3,3,4,4,5,5-Hexa­fluoro-1,2-bis(5-hydroxy­methyl-2-methyl-3-thienyl)­cyclo­pent-1-ene

The title compound, C₁₇H₁₄F₆O₂S₂, a photochromic di­aryl­ethene, is one of the most promising materials for optical memories and other optoelectronic devices. The hexafluoro­cyclopentene group and the two thio­phene rings are all planar, and the dihedral angles between the cyclo­pentene ring and the adjacent thio­phene rings are 46.4 (1) and 49.5 (1)°.

S1. Comment

Photochromic diarylethene derivatives have attracted much attention as the most promising materials for optical memories and other optoelectronic devices because of their good thermal stability, high sensitivity and multiplexed recording (Hao-Bo et al., 2003; Irie, 2000). A diarylethene with five-membered heterocyclic rings has two conformations, with the two rings in mirror symmetry (parallel conformation) and in C₂ symmetry (antiparallel conformation; Irie & Mohri, 1988; Uchida et al., 1990). According to the Woodward–Hoffmann rule, photoinduced cyclization and cycloreversion reactions can proceed in a conrotatory mode by alternate irradiation with UV and visible light only from the antiparallel conformation (Woodward & Hoffmann, 1970; Irie, 2000). In a previous paper, we have reported the allomorphism of a diarylethene compound and discussed its photochromic properties both in solution and in the single crystalline phase (Shou-Zhi et al., 2003). This compound is a good example for validating the rule exactly. In the present work, a novel photochromic diarylethene compound, (Ia), was synthesized in high yield by a simple method. The structure of this compound is presented here.

The molecular structure of (Ia) is shown in Fig. 1 and a packing diagram is shown in Fig. 2. In the perfluorocyclopentene ring, the C1—C2 bond is clearly a double bond, significantly shorter than the C1—C5 and C2—C3 single bonds. The distance between the reactive C atoms C6 and C12 is 3.596 (4) Å; this distance is short enough for the reaction theoretically to take place in the crystalline phase (Ramamurthy & Venkatesan, 1987). The dihedral angles between the perfluorocyclopentene ring and adjacent thiophene rings are 46.4 (1) and 49.5 (1)°, respectively. In addition, there exist intermolecular hydrogen-bonding interactions between molecules. There are two independent hydrogen bonds; the O1—H···O2 interaction connects two molecules into a dimer, and the O2—H···O1 interaction enables the dimers to form two-dimensional layer parallel to the (100) plane.

The molecule has approximate C₂ symmetry (antiparallel conformation) and can therefore undergo a photocyclization reaction (Yamada et al., 2000). The photochromism is shown in the scheme above. On irradiation with 254 nm UV light, the colorless single-crystal of (Ia) turned red immediately. When observed under polarized light, the red color intensity changed on rotation of the crystalline sample. This phenomenon suggests that the closed-ring isomers are regularly packed in the crystal. When the red crystal was dissolved in ethanol, the solution turned red; the absorption maximum was observed at 514 nm, as it is for the closed-ring form, (Ib), shown in the scheme above. Unfortunately, the single-crystal diffraction pattern of (Ib) could not be obtained because it was very unstable under the experimental conditions. The red color disappeared rapidly upon irradiation with 450 nm light or daylight, and the absorption spectrum of the solution containing the colorless crystal is the same as that of the open-ring form, (Ia).

S2. Experimental

The novel diarylethene (Ia) was prepared by the reduction of 1,2-bis(2-methyl-5-formyl-thien-3-yl)perfluorocyclopentene (BMFTP; Gilat et al., 1993; Shou-Zhi et al., 2002) with lithium aluminium hydride (see scheme below). To a stirred solution of LiAlH₄ (0.1723 g, 4 mmol) in anhydrous ether (50 ml) at room temperature was added dropwise a solution of BMFTP (0.8486 g, 2 mmol) in ether (20 ml), and stirring was continued for 1 h at room temperature. Aqueous sodium potassium tartrate (30%, 5 ml) was then added. The mixture was filtered after stirring for a few minutes and dried over anhydrous MgSO₄. The solvent was removed. Column chromatography (silica gel, ethyl acetate/hexane 1:1) afforded diarylethene (Ia) (0.8131 g, 95%) as colorless crystals. The structure of (Ia) was confirmed by melting point, NMR and mass spectrometry (m.p. 398 K). ¹HNMR (500 MHz, CDCl₃): δ 2.06 (s, 6H), 2.99 (s, 4H), 4.72 (s, 2H), 6.99 (s, 2H); MS m/z (M⁺): 428.

S3. Refinement

H atoms of hydroxy groups were found in a difference Fourier map and refined individually. The other H atoms were placed at idealized postions and treated as riding on their parent atoms, with C—H distances of 0.93 Å for aryl, 0.96 Å for methylene and 0.97 Å for methyl H atoms. The U_iso(H) values were set to 1.2U_eq of the parent atoms for aryl and methylene H atoms, and 1.5U_eq for methyl atoms.

Computing details

Data collection: SMART (Bruker, 1997); cell refinement: SMART; data reduction: SAINT (Bruker, 1997); program(s) used to solve structure: SHELXTL (Bruker, 1997); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.

Figures

	Fig. 1. The structure of (Ia), with 35% probability displacement ellipsoids and the atom-numbering scheme.
	Fig. 2. A packing view along the a direction, showing the hydrogen bonding.

3,3,4,4,5,5-Hexafluoro-1,2-bis(5-hydroxymethyl-2-methyl-3-thienyl)cyclopent-1- ene

Crystal data

C17H14F6O2S2	F(000) = 872
Mr = 428.40	Dx = 1.553 Mg m^−3
Monoclinic, P21/c	Melting point: 125 K
Hall symbol: -P 2ybc	Mo Kα radiation, λ = 0.71073 Å
a = 13.5688 (10) Å	Cell parameters from 6248 reflections
b = 7.5506 (6) Å	θ = 2.2–32.8°
c = 18.0929 (14) Å	µ = 0.36 mm^−1
β = 98.728 (2)°	T = 296 K
V = 1832.2 (2) Å^3	Prism, colorless
Z = 4	0.5 × 0.3 × 0.2 mm

Data collection

Bruker SMART APEX CCD diffractometer	5308 independent reflections
Radiation source: fine-focus sealed tube	4075 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.024
Detector resolution: 15µm x 15µm pixels mm^-1	θmax = 30.0°, θmin = 2.3°
ω scans	h = −19→19
Absorption correction: multi-scan (SADABS; Bruker, 1997)	k = −7→10
Tmin = 0.79, Tmax = 0.93	l = −25→25
14143 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)] = 0.063	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.118	H atoms treated by a mixture of independent and constrained refinement
S = 1.05	w = 1/[σ^2(Fo^2) + (0.001P)^2 + 2.5P] where P = (Fo^2 + 2Fc^2)/3
5308 reflections	(Δ/σ)max = 0.001
254 parameters	Δρmax = 0.75 e Å^−3
0 restraints	Δρmin = −0.58 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
S1	0.81011 (5)	0.21514 (9)	0.31531 (4)	0.05078 (17)
S2	0.94117 (4)	0.71452 (11)	0.55645 (4)	0.05488 (19)
F1	0.47722 (14)	0.5078 (3)	0.33811 (14)	0.1013 (8)
F2	0.53390 (15)	0.7091 (4)	0.27370 (9)	0.0993 (8)
F3	0.41204 (13)	0.7631 (5)	0.40481 (13)	0.1546 (16)
F4	0.5060 (3)	0.9465 (4)	0.36292 (13)	0.1499 (14)
F5	0.60270 (13)	0.9431 (3)	0.49155 (12)	0.0819 (6)
F6	0.53627 (12)	0.7024 (3)	0.51934 (10)	0.0805 (6)
O1	0.90629 (13)	0.2981 (3)	0.17097 (10)	0.0476 (4)
H1A	0.936 (2)	0.368 (4)	0.1968 (15)	0.047 (8)*
O2	0.96538 (14)	0.5359 (3)	0.71925 (11)	0.0552 (5)
H2A	0.949 (2)	0.442 (4)	0.7019 (17)	0.060 (10)*
C1	0.66526 (15)	0.6799 (3)	0.44564 (12)	0.0362 (5)
C2	0.64256 (16)	0.6003 (3)	0.37909 (12)	0.0387 (5)
C3	0.53859 (19)	0.6482 (4)	0.34276 (14)	0.0547 (7)
C4	0.5029 (2)	0.7873 (5)	0.39384 (16)	0.0647 (9)
C5	0.57794 (17)	0.7824 (4)	0.46518 (13)	0.0444 (6)
C6	0.74911 (18)	0.3309 (3)	0.37647 (13)	0.0434 (5)
C7	0.70144 (16)	0.4748 (3)	0.34218 (12)	0.0394 (5)
C8	0.71514 (17)	0.4898 (3)	0.26529 (12)	0.0415 (5)
H8A	0.6872	0.5801	0.2339	0.050*
C9	0.77224 (16)	0.3607 (3)	0.24294 (12)	0.0410 (5)
C10	0.80267 (17)	0.3339 (4)	0.16752 (13)	0.0459 (6)
H10A	0.7649	0.2361	0.1427	0.055*
H10B	0.7860	0.4394	0.1376	0.055*
C11	0.7547 (3)	0.2661 (4)	0.45555 (15)	0.0637 (8)
H11A	0.6938	0.2946	0.4738	0.095*
H11B	0.8096	0.3223	0.4865	0.095*
H11C	0.7643	0.1401	0.4569	0.095*
C12	0.85060 (16)	0.7146 (4)	0.47856 (13)	0.0424 (5)
C13	0.75881 (15)	0.6829 (3)	0.49816 (12)	0.0356 (5)
C14	0.76317 (17)	0.6596 (3)	0.57709 (12)	0.0399 (5)
H14A	0.7072	0.6379	0.5996	0.048*
C15	0.85610 (18)	0.6721 (3)	0.61577 (13)	0.0431 (5)
C16	0.8871 (2)	0.6582 (4)	0.69854 (14)	0.0530 (7)
H16A	0.9082	0.7740	0.7181	0.064*
H16B	0.8300	0.6228	0.7214	0.064*
C17	0.8797 (2)	0.7490 (5)	0.40331 (15)	0.0611 (8)
H17A	0.8248	0.8026	0.3714	0.092*
H17B	0.8968	0.6392	0.3818	0.092*
H17C	0.9361	0.8273	0.4085	0.092*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
S1	0.0599 (4)	0.0473 (4)	0.0472 (3)	0.0136 (3)	0.0147 (3)	−0.0016 (3)
S2	0.0327 (3)	0.0748 (5)	0.0545 (4)	−0.0039 (3)	−0.0020 (3)	0.0038 (4)
F1	0.0522 (10)	0.1049 (17)	0.1378 (19)	−0.0078 (11)	−0.0142 (11)	−0.0386 (15)
F2	0.0903 (14)	0.164 (2)	0.0412 (9)	0.0702 (15)	0.0033 (9)	0.0113 (12)
F3	0.0368 (9)	0.320 (5)	0.1032 (17)	0.0186 (17)	−0.0022 (10)	−0.108 (2)
F4	0.268 (4)	0.0968 (19)	0.0698 (14)	0.097 (2)	−0.0232 (18)	−0.0005 (13)
F5	0.0536 (10)	0.0660 (12)	0.1222 (16)	0.0136 (9)	0.0007 (10)	−0.0415 (12)
F6	0.0538 (9)	0.1296 (18)	0.0640 (11)	0.0213 (11)	0.0284 (8)	0.0190 (11)
O1	0.0358 (8)	0.0616 (12)	0.0456 (10)	0.0029 (8)	0.0070 (7)	−0.0106 (9)
O2	0.0499 (11)	0.0549 (12)	0.0537 (11)	−0.0027 (10)	−0.0153 (8)	0.0036 (10)
C1	0.0310 (10)	0.0421 (12)	0.0354 (10)	0.0048 (9)	0.0052 (8)	0.0011 (9)
C2	0.0341 (10)	0.0463 (13)	0.0355 (11)	0.0063 (10)	0.0048 (8)	0.0001 (10)
C3	0.0412 (13)	0.078 (2)	0.0418 (13)	0.0142 (13)	−0.0037 (10)	−0.0124 (13)
C4	0.0464 (14)	0.092 (2)	0.0516 (15)	0.0318 (16)	−0.0060 (12)	−0.0145 (16)
C5	0.0351 (11)	0.0547 (15)	0.0424 (12)	0.0071 (11)	0.0030 (9)	−0.0098 (11)
C6	0.0484 (13)	0.0428 (13)	0.0415 (12)	0.0037 (11)	0.0143 (10)	−0.0021 (10)
C7	0.0355 (11)	0.0461 (13)	0.0366 (11)	0.0038 (10)	0.0057 (9)	−0.0051 (10)
C8	0.0382 (11)	0.0499 (14)	0.0356 (11)	0.0064 (10)	0.0027 (9)	−0.0023 (10)
C9	0.0349 (11)	0.0510 (14)	0.0365 (11)	0.0019 (10)	0.0031 (9)	−0.0059 (10)
C10	0.0372 (11)	0.0621 (16)	0.0374 (11)	0.0074 (11)	0.0026 (9)	−0.0088 (11)
C11	0.091 (2)	0.0527 (17)	0.0520 (16)	0.0125 (16)	0.0276 (15)	0.0105 (13)
C12	0.0342 (11)	0.0510 (14)	0.0411 (12)	0.0014 (10)	0.0027 (9)	0.0045 (11)
C13	0.0314 (10)	0.0397 (12)	0.0349 (10)	0.0034 (9)	0.0026 (8)	−0.0018 (9)
C14	0.0371 (11)	0.0456 (13)	0.0371 (11)	0.0018 (10)	0.0056 (9)	−0.0017 (10)
C15	0.0433 (12)	0.0442 (13)	0.0395 (12)	0.0023 (11)	−0.0008 (9)	−0.0009 (10)
C16	0.0567 (15)	0.0565 (16)	0.0407 (13)	0.0040 (13)	−0.0088 (11)	−0.0024 (12)
C17	0.0488 (14)	0.083 (2)	0.0542 (16)	−0.0072 (15)	0.0153 (12)	0.0099 (15)

Geometric parameters (Å, º)

S1—C6	1.718 (2)	C6—C11	1.503 (3)
S1—C9	1.727 (3)	C7—C8	1.436 (3)
S2—C15	1.721 (3)	C8—C9	1.345 (3)
S2—C12	1.724 (2)	C8—H8A	0.9300
F1—C3	1.343 (4)	C9—C10	1.498 (3)
F2—C3	1.324 (3)	C10—H10A	0.9700
F3—C4	1.291 (4)	C10—H10B	0.9700
F4—C4	1.329 (4)	C11—H11A	0.9600
F5—C5	1.328 (3)	C11—H11B	0.9600
F6—C5	1.347 (3)	C11—H11C	0.9600
O1—C10	1.424 (3)	C12—C13	1.367 (3)
O1—H1A	0.78 (3)	C12—C17	1.497 (3)
O2—C16	1.414 (3)	C13—C14	1.431 (3)
O2—H2A	0.79 (3)	C14—C15	1.349 (3)
C1—C2	1.339 (3)	C14—H14A	0.9300
C1—C13	1.466 (3)	C15—C16	1.496 (3)
C1—C5	1.502 (3)	C16—H16A	0.9700
C2—C7	1.464 (3)	C16—H16B	0.9700
C2—C3	1.507 (3)	C17—H17A	0.9600
C3—C4	1.525 (4)	C17—H17B	0.9600
C4—C5	1.518 (3)	C17—H17C	0.9600
C6—C7	1.365 (3)
C6—S1—C9	92.73 (12)	C8—C9—S1	110.60 (18)
C15—S2—C12	92.72 (11)	C10—C9—S1	120.89 (19)
C10—O1—H1A	109 (2)	O1—C10—C9	113.12 (19)
C16—O2—H2A	109 (2)	O1—C10—H10A	109.0
C2—C1—C13	130.4 (2)	C9—C10—H10A	109.0
C2—C1—C5	111.15 (19)	O1—C10—H10B	109.0
C13—C1—C5	118.43 (19)	C9—C10—H10B	109.0
C1—C2—C7	129.3 (2)	H10A—C10—H10B	107.8
C1—C2—C3	110.9 (2)	C6—C11—H11A	109.5
C7—C2—C3	119.7 (2)	C6—C11—H11B	109.5
F2—C3—F1	105.9 (2)	H11A—C11—H11B	109.5
F2—C3—C2	113.7 (2)	C6—C11—H11C	109.5
F1—C3—C2	111.6 (2)	H11A—C11—H11C	109.5
F2—C3—C4	111.0 (3)	H11B—C11—H11C	109.5
F1—C3—C4	109.3 (3)	C13—C12—C17	130.0 (2)
C2—C3—C4	105.3 (2)	C13—C12—S2	110.65 (17)
F3—C4—F4	106.6 (3)	C17—C12—S2	119.35 (18)
F3—C4—C5	113.5 (3)	C13—C12—C6	72.50 (14)
F4—C4—C5	108.6 (3)	C17—C12—C6	78.80 (17)
F3—C4—C3	113.2 (3)	S2—C12—C6	126.13 (13)
F4—C4—C3	109.5 (3)	C12—C13—C14	112.28 (19)
C5—C4—C3	105.3 (2)	C12—C13—C1	124.6 (2)
F5—C5—F6	105.1 (2)	C14—C13—C1	123.05 (19)
F5—C5—C1	112.9 (2)	C15—C14—C13	113.7 (2)
F6—C5—C1	111.9 (2)	C15—C14—H14A	123.1
F5—C5—C4	112.6 (2)	C13—C14—H14A	123.1
F6—C5—C4	109.2 (2)	C14—C15—C16	127.8 (2)
C1—C5—C4	105.29 (19)	C14—C15—S2	110.60 (18)
C7—C6—C11	130.1 (2)	C16—C15—S2	121.58 (19)
C7—C6—S1	110.72 (17)	O2—C16—C15	113.4 (2)
C11—C6—S1	119.20 (19)	O2—C16—H16A	108.9
C7—C6—C12	73.14 (15)	C15—C16—H16A	108.9
C11—C6—C12	79.23 (16)	O2—C16—H16B	108.9
S1—C6—C12	123.80 (12)	C15—C16—H16B	108.9
C6—C7—C8	112.4 (2)	H16A—C16—H16B	107.7
C6—C7—C2	124.2 (2)	C12—C17—H17A	109.5
C8—C7—C2	123.4 (2)	C12—C17—H17B	109.5
C9—C8—C7	113.6 (2)	H17A—C17—H17B	109.5
C9—C8—H8A	123.2	C12—C17—H17C	109.5
C7—C8—H8A	123.2	H17A—C17—H17C	109.5
C8—C9—C10	128.5 (2)	H17B—C17—H17C	109.5
C13—C1—C2—C7	7.8 (4)	C1—C2—C7—C6	47.1 (4)
C5—C1—C2—C7	−173.4 (2)	C3—C2—C7—C6	−129.7 (3)
C13—C1—C2—C3	−175.2 (3)	C1—C2—C7—C8	−133.1 (3)
C5—C1—C2—C3	3.6 (3)	C3—C2—C7—C8	50.2 (4)
C1—C2—C3—F2	127.5 (3)	C6—C7—C8—C9	−0.4 (3)
C7—C2—C3—F2	−55.1 (4)	C2—C7—C8—C9	179.8 (2)
C1—C2—C3—F1	−112.7 (3)	C7—C8—C9—C10	−179.7 (2)
C7—C2—C3—F1	64.6 (3)	C7—C8—C9—S1	0.6 (3)
C1—C2—C3—C4	5.8 (3)	C6—S1—C9—C8	−0.5 (2)
C7—C2—C3—C4	−176.9 (3)	C6—S1—C9—C10	179.8 (2)
F2—C3—C4—F3	99.6 (4)	C8—C9—C10—O1	132.9 (3)
F1—C3—C4—F3	−16.9 (4)	S1—C9—C10—O1	−47.4 (3)
C2—C3—C4—F3	−136.9 (3)	C15—S2—C12—C13	0.0 (2)
F2—C3—C4—F4	−19.2 (4)	C15—S2—C12—C17	179.3 (2)
F1—C3—C4—F4	−135.7 (3)	C15—S2—C12—C6	−82.99 (14)
C2—C3—C4—F4	104.3 (3)	C7—C6—C12—C13	76.21 (19)
F2—C3—C4—C5	−135.9 (3)	C11—C6—C12—C13	−61.7 (2)
F1—C3—C4—C5	107.6 (3)	S1—C6—C12—C13	−179.79 (18)
C2—C3—C4—C5	−12.3 (3)	C7—C6—C12—C17	−62.34 (19)
C2—C1—C5—F5	−134.7 (2)	C11—C6—C12—C17	159.7 (2)
C13—C1—C5—F5	44.3 (3)	S1—C6—C12—C17	41.7 (2)
C2—C1—C5—F6	107.0 (2)	C7—C6—C12—S2	179.36 (18)
C13—C1—C5—F6	−74.0 (3)	C11—C6—C12—S2	41.4 (2)
C2—C1—C5—C4	−11.4 (3)	S1—C6—C12—S2	−76.64 (19)
C13—C1—C5—C4	167.5 (2)	C17—C12—C13—C14	−178.9 (3)
F3—C4—C5—F5	−97.9 (4)	S2—C12—C13—C14	0.3 (3)
F4—C4—C5—F5	20.4 (3)	C6—C12—C13—C14	123.1 (2)
C3—C4—C5—F5	137.7 (3)	C17—C12—C13—C1	−1.3 (5)
F3—C4—C5—F6	18.3 (4)	S2—C12—C13—C1	177.92 (19)
F4—C4—C5—F6	136.7 (3)	C6—C12—C13—C1	−59.3 (2)
C3—C4—C5—F6	−106.1 (3)	C2—C1—C13—C12	46.8 (4)
F3—C4—C5—C1	138.7 (3)	C5—C1—C13—C12	−131.9 (3)
F4—C4—C5—C1	−103.0 (3)	C2—C1—C13—C14	−135.8 (3)
C3—C4—C5—C1	14.3 (3)	C5—C1—C13—C14	45.5 (3)
C9—S1—C6—C7	0.2 (2)	C12—C13—C14—C15	−0.5 (3)
C9—S1—C6—C11	−179.6 (2)	C1—C13—C14—C15	−178.2 (2)
C9—S1—C6—C12	−82.87 (14)	C13—C14—C15—C16	178.7 (2)
C11—C6—C7—C8	179.8 (3)	C13—C14—C15—S2	0.4 (3)
S1—C6—C7—C8	0.0 (3)	C12—S2—C15—C14	−0.2 (2)
C12—C6—C7—C8	120.5 (2)	C12—S2—C15—C16	−178.6 (2)
C11—C6—C7—C2	−0.3 (4)	C14—C15—C16—O2	128.7 (3)
S1—C6—C7—C2	179.87 (19)	S2—C15—C16—O2	−53.2 (3)
C12—C6—C7—C2	−59.7 (2)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1—H1A···O2^i	0.78 (3)	2.00 (3)	2.738 (3)	159 (3)
O2—H2A···O1^ii	0.79 (3)	1.96 (3)	2.748 (3)	173 (3)

Symmetry codes: (i) −x+2, −y+1, −z+1; (ii) x, −y+1/2, z+1/2.