Poly[(μ₂-4,4′-bipyridine-κ²N:N′)bis­(μ₂-p-toluene­sulfonato-κ²O:O′)cadmium(II)]

The Cd atom in the polymeric title structure, [Cd(C₇H₇O₃S)₂(C₁₀H₈N₂)]_n, exists in a slightly distorted cis-N₂O₄Cd octa­hedral geometry. In the crystal structure, two p-toluene­sulfonate ligands bridge two Cd atoms forming a linear chain, and adjacent chains are linked through 4,4′-bipyridine ligands into a three-dimensional network.

Key indicators

• Single-crystal X-ray study
• T = 291 K
• Mean [sigma](C-C) = 0.006 Å
• R factor = 0.034
• wR factor = 0.087
• Data-to-parameter ratio = 18.1

checkCIF/PLATON results

No syntax errors found



Alert level A
PLAT220_ALERT_2_A Large Non-Solvent    C     Ueq(max)/Ueq(min) ...       4.51 Ratio
PLAT222_ALERT_3_A Large Non-Solvent    H     Ueq(max)/Ueq(min) ...       5.10 Ratio

Alert level B
PLAT241_ALERT_2_B Check High      Ueq as Compared to Neighbors for        C10
PLAT242_ALERT_2_B Check Low       Ueq as Compared to Neighbors for        C11

Alert level C
PLAT241_ALERT_2_C Check High      Ueq as Compared to Neighbors for         C9
PLAT242_ALERT_2_C Check Low       Ueq as Compared to Neighbors for         S2
PLAT242_ALERT_2_C Check Low       Ueq as Compared to Neighbors for         C8

   2 ALERT level A = In general: serious problem
   2 ALERT level B = Potentially serious problem
   3 ALERT level C = Check and explain
   0 ALERT level G = General alerts; check

   0 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   6 ALERT type 2 Indicator that the structure model may be wrong or deficient
   1 ALERT type 3 Indicator that the structure quality may be low
   0 ALERT type 4 Improvement, methodology, query or suggestion
   0 ALERT type 5 Informative message, check

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Computing details

Data collection: SMART (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEPII (Johnson, 1976); software used to prepare material for publication: SHELXL97.

Poly[(µ₂-4,4'-bipyridine-κ²N:N')bis(µ₂-p- toluenesulfonato-κ²O:O')cadmium(II)]

Crystal data

[Cd(C7H7O3S)2(C10H8N2)]	F(000) = 1232
Mr = 610.96	Dx = 1.608 Mg m^−3
Monoclinic, P21/n	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yn	Cell parameters from 6483 reflections
a = 9.7585 (7) Å	θ = 2.6–27.3°
b = 18.290 (1) Å	µ = 1.07 mm^−1
c = 14.246 (1) Å	T = 291 K
β = 96.917 (1)°	Prism, colorless
V = 2524.1 (3) Å^3	0.39 × 0.29 × 0.22 mm
Z = 4

Data collection

Bruker APEX-II area-detector diffractometer	5757 independent reflections
Radiation source: fine-focus sealed tube	4496 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.041
φ and ω scans	θmax = 27.5°, θmin = 2.4°
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	h = −12→12
Tmin = 0.615, Tmax = 0.795	k = −23→23
21285 measured reflections	l = −18→18

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) = 0.087	H-atom parameters constrained
S = 1.03	w = 1/[σ^2(Fo^2) + (0.0437P)^2 + 0.7515P] where P = (Fo^2 + 2Fc^2)/3
5757 reflections	(Δ/σ)max = 0.001
318 parameters	Δρmax = 0.51 e Å^−3
0 restraints	Δρmin = −0.68 e Å^−3

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

	x	y	z	Uiso*/Ueq
Cd1	0.74873 (2)	0.45179 (1)	0.51294 (2)	0.02405 (8)
S1	0.57991 (7)	0.59593 (4)	0.62352 (6)	0.0286 (2)
S2	0.91186 (7)	0.55112 (4)	0.33886 (5)	0.0288 (2)
O1	0.6976 (2)	0.5557 (1)	0.5941 (2)	0.0377 (5)
O2	0.4504 (2)	0.5568 (1)	0.5933 (2)	0.0403 (6)
O3	0.5779 (2)	0.6723 (1)	0.5971 (2)	0.0422 (6)
O4	0.8030 (2)	0.5335 (1)	0.3976 (2)	0.0382 (5)
O5	1.0490 (2)	0.5372 (2)	0.3885 (2)	0.0484 (7)
O6	0.8978 (3)	0.6238 (1)	0.2998 (2)	0.0508 (7)
N1	0.6491 (3)	0.3803 (1)	0.6213 (2)	0.0303 (6)
N2	0.3489 (3)	0.1441 (1)	0.9383 (2)	0.0313 (6)
C1	0.5999 (3)	0.5936 (2)	0.7494 (2)	0.034 (1)
C2	0.6295 (5)	0.5286 (2)	0.7970 (3)	0.056 (1)
C3	0.6454 (5)	0.5272 (3)	0.8949 (3)	0.071 (1)
C4	0.6335 (5)	0.5901 (3)	0.9475 (3)	0.067 (1)
C5	0.6025 (5)	0.6538 (2)	0.8993 (3)	0.063 (1)
C6	0.5834 (4)	0.6571 (2)	0.8005 (3)	0.050 (1)
C7	0.6570 (8)	0.5880 (3)	1.0552 (3)	0.112 (2)
C8	0.8952 (3)	0.4881 (2)	0.2430 (2)	0.039 (1)
C9	1.0028 (5)	0.4817 (4)	0.1887 (4)	0.109 (2)
C10	0.9904 (7)	0.4343 (4)	0.1135 (5)	0.138 (3)
C11	0.8782 (7)	0.3911 (3)	0.0910 (4)	0.086 (2)
C12	0.7746 (6)	0.3973 (3)	0.1461 (3)	0.078 (2)
C13	0.7814 (4)	0.4457 (2)	0.2218 (3)	0.058 (1)
C14	0.8683 (9)	0.3369 (4)	0.0079 (5)	0.139 (3)
C15	0.7272 (3)	0.3382 (2)	0.6836 (3)	0.044 (1)
C16	0.6731 (3)	0.2938 (2)	0.7490 (3)	0.045 (1)
C17	0.5302 (3)	0.2905 (2)	0.7511 (2)	0.031 (1)
C18	0.4504 (3)	0.3360 (2)	0.6883 (2)	0.038 (1)
C19	0.5127 (3)	0.3792 (2)	0.6256 (2)	0.035 (1)
C20	0.4680 (3)	0.2410 (2)	0.8172 (2)	0.032 (1)
C21	0.5462 (3)	0.1895 (2)	0.8709 (3)	0.043 (1)
C22	0.4838 (3)	0.1421 (2)	0.9293 (2)	0.041 (1)
C23	0.2728 (3)	0.1947 (2)	0.8881 (2)	0.039 (1)
C24	0.3261 (3)	0.2429 (2)	0.8271 (3)	0.040 (1)
H2	0.6387	0.4857	0.7633	0.067*
H3	0.6646	0.4830	0.9261	0.086*
H5	0.5939	0.6965	0.9335	0.076*
H6	0.5600	0.7009	0.7695	0.060*
H7a	0.6561	0.5382	1.0763	0.169*
H7b	0.5851	0.6148	1.0803	0.169*
H7c	0.7447	0.6097	1.0768	0.169*
H9	1.0827	0.5092	0.2029	0.131*
H10	1.0622	0.4317	0.0762	0.165*
H12	0.6964	0.3683	0.1327	0.093*
H13	0.7083	0.4489	0.2578	0.069*
H14a	0.7922	0.3042	0.0118	0.209*
H14b	0.9523	0.3092	0.0106	0.209*
H14c	0.8542	0.3633	−0.0507	0.209*
H15	0.8224	0.3387	0.6829	0.052*
H16	0.7318	0.2662	0.7914	0.054*
H18	0.3552	0.3376	0.6884	0.045*
H19	0.4567	0.4090	0.5842	0.041*
H21	0.6408	0.1866	0.8681	0.052*
H22	0.5385	0.1074	0.9636	0.049*
H23	0.1792	0.1976	0.8945	0.047*
H24	0.2686	0.2765	0.7928	0.047*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cd1	0.0203 (1)	0.0274 (1)	0.0254 (1)	0.0003 (1)	0.0065 (1)	−0.0001 (1)
S1	0.0202 (4)	0.0329 (4)	0.0332 (4)	−0.0006 (3)	0.0057 (3)	−0.0038 (3)
S2	0.0193 (3)	0.0381 (4)	0.0295 (4)	0.0002 (3)	0.0045 (3)	0.0034 (3)
O1	0.028 (1)	0.042 (1)	0.045 (1)	0.003 (1)	0.009 (1)	−0.015 (1)
O2	0.026 (1)	0.055 (2)	0.039 (1)	−0.012 (1)	−0.002 (1)	0.001 (1)
O3	0.044 (1)	0.033 (1)	0.051 (2)	0.001 (1)	0.013 (1)	0.001 (1)
O4	0.037 (1)	0.047 (1)	0.034 (1)	−0.002 (1)	0.014 (1)	0.005 (1)
O5	0.027 (1)	0.068 (2)	0.047 (2)	0.007 (1)	−0.009 (1)	−0.014 (1)
O6	0.052 (2)	0.045 (2)	0.059 (2)	0.005 (1)	0.021 (1)	0.018 (1)
N1	0.028 (1)	0.031 (1)	0.035 (2)	0.002 (1)	0.011 (1)	0.008 (1)
N2	0.028 (1)	0.031 (1)	0.036 (2)	−0.002 (1)	0.010 (1)	0.008 (1)
C1	0.028 (2)	0.040 (2)	0.034 (2)	−0.002 (1)	0.004 (1)	−0.007 (1)
C2	0.079 (3)	0.044 (2)	0.042 (2)	0.012 (2)	−0.001 (2)	−0.010 (2)
C3	0.107 (4)	0.062 (3)	0.041 (2)	0.011 (3)	−0.007 (2)	0.001 (2)
C4	0.090 (4)	0.072 (3)	0.040 (2)	−0.003 (3)	0.008 (2)	−0.006 (2)
C5	0.088 (3)	0.058 (3)	0.045 (2)	−0.004 (2)	0.013 (2)	−0.021 (2)
C6	0.063 (3)	0.041 (2)	0.046 (2)	−0.005 (2)	0.011 (2)	−0.010 (2)
C7	0.199 (7)	0.096 (5)	0.039 (3)	0.004 (5)	−0.001 (4)	−0.008 (3)
C8	0.030 (2)	0.056 (2)	0.033 (2)	−0.001 (2)	0.0042 (14)	0.000 (2)
C9	0.063 (3)	0.170 (6)	0.103 (4)	−0.040 (4)	0.044 (3)	−0.081 (4)
C10	0.097 (5)	0.202 (8)	0.127 (6)	−0.046 (5)	0.065 (4)	−0.106 (6)
C11	0.112 (5)	0.084 (4)	0.061 (3)	−0.012 (3)	0.015 (3)	−0.027 (3)
C12	0.090 (4)	0.083 (4)	0.055 (3)	−0.032 (3)	−0.006 (3)	−0.015 (3)
C13	0.052 (2)	0.075 (3)	0.047 (2)	−0.021 (2)	0.007 (2)	−0.005 (2)
C14	0.203 (9)	0.125 (6)	0.089 (5)	−0.004 (6)	0.014 (5)	−0.063 (4)
C15	0.026 (2)	0.049 (2)	0.059 (2)	0.004 (2)	0.016 (2)	0.020 (2)
C16	0.025 (2)	0.054 (2)	0.057 (2)	0.006 (2)	0.009 (2)	0.028 (2)
C17	0.028 (2)	0.032 (2)	0.034 (2)	0.002 (1)	0.010 (1)	0.008 (2)
C18	0.022 (2)	0.047 (2)	0.046 (2)	0.004 (1)	0.011 (1)	0.016 (2)
C19	0.025 (2)	0.042 (2)	0.037 (2)	0.004 (1)	0.005 (1)	0.012 (2)
C20	0.027 (2)	0.033 (2)	0.037 (2)	0.002 (1)	0.011 (1)	0.007 (1)
C21	0.025 (2)	0.049 (2)	0.058 (2)	0.007 (2)	0.015 (2)	0.024 (2)
C22	0.033 (2)	0.043 (2)	0.049 (2)	0.006 (2)	0.015 (2)	0.021 (2)
C23	0.025 (2)	0.042 (2)	0.052 (2)	0.000 (1)	0.012 (2)	0.014 (2)
C24	0.025 (2)	0.038 (2)	0.056 (2)	0.004 (1)	0.008 (2)	0.019 (2)

Geometric parameters (Å, º)

Cd1—O1	2.310 (2)	C15—C16	1.387 (4)
Cd1—O2^i	2.320 (2)	C16—C17	1.400 (4)
Cd1—O5^ii	2.289 (2)	C17—C18	1.390 (4)
Cd1—O4	2.329 (2)	C17—C20	1.488 (4)
Cd1—N1	2.324 (2)	C18—C19	1.386 (4)
Cd1—N2^iii	2.326 (2)	C20—C21	1.383 (4)
S1—O3	1.446 (2)	C20—C24	1.409 (4)
S1—O1	1.467 (2)	C21—C22	1.391 (4)
S1—O2	1.471 (2)	C23—C24	1.382 (4)
S1—C1	1.781 (3)	C2—H2	0.93
S2—O6	1.442 (3)	C3—H3	0.93
S2—O5	1.459 (2)	C5—H5	0.93
S2—O4	1.465 (2)	C6—H6	0.93
S2—C8	1.778 (4)	C7—H7a	0.96
N1—C19	1.341 (4)	C7—H7b	0.96
N1—C15	1.341 (4)	C7—H7C	0.96
N2—C22	1.339 (4)	C9—H9	0.93
N2—C23	1.340 (4)	C10—H10	0.93
C1—C2	1.382 (5)	C12—H12	0.93
C1—C6	1.389 (5)	C13—H13	0.93
C2—C3	1.385 (5)	C14—H14a	0.96
C3—C4	1.386 (6)	C14—H14b	0.96
C4—C5	1.367 (6)	C14—H14C	0.96
C4—C7	1.524 (6)	C15—H15	0.93
C5—C6	1.399 (5)	C16—H16	0.93
C8—C13	1.359 (5)	C18—H18	0.93
C8—C9	1.382 (6)	C19—H19	0.93
C9—C10	1.372 (7)	C21—H21	0.93
C10—C11	1.356 (8)	C22—H22	0.93
C11—C12	1.357 (7)	C23—H23	0.93
C11—C14	1.540 (7)	C24—H24	0.93
C12—C13	1.390 (6)
O1—Cd1—O2^i	99.65 (8)	C15—C16—C17	120.0 (3)
O1—Cd1—O4	84.63 (8)	C18—C17—C16	116.3 (3)
O1—Cd1—O5^ii	80.96 (8)	C18—C17—C20	122.2 (3)
O1—Cd1—N1	89.88 (9)	C16—C17—C20	121.6 (3)
O1—Cd1—N2^iii	167.66 (8)	C19—C18—C17	120.1 (3)
O2^i—Cd1—O4	80.02 (8)	N1—C19—C18	123.5 (3)
O2^i—Cd1—O5^ii	176.98 (8)	C21—C20—C24	116.4 (3)
O2^i—Cd1—N1	90.61 (9)	C21—C20—C17	121.6 (3)
O2^i—Cd1—N2^iii	90.91 (9)	C24—C20—C17	121.9 (3)
O4—Cd1—O5^ii	97.11 (9)	C20—C21—C22	120.2 (3)
O4—Cd1—N1	168.17 (8)	N2—C22—C21	123.2 (3)
O4—Cd1—N2^iii	91.00 (9)	N2—C23—C24	123.4 (3)
O5^ii—Cd1—N1	92.35 (9)	C23—C24—C20	119.7 (3)
O5^ii—Cd1—N2^iii	88.17 (9)	C1—C2—H2	119.9
N1—Cd1—N2^iii	96.41 (9)	C3—C2—H2	119.9
O3—S1—O1	113.4 (1)	C2—C3—H3	119.3
O3—S1—O2	114.2 (1)	C4—C3—H3	119.3
O1—S1—O2	110.3 (1)	C4—C5—H5	118.7
O3—S1—C1	106.3 (2)	C6—C5—H5	118.8
O1—S1—C1	106.4 (2)	C1—C6—H6	120.6
O2—S1—C1	105.6 (1)	C5—C6—H6	120.6
O6—S2—O5	112.8 (2)	C4—C7—H7a	109.5
O6—S2—O4	112.4 (1)	C4—C7—H7b	109.5
O5—S2—O4	111.8 (2)	H7a—C7—H7b	109.5
O6—S2—C8	107.8 (2)	C4—C7—H7C	109.5
O5—S2—C8	104.6 (2)	H7a—C7—H7C	109.5
O4—S2—C8	106.9 (2)	H7b—C7—H7C	109.5
S1—O1—Cd1	141.2 (1)	C10—C9—H9	120.3
S1—O2—Cd1^i	147.8 (2)	C8—C9—H9	120.3
S2—O4—Cd1	141.8 (1)	C11—C10—H10	118.5
S2—O5—Cd1^ii	162.7 (2)	C9—C10—H10	118.5
C19—N1—C15	116.7 (3)	C11—C12—H12	118.9
C19—N1—Cd1	122.4 (2)	C13—C12—H12	118.9
C15—N1—Cd1	120.9 (2)	C8—C13—H13	120.1
C22—N2—C23	117.1 (3)	C12—C13—H13	120.1
C22—N2—Cd1^iv	119.8 (2)	C11—C14—H14a	109.5
C23—N2—Cd1^iv	121.9 (2)	C11—C14—H14b	109.5
C2—C1—C6	119.5 (3)	H14a—C14—H14b	109.5
C2—C1—S1	120.4 (3)	C11—C14—H14C	109.5
C6—C1—S1	120.1 (3)	H14a—C14—H14C	109.5
C1—C2—C3	120.1 (4)	H14b—C14—H14C	109.5
C2—C3—C4	121.5 (4)	N1—C15—H15	118.4
C5—C4—C3	117.6 (4)	C16—C15—H15	118.4
C5—C4—C7	121.7 (4)	C15—C16—H16	120.0
C3—C4—C7	120.7 (4)	C17—C16—H16	120.0
C4—C5—C6	122.5 (4)	C19—C18—H18	120.0
C1—C6—C5	118.7 (4)	C17—C18—H18	120.0
C13—C8—C9	118.8 (4)	N1—C19—H19	118.2
C13—C8—S2	122.5 (3)	C18—C19—H19	118.2
C9—C8—S2	118.7 (3)	C20—C21—H21	119.9
C10—C9—C8	119.3 (5)	C22—C21—H21	119.9
C11—C10—C9	123.0 (5)	N2—C22—H22	118.4
C10—C11—C12	116.9 (5)	C21—C22—H22	118.4
C10—C11—C14	122.1 (6)	N2—C23—H23	118.3
C12—C11—C14	121.1 (6)	C24—C23—H23	118.3
C11—C12—C13	122.1 (5)	C23—C24—H24	120.1
C8—C13—C12	119.9 (4)	C20—C24—H24	120.1
N1—C15—C16	123.3 (3)
O3—S1—O1—Cd1	−127.8 (2)	C7—C4—C5—C6	178.7 (5)
O2—S1—O1—Cd1	1.7 (3)	C2—C1—C6—C5	2.4 (6)
C1—S1—O1—Cd1	115.7 (2)	S1—C1—C6—C5	−178.7 (3)
O5^ii—Cd1—O1—S1	−152.7 (3)	C4—C5—C6—C1	−1.7 (7)
O2^i—Cd1—O1—S1	30.3 (3)	O6—S2—C8—C13	−107.4 (3)
N1—Cd1—O1—S1	−60.3 (2)	O5—S2—C8—C13	132.3 (3)
N2^iii—Cd1—O1—S1	178.8 (3)	O4—S2—C8—C13	13.7 (4)
O4—Cd1—O1—S1	109.2 (2)	O6—S2—C8—C9	73.2 (5)
O3—S1—O2—Cd1^i	26.4 (3)	O5—S2—C8—C9	−47.0 (5)
O1—S1—O2—Cd1^i	−102.6 (3)	O4—S2—C8—C9	−165.7 (4)
C1—S1—O2—Cd1^i	142.9 (3)	C13—C8—C9—C10	2 (1)
O6—S2—O4—Cd1	−162.6 (2)	S2—C8—C9—C10	−178.8 (6)
O5—S2—O4—Cd1	−34.6 (3)	C8—C9—C10—C11	−2 (1)
C8—S2—O4—Cd1	79.3 (3)	C9—C10—C11—C12	1 (1)
O5^ii—Cd1—O4—S2	49.6 (2)	C9—C10—C11—C14	−178.4 (7)
O1—Cd1—O4—S2	129.7 (2)	C10—C11—C12—C13	0 (1)
O2^i—Cd1—O4—S2	−129.5 (2)	C14—C11—C12—C13	179.7 (5)
N1—Cd1—O4—S2	−167.6 (3)	C9—C8—C13—C12	−0.5 (7)
N2^iii—Cd1—O4—S2	−38.7 (2)	S2—C8—C13—C12	−179.9 (4)
O6—S2—O5—Cd1^ii	49.0 (6)	C11—C12—C13—C8	−0.5 (8)
O4—S2—O5—Cd1^ii	−78.8 (6)	C19—N1—C15—C16	1.3 (5)
C8—S2—O5—Cd1^ii	165.9 (6)	Cd1—N1—C15—C16	−179.2 (3)
O5^ii—Cd1—N1—C19	151.2 (3)	N1—C15—C16—C17	1.1 (6)
O1—Cd1—N1—C19	70.3 (3)	C15—C16—C17—C18	−3.0 (6)
O2^i—Cd1—N1—C19	−29.4 (3)	C15—C16—C17—C20	177.1 (3)
N2^iii—Cd1—N1—C19	−120.4 (3)	C16—C17—C18—C19	2.6 (5)
O4—Cd1—N1—C19	8.1 (6)	C20—C17—C18—C19	−177.5 (3)
O5^ii—Cd1—N1—C15	−28.3 (3)	C15—N1—C19—C18	−1.7 (5)
O1—Cd1—N1—C15	−109.2 (3)	Cd1—N1—C19—C18	178.8 (3)
O2^i—Cd1—N1—C15	151.1 (3)	C17—C18—C19—N1	−0.3 (6)
N2^iii—Cd1—N1—C15	60.2 (3)	C18—C17—C20—C21	171.9 (4)
O4—Cd1—N1—C15	−171.4 (4)	C16—C17—C20—C21	−8.2 (5)
O3—S1—C1—C2	−168.7 (3)	C18—C17—C20—C24	−6.9 (5)
O1—S1—C1—C2	−47.6 (3)	C16—C17—C20—C24	173.0 (4)
O2—S1—C1—C2	69.6 (3)	C24—C20—C21—C22	1.3 (5)
O3—S1—C1—C6	12.4 (3)	C17—C20—C21—C22	−177.5 (3)
O1—S1—C1—C6	133.5 (3)	C23—N2—C22—C21	−0.1 (5)
O2—S1—C1—C6	−109.3 (3)	Cd1^iv—N2—C22—C21	167.6 (3)
C6—C1—C2—C3	−1.4 (6)	C20—C21—C22—N2	−1.3 (6)
S1—C1—C2—C3	179.8 (4)	C22—N2—C23—C24	1.4 (5)
C1—C2—C3—C4	−0.5 (8)	Cd1^iv—N2—C23—C24	−166.0 (3)
C2—C3—C4—C5	1.3 (8)	N2—C23—C24—C20	−1.3 (6)
C2—C3—C4—C7	−177.6 (5)	C21—C20—C24—C23	−0.1 (5)
C3—C4—C5—C6	−0.2 (8)	C17—C20—C24—C23	178.7 (3)

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