.006 (1)	0.0000	0.0000
O15	0.027 (1)	0.027 (1)	0.022 (1)	−0.0026 (9)	0.0000	0.0000
Li1	0.033 (3)	0.024 (3)	0.029 (3)	0.007 (2)	0.0000	0.0000
Li2	0.023 (3)	0.024 (2)	0.023 (2)	−0.005 (2)	0.0000	0.0000
Li3	0.029 (3)	0.029 (3)	0.029 (3)	−0.002 (2)	0.0000	0.0000

Geometric parameters (Å, º)

V1—O1	1.846 (1)	O14—Li3	2.072 (6)
V1—O2	1.880 (1)	O14—Li3^ii	2.072 (6)
V1—O3	1.598 (1)	O15—Li3	2.195 (4)
V1—O4	1.882 (1)	O15—Li3^ii	2.195 (4)
V1—O5	2.308 (1)	Li1—O6^v	2.007 (5)
V1—O8^i	2.063 (1)	Li1—O10^ii	1.971 (4)
V2—O4	1.817 (1)	Li1—O11	2.144 (6)
V2—O4^ii	1.817 (1)	Li1—O11^ii	2.144 (6)
V2—O5	2.212 (2)	Li2—O11	2.016 (5)
V2—O6	1.607 (2)	Li2—O11^ii	2.016 (5)
V2—O7	2.019 (1)	Li2—O12^ii	1.954 (4)
V2—O7^ii	2.019 (1)	Li3—O12^ii	2.173 (4)
V3—O5	2.126 (1)	Li3—O13	2.094 (6)
V3—O5^i	2.126 (1)	Li3—O13^ii	2.094 (6)
V3—O7	1.898 (1)	Li3—O14	2.072 (6)
V3—O7^i	1.898 (1)	Li3—O14^ii	2.072 (6)
V3—O8	1.694 (1)	Li3—O15	2.195 (4)
V3—O8^i	1.694 (1)	Li3—O15^ii	2.195 (4)
V4—O2^i	1.833 (1)	O10—H1	0.8013
V4—O2^iii	1.833 (1)	O10—H2	0.9045
V4—O5^i	2.248 (2)	O11—H3	0.8579
V4—O7	2.016 (1)	O11—H3^ii	0.8579
V4—O7^ii	2.016 (1)	O12—H4	0.8305
V4—O9	1.595 (2)	O12—H5	0.8197
O1—V1^ii	1.846 (1)	O13—H6	0.9510
O1—Li2	2.016 (5)	O13—H6^ii	0.9510
O2—V4^i	1.833 (1)	O14—H7	0.8638
O5—V1^ii	2.308 (1)	O14—H7^ii	0.8638
O5—V3^iii	2.126 (1)	O14—H8	0.8229
O5—V4^i	2.248 (2)	O14—H8^ii	0.8229
O6—Li1^iv	2.007 (5)	O15—H9	0.9385
O8—V1^i	2.063 (1)	H3—O11	0.8579
O10—Li1	1.971 (4)	H3—O11^ii	0.8579
O11—Li1	2.144 (6)	H6—O13	0.9510
O11—Li1^ii	2.144 (6)	H6—O13^ii	0.9510
O11—Li2	2.016 (5)	H7—O14	0.8638
O11—Li2^ii	2.016 (5)	H7—O14^ii	0.8638
O12—Li2	1.954 (4)	H8—O14	0.8229
O12—Li3	2.173 (4)	H8—O14^ii	0.8229
O13—Li3	2.094 (6)	H9—O15	0.9385
O13—Li3^ii	2.094 (6)
V1—O1—V1^ii	111.11 (9)	V3—O8—V1^i	110.05 (7)
O2—V1—O1	92.51 (7)	O7—V4—O2^i	89.81 (5)
O3—V1—O1	104.82 (7)	O7^ii—V4—O2^i	154.64 (6)
O4—V1—O1	91.27 (7)	O9—V4—O2^i	104.14 (6)
O5—V1—O1	83.16 (6)	V4—O2^i—V1^i	113.42 (7)
O8^i—V1—O1	157.70 (6)	O5^i—V4—O2^i	81.12 (5)
V1—O1—Li2	123.57 (5)	O2^iii—V4—O2^i	95.00 (6)
V1—O2—V4^i	113.42 (7)	O7—V4—O2^iii	154.64 (6)
O3—V1—O2	101.68 (7)	O7^ii—V4—O2^iii	89.81 (5)
O4—V1—O2	155.11 (6)	O9—V4—O2^iii	104.14 (6)
O5—V1—O2	78.55 (6)	O5^i—V4—O2^iii	81.12 (5)
O8^i—V1—O2	84.19 (5)	V4—O2^iii—V1^iii	113.42 (7)
O4—V1—O3	101.10 (7)	V4—O5^i—V3^iii	93.24 (5)
O5—V1—O3	171.97 (6)	O7—V4—O5^i	75.04 (5)
O8^i—V1—O3	97.44 (7)	O7^ii—V4—O5^i	75.04 (5)
V1—O4—V2	113.60 (7)	O9—V4—O5^i	172.01 (8)
O5—V1—O4	77.49 (6)	V4—O5^i—V1^i	85.85 (5)
O8^i—V1—O4	83.04 (5)	V4—O5^i—V2^i	169.70 (9)
V1—O5—V1^ii	82.54 (6)	V4—O5^i—V1^iii	85.85 (5)
V1—O5—V2	86.41 (5)	O7^ii—V4—O7	75.90 (5)
V1—O5—V3	88.10 (1)	O9—V4—O7	98.75 (7)
V1—O5—V4^i	85.85 (5)	V4—O7^ii—V3^iii	108.64 (6)
O8^i—V1—O5	74.56 (5)	O9—V4—O7^ii	98.75 (7)
V1—O5—V3^iii	170.63 (6)	O1—V1^ii—O2^ii	92.51 (7)
V1—O8^i—V3	110.05 (7)	O1—V1^ii—O4^ii	91.27 (7)
O4^ii—V2—O4	95.35 (6)	O1—V1^ii—O5	83.16 (6)
O5—V2—O4	81.39 (5)	Li2—O1—V1^ii	123.57 (5)
O6—V2—O4	103.45 (6)	O1—V1^ii—O8^iii	157.70 (6)
O7—V2—O4	90.17 (6)	O1—V1^ii—O3^ii	104.82 (7)
O7^ii—V2—O4	155.66 (6)	O1—Li2—O11	123.4 (3)
V2—O4^ii—V1^ii	113.60 (7)	O1—Li2—O12	112.8 (2)
O5—V2—O4^ii	81.39 (5)	O1—Li2—O12^ii	112.8 (2)
O6—V2—O4^ii	103.45 (6)	O2—V4^i—O2^ii	95.00 (6)
O7—V2—O4^ii	155.66 (6)	O2—V4^i—O5	81.12 (5)
O7^ii—V2—O4^ii	90.17 (6)	O2—V4^i—O7^i	89.81 (5)
V2—O5—V1^ii	86.41 (5)	O2—V4^i—O7^iii	154.64 (6)
V2—O5—V3	93.29 (5)	O2—V4^i—O9^i	104.14 (6)
V2—O5—V4^i	169.70 (9)	V4^i—O5—V1^ii	85.85 (5)
V2—O5—V3^iii	93.29 (5)	O5—V1^ii—O2^ii	78.55 (6)
O6—V2—O5	172.64 (8)	O5—V1^ii—O4^ii	77.49 (6)
O7—V2—O5	76.02 (5)	V3^iii—O5—V1^ii	88.10 (1)
O7^ii—V2—O5	76.02 (5)	O5—V1^ii—O8^iii	74.56 (5)
O7—V2—O6	98.24 (6)	O5—V1^ii—O3^ii	171.97 (6)
O7^ii—V2—O6	98.24 (6)	V4^i—O5—V3^iii	93.24 (5)
V2—O6—Li1^iv	173.9 (2)	O5—V3^iii—O7^ii	80.65 (6)
V2—O7—V3	107.27 (6)	O5—V3^iii—O8^iii	87.29 (6)
V2—O7—V4	100.29 (6)	O5—V3^iii—O5^i	78.73 (5)
O7^ii—V2—O7	75.78 (5)	O5—V3^iii—O7^iii	80.42 (6)
V2—O7^ii—V3^iii	107.27 (6)	O5—V3^iii—O8^ii	166.03 (6)
V2—O7^ii—V4	100.29 (6)	O5—V4^i—O2^ii	81.12 (5)
V3—O5—V1^ii	170.63 (6)	O5—V4^i—O7^i	75.04 (5)
V3—O5—V4^i	93.24 (5)	O5—V4^i—O7^iii	75.04 (5)
O7^i—V3—O5	80.42 (6)	O5—V4^i—O9^i	172.01 (8)
O8^i—V3—O5	87.29 (6)	O8—V1^i—O2^i	84.19 (5)
V3—O5—V3^iii	101.27 (7)	O8—V1^i—O4^i	83.04 (5)
O7—V3—O5	80.65 (6)	O8—V1^i—O5^i	74.56 (5)
O5^i—V3—O5	78.73 (5)	O8—V1^i—O1^i	157.70 (6)
O8—V3—O5	166.03 (6)	O8—V1^i—O3^i	97.44 (7)
O7^i—V3—O5^i	80.65 (6)	O10—Li1—O10^ii	104.6 (3)
O8^i—V3—O5^i	166.03 (6)	O10—Li1—O11	94.0 (2)
V3—O5^i—V3^iii	101.27 (7)	O10—Li1—O6^v	104.3 (2)
V3—O5^i—V4	93.24 (5)	Li2—O11—Li1	111.4 (2)
O7—V3—O5^i	80.42 (6)	O11—Li1—O10^ii	94.0 (2)
V3—O5^i—V1^i	88.10 (1)	O11—Li1—O6^v	149.8 (3)
V3—O5^i—V2^i	93.29 (5)	O11—Li2—O12	104.0 (2)
O8—V3—O5^i	87.29 (6)	O12—Li2—O12^ii	96.1 (2)
V3—O5^i—V1^iii	170.63 (6)	Li3—O12—Li2	89.8 (2)
O7^i—V3—O7	155.43 (6)	O12—Li3—O12^ii	83.9 (2)
O8^i—V3—O7	97.26 (5)	O12—Li3—O14	90.0 (2)
V3—O7—V4	108.64 (6)	O12—Li3—O13	93.4 (2)
O8—V3—O7	97.33 (5)	O12—Li3—O15	93.33 (5)
V3—O7^i—V4^i	108.64 (6)	O13—Li3—O14	175.4 (3)
O8^i—V3—O7^i	97.33 (5)	O13—Li3—O15	86.8 (2)
V3—O7^i—V2^i	107.27 (6)	O14—Li3—O15	89.9 (2)
O8—V3—O7^i	97.26 (6)	O15—Li3—O15^ii	89.4 (2)
O8^i—V3—O8	106.68 (7)	O15^ii—Li3—O12^ii	93.33 (5)

Symmetry codes: (i) −x+1, −y+1, z; (ii) x, y, −z+1; (iii) −x+1, −y+1, −z+1; (iv) x, y−1, z; (v) x, y+1, z.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O10—H2···O4^vi	0.90	1.94	2.804 (2)	159
O11—H3···O8^vii	0.85	2.01	2.851 (2)	163
O12—H4···O10^viii	0.83	1.98	2.815 (2)	174
O12—H5···O7^vi	0.82	1.97	2.777 (2)	167
O13—H6···O8^vi	0.95	1.92	2.872 (2)	171
O14—H8···O13^ix	0.82	2.14	2.952 (3)	167
O10—H1···O2	0.79	2.18	2.969 (2)	170
O14—H7···O4	0.86	2.56	3.312 (3)	146
O15—H9···O2^vii	0.94	2.10	3.034 (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, y−1/2, −z+3/2; (ix) −x+2, −y+1, z.