Bis(benzimidazole-κN)bis­(3,5-dihydroxy­benzoato-κO)copper(II) trihydrate

In the crystal structure of the title compound, [Cu(C₇H₅O₄)₂(C₇H₆N₂)₂]·3H₂O, the Cu^II ion is coordinated by two benzimidazole (bzim) mol­ecules and two 3,5-dihydroxy­benzoate (dhba) anions in a tetra­hedrally distorted square-planar geometry. Aromatic π–π stacking is observed between parallel bzim ligands and between roughly parallel bzim and dhba units. An extensive O—H...O and N—H...O hydrogen-bonding network helps to consolidate the crystal structure.

Key indicators

• Single-crystal X-ray study
• T = 295 K
• Mean [sigma](C-C) = 0.004 Å
• R factor = 0.043
• wR factor = 0.105
• Data-to-parameter ratio = 16.2

checkCIF/PLATON results

No syntax errors found



Alert level C
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ ....          ?
PLAT220_ALERT_2_C Large Non-Solvent    C     Ueq(max)/Ueq(min) ...       2.57 Ratio

   0 ALERT level A = In general: serious problem
   0 ALERT level B = Potentially serious problem
   2 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
   1 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
   0 ALERT type 4 Improvement, methodology, query or suggestion
   0 ALERT type 5 Informative message, check

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Computing details

Data collection: PROCESS-AUTO (Rigaku, 1998); cell refinement: PROCESS-AUTO; data reduction: CrystalStructure (Rigaku/MSC, 2002); program(s) used to solve structure: SIR92 (Altomare et al., 1993); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: WinGX (Farrugia, 1999).

Bis(benzimidazole-κN)bis(3,5-dihydroxybenzoato-κO)copper(II) trihydrate

Crystal data

[Cu(C7H5O4)2(C7H6N2)2]·3H2O	F(000) = 1364
Mr = 660.08	Dx = 1.561 Mg m^−3
Monoclinic, P21/n	Mo Kα radiation, λ = 0.71075 Å
Hall symbol: -P 2yn	Cell parameters from 16422 reflections
a = 16.313 (5) Å	θ = 3.2–25.0°
b = 9.740 (2) Å	µ = 0.85 mm^−1
c = 17.838 (5) Å	T = 295 K
β = 97.605 (12)°	Prism, blue
V = 2809.4 (13) Å^3	0.33 × 0.23 × 0.10 mm
Z = 4

Data collection

Rigaku R-AXIS RAPID diffractometer	6430 independent reflections
Radiation source: fine-focus sealed tube	4732 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.051
Detector resolution: 10.00 pixels mm^-1	θmax = 27.5°, θmin = 3.1°
ω scans	h = −21→21
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	k = −11→12
Tmin = 0.735, Tmax = 0.920	l = −22→23
26824 measured reflections

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)] = 0.043	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.105	H-atom parameters constrained
S = 1.04	w = 1/[σ^2(Fo^2) + (0.0463P)^2 + 1.3478P] where P = (Fo^2 + 2Fc^2)/3
6430 reflections	(Δ/σ)max = 0.003
397 parameters	Δρmax = 0.46 e Å^−3
0 restraints	Δρmin = −0.51 e Å^−3

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
Cu	0.523352 (16)	0.23846 (3)	0.728768 (17)	0.02705 (9)
O1	0.64223 (9)	0.21813 (17)	0.75022 (10)	0.0323 (4)
O2	0.63678 (10)	0.02912 (17)	0.81960 (10)	0.0348 (4)
O3	0.93650 (10)	−0.09567 (17)	0.89023 (10)	0.0371 (4)
H3	0.9907	−0.0880	0.8979	0.056*
O4	0.94352 (10)	0.30999 (17)	0.74467 (10)	0.0332 (4)
H4	0.9127	0.3865	0.7181	0.050*
O5	0.40469 (10)	0.26706 (18)	0.70583 (10)	0.0357 (4)
O6	0.40430 (10)	0.41995 (19)	0.61298 (11)	0.0385 (4)
O7	0.11162 (12)	0.5796 (2)	0.56279 (13)	0.0568 (6)
H7	0.0610	0.5945	0.5742	0.085*
O8	0.11454 (12)	0.2475 (2)	0.76162 (12)	0.0518 (5)
H8	0.0599	0.2537	0.7509	0.078*
N31	0.51434 (12)	0.08665 (19)	0.65349 (12)	0.0294 (4)
N33	0.45771 (13)	−0.0984 (2)	0.59546 (12)	0.0356 (5)
H33	0.4215	−0.1605	0.5812	0.043*
N41	0.53075 (12)	0.3764 (2)	0.81251 (12)	0.0321 (5)
N43	0.58761 (14)	0.5522 (2)	0.87933 (12)	0.0389 (5)
H43	0.6245	0.6104	0.8979	0.047*
C11	0.76880 (13)	0.1190 (2)	0.80193 (13)	0.0241 (5)
C12	0.81087 (14)	0.0147 (2)	0.84402 (13)	0.0268 (5)
H12	0.7820	−0.0523	0.8668	0.032*
C13	0.89640 (14)	0.0121 (2)	0.85153 (13)	0.0263 (5)
C14	0.93993 (14)	0.1118 (2)	0.81898 (13)	0.0266 (5)
H14	0.9974	0.1095	0.8249	0.032*
C15	0.89723 (14)	0.2160 (2)	0.77721 (13)	0.0256 (5)
C16	0.81150 (14)	0.2207 (2)	0.76868 (14)	0.0264 (5)
H16	0.7831	0.2910	0.7411	0.032*
C17	0.67608 (14)	0.1203 (2)	0.79039 (13)	0.0269 (5)
C21	0.27723 (14)	0.3700 (2)	0.65894 (14)	0.0303 (5)
C22	0.23475 (15)	0.4643 (3)	0.61048 (16)	0.0386 (6)
H22	0.2621	0.5119	0.5760	0.046*
C23	0.15182 (15)	0.4877 (3)	0.61338 (15)	0.0366 (6)
C24	0.11065 (15)	0.4177 (3)	0.66457 (15)	0.0356 (6)
H24	0.0551	0.4355	0.6674	0.043*
C25	0.15299 (15)	0.3210 (3)	0.71149 (15)	0.0347 (6)
C26	0.23621 (14)	0.2964 (3)	0.70876 (15)	0.0333 (5)
H26	0.2643	0.2308	0.7402	0.040*
C27	0.36874 (14)	0.3519 (2)	0.65853 (14)	0.0301 (5)
C32	0.44767 (15)	0.0082 (3)	0.64041 (14)	0.0334 (6)
H32	0.3989	0.0255	0.6605	0.040*
C34	0.53641 (16)	−0.0911 (2)	0.57598 (14)	0.0321 (5)
C35	0.57805 (18)	−0.1762 (3)	0.53173 (15)	0.0408 (6)
H35	0.5534	−0.2542	0.5086	0.049*
C36	0.65745 (18)	−0.1396 (3)	0.52377 (16)	0.0453 (7)
H36	0.6880	−0.1947	0.4951	0.054*
C37	0.69352 (17)	−0.0213 (3)	0.55772 (16)	0.0441 (7)
H37	0.7471	0.0015	0.5500	0.053*
C38	0.65220 (16)	0.0630 (3)	0.60235 (15)	0.0362 (6)
H38	0.6769	0.1415	0.6248	0.043*
C39	0.57236 (15)	0.0256 (2)	0.61231 (14)	0.0300 (5)
C42	0.59862 (16)	0.4501 (3)	0.83210 (14)	0.0348 (6)
H42	0.6488	0.4322	0.8146	0.042*
C44	0.50637 (17)	0.5482 (3)	0.89323 (14)	0.0383 (6)
C45	0.4638 (2)	0.6299 (3)	0.93876 (17)	0.0512 (8)
H45	0.4888	0.7035	0.9660	0.061*
C46	0.3832 (2)	0.5959 (4)	0.94130 (18)	0.0618 (10)
H46	0.3518	0.6488	0.9703	0.074*
C47	0.3466 (2)	0.4839 (4)	0.90144 (18)	0.0593 (9)
H47	0.2917	0.4633	0.9053	0.071*
C48	0.38901 (18)	0.4023 (3)	0.85641 (16)	0.0485 (7)
H48	0.3641	0.3274	0.8303	0.058*
C49	0.47086 (16)	0.4374 (3)	0.85178 (14)	0.0347 (6)
O1W	0.81032 (18)	0.2677 (3)	0.54857 (18)	0.0909 (10)
H1A	0.8270	0.3205	0.5130	0.136*
H1B	0.7535	0.2637	0.5293	0.136*
O2W	0.62801 (13)	0.3305 (2)	0.47268 (12)	0.0493 (5)
H2A	0.6189	0.4136	0.4479	0.074*
H2B	0.6043	0.3554	0.5147	0.074*
O3W	−0.04935 (13)	0.6018 (3)	0.56466 (12)	0.0622 (6)
H3A	−0.0833	0.5430	0.5288	0.093*
H3B	−0.0783	0.5827	0.6072	0.093*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cu	0.01576 (14)	0.02784 (16)	0.03709 (17)	0.00162 (11)	0.00179 (11)	0.00016 (13)
O1	0.0159 (8)	0.0327 (9)	0.0471 (10)	0.0035 (7)	0.0002 (7)	−0.0020 (8)
O2	0.0238 (9)	0.0376 (9)	0.0446 (10)	−0.0069 (7)	0.0105 (8)	−0.0038 (8)
O3	0.0219 (9)	0.0341 (9)	0.0545 (11)	0.0028 (7)	0.0021 (8)	0.0155 (9)
O4	0.0199 (8)	0.0308 (8)	0.0500 (10)	0.0003 (7)	0.0088 (7)	0.0115 (8)
O5	0.0179 (8)	0.0422 (10)	0.0466 (10)	0.0040 (7)	0.0034 (7)	−0.0004 (9)
O6	0.0199 (9)	0.0453 (10)	0.0518 (11)	−0.0037 (7)	0.0103 (8)	0.0012 (9)
O7	0.0291 (10)	0.0697 (14)	0.0736 (15)	0.0133 (10)	0.0146 (10)	0.0345 (12)
O8	0.0239 (9)	0.0694 (14)	0.0642 (13)	0.0033 (9)	0.0142 (9)	0.0297 (11)
N31	0.0207 (10)	0.0282 (10)	0.0384 (11)	−0.0006 (8)	0.0007 (8)	0.0004 (9)
N33	0.0330 (12)	0.0315 (11)	0.0406 (12)	−0.0083 (9)	−0.0014 (10)	−0.0001 (10)
N41	0.0260 (11)	0.0351 (11)	0.0357 (11)	0.0032 (9)	0.0056 (9)	0.0004 (9)
N43	0.0404 (13)	0.0374 (12)	0.0390 (12)	−0.0057 (10)	0.0055 (10)	−0.0041 (10)
C11	0.0158 (11)	0.0254 (11)	0.0317 (12)	0.0005 (8)	0.0052 (9)	−0.0032 (9)
C12	0.0213 (12)	0.0268 (11)	0.0334 (12)	−0.0032 (9)	0.0071 (9)	0.0020 (10)
C13	0.0209 (11)	0.0252 (11)	0.0325 (12)	0.0044 (9)	0.0020 (9)	0.0007 (10)
C14	0.0161 (11)	0.0271 (11)	0.0368 (13)	0.0010 (9)	0.0041 (9)	−0.0016 (10)
C15	0.0206 (11)	0.0230 (11)	0.0338 (12)	−0.0012 (9)	0.0061 (9)	−0.0006 (10)
C16	0.0188 (11)	0.0237 (11)	0.0369 (12)	0.0026 (9)	0.0041 (9)	−0.0009 (10)
C17	0.0192 (11)	0.0271 (11)	0.0350 (12)	−0.0013 (9)	0.0054 (9)	−0.0097 (10)
C21	0.0172 (11)	0.0350 (12)	0.0387 (13)	−0.0006 (9)	0.0042 (10)	−0.0042 (11)
C22	0.0215 (12)	0.0468 (15)	0.0494 (15)	−0.0013 (11)	0.0114 (11)	0.0084 (13)
C23	0.0234 (13)	0.0406 (14)	0.0453 (15)	0.0034 (11)	0.0029 (11)	0.0096 (12)
C24	0.0186 (12)	0.0447 (14)	0.0445 (14)	0.0028 (10)	0.0076 (11)	0.0030 (12)
C25	0.0223 (12)	0.0417 (14)	0.0411 (14)	−0.0019 (11)	0.0078 (11)	0.0022 (12)
C26	0.0177 (11)	0.0407 (13)	0.0409 (14)	0.0026 (10)	0.0021 (10)	0.0026 (12)
C27	0.0192 (11)	0.0321 (12)	0.0394 (13)	−0.0025 (10)	0.0049 (10)	−0.0094 (11)
C32	0.0237 (12)	0.0353 (13)	0.0403 (14)	−0.0032 (10)	0.0007 (10)	0.0027 (11)
C34	0.0319 (13)	0.0309 (12)	0.0323 (13)	−0.0003 (10)	−0.0005 (10)	0.0039 (11)
C35	0.0501 (17)	0.0352 (14)	0.0367 (14)	0.0000 (12)	0.0042 (12)	−0.0035 (12)
C36	0.0441 (17)	0.0513 (16)	0.0417 (15)	0.0105 (14)	0.0103 (13)	−0.0048 (14)
C37	0.0292 (14)	0.0599 (18)	0.0442 (15)	0.0007 (13)	0.0089 (12)	−0.0023 (14)
C38	0.0296 (13)	0.0397 (14)	0.0391 (14)	−0.0050 (11)	0.0041 (11)	−0.0030 (12)
C39	0.0272 (13)	0.0295 (12)	0.0329 (12)	0.0019 (10)	0.0019 (10)	0.0032 (11)
C42	0.0292 (13)	0.0385 (14)	0.0370 (13)	−0.0010 (11)	0.0061 (11)	−0.0021 (12)
C44	0.0440 (16)	0.0387 (14)	0.0331 (13)	0.0084 (12)	0.0086 (12)	0.0050 (12)
C45	0.067 (2)	0.0461 (16)	0.0419 (16)	0.0145 (15)	0.0136 (15)	−0.0018 (14)
C46	0.068 (2)	0.075 (2)	0.0465 (18)	0.0318 (19)	0.0205 (17)	0.0025 (18)
C47	0.0408 (18)	0.087 (3)	0.0536 (18)	0.0151 (17)	0.0179 (15)	0.0075 (19)
C48	0.0365 (16)	0.067 (2)	0.0431 (16)	0.0032 (14)	0.0101 (13)	0.0024 (15)
C49	0.0337 (14)	0.0392 (13)	0.0322 (13)	0.0076 (11)	0.0074 (11)	0.0049 (11)
O1W	0.0811 (19)	0.0693 (17)	0.132 (3)	0.0263 (14)	0.0524 (18)	0.0497 (17)
O2W	0.0513 (13)	0.0418 (11)	0.0564 (12)	−0.0099 (9)	0.0133 (10)	−0.0029 (10)
O3W	0.0389 (12)	0.0963 (18)	0.0534 (13)	0.0070 (12)	0.0135 (10)	0.0115 (13)

Geometric parameters (Å, º)

Cu—O1	1.9365 (17)	C21—C22	1.383 (4)
Cu—O5	1.9449 (17)	C21—C27	1.504 (3)
Cu—N31	1.990 (2)	C22—C23	1.380 (3)
Cu—N41	2.001 (2)	C22—H22	0.9300
C17—O1	1.274 (3)	C23—C24	1.383 (4)
C17—O2	1.249 (3)	C24—C25	1.383 (4)
C27—O5	1.268 (3)	C24—H24	0.9300
C27—O6	1.249 (3)	C25—C26	1.386 (3)
O3—C13	1.373 (3)	C26—H26	0.9300
O3—H3	0.8804	C32—H32	0.9300
O4—C15	1.364 (3)	C34—C35	1.383 (4)
O4—H4	0.9841	C34—C39	1.398 (3)
O7—C23	1.374 (3)	C35—C36	1.369 (4)
O7—H7	0.8890	C35—H35	0.9300
O8—C25	1.361 (3)	C36—C37	1.395 (4)
O8—H8	0.8889	C36—H36	0.9300
N31—C32	1.325 (3)	C37—C38	1.380 (4)
N31—C39	1.405 (3)	C37—H37	0.9300
N33—C32	1.335 (3)	C38—C39	1.386 (3)
N33—C34	1.375 (3)	C38—H38	0.9300
N33—H33	0.8600	C42—H42	0.9300
N41—C42	1.327 (3)	C44—C45	1.388 (4)
N41—C49	1.407 (3)	C44—C49	1.390 (4)
N43—C42	1.331 (3)	C45—C46	1.362 (5)
N43—C44	1.381 (3)	C45—H45	0.9300
N43—H43	0.8600	C46—C47	1.393 (5)
C11—C12	1.389 (3)	C46—H46	0.9300
C11—C16	1.389 (3)	C47—C48	1.379 (4)
C11—C17	1.499 (3)	C47—H47	0.9300
C12—C13	1.384 (3)	C48—C49	1.391 (4)
C12—H12	0.9300	C48—H48	0.9300
C13—C14	1.376 (3)	O1W—H1A	0.8873
C14—C15	1.390 (3)	O1W—H1B	0.9458
C14—H14	0.9300	O2W—H2A	0.9250
C15—C16	1.388 (3)	O2W—H2B	0.9195
C16—H16	0.9300	O3W—H3A	0.9747
C21—C26	1.382 (4)	O3W—H3B	0.9634
O1—Cu—O5	177.50 (7)	C25—C24—H24	120.4
O1—Cu—N31	92.29 (7)	O8—C25—C24	121.3 (2)
O5—Cu—N31	88.96 (8)	O8—C25—C26	118.1 (2)
O1—Cu—N41	87.78 (8)	C24—C25—C26	120.6 (2)
O5—Cu—N41	91.19 (8)	C21—C26—C25	119.6 (2)
N31—Cu—N41	174.07 (8)	C21—C26—H26	120.2
C17—O1—Cu	122.41 (15)	C25—C26—H26	120.2
C13—O3—H3	114.5	O6—C27—O5	124.4 (2)
C15—O4—H4	115.9	O6—C27—C21	119.2 (2)
C27—O5—Cu	126.38 (16)	O5—C27—C21	116.4 (2)
C23—O7—H7	109.5	N31—C32—N33	113.0 (2)
C25—O8—H8	111.0	N31—C32—H32	123.5
C32—N31—C39	104.9 (2)	N33—C32—H32	123.5
C32—N31—Cu	122.23 (18)	N33—C34—C35	131.2 (2)
C39—N31—Cu	132.29 (16)	N33—C34—C39	105.9 (2)
C32—N33—C34	107.7 (2)	C35—C34—C39	123.0 (3)
C32—N33—H33	126.1	C36—C35—C34	116.5 (3)
C34—N33—H33	126.1	C36—C35—H35	121.8
C42—N41—C49	104.5 (2)	C34—C35—H35	121.8
C42—N41—Cu	121.71 (17)	C35—C36—C37	121.4 (3)
C49—N41—Cu	132.69 (17)	C35—C36—H36	119.3
C42—N43—C44	107.8 (2)	C37—C36—H36	119.3
C42—N43—H43	126.1	C38—C37—C36	122.1 (3)
C44—N43—H43	126.1	C38—C37—H37	118.9
C12—C11—C16	120.8 (2)	C36—C37—H37	118.9
C12—C11—C17	119.9 (2)	C37—C38—C39	117.2 (2)
C16—C11—C17	119.3 (2)	C37—C38—H38	121.4
C13—C12—C11	119.1 (2)	C39—C38—H38	121.4
C13—C12—H12	120.5	C38—C39—C34	119.8 (2)
C11—C12—H12	120.5	C38—C39—N31	131.7 (2)
O3—C13—C14	120.9 (2)	C34—C39—N31	108.4 (2)
O3—C13—C12	118.0 (2)	N41—C42—N43	113.2 (2)
C14—C13—C12	121.1 (2)	N41—C42—H42	123.4
C13—C14—C15	119.4 (2)	N43—C42—H42	123.4
C13—C14—H14	120.3	N43—C44—C45	131.0 (3)
C15—C14—H14	120.3	N43—C44—C49	105.6 (2)
O4—C15—C16	122.5 (2)	C45—C44—C49	123.4 (3)
O4—C15—C14	116.8 (2)	C46—C45—C44	116.2 (3)
C16—C15—C14	120.6 (2)	C46—C45—H45	121.9
C15—C16—C11	119.0 (2)	C44—C45—H45	121.9
C15—C16—H16	120.5	C45—C46—C47	121.5 (3)
C11—C16—H16	120.5	C45—C46—H46	119.2
O2—C17—O1	123.9 (2)	C47—C46—H46	119.2
O2—C17—C11	120.1 (2)	C48—C47—C46	122.3 (3)
O1—C17—C11	116.0 (2)	C48—C47—H47	118.8
C26—C21—C22	120.1 (2)	C46—C47—H47	118.8
C26—C21—C27	120.5 (2)	C47—C48—C49	116.9 (3)
C22—C21—C27	119.4 (2)	C47—C48—H48	121.5
C23—C22—C21	119.9 (2)	C49—C48—H48	121.5
C23—C22—H22	120.0	C44—C49—C48	119.6 (3)
C21—C22—H22	120.0	C44—C49—N41	108.9 (2)
O7—C23—C22	117.9 (2)	C48—C49—N41	131.4 (3)
O7—C23—C24	121.6 (2)	H1A—O1W—H1B	98.1
C22—C23—C24	120.5 (2)	H2A—O2W—H2B	95.8
C23—C24—C25	119.2 (2)	H3A—O3W—H3B	96.1
C23—C24—H24	120.4

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N33—H33···O2W^i	0.86	2.03	2.845 (3)	158
N43—H43···O1W^ii	0.86	2.03	2.875 (4)	167
O3—H3···O6^iii	0.88	1.75	2.610 (2)	165
O4—H4···O2^ii	0.98	1.70	2.681 (3)	174
O7—H7···O3W	0.89	1.79	2.639 (3)	160
O8—H8···O4^iv	0.89	1.97	2.832 (3)	165
O1W—H1A···O7^v	0.89	2.03	2.907 (4)	168
O1W—H1B···O2W	0.95	2.26	3.160 (4)	160
O2W—H2A···O6^v	0.92	1.96	2.882 (3)	175
O2W—H2B···O3^ii	0.92	1.96	2.878 (3)	175
O3W—H3A···O7^vi	0.97	2.03	2.951 (3)	158
O3W—H3B···O2^vii	0.96	1.79	2.753 (3)	173

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