The title compound, (C4H12N)2[Co(H2O)6][β–Mo8O26], contains β-octamolybdate ([β-Mo8O26]4−), tetramethylammonium and [Co(H2O)6]2+ ions. The [β-Mo8O26]4− anion and [Co(H2O)6]2+ cations lie on inversion centers, and the tetramethylammonium cations lie on twofold rotation axes.
Supporting information
CCDC reference: 242022
Key indicators
- Single-crystal X-ray study
- T = 293 K
- Mean (N-C) = 0.014 Å
- R factor = 0.039
- wR factor = 0.105
- Data-to-parameter ratio = 13.4
checkCIF/PLATON results
No syntax errors found
Alert level C
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ .... ?
PLAT244_ALERT_4_C Low Solvent U(eq) as Compared to Neighbors .... N1
PLAT244_ALERT_4_C Low Solvent U(eq) as Compared to Neighbors .... N2
PLAT720_ALERT_4_C Number of Unusual/Non-Standard Label(s) ........ 9
PLAT764_ALERT_4_C Overcomplete CIF Bond List Detected (Rep/Expd) . 1.18 Ratio
PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 2
Co H12 O6
PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 3
C4 H12 N
0 ALERT level A = In general: serious problem
0 ALERT level B = Potentially serious problem
7 ALERT level C = Check and explain
0 ALERT level G = General alerts; check
1 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
0 ALERT type 2 Indicator that the structure model may be wrong or deficient
0 ALERT type 3 Indicator that the structure quality may be low
6 ALERT type 4 Improvement, methodology, query or suggestion
Data collection: SMART (Siemens, 1996); cell refinement: SMART and SAINT (Siemens,1994); data reduction: XPREP in SHELXTL (Siemens, 1994); program(s) used to solve structure: SHELXTL; program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.
Bis(tetramethylammonium) hexaaquacobalt(II)
β-octamolybdate(vi)
top
Crystal data top
(C4H12N)2[Co(H2O)6][Mo8O26] | F(000) = 2868 |
Mr = 1498.84 | Dx = 2.749 Mg m−3 |
Monoclinic, C2/c | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -C 2yc | Cell parameters from 3856 reflections |
a = 16.0338 (10) Å | θ = 2.0–25.1° |
b = 13.6400 (8) Å | µ = 3.23 mm−1 |
c = 16.6764 (10) Å | T = 293 K |
β = 96.779 (1)° | Prism, red |
V = 3621.6 (4) Å3 | 0.43 × 0.22 × 0.20 mm |
Z = 4 | |
Data collection top
Bruker SMART CCD area-detector diffractometer | 3195 independent reflections |
Radiation source: fine-focus sealed tube | 2825 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.021 |
φ and ω scans | θmax = 25.1°, θmin = 2.0° |
Absorption correction: multi-scan (SADABS; Sheldrick, 1996) | h = −12→19 |
Tmin = 0.421, Tmax = 0.525 | k = −16→14 |
5426 measured reflections | l = −19→19 |
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)] = 0.039 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.105 | H atoms treated by a mixture of independent and constrained refinement |
S = 1.10 | w = 1/[σ2(Fo2) + (0.0357P)2 + 82.4908P] where P = (Fo2 + 2Fc2)/3 |
3195 reflections | (Δ/σ)max = 0.018 |
239 parameters | Δρmax = 0.68 e Å−3 |
0 restraints | Δρmin = −1.02 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 | |
Mo1 | 0.25091 (4) | 0.83709 (4) | 0.42069 (4) | 0.02126 (17) | |
Mo2 | 0.39635 (4) | 0.85422 (5) | 0.57132 (4) | 0.02574 (18) | |
Mo3 | 0.10500 (4) | 0.85708 (5) | 0.53760 (4) | 0.02534 (18) | |
Mo4 | 0.25069 (4) | 0.87542 (5) | 0.69005 (4) | 0.02813 (18) | |
Co1 | 0.2500 | 1.2500 | 0.5000 | 0.0247 (3) | |
OW1 | 0.2267 (4) | 1.1894 (5) | 0.6112 (4) | 0.0419 (14) | |
HW1A | 0.2385 | 1.1309 | 0.6121 | 0.10 (5)* | |
HW1B | 0.2196 | 1.2307 | 0.6454 | 0.13 (7)* | |
O1 | 0.5009 (3) | 0.8290 (5) | 0.5876 (4) | 0.0400 (14) | |
OW2 | 0.3282 (3) | 1.3546 (4) | 0.5599 (3) | 0.0329 (12) | |
HW2A | 0.2997 | 1.3954 | 0.5804 | 0.06 (3)* | |
HW2B | 0.3659 | 1.3802 | 0.5383 | 0.05 (3)* | |
O2 | 0.2503 (3) | 0.7921 (4) | 0.3226 (3) | 0.0288 (11) | |
OW3 | 0.1489 (4) | 1.3403 (4) | 0.5117 (4) | 0.0413 (15) | |
HW3B | 0.1545 | 1.3919 | 0.4877 | 0.14 (7)* | |
HW3A | 0.1108 | 1.3271 | 0.5386 | 0.07 (4)* | |
O3 | 0.1108 (4) | 0.9798 (4) | 0.5207 (4) | 0.0381 (13) | |
O4 | 0.2506 (4) | 0.8613 (4) | 0.7913 (4) | 0.0451 (15) | |
O5 | 0.0007 (3) | 0.8312 (5) | 0.5291 (4) | 0.0431 (15) | |
O6 | 0.3906 (4) | 0.9770 (4) | 0.5537 (3) | 0.0387 (14) | |
O7 | 0.2499 (3) | 0.6687 (4) | 0.4499 (3) | 0.0245 (11) | |
O8 | 0.1344 (3) | 0.8506 (4) | 0.6511 (3) | 0.0314 (12) | |
O9 | 0.1320 (3) | 0.8131 (4) | 0.4291 (3) | 0.0244 (11) | |
O10 | 0.3690 (3) | 0.8117 (4) | 0.4570 (3) | 0.0259 (11) | |
O11 | 0.2514 (4) | 0.9986 (4) | 0.6746 (4) | 0.0421 (14) | |
O12 | 0.3661 (3) | 0.8478 (4) | 0.6769 (3) | 0.0283 (11) | |
O13 | 0.2502 (3) | 0.9597 (4) | 0.4103 (3) | 0.0306 (12) | |
N1 | 0.5000 | 1.1287 (7) | 0.7500 | 0.034 (2) | |
N2 | 0.0000 | 0.9396 (7) | 0.2500 | 0.030 (2) | |
C1 | 0.4479 (9) | 1.1910 (13) | 0.6923 (9) | 0.105 (6) | |
H1A | 0.4130 | 1.2323 | 0.7210 | 0.157* | |
H1B | 0.4132 | 1.1505 | 0.6550 | 0.157* | |
H1C | 0.4835 | 1.2310 | 0.6633 | 0.157* | |
C2 | 0.5554 (8) | 1.0666 (11) | 0.7059 (9) | 0.086 (4) | |
H2A | 0.5890 | 1.0253 | 0.7435 | 0.130* | |
H2B | 0.5914 | 1.1077 | 0.6783 | 0.130* | |
H2C | 0.5217 | 1.0267 | 0.6673 | 0.130* | |
C3 | 0.0569 (7) | 0.8774 (9) | 0.2072 (7) | 0.065 (3) | |
H3A | 0.0241 | 0.8370 | 0.1683 | 0.098* | |
H3B | 0.0901 | 0.8366 | 0.2456 | 0.098* | |
H3C | 0.0933 | 0.9186 | 0.1802 | 0.098* | |
C4 | 0.0514 (6) | 1.0029 (7) | 0.3098 (5) | 0.044 (2) | |
H4A | 0.0149 | 1.0434 | 0.3373 | 0.066* | |
H4B | 0.0876 | 1.0437 | 0.2822 | 0.066* | |
H4C | 0.0847 | 0.9624 | 0.3483 | 0.066* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Mo1 | 0.0183 (3) | 0.0176 (3) | 0.0288 (3) | 0.0025 (2) | 0.0069 (2) | 0.0052 (2) |
Mo2 | 0.0207 (3) | 0.0224 (3) | 0.0347 (4) | −0.0018 (2) | 0.0053 (3) | 0.0026 (3) |
Mo3 | 0.0207 (3) | 0.0236 (3) | 0.0332 (4) | 0.0067 (2) | 0.0098 (3) | 0.0041 (3) |
Mo4 | 0.0325 (4) | 0.0239 (3) | 0.0290 (4) | 0.0049 (3) | 0.0084 (3) | 0.0003 (3) |
Co1 | 0.0214 (7) | 0.0182 (7) | 0.0355 (8) | −0.0006 (5) | 0.0072 (6) | 0.0009 (6) |
OW1 | 0.059 (4) | 0.030 (3) | 0.038 (3) | −0.003 (3) | 0.012 (3) | 0.004 (3) |
O1 | 0.022 (3) | 0.048 (4) | 0.050 (4) | −0.003 (2) | 0.002 (2) | 0.002 (3) |
OW2 | 0.029 (3) | 0.028 (3) | 0.045 (3) | −0.006 (2) | 0.015 (3) | −0.006 (2) |
O2 | 0.028 (3) | 0.028 (3) | 0.031 (3) | 0.006 (2) | 0.008 (2) | 0.010 (2) |
OW3 | 0.031 (3) | 0.030 (3) | 0.067 (4) | 0.008 (2) | 0.022 (3) | 0.014 (3) |
O3 | 0.047 (3) | 0.021 (3) | 0.047 (3) | 0.005 (3) | 0.011 (3) | 0.006 (2) |
O4 | 0.060 (4) | 0.040 (4) | 0.036 (3) | 0.007 (3) | 0.010 (3) | 0.000 (3) |
O5 | 0.025 (3) | 0.046 (4) | 0.061 (4) | 0.006 (3) | 0.014 (3) | 0.009 (3) |
O6 | 0.046 (3) | 0.023 (3) | 0.045 (3) | −0.010 (3) | 0.000 (3) | 0.003 (2) |
O7 | 0.024 (3) | 0.019 (2) | 0.031 (3) | 0.001 (2) | 0.006 (2) | 0.001 (2) |
O8 | 0.034 (3) | 0.032 (3) | 0.032 (3) | 0.010 (2) | 0.016 (2) | 0.004 (2) |
O9 | 0.016 (2) | 0.024 (3) | 0.033 (3) | 0.002 (2) | 0.005 (2) | 0.004 (2) |
O10 | 0.021 (2) | 0.024 (3) | 0.035 (3) | 0.001 (2) | 0.010 (2) | 0.005 (2) |
O11 | 0.056 (4) | 0.026 (3) | 0.045 (3) | 0.003 (3) | 0.008 (3) | −0.001 (3) |
O12 | 0.026 (3) | 0.029 (3) | 0.029 (3) | 0.003 (2) | 0.002 (2) | 0.001 (2) |
O13 | 0.029 (3) | 0.018 (3) | 0.045 (3) | −0.002 (2) | 0.006 (2) | 0.005 (2) |
N1 | 0.033 (5) | 0.031 (5) | 0.037 (5) | 0.000 | 0.005 (4) | 0.000 |
N2 | 0.021 (4) | 0.033 (5) | 0.033 (5) | 0.000 | −0.003 (4) | 0.000 |
C1 | 0.089 (10) | 0.127 (14) | 0.094 (10) | 0.046 (10) | −0.001 (8) | 0.056 (10) |
C2 | 0.068 (8) | 0.091 (10) | 0.107 (11) | 0.021 (7) | 0.039 (8) | −0.008 (8) |
C3 | 0.052 (6) | 0.067 (7) | 0.078 (8) | 0.017 (5) | 0.012 (6) | −0.031 (6) |
C4 | 0.041 (5) | 0.046 (5) | 0.041 (5) | −0.002 (4) | −0.010 (4) | −0.008 (4) |
Geometric parameters (Å, º) top
Mo1—O13 | 1.681 (5) | OW2—HW2A | 0.8200 |
Mo1—O2 | 1.746 (5) | OW2—HW2B | 0.8184 |
Mo1—O10 | 1.950 (5) | O2—Mo4i | 2.295 (5) |
Mo1—O9 | 1.956 (5) | OW3—HW3B | 0.8200 |
Mo1—O7i | 2.162 (5) | OW3—HW3A | 0.8191 |
Mo1—O7 | 2.348 (5) | O7—Mo1i | 2.162 (5) |
Mo2—O1 | 1.701 (5) | O7—Mo3i | 2.338 (5) |
Mo2—O6 | 1.701 (5) | O7—Mo2i | 2.350 (5) |
Mo2—O12 | 1.882 (5) | O7—Mo4i | 2.409 (5) |
Mo2—O10 | 1.992 (5) | O9—Mo2i | 2.327 (5) |
Mo2—O9i | 2.327 (5) | O10—Mo3i | 2.339 (5) |
Mo2—O7i | 2.350 (5) | N1—C1iii | 1.469 (12) |
Mo3—O5 | 1.699 (6) | N1—C1 | 1.469 (12) |
Mo3—O3 | 1.701 (5) | N1—C2iii | 1.483 (12) |
Mo3—O8 | 1.898 (5) | N1—C2 | 1.483 (12) |
Mo3—O9 | 2.002 (5) | N2—C3 | 1.488 (11) |
Mo3—O7i | 2.338 (5) | N2—C3iv | 1.488 (11) |
Mo3—O10i | 2.339 (5) | N2—C4 | 1.492 (10) |
Mo4—O4 | 1.699 (6) | N2—C4iv | 1.492 (10) |
Mo4—O11 | 1.700 (6) | C1—H1A | 0.9600 |
Mo4—O12 | 1.926 (5) | C1—H1B | 0.9600 |
Mo4—O8 | 1.931 (6) | C1—H1C | 0.9600 |
Mo4—O2i | 2.295 (5) | C2—H2A | 0.9600 |
Mo4—O7i | 2.409 (5) | C2—H2B | 0.9600 |
Co1—OW3ii | 2.063 (5) | C2—H2C | 0.9600 |
Co1—OW3 | 2.063 (5) | C3—H3A | 0.9600 |
Co1—OW2ii | 2.076 (5) | C3—H3B | 0.9600 |
Co1—OW2 | 2.076 (5) | C3—H3C | 0.9600 |
Co1—OW1 | 2.104 (6) | C4—H4A | 0.9600 |
Co1—OW1ii | 2.104 (6) | C4—H4B | 0.9600 |
OW1—HW1A | 0.8200 | C4—H4C | 0.9600 |
OW1—HW1B | 0.8200 | | |
| | | |
O13—Mo1—O2 | 104.7 (3) | OW3ii—Co1—OW1ii | 85.9 (3) |
O13—Mo1—O10 | 101.7 (2) | OW3—Co1—OW1ii | 94.1 (3) |
O2—Mo1—O10 | 97.2 (2) | OW2ii—Co1—OW1ii | 90.3 (2) |
O13—Mo1—O9 | 100.3 (2) | OW2—Co1—OW1ii | 89.7 (2) |
O2—Mo1—O9 | 96.4 (2) | OW1—Co1—OW1ii | 180.000 (1) |
O10—Mo1—O9 | 150.2 (2) | Co1—OW1—HW1A | 109.5 |
O13—Mo1—O7i | 98.0 (2) | Co1—OW1—HW1B | 113.4 |
O2—Mo1—O7i | 157.3 (2) | HW1A—OW1—HW1B | 135.1 |
O10—Mo1—O7i | 78.67 (19) | Co1—OW2—HW2A | 109.5 |
O9—Mo1—O7i | 78.57 (19) | Co1—OW2—HW2B | 121.1 |
O13—Mo1—O7 | 173.8 (2) | HW2A—OW2—HW2B | 111.8 |
O2—Mo1—O7 | 81.4 (2) | Mo1—O2—Mo4i | 115.8 (2) |
O10—Mo1—O7 | 78.01 (19) | Co1—OW3—HW3B | 109.5 |
O9—Mo1—O7 | 77.93 (18) | Co1—OW3—HW3A | 124.4 |
O7i—Mo1—O7 | 75.9 (2) | HW3B—OW3—HW3A | 126.0 |
O1—Mo2—O6 | 105.0 (3) | Mo1i—O7—Mo3i | 91.61 (18) |
O1—Mo2—O12 | 101.5 (3) | Mo1i—O7—Mo1 | 104.1 (2) |
O6—Mo2—O12 | 101.1 (3) | Mo3i—O7—Mo1 | 97.73 (18) |
O1—Mo2—O10 | 101.2 (3) | Mo1i—O7—Mo2i | 91.26 (17) |
O6—Mo2—O10 | 96.9 (2) | Mo3i—O7—Mo2i | 163.3 (2) |
O12—Mo2—O10 | 146.1 (2) | Mo1—O7—Mo2i | 97.50 (18) |
O1—Mo2—O9i | 89.5 (2) | Mo1i—O7—Mo4i | 163.4 (2) |
O6—Mo2—O9i | 163.4 (2) | Mo3i—O7—Mo4i | 86.50 (16) |
O12—Mo2—O9i | 83.4 (2) | Mo1—O7—Mo4i | 92.47 (17) |
O10—Mo2—O9i | 71.99 (19) | Mo2i—O7—Mo4i | 86.07 (16) |
O1—Mo2—O7i | 160.7 (2) | Mo3—O8—Mo4 | 116.3 (3) |
O6—Mo2—O7i | 94.1 (2) | Mo1—O9—Mo3 | 109.3 (2) |
O12—Mo2—O7i | 76.8 (2) | Mo1—O9—Mo2i | 110.8 (2) |
O10—Mo2—O7i | 73.42 (18) | Mo3—O9—Mo2i | 103.5 (2) |
O9i—Mo2—O7i | 71.21 (16) | Mo1—O10—Mo2 | 109.9 (2) |
O5—Mo3—O3 | 105.3 (3) | Mo1—O10—Mo3i | 110.4 (2) |
O5—Mo3—O8 | 101.5 (3) | Mo2—O10—Mo3i | 103.4 (2) |
O3—Mo3—O8 | 101.5 (3) | Mo2—O12—Mo4 | 117.1 (3) |
O5—Mo3—O9 | 100.3 (3) | C1iii—N1—C1 | 109.2 (16) |
O3—Mo3—O9 | 97.1 (2) | C1iii—N1—C2iii | 109.4 (9) |
O8—Mo3—O9 | 146.4 (2) | C1—N1—C2iii | 109.1 (9) |
O5—Mo3—O7i | 159.4 (2) | C1iii—N1—C2 | 109.1 (9) |
O3—Mo3—O7i | 95.1 (2) | C1—N1—C2 | 109.4 (9) |
O8—Mo3—O7i | 77.1 (2) | C2iii—N1—C2 | 110.5 (13) |
O9—Mo3—O7i | 73.54 (18) | C3—N2—C3iv | 110.5 (12) |
O5—Mo3—O10i | 88.2 (2) | C3—N2—C4 | 109.2 (6) |
O3—Mo3—O10i | 164.0 (2) | C3iv—N2—C4 | 109.3 (6) |
O8—Mo3—O10i | 83.9 (2) | C3—N2—C4iv | 109.3 (6) |
O9—Mo3—O10i | 71.56 (18) | C3iv—N2—C4iv | 109.2 (6) |
O7i—Mo3—O10i | 71.20 (17) | C4—N2—C4iv | 109.2 (9) |
O4—Mo4—O11 | 105.2 (3) | N1—C1—H1A | 109.5 |
O4—Mo4—O12 | 101.8 (3) | N1—C1—H1B | 109.5 |
O11—Mo4—O12 | 98.7 (3) | H1A—C1—H1B | 109.5 |
O4—Mo4—O8 | 101.6 (3) | N1—C1—H1C | 109.5 |
O11—Mo4—O8 | 98.4 (3) | H1A—C1—H1C | 109.5 |
O12—Mo4—O8 | 146.1 (2) | H1B—C1—H1C | 109.5 |
O4—Mo4—O2i | 88.7 (2) | N1—C2—H2A | 109.5 |
O11—Mo4—O2i | 166.0 (2) | N1—C2—H2B | 109.5 |
O12—Mo4—O2i | 78.0 (2) | H2A—C2—H2B | 109.5 |
O8—Mo4—O2i | 78.4 (2) | N1—C2—H2C | 109.5 |
O4—Mo4—O7i | 159.0 (2) | H2A—C2—H2C | 109.5 |
O11—Mo4—O7i | 95.7 (2) | H2B—C2—H2C | 109.5 |
O12—Mo4—O7i | 74.59 (19) | N2—C3—H3A | 109.5 |
O8—Mo4—O7i | 74.78 (19) | N2—C3—H3B | 109.5 |
O2i—Mo4—O7i | 70.28 (17) | H3A—C3—H3B | 109.5 |
OW3ii—Co1—OW3 | 180.000 (2) | N2—C3—H3C | 109.5 |
OW3ii—Co1—OW2ii | 88.9 (2) | H3A—C3—H3C | 109.5 |
OW3—Co1—OW2ii | 91.1 (2) | H3B—C3—H3C | 109.5 |
OW3ii—Co1—OW2 | 91.1 (2) | N2—C4—H4A | 109.5 |
OW3—Co1—OW2 | 88.9 (2) | N2—C4—H4B | 109.5 |
OW2ii—Co1—OW2 | 180.000 (1) | H4A—C4—H4B | 109.5 |
OW3ii—Co1—OW1 | 94.1 (3) | N2—C4—H4C | 109.5 |
OW3—Co1—OW1 | 85.9 (3) | H4A—C4—H4C | 109.5 |
OW2ii—Co1—OW1 | 89.7 (2) | H4B—C4—H4C | 109.5 |
OW2—Co1—OW1 | 90.3 (2) | | |
Symmetry codes: (i) −x+1/2, −y+3/2, −z+1; (ii) −x+1/2, −y+5/2, −z+1; (iii) −x+1, y, −z+3/2; (iv) −x, y, −z+1/2. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
OW1—HW1A···O11 | 0.82 | 2.08 | 2.819 (8) | 150 |
OW1—HW1B···O4v | 0.82 | 2.10 | 2.852 (9) | 153 |
OW2—HW2A···O13ii | 0.82 | 2.14 | 2.897 (7) | 152 |
OW2—HW2A···O4v | 0.82 | 2.42 | 2.916 (8) | 120 |
OW2—HW2B···O3ii | 0.82 | 2.20 | 2.859 (8) | 138 |
OW2—HW2B···O5vi | 0.82 | 2.28 | 2.889 (8) | 131 |
OW3—HW3B···O6ii | 0.82 | 2.02 | 2.764 (8) | 151 |
OW3—HW3A···O1vii | 0.82 | 2.03 | 2.822 (8) | 163 |
Symmetry codes: (ii) −x+1/2, −y+5/2, −z+1; (v) −x+1/2, y+1/2, −z+3/2; (vi) x+1/2, y+1/2, z; (vii) x−1/2, y+1/2, z. |