The title compound contains a network of [V4As6O30H6]4- clusters, each of which is accompanied by two dabconium (doubly protonated 1,4-diazabicyclo[2.2.2]octane) cations and eight water molecules. A complex hydrogen-bonding network stabilizes the crystal packing.
Supporting information
CCDC reference: 189859
Key indicators
- Single-crystal X-ray study
- T = 293 K
- Mean (C-C) = 0.006 Å
- R factor = 0.028
- wR factor = 0.071
- Data-to-parameter ratio = 20.6
checkCIF results
No syntax errors found
ADDSYM reports no extra symmetry
Alert Level C:
REFLT_03
From the CIF: _diffrn_reflns_theta_max 30.21
From the CIF: _reflns_number_total 6021
TEST2: Reflns within _diffrn_reflns_theta_max
Count of symmetry unique reflns 6669
Completeness (_total/calc) 90.28%
Alert C: < 95% complete
General Notes
FORMU_01 There is a discrepancy between the atom counts in the
_chemical_formula_sum and _chemical_formula_moiety. This is
usually due to the moiety formula being in the wrong format.
Atom count from _chemical_formula_sum: C6 H25 As3 N2 O19 V2
Atom count from _chemical_formula_moiety:C12 H50 As6 N4 O38 V4
ABSTM_02 When printed, the submitted absorption T values will be replaced
by the scaled T values. Since the ratio of scaled T's is
identical to the ratio of reported T values, the scaling does
not imply a change to the absorption corrections used in the
study.
Ratio of Tmax expected/reported 0.530
Tmax scaled 0.119 Tmin scaled 0.093
0 Alert Level A = Potentially serious problem
0 Alert Level B = Potential problem
1 Alert Level C = Please check
Data collection: SMART (Bruker, 1999); cell refinement: SMART; data reduction: SMART; 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.
Crystal data top
(C6H14N2)2[V4As6O30H6]·8H2O | F(000) = 744 |
Mr = 755.91 | Dx = 2.239 Mg m−3 |
Triclinic, P1 | Melting point: decomposes before melting K |
a = 9.6824 (5) Å | Mo Kα radiation, λ = 0.71073 Å |
b = 11.0733 (7) Å | Cell parameters from 3766 reflections |
c = 11.8967 (7) Å | θ = 2.1–30.1° |
α = 94.546 (2)° | µ = 5.32 mm−1 |
β = 101.557 (2)° | T = 293 K |
γ = 114.193 (2)° | Chunk, orange |
V = 1121.16 (11) Å3 | 0.50 × 0.40 × 0.40 mm |
Z = 2 | |
Data collection top
Bruker SMART1000 CCD diffractometer | 6021 independent reflections |
Radiation source: fine-focus sealed tube | 4987 reflections with I > 2σ()' |
Graphite monochromator | Rint = 0.015 |
ω scans | θmax = 30.2°, θmin = 2.1° |
Absorption correction: multi-scan (SADABS; Bruker, 1999) | h = −13→13 |
Tmin = 0.176, Tmax = 0.225 | k = −10→15 |
7764 measured reflections | l = −16→8 |
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)] = 0.028 | H-atom parameters constrained |
wR(F2) = 0.071 | w = 1/[σ2(Fo2) + (0.041P)2] where P = (Fo2 + 2Fc2)/3 |
S = 0.97 | (Δ/σ)max = 0.001 |
6021 reflections | Δρmax = 0.60 e Å−3 |
292 parameters | Δρmin = −0.82 e Å−3 |
0 restraints | Extinction correction: SHELXL97, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
Primary atom site location: structure-invariant direct methods | Extinction coefficient: 0.0025 (4) |
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 | |
V1 | 0.65452 (5) | 0.77980 (4) | 0.61404 (4) | 0.02073 (10) | |
V2 | 0.58641 (5) | 0.54350 (4) | 0.76000 (4) | 0.02084 (10) | |
As1 | 0.58581 (3) | 0.78147 (2) | 0.33273 (2) | 0.01968 (7) | |
As2 | 0.66837 (3) | 0.48861 (2) | 0.47031 (2) | 0.01778 (7) | |
As3 | 0.94147 (3) | 0.73424 (3) | 0.76272 (2) | 0.02442 (8) | |
O1 | 0.6256 (2) | 0.53455 (17) | 0.34055 (15) | 0.0209 (4) | |
O2 | 0.5701 (2) | 0.31980 (17) | 0.45954 (16) | 0.0211 (4) | |
O3 | 0.4199 (2) | 0.63745 (17) | 0.28393 (17) | 0.0235 (4) | |
O4 | 0.6037 (2) | 0.70664 (17) | 0.74747 (16) | 0.0230 (4) | |
O5 | 0.6480 (2) | 0.57482 (17) | 0.58194 (15) | 0.0196 (3) | |
O6 | 0.8654 (2) | 0.83099 (18) | 0.69252 (17) | 0.0263 (4) | |
O7 | 0.6980 (2) | 0.8180 (2) | 0.24049 (18) | 0.0290 (4) | |
O8 | 0.6959 (2) | 0.78996 (18) | 0.46561 (16) | 0.0244 (4) | |
O9 | 0.8594 (2) | 0.5176 (2) | 0.49243 (18) | 0.0294 (4) | |
H9 | 0.9168 | 0.5761 | 0.5676 | 0.035* | |
O10 | 1.0341 (2) | 0.6813 (2) | 0.68360 (19) | 0.0335 (5) | |
O11 | 0.5100 (2) | 0.89555 (19) | 0.34370 (19) | 0.0310 (5) | |
H11 | 0.5748 | 0.9812 | 0.3498 | 0.037* | |
O12 | 0.5439 (2) | 0.5250 (2) | 0.88139 (17) | 0.0332 (5) | |
O13 | 0.8100 (2) | 0.60699 (19) | 0.81023 (17) | 0.0279 (4) | |
O14 | 0.6484 (2) | 0.91935 (18) | 0.64181 (19) | 0.0314 (4) | |
O15 | 1.0627 (3) | 0.8341 (2) | 0.89093 (18) | 0.0403 (5) | |
H15 | 1.1588 | 0.8800 | 0.8801 | 0.048* | |
O20 | 0.3350 (3) | 0.0102 (2) | 0.8958 (2) | 0.0419 (6) | |
H20 | 0.3254 | 0.0615 | 0.8419 | 0.050* | |
H21 | 0.3912 | 0.0609 | 0.9697 | 0.050* | |
O21 | 0.7046 (3) | 1.1523 (2) | 0.3799 (3) | 0.0637 (9) | |
H22 | 0.7948 | 1.1896 | 0.3628 | 0.063 (13)* | |
H23 | 0.6614 | 1.1983 | 0.4117 | 0.24 (4)* | |
O22 | 0.6954 (3) | 0.3441 (3) | 0.9789 (2) | 0.0537 (7) | |
H24 | 0.6056 | 0.3634 | 0.9487 | 0.064* | |
H25 | 0.6410 | 0.2866 | 1.0320 | 0.064* | |
O23 | 0.5113 (3) | 0.1620 (3) | 0.1110 (2) | 0.0545 (7) | |
H26 | 0.4721 | 0.2064 | 0.1586 | 0.065* | |
H27 | 0.5648 | 0.1337 | 0.1512 | 0.065* | |
N1 | 1.0736 (3) | 0.2422 (2) | 0.7741 (2) | 0.0288 (5) | |
H1 | 1.1529 | 0.2198 | 0.7688 | 0.035* | |
N2 | 0.8561 (3) | 0.3017 (3) | 0.7871 (3) | 0.0387 (6) | |
H2 | 0.7766 | 0.3240 | 0.7923 | 0.046* | |
C1 | 0.9750 (4) | 0.2232 (4) | 0.6545 (3) | 0.0415 (8) | |
H1A | 0.9229 | 0.1285 | 0.6194 | 0.050* | |
H1B | 1.0401 | 0.2720 | 0.6059 | 0.050* | |
C2 | 1.1409 (4) | 0.3838 (3) | 0.8336 (3) | 0.0425 (8) | |
H2A | 1.1953 | 0.4434 | 0.7852 | 0.051* | |
H2B | 1.2153 | 0.3976 | 0.9069 | 0.051* | |
C3 | 0.9752 (4) | 0.1522 (3) | 0.8428 (3) | 0.0386 (7) | |
H3A | 1.0355 | 0.1692 | 0.9228 | 0.046* | |
H3B | 0.9418 | 0.0587 | 0.8096 | 0.046* | |
C4 | 0.8543 (4) | 0.2755 (5) | 0.6636 (3) | 0.0559 (11) | |
H4A | 0.8790 | 0.3578 | 0.6319 | 0.067* | |
H4B | 0.7511 | 0.2094 | 0.6193 | 0.067* | |
C5 | 1.0080 (4) | 0.4143 (4) | 0.8557 (5) | 0.0620 (13) | |
H5A | 1.0118 | 0.4225 | 0.9382 | 0.074* | |
H5B | 1.0179 | 0.4986 | 0.8317 | 0.074* | |
C6 | 0.8341 (4) | 0.1795 (3) | 0.8397 (3) | 0.0342 (7) | |
H6A | 0.7401 | 0.1030 | 0.7936 | 0.041* | |
H6B | 0.8225 | 0.1937 | 0.9181 | 0.041* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
V1 | 0.0214 (2) | 0.01598 (19) | 0.0233 (2) | 0.00764 (16) | 0.00426 (16) | 0.00247 (16) |
V2 | 0.0211 (2) | 0.0216 (2) | 0.0205 (2) | 0.00935 (16) | 0.00606 (16) | 0.00478 (16) |
As1 | 0.01754 (12) | 0.01954 (13) | 0.02521 (14) | 0.00981 (9) | 0.00721 (10) | 0.00748 (10) |
As2 | 0.01647 (12) | 0.01708 (12) | 0.02121 (13) | 0.00850 (9) | 0.00561 (9) | 0.00252 (9) |
As3 | 0.01895 (13) | 0.02699 (14) | 0.02298 (14) | 0.00748 (10) | 0.00215 (10) | 0.00352 (10) |
O1 | 0.0204 (8) | 0.0223 (9) | 0.0212 (9) | 0.0095 (7) | 0.0068 (7) | 0.0057 (7) |
O2 | 0.0203 (8) | 0.0171 (8) | 0.0267 (9) | 0.0091 (7) | 0.0058 (7) | 0.0032 (7) |
O3 | 0.0195 (8) | 0.0195 (8) | 0.0296 (10) | 0.0075 (7) | 0.0047 (7) | 0.0046 (7) |
O4 | 0.0256 (9) | 0.0217 (9) | 0.0219 (9) | 0.0111 (7) | 0.0063 (7) | 0.0006 (7) |
O5 | 0.0213 (8) | 0.0183 (8) | 0.0202 (9) | 0.0096 (7) | 0.0062 (7) | 0.0015 (7) |
O6 | 0.0224 (9) | 0.0206 (9) | 0.0307 (10) | 0.0059 (7) | 0.0025 (8) | 0.0068 (8) |
O7 | 0.0271 (10) | 0.0367 (11) | 0.0347 (11) | 0.0192 (8) | 0.0168 (8) | 0.0168 (9) |
O8 | 0.0212 (9) | 0.0247 (9) | 0.0255 (10) | 0.0085 (7) | 0.0044 (7) | 0.0065 (7) |
O9 | 0.0175 (9) | 0.0360 (11) | 0.0344 (11) | 0.0132 (8) | 0.0049 (8) | −0.0005 (9) |
O10 | 0.0233 (10) | 0.0400 (12) | 0.0349 (12) | 0.0131 (9) | 0.0059 (8) | 0.0020 (9) |
O11 | 0.0246 (10) | 0.0217 (9) | 0.0509 (13) | 0.0136 (8) | 0.0099 (9) | 0.0082 (9) |
O12 | 0.0373 (12) | 0.0386 (11) | 0.0249 (10) | 0.0151 (9) | 0.0120 (9) | 0.0093 (9) |
O13 | 0.0204 (9) | 0.0294 (10) | 0.0315 (11) | 0.0093 (8) | 0.0027 (8) | 0.0109 (8) |
O14 | 0.0346 (11) | 0.0191 (9) | 0.0396 (12) | 0.0130 (8) | 0.0066 (9) | 0.0015 (8) |
O15 | 0.0286 (11) | 0.0472 (13) | 0.0253 (11) | 0.0015 (9) | −0.0002 (9) | 0.0005 (9) |
O20 | 0.0432 (13) | 0.0325 (11) | 0.0351 (12) | 0.0064 (10) | −0.0005 (10) | 0.0095 (9) |
O21 | 0.0466 (15) | 0.0256 (12) | 0.124 (3) | 0.0102 (11) | 0.0504 (17) | −0.0001 (14) |
O22 | 0.0526 (16) | 0.0596 (16) | 0.0576 (17) | 0.0308 (13) | 0.0163 (13) | 0.0165 (13) |
O23 | 0.0704 (19) | 0.0738 (18) | 0.0350 (13) | 0.0497 (16) | 0.0093 (13) | 0.0025 (12) |
N1 | 0.0239 (11) | 0.0364 (13) | 0.0321 (13) | 0.0191 (10) | 0.0081 (10) | 0.0039 (10) |
N2 | 0.0261 (12) | 0.0374 (14) | 0.0624 (19) | 0.0208 (11) | 0.0165 (12) | 0.0108 (13) |
C1 | 0.0371 (17) | 0.059 (2) | 0.0278 (16) | 0.0199 (15) | 0.0092 (13) | 0.0106 (14) |
C2 | 0.0257 (15) | 0.0376 (17) | 0.057 (2) | 0.0096 (13) | 0.0097 (15) | −0.0050 (15) |
C3 | 0.052 (2) | 0.0402 (17) | 0.0368 (17) | 0.0277 (15) | 0.0183 (15) | 0.0158 (14) |
C4 | 0.0364 (18) | 0.095 (3) | 0.053 (2) | 0.038 (2) | 0.0169 (17) | 0.042 (2) |
C5 | 0.0364 (19) | 0.0291 (17) | 0.114 (4) | 0.0116 (14) | 0.021 (2) | −0.010 (2) |
C6 | 0.0361 (16) | 0.0364 (16) | 0.0297 (15) | 0.0128 (13) | 0.0138 (13) | 0.0064 (12) |
Geometric parameters (Å, º) top
V1—O14 | 1.5819 (19) | O21—H22 | 0.8739 |
V1—O6 | 1.8879 (19) | O21—H23 | 0.8855 |
V1—O8 | 1.8892 (19) | O22—H24 | 0.9850 |
V1—O4 | 1.8996 (18) | O22—H25 | 1.0018 |
V1—O2i | 1.9576 (18) | O23—H26 | 0.9503 |
V1—O5 | 2.2443 (17) | O23—H27 | 0.8070 |
V2—O12 | 1.585 (2) | N1—C2 | 1.478 (4) |
V2—O4 | 1.7661 (18) | N1—C1 | 1.491 (4) |
V2—O13 | 1.9252 (19) | N1—C3 | 1.495 (4) |
V2—O1i | 1.9469 (18) | N1—H1 | 0.9100 |
V2—O3i | 2.0029 (19) | N2—C4 | 1.470 (5) |
V2—O5 | 2.3272 (18) | N2—C6 | 1.490 (4) |
As1—O7 | 1.6539 (18) | N2—C5 | 1.496 (5) |
As1—O3 | 1.6852 (18) | N2—H2 | 0.9100 |
As1—O8 | 1.6920 (18) | C1—C4 | 1.519 (5) |
As1—O11 | 1.7098 (19) | C1—H1A | 0.9700 |
As2—O5 | 1.6651 (17) | C1—H1B | 0.9700 |
As2—O1 | 1.6894 (17) | C2—C5 | 1.522 (5) |
As2—O2 | 1.6945 (17) | C2—H2A | 0.9700 |
As2—O9 | 1.7027 (18) | C2—H2B | 0.9700 |
As3—O10 | 1.648 (2) | C3—C6 | 1.510 (5) |
As3—O13 | 1.6939 (18) | C3—H3A | 0.9700 |
As3—O15 | 1.696 (2) | C3—H3B | 0.9700 |
As3—O6 | 1.7120 (19) | C4—H4A | 0.9700 |
O9—H9 | 0.9702 | C4—H4B | 0.9700 |
O11—H11 | 0.8835 | C5—H5A | 0.9700 |
O15—H15 | 0.9009 | C5—H5B | 0.9700 |
O20—H20 | 0.9059 | C6—H6A | 0.9700 |
O20—H21 | 0.9298 | C6—H6B | 0.9700 |
| | | |
O14—V1—O6 | 99.03 (10) | As2—O9—H9 | 108.0 |
O14—V1—O8 | 99.98 (10) | As1—O11—H11 | 117.0 |
O6—V1—O8 | 93.80 (8) | As3—O13—V2 | 124.54 (10) |
O14—V1—O4 | 100.12 (10) | As3—O15—H15 | 108.6 |
O6—V1—O4 | 86.14 (8) | H20—O20—H21 | 112.7 |
O8—V1—O4 | 159.65 (8) | H22—O21—H23 | 123.9 |
O14—V1—O2i | 94.53 (9) | H24—O22—H25 | 92.5 |
O6—V1—O2i | 164.97 (8) | H26—O23—H27 | 109.8 |
O8—V1—O2i | 90.22 (8) | C2—N1—C1 | 110.7 (3) |
O4—V1—O2i | 85.09 (8) | C2—N1—C3 | 109.7 (2) |
O14—V1—O5 | 175.43 (9) | C1—N1—C3 | 109.1 (2) |
O6—V1—O5 | 83.30 (7) | C2—N1—H1 | 109.1 |
O8—V1—O5 | 83.73 (7) | C1—N1—H1 | 109.1 |
O4—V1—O5 | 76.04 (7) | C3—N1—H1 | 109.1 |
O2i—V1—O5 | 82.74 (7) | C4—N2—C6 | 110.3 (3) |
O12—V2—O4 | 102.49 (10) | C4—N2—C5 | 111.4 (3) |
O12—V2—O13 | 99.81 (10) | C6—N2—C5 | 108.0 (3) |
O4—V2—O13 | 92.37 (8) | C4—N2—H2 | 109.0 |
O12—V2—O1i | 98.36 (10) | C6—N2—H2 | 109.0 |
O4—V2—O1i | 90.12 (8) | C5—N2—H2 | 109.0 |
O13—V2—O1i | 160.67 (8) | N1—C1—C4 | 108.6 (3) |
O12—V2—O3i | 98.45 (10) | N1—C1—H1A | 110.0 |
O4—V2—O3i | 159.01 (8) | C4—C1—H1A | 110.0 |
O13—V2—O3i | 85.55 (8) | N1—C1—H1B | 110.0 |
O1i—V2—O3i | 85.29 (7) | C4—C1—H1B | 110.0 |
O12—V2—O5 | 178.77 (9) | H1A—C1—H1B | 108.4 |
O4—V2—O5 | 76.31 (7) | N1—C2—C5 | 108.4 (3) |
O13—V2—O5 | 80.52 (7) | N1—C2—H2A | 110.0 |
O1i—V2—O5 | 81.46 (7) | C5—C2—H2A | 110.0 |
O3i—V2—O5 | 82.75 (7) | N1—C2—H2B | 110.0 |
O7—As1—O3 | 113.76 (10) | C5—C2—H2B | 110.0 |
O7—As1—O8 | 108.98 (10) | H2A—C2—H2B | 108.4 |
O3—As1—O8 | 114.53 (9) | N1—C3—C6 | 108.7 (2) |
O7—As1—O11 | 109.71 (10) | N1—C3—H3A | 110.0 |
O3—As1—O11 | 100.58 (9) | C6—C3—H3A | 110.0 |
O8—As1—O11 | 108.86 (10) | N1—C3—H3B | 110.0 |
O5—As2—O1 | 114.52 (8) | C6—C3—H3B | 110.0 |
O5—As2—O2 | 112.76 (8) | H3A—C3—H3B | 108.3 |
O1—As2—O2 | 110.59 (9) | N2—C4—C1 | 108.7 (3) |
O5—As2—O9 | 109.41 (9) | N2—C4—H4A | 110.0 |
O1—As2—O9 | 104.43 (9) | C1—C4—H4A | 110.0 |
O2—As2—O9 | 104.27 (9) | N2—C4—H4B | 110.0 |
O10—As3—O13 | 112.23 (10) | C1—C4—H4B | 110.0 |
O10—As3—O15 | 112.17 (11) | H4A—C4—H4B | 108.3 |
O13—As3—O15 | 101.20 (10) | N2—C5—C2 | 108.3 (3) |
O10—As3—O6 | 111.22 (10) | N2—C5—H5A | 110.0 |
O13—As3—O6 | 114.03 (9) | C2—C5—H5A | 110.0 |
O15—As3—O6 | 105.38 (11) | N2—C5—H5B | 110.0 |
As2—O1—V2i | 122.07 (9) | C2—C5—H5B | 110.0 |
As2—O2—V1i | 122.51 (10) | H5A—C5—H5B | 108.4 |
As1—O3—V2i | 124.36 (10) | N2—C6—C3 | 108.7 (2) |
V2—O4—V1 | 119.80 (10) | N2—C6—H6A | 109.9 |
As2—O5—V1 | 133.04 (9) | C3—C6—H6A | 109.9 |
As2—O5—V2 | 138.98 (9) | N2—C6—H6B | 109.9 |
V1—O5—V2 | 87.86 (6) | C3—C6—H6B | 109.9 |
As3—O6—V1 | 127.43 (10) | H6A—C6—H6B | 108.3 |
As1—O8—V1 | 132.74 (11) | | |
Symmetry code: (i) −x+1, −y+1, −z+1. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
O9—H9···O10 | 0.97 | 1.61 | 2.571 (3) | 171 |
O11—H11···O21 | 0.88 | 1.75 | 2.629 (3) | 173 |
O15—H15···O20ii | 0.90 | 1.68 | 2.542 (3) | 158 |
O20—H20···O7i | 0.91 | 1.78 | 2.670 (3) | 168 |
O20—H21···O23iii | 0.93 | 1.81 | 2.740 (4) | 177 |
O21—H22···O10iv | 0.87 | 1.91 | 2.745 (3) | 160 |
O21—H23···O2v | 0.89 | 1.99 | 2.868 (3) | 170 |
O21—H23···O14vi | 0.89 | 2.65 | 3.125 (3) | 115 |
O22—H24···O12 | 0.99 | 2.26 | 3.100 (3) | 142 |
O22—H25···O23iii | 1.00 | 1.90 | 2.897 (4) | 171 |
O23—H26···O4i | 0.95 | 1.86 | 2.808 (3) | 180 |
O23—H27···O20vii | 0.81 | 2.27 | 2.864 (3) | 131 |
N1—H1···O7viii | 0.91 | 1.68 | 2.591 (3) | 179 |
N2—H2···O3i | 0.91 | 2.16 | 2.995 (3) | 152 |
N2—H2···O22 | 0.91 | 2.52 | 3.114 (4) | 123 |
Symmetry codes: (i) −x+1, −y+1, −z+1; (ii) x+1, y+1, z; (iii) x, y, z+1; (iv) −x+2, −y+2, −z+1; (v) x, y+1, z; (vi) −x+1, −y+2, −z+1; (vii) −x+1, −y, −z+1; (viii) −x+2, −y+1, −z+1. |