3-Methyl-1-(morpholinocarbonyl­meth­yl)imidazolium hexa­fluoro­phosphate

In the title compound, C₁₀H₁₆N₃O₂⁺·PF₆^-, the morpholine ring adopts a chair conformation and the methyl­imidazole and morpholine rings are anti to one another.

Key indicators

• Single-crystal X-ray study
• T = 296 K
• Mean [sigma](C-C) = 0.004 Å
• R factor = 0.063
• wR factor = 0.152
• Data-to-parameter ratio = 17.0

checkCIF/PLATON results

No syntax errors found



Alert level B
PLAT241_ALERT_2_B Check High      Ueq as Compared to Neighbors for         C7

Alert level C
PLAT220_ALERT_2_C Large Non-Solvent    C     Ueq(max)/Ueq(min) ...       2.61 Ratio
PLAT241_ALERT_2_C Check High      Ueq as Compared to Neighbors for         C8
PLAT242_ALERT_2_C Check Low       Ueq as Compared to Neighbors for         N2
PLAT242_ALERT_2_C Check Low       Ueq as Compared to Neighbors for         N3
PLAT244_ALERT_4_C Low   'Solvent' Ueq as Compared to Neighbors for         P1
PLAT250_ALERT_2_C Large U3/U1 Ratio for Average U(i,j) Tensor ....       2.08

   0 ALERT level A = In general: serious problem
   1 ALERT level B = Potentially serious problem
   6 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
   6 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

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Computing details

Data collection: PROCESS-AUTO (Rigaku,1998); cell refinement: PROCESS-AUTO; data reduction: CrystalStructure (Rigaku/MSC,2004); program(s) used to solve structure: SIR97 (Altomare et al., 1999); program(s) used to refine structure: CRYSTALS (Betteridge et al., 20036); molecular graphics: ORTEP-3 for Windows (Farrugia,1997); software used to prepare material for publication: CrystalStructure.

(I)

Crystal data

C10H16N3O2^+·F6P^−	F(000) = 728.00
Mr = 355.22	Dx = 1.588 Mg m^−3
Monoclinic, P21/c	Melting point: 139 K
Hall symbol: -P 2ybc	Mo Kα radiation, λ = 0.71075 Å
a = 13.075 (4) Å	Cell parameters from 11370 reflections
b = 9.682 (4) Å	θ = 3.0–27.5°
c = 11.888 (4) Å	µ = 0.26 mm^−1
β = 99.134 (18)°	T = 296 K
V = 1485.9 (9) Å^3	Chunk, colorless
Z = 4	0.55 × 0.47 × 0.42 mm

Data collection

Rigaku R-AXIS RAPID diffractometer	2334 reflections with F^2 > 2σ(F^2)
Detector resolution: 10.00 pixels mm^-1	Rint = 0.034
ω scans	θmax = 27.5°
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	h = −16→16
Tmin = 0.863, Tmax = 0.896	k = −12→12
14263 measured reflections	l = −15→15
3393 independent reflections

Refinement

Refinement on F^2	w = 1/[0.0005Fo^2 + 5σ(Fo^2)]/(4Fo^2)
R[F^2 > 2σ(F^2)] = 0.063	(Δ/σ)max < 0.001
wR(F^2) = 0.152	Δρmax = 0.59 e Å^−3
S = 1.01	Δρmin = −0.50 e Å^−3
3393 reflections	Extinction correction: Larson (1970)
200 parameters	Extinction coefficient: 653 (64)
H-atom parameters constrained

Special details

Geometry. ENTER SPECIAL DETAILS OF THE MOLECULAR GEOMETRY

Refinement. Refinement using all reflections. The weighted R-factor (wR) and goodness of fit (S) are based on F². R-factor (gt) are based on F. The threshold expression of F² > 2.0 σ(F²) is used only for calculating R-factor (gt).

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

	x	y	z	Uiso*/Ueq
P1	0.75792 (6)	0.42237 (9)	0.44878 (6)	0.0586 (2)
F1	0.64745 (14)	0.4807 (2)	0.46362 (19)	0.1022 (8)
F2	0.7102 (2)	0.2777 (2)	0.4210 (2)	0.1415 (12)
F3	0.86721 (17)	0.3682 (2)	0.4362 (2)	0.1240 (9)
F4	0.8007 (2)	0.5699 (2)	0.4802 (2)	0.1582 (13)
F5	0.73837 (18)	0.4693 (2)	0.32198 (18)	0.1256 (10)
F6	0.77186 (17)	0.3757 (2)	0.57688 (17)	0.1184 (9)
O1	1.00790 (12)	1.0258 (2)	0.64929 (16)	0.0548 (5)
O2	0.66192 (12)	0.84462 (19)	0.62289 (14)	0.0504 (5)
N1	0.83515 (13)	0.8502 (2)	0.62701 (19)	0.0440 (6)
N2	0.66476 (14)	0.6437 (2)	0.77814 (18)	0.0453 (6)
N3	0.52767 (16)	0.6426 (2)	0.85523 (18)	0.0470 (6)
C1	0.74813 (17)	0.8011 (2)	0.6584 (2)	0.0399 (6)
C2	0.93947 (18)	0.7963 (2)	0.6626 (2)	0.0574 (8)
C3	1.0072 (2)	0.9080 (3)	0.7198 (2)	0.0634 (9)
C4	0.9056 (2)	1.0790 (2)	0.6179 (2)	0.0538 (8)
C5	0.83414 (19)	0.9723 (2)	0.5558 (2)	0.0480 (7)
C6	0.76366 (18)	0.6849 (2)	0.7474 (2)	0.0502 (7)
C7	0.6061 (2)	0.5365 (4)	0.7350 (3)	0.1041 (14)
C8	0.5208 (2)	0.5365 (4)	0.7831 (3)	0.0953 (13)
C9	0.61612 (19)	0.7048 (2)	0.8519 (2)	0.0491 (7)
C10	0.4509 (2)	0.6810 (3)	0.9272 (2)	0.0778 (11)
H7	0.6221	0.4736	0.6813	0.125*
H8	0.4663	0.4740	0.7689	0.114*
H9	0.6405	0.7811	0.8956	0.059*
H21	0.9672	0.7639	0.5964	0.069*
H22	0.9370	0.7203	0.7153	0.069*
H31	0.9819	0.9347	0.7891	0.076*
H32	1.0773	0.8730	0.7387	0.076*
H41	0.9081	1.1584	0.5686	0.065*
H42	0.8792	1.1070	0.6861	0.065*
H51	0.7644	1.0092	0.5398	0.058*
H52	0.8574	0.9481	0.4848	0.058*
H61	0.7952	0.6060	0.7161	0.060*
H62	0.8088	0.7173	0.8149	0.060*
H101	0.4657	0.7721	0.9573	0.093*
H102	0.4537	0.6164	0.9889	0.093*
H103	0.3829	0.6796	0.8826	0.093*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
P1	0.0601 (5)	0.0567 (5)	0.0642 (5)	0.0138 (3)	0.0264 (3)	0.0153 (4)
F1	0.0776 (13)	0.132 (2)	0.1055 (16)	0.0446 (12)	0.0409 (11)	0.0379 (13)
F2	0.173 (2)	0.0871 (18)	0.178 (2)	−0.0389 (17)	0.068 (2)	−0.0232 (18)
F3	0.0914 (15)	0.141 (2)	0.157 (2)	0.0620 (15)	0.0732 (15)	0.0594 (17)
F4	0.135 (2)	0.086 (2)	0.252 (3)	−0.0249 (16)	0.025 (2)	−0.029 (2)
F5	0.1296 (19)	0.178 (2)	0.0798 (15)	0.0407 (18)	0.0507 (14)	0.0580 (16)
F6	0.1101 (16)	0.175 (2)	0.0744 (14)	0.0553 (16)	0.0269 (12)	0.0421 (15)
O1	0.0424 (10)	0.0534 (11)	0.0697 (13)	−0.0106 (8)	0.0127 (9)	0.0052 (10)
O2	0.0315 (8)	0.0610 (12)	0.0592 (11)	0.0028 (8)	0.0087 (7)	0.0080 (9)
N1	0.0308 (9)	0.0413 (12)	0.0623 (13)	0.0008 (8)	0.0143 (9)	0.0034 (10)
N2	0.0409 (11)	0.0458 (13)	0.0515 (13)	−0.0072 (9)	0.0139 (10)	0.0024 (10)
N3	0.0376 (10)	0.0555 (14)	0.0496 (13)	−0.0032 (9)	0.0120 (9)	0.0029 (11)
C1	0.0321 (11)	0.0413 (14)	0.0480 (14)	0.0009 (10)	0.0117 (10)	−0.0050 (11)
C2	0.0335 (12)	0.0472 (16)	0.094 (2)	0.0037 (11)	0.0185 (13)	0.0127 (15)
C3	0.0403 (14)	0.071 (2)	0.077 (2)	−0.0034 (14)	0.0056 (14)	0.0179 (17)
C4	0.0538 (15)	0.0458 (16)	0.0645 (18)	−0.0015 (13)	0.0176 (13)	0.0097 (14)
C5	0.0396 (13)	0.0550 (16)	0.0513 (15)	−0.0016 (11)	0.0125 (11)	0.0087 (13)
C6	0.0339 (12)	0.0498 (16)	0.0689 (18)	−0.0010 (11)	0.0138 (12)	0.0113 (13)
C7	0.109 (2)	0.106 (3)	0.115 (3)	−0.066 (2)	0.071 (2)	−0.066 (2)
C8	0.073 (2)	0.121 (3)	0.102 (2)	−0.063 (2)	0.047 (2)	−0.050 (2)
C9	0.0471 (14)	0.0464 (15)	0.0554 (17)	−0.0095 (12)	0.0129 (12)	−0.0055 (13)
C10	0.0642 (19)	0.081 (2)	0.100 (2)	0.0065 (17)	0.0481 (19)	0.004 (2)

Geometric parameters (Å, º)

P1—F1	1.587 (2)	C2—C3	1.491 (3)
P1—F2	1.548 (2)	C4—C5	1.506 (3)
P1—F3	1.551 (2)	C7—C8	1.332 (5)
P1—F4	1.557 (2)	C2—H21	0.970
P1—F5	1.556 (2)	C2—H22	0.970
P1—F6	1.571 (2)	C3—H31	0.970
O1—C3	1.417 (3)	C3—H32	0.970
O1—C4	1.426 (3)	C4—H41	0.970
O2—C1	1.215 (2)	C4—H42	0.970
N1—C1	1.340 (3)	C5—H51	0.970
N1—C2	1.459 (2)	C5—H52	0.970
N1—C5	1.453 (3)	C6—H61	0.970
N2—C6	1.454 (3)	C6—H62	0.970
N2—C7	1.343 (4)	C7—H7	0.930
N2—C9	1.304 (3)	C8—H8	0.930
N3—C8	1.331 (4)	C9—H9	0.930
N3—C9	1.310 (3)	C10—H101	0.960
N3—C10	1.467 (4)	C10—H102	0.960
C1—C6	1.535 (3)	C10—H103	0.960
F1···C7	3.398 (4)	C9···H8^x	3.086
F1···C8^i	3.379 (3)	C9···H51^ix	3.415
F1···C9^ii	3.321 (3)	C10···H7^x	3.195
F1···C10^iii	3.505 (4)	C10···H51^iii	3.346
F2···C10^iii	3.126 (4)	C10···H102^xii	3.233
F3···C2^iv	3.354 (3)	H7···P1	3.549
F3···C4^v	3.523 (3)	H7···F1	2.661
F4···N1	3.220 (3)	H7···F6	2.654
F4···C1	3.231 (4)	H7···C10^iii	3.195
F4···C2	3.399 (4)	H7···H101^iii	2.690
F4···C6	3.473 (4)	H7···H103^iii	2.944
F4···C9^ii	3.426 (3)	H8···F1^i	2.956
F5···O2^ii	3.016 (2)	H8···F5^i	2.777
F5···N1^ii	3.311 (3)	H8···O2^iii	2.592
F5···C1^ii	2.970 (3)	H8···N3^iii	3.538
F5···C4^ii	3.546 (3)	H8···C1^iii	3.490
F5···C6^ii	3.493 (3)	H8···C9^iii	3.086
F5···C8^i	3.421 (3)	H8···H9^iii	2.898
F5···C9^ii	3.581 (3)	H8···H101^iii	3.549
F6···C3^vi	3.474 (3)	H8···H102^xii	3.032
F6···C4^v	3.359 (3)	H9···P1^ix	3.270
F6···C7	3.457 (4)	H9···F1^ix	2.441
F6···C10^iii	3.463 (4)	H9···F4^ix	2.609
O1···O1^vii	3.558 (2)	H9···F5^ix	2.933
O1···C2^viii	3.442 (3)	H9···O2^ix	2.936
O1···C5^vii	3.437 (3)	H9···C1^ix	3.313
O1···C6^viii	3.411 (2)	H9···H8^x	2.898
O2···F5^ix	3.016 (2)	H9···H51^ix	3.546
O2···N3^ii	3.384 (2)	H21···F3^iv	2.596
O2···C8^x	3.355 (4)	H21···F4	3.037
O2···C9^ii	3.217 (3)	H21···C4^vii	3.593
O2···C10^x	3.586 (3)	H21···H31^vi	3.488
O2···C10^ii	3.324 (3)	H21···H41^vii	2.844
N1···F4	3.220 (3)	H21···H42^vi	3.373
N1···F5^ix	3.311 (3)	H22···F3^iv	3.463
N3···O2^ix	3.384 (2)	H22···F4	3.396
C1···F4	3.231 (4)	H22···O1^vi	2.508
C1···F5^ix	2.970 (3)	H22···C3^vi	3.177
C2···F3^iv	3.354 (3)	H22···C4^vi	2.957
C2···F4	3.399 (4)	H22···H31^vi	2.965
C2···O1^vi	3.442 (3)	H22···H32^vi	3.417
C3···F6^viii	3.474 (3)	H22···H41^vi	3.068
C4···F3^xi	3.523 (3)	H22···H42^vi	2.731
C4···F5^ix	3.546 (3)	H31···F3^viii	3.595
C4···F6^xi	3.359 (3)	H31···F3^ix	3.128
C5···O1^vii	3.437 (3)	H31···F4^ix	3.533
C6···F4	3.473 (4)	H31···F5^ix	3.399
C6···F5^ix	3.493 (3)	H31···F6^viii	3.406
C6···O1^vi	3.411 (2)	H31···H21^viii	3.488
C7···F1	3.398 (4)	H31···H22^viii	2.965
C7···F6	3.457 (4)	H31···H41^vi	3.363
C8···F1^i	3.379 (3)	H31···H61^viii	3.363
C8···F5^i	3.421 (3)	H32···F3^iv	3.284
C8···O2^iii	3.355 (4)	H32···F6^viii	2.706
C9···F1^ix	3.321 (3)	H32···C4^vi	3.307
C9···F4^ix	3.426 (3)	H32···H22^viii	3.417
C9···F5^ix	3.581 (3)	H32···H41^vi	3.076
C9···O2^ix	3.217 (3)	H32···H42^vi	2.755
C10···F1^x	3.505 (4)	H32···H52^vii	3.393
C10···F2^x	3.126 (4)	H32···H61^viii	2.806
C10···F6^x	3.463 (4)	H41···P1^xi	3.395
C10···O2^iii	3.586 (3)	H41···F2^xi	3.109
C10···O2^ix	3.324 (3)	H41···F3^xi	2.573
P1···H7	3.549	H41···F6^xi	2.768
P1···H9^ii	3.270	H41···O1^vii	3.465
P1···H41^v	3.395	H41···C3^viii	3.537
P1···H101^iii	3.599	H41···H21^vii	2.844
F1···H7	2.661	H41···H22^viii	3.068
F1···H8^i	2.956	H41···H31^viii	3.363
F1···H9^ii	2.441	H41···H32^viii	3.076
F1···H61	3.517	H41···H52^vii	3.390
F1···H101^iii	2.756	H42···F3^ix	3.012
F1···H101^ii	3.365	H42···F5^ix	2.737
F1···H103^iii	3.497	H42···F6^xi	3.138
F2···H41^v	3.109	H42···C2^viii	3.296
F2···H51^v	2.990	H42···C3^viii	3.380
F2···H101^iii	2.906	H42···H21^viii	3.373
F2···H102^iii	2.984	H42···H22^viii	2.731
F2···H103^iii	2.956	H42···H32^viii	2.755
F3···H21^iv	2.596	H42···H103^x	3.467
F3···H22^iv	3.463	H51···F2^xi	2.990
F3···H31^vi	3.595	H51···F5^ix	3.432
F3···H31^ii	3.128	H51···F6^xi	3.576
F3···H32^iv	3.284	H51···N2^ii	3.504
F3···H41^v	2.573	H51···C9^ii	3.415
F3···H42^ii	3.012	H51···C10^x	3.346
F4···H9^ii	2.609	H51···H9^ii	3.546
F4···H21	3.037	H51···H62^ii	3.575
F4···H22	3.396	H51···H102^x	3.003
F4···H31^ii	3.533	H51···H103^x	2.801
F4···H61	2.839	H52···O1^vii	2.569
F4···H62^ii	2.860	H52···N2^ii	3.348
F5···H8^i	2.777	H52···C3^vii	3.516
F5···H9^ii	2.933	H52···C4^vii	3.515
F5···H31^ii	3.399	H52···C6^ii	3.167
F5···H42^ii	2.737	H52···H32^vii	3.393
F5···H51^ii	3.432	H52···H41^vii	3.390
F5···H62^ii	3.176	H52···H61^ii	3.213
F5···H103^i	3.047	H52···H62^ii	2.577
F6···H7	2.654	H61···F1	3.517
F6···H31^vi	3.406	H61···F4	2.839
F6···H32^vi	2.706	H61···F6	2.764
F6···H41^v	2.768	H61···O1^vi	2.913
F6···H42^v	3.138	H61···C3^vi	3.211
F6···H51^v	3.576	H61···H31^vi	3.363
F6···H61	2.764	H61···H32^vi	2.806
F6···H101^iii	3.228	H61···H52^ix	3.213
F6···H103^iii	2.871	H62···F4^ix	2.860
O1···H22^viii	2.508	H62···F5^ix	3.176
O1···H41^vii	3.465	H62···O1^vi	3.007
O1···H52^vii	2.569	H62···C5^ix	3.373
O1···H61^viii	2.913	H62···H51^ix	3.575
O1···H62^viii	3.007	H62···H52^ix	2.577
O2···H8^x	2.592	H101···P1^x	3.599
O2···H9^ii	2.936	H101···F1^x	2.756
O2···H101^ii	3.183	H101···F1^ix	3.365
O2···H102^x	3.216	H101···F2^x	2.906
O2···H102^ii	2.952	H101···F6^x	3.228
O2···H103^x	3.295	H101···O2^ix	3.183
N2···H51^ix	3.504	H101···C7^x	3.461
N2···H52^ix	3.348	H101···H7^x	2.690
N3···H8^x	3.538	H101···H8^x	3.549
N3···H102^xii	3.104	H102···F2^x	2.984
C1···H8^x	3.490	H102···O2^iii	3.216
C1···H9^ii	3.313	H102···O2^ix	2.952
C2···H42^vi	3.296	H102···N3^xii	3.104
C3···H22^viii	3.177	H102···C8^xii	3.060
C3···H41^vi	3.537	H102···C10^xii	3.233
C3···H42^vi	3.380	H102···H8^xii	3.032
C3···H52^vii	3.516	H102···H51^iii	3.003
C3···H61^viii	3.211	H102···H102^xii	2.553
C4···H21^vii	3.593	H103···F1^x	3.497
C4···H22^viii	2.957	H103···F2^x	2.956
C4···H32^viii	3.307	H103···F5^i	3.047
C4···H52^vii	3.515	H103···F6^x	2.871
C5···H62^ii	3.373	H103···O2^iii	3.295
C6···H52^ix	3.167	H103···H7^x	2.944
C7···H101^iii	3.461	H103···H42^iii	3.467
C8···H102^xii	3.060	H103···H51^iii	2.801
F1—P1—F2	90.14 (15)	N1—C2—H22	109.5
F1—P1—F3	178.58 (13)	C3—C2—H21	109.5
F1—P1—F4	86.88 (14)	C3—C2—H22	109.5
F1—P1—F5	89.51 (12)	H21—C2—H22	109.5
F1—P1—F6	87.83 (12)	O1—C3—H31	108.9
F2—P1—F3	91.15 (15)	O1—C3—H32	108.9
F2—P1—F4	176.79 (18)	C2—C3—H31	108.9
F2—P1—F5	93.37 (15)	C2—C3—H32	108.9
F2—P1—F6	85.84 (15)	H31—C3—H32	109.5
F3—P1—F4	91.81 (15)	O1—C4—H41	109.0
F3—P1—F5	91.00 (13)	O1—C4—H42	109.0
F3—P1—F6	91.68 (13)	C5—C4—H41	109.0
F4—P1—F5	87.82 (16)	C5—C4—H42	109.0
F4—P1—F6	92.83 (16)	H41—C4—H42	109.5
F5—P1—F6	177.22 (13)	N1—C5—H51	109.6
C3—O1—C4	110.6 (2)	N1—C5—H52	109.6
C1—N1—C2	126.1 (2)	C4—C5—H51	109.6
C1—N1—C5	121.44 (19)	C4—C5—H52	109.6
C2—N1—C5	112.4 (2)	H51—C5—H52	109.5
C6—N2—C7	126.4 (2)	N2—C6—H61	109.2
C6—N2—C9	126.3 (2)	N2—C6—H62	109.2
C7—N2—C9	107.3 (2)	C1—C6—H61	109.2
C8—N3—C9	107.8 (2)	C1—C6—H62	109.2
C8—N3—C10	126.1 (2)	H61—C6—H62	109.5
C9—N3—C10	126.1 (2)	N2—C7—H7	126.2
O2—C1—N1	124.2 (2)	C8—C7—H7	126.2
O2—C1—C6	120.5 (2)	N3—C8—H8	126.2
N1—C1—C6	115.27 (19)	C7—C8—H8	126.2
N1—C2—C3	109.4 (2)	N2—C9—H9	125.1
O1—C3—C2	111.9 (2)	N3—C9—H9	125.1
O1—C4—C5	111.4 (2)	N3—C10—H101	109.5
N1—C5—C4	109.0 (2)	N3—C10—H102	109.5
N2—C6—C1	110.38 (18)	N3—C10—H103	109.5
N2—C7—C8	107.6 (3)	H101—C10—H102	109.5
N3—C8—C7	107.5 (3)	H101—C10—H103	109.5
N2—C9—N3	109.8 (2)	H102—C10—H103	109.5
N1—C2—H21	109.5
C3—O1—C4—C5	−58.7 (2)	C9—N2—C6—C1	−82.4 (3)
C4—O1—C3—C2	58.6 (3)	C7—N2—C9—N3	−1.5 (3)
C1—N1—C2—C3	−121.9 (2)	C9—N2—C7—C8	1.1 (3)
C2—N1—C1—O2	−176.5 (2)	C8—N3—C9—N2	1.4 (3)
C2—N1—C1—C6	5.1 (3)	C9—N3—C8—C7	−0.7 (3)
C1—N1—C5—C4	121.9 (2)	C10—N3—C8—C7	−179.6 (2)
C5—N1—C1—O2	7.0 (3)	C10—N3—C9—N2	−179.7 (2)
C5—N1—C1—C6	−171.4 (2)	O2—C1—C6—N2	−0.7 (3)
C2—N1—C5—C4	−55.1 (2)	N1—C1—C6—N2	177.8 (2)
C5—N1—C2—C3	54.9 (3)	N1—C2—C3—O1	−55.9 (3)
C6—N2—C7—C8	−178.3 (2)	O1—C4—C5—N1	56.5 (2)
C7—N2—C6—C1	96.9 (3)	N2—C7—C8—N3	−0.2 (4)
C6—N2—C9—N3	177.9 (2)

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