Hydrogen-bonding patterns in pyrimethaminium 3-chloro­benzoate

In the crystal structure of the title compound, 2,4-diamino-5-(4-chloro­phen­yl)-6-ethyl­pyrimidin-1-ium 3-chloro­benzoate, C₁₂H₁₄ClN₄⁺·C₇H₄ClO₂⁻, the cation inter­acts with the carboxyl­ate group of the anion through a pair of N—H...O hydrogen bonds, forming a cyclic hydrogen-bonded motif [graph-set notation R₂²(8)]. This motif self-assembles through a complementary DDAA array of quadruple hydrogen bonds. The pyrimethamine cations are paired about inversion centers through N—H...N hydrogen bonds involving a pyrimidine N atom and the 4-amino group of the pyrimethamine cations. Concurrent with hydrogen bonding are Cl...Cl and sandwich stacking inter­actions.

Key indicators

• Single-crystal X-ray study
• T = 170 K
• Mean [sigma](C-C) = 0.004 Å
• R factor = 0.044
• wR factor = 0.122
• Data-to-parameter ratio = 14.8

checkCIF/PLATON results

No syntax errors found



Alert level C
PLAT230_ALERT_2_C Hirshfeld Test Diff for    O2     -   C15     ..       5.11 su
PLAT420_ALERT_2_C D-H Without Acceptor       N4     -   H4B    ...          ?
PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd.  #          1
              C12 H14 Cl N4

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

   0 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   2 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
   1 ALERT type 4 Improvement, methodology, query or suggestion
   0 ALERT type 5 Informative message, check

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Computing details

Data collection: CrysAlis CCD (Oxford Diffraction, 2004); cell refinement: CrysAlis RED (Oxford Diffraction, 2004); data reduction: CrysAlis RED; 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: PLATON (Spek, 2003}.

2,4-diamino-5-(4-chlorophenyl)-6-ethylpyrimidin-1-ium 3-chlorobenzoate

Crystal data

C12H14ClN4^+·C7H4ClO2^−	Z = 2
Mr = 405.27	F(000) = 420
Triclinic, P1	Dx = 1.444 Mg m^−3
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 9.139 (2) Å	Cell parameters from 2044 reflections
b = 10.337 (2) Å	θ = 3.1–26.1°
c = 11.121 (2) Å	µ = 0.37 mm^−1
α = 65.90 (3)°	T = 170 K
β = 82.80 (3)°	Prism, colourless
γ = 76.45 (3)°	0.4 × 0.3 × 0.1 mm
V = 931.8 (4) Å^3

Data collection

Kuma KM-4-CCD κ-geometry diffractometer	3616 independent reflections
Radiation source: fine-focus sealed tube	2359 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.055
ω scans	θmax = 26.1°, θmin = 3.1°
Absorption correction: numerical (CrysAlis RED; Clark & Reid, 1995; Oxford Diffraction, 2004)	h = −11→9
Tmin = 0.770, Tmax = 0.924	k = −12→12
7913 measured reflections	l = −12→13

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)] = 0.044	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.122	H-atom parameters constrained
S = 0.97	w = 1/[σ^2(Fo^2) + (0.0619P)^2] where P = (Fo^2 + 2Fc^2)/3
3616 reflections	(Δ/σ)max < 0.001
245 parameters	Δρmax = 0.24 e Å^−3
0 restraints	Δρmin = −0.26 e Å^−3

Special details

Geometry. Bond distances, angles etc. have been calculated using the rounded fractional coordinates. All e.s.d.'s are estimated from the variances of the (full) variance-covariance matrix. The cell e.s.d.'s are taken into account in the estimation of distances, angles and torsion angles

Refinement. Refinement on F² for ALL reflections except those flagged by the user for potential systematic errors. Weighted R-factors wR and all goodnesses of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The observed criterion of F² > σ(F²) is used only for calculating -R-factor-obs 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
Cl1	0.77459 (8)	−0.74814 (7)	0.65211 (8)	0.0471 (3)
N1	0.6618 (2)	0.1332 (2)	0.26512 (19)	0.0269 (7)
N2	0.5194 (2)	0.3155 (2)	0.0992 (2)	0.0311 (7)
N3	0.5327 (2)	0.0799 (2)	0.12575 (19)	0.0248 (7)
N4	0.5461 (2)	−0.1560 (2)	0.1608 (2)	0.0302 (7)
C2	0.5702 (3)	0.1749 (3)	0.1636 (2)	0.0247 (8)
C4	0.5780 (3)	−0.0617 (2)	0.2018 (2)	0.0236 (8)
C5	0.6600 (2)	−0.1108 (2)	0.3193 (2)	0.0233 (8)
C6	0.7077 (3)	−0.0093 (3)	0.3440 (2)	0.0251 (8)
C7	0.8112 (3)	−0.0420 (3)	0.4525 (3)	0.0327 (9)
C8	0.7296 (3)	−0.0655 (3)	0.5859 (3)	0.0460 (11)
C9	0.6923 (3)	−0.2685 (2)	0.4057 (2)	0.0245 (8)
C10	0.5939 (3)	−0.3272 (3)	0.5105 (2)	0.0295 (8)
C11	0.6181 (3)	−0.4734 (3)	0.5874 (3)	0.0313 (8)
C12	0.7421 (3)	−0.5629 (3)	0.5590 (3)	0.0294 (8)
C13	0.8415 (3)	−0.5086 (3)	0.4559 (3)	0.0299 (8)
C14	0.8170 (3)	−0.3615 (3)	0.3805 (2)	0.0282 (8)
Cl2	0.93722 (9)	0.94582 (8)	−0.11886 (7)	0.0502 (3)
O1	0.80158 (19)	0.33299 (18)	0.25822 (18)	0.0381 (6)
O2	0.63366 (18)	0.52881 (17)	0.14315 (16)	0.0323 (6)
C15	0.7665 (3)	0.4624 (3)	0.1799 (2)	0.0296 (9)
C16	0.8918 (3)	0.5475 (3)	0.1271 (2)	0.0258 (8)
C17	0.8624 (3)	0.6897 (3)	0.0353 (2)	0.0275 (8)
C18	0.9749 (3)	0.7684 (3)	−0.0036 (2)	0.0309 (9)
C19	1.1169 (3)	0.7081 (3)	0.0459 (3)	0.0372 (10)
C20	1.1480 (3)	0.5662 (3)	0.1333 (3)	0.0367 (10)
C21	1.0369 (3)	0.4844 (3)	0.1737 (2)	0.0310 (8)
H1	0.69170	0.19790	0.28030	0.0320*
H2A	0.46250	0.34540	0.03320	0.0370*
H2B	0.54330	0.37670	0.12340	0.0370*
H4A	0.49890	−0.12560	0.08910	0.0360*
H4B	0.57280	−0.24740	0.20610	0.0360*
H7A	0.86280	0.03750	0.42860	0.0390*
H7B	0.88680	−0.12820	0.46050	0.0390*
H8A	0.65190	0.01780	0.57810	0.0690*
H8B	0.80010	−0.07980	0.64950	0.0690*
H8C	0.68550	−0.14930	0.61390	0.0690*
H10	0.51000	−0.26630	0.52870	0.0350*
H11	0.55200	−0.51090	0.65720	0.0380*
H13	0.92430	−0.57050	0.43730	0.0360*
H14	0.88480	−0.32440	0.31210	0.0340*
H17	0.76730	0.73150	0.00030	0.0330*
H19	1.19120	0.76300	0.02050	0.0450*
H20	1.24430	0.52450	0.16560	0.0440*
H21	1.05910	0.38790	0.23170	0.0370*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cl1	0.0595 (5)	0.0213 (4)	0.0498 (5)	−0.0079 (3)	−0.0113 (4)	−0.0009 (3)
N1	0.0345 (11)	0.0220 (11)	0.0271 (12)	−0.0088 (9)	−0.0086 (10)	−0.0088 (10)
N2	0.0371 (12)	0.0219 (11)	0.0348 (13)	−0.0059 (9)	−0.0144 (10)	−0.0080 (10)
N3	0.0275 (11)	0.0219 (11)	0.0250 (12)	−0.0074 (9)	−0.0041 (9)	−0.0071 (9)
N4	0.0423 (12)	0.0223 (11)	0.0273 (12)	−0.0076 (9)	−0.0127 (10)	−0.0072 (10)
C2	0.0252 (13)	0.0249 (13)	0.0223 (14)	−0.0072 (10)	−0.0004 (11)	−0.0066 (11)
C4	0.0252 (13)	0.0228 (13)	0.0240 (14)	−0.0076 (10)	−0.0008 (11)	−0.0090 (11)
C5	0.0267 (13)	0.0216 (13)	0.0206 (14)	−0.0043 (10)	−0.0023 (11)	−0.0072 (11)
C6	0.0282 (13)	0.0253 (13)	0.0216 (14)	−0.0065 (10)	−0.0015 (11)	−0.0081 (11)
C7	0.0387 (15)	0.0246 (14)	0.0359 (16)	−0.0060 (11)	−0.0122 (12)	−0.0101 (12)
C8	0.0587 (19)	0.0499 (19)	0.0323 (18)	−0.0084 (15)	−0.0113 (14)	−0.0176 (15)
C9	0.0319 (13)	0.0217 (13)	0.0207 (14)	−0.0062 (10)	−0.0096 (11)	−0.0062 (11)
C10	0.0325 (14)	0.0267 (14)	0.0279 (15)	−0.0040 (11)	−0.0026 (12)	−0.0098 (12)
C11	0.0354 (15)	0.0297 (14)	0.0264 (15)	−0.0116 (12)	−0.0005 (12)	−0.0060 (12)
C12	0.0408 (15)	0.0183 (13)	0.0279 (15)	−0.0058 (11)	−0.0140 (12)	−0.0044 (11)
C13	0.0339 (14)	0.0263 (14)	0.0302 (15)	−0.0008 (11)	−0.0070 (12)	−0.0130 (12)
C14	0.0342 (14)	0.0271 (14)	0.0236 (14)	−0.0082 (11)	−0.0039 (11)	−0.0083 (12)
Cl2	0.0711 (5)	0.0346 (4)	0.0417 (5)	−0.0234 (4)	−0.0111 (4)	−0.0024 (3)
O1	0.0519 (11)	0.0224 (10)	0.0400 (12)	−0.0112 (8)	−0.0178 (9)	−0.0057 (9)
O2	0.0340 (10)	0.0286 (10)	0.0333 (11)	−0.0072 (8)	−0.0081 (8)	−0.0088 (9)
C15	0.0438 (16)	0.0259 (14)	0.0244 (15)	−0.0094 (12)	−0.0062 (12)	−0.0125 (12)
C16	0.0345 (14)	0.0247 (13)	0.0229 (14)	−0.0051 (11)	−0.0039 (11)	−0.0136 (12)
C17	0.0326 (14)	0.0271 (14)	0.0258 (15)	−0.0057 (11)	−0.0038 (11)	−0.0129 (12)
C18	0.0411 (16)	0.0294 (14)	0.0250 (15)	−0.0116 (12)	−0.0009 (12)	−0.0110 (12)
C19	0.0367 (16)	0.0465 (18)	0.0334 (17)	−0.0170 (13)	0.0036 (13)	−0.0174 (14)
C20	0.0310 (15)	0.0487 (18)	0.0349 (17)	−0.0044 (13)	−0.0038 (13)	−0.0220 (15)
C21	0.0387 (15)	0.0264 (14)	0.0276 (15)	−0.0001 (11)	−0.0052 (12)	−0.0127 (12)

Geometric parameters (Å, º)

Cl1—C12	1.737 (3)	C11—C12	1.378 (4)
Cl2—C18	1.738 (3)	C12—C13	1.381 (4)
O1—C15	1.252 (3)	C13—C14	1.383 (4)
O2—C15	1.272 (3)	C7—H7A	0.9696
N1—C6	1.365 (4)	C7—H7B	0.9703
N1—C2	1.353 (3)	C8—H8C	0.9600
N2—C2	1.326 (4)	C8—H8A	0.9598
N3—C2	1.338 (4)	C8—H8B	0.9599
N3—C4	1.350 (3)	C10—H10	0.9296
N4—C4	1.331 (3)	C11—H11	0.9296
N1—H1	0.8602	C13—H13	0.9310
N2—H2A	0.8601	C14—H14	0.9298
N2—H2B	0.8596	C15—C16	1.520 (4)
N4—H4A	0.8595	C16—C17	1.390 (4)
N4—H4B	0.8603	C16—C21	1.394 (4)
C4—C5	1.433 (3)	C17—C18	1.378 (4)
C5—C9	1.495 (3)	C18—C19	1.377 (4)
C5—C6	1.359 (4)	C19—C20	1.374 (5)
C6—C7	1.506 (4)	C20—C21	1.388 (4)
C7—C8	1.526 (4)	C17—H17	0.9301
C9—C14	1.389 (4)	C19—H19	0.9298
C9—C10	1.397 (3)	C20—H20	0.9297
C10—C11	1.378 (4)	C21—H21	0.9299
Cl1···Cl2^i	3.2969 (13)	C21···C17^xi	3.405 (4)
Cl1···N4^ii	3.471 (2)	C21···C13^vi	3.430 (4)
Cl2···Cl2^iii	3.6526 (14)	C21···C16^xi	3.461 (3)
Cl2···Cl1^iv	3.2969 (13)	C2···H19^xi	2.7968
Cl2···H8B^v	3.1303	C4···H4A^ix	3.0863
O1···C13^vi	3.327 (4)	C5···H8A^viii	3.0245
O1···N1	2.643 (3)	C9···H4B	2.5036
O2···N2^vii	2.856 (3)	C9···H8C	3.0234
O2···N2	2.877 (3)	C9···H7B	2.7992
O2···N4^vi	3.249 (3)	C10···H8C	2.8451
O1···H2B	2.8032	C11···H20^xiii	2.9623
O1···H21	2.5027	C13···H13^xii	2.9851
O1···H1	1.8259	C14···H13^xii	3.0738
O1···H7A	2.8234	C14···H4B	2.8490
O2···H2B	2.0343	C15···H2B	2.6388
O2···H4B^vi	2.6025	C15···H2A^vii	3.0648
O2···H17	2.5298	C15···H1	2.7168
O2···H11^viii	2.5904	C16···H14^vi	2.8535
O2···H2A^vii	2.0306	C17···H14^vi	3.0523
N1···O1	2.643 (3)	C21···H14^vi	2.9779
N2···O2	2.877 (3)	C21···H13^vi	2.8519
N2···O2^vii	2.856 (3)	H1···O1	1.8259
N2···C15	3.382 (4)	H1···H2B	2.2550
N3···N4^ix	3.091 (3)	H1···H7A	2.2611
N4···C17^x	3.390 (4)	H1···C15	2.7168
N4···C14	3.380 (3)	H2A···O2^vii	2.0306
N4···Cl1^ii	3.471 (2)	H2A···H17^vii	2.5301
N4···O2^x	3.249 (3)	H2A···C15^vii	3.0648
N4···N3^ix	3.091 (3)	H2B···O1	2.8032
N2···H19^xi	2.9016	H2B···H1	2.2550
N3···H4A^ix	2.2810	H2B···C15	2.6388
N4···H17^x	2.8834	H2B···O2	2.0343
C2···C19^xi	3.566 (4)	H4A···N3^ix	2.2810
C8···C9	3.532 (4)	H4A···H4A^ix	2.5461
C9···C8	3.532 (4)	H4A···C4^ix	3.0863
C11···C11^ii	3.350 (4)	H4B···C9	2.5036
C13···C14^xii	3.510 (4)	H4B···C14	2.8490
C13···C15^x	3.370 (4)	H4B···O2^x	2.6025
C13···C21^x	3.430 (4)	H7A···O1	2.8234
C13···C13^xii	3.238 (4)	H7A···H1	2.2611
C13···C16^x	3.448 (4)	H7B···C9	2.7992
C13···O1^x	3.327 (4)	H8A···H10^viii	2.5232
C14···N4	3.380 (3)	H8A···C5^viii	3.0245
C14···C13^xii	3.510 (4)	H8B···Cl2^xiv	3.1303
C14···C15^x	3.532 (4)	H8C···C9	3.0234
C14···C21^x	3.493 (4)	H8C···C10	2.8451
C14···C16^x	3.267 (4)	H10···H8A^viii	2.5232
C15···C14^vi	3.532 (4)	H11···O2^viii	2.5904
C15···C13^vi	3.370 (4)	H13···C14^xii	3.0738
C15···C19^xi	3.551 (4)	H13···C21^x	2.8519
C15···N2	3.382 (4)	H13···C13^xii	2.9851
C15···C20^xi	3.589 (4)	H14···C17^x	3.0523
C16···C16^xi	3.581 (4)	H14···C21^x	2.9779
C16···C21^xi	3.461 (3)	H14···C16^x	2.8535
C16···C13^vi	3.448 (4)	H17···O2	2.5298
C16···C14^vi	3.267 (4)	H17···N4^vi	2.8834
C17···N4^vi	3.390 (4)	H17···H2A^vii	2.5301
C17···C21^xi	3.405 (4)	H19···N2^xi	2.9016
C19···C15^xi	3.551 (4)	H19···C2^xi	2.7968
C19···C2^xi	3.566 (4)	H20···C11^xiii	2.9623
C20···C15^xi	3.589 (4)	H21···O1	2.5027
C21···C14^vi	3.493 (4)
C2—N1—C6	121.4 (2)	H7A—C7—H7B	107.74
C2—N3—C4	116.9 (2)	C7—C8—H8A	109.46
C2—N1—H1	119.30	C7—C8—H8B	109.45
C6—N1—H1	119.28	C7—C8—H8C	109.44
C2—N2—H2A	119.93	H8A—C8—H8B	109.50
C2—N2—H2B	120.03	H8A—C8—H8C	109.47
H2A—N2—H2B	120.04	H8B—C8—H8C	109.51
H4A—N4—H4B	120.01	C9—C10—H10	119.25
C4—N4—H4A	120.03	C11—C10—H10	119.22
C4—N4—H4B	119.96	C10—C11—H11	120.60
N1—C2—N3	122.3 (3)	C12—C11—H11	120.62
N2—C2—N3	119.9 (2)	C12—C13—H13	120.30
N1—C2—N2	117.8 (3)	C14—C13—H13	120.27
N3—C4—N4	116.7 (2)	C9—C14—H14	119.60
N3—C4—C5	122.6 (2)	C13—C14—H14	119.62
N4—C4—C5	120.6 (2)	O1—C15—O2	125.0 (3)
C4—C5—C6	117.1 (2)	O1—C15—C16	117.5 (2)
C4—C5—C9	119.44 (19)	O2—C15—C16	117.5 (2)
C6—C5—C9	123.5 (2)	C15—C16—C17	120.7 (3)
N1—C6—C5	118.9 (2)	C15—C16—C21	119.9 (2)
N1—C6—C7	116.4 (3)	C17—C16—C21	119.4 (3)
C5—C6—C7	124.7 (3)	C16—C17—C18	119.7 (3)
C6—C7—C8	113.3 (2)	Cl2—C18—C17	119.3 (2)
C5—C9—C10	120.7 (2)	Cl2—C18—C19	119.6 (2)
C5—C9—C14	121.0 (2)	C17—C18—C19	121.1 (3)
C10—C9—C14	118.2 (2)	C18—C19—C20	119.5 (3)
C9—C10—C11	121.5 (3)	C19—C20—C21	120.5 (3)
C10—C11—C12	118.8 (3)	C16—C21—C20	119.7 (3)
Cl1—C12—C11	120.1 (2)	C16—C17—H17	120.18
Cl1—C12—C13	118.7 (2)	C18—C17—H17	120.16
C11—C12—C13	121.2 (3)	C18—C19—H19	120.29
C12—C13—C14	119.4 (3)	C20—C19—H19	120.20
C9—C14—C13	120.8 (2)	C19—C20—H20	119.78
C6—C7—H7A	108.93	C21—C20—H20	119.68
C6—C7—H7B	108.91	C16—C21—H21	120.12
C8—C7—H7A	108.90	C20—C21—H21	120.14
C8—C7—H7B	108.87
C6—N1—C2—N2	173.9 (2)	C14—C9—C10—C11	−0.3 (4)
C6—N1—C2—N3	−7.4 (4)	C5—C9—C14—C13	−176.1 (2)
C2—N1—C6—C5	0.1 (4)	C10—C9—C14—C13	1.1 (4)
C2—N1—C6—C7	179.2 (2)	C9—C10—C11—C12	−0.3 (4)
C4—N3—C2—N1	6.5 (4)	C10—C11—C12—C13	0.2 (5)
C4—N3—C2—N2	−174.8 (2)	C10—C11—C12—Cl1	−179.0 (2)
C2—N3—C4—N4	−177.2 (2)	C11—C12—C13—C14	0.6 (5)
C2—N3—C4—C5	1.1 (3)	Cl1—C12—C13—C14	179.8 (2)
N4—C4—C5—C9	−8.0 (3)	C12—C13—C14—C9	−1.3 (4)
N3—C4—C5—C6	−7.9 (3)	O1—C15—C16—C17	177.1 (2)
N3—C4—C5—C9	173.7 (2)	O1—C15—C16—C21	−4.8 (4)
N4—C4—C5—C6	170.4 (2)	O2—C15—C16—C17	−4.2 (4)
C9—C5—C6—N1	−174.6 (2)	O2—C15—C16—C21	173.9 (2)
C9—C5—C6—C7	6.3 (4)	C15—C16—C17—C18	175.0 (2)
C4—C5—C9—C10	−92.0 (3)	C21—C16—C17—C18	−3.1 (4)
C4—C5—C6—C7	−172.0 (2)	C15—C16—C21—C20	−174.8 (3)
C4—C5—C6—N1	7.0 (3)	C17—C16—C21—C20	3.3 (4)
C4—C5—C9—C14	85.1 (3)	C16—C17—C18—Cl2	179.8 (2)
C6—C5—C9—C10	89.7 (3)	C16—C17—C18—C19	0.7 (4)
C6—C5—C9—C14	−93.2 (3)	Cl2—C18—C19—C20	−177.6 (2)
C5—C6—C7—C8	−83.2 (4)	C17—C18—C19—C20	1.4 (4)
N1—C6—C7—C8	97.7 (3)	C18—C19—C20—C21	−1.2 (5)
C5—C9—C10—C11	176.9 (2)	C19—C20—C21—C16	−1.2 (4)

Symmetry codes: (i) x, y−2, z+1; (ii) −x+1, −y−1, −z+1; (iii) −x+2, −y+2, −z; (iv) x, y+2, z−1; (v) x, y+1, z−1; (vi) x, y+1, z; (vii) −x+1, −y+1, −z; (viii) −x+1, −y, −z+1; (ix) −x+1, −y, −z; (x) x, y−1, z; (xi) −x+2, −y+1, −z; (xii) −x+2, −y−1, −z+1; (xiii) −x+2, −y, −z+1; (xiv) x, y−1, z+1.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1···O1	0.86	1.83	2.643 (3)	158
N2—H2A···O2^vii	0.86	2.03	2.856 (3)	161
N2—H2B···O2	0.86	2.03	2.877 (3)	167
N4—H4A···N3^ix	0.86	2.28	3.091 (3)	157
C11—H11···O2^viii	0.93	2.59	3.477 (4)	160

Symmetry codes: (vii) −x+1, −y+1, −z; (viii) −x+1, −y, −z+1; (ix) −x+1, −y, −z.