Polymeric tri­aqua­bis(μ₃-3-carboxy­benzene­sulfonato)­barium(II)

The Ba atom in the title polymeric compound, poly­[[tri­aqua­barium(II)]-di-μ₃-3-carboxy­benzene­sulfonato] [Ba(C₇H₅O₅S)₂(H₂O)₃]_n, exists in a nine-coordinate tricapped trigonal prismatic geometry; the dianionic units engage in μ₃-bridging, giving a three-dimensional network. The crystal packing network is dominated by hydrogen bonds.

Key indicators

• Single-crystal X-ray study
• T = 295 K
• Mean [sigma](C-C) = 0.003 Å
• R factor = 0.017
• wR factor = 0.046
• Data-to-parameter ratio = 14.5

checkCIF/PLATON results

No syntax errors found



Alert level C
ABSTM02_ALERT_3_C  The ratio of expected to reported Tmax/Tmin(RR') is < 0.90
            Tmin and Tmax reported:      0.392     0.636
            Tmin' and Tmax expected:      0.440     0.639
            RR' =      0.895
            Please check that your absorption correction is appropriate.
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ ....          ?
PLAT061_ALERT_3_C Tmax/Tmin Range Test RR' too Large .............       0.87
PLAT720_ALERT_4_C Number of Unusual/Non-Standard Label(s) ........          6
PLAT731_ALERT_1_C Bond    Calc     0.84(3), Rep   0.840(10) ......       3.00 su-Rat
              O3W  -H3W1    1.555   1.555
PLAT735_ALERT_1_C D-H     Calc     0.84(3), Rep   0.840(10) ......       3.00 su-Rat
              O3W  -H5#     1.555   1.555

   0 ALERT level A = In general: serious problem
   0 ALERT level B = Potentially serious problem
   6 ALERT level C = Check and explain
   0 ALERT level G = General alerts; check

   3 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
   2 ALERT type 3 Indicator that the structure quality may be low
   1 ALERT type 4 Improvement, methodology, query or suggestion

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Computing details

Data collection: RAPID-AUTO (Rigaku, 1998); cell refinement: RAPID-AUTO; data reduction: CrystalStructure (Rigaku/MSC, 2002); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEPII (Johnson, 1976); software used to prepare material for publication: SHELXL97.

poly[[triaquabarium(II)]-di-µ₃-3-carboxybenzenesulfonato]

Crystal data

[Ba(C7H5O5S)2(H2O)3]	F(000) = 1168
Mr = 593.73	Dx = 2.053 Mg m^−3
Monoclinic, P21/n	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yn	Cell parameters from 17416 reflections
a = 10.259 (2) Å	θ = 3.0–27.5°
b = 8.775 (2) Å	µ = 2.35 mm^−1
c = 21.813 (4) Å	T = 295 K
β = 101.93 (3)°	Block, colourless
V = 1921.2 (7) Å^3	0.34 × 0.26 × 0.19 mm
Z = 4

Data collection

Rigaki R-AXIS-RAPID IP diffractometer	4402 independent reflections
Radiation source: fine-focus sealed tube	4132 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.017
ω scans	θmax = 27.5°, θmin = 3.0°
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	h = −13→13
Tmin = 0.392, Tmax = 0.636	k = −11→11
18503 measured reflections	l = −28→28

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.017	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.046	H atoms treated by a mixture of independent and constrained refinement
S = 1.01	w = 1/[σ^2(Fo^2) + (0.0311P)^2 + 0.7392P] where P = (Fo^2 + 2Fc^2)/3
4402 reflections	(Δ/σ)max = 0.001
303 parameters	Δρmax = 0.52 e Å^−3
11 restraints	Δρmin = −0.30 e Å^−3

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Ba1	0.508805 (9)	0.40600 (1)	0.76067 (1)	0.0187 (1)
S1	0.77415 (4)	0.54726 (5)	0.65836 (2)	0.02030 (9)
S2	0.32866 (4)	0.02221 (5)	0.67772 (2)	0.02156 (9)
O1w	0.5262 (2)	0.7175 (2)	0.7636 (1)	0.0399 (4)
O2w	0.3822 (1)	0.1753 (2)	0.8291 (1)	0.0296 (3)
O3w	0.7881 (2)	0.5805 (2)	0.8210 (1)	0.0488 (4)
O1	0.6861 (1)	0.4439 (2)	0.6827 (1)	0.0319 (3)
O2	0.7990 (1)	0.6882 (2)	0.6941 (1)	0.0293 (3)
O3	0.8968 (1)	0.4716 (2)	0.6511 (1)	0.0299 (3)
O4	0.7675 (2)	0.3742 (2)	0.4280 (1)	0.0358 (3)
O5	0.6250 (1)	0.5158 (2)	0.3604 (1)	0.0323 (3)
O6	0.4301 (1)	0.1386 (2)	0.6965 (1)	0.0333 (3)
O7	0.2461 (1)	0.0042 (2)	0.7245 (1)	0.0314 (3)
O8	0.3843 (2)	−0.1201 (2)	0.6611 (1)	0.0391 (4)
O9	0.2468 (2)	−0.0768 (2)	0.4352 (1)	0.0386 (4)
O10	0.0792 (2)	0.0697 (2)	0.3875 (1)	0.0366 (3)
C1	0.6905 (2)	0.6004 (2)	0.5817 (1)	0.0197 (3)
C2	0.7145 (2)	0.5200 (2)	0.5304 (1)	0.0207 (3)
C3	0.6487 (2)	0.5621 (2)	0.4702 (1)	0.0207 (3)
C4	0.5589 (2)	0.6825 (2)	0.4622 (1)	0.0248 (3)
C5	0.5350 (2)	0.7612 (2)	0.5141 (1)	0.0291 (4)
C6	0.6011 (2)	0.7209 (2)	0.5739 (1)	0.0260 (4)
C7	0.6771 (2)	0.4829 (2)	0.4140 (1)	0.0232 (3)
C8	0.2228 (2)	0.0913 (2)	0.6093 (1)	0.0217 (3)
C9	0.2271 (2)	0.0265 (2)	0.5517 (1)	0.0226 (3)
C10	0.1481 (2)	0.0879 (2)	0.4977 (1)	0.0229 (3)
C11	0.0652 (2)	0.2107 (2)	0.5017 (1)	0.0291 (4)
C12	0.0615 (2)	0.2743 (2)	0.5596 (1)	0.0320 (4)
C13	0.1406 (2)	0.2154 (2)	0.6134 (1)	0.0283 (4)
C14	0.1535 (2)	0.0264 (2)	0.4349 (1)	0.0257 (4)
H4o	0.790 (3)	0.346 (3)	0.3947 (8)	0.05 (1)*
H9o	0.254 (3)	−0.094 (3)	0.398 (1)	0.05 (1)*
H1w1	0.557 (3)	0.782 (2)	0.791 (1)	0.06 (1)*
H1w2	0.484 (2)	0.763 (2)	0.731 (1)	0.05 (1)*
H2w1	0.446 (2)	0.111 (2)	0.839 (1)	0.06 (1)*
H2w2	0.327 (2)	0.139 (3)	0.798 (1)	0.07 (1)*
H3w1	0.763 (3)	0.655 (3)	0.797 (2)	0.11 (2)*
H3w2	0.869 (1)	0.560 (4)	0.822 (2)	0.09 (1)*
H2	0.7739	0.4387	0.5361	0.025*
H4	0.5147	0.7104	0.4221	0.030*
H5	0.4744	0.8413	0.5086	0.035*
H6	0.5855	0.7742	0.6086	0.031*
H9	0.2819	−0.0567	0.5492	0.027*
H11	0.0119	0.2505	0.4655	0.035*
H12	0.0058	0.3566	0.5621	0.038*
H13	0.1389	0.2585	0.6522	0.034*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1	0.02171 (6)	0.02063 (6)	0.01324 (6)	0.00162 (3)	0.00241 (4)	0.00142 (3)
S1	0.0211 (2)	0.0256 (2)	0.0143 (2)	−0.0035 (2)	0.0039 (2)	−0.0014 (2)
S2	0.0240 (2)	0.0257 (2)	0.0146 (2)	−0.0022 (2)	0.0029 (2)	−0.0011 (2)
O1w	0.058 (1)	0.0234 (7)	0.0352 (9)	−0.0005 (6)	0.0031 (8)	0.0003 (6)
O2w	0.0286 (7)	0.0370 (7)	0.0233 (7)	−0.0033 (6)	0.0054 (5)	−0.0013 (6)
O3w	0.054 (1)	0.064 (1)	0.0318 (9)	0.0063 (8)	0.0172 (8)	0.0159 (8)
O1	0.0367 (7)	0.0366 (7)	0.0242 (7)	−0.0112 (6)	0.0107 (6)	0.0030 (6)
O2	0.0340 (7)	0.0314 (7)	0.0215 (6)	−0.0070 (5)	0.0032 (5)	−0.0071 (5)
O3	0.0257 (6)	0.0404 (7)	0.0233 (6)	0.0055 (6)	0.0039 (5)	0.0007 (6)
O4	0.0471 (9)	0.0418 (8)	0.0176 (7)	0.0192 (7)	0.0044 (6)	−0.0017 (6)
O5	0.0368 (7)	0.0416 (7)	0.0158 (6)	0.0050 (6)	−0.0005 (5)	0.0012 (6)
O6	0.0310 (7)	0.0406 (7)	0.0264 (7)	−0.0131 (6)	0.0016 (6)	−0.0020 (6)
O7	0.0317 (7)	0.0446 (8)	0.0189 (6)	−0.0090 (6)	0.0072 (5)	−0.0005 (6)
O8	0.0528 (9)	0.0378 (7)	0.0235 (7)	0.0164 (7)	0.0005 (6)	−0.0031 (6)
O9	0.0464 (9)	0.0493 (9)	0.0182 (7)	0.0162 (7)	0.0019 (6)	−0.0012 (6)
O10	0.0374 (8)	0.0515 (9)	0.0173 (6)	0.0037 (6)	−0.0025 (6)	0.0051 (6)
C1	0.0193 (8)	0.0246 (8)	0.0150 (8)	−0.0047 (6)	0.0031 (6)	−0.0011 (6)
C2	0.0195 (7)	0.0243 (8)	0.0179 (8)	0.0000 (6)	0.0029 (6)	−0.0005 (6)
C3	0.0201 (8)	0.0251 (7)	0.0163 (8)	−0.0042 (6)	0.0027 (6)	−0.0005 (6)
C4	0.0233 (8)	0.0275 (8)	0.0218 (8)	0.0003 (7)	0.0007 (7)	0.0030 (7)
C5	0.0273 (9)	0.0266 (8)	0.0333 (10)	0.0055 (7)	0.0059 (8)	0.0006 (8)
C6	0.0268 (8)	0.0274 (8)	0.0250 (9)	−0.0003 (7)	0.0078 (7)	−0.0044 (7)
C7	0.0249 (8)	0.0257 (8)	0.0180 (8)	−0.0012 (7)	0.0021 (6)	0.0011 (7)
C8	0.0216 (8)	0.0263 (8)	0.0172 (8)	−0.0035 (6)	0.0037 (6)	0.0010 (6)
C9	0.0222 (8)	0.0254 (8)	0.0199 (8)	0.0002 (7)	0.0035 (6)	0.0001 (7)
C10	0.0210 (8)	0.0292 (9)	0.0177 (8)	−0.0041 (6)	0.0023 (7)	0.0013 (6)
C11	0.0228 (8)	0.0351 (9)	0.0275 (9)	0.0013 (7)	0.0010 (7)	0.0065 (8)
C12	0.0277 (9)	0.0335 (9)	0.0356 (10)	0.0068 (8)	0.0082 (8)	0.0020 (8)
C13	0.0285 (9)	0.0319 (9)	0.0262 (9)	−0.0006 (7)	0.0093 (7)	−0.0039 (8)
C14	0.0261 (8)	0.0318 (9)	0.0178 (8)	−0.0047 (7)	0.0011 (7)	0.0031 (7)

Geometric parameters (Å, º)

Ba1—O1	2.754 (2)	C4—C5	1.391 (3)
Ba1—O2^i	2.777 (1)	C5—C6	1.387 (3)
Ba1—O5^ii	2.799 (2)	C8—C9	1.388 (2)
Ba1—O6	2.765 (2)	C8—C13	1.392 (2)
Ba1—O7^iii	2.834 (1)	C9—C10	1.392 (3)
Ba1—O10^iv	2.718 (2)	C10—C11	1.387 (3)
Ba1—O1w	2.739 (2)	C10—C14	1.484 (3)
Ba1—O2w	2.969 (2)	C11—C12	1.387 (3)
Ba1—O3w	3.276 (2)	C12—C13	1.383 (3)
S1—O2	1.456 (1)	O4—H4o	0.84 (1)
S1—O1	1.456 (1)	O9—H9o	0.85 (1)
S1—O3	1.460 (1)	O1w—H1w1	0.84 (1)
S1—C1	1.777 (2)	O1w—H1w2	0.85 (1)
S2—O8	1.450 (2)	O2w—H2w1	0.86 (1)
S2—O6	1.456 (1)	O2w—H2w2	0.85 (1)
S2—O7	1.464 (1)	O3w—H3w1	0.84 (1)
S2—C8	1.762 (2)	O3w—H3w2	0.85 (1)
O4—C7	1.321 (2)	C2—H2	0.93
O5—C7	1.215 (2)	C4—H4	0.93
O9—C14	1.316 (2)	C5—H5	0.93
O10—C14	1.213 (2)	C6—H6	0.93
C1—C2	1.386 (2)	C9—H9	0.93
C1—C6	1.388 (2)	C11—H11	0.93
C2—C3	1.398 (2)	C12—H12	0.93
C3—C4	1.389 (2)	C13—H13	0.93
C3—C7	1.488 (2)
O1—Ba1—O10^iv	123.24 (5)	C2—C1—C6	120.8 (2)
O1—Ba1—O2^i	77.96 (4)	C2—C1—S1	119.6 (1)
O1—Ba1—O5^ii	69.23 (5)	C6—C1—S1	119.5 (1)
O1—Ba1—O6	87.20 (4)	C1—C2—C3	119.5 (2)
O1—Ba1—O7^iii	140.91 (4)	C4—C3—C2	119.9 (2)
O1—Ba1—O1w	81.14 (4)	C4—C3—C7	119.3 (2)
O1—Ba1—O2w	143.70 (4)	C2—C3—C7	120.8 (2)
O1—Ba1—O3w	63.72 (4)	C3—C4—C5	120.0 (2)
O2^i—Ba1—O5^ii	132.67 (4)	C6—C5—C4	120.4 (2)
O2^i—Ba1—O6	72.97 (5)	C5—C6—C1	119.4 (2)
O2^i—Ba1—O7^iii	140.60 (4)	O5—C7—O4	122.8 (2)
O2^i—Ba1—O10^iv	70.91 (5)	O5—C7—C3	124.0 (2)
O2^i—Ba1—O1w	129.84 (5)	O4—C7—C3	113.3 (2)
O2^i—Ba1—O2w	72.80 (4)	C9—C8—C13	120.8 (2)
O2^i—Ba1—O3w	71.40 (5)	C9—C8—S2	119.8 (1)
O5^ii—Ba1—O6	72.29 (4)	C13—C8—S2	119.3 (1)
O5^ii—Ba1—O7^iii	75.47 (5)	C8—C9—C10	119.0 (2)
O5^ii—Ba1—O10^iv	156.37 (4)	C11—C10—C9	120.4 (2)
O5^ii—Ba1—O1w	78.13 (4)	C11—C10—C14	118.8 (2)
O5^ii—Ba1—O2w	117.50 (4)	C9—C10—C14	120.9 (2)
O5^ii—Ba1—O3w	118.83 (5)	C10—C11—C12	120.1 (2)
O6—Ba1—O7^iii	97.81 (5)	C13—C12—C11	120.1 (2)
O6—Ba1—O10^iv	124.72 (4)	C12—C13—C8	119.6 (2)
O6—Ba1—O1w	150.39 (4)	O10—C14—O9	123.2 (2)
O6—Ba1—O2w	64.13 (4)	O10—C14—C10	122.5 (2)
O6—Ba1—O3w	137.69 (5)	O9—C14—C10	114.4 (2)
O7^iii—Ba1—O10^iv	85.26 (5)	C7—O4—H4o	109 (2)
O7^iii—Ba1—O1w	75.59 (5)	C14—O9—H9o	109 (2)
O7^iii—Ba1—O2w	68.90 (4)	Ba1—O1w—H1w1	135 (2)
O7^iii—Ba1—O3w	124.28 (5)	Ba1—O1w—H1w2	116 (2)
O10^iv—Ba1—O1w	84.00 (5)	H1w1—O1w—H1w2	109 (2)
O10^iv—Ba1—O2w	66.02 (4)	Ba1—O2w—H2w1	101 (2)
O10^iv—Ba1—O3w	61.85 (5)	Ba1—O2w—H2w2	98 (2)
O1w—Ba1—O2w	134.56 (4)	H2w1—O2w—H2w2	108 (2)
O1w—Ba1—O3w	58.46 (5)	Ba1—O3w—H3w1	89 (3)
O2w—Ba1—O3w	123.63 (4)	Ba1—O3w—H3w2	133 (3)
O2—S1—O1	112.7 (1)	H3w1—O3w—H3w2	110 (2)
O2—S1—O3	112.6 (1)	C1—C2—H2	120.2
O1—S1—O3	111.7 (1)	C3—C2—H2	120.2
O2—S1—C1	106.2 (1)	C3—C4—H4	120.0
O1—S1—C1	107.0 (1)	C5—C4—H4	120.0
O3—S1—C1	106.0 (1)	C6—C5—H5	119.8
O8—S2—O6	112.3 (1)	C4—C5—H5	119.8
O8—S2—O7	113.3 (1)	C5—C6—H6	120.3
O6—S2—O7	111.3 (1)	C1—C6—H6	120.3
O8—S2—C8	106.9 (1)	C8—C9—H9	120.5
O6—S2—C8	106.1 (1)	C10—C9—H9	120.5
O7—S2—C8	106.5 (1)	C10—C11—H11	119.9
S1—O1—Ba1	147.1 (1)	C12—C11—H11	120.0
S1—O2—Ba1^v	143.9 (1)	C13—C12—H12	119.9
C7—O5—Ba1^ii	176.7 (1)	C11—C12—H12	119.9
S2—O6—Ba1	148.8 (1)	C12—C13—H13	120.2
S2—O7—Ba1^vi	142.5 (1)	C8—C13—H13	120.2
C14—O10—Ba1^vii	151.7 (1)
O2—S1—O1—Ba1	13.4 (2)	S1—C1—C2—C3	−179.9 (1)
O3—S1—O1—Ba1	141.5 (1)	C1—C2—C3—C4	−0.8 (3)
C1—S1—O1—Ba1	−102.9 (2)	C1—C2—C3—C7	177.0 (2)
O10^iv—Ba1—O1—S1	−65.1 (2)	C2—C3—C4—C5	0.3 (3)
O1w—Ba1—O1—S1	11.7 (2)	C7—C3—C4—C5	−177.6 (2)
O6—Ba1—O1—S1	164.4 (2)	C3—C4—C5—C6	0.4 (3)
O2^i—Ba1—O1—S1	−122.4 (2)	C4—C5—C6—C1	−0.5 (3)
O5^ii—Ba1—O1—S1	92.3 (2)	C2—C1—C6—C5	0.0 (3)
O7^iii—Ba1—O1—S1	65.5 (2)	S1—C1—C6—C5	−179.4 (1)
O2w—Ba1—O1—S1	−159.2 (1)	C4—C3—C7—O5	−0.9 (3)
O3w—Ba1—O1—S1	−47.4 (2)	C2—C3—C7—O5	−178.8 (2)
O1—S1—O2—Ba1^v	143.2 (1)	C4—C3—C7—O4	177.8 (2)
O3—S1—O2—Ba1^v	15.7 (2)	C2—C3—C7—O4	−0.1 (2)
C1—S1—O2—Ba1^v	−100.0 (1)	O8—S2—C8—C9	−12.5 (2)
O8—S2—O6—Ba1	−157.7 (1)	O6—S2—C8—C9	107.5 (2)
O7—S2—O6—Ba1	−29.5 (2)	O7—S2—C8—C9	−133.9 (1)
C8—S2—O6—Ba1	85.9 (2)	O8—S2—C8—C13	170.6 (2)
O10^iv—Ba1—O6—S2	73.5 (2)	O6—S2—C8—C13	−69.4 (2)
O1w—Ba1—O6—S2	−90.6 (2)	O7—S2—C8—C13	49.2 (2)
O1—Ba1—O6—S2	−157.2 (2)	C13—C8—C9—C10	0.3 (3)
O2^i—Ba1—O6—S2	124.6 (2)	S2—C8—C9—C10	−176.5 (1)
O5^ii—Ba1—O6—S2	−88.1 (2)	C8—C9—C10—C11	−0.9 (3)
O7^iii—Ba1—O6—S2	−16.1 (2)	C8—C9—C10—C14	177.5 (2)
O2w—Ba1—O6—S2	45.8 (2)	C9—C10—C11—C12	0.7 (3)
O3w—Ba1—O6—S2	158.3 (1)	C14—C10—C11—C12	−177.7 (2)
O8—S2—O7—Ba1^vi	−76.9 (2)	C10—C11—C12—C13	0.0 (3)
O6—S2—O7—Ba1^vi	155.5 (1)	C11—C12—C13—C8	−0.6 (3)
C8—S2—O7—Ba1^vi	40.3 (2)	C9—C8—C13—C12	0.4 (3)
O2—S1—C1—C2	145.2 (1)	S2—C8—C13—C12	177.3 (2)
O1—S1—C1—C2	−94.2 (2)	Ba1^vii—O10—C14—O9	−14.5 (4)
O3—S1—C1—C2	25.2 (2)	Ba1^vii—O10—C14—C10	164.4 (2)
O2—S1—C1—C6	−35.4 (2)	C11—C10—C14—O10	−7.2 (3)
O1—S1—C1—C6	85.2 (2)	C9—C10—C14—O10	174.4 (2)
O3—S1—C1—C6	−155.4 (1)	C11—C10—C14—O9	171.8 (2)
C6—C1—C2—C3	0.7 (3)	C9—C10—C14—O9	−6.6 (3)

Symmetry codes: (i) −x+3/2, y−1/2, −z+3/2; (ii) −x+1, −y+1, −z+1; (iii) −x+1/2, y+1/2, −z+3/2; (iv) x+1/2, −y+1/2, z+1/2; (v) −x+3/2, y+1/2, −z+3/2; (vi) −x+1/2, y−1/2, −z+3/2; (vii) x−1/2, −y+1/2, z−1/2.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O4—H4o···O2w^viii	0.84 (1)	1.88 (1)	2.697 (2)	163 (3)
O9—H9o···O3w^vii	0.85 (1)	1.78 (1)	2.611 (2)	165 (3)
O1w—H1w1···O3^v	0.84 (1)	2.08 (1)	2.907 (2)	168 (2)
O1w—H1w2···O8^ix	0.85 (1)	1.95 (1)	2.793 (2)	176 (2)
O2w—H2w1···O3^i	0.86 (1)	2.00 (1)	2.849 (2)	170 (3)
O2w—H2w2···O7	0.85 (1)	2.03 (1)	2.845 (2)	161 (3)
O3w—H3w1···O2	0.84 (1)	2.36 (3)	2.949 (2)	127 (3)
O3w—H3w2···O6^v	0.85 (1)	2.28 (2)	3.036 (2)	148 (3)

Symmetry codes: (i) −x+3/2, y−1/2, −z+3/2; (v) −x+3/2, y+1/2, −z+3/2; (vii) x−1/2, −y+1/2, z−1/2; (viii) x+1/2, −y+1/2, z−1/2; (ix) x, y+1, z.