The 1:2/3 adduct of manganese(II) terephthalate with N,N-di­methyl­form­amide

Manganese(II) terephthalate crystallizes from N,N-di­methyl­form­amide under solvothermal conditions as a DMF adduct, [Mn₃(C₈H₄O₄)₃(C₃H₇NO)₂]; the compound is formally bis(N,N-di­methyl­form­amide)­tri-μ₅,μ₅,μ₄-tereph­th­alato-tri­man­ganese, which adopts a polymeric three-dimensional network structure. One of the tetraanions lies on a general position and binds to five Mn atoms, with one carboxyl group functioning as a μ₂-bridge and the other as a μ₃-bridge. The other lies on an inversion center, the dianion functioning in the μ₄-bridging mode. One Mn atom lies on a general position and is surrounded by six O atoms belonging to tetraanions. The other lies on a twofold axis and is also surrounded by six O atoms, one of which belongs to the DMF mol­ecule.

Key indicators

• Single-crystal X-ray study
• T = 295 K
• Mean [sigma](C-C) = 0.005 Å
• R factor = 0.041
• wR factor = 0.109
• Data-to-parameter ratio = 15.6

checkCIF/PLATON results

No syntax errors found



Alert level A
PLAT220_ALERT_2_A Large Non-Solvent    C     Ueq(max)/Ueq(min) ...       6.89 Ratio

Author Response: The DMF is disordered.

PLAT222_ALERT_3_A Large Non-Solvent    H     Ueq(max)/Ueq(min) ...       5.07 Ratio

Author Response: The DMF is disordered.

Alert level B
PLAT241_ALERT_2_B Check High   U(eq) as Compared to Neighbors  for         O6
PLAT241_ALERT_2_B Check High   U(eq) as Compared to Neighbors  for        C14
PLAT241_ALERT_2_B Check High   U(eq) as Compared to Neighbors  for       C14'
PLAT241_ALERT_2_B Check High   U(eq) as Compared to Neighbors  for        C15
PLAT241_ALERT_2_B Check High   U(eq) as Compared to Neighbors  for       C15'

Alert level C
PLAT213_ALERT_2_C Atom O6      has ADP max/min Ratio .............       3.10 prolat
PLAT241_ALERT_2_C Check High   U(eq) as Compared to Neighbors  for         O7
PLAT242_ALERT_2_C Check Low    U(eq) as Compared to Neighbors  for        Mn1
PLAT242_ALERT_2_C Check Low    U(eq) as Compared to Neighbors  for        Mn2
PLAT242_ALERT_2_C Check Low    U(eq) as Compared to Neighbors  for         N1
PLAT242_ALERT_2_C Check Low    U(eq) as Compared to Neighbors  for        N1'
PLAT242_ALERT_2_C Check Low    U(eq) as Compared to Neighbors  for        C13
PLAT242_ALERT_2_C Check Low    U(eq) as Compared to Neighbors  for       C13'
PLAT301_ALERT_3_C Main Residue  Disorder .........................      14.00 Perc.

   2 ALERT level A = In general: serious problem
   5 ALERT level B = Potentially serious problem
   9 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
  14 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
   0 ALERT type 4 Improvement, methodology, query or suggestion

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Computing details

Data collection: SMART (Bruker, 2002); cell refinement: SAINT (Bruker, 2002); data reduction: SAINT; 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.

bis(N,N-dimethylformamide)tri-µ₅,µ₅,µ₄-terephathalato-dimanganese

Crystal data

[Mn3(C8H4O4)3(C3H7NO)2]	F(000) = 1628
Mr = 803.35	Dx = 1.639 Mg m^−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2yc	Cell parameters from 4576 reflections
a = 25.022 (1) Å	θ = 2.1–27.0°
b = 9.5340 (5) Å	µ = 1.22 mm^−1
c = 17.923 (1) Å	T = 295 K
β = 130.417 (1)°	Prism, colorless
V = 3255.2 (3) Å^3	0.16 × 0.14 × 0.14 mm
Z = 4

Data collection

Bruker APEX area-detector diffractometer	3722 independent reflections
Radiation source: fine-focus sealed tube	3116 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.035
φ and ω scans	θmax = 27.5°, θmin = 2.1°
Absorption correction: multi-scan (SADABS; Bruker, 2002)	h = −32→31
Tmin = 0.748, Tmax = 0.848	k = −12→12
17473 measured reflections	l = −22→23

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)] = 0.041	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.109	H-atom parameters constrained
S = 1.03	w = 1/[σ^2(Fo^2) + (0.0614P)^2 + 3.4074P] where P = (Fo^2 + 2Fc^2)/3
3722 reflections	(Δ/σ)max = 0.001
238 parameters	Δρmax = 0.58 e Å^−3
59 restraints	Δρmin = −0.50 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Mn1	0.5000	0.78874 (5)	0.7500	0.02143 (14)
Mn2	0.676027 (18)	0.69627 (4)	0.88450 (2)	0.02533 (13)
O1	0.54346 (10)	0.9393 (2)	0.71485 (14)	0.0379 (5)
O2	0.65852 (10)	0.9003 (2)	0.82750 (13)	0.0419 (5)
O3	0.59784 (9)	1.2354 (2)	0.41180 (12)	0.0291 (4)
O4	0.71090 (9)	1.2113 (2)	0.52795 (12)	0.0315 (4)
O5	0.55072 (10)	0.6262 (2)	0.73165 (13)	0.0375 (5)
O6	0.64557 (10)	0.6115 (3)	0.74958 (15)	0.0634 (8)
O7	0.67978 (14)	0.4911 (3)	0.9343 (2)	0.0659 (7)
C1	0.60536 (13)	0.9497 (3)	0.74780 (18)	0.0308 (6)
C2	0.61746 (13)	1.0253 (3)	0.68600 (18)	0.0296 (5)
C3	0.56297 (14)	1.0902 (3)	0.5996 (2)	0.0399 (7)
C4	0.57300 (14)	1.1471 (3)	0.5385 (2)	0.0376 (7)
C5	0.63862 (12)	1.1438 (3)	0.56515 (17)	0.0255 (5)
C6	0.69391 (14)	1.0835 (4)	0.6537 (2)	0.0487 (9)
C7	0.68287 (15)	1.0237 (4)	0.7126 (2)	0.0503 (9)
C8	0.64929 (12)	1.1998 (2)	0.49755 (16)	0.0221 (5)
C9	0.58089 (13)	0.5973 (3)	0.69912 (18)	0.0349 (6)
C10	0.53902 (13)	0.5447 (3)	0.59602 (17)	0.0281 (5)
C11	0.46920 (14)	0.5103 (3)	0.54172 (19)	0.0381 (7)
C12	0.43027 (14)	0.4655 (3)	0.4458 (2)	0.0401 (7)
N1	0.6489 (5)	0.2855 (7)	0.9554 (7)	0.089 (2)	0.50
C13	0.6418 (4)	0.3994 (6)	0.9050 (6)	0.0602 (13)	0.50
C14	0.6011 (6)	0.1786 (11)	0.9152 (10)	0.152 (5)	0.50
C15	0.7090 (7)	0.2751 (14)	1.0554 (8)	0.135 (4)	0.50
N1'	0.6707 (4)	0.2867 (8)	0.9869 (7)	0.089 (2)	0.50
C13'	0.6962 (4)	0.4162 (7)	0.9932 (6)	0.0602 (13)	0.50
C14'	0.7012 (7)	0.2144 (13)	1.0741 (9)	0.152 (5)	0.50
C15'	0.6169 (6)	0.2265 (13)	0.8995 (9)	0.135 (4)	0.50
H3	0.5190	1.0958	0.5822	0.048*
H4	0.5355	1.1876	0.4793	0.045*
H6	0.7387	1.0835	0.6735	0.058*
H7	0.7201	0.9814	0.7712	0.060*
H11	0.4483	0.5172	0.5696	0.046*
H12	0.3832	0.4421	0.4094	0.048*
H13	0.6017	0.4034	0.8393	0.072*	0.50
H14a	0.5603	0.2033	0.8497	0.228*	0.50
H14b	0.5877	0.1627	0.9541	0.228*	0.50
H14c	0.6216	0.0947	0.9138	0.228*	0.50
H15a	0.7316	0.3649	1.0788	0.203*	0.50
H15b	0.7409	0.2078	1.0633	0.203*	0.50
H15c	0.6954	0.2456	1.0922	0.203*	0.50
H13'	0.7329	0.4466	1.0566	0.072*	0.50
H14d	0.7472	0.2516	1.1252	0.228*	0.50
H14e	0.7049	0.1167	1.0651	0.228*	0.50
H14f	0.6726	0.2253	1.0919	0.228*	0.50
H15d	0.6139	0.2682	0.8481	0.203*	0.50
H15e	0.5737	0.2412	0.8866	0.203*	0.50
H15f	0.6254	0.1277	0.9023	0.203*	0.50

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mn1	0.0168 (2)	0.0325 (3)	0.0188 (3)	0.000	0.0132 (2)	0.000
Mn2	0.0191 (2)	0.0384 (2)	0.0164 (2)	0.00033 (15)	0.01055 (16)	−0.00580 (14)
O1	0.0323 (10)	0.0537 (12)	0.0372 (10)	−0.0005 (9)	0.0267 (9)	0.0119 (9)
O2	0.0313 (10)	0.0607 (13)	0.0290 (10)	−0.0026 (9)	0.0174 (9)	0.0159 (9)
O3	0.0233 (9)	0.0445 (10)	0.0187 (8)	0.0036 (8)	0.0133 (8)	0.0068 (7)
O4	0.0194 (8)	0.0540 (12)	0.0209 (8)	−0.0022 (8)	0.0129 (7)	0.0071 (8)
O5	0.0375 (10)	0.0515 (12)	0.0241 (9)	0.0062 (9)	0.0202 (9)	−0.0088 (8)
O6	0.0260 (10)	0.121 (2)	0.0289 (11)	−0.0084 (12)	0.0115 (9)	−0.0384 (13)
O7	0.0698 (17)	0.0382 (13)	0.0763 (18)	0.0015 (12)	0.0414 (15)	0.0046 (12)
C1	0.0323 (13)	0.0404 (14)	0.0245 (13)	−0.0026 (11)	0.0205 (12)	0.0030 (11)
C2	0.0270 (12)	0.0405 (14)	0.0253 (12)	−0.0016 (11)	0.0187 (11)	0.0047 (10)
C3	0.0263 (13)	0.0618 (19)	0.0396 (15)	0.0063 (13)	0.0250 (13)	0.0172 (14)
C4	0.0244 (12)	0.0582 (18)	0.0324 (14)	0.0103 (12)	0.0194 (12)	0.0208 (13)
C5	0.0233 (11)	0.0350 (13)	0.0212 (11)	−0.0036 (10)	0.0157 (10)	0.0018 (10)
C6	0.0212 (13)	0.092 (3)	0.0345 (15)	0.0062 (14)	0.0187 (12)	0.0266 (16)
C7	0.0245 (13)	0.090 (3)	0.0304 (14)	0.0070 (15)	0.0150 (12)	0.0284 (16)
C8	0.0195 (11)	0.0318 (12)	0.0162 (10)	−0.0007 (9)	0.0120 (9)	0.0013 (9)
C9	0.0273 (13)	0.0485 (16)	0.0192 (12)	0.0038 (11)	0.0108 (11)	−0.0104 (11)
C10	0.0235 (12)	0.0377 (13)	0.0181 (11)	0.0004 (10)	0.0112 (10)	−0.0076 (10)
C11	0.0302 (13)	0.0618 (18)	0.0287 (13)	−0.0074 (13)	0.0220 (12)	−0.0163 (13)
C12	0.0226 (12)	0.065 (2)	0.0299 (14)	−0.0108 (12)	0.0159 (11)	−0.0217 (13)
N1	0.108 (5)	0.054 (2)	0.147 (6)	−0.013 (3)	0.101 (5)	−0.007 (3)
C13	0.061 (3)	0.046 (3)	0.077 (3)	0.000 (2)	0.046 (3)	−0.005 (3)
C14	0.181 (9)	0.127 (8)	0.177 (9)	−0.009 (6)	0.128 (7)	0.008 (6)
C15	0.122 (7)	0.139 (8)	0.167 (9)	−0.017 (6)	0.104 (6)	−0.048 (6)
N1'	0.108 (5)	0.054 (2)	0.147 (6)	−0.013 (3)	0.101 (5)	−0.007 (3)
C13'	0.061 (3)	0.046 (3)	0.077 (3)	0.000 (2)	0.046 (3)	−0.005 (3)
C14'	0.181 (9)	0.127 (8)	0.177 (9)	−0.009 (6)	0.128 (7)	0.008 (6)
C15'	0.122 (7)	0.139 (8)	0.167 (9)	−0.017 (6)	0.104 (6)	−0.048 (6)

Geometric parameters (Å, º)

Mn1—O1	2.128 (2)	C10—C12^v	1.382 (4)
Mn1—O1^i	2.128 (2)	C11—C12	1.384 (4)
Mn1—O3^ii	2.291 (2)	C12—C10^v	1.382 (4)
Mn1—O3^iii	2.291 (2)	C12—H12	0.9300
Mn1—O5	2.159 (2)	N1—C13	1.348 (7)
Mn1—O5^i	2.159 (2)	N1—C14	1.369 (8)
Mn2—O2	2.107 (2)	N1—C15	1.410 (8)
Mn2—O3^ii	2.394 (2)	N1'—C13'	1.360 (7)
Mn2—O6	2.166 (2)	N1'—C15'	1.364 (8)
Mn2—O7	2.127 (3)	N1'—C14'	1.398 (8)
Mn2—O4^ii	2.289 (2)	C3—H3	0.93
Mn2—O4^iv	2.175 (2)	C4—H4	0.93
O1—C1	1.254 (3)	C6—H6	0.93
O2—C1	1.252 (3)	C7—H7	0.93
O3—C8	1.253 (3)	C11—H11	0.93
O4—C8	1.263 (3)	C13—H13	0.93
O5—C9	1.248 (3)	C14—H14a	0.96
O6—C9	1.248 (3)	C14—H14b	0.96
O7—C13'	1.109 (7)	C14—H14c	0.96
O7—C13	1.138 (6)	C15—H15a	0.96
C1—C2	1.507 (3)	C15—H15b	0.96
C2—C7	1.377 (4)	C15—H15c	0.96
C2—C3	1.379 (4)	C13'—H13'	0.93
C3—C4	1.383 (4)	C14'—H14d	0.96
C4—C5	1.381 (3)	C14'—H14e	0.96
C5—C6	1.384 (4)	C14'—H14f	0.96
C5—C8	1.498 (3)	C15'—H15d	0.96
C6—C7	1.376 (4)	C15'—H15e	0.96
C9—C10	1.501 (3)	C15'—H15f	0.96
C10—C11	1.379 (4)
O1—Mn1—O1^i	95.2 (1)	C4—C5—C8	120.5 (2)
O1—Mn1—O3^ii	96.4 (1)	C6—C5—C8	120.4 (2)
O1—Mn1—O3^iii	91.4 (1)	C7—C6—C5	120.2 (2)
O1—Mn1—O5	88.6 (1)	C6—C7—C2	121.0 (3)
O1—Mn1—O5^i	173.2 (1)	O3—C8—O4	120.1 (2)
O1^i—Mn1—O3^ii	91.4 (1)	O3—C8—C5	120.6 (2)
O1^i—Mn1—O3^iii	96.4 (1)	O4—C8—C5	119.3 (2)
O1^i—Mn1—O5	173.2 (1)	O5—C9—O6	122.1 (2)
O1^i—Mn1—O5^i	88.6 (1)	O5—C9—C10	119.9 (2)
O3^ii—Mn1—O3^iii	168.5 (1)	O6—C9—C10	118.1 (2)
O3^ii—Mn1—O5	82.5 (1)	C11—C10—C12^v	119.7 (2)
O3^ii—Mn1—O5^i	89.2 (1)	C11—C10—C9	120.1 (2)
O3^iii—Mn1—O5	89.2 (1)	C12^v—C10—C9	120.1 (2)
O3^iii—Mn1—O5^i	82.5 (1)	C10—C11—C12	120.0 (2)
O5—Mn1—O5^i	88.3 (1)	C10^v—C12—C11	120.3 (2)
O2—Mn2—O3^ii	84.7 (1)	C10^v—C12—H12	119.9
O2—Mn2—O4^ii	89.8 (1)	C13—N1—C14	123.9 (6)
O2—Mn2—O4^iv	93.1 (1)	C13—N1—C15	118.5 (6)
O2—Mn2—O6	89.5 (1)	C14—N1—C15	117.6 (6)
O2—Mn2—O7	172.5 (1)	O7—C13—N1	127.0 (7)
O3^ii—Mn2—O4^ii	55.4 (1)	C13'—N1'—C15'	122.6 (6)
O3^ii—Mn2—O4^iv	133.5 (1)	C13'—N1'—C14'	117.9 (6)
O3^ii—Mn2—O6	126.0 (1)	C15'—N1'—C14'	119.6 (6)
O3^ii—Mn2—O7	89.1 (1)	O7—C13'—N1'	129.9 (7)
O4^ii—Mn2—O4^iv	78.1 (1)	C2—C3—H3	119.7
O4^ii—Mn2—O6	178.4 (1)	C4—C3—H3	119.7
O4^ii—Mn2—O7	90.1 (1)	C5—C4—H4	119.9
O4^iv—Mn2—O6	100.5 (1)	C3—C4—H4	119.9
O4^iv—Mn2—O7	94.3 (1)	C7—C6—H6	119.9
O6—Mn2—O7	90.8 (1)	C5—C6—H6	119.9
C1—O1—Mn1	128.8 (2)	C6—C7—H7	119.5
C1—O2—Mn2	129.3 (2)	C2—C7—H7	119.5
C8—O3—Mn1^iii	158.5 (2)	C10—C11—H11	120.0
C8—O3—Mn2^vi	89.9 (1)	C12—C11—H11	120.0
Mn1^iii—O3—Mn2^vi	96.5 (1)	C11—C12—H12	119.9
C8—O4—Mn2^vii	163.4 (2)	O7—C13—H13	116.5
C8—O4—Mn2^vi	94.5 (1)	N1—C13—H13	116.5
Mn2^vii—O4—Mn2^vi	101.9 (1)	O7—C13'—H13'	115.1
C9—O5—Mn1	145.4 (2)	N1'—C13'—H13'	115.1
C9—O6—Mn2	101.6 (2)	N1'—C14'—H14d	109.5
C13'—O7—C13	68.1 (6)	N1'—C14'—H14e	109.5
C13'—O7—Mn2	151.6 (4)	H14d—C14'—H14e	109.5
C13—O7—Mn2	135.7 (4)	N1'—C14'—H14f	109.5
O2—C1—O1	125.6 (2)	H14d—C14'—H14f	109.5
O2—C1—C2	116.6 (2)	H14e—C14'—H14f	109.5
O1—C1—C2	117.9 (2)	N1'—C15'—H15d	109.5
C7—C2—C3	118.8 (2)	N1'—C15'—H15e	109.5
C7—C2—C1	120.0 (2)	H15d—C15'—H15e	109.5
C3—C2—C1	121.1 (2)	N1'—C15'—H15f	109.5
C2—C3—C4	120.7 (2)	H15d—C15'—H15f	109.5
C5—C4—C3	120.2 (2)	H15e—C15'—H15f	109.5
C4—C5—C6	119.1 (2)
O1^i—Mn1—O1—C1	126.6 (2)	C4—C5—C6—C7	2.1 (5)
O5—Mn1—O1—C1	−47.7 (2)	C8—C5—C6—C7	−175.6 (3)
O3^iii—Mn1—O1—C1	−136.9 (2)	C5—C6—C7—C2	−1.5 (6)
O3^ii—Mn1—O1—C1	34.6 (2)	C3—C2—C7—C6	−1.0 (5)
O6—Mn2—O2—C1	52.4 (2)	C1—C2—C7—C6	175.4 (3)
O4^iv—Mn2—O2—C1	152.8 (2)	Mn1^iii—O3—C8—O4	106.8 (4)
O4^ii—Mn2—O2—C1	−129.1 (2)	Mn2^vi—O3—C8—O4	−0.9 (2)
O3^ii—Mn2—O2—C1	−73.8 (2)	Mn1^iii—O3—C8—C5	−73.4 (5)
O1—Mn1—O5—C9	−14.5 (3)	Mn2^vi—O3—C8—C5	178.9 (2)
O3^iii—Mn1—O5—C9	76.9 (3)	Mn2^vii—O4—C8—O3	−169.9 (5)
O3^ii—Mn1—O5—C9	−111.1 (3)	Mn2^vi—O4—C8—O3	1.0 (2)
O2—Mn2—O6—C9	−89.2 (2)	Mn2^vii—O4—C8—C5	10.3 (7)
O7—Mn2—O6—C9	83.3 (2)	Mn2^vi—O4—C8—C5	−178.8 (2)
O4^iv—Mn2—O6—C9	177.8 (2)	C4—C5—C8—O3	−8.2 (4)
O3^ii—Mn2—O6—C9	−6.1 (3)	C6—C5—C8—O3	169.4 (3)
O6—Mn2—O7—C13'	163.5 (8)	C4—C5—C8—O4	171.6 (3)
O4^iv—Mn2—O7—C13'	63.0 (8)	C6—C5—C8—O4	−10.8 (4)
O4^ii—Mn2—O7—C13'	−15.1 (8)	Mn1—O5—C9—O6	88.7 (4)
O3^ii—Mn2—O7—C13'	−70.5 (8)	Mn1—O5—C9—C10	−90.8 (4)
O6—Mn2—O7—C13	−55.4 (5)	Mn2—O6—C9—O5	−1.9 (4)
O4^iv—Mn2—O7—C13	−156.0 (5)	Mn2—O6—C9—C10	177.7 (2)
O4^ii—Mn2—O7—C13	126.0 (5)	O5—C9—C10—C11	−8.8 (4)
O3^ii—Mn2—O7—C13	70.5 (5)	O6—C9—C10—C11	171.7 (3)
Mn2—O2—C1—O1	49.5 (4)	O5—C9—C10—C12^v	169.3 (3)
Mn2—O2—C1—C2	−129.1 (2)	O6—C9—C10—C12^v	−10.2 (4)
Mn1—O1—C1—O2	−22.1 (4)	C12^v—C10—C11—C12	0.1 (5)
Mn1—O1—C1—C2	156.5 (2)	C9—C10—C11—C12	178.3 (3)
O2—C1—C2—C7	7.4 (4)	C10—C11—C12—C10^v	−0.1 (5)
O1—C1—C2—C7	−171.4 (3)	C13'—O7—C13—N1	−5.1 (6)
O2—C1—C2—C3	−176.4 (3)	Mn2—O7—C13—N1	−166.4 (4)
O1—C1—C2—C3	4.9 (4)	C14—N1—C13—O7	−179.9 (4)
C7—C2—C3—C4	2.9 (5)	C15—N1—C13—O7	0.2 (4)
C1—C2—C3—C4	−173.4 (3)	C13—O7—C13'—N1'	9.3 (6)
C2—C3—C4—C5	−2.3 (5)	Mn2—O7—C13'—N1'	161.1 (6)
C3—C4—C5—C6	−0.2 (5)	C15'—N1'—C13'—O7	0.1 (5)
C3—C4—C5—C8	177.5 (3)	C14'—N1'—C13'—O7	−179.6 (4)

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