Synthesis and structure of trans-bis­(4-amino-3-nitro­benzoato-κO)bis­(4-amino-3-nitro­benzoic acid-κO)di­aqua­manganese(II) dihydrate

The manganese title complex, [Mn(C₇H₅N₂O₄)₂(C₇H₆N₂O₄)₂(H₂O)₂]·2H₂O, is one of the first 4-amino 3-nitro­benzoic acid (4 A3NBA) monoligand metal complexes to be synthesized. It crystallizes in the centrosymmetric monoclinic space group P2₁/n with the complex mol­ecules located on inversion centers. Four 4 A3NBA ligand mol­ecules are monodentately coordinated by the Mn²⁺ ion through the carb­oxy­lic oxygen atoms while the other two positions of the inner coordination sphere are occupied by water mol­ecules, giving rise to a distorted octa­hedron, and two water mol­ecules are in the outer coordination sphere. There are two intra­molecular hydrogen bonds in the complex mol­ecule. The first is of the common N—H...O=N type, while the second is a rarely occurring very strong hydrogen bond in which a common proton is shared by two uncoordinated oxygen atoms of neighboring carboxyl­ate groups. In the crystal, an intricate system of inter­molecular hydrogen bonds links the complex mol­ecules into a three-dimensional-network.

Key indicators

Structure: I

• Single-crystal X-ray study
• T = 293 K
• Mean [sigma](C-C) = 0.002 Å
• R factor = 0.035
• wR factor = 0.097
• Data-to-parameter ratio = 12.2

checkCIF/PLATON results

No syntax errors found



Alert level C
PLAT222_ALERT_3_C NonSolvent Resd 1  H   Uiso(max)/Uiso(min) Range        4.4 Ratio
PLAT241_ALERT_2_C High   'MainMol' Ueq as Compared to Neighbors of         O1 Check
PLAT242_ALERT_2_C Low    'MainMol' Ueq as Compared to Neighbors of        Mn1 Check
PLAT250_ALERT_2_C Large U3/U1 Ratio for <U(i,j)> Tensor(Resd    1)        2.1 Note
PLAT417_ALERT_2_C Short Inter D-H..H-D       H1WB     ..H2WB     .       2.12 Ang.
                                                      x,y,z  =      1_555 Check
PLAT911_ALERT_3_C Missing FCF Refl Between Thmin & STh/L=    0.600          6 Report
                2  0  0,  -2  2  1,   0  3  1,  -2  1  2,   3  0  5,   1  1  7,

Alert level G
PLAT002_ALERT_2_G Number of Distance or Angle Restraints on AtSite          3 Note
PLAT007_ALERT_5_G Number of Unrefined Donor-H Atoms ..............          6 Report
              H2A   H2B   H4A   H4B   H2WA  H2WB
PLAT172_ALERT_4_G The CIF-Embedded .res File Contains DFIX Records          2 Report
PLAT199_ALERT_1_G Reported _cell_measurement_temperature ..... (K)        293 Check
PLAT200_ALERT_1_G Reported   _diffrn_ambient_temperature ..... (K)        293 Check
PLAT303_ALERT_2_G Full Occupancy Atom H2O       with # Connections       2.00 Check
PLAT480_ALERT_4_G Long H...A H-Bond Reported H9       ..N2       .       2.66 Ang.
PLAT480_ALERT_4_G Long H...A H-Bond Reported H2WB     ..O5       .       2.65 Ang.
PLAT720_ALERT_4_G Number of Unusual/Non-Standard Labels ..........          4 Note
              H1WA    H1WB    H2WA    H2WB
PLAT794_ALERT_5_G Tentative Bond Valency for Mn1       (II)      .       2.21 Info
PLAT860_ALERT_3_G Number of Least-Squares Restraints .............          3 Note
PLAT899_ALERT_4_G SHELXL2018 is Deprecated and Succeeded by SHELXL     2019/3 Note
PLAT912_ALERT_4_G Missing # of FCF Reflections Above STh/L=  0.600         19 Note
PLAT913_ALERT_3_G Missing # of Very Strong Reflections in FCF ....          3 Note
                2  0  0,  -2  2  1,  -2  1  2,
PLAT933_ALERT_2_G Number of HKL-OMIT Records in Embedded .res File          6 Note
                3  0  5,   1  1  7,   0  3  1,  -2  1  2,   2  0  0,  -2  2  1,
PLAT941_ALERT_3_G Average HKL Measurement Multiplicity ...........        1.0 Low
PLAT965_ALERT_2_G The SHELXL WEIGHT Optimisation has not Converged     Please Check
PLAT969_ALERT_5_G The 'Henn et al.' R-Factor-gap value ...........       2.88 Note
              Predicted wR2: Based on SigI   2  3.38 or SHELX Weight  9.60       
PLAT978_ALERT_2_G Number C-C Bonds with Positive Residual Density.         11 Info

   0 ALERT level A = Most likely a serious problem - resolve or explain
   0 ALERT level B = A potentially serious problem, consider carefully
   6 ALERT level C = Check. Ensure it is not caused by an omission or oversight
  19 ALERT level G = General information/check it is not something unexpected

   2 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   9 ALERT type 2 Indicator that the structure model may be wrong or deficient
   5 ALERT type 3 Indicator that the structure quality may be low
   6 ALERT type 4 Improvement, methodology, query or suggestion
   3 ALERT type 5 Informative message, check

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Computing details

trans-Bis(4-amino-3-nitrobenzoato-κO)bis(4-amino-3-nitrobenzoic acid-κO)diaquamanganese(II) dihydrate

Crystal data

[Mn(C7H5MnN2O4)2(C7H6MnN2O4)2(H2O)2]·2H2O	F(000) = 878
Mr = 853.54	Dx = 1.672 Mg m^−3
Monoclinic, P21/n	Cu Kα radiation, λ = 1.54184 Å
a = 7.0419 (1) Å	Cell parameters from 11377 reflections
b = 19.2513 (3) Å	θ = 2.3–71.4°
c = 12.7175 (2) Å	µ = 4.08 mm^−1
β = 100.513 (2)°	T = 293 K
V = 1695.12 (5) Å^3	Block, light pink
Z = 2	0.28 × 0.22 × 0.14 mm

Data collection

XtaLAB Synergy, Single source at home/near, HyPix3000 diffractometer	3291 independent reflections
Radiation source: micro-focus sealed X-ray tube	2966 reflections with I > 2σ(I)
Detector resolution: 10.0000 pixels mm^-1	Rint = 0.037
ω scans	θmax = 71.5°, θmin = 4.2°
Absorption correction: multi-scan (CrysAlisPro; Rigaku OD, 2023)	h = −8→8
Tmin = 0.523, Tmax = 1.000	k = −23→22
3291 measured reflections	l = −15→15

Refinement

Refinement on F^2	Primary atom site location: dual
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.035	Hydrogen site location: mixed
wR(F^2) = 0.097	H atoms treated by a mixture of independent and constrained refinement
S = 1.06	w = 1/[σ^2(Fo^2) + (0.0608P)^2 + 0.2227P] where P = (Fo^2 + 2Fc^2)/3
3291 reflections	(Δ/σ)max < 0.001
269 parameters	Δρmax = 0.27 e Å^−3
3 restraints	Δρmin = −0.44 e Å^−3

Special details

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. The hydrogen atoms of water molecules and amino groups were located in difference-Fourier maps and refined freely. The H atoms of the benzene ring were calculated geometrically with C—H = 0.93 A° and U_iso(H) = 1.2U_eq(C).

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

	x	y	z	Uiso*/Ueq
Mn1	0.500000	0.500000	0.000000	0.02947 (13)
O1	0.4809 (2)	0.39058 (6)	0.03322 (11)	0.0489 (4)
O1W	0.8075 (2)	0.50832 (7)	0.05836 (12)	0.0464 (3)
H1WA	0.848 (4)	0.5418 (9)	0.0964 (19)	0.070*
H1WB	0.879 (4)	0.4760 (9)	0.078 (2)	0.070*
O2	0.6022 (2)	0.36153 (7)	0.20147 (10)	0.0515 (4)
H2O	0.619 (6)	0.422 (2)	0.242 (3)	0.155 (15)*
O3	0.5562 (2)	0.13009 (7)	0.31842 (10)	0.0560 (4)
O4	0.4652 (2)	0.04466 (7)	0.21207 (11)	0.0545 (4)
O5	0.4355 (2)	0.52907 (8)	0.15374 (10)	0.0457 (3)
O6	0.6122 (2)	0.47449 (7)	0.29174 (10)	0.0483 (4)
O7	0.7667 (2)	0.59190 (8)	0.62838 (11)	0.0590 (4)
O8	0.6914 (2)	0.69874 (8)	0.65088 (11)	0.0612 (4)
N1	0.4964 (2)	0.10712 (7)	0.22733 (11)	0.0363 (3)
N2	0.3472 (2)	0.06488 (7)	0.00606 (12)	0.0431 (4)
H2A	0.302809	0.057204	−0.060340	0.052*
H2B	0.365807	0.034904	0.056060	0.052*
N3	0.6948 (2)	0.64740 (8)	0.59270 (12)	0.0410 (4)
N4	0.5654 (3)	0.77954 (8)	0.48424 (14)	0.0481 (4)
H4A	0.587279	0.778868	0.553450	0.058*
H4B	0.516269	0.814368	0.445160	0.058*
C1	0.4755 (2)	0.27328 (8)	0.08203 (13)	0.0297 (3)
C2	0.5071 (2)	0.22409 (8)	0.16193 (13)	0.0294 (3)
H2	0.557893	0.237429	0.231674	0.035*
C3	0.4636 (2)	0.15439 (8)	0.13907 (12)	0.0291 (3)
C4	0.3884 (2)	0.13131 (8)	0.03426 (12)	0.0298 (3)
C5	0.3551 (3)	0.18352 (9)	−0.04571 (13)	0.0351 (4)
H5	0.303735	0.170966	−0.115751	0.042*
C6	0.3963 (2)	0.25158 (9)	−0.02257 (13)	0.0333 (4)
H6	0.371609	0.284412	−0.076992	0.040*
C7	0.5212 (2)	0.34754 (8)	0.10562 (13)	0.0335 (4)
C8	0.5352 (2)	0.59261 (9)	0.31259 (13)	0.0330 (4)
C9	0.6043 (2)	0.59219 (9)	0.42108 (13)	0.0338 (4)
H9	0.643858	0.550494	0.455105	0.041*
C10	0.6160 (2)	0.65326 (9)	0.48065 (13)	0.0333 (4)
C11	0.5581 (2)	0.71818 (9)	0.43305 (15)	0.0358 (4)
C12	0.4899 (3)	0.71660 (9)	0.32115 (15)	0.0409 (4)
H12	0.453293	0.758055	0.285614	0.049*
C13	0.4760 (3)	0.65655 (10)	0.26390 (14)	0.0384 (4)
H13	0.426366	0.657803	0.190964	0.046*
C14	0.5253 (3)	0.52789 (9)	0.24730 (13)	0.0352 (4)
O2W	1.0872 (2)	0.40951 (8)	0.13520 (11)	0.0542 (4)
H2WA	1.119577	0.406931	0.203299	0.081*
H2WB	1.161577	0.433931	0.103999	0.081*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mn1	0.0436 (2)	0.02138 (19)	0.01972 (19)	−0.00214 (14)	−0.00417 (15)	0.00137 (12)
O1	0.0807 (10)	0.0235 (6)	0.0358 (7)	−0.0052 (6)	−0.0070 (6)	0.0050 (5)
O1W	0.0456 (7)	0.0419 (8)	0.0444 (8)	0.0030 (6)	−0.0114 (6)	−0.0121 (6)
O2	0.0808 (10)	0.0297 (7)	0.0340 (7)	−0.0014 (6)	−0.0157 (6)	−0.0019 (5)
O3	0.0926 (11)	0.0393 (7)	0.0283 (7)	−0.0025 (7)	−0.0099 (7)	0.0063 (5)
O4	0.0851 (10)	0.0251 (6)	0.0454 (8)	−0.0059 (6)	−0.0086 (7)	0.0091 (5)
O5	0.0584 (8)	0.0528 (8)	0.0221 (6)	0.0066 (6)	−0.0030 (5)	−0.0078 (5)
O6	0.0748 (9)	0.0322 (7)	0.0303 (7)	0.0027 (6)	−0.0106 (6)	−0.0053 (5)
O7	0.0864 (11)	0.0519 (9)	0.0318 (7)	0.0122 (8)	−0.0079 (7)	0.0002 (6)
O8	0.0824 (11)	0.0605 (9)	0.0366 (8)	0.0046 (8)	−0.0006 (7)	−0.0225 (7)
N1	0.0459 (8)	0.0285 (7)	0.0305 (7)	0.0019 (6)	−0.0038 (6)	0.0066 (5)
N2	0.0643 (10)	0.0265 (7)	0.0336 (8)	−0.0027 (7)	−0.0044 (7)	−0.0028 (6)
N3	0.0479 (9)	0.0443 (9)	0.0287 (7)	−0.0013 (7)	0.0012 (6)	−0.0084 (6)
N4	0.0589 (10)	0.0334 (8)	0.0510 (10)	0.0015 (7)	0.0072 (8)	−0.0093 (7)
C1	0.0353 (8)	0.0235 (8)	0.0280 (8)	0.0022 (6)	0.0001 (6)	0.0019 (6)
C2	0.0360 (8)	0.0249 (8)	0.0247 (7)	0.0012 (6)	−0.0010 (6)	−0.0008 (6)
C3	0.0347 (8)	0.0242 (8)	0.0267 (8)	0.0035 (6)	0.0011 (6)	0.0042 (6)
C4	0.0333 (8)	0.0243 (7)	0.0299 (8)	0.0013 (6)	0.0003 (6)	−0.0020 (6)
C5	0.0468 (9)	0.0304 (9)	0.0244 (8)	−0.0012 (7)	−0.0036 (7)	−0.0015 (6)
C6	0.0422 (9)	0.0282 (8)	0.0268 (8)	0.0010 (7)	−0.0013 (7)	0.0045 (6)
C7	0.0421 (9)	0.0248 (8)	0.0307 (8)	0.0003 (7)	−0.0012 (7)	0.0030 (6)
C8	0.0391 (9)	0.0335 (9)	0.0252 (8)	−0.0017 (7)	0.0030 (6)	−0.0033 (6)
C9	0.0394 (9)	0.0312 (8)	0.0286 (8)	0.0011 (7)	0.0004 (7)	−0.0015 (6)
C10	0.0362 (8)	0.0354 (9)	0.0264 (8)	−0.0002 (7)	0.0012 (7)	−0.0027 (6)
C11	0.0331 (8)	0.0337 (9)	0.0402 (9)	−0.0015 (7)	0.0058 (7)	−0.0043 (7)
C12	0.0484 (10)	0.0324 (9)	0.0401 (10)	0.0039 (8)	0.0032 (8)	0.0050 (7)
C13	0.0437 (9)	0.0418 (10)	0.0271 (8)	0.0016 (8)	−0.0005 (7)	0.0029 (7)
C14	0.0432 (9)	0.0372 (9)	0.0237 (8)	−0.0032 (7)	0.0021 (7)	−0.0037 (7)
O2W	0.0659 (9)	0.0496 (8)	0.0448 (8)	0.0015 (7)	0.0040 (7)	0.0036 (6)

Geometric parameters (Å, º)

Mn1—O1^i	2.1575 (12)	N4—H4A	0.8655
Mn1—O1	2.1575 (12)	N4—H4B	0.8680
Mn1—O5^i	2.1600 (13)	C1—C2	1.377 (2)
Mn1—O5	2.1600 (13)	C1—C6	1.409 (2)
Mn1—O1W	2.1630 (14)	C1—C7	1.484 (2)
Mn1—O1W^i	2.1630 (14)	C2—C3	1.395 (2)
O1—C7	1.233 (2)	C2—H2	0.9300
O1W—H1WA	0.827 (16)	C3—C4	1.413 (2)
O1W—H1WB	0.813 (16)	C4—C5	1.419 (2)
O2—C7	1.277 (2)	C5—C6	1.363 (2)
O2—H2O	1.27 (4)	C5—H5	0.9300
O3—N1	1.2398 (19)	C6—H6	0.9300
O4—N1	1.2314 (19)	C8—C9	1.377 (2)
O5—C14	1.242 (2)	C8—C13	1.406 (2)
O6—C14	1.275 (2)	C8—C14	1.492 (2)
O6—H2O	1.20 (4)	C9—C10	1.393 (2)
O7—N3	1.233 (2)	C9—H9	0.9300
O8—N3	1.237 (2)	C10—C11	1.416 (2)
N1—C3	1.4307 (19)	C11—C12	1.417 (3)
N2—C4	1.345 (2)	C12—C13	1.360 (3)
N2—H2A	0.8581	C12—H12	0.9300
N2—H2B	0.8510	C13—H13	0.9300
N3—C10	1.436 (2)	O2W—H2WA	0.8558
N4—C11	1.345 (2)	O2W—H2WB	0.8537
O1^i—Mn1—O1	180.0	C3—C2—H2	119.7
O1^i—Mn1—O5^i	92.57 (6)	C2—C3—C4	121.96 (14)
O1—Mn1—O5^i	87.43 (6)	C2—C3—N1	116.77 (14)
O1^i—Mn1—O5	87.43 (6)	C4—C3—N1	121.27 (14)
O1—Mn1—O5	92.57 (6)	N2—C4—C3	125.16 (15)
O5^i—Mn1—O5	180.0	N2—C4—C5	118.87 (14)
O1^i—Mn1—O1W	84.29 (5)	C3—C4—C5	115.97 (14)
O1—Mn1—O1W	95.71 (5)	C6—C5—C4	121.70 (15)
O5^i—Mn1—O1W	88.12 (5)	C6—C5—H5	119.1
O5—Mn1—O1W	91.88 (5)	C4—C5—H5	119.1
O1^i—Mn1—O1W^i	95.71 (5)	C5—C6—C1	121.42 (15)
O1—Mn1—O1W^i	84.29 (5)	C5—C6—H6	119.3
O5^i—Mn1—O1W^i	91.88 (5)	C1—C6—H6	119.3
O5—Mn1—O1W^i	88.12 (5)	O1—C7—O2	124.97 (16)
O1W—Mn1—O1W^i	180.0	O1—C7—C1	118.99 (15)
C7—O1—Mn1	142.04 (12)	O2—C7—C1	116.03 (14)
Mn1—O1W—H1WA	118.6 (17)	C9—C8—C13	117.94 (15)
Mn1—O1W—H1WB	125.3 (18)	C9—C8—C14	121.66 (15)
H1WA—O1W—H1WB	106 (2)	C13—C8—C14	120.40 (15)
C7—O2—H2O	124.8 (18)	C8—C9—C10	121.00 (16)
C14—O5—Mn1	135.11 (13)	C8—C9—H9	119.5
C14—O6—H2O	120.4 (19)	C10—C9—H9	119.5
O4—N1—O3	121.07 (14)	C9—C10—C11	121.91 (15)
O4—N1—C3	119.93 (14)	C9—C10—N3	116.57 (15)
O3—N1—C3	119.00 (14)	C11—C10—N3	121.50 (15)
C4—N2—H2A	116.6	N4—C11—C10	125.85 (17)
C4—N2—H2B	116.7	N4—C11—C12	118.74 (17)
H2A—N2—H2B	126.7	C10—C11—C12	115.41 (15)
O7—N3—O8	121.58 (15)	C13—C12—C11	122.26 (16)
O7—N3—C10	119.44 (14)	C13—C12—H12	118.9
O8—N3—C10	118.98 (16)	C11—C12—H12	118.9
C11—N4—H4A	117.6	C12—C13—C8	121.45 (16)
C11—N4—H4B	115.2	C12—C13—H13	119.3
H4A—N4—H4B	124.9	C8—C13—H13	119.3
C2—C1—C6	118.40 (14)	O5—C14—O6	123.99 (16)
C2—C1—C7	120.90 (14)	O5—C14—C8	118.82 (16)
C6—C1—C7	120.70 (14)	O6—C14—C8	117.19 (15)
C1—C2—C3	120.53 (15)	H2WA—O2W—H2WB	115.4
C1—C2—H2	119.7
C6—C1—C2—C3	0.7 (2)	C13—C8—C9—C10	−0.2 (3)
C7—C1—C2—C3	179.94 (15)	C14—C8—C9—C10	178.81 (16)
C1—C2—C3—C4	0.8 (3)	C8—C9—C10—C11	−0.1 (3)
C1—C2—C3—N1	−178.46 (15)	C8—C9—C10—N3	−178.47 (16)
O4—N1—C3—C2	−178.27 (16)	O7—N3—C10—C9	7.9 (3)
O3—N1—C3—C2	1.7 (2)	O8—N3—C10—C9	−173.23 (17)
O4—N1—C3—C4	2.5 (2)	O7—N3—C10—C11	−170.52 (17)
O3—N1—C3—C4	−177.55 (16)	O8—N3—C10—C11	8.4 (3)
C2—C3—C4—N2	178.46 (16)	C9—C10—C11—N4	−179.64 (18)
N1—C3—C4—N2	−2.3 (3)	N3—C10—C11—N4	−1.3 (3)
C2—C3—C4—C5	−1.7 (2)	C9—C10—C11—C12	−0.6 (3)
N1—C3—C4—C5	177.57 (15)	N3—C10—C11—C12	177.70 (16)
N2—C4—C5—C6	−179.08 (17)	N4—C11—C12—C13	−179.19 (18)
C3—C4—C5—C6	1.0 (3)	C10—C11—C12—C13	1.7 (3)
C4—C5—C6—C1	0.5 (3)	C11—C12—C13—C8	−2.1 (3)
C2—C1—C6—C5	−1.4 (3)	C9—C8—C13—C12	1.3 (3)
C7—C1—C6—C5	179.42 (17)	C14—C8—C13—C12	−177.73 (17)
Mn1—O1—C7—O2	0.8 (3)	Mn1—O5—C14—O6	−51.2 (3)
Mn1—O1—C7—C1	−178.67 (15)	Mn1—O5—C14—C8	128.20 (16)
C2—C1—C7—O1	−175.97 (17)	C9—C8—C14—O5	169.25 (17)
C6—C1—C7—O1	3.2 (3)	C13—C8—C14—O5	−11.7 (3)
C2—C1—C7—O2	4.5 (3)	C9—C8—C14—O6	−11.3 (3)
C6—C1—C7—O2	−176.31 (16)	C13—C8—C14—O6	167.69 (17)

Symmetry code: (i) −x+1, −y+1, −z.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1W—H1WA···O3^ii	0.83 (2)	2.06 (2)	2.8850 (19)	176 (2)
O1W—H1WA···O4^ii	0.83 (2)	2.55 (2)	3.1418 (19)	130 (2)
O1W—H1WA···N1^ii	0.83 (2)	2.63 (2)	3.4029 (19)	157 (2)
O1W—H1WB···O2W	0.81 (2)	1.98 (2)	2.784 (2)	170 (2)
O2—H2O···O5	1.27 (4)	2.57 (4)	3.448 (2)	124 (2)
O6—H2O···O2	1.20 (4)	1.27 (4)	2.4541 (18)	168 (4)
N2—H2A···O6^iii	0.86	2.19	3.0160 (19)	162
N2—H2B···O4	0.85	1.99	2.629 (2)	131
N4—H4A···O8	0.87	2.03	2.648 (2)	128
N4—H4B···O2W^ii	0.87	2.16	3.021 (2)	173
C5—H5···O2^iii	0.93	2.57	3.489 (2)	170
C9—H9···N2^iv	0.93	2.66	3.544 (2)	160
C12—H12···O8^v	0.93	2.42	3.178 (2)	138
O2W—H2WA···O7^vi	0.86	2.14	2.995 (2)	173
O2W—H2WB···O1W^vii	0.85	2.39	3.127 (2)	145
O2W—H2WB···O5^viii	0.85	2.65	3.341 (2)	139

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