In the title compound, [Cd(C9H6O5)(C3H4N2)(H2O)2]·3H2O, the carboxylatophenoxyacetate dianion links the water- and imidazole-coordinated Cd atoms into a zigzag chain that runs along the c axis of the monoclinic unit cell; the chelation by the carboxylate arms leads to a seven-coordinate pentagonal–bipyramidal geometry for the Cd atom. The chains are linked into a three-dimensional network by hydrogen bonds.
Supporting information
CCDC reference: 268453
Key indicators
- Single-crystal X-ray study
- T = 295 K
- Mean (C-C) = 0.003 Å
- Disorder in solvent or counterion
- R factor = 0.024
- wR factor = 0.063
- Data-to-parameter ratio = 16.9
checkCIF/PLATON results
No syntax errors found
Alert level B
PLAT061_ALERT_3_B Tmax/Tmin Range Test RR' too Large ............. 0.75
PLAT417_ALERT_2_B Short Inter D-H..H-D H4W1 .. H5W1 .. 2.01 Ang.
PLAT737_ALERT_1_B D...A Calc 2.810(10), Rep 2.809(2) ...... 5.00 su-Rat
O3W -O4 1.555 3.666
PLAT737_ALERT_1_B D...A Calc 2.840(10), Rep 2.839(2) ...... 5.00 su-Rat
O3W -O5 1.555 4.576
PLAT737_ALERT_1_B D...A Calc 2.822(17), Rep 2.823(3) ...... 5.67 su-Rat
N2 -O3W 1.555 3.566
Alert level C
ABSTM02_ALERT_3_C The ratio of expected to reported Tmax/Tmin(RR') is < 0.90
Tmin and Tmax reported: 0.478 0.801
Tmin' and Tmax expected: 0.623 0.793
RR' = 0.760
Please check that your absorption correction is appropriate.
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ .... ?
PLAT094_ALERT_2_C Ratio of Maximum / Minimum Residual Density .... 2.16
PLAT241_ALERT_2_C Check High Ueq as Compared to Neighbors for O3
PLAT302_ALERT_4_C Anion/Solvent Disorder ......................... 25.00 Perc.
PLAT417_ALERT_2_C Short Inter D-H..H-D H3W1 .. H4W2 .. 2.14 Ang.
PLAT720_ALERT_4_C Number of Unusual/Non-Standard Label(s) ........ 13
PLAT737_ALERT_1_C D...A Calc 2.777(9), Rep 2.775(3) ...... 3.00 su-Rat
O4W -O3W 1.555 2.556
0 ALERT level A = In general: serious problem
5 ALERT level B = Potentially serious problem
8 ALERT level C = Check and explain
0 ALERT level G = General alerts; check
5 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
4 ALERT type 2 Indicator that the structure model may be wrong or deficient
2 ALERT type 3 Indicator that the structure quality may be low
2 ALERT type 4 Improvement, methodology, query or suggestion
Data collection: RAPID-AUTO (Rigaku, 1998); cell refinement: RAPID-AUTO; data reduction: CrystalStructure (Rigaku/MSC, 2002); 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.
catena-Poly[[[diaqua(imidazole)cadmium(II)]-µ-3-carboxylatophenoxyacetato] trihydrate]
top
Crystal data top
[Cd(C9H6O5)(C3H4N2)(H2O)2]·3H2O | F(000) = 936 |
Mr = 464.70 | Dx = 1.746 Mg m−3 |
Monoclinic, P21/n | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -P 2yn | Cell parameters from 15434 reflections |
a = 8.574 (2) Å | θ = 3.0–27.5° |
b = 11.467 (2) Å | µ = 1.29 mm−1 |
c = 18.374 (3) Å | T = 295 K |
β = 101.88 (3)° | Block, colorless |
V = 1767.9 (6) Å3 | 0.36 × 0.25 × 0.18 mm |
Z = 4 | |
Data collection top
Rigaki R-AXIS RAPID IP diffractometer | 3995 independent reflections |
Radiation source: fine-focus sealed tube | 3607 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.018 |
ω scans | θmax = 27.5°, θmin = 3.0° |
Absorption correction: multi-scan (ABSCOR; Higashi, 1995) | h = −11→9 |
Tmin = 0.478, Tmax = 0.801 | k = −14→14 |
16669 measured reflections | l = −23→23 |
Refinement top
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.024 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.063 | H-atom parameters constrained |
S = 1.06 | w = 1/[σ2(Fo2) + (0.0394P)2 + 0.5011P] where P = (Fo2 + 2Fc2)/3 |
3995 reflections | (Δ/σ)max = 0.001 |
237 parameters | Δρmax = 0.67 e Å−3 |
0 restraints | Δρmin = −0.31 e Å−3 |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Cd1 | 0.46649 (2) | 0.58361 (1) | 0.64668 (1) | 0.03011 (6) | |
O1 | 0.5231 (2) | 0.7900 (1) | 0.6438 (1) | 0.0423 (3) | |
O2 | 0.5552 (2) | 0.6852 (1) | 0.5486 (1) | 0.0370 (3) | |
O3 | 0.7954 (2) | 0.9455 (1) | 0.3878 (1) | 0.0540 (5) | |
O4 | 0.8890 (2) | 0.8888 (1) | 0.2652 (1) | 0.0450 (4) | |
O5 | 0.9147 (2) | 1.0709 (1) | 0.2335 (1) | 0.0419 (4) | |
O1w | 0.7272 (2) | 0.5770 (2) | 0.7043 (1) | 0.0567 (5) | |
O2w | 0.5260 (3) | 0.4120 (1) | 0.5880 (1) | 0.0549 (5) | |
O3w | 0.1465 (2) | 0.3097 (1) | 0.650 (1) | 0.0500 (4) | |
O4w | 0.5884 (3) | 0.8880 (2) | 0.7780 (1) | 0.0983 (9) | |
O5w | 0.8634 (4) | 0.7632 (3) | 0.7895 (2) | 0.067 (1) | 0.747 (7) |
O5w' | 0.974 (2) | 0.7088 (9) | 0.7973 (5) | 0.077 (4) | 0.253 (7) |
N1 | 0.2123 (2) | 0.6040 (2) | 0.5866 (1) | 0.0396 (4) | |
N2 | 0.0056 (2) | 0.6425 (2) | 0.4983 (1) | 0.0475 (4) | |
C1 | 0.0807 (3) | 0.6189 (2) | 0.6174 (1) | 0.0464 (5) | |
C2 | −0.0465 (3) | 0.6423 (2) | 0.5638 (2) | 0.0524 (6) | |
C3 | 0.1611 (3) | 0.6186 (2) | 0.5143 (1) | 0.0420 (5) | |
C4 | 0.5689 (2) | 0.7803 (2) | 0.5832 (1) | 0.0307 (4) | |
C5 | 0.6455 (2) | 0.8823 (2) | 0.5533 (1) | 0.0306 (4) | |
C6 | 0.6776 (3) | 0.9855 (2) | 0.5935 (1) | 0.0423 (5) | |
C7 | 0.7516 (3) | 1.0766 (2) | 0.5648 (1) | 0.0475 (6) | |
C8 | 0.7929 (3) | 1.0670 (2) | 0.4959 (1) | 0.0397 (5) | |
C9 | 0.7602 (2) | 0.9649 (2) | 0.4563 (1) | 0.0354 (4) | |
C10 | 0.6870 (2) | 0.8723 (2) | 0.4849 (1) | 0.0339 (4) | |
C11 | 0.8541 (3) | 1.0392 (2) | 0.3513 (1) | 0.0397 (4) | |
C12 | 0.8871 (2) | 0.9944 (2) | 0.2785 (1) | 0.0351 (4) | |
H1w1 | 0.7778 | 0.6301 | 0.7288 | 0.068* | |
H1w2 | 0.7796 | 0.5173 | 0.7088 | 0.068* | |
H2w1 | 0.5459 | 0.3583 | 0.6181 | 0.066* | |
H2w2 | 0.4911 | 0.3823 | 0.5465 | 0.066* | |
H3w1 | 0.1486 | 0.2442 | 0.6688 | 0.060* | |
H3w2 | 0.2330 | 0.3420 | 0.6669 | 0.060* | |
H4w1 | 0.5656 | 0.8635 | 0.7345 | 0.118* | |
H4w2 | 0.5251 | 0.8594 | 0.8014 | 0.118* | |
H5w1 | 0.7903 | 0.8091 | 0.7730 | 0.081* | 0.747 (7) |
H5w2 | 0.9313 | 0.7802 | 0.7655 | 0.081* | 0.747 (7) |
H5w3 | 1.0335 | 0.7323 | 0.7700 | 0.092* | 0.253 (7) |
H5w4 | 1.0267 | 0.6542 | 0.8216 | 0.092* | 0.253 (7) |
H2n | −0.0514 | 0.6556 | 0.4548 | 0.066 (9)* | |
H1 | 0.0801 | 0.6136 | 0.6678 | 0.056* | |
H2 | −0.1500 | 0.6557 | 0.5699 | 0.063* | |
H3 | 0.2251 | 0.6130 | 0.4792 | 0.050* | |
H6 | 0.6493 | 0.9931 | 0.6394 | 0.051* | |
H7 | 0.7740 | 1.1452 | 0.5920 | 0.057* | |
H8 | 0.8421 | 1.1287 | 0.4768 | 0.048* | |
H10 | 0.6660 | 0.8035 | 0.4579 | 0.041* | |
H11a | 0.9513 | 1.0696 | 0.3821 | 0.048* | |
H11b | 0.7761 | 1.1016 | 0.3420 | 0.048* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Cd1 | 0.03079 (9) | 0.03483 (9) | 0.02574 (9) | −0.00194 (5) | 0.00822 (6) | 0.00106 (5) |
O1 | 0.059 (1) | 0.043 (1) | 0.030 (1) | −0.007 (1) | 0.023 (1) | −0.001 (1) |
O2 | 0.047 (1) | 0.036 (1) | 0.030 (1) | −0.007 (1) | 0.015 (1) | −0.002 (1) |
O3 | 0.094 (1) | 0.038 (1) | 0.042 (1) | −0.013 (1) | 0.042 (1) | −0.007 (1) |
O4 | 0.066 (1) | 0.041 (1) | 0.033 (1) | 0.001 (1) | 0.022 (1) | 0.001 (1) |
O5 | 0.052 (1) | 0.045 (1) | 0.033 (1) | 0.000 (1) | 0.019 (1) | 0.007 (1) |
O1w | 0.041 (1) | 0.049 (1) | 0.070 (1) | 0.003 (1) | −0.011 (1) | −0.011 (1) |
O2w | 0.086 (1) | 0.045 (1) | 0.033 (1) | 0.007 (1) | 0.010 (1) | −0.008 (1) |
O3w | 0.055 (1) | 0.040 (1) | 0.051 (1) | −0.005 (1) | 0.002 (1) | 0.008 (1) |
O4w | 0.120 (2) | 0.112 (2) | 0.076 (2) | −0.070 (2) | 0.049 (2) | −0.047 (1) |
O5w | 0.067 (2) | 0.061 (2) | 0.072 (2) | −0.019 (2) | 0.009 (2) | −0.007 (1) |
O5w' | 0.079 (8) | 0.060 (6) | 0.087 (6) | −0.022 (5) | 0.007 (5) | 0.017 (4) |
N1 | 0.033 (1) | 0.046 (1) | 0.040 (1) | 0.000 (1) | 0.009 (1) | 0.004 (1) |
N2 | 0.040 (1) | 0.049 (1) | 0.049 (1) | 0.001 (1) | −0.002 (1) | 0.007 (1) |
C1 | 0.039 (1) | 0.058 (1) | 0.044 (1) | 0.003 (1) | 0.015 (1) | 0.001 (1) |
C2 | 0.035 (1) | 0.057 (2) | 0.066 (2) | 0.009 (1) | 0.012 (1) | 0.002 (1) |
C3 | 0.038 (1) | 0.048 (1) | 0.041 (1) | −0.004 (1) | 0.008 (1) | 0.005 (1) |
C4 | 0.032 (1) | 0.034 (1) | 0.027 (1) | 0.001 (1) | 0.008 (1) | 0.002 (1) |
C5 | 0.033 (1) | 0.033 (1) | 0.027 (1) | 0.001 (1) | 0.009 (1) | 0.001 (1) |
C6 | 0.057 (1) | 0.041 (1) | 0.033 (1) | −0.004 (1) | 0.020 (1) | −0.004 (1) |
C7 | 0.069 (2) | 0.037 (1) | 0.041 (1) | −0.010 (1) | 0.021 (1) | −0.009 (1) |
C8 | 0.051 (1) | 0.035 (1) | 0.039 (1) | −0.006 (1) | 0.021 (1) | −0.002 (1) |
C9 | 0.045 (1) | 0.036 (1) | 0.029 (1) | 0.002 (1) | 0.016 (1) | 0.001 (1) |
C10 | 0.044 (1) | 0.031 (1) | 0.029 (1) | 0.000 (1) | 0.012 (1) | −0.003 (1) |
C11 | 0.052 (1) | 0.040 (1) | 0.033 (1) | 0.000 (1) | 0.020 (1) | 0.002 (1) |
C12 | 0.034 (1) | 0.043 (1) | 0.030 (1) | 0.001 (1) | 0.010 (1) | 0.003 (1) |
Geometric parameters (Å, º) top
Cd1—O1 | 2.418 (2) | C9—C10 | 1.390 (3) |
Cd1—O2 | 2.398 (1) | C11—C12 | 1.513 (3) |
Cd1—O4i | 2.424 (2) | O1w—H1w1 | 0.82 |
Cd1—O5i | 2.484 (2) | O1w—H1w2 | 0.81 |
Cd1—O1w | 2.270 (2) | O2w—H2w1 | 0.82 |
Cd1—O2w | 2.350 (2) | O2w—H2w2 | 0.83 |
Cd1—N1 | 2.244 (2) | O3w—H3w1 | 0.82 |
O1—C4 | 1.259 (2) | O3w—H3w2 | 0.83 |
O2—C4 | 1.256 (2) | O4w—H4w1 | 0.83 |
O3—C9 | 1.373 (2) | O4w—H4w2 | 0.83 |
O3—C11 | 1.413 (3) | O5w—H5w1 | 0.83 |
O4—C12 | 1.236 (3) | O5w—H5w2 | 0.82 |
O5—C12 | 1.260 (2) | O5w'—H5w3 | 0.83 |
N1—C3 | 1.321 (3) | O5w'—H5w4 | 0.84 |
N1—C1 | 1.373 (3) | N2—H2n | 0.86 |
N2—C3 | 1.333 (3) | C1—H1 | 0.93 |
N2—C2 | 1.368 (3) | C2—H2 | 0.93 |
C1—C2 | 1.338 (3) | C3—H3 | 0.93 |
C4—C5 | 1.500 (3) | C6—H6 | 0.93 |
C5—C10 | 1.380 (3) | C7—H7 | 0.93 |
C5—C6 | 1.391 (3) | C8—H8 | 0.93 |
C6—C7 | 1.382 (3) | C10—H10 | 0.93 |
C7—C8 | 1.386 (3) | C11—H11a | 0.97 |
C8—C9 | 1.377 (3) | C11—H11b | 0.97 |
| | | |
O1—Cd1—O2 | 53.98 (5) | C9—C8—C7 | 119.2 (2) |
O1—Cd1—O4i | 89.16 (5) | O3—C9—C8 | 124.3 (2) |
O1—Cd1—O5i | 140.81 (5) | O3—C9—C10 | 115.1 (2) |
O1—Cd1—O1w | 81.97 (6) | C8—C9—C10 | 120.6 (2) |
O1—Cd1—O2w | 138.24 (6) | C5—C10—C9 | 120.1 (2) |
O1—Cd1—N1 | 93.80 (6) | O3—C11—C12 | 108.1 (2) |
O2—Cd1—O4i | 143.11 (5) | O4—C12—O5 | 122.7 (2) |
O2—Cd1—O5i | 162.83 (5) | O4—C12—C11 | 121.3 (2) |
O2—Cd1—O1w | 86.15 (7) | O5—C12—C11 | 116.0 (2) |
O2—Cd1—O2w | 85.97 (6) | Cd1—O1w—H1w1 | 125.9 |
O2—Cd1—N1 | 90.32 (6) | Cd1—O1w—H1w2 | 123.1 |
O4i—Cd1—O5i | 53.00 (5) | H1w1—O1w—H1w2 | 110.4 |
O4i—Cd1—O1w | 90.63 (8) | Cd1—O2w—H2w1 | 110.7 |
O4i—Cd1—O2w | 130.29 (6) | Cd1—O2w—H2w2 | 133.7 |
O4i—Cd1—N1 | 90.60 (7) | H2w1—O2w—H2w2 | 107.2 |
O5i—Cd1—O1w | 88.01 (7) | H3w1—O3w—H3w2 | 108.1 |
O5i—Cd1—O2w | 77.38 (6) | H4w1—O4w—H4w2 | 108.5 |
O5i—Cd1—N1 | 96.11 (6) | H5w1—O5w—H5w2 | 102.7 |
O1w—Cd1—O2w | 84.25 (7) | H5w3—O5w'—H5w4 | 103.6 |
O1w—Cd1—N1 | 175.58 (7) | C3—N2—H2n | 126.3 |
O2w—Cd1—N1 | 98.17 (7) | C2—N2—H2n | 126.3 |
C4—O1—Cd1 | 92.0 (1) | C2—C1—H1 | 125.2 |
C4—O2—Cd1 | 93.0 (1) | N1—C1—H1 | 125.2 |
C9—O3—C11 | 118.6 (2) | C1—C2—H2 | 126.8 |
C12—O4—Cd1ii | 93.8 (1) | N2—C2—H2 | 126.8 |
C12—O5—Cd1ii | 90.4 (1) | N1—C3—H3 | 124.5 |
C3—N1—C1 | 105.5 (2) | N2—C3—H3 | 124.5 |
C3—N1—Cd1 | 126.6 (2) | C7—C6—H6 | 120.1 |
C1—N1—Cd1 | 127.4 (2) | C5—C6—H6 | 120.1 |
C3—N2—C2 | 107.4 (2) | C6—C7—H7 | 119.6 |
C2—C1—N1 | 109.7 (2) | C8—C7—H7 | 119.6 |
C1—C2—N2 | 106.5 (2) | C9—C8—H8 | 120.4 |
N1—C3—N2 | 111.0 (2) | C7—C8—H8 | 120.4 |
O2—C4—O1 | 120.7 (2) | C5—C10—H10 | 119.9 |
O2—C4—C5 | 119.6 (2) | C9—C10—H10 | 119.9 |
O1—C4—C5 | 119.7 (2) | O3—C11—H11a | 110.1 |
C10—C5—C6 | 119.6 (2) | C12—C11—H11a | 110.1 |
C10—C5—C4 | 118.9 (2) | O3—C11—H11b | 110.1 |
C6—C5—C4 | 121.5 (2) | C12—C11—H11b | 110.1 |
C7—C6—C5 | 119.8 (2) | H11a—C11—H11b | 108.4 |
C6—C7—C8 | 120.7 (2) | | |
| | | |
N1—Cd1—O1—C4 | −91.1 (1) | C2—N2—C3—N1 | −0.5 (3) |
O1w—Cd1—O1—C4 | 87.6 (1) | Cd1—O2—C4—O1 | −6.3 (2) |
O2w—Cd1—O1—C4 | 15.6 (2) | Cd1—O2—C4—C5 | 171.6 (2) |
O2—Cd1—O1—C4 | −3.5 (1) | Cd1—O1—C4—O2 | 6.3 (2) |
O4i—Cd1—O1—C4 | 178.3 (1) | Cd1—O1—C4—C5 | −171.7 (2) |
O5i—Cd1—O1—C4 | 164.4 (1) | O2—C4—C5—C10 | 5.6 (3) |
N1—Cd1—O2—C4 | 98.0 (1) | O1—C4—C5—C10 | −176.5 (2) |
O1w—Cd1—O2—C4 | −79.4 (1) | O2—C4—C5—C6 | −173.4 (2) |
O2w—Cd1—O2—C4 | −163.9 (1) | O1—C4—C5—C6 | 4.5 (3) |
O1—Cd1—O2—C4 | 3.5 (1) | C10—C5—C6—C7 | −0.5 (3) |
O4i—Cd1—O2—C4 | 6.5 (2) | C4—C5—C6—C7 | 178.5 (2) |
O5i—Cd1—O2—C4 | −149.8 (2) | C5—C6—C7—C8 | 0.7 (4) |
O2w—Cd1—N1—C3 | −61.4 (2) | C6—C7—C8—C9 | −0.4 (4) |
O2—Cd1—N1—C3 | 24.6 (2) | C11—O3—C9—C8 | −6.8 (3) |
O1—Cd1—N1—C3 | 78.5 (2) | C11—O3—C9—C10 | 173.3 (2) |
O4i—Cd1—N1—C3 | 167.7 (2) | C7—C8—C9—O3 | 180.0 (2) |
O5i—Cd1—N1—C3 | −139.5 (2) | C7—C8—C9—C10 | −0.2 (4) |
O2w—Cd1—N1—C1 | 127.8 (2) | C6—C5—C10—C9 | −0.1 (3) |
O2—Cd1—N1—C1 | −146.2 (2) | C4—C5—C10—C9 | −179.1 (2) |
O1—Cd1—N1—C1 | −92.3 (2) | O3—C9—C10—C5 | −179.7 (2) |
O4i—Cd1—N1—C1 | −3.1 (2) | C8—C9—C10—C5 | 0.4 (3) |
O5i—Cd1—N1—C1 | 49.7 (2) | C9—O3—C11—C12 | 178.6 (2) |
C3—N1—C1—C2 | −0.1 (3) | Cd1ii—O4—C12—O5 | 2.4 (2) |
Cd1—N1—C1—C2 | 172.3 (2) | Cd1ii—O4—C12—C11 | −176.3 (2) |
N1—C1—C2—N2 | −0.2 (3) | Cd1ii—O5—C12—O4 | −2.4 (2) |
C3—N2—C2—C1 | 0.4 (3) | Cd1ii—O5—C12—C11 | 176.5 (2) |
C1—N1—C3—N2 | 0.4 (3) | O3—C11—C12—O4 | −12.6 (3) |
Cd1—N1—C3—N2 | −172.1 (1) | O3—C11—C12—O5 | 168.6 (2) |
Symmetry codes: (i) x−1/2, −y+3/2, z+1/2; (ii) x+1/2, −y+3/2, z−1/2. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
O1w—H1w1···O5w | 0.82 | 1.94 | 2.760 (3) | 171 |
O1w—H1w2···O4wiii | 0.81 | 1.85 | 2.662 (3) | 176 |
O2w—H2w1···O5wiii | 0.82 | 2.03 | 2.828 (3) | 163 |
O2w—H2w2···O2iv | 0.83 | 1.88 | 2.703 (2) | 171 |
O3w—H3w1···O4iv | 0.82 | 2.02 | 2.809 (2) | 161 |
O3w—H3w2···O5i | 0.83 | 2.03 | 2.839 (2) | 163 |
O4w—H4w2···O3wv | 0.83 | 1.96 | 2.775 (3) | 172 |
O4w—H4w1···O1 | 0.83 | 1.84 | 2.663 (3) | 172 |
O5w—H5w1···O4w | 0.83 | 1.97 | 2.729 (5) | 152 |
O5w—H5w2···O5vi | 0.82 | 2.16 | 2.784 (3) | 133 |
O5w′—H5w3···O5vi | 0.83 | 2.30 | 2.799 (8) | 119 |
N2—H2n···O3wvii | 0.86 | 1.97 | 2.823 (3) | 170 |
Symmetry codes: (i) x−1/2, −y+3/2, z+1/2; (iii) −x+3/2, y−1/2, −z+3/2; (iv) −x+1, −y+1, −z+1; (v) −x+1/2, y+1/2, −z+3/2; (vi) −x+2, −y+2, −z+1; (vii) −x, −y+1, −z+1. |