Two Zn^II mononuclear coordination compounds with pyridine­di­carboxyl­ate and auxiliary N-(pyridin-4-yl­methylidene)hydroxylamine ligands

Two new mononuclear coordination compounds, bis{4-[(hy­droxyimino)methyl]pyridinium} di­aqua­bis­(pyridine-2,5-di­car­boxyl­ato-κ²N,O²)zincate(II), (C₆H₇N₂O)₂[Zn(C₇H₃NO₄)₂(H₂O)₂], (1), and (pyridine-2,6-dicarboxylato-κ³O²,N,O⁶)bis[N-(pyridin-4-ylmethylidene-κN)hydroxylamine]zinc(II), [Zn(C₇H₃NO₄)(C₆H₆N₂O)₂], (2), have been synthesized and characterized by single-crystal X-ray diffractometry. The centrosymmetric Zn^II cation in (1) is octa­hedrally coordinated by two chelating pyridine-2,5-di­carboxyl­ate ligands and by two water mol­ecules in a distorted octa­hedral geometry. In (2), the Zn^II cation is coordinated by a tridentate pyridine-2,6-di­­carboxyl­ate dianion and by two N-(pyridin-4-ylmethylidene)hydroxylamine mol­ecules in a distorted C₂-symmetric trigonal bipyramidal coordination geometry.

Computing details

For both compounds, data collection: CrysAlis PRO (Agilent, 2011); cell refinement: CrysAlis PRO (Agilent, 2011); data reduction: CrysAlis PRO (Agilent, 2011); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: Mercury (Macrae et al., 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

(cl_2372) Bis{4-[(hydroxyimino)methyl]pyridinium} diaquabis[pyridine-2,5-dicarboxylato-κ²N,O²]zincate(II)

Crystal data

(C6H7N2O)2[Zn(C7H3NO4)2(H2O)2]	F(000) = 696
Mr = 677.88	Dx = 1.677 Mg m^−3
Monoclinic, P21/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybc	Cell parameters from 2019 reflections
a = 7.2649 (3) Å	θ = 3.0–29.1°
b = 10.6796 (3) Å	µ = 1.00 mm^−1
c = 17.4288 (5) Å	T = 293 K
β = 96.823 (3)°	Prism, colourless
V = 1342.66 (8) Å^3	0.40 × 0.30 × 0.12 mm
Z = 2

Data collection

Agilent Xcalibur diffractometer with Eos detector	2009 reflections with I > 2σ(I)
Radiation source: Enhance (Mo) X-ray Source	Rint = 0.027
Graphite monochromator	θmax = 25.0°, θmin = 3.0°
Absorption correction: multi-scan (CrysAlisPro; Agilent, 2011)	h = −6→8
Tmin = 0.692, Tmax = 0.890	k = −8→12
4758 measured reflections	l = −18→20
2375 independent reflections

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.034	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.091	H atoms treated by a mixture of independent and constrained refinement
S = 1.00	w = 1/[σ^2(Fo^2) + (0.046P)^2 + 0.3978P] where P = (Fo^2 + 2Fc^2)/3
2375 reflections	(Δ/σ)max < 0.001
213 parameters	Δρmax = 0.26 e Å^−3
0 restraints	Δρmin = −0.32 e Å^−3

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
Zn1	0.0000	1.0000	0.5000	0.03213 (16)
O1	0.1480 (2)	0.87462 (16)	0.57416 (9)	0.0345 (4)
O2	0.1997 (2)	0.67034 (17)	0.59075 (9)	0.0364 (4)
O3	−0.2347 (3)	0.7994 (2)	0.20303 (10)	0.0565 (6)
O4	−0.1572 (3)	0.59923 (19)	0.20201 (9)	0.0463 (5)
O5	0.6928 (3)	0.62272 (18)	0.56537 (9)	0.0437 (5)
H5	0.7139	0.6677	0.6035	0.066*
N1	−0.0158 (2)	0.83978 (18)	0.42997 (10)	0.0244 (4)
N2	0.3206 (3)	0.7544 (2)	0.23171 (11)	0.0329 (5)
H2	0.2725	0.7808	0.1872	0.039*
N3	0.6065 (2)	0.6915 (2)	0.50495 (11)	0.0304 (5)
C1	0.1410 (3)	0.7632 (2)	0.55140 (12)	0.0258 (5)
C2	0.0578 (3)	0.7386 (2)	0.46863 (12)	0.0232 (5)
C3	0.0613 (3)	0.6228 (2)	0.43506 (12)	0.0268 (5)
H3	0.1111	0.5543	0.4633	0.032*
C4	−0.0109 (3)	0.6094 (2)	0.35803 (12)	0.0271 (5)
H4	−0.0097	0.5317	0.3340	0.032*
C5	−0.0846 (3)	0.7126 (2)	0.31730 (12)	0.0241 (5)
C6	−0.0842 (3)	0.8259 (2)	0.35599 (12)	0.0270 (5)
H6	−0.1341	0.8956	0.3291	0.032*
C7	−0.1647 (3)	0.7033 (2)	0.23321 (13)	0.0292 (5)
C8	0.3419 (3)	0.8343 (3)	0.29097 (13)	0.0342 (6)
H8	0.3013	0.9166	0.2840	0.041*
C9	0.4236 (3)	0.7959 (2)	0.36235 (13)	0.0293 (5)
H9	0.4397	0.8519	0.4035	0.035*
C10	0.4817 (3)	0.6725 (2)	0.37234 (12)	0.0256 (5)
C11	0.4506 (3)	0.5914 (3)	0.30967 (13)	0.0313 (5)
H11	0.4833	0.5074	0.3154	0.038*
C12	0.3718 (3)	0.6352 (3)	0.23970 (14)	0.0339 (6)
H12	0.3538	0.5813	0.1975	0.041*
C13	0.5728 (3)	0.6227 (2)	0.44512 (13)	0.0297 (5)
H13	0.6071	0.5387	0.4479	0.036*
O1W	0.2524 (3)	1.05364 (19)	0.44816 (11)	0.0375 (4)
H1W	0.215 (5)	1.076 (4)	0.397 (2)	0.092 (13)*
H2W	0.311 (4)	1.107 (3)	0.4665 (18)	0.053 (11)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Zn1	0.0528 (3)	0.0210 (2)	0.0197 (2)	0.00606 (17)	−0.00757 (17)	−0.00448 (16)
O1	0.0539 (10)	0.0251 (10)	0.0208 (8)	0.0039 (8)	−0.0105 (7)	−0.0035 (8)
O2	0.0565 (11)	0.0274 (10)	0.0217 (8)	0.0062 (8)	−0.0095 (7)	0.0013 (8)
O3	0.0982 (16)	0.0419 (13)	0.0233 (9)	0.0129 (11)	−0.0183 (10)	−0.0019 (9)
O4	0.0782 (13)	0.0361 (12)	0.0225 (9)	−0.0041 (10)	−0.0030 (8)	−0.0084 (9)
O5	0.0701 (12)	0.0344 (11)	0.0216 (9)	0.0110 (9)	−0.0155 (8)	−0.0009 (8)
N1	0.0314 (10)	0.0244 (11)	0.0163 (9)	0.0001 (8)	−0.0011 (7)	−0.0003 (8)
N2	0.0363 (11)	0.0409 (14)	0.0193 (10)	−0.0015 (9)	−0.0056 (8)	0.0045 (10)
N3	0.0353 (11)	0.0312 (12)	0.0231 (10)	0.0016 (9)	−0.0039 (8)	0.0023 (9)
C1	0.0296 (12)	0.0283 (14)	0.0186 (11)	0.0024 (10)	−0.0009 (9)	0.0001 (10)
C2	0.0262 (11)	0.0244 (12)	0.0187 (11)	−0.0003 (9)	0.0018 (8)	−0.0002 (10)
C3	0.0333 (12)	0.0239 (13)	0.0224 (12)	0.0024 (10)	−0.0005 (9)	0.0021 (10)
C4	0.0332 (12)	0.0224 (13)	0.0253 (12)	−0.0011 (10)	0.0023 (9)	−0.0038 (10)
C5	0.0273 (11)	0.0262 (13)	0.0184 (11)	−0.0031 (9)	0.0012 (8)	−0.0022 (10)
C6	0.0354 (12)	0.0238 (13)	0.0203 (11)	0.0025 (10)	−0.0031 (9)	0.0014 (10)
C7	0.0372 (13)	0.0311 (15)	0.0188 (11)	−0.0055 (11)	0.0009 (9)	−0.0015 (11)
C8	0.0413 (14)	0.0283 (14)	0.0316 (13)	0.0012 (11)	−0.0013 (10)	0.0028 (12)
C9	0.0356 (12)	0.0302 (14)	0.0210 (11)	−0.0003 (10)	−0.0018 (9)	−0.0023 (11)
C10	0.0250 (11)	0.0301 (13)	0.0212 (11)	−0.0020 (9)	0.0009 (9)	0.0028 (10)
C11	0.0389 (13)	0.0281 (14)	0.0257 (12)	0.0019 (10)	−0.0006 (10)	−0.0024 (11)
C12	0.0421 (14)	0.0352 (15)	0.0228 (12)	−0.0028 (11)	−0.0026 (10)	−0.0021 (11)
C13	0.0361 (13)	0.0281 (13)	0.0231 (12)	0.0015 (10)	−0.0037 (9)	0.0007 (11)
O1W	0.0544 (12)	0.0317 (11)	0.0250 (10)	−0.0045 (10)	−0.0006 (8)	0.0001 (9)

Geometric parameters (Å, º)

Zn1—O1^i	2.0712 (16)	N2—C8	1.335 (3)
Zn1—O1	2.0712 (16)	N3—C13	1.276 (3)
Zn1—N1	2.0969 (19)	C1—C2	1.519 (3)
Zn1—N1^i	2.0970 (19)	C2—C3	1.371 (3)
Zn1—O1W	2.214 (2)	C3—C4	1.389 (3)
Zn1—O1W^i	2.214 (2)	C4—C5	1.384 (3)
O1—C1	1.253 (3)	C5—C6	1.384 (3)
O2—C1	1.251 (3)	C5—C7	1.515 (3)
O3—C7	1.235 (3)	C8—C9	1.376 (3)
O4—C7	1.241 (3)	C9—C10	1.388 (3)
O5—N3	1.373 (2)	C10—C11	1.391 (3)
N1—C6	1.334 (3)	C10—C13	1.460 (3)
N1—C2	1.349 (3)	C11—C12	1.367 (3)
N2—C12	1.329 (3)
O1^i—Zn1—O1	180.00 (7)	O2—C1—C2	117.0 (2)
O1^i—Zn1—N1	100.13 (7)	O1—C1—C2	117.5 (2)
O1—Zn1—N1	79.87 (7)	N1—C2—C3	122.41 (19)
O1^i—Zn1—N1^i	79.87 (7)	N1—C2—C1	115.2 (2)
O1—Zn1—N1^i	100.13 (7)	C3—C2—C1	122.4 (2)
N1—Zn1—N1^i	180.000 (1)	C2—C3—C4	118.8 (2)
O1^i—Zn1—O1W	88.38 (7)	C5—C4—C3	119.5 (2)
O1—Zn1—O1W	91.62 (7)	C4—C5—C6	117.9 (2)
N1—Zn1—O1W	87.95 (7)	C4—C5—C7	121.6 (2)
N1^i—Zn1—O1W	92.05 (7)	C6—C5—C7	120.5 (2)
O1^i—Zn1—O1W^i	91.62 (7)	N1—C6—C5	123.2 (2)
O1—Zn1—O1W^i	88.38 (7)	O3—C7—O4	126.5 (2)
N1—Zn1—O1W^i	92.05 (7)	O3—C7—C5	116.7 (2)
N1^i—Zn1—O1W^i	87.95 (7)	O4—C7—C5	116.8 (2)
O1W—Zn1—O1W^i	180.0	N2—C8—C9	120.5 (2)
C1—O1—Zn1	114.68 (14)	C8—C9—C10	119.3 (2)
C6—N1—C2	118.3 (2)	C9—C10—C11	118.3 (2)
C6—N1—Zn1	129.93 (16)	C9—C10—C13	123.7 (2)
C2—N1—Zn1	111.81 (13)	C11—C10—C13	118.0 (2)
C12—N2—C8	121.7 (2)	C12—C11—C10	119.9 (2)
C13—N3—O5	110.1 (2)	N2—C12—C11	120.2 (2)
O2—C1—O1	125.5 (2)	N3—C13—C10	121.6 (2)

Symmetry code: (i) −x, −y+2, −z+1.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O5—H5···O3^ii	0.82	1.77	2.535 (2)	156
N2—H2···O2^iii	0.86	1.78	2.635 (2)	173
N2—H2···O1^iii	0.86	2.65	3.193 (2)	122
O1W—H1W···O4^iv	0.94 (4)	1.74 (4)	2.671 (2)	173 (4)
O1W—H2W···N3^v	0.76 (3)	2.27 (3)	2.988 (3)	157 (3)

Symmetry codes: (ii) x+1, −y+3/2, z+1/2; (iii) x, −y+3/2, z−1/2; (iv) −x, y+1/2, −z+1/2; (v) −x+1, −y+2, −z+1.

(cl_2371) (Pyridine-2,6-dicarboxylato-κ³O²,N,O⁶)bis[N-(pyridin-4-ylmethylidene)hydroxylamine-κN¹]zinc(II)

Crystal data

[Zn(C7H3NO4)(C6H6N2O)2]	F(000) = 968
Mr = 474.73	Dx = 1.639 Mg m^−3
Orthorhombic, Pbcn	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2ab	Cell parameters from 1593 reflections
a = 6.7644 (2) Å	θ = 3.0–29.0°
b = 18.5124 (5) Å	µ = 1.33 mm^−1
c = 15.3595 (6) Å	T = 293 K
V = 1923.40 (11) Å^3	Block, colourless
Z = 4	0.35 × 0.25 × 0.25 mm

Data collection

Agilent Xcalibur diffractometer with Eos detector	1693 independent reflections
Radiation source: Enhance (Mo) X-ray Source	1390 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.023
Detector resolution: 15.9914 pixels mm^-1	θmax = 25.0°, θmin = 3.2°
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2011)	h = −8→4
Tmin = 0.654, Tmax = 0.733	k = −22→12
4548 measured reflections	l = −18→10

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.032	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.083	H-atom parameters constrained
S = 1.00	w = 1/[σ^2(Fo^2) + (0.043P)^2 + 0.5499P] where P = (Fo^2 + 2Fc^2)/3
1693 reflections	(Δ/σ)max < 0.001
142 parameters	Δρmax = 0.24 e Å^−3
0 restraints	Δρmin = −0.26 e Å^−3

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
Zn1	0.0000	0.31494 (2)	0.2500	0.04058 (17)
O1	0.7094 (3)	0.05551 (11)	−0.06470 (13)	0.0628 (6)
H1	0.8256	0.0627	−0.0771	0.094*
O2	0.2647 (2)	0.34129 (10)	0.32226 (12)	0.0486 (4)
O3	0.4386 (3)	0.43657 (12)	0.36843 (14)	0.0694 (6)
N1	0.1395 (3)	0.24930 (10)	0.16438 (14)	0.0402 (5)
N2	0.6391 (3)	0.11239 (12)	−0.01473 (14)	0.0460 (5)
N3	0.0000	0.42277 (15)	0.2500	0.0342 (6)
C1	0.3293 (3)	0.26191 (13)	0.14281 (17)	0.0460 (7)
H1A	0.3909	0.3029	0.1650	0.055*
C2	0.4356 (3)	0.21708 (14)	0.08958 (17)	0.0427 (6)
H2	0.5652	0.2287	0.0750	0.051*
C3	0.3506 (3)	0.15458 (14)	0.05753 (15)	0.0386 (6)
C4	0.1531 (3)	0.14219 (14)	0.07819 (18)	0.0467 (7)
H4	0.0886	0.1016	0.0566	0.056*
C5	0.0544 (4)	0.19001 (14)	0.13039 (19)	0.0472 (7)
H5	−0.0778	0.1811	0.1430	0.057*
C6	0.4585 (3)	0.10206 (15)	0.00495 (17)	0.0450 (6)
H6	0.3946	0.0606	−0.0144	0.054*
C8	0.1482 (3)	0.45774 (13)	0.28816 (15)	0.0375 (6)
C9	0.1529 (4)	0.53201 (14)	0.28938 (18)	0.0521 (7)
H9	0.2563	0.5567	0.3160	0.062*
C10	0.0000	0.5690 (2)	0.2500	0.0593 (12)
H10	0.0000	0.6192	0.2500	0.071*
C7	0.2989 (3)	0.40795 (15)	0.32989 (16)	0.0441 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Zn1	0.0308 (2)	0.0331 (2)	0.0579 (3)	0.000	0.00167 (17)	0.000
O1	0.0392 (10)	0.0750 (13)	0.0743 (13)	−0.0033 (10)	0.0219 (10)	−0.0189 (12)
O2	0.0320 (9)	0.0525 (10)	0.0613 (11)	0.0080 (8)	−0.0096 (8)	0.0047 (10)
O3	0.0421 (10)	0.0892 (15)	0.0768 (15)	−0.0133 (11)	−0.0287 (11)	0.0009 (13)
N1	0.0293 (10)	0.0373 (10)	0.0538 (13)	−0.0025 (9)	0.0040 (9)	0.0003 (10)
N2	0.0371 (11)	0.0571 (13)	0.0437 (12)	0.0022 (10)	0.0085 (9)	−0.0001 (11)
N3	0.0259 (14)	0.0354 (14)	0.0412 (16)	0.000	−0.0069 (12)	0.000
C1	0.0356 (13)	0.0400 (13)	0.0623 (17)	−0.0079 (11)	0.0039 (12)	0.0012 (13)
C2	0.0277 (11)	0.0482 (14)	0.0523 (16)	−0.0050 (12)	0.0045 (11)	0.0055 (14)
C3	0.0308 (12)	0.0470 (14)	0.0381 (13)	−0.0008 (11)	−0.0003 (10)	0.0055 (12)
C4	0.0338 (13)	0.0473 (15)	0.0589 (17)	−0.0081 (12)	0.0032 (12)	−0.0108 (14)
C5	0.0270 (11)	0.0517 (15)	0.0630 (18)	−0.0061 (12)	0.0066 (12)	−0.0056 (14)
C6	0.0350 (13)	0.0537 (15)	0.0462 (15)	−0.0044 (12)	0.0035 (11)	−0.0047 (14)
C8	0.0320 (12)	0.0443 (14)	0.0361 (13)	−0.0065 (11)	−0.0039 (11)	−0.0008 (12)
C9	0.0617 (17)	0.0460 (15)	0.0486 (16)	−0.0168 (14)	−0.0092 (15)	−0.0059 (14)
C10	0.089 (3)	0.035 (2)	0.054 (2)	0.000	−0.007 (2)	0.000
C7	0.0278 (12)	0.0613 (16)	0.0433 (14)	−0.0024 (12)	−0.0058 (11)	0.0023 (14)

Geometric parameters (Å, º)

Zn1—N3	1.996 (3)	N3—C8	1.329 (3)
Zn1—N1	2.0239 (19)	N3—C8^i	1.329 (3)
Zn1—N1^i	2.0239 (19)	C1—C2	1.369 (3)
Zn1—O2	2.1623 (16)	C2—C3	1.383 (3)
Zn1—O2^i	2.1623 (16)	C3—C4	1.392 (3)
O1—N2	1.387 (3)	C3—C6	1.459 (3)
O2—C7	1.261 (3)	C4—C5	1.368 (3)
O3—C7	1.235 (3)	C8—C9	1.375 (4)
N1—C5	1.345 (3)	C8—C7	1.517 (3)
N1—C1	1.346 (3)	C9—C10	1.379 (3)
N2—C6	1.272 (3)	C10—C9^i	1.379 (3)
N3—Zn1—N1	126.90 (5)	C8^i—N3—Zn1	119.15 (14)
N3—Zn1—N1^i	126.90 (5)	N1—C1—C2	122.9 (2)
N1—Zn1—N1^i	106.21 (11)	C1—C2—C3	120.1 (2)
N3—Zn1—O2	76.96 (5)	C2—C3—C4	117.1 (2)
N1—Zn1—O2	94.75 (7)	C2—C3—C6	123.1 (2)
N1^i—Zn1—O2	100.84 (7)	C4—C3—C6	119.8 (2)
N3—Zn1—O2^i	76.96 (5)	C5—C4—C3	119.7 (2)
N1—Zn1—O2^i	100.84 (7)	N1—C5—C4	123.1 (2)
N1^i—Zn1—O2^i	94.75 (7)	N2—C6—C3	120.8 (2)
O2—Zn1—O2^i	153.93 (10)	N3—C8—C9	120.7 (2)
C7—O2—Zn1	114.86 (15)	N3—C8—C7	113.4 (2)
C5—N1—C1	117.0 (2)	C9—C8—C7	125.9 (2)
C5—N1—Zn1	122.88 (16)	C8—C9—C10	118.2 (3)
C1—N1—Zn1	120.03 (16)	C9^i—C10—C9	120.6 (4)
C6—N2—O1	110.3 (2)	O3—C7—O2	127.2 (2)
C8—N3—C8^i	121.7 (3)	O3—C7—C8	117.2 (2)
C8—N3—Zn1	119.15 (14)	O2—C7—C8	115.6 (2)

Symmetry code: (i) −x, y, −z+1/2.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1—H1···O3^ii	0.82	1.80	2.597 (2)	163

Symmetry code: (ii) −x+3/2, −y+1/2, z−1/2.