The title compound is a binuclear lanthanum(III) complex having each metal ion in decacoordination with oxygen atoms from 1,4-chdc
2− ligands, acetate groups and coordinated water molecules to form a distorted bicapped square antiprismatic geometry. The strong intermolecular O–H

O and weak C–H

O interactions lead to the construction of a three-dimensional supramolecular architecture.
Supporting information
CCDC reference: 1546730
Key indicators
- Single-crystal X-ray study
- T = 293 K
- Mean
(C-C) = 0.016 Å
- R factor = 0.041
- wR factor = 0.146
- Data-to-parameter ratio = 13.8
checkCIF/PLATON results
No syntax errors found
Alert level C
PLAT342_ALERT_3_C Low Bond Precision on C-C Bonds ............... 0.01589 Ang.
Alert level G
PLAT002_ALERT_2_G Number of Distance or Angle Restraints on AtSite 9 Note
PLAT004_ALERT_5_G Polymeric Structure Found with Maximum Dimension 2 Info
PLAT042_ALERT_1_G Calc. and Reported MoietyFormula Strings Differ Please Check
PLAT045_ALERT_1_G Calculated and Reported Z Differ by a Factor ... 2.00 Check
PLAT083_ALERT_2_G SHELXL Second Parameter in WGHT Unusually Large 6.15 Why ?
PLAT154_ALERT_1_G The s.u.'s on the Cell Angles are Equal ..(Note) 0.005 Degree
PLAT171_ALERT_4_G The CIF-Embedded .res File Contains EADP Records 3 Report
PLAT172_ALERT_4_G The CIF-Embedded .res File Contains DFIX Records 6 Report
PLAT180_ALERT_4_G Check Cell Rounding: # of Values Ending with 0 = 3 Note
PLAT199_ALERT_1_G Reported _cell_measurement_temperature ..... (K) 293 Check
PLAT200_ALERT_1_G Reported _diffrn_ambient_temperature ..... (K) 293 Check
PLAT764_ALERT_4_G Overcomplete CIF Bond List Detected (Rep/Expd) . 1.36 Ratio
PLAT790_ALERT_4_G Centre of Gravity not Within Unit Cell: Resd. # 2 Note
H2 O
PLAT860_ALERT_3_G Number of Least-Squares Restraints ............. 9 Note
PLAT870_ALERT_4_G ALERTS Related to Twinning Effects Suppressed .. ! Info
PLAT910_ALERT_3_G Missing # of FCF Reflection(s) Below Theta(Min). 1 Note
0 ALERT level A = Most likely a serious problem - resolve or explain
0 ALERT level B = A potentially serious problem, consider carefully
1 ALERT level C = Check. Ensure it is not caused by an omission or oversight
16 ALERT level G = General information/check it is not something unexpected
5 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
3 ALERT type 3 Indicator that the structure quality may be low
6 ALERT type 4 Improvement, methodology, query or suggestion
1 ALERT type 5 Informative message, check
Data collection: APEX2 (Bruker, 2004); cell refinement: APEX2 and SAINT (Bruker, 2004); data reduction: SAINT and XPREP (Bruker, 2004); program(s) used to solve structure: SIR92 (Sheldrick, 2015); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015); molecular graphics: DIAMOND (Brandenburg, 2010); software used to prepare material for publication: SHELXL2014 (Sheldrick, 2015) and publCIF (Westrip, 2010)'.
Poly[[di-µ
3-acetato-tetraaquabis(µ
2-cyclohexane-1,4-dicarboxylato)dilanthanum(III)] dihydrate]
top
Crystal data top
[La2(C2H3O2)2(C8H10O4)2(H2O)4]·2H2O | Z = 1 |
Mr = 844.32 | F(000) = 416 |
Triclinic, P1 | Dx = 1.960 Mg m−3 |
a = 6.9341 (8) Å | Mo Kα radiation, λ = 0.71073 Å |
b = 8.9597 (13) Å | Cell parameters from 7100 reflections |
c = 12.3030 (16) Å | θ = 2.8–30.9° |
α = 110.217 (5)° | µ = 3.02 mm−1 |
β = 91.060 (5)° | T = 293 K |
γ = 93.280 (5)° | Block, colourless |
V = 715.49 (16) Å3 | 0.20 × 0.15 × 0.15 mm |
Data collection top
Bruker Kappa APEXII CCD diffractometer | 2815 independent reflections |
Radiation source: Sealed tube | 2447 reflections with I > 2σ(I) |
ω and φ scan | θmax = 26.0°, θmin = 2.4° |
Absorption correction: multi-scan (SADABS; Bruker, 2004) | h = −8→8 |
Tmin = 0.60, Tmax = 0.74 | k = −11→10 |
2818 measured reflections | l = 0→15 |
Refinement top
Refinement on F2 | 9 restraints |
Least-squares matrix: full | Hydrogen site location: mixed |
R[F2 > 2σ(F2)] = 0.041 | H atoms treated by a mixture of independent and constrained refinement |
wR(F2) = 0.146 | w = 1/[σ2(Fo2) + (0.0821P)2 + 6.1459P] where P = (Fo2 + 2Fc2)/3 |
S = 1.07 | (Δ/σ)max = 0.005 |
2818 reflections | Δρmax = 2.17 e Å−3 |
204 parameters | Δρmin = −2.46 e Å−3 |
Special details top
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. |
Refinement. Refined as a two-component twin. |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
C1 | 0.2377 (17) | 0.7936 (10) | 0.7752 (7) | 0.0203 (18) | |
C2 | 0.2486 (18) | 0.7706 (11) | 0.8920 (8) | 0.030 (2) | |
H2 | 0.2447 | 0.8760 | 0.9522 | 0.036* | |
C3 | 0.0724 (17) | 0.6681 (16) | 0.9058 (11) | 0.033 (3) | |
H3A | 0.0698 | 0.6715 | 0.9855 | 0.040* | |
H3B | −0.0448 | 0.7116 | 0.8889 | 0.040* | |
C4 | 0.0778 (17) | 0.4962 (14) | 0.8253 (10) | 0.030 (3) | |
H4A | 0.0694 | 0.4919 | 0.7455 | 0.036* | |
H4B | −0.0331 | 0.4339 | 0.8379 | 0.036* | |
C5 | 0.2631 (16) | 0.4239 (11) | 0.8460 (7) | 0.024 (2) | |
H5 | 0.2633 | 0.4196 | 0.9245 | 0.028* | |
C6 | 0.4375 (16) | 0.5264 (15) | 0.8372 (11) | 0.030 (3) | |
H6A | 0.4468 | 0.5213 | 0.7574 | 0.036* | |
H6B | 0.5526 | 0.4836 | 0.8576 | 0.036* | |
C7 | 0.4325 (17) | 0.6994 (14) | 0.9147 (10) | 0.028 (2) | |
H7A | 0.5438 | 0.7602 | 0.9010 | 0.034* | |
H7B | 0.4403 | 0.7067 | 0.9952 | 0.034* | |
C8 | 0.2736 (16) | 0.2574 (10) | 0.7614 (8) | 0.0229 (19) | |
C9 | 0.7522 (14) | 1.0347 (9) | 0.6555 (7) | 0.0141 (16) | |
C10 | 0.7542 (18) | 1.0729 (13) | 0.7831 (8) | 0.030 (2) | |
H10A | 0.7030 | 1.1749 | 0.8194 | 0.046* | |
H10B | 0.8846 | 1.0758 | 0.8118 | 0.046* | |
H10C | 0.6763 | 0.9926 | 0.8006 | 0.046* | |
O1 | 0.3916 (11) | 0.7991 (10) | 0.7225 (7) | 0.0280 (18) | |
O2 | 0.0804 (11) | 0.8116 (10) | 0.7334 (7) | 0.0272 (18) | |
O3 | −0.0144 (11) | 0.6946 (10) | 0.4871 (7) | 0.0310 (18) | |
O4 | 0.3865 (13) | 0.6914 (10) | 0.4470 (8) | 0.039 (2) | |
O5 | 0.5999 (10) | 0.9978 (10) | 0.5957 (6) | 0.0219 (16) | |
O6 | 0.9100 (10) | 1.0455 (9) | 0.6066 (6) | 0.0220 (16) | |
O7 | 0.2827 (11) | 0.2366 (7) | 0.6530 (5) | 0.0223 (14) | |
O8 | 0.2635 (12) | 0.1397 (7) | 0.7932 (5) | 0.0283 (15) | |
O9 | −0.2682 (13) | 0.6345 (9) | 0.6499 (7) | 0.0384 (18) | |
La1 | 0.23952 (8) | 0.92768 (5) | 0.58722 (4) | 0.01486 (18) | |
H4C | 0.474 (15) | 0.704 (14) | 0.398 (8) | 0.05 (3)* | |
H4D | 0.326 (16) | 0.597 (8) | 0.406 (8) | 0.05 (3)* | |
H3C | −0.088 (14) | 0.668 (17) | 0.538 (9) | 0.06 (3)* | |
H3D | −0.105 (12) | 0.705 (17) | 0.437 (9) | 0.06 (3)* | |
H9A | −0.207 (15) | 0.687 (15) | 0.719 (6) | 0.06 (3)* | |
H9B | −0.388 (9) | 0.669 (17) | 0.663 (10) | 0.06 (3)* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
C1 | 0.026 (5) | 0.012 (4) | 0.025 (4) | −0.004 (4) | 0.006 (5) | 0.008 (3) |
C2 | 0.047 (7) | 0.023 (5) | 0.019 (4) | 0.003 (5) | −0.002 (5) | 0.008 (4) |
C3 | 0.029 (7) | 0.041 (7) | 0.034 (7) | 0.011 (5) | 0.007 (5) | 0.017 (6) |
C4 | 0.031 (7) | 0.027 (6) | 0.030 (6) | 0.004 (5) | 0.003 (4) | 0.005 (5) |
C5 | 0.030 (6) | 0.026 (5) | 0.016 (4) | −0.005 (4) | −0.002 (4) | 0.011 (4) |
C6 | 0.022 (6) | 0.037 (7) | 0.033 (6) | 0.004 (5) | −0.005 (4) | 0.014 (5) |
C7 | 0.041 (8) | 0.025 (6) | 0.017 (5) | 0.001 (5) | −0.004 (4) | 0.007 (4) |
C8 | 0.017 (5) | 0.024 (5) | 0.029 (5) | 0.002 (4) | −0.001 (4) | 0.012 (4) |
C9 | 0.010 (4) | 0.012 (3) | 0.018 (4) | 0.003 (4) | −0.002 (4) | 0.001 (3) |
C10 | 0.026 (6) | 0.042 (6) | 0.020 (4) | −0.006 (5) | 0.003 (5) | 0.007 (4) |
O1 | 0.016 (4) | 0.039 (5) | 0.039 (5) | 0.005 (3) | 0.005 (3) | 0.025 (4) |
O2 | 0.026 (5) | 0.031 (5) | 0.028 (4) | 0.004 (3) | −0.005 (3) | 0.015 (4) |
O3 | 0.026 (5) | 0.035 (5) | 0.034 (5) | −0.005 (3) | −0.002 (3) | 0.017 (4) |
O4 | 0.033 (5) | 0.022 (4) | 0.051 (5) | −0.009 (3) | 0.023 (4) | −0.001 (4) |
O5 | 0.012 (4) | 0.037 (4) | 0.020 (4) | −0.001 (3) | 0.002 (3) | 0.014 (3) |
O6 | 0.011 (4) | 0.032 (4) | 0.025 (4) | −0.001 (3) | 0.002 (3) | 0.011 (3) |
O7 | 0.025 (4) | 0.024 (3) | 0.018 (3) | 0.001 (3) | 0.006 (3) | 0.007 (2) |
O8 | 0.042 (4) | 0.021 (3) | 0.024 (3) | −0.001 (4) | −0.004 (3) | 0.011 (3) |
O9 | 0.023 (5) | 0.033 (4) | 0.057 (5) | 0.004 (4) | 0.004 (4) | 0.013 (4) |
La1 | 0.0121 (3) | 0.0169 (3) | 0.0169 (3) | 0.0017 (2) | 0.0015 (2) | 0.00745 (18) |
Geometric parameters (Å, º) top
C1—O2 | 1.240 (13) | C9—La1ii | 3.119 (8) |
C1—O1 | 1.266 (13) | C10—H10A | 0.9600 |
C1—C2 | 1.522 (12) | C10—H10B | 0.9600 |
C1—La1 | 2.952 (8) | C10—H10C | 0.9600 |
C2—C7 | 1.521 (17) | O1—La1 | 2.570 (7) |
C2—C3 | 1.533 (17) | O2—La1 | 2.601 (8) |
C2—H2 | 0.9800 | O3—La1 | 2.588 (8) |
C3—C4 | 1.519 (18) | O3—H3C | 0.90 (2) |
C3—H3A | 0.9700 | O3—H3D | 0.90 (2) |
C3—H3B | 0.9700 | O4—La1 | 2.506 (8) |
C4—C5 | 1.527 (16) | O4—H4C | 0.90 (2) |
C4—H4A | 0.9700 | O4—H4D | 0.89 (2) |
C4—H4B | 0.9700 | O5—La1 | 2.533 (7) |
C5—C8 | 1.502 (12) | O5—La1ii | 2.792 (7) |
C5—C6 | 1.505 (15) | O6—La1iii | 2.552 (7) |
C5—H5 | 0.9800 | O6—La1ii | 2.674 (7) |
C6—C7 | 1.516 (17) | O7—La1i | 2.598 (6) |
C6—H6A | 0.9700 | O8—La1i | 2.585 (6) |
C6—H6B | 0.9700 | O9—H9A | 0.90 (2) |
C7—H7A | 0.9700 | O9—H9B | 0.90 (2) |
C7—H7B | 0.9700 | La1—O6iv | 2.552 (7) |
C8—O8 | 1.244 (11) | La1—O8v | 2.585 (6) |
C8—O7 | 1.284 (11) | La1—O7v | 2.598 (6) |
C8—La1i | 2.983 (9) | La1—O6ii | 2.674 (7) |
C9—O5 | 1.237 (11) | La1—O5ii | 2.792 (7) |
C9—O6 | 1.273 (11) | La1—C8v | 2.983 (9) |
C9—C10 | 1.487 (11) | | |
| | | |
O2—C1—O1 | 120.1 (8) | C9—O6—La1ii | 98.1 (5) |
O2—C1—C2 | 120.4 (9) | La1iii—O6—La1ii | 115.2 (3) |
O1—C1—C2 | 119.5 (10) | C8—O7—La1i | 94.3 (5) |
O2—C1—La1 | 61.6 (5) | C8—O8—La1i | 96.0 (5) |
O1—C1—La1 | 60.2 (5) | H9A—O9—H9B | 101 (3) |
C2—C1—La1 | 164.8 (6) | O4—La1—O5 | 73.2 (3) |
C1—C2—C7 | 114.2 (9) | O4—La1—O6iv | 135.8 (3) |
C1—C2—C3 | 110.9 (9) | O5—La1—O6iv | 143.4 (2) |
C7—C2—C3 | 109.4 (8) | O4—La1—O1 | 77.7 (3) |
C1—C2—H2 | 107.4 | O5—La1—O1 | 73.8 (2) |
C7—C2—H2 | 107.4 | O6iv—La1—O1 | 126.4 (2) |
C3—C2—H2 | 107.4 | O4—La1—O8v | 146.0 (3) |
C4—C3—C2 | 111.4 (9) | O5—La1—O8v | 82.5 (3) |
C4—C3—H3A | 109.4 | O6iv—La1—O8v | 76.9 (2) |
C2—C3—H3A | 109.4 | O1—La1—O8v | 72.8 (2) |
C4—C3—H3B | 109.4 | O4—La1—O3 | 67.5 (3) |
C2—C3—H3B | 109.4 | O5—La1—O3 | 140.7 (3) |
H3A—C3—H3B | 108.0 | O6iv—La1—O3 | 73.0 (3) |
C3—C4—C5 | 111.4 (10) | O1—La1—O3 | 96.1 (3) |
C3—C4—H4A | 109.4 | O8v—La1—O3 | 131.7 (3) |
C5—C4—H4A | 109.4 | O4—La1—O7v | 138.0 (2) |
C3—C4—H4B | 109.4 | O5—La1—O7v | 73.7 (2) |
C5—C4—H4B | 109.4 | O6iv—La1—O7v | 69.9 (2) |
H4A—C4—H4B | 108.0 | O1—La1—O7v | 116.4 (2) |
C8—C5—C6 | 110.0 (9) | O8v—La1—O7v | 49.88 (18) |
C8—C5—C4 | 111.2 (9) | O3—La1—O7v | 140.6 (2) |
C6—C5—C4 | 110.4 (8) | O4—La1—O2 | 103.1 (3) |
C8—C5—H5 | 108.4 | O5—La1—O2 | 121.8 (2) |
C6—C5—H5 | 108.4 | O6iv—La1—O2 | 78.8 (2) |
C4—C5—H5 | 108.4 | O1—La1—O2 | 49.7 (2) |
C5—C6—C7 | 113.4 (9) | O8v—La1—O2 | 69.9 (2) |
C5—C6—H6A | 108.9 | O3—La1—O2 | 67.7 (3) |
C7—C6—H6A | 108.9 | O7v—La1—O2 | 116.2 (2) |
C5—C6—H6B | 108.9 | O4—La1—O6ii | 83.0 (3) |
C7—C6—H6B | 108.9 | O5—La1—O6ii | 107.7 (2) |
H6A—C6—H6B | 107.7 | O6iv—La1—O6ii | 64.8 (3) |
C6—C7—C2 | 111.4 (9) | O1—La1—O6ii | 159.3 (3) |
C6—C7—H7A | 109.3 | O8v—La1—O6ii | 127.8 (2) |
C2—C7—H7A | 109.3 | O3—La1—O6ii | 69.3 (2) |
C6—C7—H7B | 109.3 | O7v—La1—O6ii | 83.2 (2) |
C2—C7—H7B | 109.3 | O2—La1—O6ii | 129.9 (2) |
H7A—C7—H7B | 108.0 | O4—La1—O5ii | 68.8 (3) |
O8—C8—O7 | 119.6 (8) | O5—La1—O5ii | 61.3 (3) |
O8—C8—C5 | 121.6 (8) | O6iv—La1—O5ii | 103.7 (2) |
O7—C8—C5 | 118.7 (7) | O1—La1—O5ii | 129.6 (2) |
O8—C8—La1i | 59.5 (5) | O8v—La1—O5ii | 119.3 (2) |
O7—C8—La1i | 60.3 (4) | O3—La1—O5ii | 104.2 (2) |
C5—C8—La1i | 172.5 (8) | O7v—La1—O5ii | 72.9 (2) |
O5—C9—O6 | 118.9 (7) | O2—La1—O5ii | 170.7 (2) |
O5—C9—C10 | 121.7 (9) | O6ii—La1—O5ii | 46.51 (19) |
O6—C9—C10 | 119.4 (9) | O4—La1—C1 | 93.6 (3) |
O5—C9—La1ii | 63.3 (4) | O5—La1—C1 | 97.2 (3) |
O6—C9—La1ii | 58.1 (4) | O6iv—La1—C1 | 101.4 (3) |
C10—C9—La1ii | 161.8 (6) | O1—La1—C1 | 25.3 (3) |
C9—C10—H10A | 109.5 | O8v—La1—C1 | 65.9 (2) |
C9—C10—H10B | 109.5 | O3—La1—C1 | 84.1 (3) |
H10A—C10—H10B | 109.5 | O7v—La1—C1 | 115.7 (2) |
C9—C10—H10C | 109.5 | O2—La1—C1 | 24.8 (3) |
H10A—C10—H10C | 109.5 | O6ii—La1—C1 | 152.5 (3) |
H10B—C10—H10C | 109.5 | O5ii—La1—C1 | 154.8 (3) |
C1—O1—La1 | 94.4 (6) | O4—La1—C8v | 151.3 (3) |
C1—O2—La1 | 93.6 (6) | O5—La1—C8v | 78.0 (3) |
La1—O3—H3C | 113 (9) | O6iv—La1—C8v | 70.6 (3) |
La1—O3—H3D | 120 (9) | O1—La1—C8v | 94.8 (3) |
H3C—O3—H3D | 101 (3) | O8v—La1—C8v | 24.5 (2) |
La1—O4—H4C | 121 (8) | O3—La1—C8v | 141.2 (3) |
La1—O4—H4D | 127 (8) | O7v—La1—C8v | 25.4 (2) |
H4C—O4—H4D | 102 (3) | O2—La1—C8v | 92.3 (3) |
C9—O5—La1 | 147.1 (6) | O6ii—La1—C8v | 105.7 (2) |
C9—O5—La1ii | 93.4 (5) | O5ii—La1—C8v | 97.0 (2) |
La1—O5—La1ii | 118.7 (3) | C1—La1—C8v | 90.4 (2) |
C9—O6—La1iii | 138.0 (6) | | |
| | | |
O2—C1—C2—C7 | 161.8 (9) | C4—C5—C8—O7 | 63.7 (13) |
O1—C1—C2—C7 | −20.4 (13) | O2—C1—O1—La1 | 15.4 (9) |
La1—C1—C2—C7 | −105 (3) | C2—C1—O1—La1 | −162.5 (7) |
O2—C1—C2—C3 | 37.7 (12) | O1—C1—O2—La1 | −15.2 (9) |
O1—C1—C2—C3 | −144.5 (9) | C2—C1—O2—La1 | 162.6 (7) |
La1—C1—C2—C3 | 131 (3) | O6—C9—O5—La1 | 174.3 (8) |
C1—C2—C3—C4 | 69.6 (12) | C10—C9—O5—La1 | −8.2 (16) |
C7—C2—C3—C4 | −57.2 (11) | La1ii—C9—O5—La1 | −168.1 (12) |
C2—C3—C4—C5 | 57.2 (12) | O6—C9—O5—La1ii | −17.7 (8) |
C3—C4—C5—C8 | −176.5 (9) | C10—C9—O5—La1ii | 159.9 (7) |
C3—C4—C5—C6 | −54.1 (12) | O5—C9—O6—La1iii | −124.4 (8) |
C8—C5—C6—C7 | 176.5 (9) | C10—C9—O6—La1iii | 58.0 (12) |
C4—C5—C6—C7 | 53.4 (11) | La1ii—C9—O6—La1iii | −143.1 (9) |
C5—C6—C7—C2 | −55.0 (12) | O5—C9—O6—La1ii | 18.6 (9) |
C1—C2—C7—C6 | −69.6 (12) | C10—C9—O6—La1ii | −158.9 (7) |
C3—C2—C7—C6 | 55.3 (11) | O8—C8—O7—La1i | 4.7 (11) |
C6—C5—C8—O8 | 124.8 (11) | C5—C8—O7—La1i | −171.5 (9) |
C4—C5—C8—O8 | −112.5 (12) | O7—C8—O8—La1i | −4.8 (11) |
C6—C5—C8—O7 | −59.0 (13) | C5—C8—O8—La1i | 171.4 (9) |
Symmetry codes: (i) x, y−1, z; (ii) −x+1, −y+2, −z+1; (iii) x+1, y, z; (iv) x−1, y, z; (v) x, y+1, z. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
C10—H10C···O1 | 0.96 | 2.49 | 3.295 (14) | 141 |
O4—H4C···O7vi | 0.90 (2) | 1.92 (5) | 2.771 (10) | 158 (12) |
O4—H4D···O9vii | 0.89 (2) | 1.96 (6) | 2.812 (11) | 158 (12) |
O3—H3C···O9 | 0.90 (2) | 1.97 (3) | 2.858 (12) | 172 (13) |
O3—H3D···O7vii | 0.90 (2) | 1.86 (3) | 2.750 (11) | 170 (14) |
O9—H9A···O2 | 0.90 (2) | 2.20 (11) | 2.786 (12) | 122 (11) |
O9—H9B···O1iv | 0.90 (2) | 1.97 (5) | 2.846 (11) | 164 (13) |
Symmetry codes: (iv) x−1, y, z; (vi) −x+1, −y+1, −z+1; (vii) −x, −y+1, −z+1. |