A discrete zinc(II) coordination complex, [Zn(bpy)(H2O)4](tp) [bpy = 2,2′-bipyridine (C10H8N2) and tp = terephthalate (C8H4O4)], has been prepared from the hydrothermal reaction of Zn(CH3COO)2·2H2O, bpy and terephthalic acid in water. The zinc ion has a distorted octahedral coordination environment, with two N atoms from bpy and four water molecules. The terephthalate anion does not coordinate to the ZnII metal center. Hydrogen bonds and π–π stacking interactions play important roles in the production of a three-dimensional supramolecular structure.
Supporting information
CCDC reference: 234786
Key indicators
- Single-crystal X-ray study
- T = 293 K
- Mean (C-C) = 0.007 Å
- R factor = 0.060
- wR factor = 0.201
- Data-to-parameter ratio = 15.7
checkCIF/PLATON results
No syntax errors found
Alert level C
PLAT094_ALERT_2_C Ratio of Maximum / Minimum Residual Density .... 3.90
PLAT152_ALERT_1_C Supplied and Calc Volume s.u. Inconsistent ..... ?
PLAT250_ALERT_2_C Large U3/U1 ratio for average U(i,j) tensor .... 2.08
PLAT341_ALERT_3_C Low Bond Precision on C-C bonds (x 1000) Ang ... 7
PLAT731_ALERT_1_C Bond Calc 0.85(7), Rep 0.85(2) ...... 3.50 su-Rat
O8W -H2 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.84(6), Rep 0.84(2) ...... 3.00 su-Rat
O7W -H7 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.85(7), Rep 0.85(2) ...... 3.50 su-Rat
O7W -H3 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.85(6), Rep 0.85(2) ...... 3.00 su-Rat
O6W -H6 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.84(6), Rep 0.84(2) ...... 3.00 su-Rat
O6W -H1 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.85(6), Rep 0.85(2) ...... 3.00 su-Rat
O5W -H5 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.85(5), Rep 0.84(2) ...... 2.50 su-Rat
O5W -H11 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.84(6), Rep 0.84(2) ...... 3.00 su-Rat
O7W -H7 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.85(6), Rep 0.85(2) ...... 3.00 su-Rat
O6W -H6 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.85(6), Rep 0.85(2) ...... 3.00 su-Rat
O5W -H5 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.85(7), Rep 0.85(2) ...... 3.50 su-Rat
O7W -H3 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.85(7), Rep 0.85(2) ...... 3.50 su-Rat
O8W -H2 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.84(6), Rep 0.84(2) ...... 3.00 su-Rat
O6W -H1 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.85(5), Rep 0.84(2) ...... 2.50 su-Rat
O5W -H11 1.555 1.555
PLAT736_ALERT_1_C H...A Calc 1.79(6), Rep 1.78(2) ...... 3.00 su-Rat
H6 -O1 1.555 1.555
PLAT736_ALERT_1_C H...A Calc 1.91(7), Rep 1.90(3) ...... 2.33 su-Rat
H3 -O3 1.555 1.654
PLAT736_ALERT_1_C H...A Calc 1.91(6), Rep 1.90(2) ...... 3.00 su-Rat
H2 -O2 1.555 1.555
PLAT736_ALERT_1_C H...A Calc 1.87(5), Rep 1.87(2) ...... 2.50 su-Rat
H11 -O1 1.555 4.575
PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 2
C8 H4 O4
0 ALERT level A = In general: serious problem
0 ALERT level B = Potentially serious problem
23 ALERT level C = Check and explain
0 ALERT level G = General alerts; check
19 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
2 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
1 ALERT type 4 Improvement, methodology, query or suggestion
Data collection: PROCESS-AUTO (Rigaku, 1998); cell refinement: PROCESS-AUTO; data reduction: RAPID-AUTO (Rigaku, 1998); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: SHELXTL/PC (Sheldrick, 1997).
Tetraaqua(2,2'-bipyridine)zinc(II) terephthalate
top
Crystal data top
[Zn(C10H8N2)(H2O)4](C8H4O4) | F(000) = 944 |
Mr = 457.73 | Dx = 1.556 Mg m−3 |
Monoclinic, P21/c | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -P 2ybc | Cell parameters from 13997 reflections |
a = 7.641 (2) Å | θ = 1.7–27.5° |
b = 23.508 (5) Å | µ = 1.31 mm−1 |
c = 11.134 (2) Å | T = 293 K |
β = 102.40 (3)° | Block, colorless |
V = 1953.5 (7) Å3 | 0.41 × 0.38 × 0.23 mm |
Z = 4 | |
Data collection top
Rigaku R-AXIS RAPID diffractometer | 4476 independent reflections |
Radiation source: fine-focus sealed tube | 3222 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.054 |
Detector resolution: 10.00 pixels mm-1 | θmax = 27.5°, θmin = 1.7° |
ω scans | h = 0→9 |
Absorption correction: multi-scan (ABSCOR; Higashi, 1995) | k = 0→30 |
Tmin = 0.540, Tmax = 0.737 | l = −14→14 |
4476 measured reflections | |
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)] = 0.060 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.202 | H atoms treated by a mixture of independent and constrained refinement |
S = 1.10 | w = 1/[σ2(Fo2)(0.1219P)2.4398P] where P = (Fo2 + 2Fc2)/3 |
4476 reflections | (Δ/σ)max < 0.001 |
286 parameters | Δρmax = 2.25 e Å−3 |
8 restraints | Δρmin = −0.58 e Å−3 |
Special details top
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 (Å2) top | x | y | z | Uiso*/Ueq | |
Zn1 | 0.71111 (6) | 0.63942 (2) | 0.77627 (4) | 0.02283 (19) | |
O8W | 0.4267 (5) | 0.63496 (17) | 0.7618 (3) | 0.0398 (8) | |
O4 | −0.1296 (4) | 0.69475 (15) | 1.4610 (3) | 0.0348 (8) | |
O7W | 0.9920 (5) | 0.64433 (19) | 0.7876 (3) | 0.0433 (9) | |
O6W | 0.7243 (5) | 0.70105 (15) | 0.9069 (3) | 0.0387 (8) | |
O2 | 0.2964 (5) | 0.66631 (18) | 0.9635 (3) | 0.0408 (9) | |
N1 | 0.7397 (5) | 0.57087 (15) | 0.9059 (4) | 0.0301 (8) | |
O5W | 0.6744 (5) | 0.69313 (14) | 0.6297 (3) | 0.0326 (7) | |
O3 | 0.1231 (5) | 0.66285 (18) | 1.5811 (3) | 0.0432 (9) | |
C10 | 0.7093 (9) | 0.5640 (2) | 0.5447 (5) | 0.0451 (13) | |
H20A | 0.6891 | 0.5982 | 0.5022 | 0.080* | |
N2 | 0.7144 (5) | 0.56418 (16) | 0.6649 (3) | 0.0312 (8) | |
O1 | 0.5448 (4) | 0.69988 (14) | 1.0846 (3) | 0.0349 (7) | |
C17 | 0.3118 (6) | 0.6841 (2) | 1.3916 (4) | 0.0306 (10) | |
H36A | 0.3810 | 0.6833 | 1.4713 | 0.080* | |
C20 | 0.0341 (6) | 0.68061 (17) | 1.4817 (4) | 0.0254 (9) | |
C19 | 0.3831 (6) | 0.68417 (18) | 1.0655 (4) | 0.0264 (9) | |
C15 | 0.0218 (6) | 0.6857 (2) | 1.2528 (4) | 0.0320 (10) | |
H32A | −0.1025 | 0.6872 | 1.2393 | 0.080* | |
C16 | 0.1238 (6) | 0.68378 (17) | 1.3723 (4) | 0.0233 (8) | |
C11 | 0.7480 (6) | 0.51835 (19) | 0.8605 (4) | 0.0308 (9) | |
C12 | 0.7442 (6) | 0.51529 (19) | 0.7271 (4) | 0.0303 (9) | |
C1 | 0.7436 (8) | 0.5767 (2) | 1.0266 (5) | 0.0415 (12) | |
H11A | 0.7367 | 0.6132 | 1.0578 | 0.080* | |
C13 | 0.2912 (6) | 0.68542 (17) | 1.1718 (4) | 0.0239 (8) | |
C18 | 0.3945 (6) | 0.6857 (2) | 1.2920 (4) | 0.0305 (10) | |
H35A | 0.5189 | 0.6869 | 1.3052 | 0.080* | |
C14 | 0.1054 (6) | 0.6855 (2) | 1.1535 (4) | 0.0325 (10) | |
H33A | 0.0362 | 0.6854 | 1.0739 | 0.080* | |
C4 | 0.7599 (9) | 0.4708 (2) | 0.9366 (5) | 0.0475 (14) | |
H14A | 0.7657 | 0.4345 | 0.9042 | 0.080* | |
C7 | 0.7695 (9) | 0.4650 (2) | 0.6667 (6) | 0.0489 (14) | |
H17A | 0.7906 | 0.4311 | 0.7107 | 0.080* | |
C9 | 0.7327 (10) | 0.5151 (3) | 0.4792 (6) | 0.0587 (17) | |
H19A | 0.7276 | 0.5164 | 0.3951 | 0.080* | |
C2 | 0.7575 (10) | 0.5310 (3) | 1.1070 (6) | 0.0578 (16) | |
H12A | 0.7627 | 0.5364 | 1.1904 | 0.080* | |
C8 | 0.7634 (10) | 0.4653 (3) | 0.5431 (6) | 0.0594 (17) | |
H18A | 0.7801 | 0.4317 | 0.5027 | 0.080* | |
C3 | 0.7632 (10) | 0.4774 (3) | 1.0586 (6) | 0.0606 (18) | |
H13A | 0.7693 | 0.4457 | 1.1091 | 0.080* | |
H7 | 1.066 (9) | 0.654 (3) | 0.852 (4) | 0.080* | |
H6 | 0.668 (9) | 0.700 (4) | 0.965 (5) | 0.080* | |
H5 | 0.749 (8) | 0.696 (3) | 0.583 (6) | 0.080* | |
H4 | 0.375 (11) | 0.644 (3) | 0.690 (3) | 0.080* | |
H3 | 1.050 (10) | 0.650 (3) | 0.732 (6) | 0.080* | |
H2 | 0.377 (10) | 0.647 (3) | 0.818 (5) | 0.080* | |
H1 | 0.783 (9) | 0.7315 (19) | 0.911 (7) | 0.080* | |
H11 | 0.626 (10) | 0.7256 (16) | 0.620 (7) | 0.080* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn1 | 0.0272 (3) | 0.0227 (3) | 0.0203 (3) | 0.00129 (19) | 0.00877 (18) | 0.00109 (18) |
O8W | 0.0292 (17) | 0.061 (2) | 0.0305 (17) | 0.0017 (16) | 0.0096 (14) | −0.0010 (17) |
O4 | 0.0336 (17) | 0.0439 (19) | 0.0315 (17) | 0.0144 (15) | 0.0171 (14) | 0.0109 (14) |
O7W | 0.0254 (17) | 0.078 (3) | 0.0287 (18) | −0.0013 (17) | 0.0097 (14) | 0.0018 (18) |
O6W | 0.051 (2) | 0.0325 (17) | 0.0410 (19) | −0.0118 (16) | 0.0294 (17) | −0.0148 (15) |
O2 | 0.0386 (18) | 0.067 (2) | 0.0198 (16) | −0.0089 (18) | 0.0138 (13) | −0.0075 (15) |
N1 | 0.034 (2) | 0.0264 (18) | 0.033 (2) | 0.0020 (16) | 0.0123 (16) | 0.0050 (15) |
O5W | 0.0381 (18) | 0.0323 (17) | 0.0327 (17) | 0.0093 (14) | 0.0196 (14) | 0.0103 (14) |
O3 | 0.0387 (19) | 0.068 (2) | 0.0251 (17) | 0.0103 (18) | 0.0117 (14) | 0.0077 (16) |
C10 | 0.072 (4) | 0.037 (3) | 0.029 (2) | −0.001 (3) | 0.017 (2) | −0.002 (2) |
N2 | 0.040 (2) | 0.0257 (18) | 0.0298 (19) | 0.0007 (16) | 0.0127 (16) | −0.0012 (15) |
O1 | 0.0339 (17) | 0.0378 (17) | 0.0377 (18) | −0.0122 (15) | 0.0184 (14) | −0.0107 (15) |
C17 | 0.030 (2) | 0.039 (2) | 0.024 (2) | −0.0044 (19) | 0.0088 (17) | −0.0036 (18) |
C20 | 0.034 (2) | 0.026 (2) | 0.0220 (19) | 0.0027 (17) | 0.0184 (17) | 0.0006 (16) |
C19 | 0.032 (2) | 0.024 (2) | 0.026 (2) | −0.0020 (17) | 0.0120 (17) | −0.0002 (16) |
C15 | 0.027 (2) | 0.045 (3) | 0.025 (2) | 0.0048 (19) | 0.0067 (17) | 0.0020 (19) |
C16 | 0.026 (2) | 0.027 (2) | 0.0202 (18) | 0.0029 (16) | 0.0119 (15) | 0.0014 (15) |
C11 | 0.033 (2) | 0.026 (2) | 0.034 (2) | 0.0010 (18) | 0.0070 (18) | 0.0047 (18) |
C12 | 0.031 (2) | 0.024 (2) | 0.035 (2) | 0.0008 (17) | 0.0072 (18) | −0.0034 (18) |
C1 | 0.054 (3) | 0.042 (3) | 0.031 (2) | 0.005 (2) | 0.016 (2) | 0.007 (2) |
C13 | 0.029 (2) | 0.026 (2) | 0.0186 (18) | −0.0033 (16) | 0.0105 (15) | −0.0002 (16) |
C18 | 0.025 (2) | 0.041 (3) | 0.028 (2) | −0.0049 (19) | 0.0113 (17) | −0.0036 (18) |
C14 | 0.032 (2) | 0.044 (3) | 0.022 (2) | 0.003 (2) | 0.0067 (17) | 0.0002 (18) |
C4 | 0.066 (4) | 0.027 (2) | 0.050 (3) | 0.004 (2) | 0.014 (3) | 0.008 (2) |
C7 | 0.067 (4) | 0.027 (2) | 0.054 (3) | 0.005 (2) | 0.016 (3) | −0.008 (2) |
C9 | 0.091 (5) | 0.050 (4) | 0.040 (3) | −0.003 (3) | 0.026 (3) | −0.012 (3) |
C2 | 0.079 (5) | 0.058 (4) | 0.038 (3) | 0.007 (3) | 0.018 (3) | 0.016 (3) |
C8 | 0.090 (5) | 0.041 (3) | 0.052 (3) | 0.008 (3) | 0.024 (3) | −0.018 (3) |
C3 | 0.094 (5) | 0.045 (3) | 0.043 (3) | 0.001 (3) | 0.014 (3) | 0.022 (3) |
Geometric parameters (Å, º) top
Zn1—O5W | 2.034 (3) | C17—H36A | 0.9300 |
Zn1—O6W | 2.040 (3) | C20—C16 | 1.523 (5) |
Zn1—O7W | 2.126 (4) | C19—C13 | 1.501 (6) |
Zn1—N1 | 2.143 (4) | C15—C14 | 1.391 (6) |
Zn1—O8W | 2.147 (4) | C15—C16 | 1.391 (6) |
Zn1—N2 | 2.164 (4) | C15—H32A | 0.9300 |
O8W—H4 | 0.84 (2) | C11—C4 | 1.395 (7) |
O8W—H2 | 0.85 (2) | C11—C12 | 1.481 (7) |
O4—C20 | 1.266 (5) | C12—C7 | 1.394 (7) |
O7W—H7 | 0.84 (2) | C1—C2 | 1.387 (7) |
O7W—H3 | 0.85 (2) | C1—H11A | 0.9300 |
O6W—H6 | 0.85 (2) | C13—C14 | 1.390 (6) |
O6W—H1 | 0.84 (2) | C13—C18 | 1.400 (6) |
O2—C19 | 1.257 (5) | C18—H35A | 0.9300 |
N1—C11 | 1.341 (6) | C14—H33A | 0.9300 |
N1—C1 | 1.345 (6) | C4—C3 | 1.361 (9) |
O5W—H5 | 0.85 (2) | C4—H14A | 0.9300 |
O5W—H11 | 0.84 (2) | C7—C8 | 1.368 (9) |
O3—C20 | 1.240 (5) | C7—H17A | 0.9300 |
C10—N2 | 1.330 (6) | C9—C8 | 1.364 (9) |
C10—C9 | 1.392 (8) | C9—H19A | 0.9300 |
C10—H20A | 0.9300 | C2—C3 | 1.375 (9) |
N2—C12 | 1.336 (6) | C2—H12A | 0.9300 |
O1—C19 | 1.263 (6) | C8—H18A | 0.9300 |
C17—C18 | 1.390 (6) | C3—H13A | 0.9300 |
C17—C16 | 1.406 (6) | | |
| | | |
O5W—Zn1—O6W | 96.22 (15) | O1—C19—C13 | 117.9 (4) |
O5W—Zn1—O7W | 88.71 (14) | C14—C15—C16 | 120.1 (4) |
O6W—Zn1—O7W | 91.41 (15) | C14—C15—H32A | 119.9 |
O5W—Zn1—N1 | 169.56 (15) | C16—C15—H32A | 119.9 |
O6W—Zn1—N1 | 94.11 (15) | C15—C16—C17 | 119.3 (4) |
O7W—Zn1—N1 | 92.60 (15) | C15—C16—C20 | 120.7 (4) |
O5W—Zn1—O8W | 90.41 (14) | C17—C16—C20 | 119.9 (4) |
O6W—Zn1—O8W | 88.98 (15) | N1—C11—C4 | 120.7 (5) |
O7W—Zn1—O8W | 179.07 (14) | N1—C11—C12 | 115.5 (4) |
N1—Zn1—O8W | 88.21 (15) | C4—C11—C12 | 123.7 (4) |
O5W—Zn1—N2 | 93.67 (14) | N2—C12—C7 | 120.4 (5) |
O6W—Zn1—N2 | 169.89 (15) | N2—C12—C11 | 116.3 (4) |
O7W—Zn1—N2 | 86.70 (16) | C7—C12—C11 | 123.3 (4) |
N1—Zn1—N2 | 76.08 (15) | N1—C1—C2 | 123.2 (5) |
O8W—Zn1—N2 | 93.06 (15) | N1—C1—H11A | 118.4 |
Zn1—O8W—H4 | 109 (6) | C2—C1—H11A | 118.4 |
Zn1—O8W—H2 | 123 (6) | C14—C13—C18 | 119.2 (4) |
H4—O8W—H2 | 116 (8) | C14—C13—C19 | 121.4 (4) |
Zn1—O7W—H7 | 123 (6) | C18—C13—C19 | 119.4 (4) |
Zn1—O7W—H3 | 130 (6) | C17—C18—C13 | 120.2 (4) |
H7—O7W—H3 | 103 (8) | C17—C18—H35A | 119.9 |
Zn1—O6W—H6 | 124 (6) | C13—C18—H35A | 119.9 |
Zn1—O6W—H1 | 126 (6) | C13—C14—C15 | 120.8 (4) |
H6—O6W—H1 | 110 (8) | C13—C14—H33A | 119.6 |
C11—N1—C1 | 118.6 (4) | C15—C14—H33A | 119.6 |
C11—N1—Zn1 | 116.4 (3) | C3—C4—C11 | 119.9 (5) |
C1—N1—Zn1 | 125.0 (3) | C3—C4—H14A | 120.0 |
Zn1—O5W—H5 | 123 (5) | C11—C4—H14A | 120.0 |
Zn1—O5W—H11 | 130 (5) | C8—C7—C12 | 120.1 (5) |
H5—O5W—H11 | 100 (7) | C8—C7—H17A | 119.9 |
N2—C10—C9 | 123.4 (5) | C12—C7—H17A | 119.9 |
N2—C10—H20A | 118.3 | C8—C9—C10 | 117.5 (5) |
C9—C10—H20A | 118.3 | C8—C9—H19A | 121.2 |
C10—N2—C12 | 118.9 (4) | C10—C9—H19A | 121.2 |
C10—N2—Zn1 | 125.3 (3) | C3—C2—C1 | 117.5 (6) |
C12—N2—Zn1 | 115.3 (3) | C3—C2—H12A | 121.3 |
C18—C17—C16 | 120.2 (4) | C1—C2—H12A | 121.3 |
C18—C17—H36A | 119.9 | C9—C8—C7 | 119.7 (5) |
C16—C17—H36A | 119.9 | C9—C8—H18A | 120.2 |
O3—C20—O4 | 125.6 (4) | C7—C8—H18A | 120.2 |
O3—C20—C16 | 118.4 (4) | C4—C3—C2 | 120.1 (5) |
O4—C20—C16 | 116.0 (4) | C4—C3—H13A | 120.0 |
O2—C19—O1 | 123.8 (4) | C2—C3—H13A | 120.0 |
O2—C19—C13 | 118.3 (4) | | |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
O7W—H7···O2i | 0.84 (2) | 1.95 (4) | 2.749 (5) | 159 (8) |
O6W—H6···O1 | 0.85 (2) | 1.78 (2) | 2.638 (5) | 178 (9) |
O5W—H5···O4ii | 0.85 (2) | 1.80 (3) | 2.643 (4) | 167 (8) |
O8W—H4···O3iii | 0.84 (2) | 2.09 (6) | 2.803 (5) | 142 (8) |
O7W—H3···O3ii | 0.85 (2) | 1.90 (3) | 2.732 (5) | 166 (8) |
O8W—H2···O2 | 0.85 (2) | 1.90 (2) | 2.745 (5) | 170 (8) |
O6W—H1···O4iv | 0.84 (2) | 1.90 (3) | 2.706 (5) | 160 (8) |
O5W—H11···O1v | 0.84 (2) | 1.87 (2) | 2.710 (5) | 171 (8) |
Symmetry codes: (i) x+1, y, z; (ii) x+1, y, z−1; (iii) x, y, z−1; (iv) x+1, −y+3/2, z−1/2; (v) x, −y+3/2, z−1/2. |