A one-dimensional silver(I) coordination polymer based on 5-methyl-1,3,4-thia­diazol-2-amine and pyridine-2,3-di­carboxyl­ate

The bifunctional pyridine-2,3-di­carb­oxy­lic acid (H₂pdc) ligand has one N atom and four O atoms, which could bind more than one Ag^I centre with diverse binding modes. A novel infinite one-dimensional Ag^I coordination polymer, namely catena-poly[[silver(I)-(μ₂-pyridine-2,3-di­carboxyl­ato-κ²N:O³)-silver(I)-tris­(μ₂-5-methyl-1,3,4-thio­diazol-2-amine-κ²N:N′)] monohydrate ethanol monosolvate], {[Ag₂(C₇H₃NO₄)(C₃H₅N₃S)₃]·H₂O·C₂H₅OH}_n, has been synthesized using H₂pdc and 5-methyl-1,3,4-thia­diazol-2-amine (tda), and characterized by single-crystal X-ray diffraction. One Ag^I atom is located in a four-coordinated AgN₄ tetra­hedral geometry and the other Ag^I atom is in a tetra­hedral AgN₃O geometry. A dinuclear Ag^I cluster formed by three tda ligands with a paddelwheel configuration is bridged by the dianionic pdc²⁻ ligand into a one-dimensional coordination polymer. Inter­chain N—H...O hydrogen bonds extend the one-dimensional chains into an undulating two-dimensional sheet. The sheets are further packed into a three-dimensional supra­molecular framework by inter­chain N—H...O hydrogen bonds.

Computing details

Data collection: SMART (Bruker, 2012); cell refinement: SMART (Bruker, 2012); data reduction: SAINT (Bruker, 2012); program(s) used to solve structure: SHELXT (Sheldrick, 2015a) and OLEX2 (Dolomanov et al., 2009); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015b) and OLEX2 (Dolomanov et al., 2009); molecular graphics: DIAMOND (Brandenburg, 2008); software used to prepare material for publication: publCIF (Westrip, 2010) and PLATON (Spek, 2009).

catena-Poly[[silver(I)-(µ₂-pyridine-2,3-dicarboxylato-κ²N:O³)-silver(I)-tris(µ₂-5-methyl-1,3,4-thiodiazol-2-amine-κ²N:N')] monohydrate ethanol monosolvate]

Crystal data

[Ag2(C7H3NO4)(C3H5N3S)3]·H2O·C2H6O	F(000) = 1576
Mr = 790.38	Dx = 2.016 Mg m^−3
Monoclinic, P21/n	Mo Kα radiation, λ = 0.71073 Å
a = 8.3665 (4) Å	Cell parameters from 8981 reflections
b = 23.1277 (11) Å	θ = 2.8–27.6°
c = 13.5984 (7) Å	µ = 1.80 mm^−1
β = 98.221 (1)°	T = 100 K
V = 2604.2 (2) Å^3	Block, yellow
Z = 4	0.22 × 0.20 × 0.18 mm

Data collection

Bruker SMART CCD area-detector diffractometer	5458 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.018
phi and ω scans	θmax = 27.6°, θmin = 1.8°
Absorption correction: multi-scan (SADABS; Bruker, 2012)	h = −6→10
Tmin = 0.705, Tmax = 0.728	k = −30→29
15594 measured reflections	l = −16→16
5918 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)] = 0.027	Hydrogen site location: mixed
wR(F^2) = 0.065	H atoms treated by a mixture of independent and constrained refinement
S = 1.09	w = 1/[σ^2(Fo^2) + (0.0262P)^2 + 4.0926P] where P = (Fo^2 + 2Fc^2)/3
5918 reflections	(Δ/σ)max = 0.001
337 parameters	Δρmax = 1.34 e Å^−3
7 restraints	Δρmin = −0.82 e Å^−3

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Ag1	0.31342 (2)	0.12131 (2)	0.21967 (2)	0.01782 (6)
Ag2	0.26584 (2)	0.26895 (2)	0.20782 (2)	0.01788 (6)
S1	−0.04351 (9)	0.17446 (3)	−0.07942 (5)	0.01951 (14)
S2	0.82115 (8)	0.22203 (3)	0.17491 (6)	0.02212 (15)
S3	−0.01904 (10)	0.18514 (4)	0.46437 (6)	0.02778 (16)
N1	0.5476 (3)	0.17953 (10)	0.19762 (17)	0.0175 (5)
N2	0.5309 (3)	0.23914 (9)	0.20876 (18)	0.0179 (5)
N3	0.6849 (3)	0.32419 (11)	0.2079 (2)	0.0281 (6)
H3A	0.603 (3)	0.3452 (14)	0.216 (3)	0.034*
H3B	0.781 (3)	0.3381 (15)	0.201 (3)	0.034*
N4	0.1506 (3)	0.22545 (10)	0.33860 (17)	0.0181 (5)
N5	0.1617 (3)	0.16546 (10)	0.33185 (17)	0.0189 (5)
N6	0.0645 (4)	0.08011 (12)	0.3967 (2)	0.0309 (6)
H6A	0.026 (4)	0.0638 (15)	0.449 (2)	0.037*
H6B	0.096 (4)	0.0587 (14)	0.348 (2)	0.037*
N7	0.1589 (3)	0.21290 (9)	0.06377 (17)	0.0164 (4)
N8	0.1552 (3)	0.15329 (9)	0.07817 (17)	0.0172 (5)
N9	0.0245 (3)	0.07007 (10)	0.00749 (18)	0.0205 (5)
H9A	0.050 (4)	0.0502 (13)	0.0639 (17)	0.025*
H9B	−0.061 (3)	0.0589 (14)	−0.033 (2)	0.025*
N10	0.0586 (3)	0.54262 (9)	0.19787 (17)	0.0156 (4)
O1	0.2551 (2)	0.37189 (8)	0.16865 (16)	0.0248 (4)
O2	0.0125 (3)	0.34120 (8)	0.19185 (18)	0.0310 (5)
O3	0.2492 (3)	0.44391 (9)	0.35920 (16)	0.0290 (5)
O4	0.3729 (2)	0.51789 (9)	0.29542 (17)	0.0285 (5)
C1	0.7371 (4)	0.10357 (14)	0.1620 (3)	0.0308 (7)
H1A	0.6515	0.0774	0.1766	0.046*
H1B	0.8377	0.0944	0.2055	0.046*
H1C	0.7531	0.0990	0.0925	0.046*
C2	0.6898 (3)	0.16445 (12)	0.1796 (2)	0.0190 (5)
C3	0.6649 (3)	0.26732 (12)	0.1997 (2)	0.0174 (5)
C4	0.0213 (4)	0.30328 (13)	0.4228 (2)	0.0260 (6)
H4A	0.0814	0.3289	0.3838	0.039*
H4B	0.0516	0.3117	0.4937	0.039*
H4C	−0.0948	0.3097	0.4040	0.039*
C5	0.0604 (3)	0.24235 (13)	0.4031 (2)	0.0211 (6)
C6	0.0783 (3)	0.13841 (13)	0.3920 (2)	0.0210 (6)
C7	0.0401 (4)	0.29227 (12)	−0.0412 (2)	0.0236 (6)
H7A	−0.0682	0.3046	−0.0307	0.035*
H7B	0.0523	0.2974	−0.1113	0.035*
H7C	0.1212	0.3156	0.0003	0.035*
C8	0.0631 (3)	0.23028 (11)	−0.01375 (19)	0.0156 (5)
C9	0.0535 (3)	0.12705 (11)	0.01016 (19)	0.0153 (5)
C10	0.1095 (3)	0.38008 (11)	0.1771 (2)	0.0181 (5)
C11	0.0427 (3)	0.44062 (11)	0.16195 (19)	0.0143 (5)
C12	−0.0946 (3)	0.44998 (12)	0.0934 (2)	0.0184 (5)
H12	−0.1476	0.4184	0.0579	0.022*
C13	−0.1540 (3)	0.50573 (12)	0.0768 (2)	0.0196 (5)
H13	−0.2474	0.5131	0.0300	0.023*
C14	−0.0728 (3)	0.55029 (12)	0.1306 (2)	0.0186 (5)
H14	−0.1127	0.5885	0.1191	0.022*
C15	0.1163 (3)	0.48839 (11)	0.21378 (19)	0.0141 (5)
C16	0.2591 (3)	0.48240 (11)	0.2964 (2)	0.0177 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ag1	0.01853 (11)	0.01312 (10)	0.02070 (11)	0.00154 (7)	−0.00094 (8)	0.00353 (8)
Ag2	0.01827 (11)	0.01277 (10)	0.02191 (11)	0.00216 (7)	0.00051 (8)	−0.00142 (8)
S1	0.0245 (3)	0.0156 (3)	0.0155 (3)	−0.0007 (3)	−0.0070 (3)	0.0005 (3)
S2	0.0139 (3)	0.0261 (4)	0.0271 (4)	−0.0035 (3)	0.0051 (3)	−0.0011 (3)
S3	0.0295 (4)	0.0347 (4)	0.0210 (4)	−0.0026 (3)	0.0097 (3)	−0.0007 (3)
N1	0.0173 (11)	0.0159 (11)	0.0197 (12)	0.0000 (9)	0.0038 (9)	0.0005 (9)
N2	0.0160 (11)	0.0139 (11)	0.0236 (12)	−0.0004 (8)	0.0018 (9)	0.0022 (9)
N3	0.0290 (14)	0.0201 (12)	0.0359 (15)	−0.0058 (11)	0.0075 (12)	0.0002 (11)
N4	0.0148 (11)	0.0206 (12)	0.0182 (12)	0.0020 (9)	0.0000 (9)	−0.0008 (9)
N5	0.0182 (11)	0.0181 (11)	0.0199 (12)	−0.0004 (9)	0.0006 (9)	0.0007 (9)
N6	0.0386 (16)	0.0251 (14)	0.0297 (15)	−0.0040 (12)	0.0077 (12)	0.0043 (11)
N7	0.0183 (11)	0.0114 (10)	0.0181 (11)	0.0001 (8)	−0.0017 (9)	0.0013 (9)
N8	0.0205 (11)	0.0111 (10)	0.0179 (11)	0.0000 (9)	−0.0044 (9)	0.0004 (9)
N9	0.0245 (13)	0.0148 (11)	0.0191 (12)	−0.0029 (9)	−0.0070 (9)	−0.0002 (9)
N10	0.0163 (11)	0.0118 (10)	0.0180 (11)	0.0007 (8)	0.0003 (8)	0.0003 (8)
O1	0.0244 (11)	0.0165 (10)	0.0331 (12)	0.0063 (8)	0.0030 (9)	0.0015 (8)
O2	0.0390 (13)	0.0119 (9)	0.0432 (14)	−0.0060 (9)	0.0099 (10)	0.0016 (9)
O3	0.0268 (11)	0.0323 (12)	0.0246 (11)	0.0014 (9)	−0.0074 (9)	0.0081 (9)
O4	0.0218 (11)	0.0238 (11)	0.0355 (12)	−0.0049 (8)	−0.0108 (9)	0.0004 (9)
C1	0.0291 (17)	0.0258 (16)	0.0396 (19)	0.0036 (13)	0.0122 (14)	−0.0013 (14)
C2	0.0176 (13)	0.0211 (13)	0.0186 (13)	−0.0021 (11)	0.0039 (10)	0.0002 (11)
C3	0.0156 (12)	0.0196 (13)	0.0164 (13)	−0.0012 (10)	0.0008 (10)	0.0017 (10)
C4	0.0271 (16)	0.0274 (16)	0.0232 (15)	0.0073 (12)	0.0027 (12)	−0.0049 (12)
C5	0.0202 (14)	0.0269 (15)	0.0148 (13)	0.0018 (11)	−0.0024 (10)	−0.0032 (11)
C6	0.0166 (13)	0.0276 (15)	0.0177 (13)	−0.0023 (11)	−0.0019 (10)	0.0028 (11)
C7	0.0331 (16)	0.0160 (13)	0.0189 (14)	−0.0004 (11)	−0.0064 (12)	0.0028 (11)
C8	0.0147 (12)	0.0177 (13)	0.0141 (12)	−0.0002 (10)	0.0011 (9)	0.0010 (10)
C9	0.0171 (12)	0.0158 (12)	0.0126 (12)	0.0012 (10)	0.0012 (9)	0.0000 (10)
C10	0.0282 (15)	0.0105 (12)	0.0151 (13)	0.0005 (10)	0.0012 (11)	−0.0012 (10)
C11	0.0164 (12)	0.0118 (12)	0.0147 (12)	−0.0014 (9)	0.0027 (9)	0.0006 (9)
C12	0.0187 (13)	0.0186 (13)	0.0172 (13)	−0.0051 (10)	−0.0005 (10)	−0.0014 (10)
C13	0.0140 (12)	0.0237 (14)	0.0195 (14)	0.0018 (10)	−0.0028 (10)	0.0030 (11)
C14	0.0186 (13)	0.0158 (13)	0.0206 (14)	0.0056 (10)	0.0002 (10)	0.0037 (10)
C15	0.0151 (12)	0.0126 (12)	0.0143 (12)	0.0002 (9)	0.0014 (9)	−0.0012 (10)
C16	0.0191 (13)	0.0140 (12)	0.0178 (13)	0.0059 (10)	−0.0043 (10)	−0.0064 (10)

Geometric parameters (Å, º)

Ag1—N8	2.296 (2)	N9—H9A	0.894 (18)
Ag1—N10^i	2.318 (2)	N9—H9B	0.874 (18)
Ag1—N5	2.352 (2)	N10—C14	1.338 (3)
Ag1—N1	2.431 (2)	N10—C15	1.350 (3)
Ag2—N2	2.320 (2)	N10—Ag1^ii	2.318 (2)
Ag2—N4	2.365 (2)	O1—C10	1.255 (3)
Ag2—N7	2.412 (2)	O2—C10	1.246 (3)
Ag2—O1	2.4386 (19)	O3—C16	1.244 (3)
S1—C8	1.741 (3)	O4—C16	1.259 (3)
S1—C9	1.750 (3)	C1—C2	1.491 (4)
S2—C2	1.733 (3)	C1—H1A	0.9800
S2—C3	1.745 (3)	C1—H1B	0.9800
S3—C6	1.740 (3)	C1—H1C	0.9800
S3—C5	1.745 (3)	C4—C5	1.480 (4)
N1—C2	1.296 (3)	C4—H4A	0.9800
N1—N2	1.396 (3)	C4—H4B	0.9800
N2—C3	1.318 (3)	C4—H4C	0.9800
N3—C3	1.328 (4)	C7—C8	1.487 (4)
N3—H3A	0.864 (18)	C7—H7A	0.9800
N3—H3B	0.884 (18)	C7—H7B	0.9800
N4—C5	1.297 (4)	C7—H7C	0.9800
N4—N5	1.395 (3)	C10—C11	1.511 (3)
N5—C6	1.308 (4)	C11—C12	1.389 (4)
N6—C6	1.355 (4)	C11—C15	1.404 (3)
N6—H6A	0.901 (18)	C12—C13	1.389 (4)
N6—H6B	0.894 (18)	C12—H12	0.9500
N7—C8	1.294 (3)	C13—C14	1.384 (4)
N7—N8	1.393 (3)	C13—H13	0.9500
N8—C9	1.312 (3)	C14—H14	0.9500
N9—C9	1.340 (3)	C15—C16	1.525 (3)
N8—Ag1—N10^i	146.03 (8)	N1—C2—C1	123.8 (3)
N8—Ag1—N5	95.96 (8)	N1—C2—S2	113.8 (2)
N10^i—Ag1—N5	106.36 (8)	C1—C2—S2	122.4 (2)
N8—Ag1—N1	95.54 (8)	N2—C3—N3	125.4 (3)
N10^i—Ag1—N1	99.78 (8)	N2—C3—S2	113.1 (2)
N5—Ag1—N1	111.02 (8)	N3—C3—S2	121.5 (2)
N2—Ag2—N4	111.20 (8)	C5—C4—H4A	109.5
N2—Ag2—N7	95.04 (8)	C5—C4—H4B	109.5
N4—Ag2—N7	103.79 (8)	H4A—C4—H4B	109.5
N2—Ag2—O1	107.25 (7)	C5—C4—H4C	109.5
N4—Ag2—O1	124.98 (7)	H4A—C4—H4C	109.5
N7—Ag2—O1	110.46 (7)	H4B—C4—H4C	109.5
C8—S1—C9	87.42 (12)	N4—C5—C4	125.1 (3)
C2—S2—C3	87.59 (13)	N4—C5—S3	113.1 (2)
C6—S3—C5	87.71 (14)	C4—C5—S3	121.8 (2)
C2—N1—N2	113.3 (2)	N5—C6—N6	124.2 (3)
C2—N1—Ag1	130.69 (18)	N5—C6—S3	113.0 (2)
N2—N1—Ag1	115.99 (16)	N6—C6—S3	122.7 (2)
C3—N2—N1	112.2 (2)	C8—C7—H7A	109.5
C3—N2—Ag2	132.68 (18)	C8—C7—H7B	109.5
N1—N2—Ag2	113.80 (16)	H7A—C7—H7B	109.5
C3—N3—H3A	118 (2)	C8—C7—H7C	109.5
C3—N3—H3B	117 (2)	H7A—C7—H7C	109.5
H3A—N3—H3B	124 (3)	H7B—C7—H7C	109.5
C5—N4—N5	113.3 (2)	N7—C8—C7	123.2 (2)
C5—N4—Ag2	136.0 (2)	N7—C8—S1	113.6 (2)
N5—N4—Ag2	109.59 (16)	C7—C8—S1	123.2 (2)
C6—N5—N4	112.8 (2)	N8—C9—N9	124.8 (2)
C6—N5—Ag1	125.70 (19)	N8—C9—S1	112.97 (19)
N4—N5—Ag1	121.47 (16)	N9—C9—S1	122.2 (2)
C6—N6—H6A	120 (2)	O2—C10—O1	124.7 (2)
C6—N6—H6B	119 (2)	O2—C10—C11	117.0 (2)
H6A—N6—H6B	122 (3)	O1—C10—C11	118.2 (2)
C8—N7—N8	113.5 (2)	C12—C11—C15	118.4 (2)
C8—N7—Ag2	127.54 (18)	C12—C11—C10	119.4 (2)
N8—N7—Ag2	115.52 (15)	C15—C11—C10	122.3 (2)
C9—N8—N7	112.6 (2)	C11—C12—C13	119.8 (2)
C9—N8—Ag1	132.80 (18)	C11—C12—H12	120.1
N7—N8—Ag1	114.49 (15)	C13—C12—H12	120.1
C9—N9—H9A	118 (2)	C14—C13—C12	117.9 (2)
C9—N9—H9B	116 (2)	C14—C13—H13	121.0
H9A—N9—H9B	117 (3)	C12—C13—H13	121.0
C14—N10—C15	118.2 (2)	N10—C14—C13	123.8 (2)
C14—N10—Ag1^ii	120.29 (17)	N10—C14—H14	118.1
C15—N10—Ag1^ii	121.49 (17)	C13—C14—H14	118.1
C10—O1—Ag2	97.66 (16)	N10—C15—C11	122.0 (2)
C2—C1—H1A	109.5	N10—C15—C16	115.3 (2)
C2—C1—H1B	109.5	C11—C15—C16	122.6 (2)
H1A—C1—H1B	109.5	O3—C16—O4	126.7 (2)
C2—C1—H1C	109.5	O3—C16—C15	116.7 (2)
H1A—C1—H1C	109.5	O4—C16—C15	116.6 (2)
H1B—C1—H1C	109.5
C2—N1—N2—C3	−0.8 (3)	N8—N7—C8—C7	176.7 (2)
Ag1—N1—N2—C3	177.41 (18)	Ag2—N7—C8—C7	18.9 (4)
C2—N1—N2—Ag2	167.85 (19)	N8—N7—C8—S1	−0.4 (3)
Ag1—N1—N2—Ag2	−14.0 (2)	Ag2—N7—C8—S1	−158.19 (13)
C5—N4—N5—C6	0.2 (3)	C9—S1—C8—N7	0.9 (2)
Ag2—N4—N5—C6	−169.88 (18)	C9—S1—C8—C7	−176.2 (3)
C5—N4—N5—Ag1	179.07 (18)	N7—N8—C9—N9	−178.8 (3)
Ag2—N4—N5—Ag1	9.0 (2)	Ag1—N8—C9—N9	−3.4 (4)
C8—N7—N8—C9	−0.6 (3)	N7—N8—C9—S1	1.2 (3)
Ag2—N7—N8—C9	160.06 (18)	Ag1—N8—C9—S1	176.65 (14)
C8—N7—N8—Ag1	−176.86 (18)	C8—S1—C9—N8	−1.2 (2)
Ag2—N7—N8—Ag1	−16.2 (2)	C8—S1—C9—N9	178.8 (2)
N2—N1—C2—C1	−178.3 (3)	Ag2—O1—C10—O2	−5.8 (3)
Ag1—N1—C2—C1	3.9 (4)	Ag2—O1—C10—C11	178.3 (2)
N2—N1—C2—S2	0.3 (3)	O2—C10—C11—C12	−50.2 (4)
Ag1—N1—C2—S2	−177.51 (13)	O1—C10—C11—C12	125.9 (3)
C3—S2—C2—N1	0.1 (2)	O2—C10—C11—C15	130.9 (3)
C3—S2—C2—C1	178.7 (3)	O1—C10—C11—C15	−52.9 (4)
N1—N2—C3—N3	−179.2 (3)	C15—C11—C12—C13	0.8 (4)
Ag2—N2—C3—N3	15.1 (4)	C10—C11—C12—C13	−178.1 (2)
N1—N2—C3—S2	0.9 (3)	C11—C12—C13—C14	−0.3 (4)
Ag2—N2—C3—S2	−164.92 (14)	C15—N10—C14—C13	0.5 (4)
C2—S2—C3—N2	−0.6 (2)	Ag1^ii—N10—C14—C13	178.6 (2)
C2—S2—C3—N3	179.4 (3)	C12—C13—C14—N10	−0.4 (4)
N5—N4—C5—C4	−177.3 (3)	C14—N10—C15—C11	0.1 (4)
Ag2—N4—C5—C4	−10.8 (4)	Ag1^ii—N10—C15—C11	−177.95 (18)
N5—N4—C5—S3	0.8 (3)	C14—N10—C15—C16	−176.0 (2)
Ag2—N4—C5—S3	167.31 (15)	Ag1^ii—N10—C15—C16	6.0 (3)
C6—S3—C5—N4	−1.2 (2)	C12—C11—C15—N10	−0.8 (4)
C6—S3—C5—C4	176.9 (2)	C10—C11—C15—N10	178.1 (2)
N4—N5—C6—N6	177.4 (3)	C12—C11—C15—C16	175.0 (2)
Ag1—N5—C6—N6	−1.4 (4)	C10—C11—C15—C16	−6.1 (4)
N4—N5—C6—S3	−1.1 (3)	N10—C15—C16—O3	130.6 (3)
Ag1—N5—C6—S3	−179.95 (12)	C11—C15—C16—O3	−45.5 (4)
C5—S3—C6—N5	1.3 (2)	N10—C15—C16—O4	−47.6 (3)
C5—S3—C6—N6	−177.2 (3)	C11—C15—C16—O4	136.3 (3)

Symmetry codes: (i) −x+1/2, y−1/2, −z+1/2; (ii) −x+1/2, y+1/2, −z+1/2.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N3—H3B···O2^iii	0.88 (3)	1.96 (3)	2.808 (4)	161 (3)
N6—H6B···O4^i	0.90 (3)	2.22 (3)	3.092 (4)	166 (3)
N9—H9A···O4^i	0.89 (3)	2.07 (2)	2.953 (3)	170 (3)
N9—H9B···O3^iv	0.88 (3)	2.00 (3)	2.854 (3)	164 (3)

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