In the title compound, [Zn(C
3H
10N
2)
3]Cl
2·2H
2O, a complex three-dimensional network of N—H
O, N—H
Cl and O—H
Cl hydrogen bonds helps to establish the crystal packing.
Supporting information
CCDC reference: 647203
Key indicators
- Single-crystal X-ray study
- T = 293 K
- Mean (C-C) = 0.008 Å
- R factor = 0.042
- wR factor = 0.102
- Data-to-parameter ratio = 21.5
checkCIF/PLATON results
No syntax errors found
Alert level C
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ .... ?
PLAT062_ALERT_4_C Rescale T(min) & T(max) by ..................... 0.99
PLAT230_ALERT_2_C Hirshfeld Test Diff for N1 - C1 .. 5.63 su
PLAT232_ALERT_2_C Hirshfeld Test Diff (M-X) Zn1 - N3 .. 5.80 su
PLAT232_ALERT_2_C Hirshfeld Test Diff (M-X) Zn1 - N4 .. 7.92 su
PLAT341_ALERT_3_C Low Bond Precision on C-C bonds (x 1000) Ang ... 8
PLAT420_ALERT_2_C D-H Without Acceptor N2 - H3 ... ?
PLAT420_ALERT_2_C D-H Without Acceptor N4 - H13 ... ?
Alert level G
REFLT03_ALERT_4_G WARNING: Large fraction of Friedel related reflns may
be needed to determine absolute structure
From the CIF: _diffrn_reflns_theta_max 30.03
From the CIF: _reflns_number_total 3984
Count of symmetry unique reflns 2832
Completeness (_total/calc) 140.68%
TEST3: Check Friedels for noncentro structure
Estimate of Friedel pairs measured 1152
Fraction of Friedel pairs measured 0.407
Are heavy atom types Z>Si present yes
PLAT199_ALERT_1_G Check the Reported _cell_measurement_temperature 293 K
PLAT200_ALERT_1_G Check the Reported _diffrn_ambient_temperature . 293 K
PLAT792_ALERT_1_G Check the Absolute Configuration of C2 = ... S
PLAT792_ALERT_1_G Check the Absolute Configuration of C5 = ... S
PLAT792_ALERT_1_G Check the Absolute Configuration of C8 = ... S
0 ALERT level A = In general: serious problem
0 ALERT level B = Potentially serious problem
8 ALERT level C = Check and explain
6 ALERT level G = General alerts; check
6 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
5 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
2 ALERT type 4 Improvement, methodology, query or suggestion
0 ALERT type 5 Informative message, check
Data collection: SMART (Bruker, 1999); cell refinement: SAINT (Bruker, 1999); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 (Farrugia, 1997); software used to prepare material for publication: SHELXL97.
Tris(propane-1,2-diamine-
κ2N,
N')zinc(II) dichloride dihydrate
top
Crystal data top
[Zn(C3H10N2)3]Cl2·2H2O | F(000) = 840 |
Mr = 394.69 | Dx = 1.356 Mg m−3 |
Monoclinic, Cc | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: C -2yc | Cell parameters from 2649 reflections |
a = 12.6384 (9) Å | θ = 2.4–25.3° |
b = 17.2427 (12) Å | µ = 1.56 mm−1 |
c = 8.8721 (6) Å | T = 293 K |
β = 90.777 (1)° | Block, colourless |
V = 1933.2 (2) Å3 | 0.37 × 0.18 × 0.17 mm |
Z = 4 | |
Data collection top
Bruker SMART1000 CCD diffractometer | 3984 independent reflections |
Radiation source: fine-focus sealed tube | 3019 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.032 |
ω scans | θmax = 30.0°, θmin = 2.4° |
Absorption correction: multi-scan (SADABS; Bruker, 1999) | h = −17→10 |
Tmin = 0.597, Tmax = 0.778 | k = −24→23 |
8264 measured reflections | l = −12→10 |
Refinement top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | Hydrogen site location: difmap and geom |
R[F2 > 2σ(F2)] = 0.042 | H-atom parameters constrained |
wR(F2) = 0.102 | w = 1/[σ2(Fo2) + (0.0534P)2] where P = (Fo2 + 2Fc2)/3 |
S = 0.97 | (Δ/σ)max = 0.002 |
3984 reflections | Δρmax = 0.45 e Å−3 |
185 parameters | Δρmin = −0.28 e Å−3 |
2 restraints | Absolute structure: Flack (1983), 1152 Friedel pairs |
Primary atom site location: structure-invariant direct methods | Absolute structure parameter: 0.190 (17) |
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 | 0.15068 (4) | 0.19751 (2) | 0.16002 (4) | 0.03674 (12) | |
N1 | 0.2977 (4) | 0.2017 (2) | 0.0287 (5) | 0.0523 (12) | |
H1 | 0.2824 | 0.2008 | −0.0706 | 0.063* | |
H2 | 0.3337 | 0.2455 | 0.0497 | 0.063* | |
N2 | 0.2455 (3) | 0.1092 (3) | 0.2807 (5) | 0.0500 (11) | |
H3 | 0.2381 | 0.1144 | 0.3809 | 0.060* | |
H4 | 0.2242 | 0.0612 | 0.2539 | 0.060* | |
C1 | 0.3615 (4) | 0.1335 (3) | 0.0708 (6) | 0.0542 (13) | |
H5 | 0.4341 | 0.1411 | 0.0398 | 0.065* | |
H6 | 0.3340 | 0.0879 | 0.0196 | 0.065* | |
C2 | 0.3585 (4) | 0.1213 (3) | 0.2385 (6) | 0.0504 (12) | |
H7 | 0.3849 | 0.1683 | 0.2887 | 0.061* | |
C3 | 0.4280 (5) | 0.0527 (4) | 0.2868 (8) | 0.0848 (19) | |
H8 | 0.4206 | 0.0440 | 0.3930 | 0.127* | |
H9 | 0.5006 | 0.0640 | 0.2652 | 0.127* | |
H10 | 0.4063 | 0.0071 | 0.2325 | 0.127* | |
N3 | 0.0868 (4) | 0.3017 (2) | 0.0502 (5) | 0.0497 (11) | |
H11 | 0.1083 | 0.3040 | −0.0460 | 0.060* | |
H12 | 0.0156 | 0.3005 | 0.0502 | 0.060* | |
N4 | 0.2025 (4) | 0.2872 (2) | 0.3223 (5) | 0.0489 (11) | |
H13 | 0.1975 | 0.2693 | 0.4173 | 0.059* | |
H14 | 0.2703 | 0.3004 | 0.3059 | 0.059* | |
C4 | 0.1260 (4) | 0.3713 (3) | 0.1354 (6) | 0.0572 (14) | |
H15 | 0.1953 | 0.3857 | 0.0993 | 0.069* | |
H16 | 0.0783 | 0.4145 | 0.1175 | 0.069* | |
C5 | 0.1327 (4) | 0.3549 (3) | 0.3001 (5) | 0.0512 (11) | |
H17 | 0.0618 | 0.3395 | 0.3319 | 0.061* | |
C6 | 0.1649 (5) | 0.4231 (3) | 0.3949 (7) | 0.0716 (16) | |
H18 | 0.1680 | 0.4080 | 0.4990 | 0.107* | |
H19 | 0.1141 | 0.4641 | 0.3820 | 0.107* | |
H20 | 0.2333 | 0.4410 | 0.3644 | 0.107* | |
N5 | 0.0764 (4) | 0.1135 (3) | 0.0091 (5) | 0.0530 (11) | |
H21 | 0.0741 | 0.1324 | −0.0854 | 0.064* | |
H22 | 0.1144 | 0.0693 | 0.0087 | 0.064* | |
N6 | 0.0037 (4) | 0.1724 (3) | 0.2831 (5) | 0.0504 (11) | |
H23 | 0.0175 | 0.1697 | 0.3828 | 0.060* | |
H24 | −0.0439 | 0.2105 | 0.2669 | 0.060* | |
C7 | −0.0327 (5) | 0.0973 (3) | 0.0612 (6) | 0.0571 (14) | |
H25 | −0.0553 | 0.0471 | 0.0232 | 0.069* | |
H26 | −0.0805 | 0.1362 | 0.0202 | 0.069* | |
C8 | −0.0395 (4) | 0.0975 (3) | 0.2286 (6) | 0.0507 (12) | |
H27 | 0.0064 | 0.0561 | 0.2675 | 0.061* | |
C9 | −0.1489 (5) | 0.0813 (4) | 0.2779 (8) | 0.0782 (17) | |
H28 | −0.1518 | 0.0840 | 0.3859 | 0.117* | |
H29 | −0.1695 | 0.0304 | 0.2452 | 0.117* | |
H30 | −0.1963 | 0.1190 | 0.2347 | 0.117* | |
Cl1 | 0.44920 (12) | 0.35064 (9) | 0.16614 (16) | 0.0630 (4) | |
Cl2 | 0.82637 (11) | 0.31616 (9) | 0.14336 (16) | 0.0610 (4) | |
O1 | 0.6597 (4) | 0.4532 (2) | 0.1305 (5) | 0.0809 (14) | |
H31 | 0.6006 | 0.4251 | 0.1404 | 0.097* | |
H32 | 0.7073 | 0.4143 | 0.1341 | 0.097* | |
O2 | 0.6187 (4) | 0.2166 (2) | 0.2024 (5) | 0.0843 (13) | |
H33 | 0.5701 | 0.2546 | 0.1922 | 0.101* | |
H34 | 0.6777 | 0.2445 | 0.1859 | 0.101* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn1 | 0.0343 (2) | 0.0407 (2) | 0.0352 (2) | 0.0012 (3) | −0.00068 (15) | 0.0019 (3) |
N1 | 0.048 (3) | 0.072 (3) | 0.036 (2) | −0.004 (2) | 0.0045 (18) | 0.0002 (19) |
N2 | 0.052 (3) | 0.057 (3) | 0.041 (2) | 0.006 (2) | 0.0018 (19) | 0.0009 (18) |
C1 | 0.053 (3) | 0.057 (3) | 0.053 (3) | 0.014 (3) | 0.008 (2) | 0.002 (2) |
C2 | 0.033 (3) | 0.060 (3) | 0.059 (3) | 0.011 (2) | −0.003 (2) | 0.002 (2) |
C3 | 0.062 (4) | 0.099 (5) | 0.093 (5) | 0.026 (3) | −0.012 (3) | 0.017 (4) |
N3 | 0.048 (3) | 0.069 (3) | 0.032 (2) | 0.005 (2) | 0.0008 (18) | 0.0057 (18) |
N4 | 0.053 (3) | 0.056 (2) | 0.038 (2) | 0.0064 (18) | 0.0002 (19) | 0.0080 (17) |
C4 | 0.064 (4) | 0.040 (2) | 0.069 (4) | 0.001 (2) | −0.002 (3) | 0.013 (2) |
C5 | 0.049 (3) | 0.052 (3) | 0.053 (3) | 0.006 (2) | 0.004 (2) | −0.001 (2) |
C6 | 0.077 (4) | 0.053 (3) | 0.084 (4) | 0.007 (3) | −0.012 (3) | −0.009 (3) |
N5 | 0.056 (3) | 0.063 (3) | 0.039 (2) | 0.002 (2) | −0.006 (2) | −0.0029 (19) |
N6 | 0.051 (3) | 0.057 (3) | 0.043 (2) | 0.002 (2) | 0.0037 (19) | 0.0064 (19) |
C7 | 0.052 (4) | 0.065 (3) | 0.053 (3) | −0.011 (3) | −0.009 (2) | −0.007 (2) |
C8 | 0.049 (3) | 0.049 (3) | 0.054 (3) | −0.013 (2) | 0.001 (2) | 0.007 (2) |
C9 | 0.058 (4) | 0.092 (4) | 0.085 (4) | −0.025 (3) | 0.014 (3) | 0.010 (3) |
Cl1 | 0.0502 (8) | 0.0807 (10) | 0.0579 (8) | −0.0081 (7) | −0.0025 (6) | −0.0049 (7) |
Cl2 | 0.0456 (8) | 0.0802 (9) | 0.0573 (8) | 0.0112 (6) | 0.0017 (6) | 0.0096 (7) |
O1 | 0.070 (3) | 0.0533 (19) | 0.120 (4) | 0.004 (2) | 0.011 (3) | 0.006 (2) |
O2 | 0.074 (3) | 0.075 (3) | 0.104 (4) | 0.004 (2) | 0.008 (2) | −0.004 (2) |
Geometric parameters (Å, º) top
Zn1—N5 | 2.177 (4) | C4—C5 | 1.489 (7) |
Zn1—N3 | 2.193 (4) | C4—H15 | 0.9700 |
Zn1—N4 | 2.206 (4) | C4—H16 | 0.9700 |
Zn1—N2 | 2.207 (4) | C5—C6 | 1.499 (7) |
Zn1—N1 | 2.207 (5) | C5—H17 | 0.9800 |
Zn1—N6 | 2.211 (4) | C6—H18 | 0.9600 |
N1—C1 | 1.472 (6) | C6—H19 | 0.9600 |
N1—H1 | 0.9000 | C6—H20 | 0.9600 |
N1—H2 | 0.9000 | N5—C7 | 1.487 (7) |
N2—C2 | 1.496 (6) | N5—H21 | 0.9000 |
N2—H3 | 0.9000 | N5—H22 | 0.9000 |
N2—H4 | 0.9000 | N6—C8 | 1.480 (6) |
C1—C2 | 1.504 (7) | N6—H23 | 0.9000 |
C1—H5 | 0.9700 | N6—H24 | 0.9000 |
C1—H6 | 0.9700 | C7—C8 | 1.488 (7) |
C2—C3 | 1.531 (7) | C7—H25 | 0.9700 |
C2—H7 | 0.9800 | C7—H26 | 0.9700 |
C3—H8 | 0.9600 | C8—C9 | 1.484 (8) |
C3—H9 | 0.9600 | C8—H27 | 0.9800 |
C3—H10 | 0.9600 | C9—H28 | 0.9600 |
N3—C4 | 1.498 (6) | C9—H29 | 0.9600 |
N3—H11 | 0.9000 | C9—H30 | 0.9600 |
N3—H12 | 0.9000 | O1—H31 | 0.8954 |
N4—C5 | 1.476 (6) | O1—H32 | 0.9005 |
N4—H13 | 0.9000 | O2—H33 | 0.9009 |
N4—H14 | 0.9000 | O2—H34 | 0.9006 |
| | | |
N5—Zn1—N3 | 96.84 (17) | C5—N4—H14 | 110.3 |
N5—Zn1—N4 | 171.74 (19) | Zn1—N4—H14 | 110.3 |
N3—Zn1—N4 | 79.63 (16) | H13—N4—H14 | 108.5 |
N5—Zn1—N2 | 93.77 (14) | C5—C4—N3 | 111.0 (4) |
N3—Zn1—N2 | 167.30 (18) | C5—C4—H15 | 109.4 |
N4—Zn1—N2 | 90.72 (17) | N3—C4—H15 | 109.4 |
N5—Zn1—N1 | 93.22 (16) | C5—C4—H16 | 109.4 |
N3—Zn1—N1 | 92.65 (17) | N3—C4—H16 | 109.4 |
N4—Zn1—N1 | 94.40 (17) | H15—C4—H16 | 108.0 |
N2—Zn1—N1 | 79.79 (17) | N4—C5—C4 | 107.9 (4) |
N5—Zn1—N6 | 79.36 (17) | N4—C5—C6 | 112.8 (4) |
N3—Zn1—N6 | 94.20 (18) | C4—C5—C6 | 114.4 (4) |
N4—Zn1—N6 | 93.38 (17) | N4—C5—H17 | 107.1 |
N2—Zn1—N6 | 94.59 (16) | C4—C5—H17 | 107.1 |
N1—Zn1—N6 | 170.44 (16) | C6—C5—H17 | 107.1 |
C1—N1—Zn1 | 107.6 (3) | C5—C6—H18 | 109.5 |
C1—N1—H1 | 110.2 | C5—C6—H19 | 109.5 |
Zn1—N1—H1 | 110.2 | H18—C6—H19 | 109.5 |
C1—N1—H2 | 110.2 | C5—C6—H20 | 109.5 |
Zn1—N1—H2 | 110.2 | H18—C6—H20 | 109.5 |
H1—N1—H2 | 108.5 | H19—C6—H20 | 109.5 |
C2—N2—Zn1 | 107.2 (3) | C7—N5—Zn1 | 109.1 (3) |
C2—N2—H3 | 110.3 | C7—N5—H21 | 109.9 |
Zn1—N2—H3 | 110.3 | Zn1—N5—H21 | 109.9 |
C2—N2—H4 | 110.3 | C7—N5—H22 | 109.9 |
Zn1—N2—H4 | 110.3 | Zn1—N5—H22 | 109.9 |
H3—N2—H4 | 108.5 | H21—N5—H22 | 108.3 |
N1—C1—C2 | 109.9 (4) | C8—N6—Zn1 | 108.5 (3) |
N1—C1—H5 | 109.7 | C8—N6—H23 | 110.0 |
C2—C1—H5 | 109.7 | Zn1—N6—H23 | 110.0 |
N1—C1—H6 | 109.7 | C8—N6—H24 | 110.0 |
C2—C1—H6 | 109.7 | Zn1—N6—H24 | 110.0 |
H5—C1—H6 | 108.2 | H23—N6—H24 | 108.4 |
N2—C2—C1 | 107.7 (4) | N5—C7—C8 | 112.1 (4) |
N2—C2—C3 | 111.5 (5) | N5—C7—H25 | 109.2 |
C1—C2—C3 | 111.3 (5) | C8—C7—H25 | 109.2 |
N2—C2—H7 | 108.8 | N5—C7—H26 | 109.2 |
C1—C2—H7 | 108.8 | C8—C7—H26 | 109.2 |
C3—C2—H7 | 108.8 | H25—C7—H26 | 107.9 |
C2—C3—H8 | 109.5 | N6—C8—C9 | 114.1 (5) |
C2—C3—H9 | 109.5 | N6—C8—C7 | 107.6 (4) |
H8—C3—H9 | 109.5 | C9—C8—C7 | 111.1 (5) |
C2—C3—H10 | 109.5 | N6—C8—H27 | 107.9 |
H8—C3—H10 | 109.5 | C9—C8—H27 | 107.9 |
H9—C3—H10 | 109.5 | C7—C8—H27 | 107.9 |
C4—N3—Zn1 | 108.3 (3) | C8—C9—H28 | 109.5 |
C4—N3—H11 | 110.0 | C8—C9—H29 | 109.5 |
Zn1—N3—H11 | 110.0 | H28—C9—H29 | 109.5 |
C4—N3—H12 | 110.0 | C8—C9—H30 | 109.5 |
Zn1—N3—H12 | 110.0 | H28—C9—H30 | 109.5 |
H11—N3—H12 | 108.4 | H29—C9—H30 | 109.5 |
C5—N4—Zn1 | 107.2 (3) | H31—O1—H32 | 98.8 |
C5—N4—H13 | 110.3 | H33—O2—H34 | 99.3 |
Zn1—N4—H13 | 110.3 | | |
| | | |
N5—Zn1—N1—C1 | −80.2 (4) | N1—Zn1—N4—C5 | 114.0 (3) |
N3—Zn1—N1—C1 | −177.2 (3) | N6—Zn1—N4—C5 | −71.6 (3) |
N4—Zn1—N1—C1 | 103.0 (3) | Zn1—N3—C4—C5 | −35.8 (5) |
N2—Zn1—N1—C1 | 13.1 (4) | Zn1—N4—C5—C4 | −47.8 (4) |
N5—Zn1—N2—C2 | 109.9 (3) | Zn1—N4—C5—C6 | −175.2 (4) |
N3—Zn1—N2—C2 | −36.8 (9) | N3—C4—C5—N4 | 57.1 (6) |
N4—Zn1—N2—C2 | −77.0 (3) | N3—C4—C5—C6 | −176.5 (4) |
N1—Zn1—N2—C2 | 17.4 (3) | N3—Zn1—N5—C7 | −84.8 (4) |
N6—Zn1—N2—C2 | −170.4 (3) | N2—Zn1—N5—C7 | 102.1 (4) |
Zn1—N1—C1—C2 | −42.3 (5) | N1—Zn1—N5—C7 | −177.9 (4) |
Zn1—N2—C2—C1 | −44.8 (4) | N6—Zn1—N5—C7 | 8.2 (3) |
Zn1—N2—C2—C3 | −167.2 (4) | N5—Zn1—N6—C8 | 19.8 (3) |
N1—C1—C2—N2 | 59.8 (6) | N3—Zn1—N6—C8 | 116.0 (3) |
N1—C1—C2—C3 | −177.7 (5) | N4—Zn1—N6—C8 | −164.2 (3) |
N5—Zn1—N3—C4 | 179.4 (3) | N2—Zn1—N6—C8 | −73.2 (3) |
N4—Zn1—N3—C4 | 6.9 (3) | Zn1—N5—C7—C8 | −36.0 (5) |
N2—Zn1—N3—C4 | −34.1 (10) | Zn1—N6—C8—C9 | −168.0 (4) |
N1—Zn1—N3—C4 | −87.0 (4) | Zn1—N6—C8—C7 | −44.2 (5) |
N6—Zn1—N3—C4 | 99.6 (3) | N5—C7—C8—N6 | 54.4 (6) |
N3—Zn1—N4—C5 | 22.1 (3) | N5—C7—C8—C9 | 180.0 (5) |
N2—Zn1—N4—C5 | −166.2 (3) | | |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
N1—H1···Cl2i | 0.90 | 2.62 | 3.457 (5) | 155 |
N1—H2···Cl1 | 0.90 | 2.54 | 3.419 (5) | 166 |
N2—H3···Cl2ii | 0.90 | 2.83 | 3.601 (5) | 144 |
N2—H4···O1iii | 0.90 | 2.30 | 3.185 (6) | 166 |
N3—H11···O2i | 0.90 | 2.27 | 3.133 (6) | 162 |
N3—H12···Cl2iv | 0.90 | 2.56 | 3.414 (5) | 160 |
N4—H14···Cl1 | 0.90 | 2.73 | 3.599 (5) | 162 |
N5—H21···Cl1i | 0.90 | 2.71 | 3.477 (5) | 144 |
N5—H22···O1iii | 0.90 | 2.34 | 3.143 (6) | 148 |
N6—H23···Cl1ii | 0.90 | 2.69 | 3.499 (5) | 150 |
N6—H24···Cl2iv | 0.90 | 2.68 | 3.553 (5) | 165 |
O1—H31···Cl1 | 0.90 | 2.32 | 3.214 (5) | 179 |
O1—H32···Cl2 | 0.90 | 2.27 | 3.166 (5) | 180 |
O2—H33···Cl1 | 0.90 | 2.26 | 3.164 (5) | 180 |
O2—H34···Cl2 | 0.90 | 2.29 | 3.186 (5) | 180 |
Symmetry codes: (i) x−1/2, −y+1/2, z−1/2; (ii) x−1/2, −y+1/2, z+1/2; (iii) x−1/2, y−1/2, z; (iv) x−1, y, z. |