Hydrogen-bond patterns in the congruent complex 4-nitro­phenol-acetamide (1/1)

Fusion of 4-nitro­phenol and acetamide in a 1:1 molar ratio gives the title product, C₆H₅NO₃·C₂H₅NO, (III), which has the character of a pure covalently bonded compound, having a high sharp melting point. Complex (III) (m.p. 371.9-372.9 K) can be recrystallized from various solvents and forms eutectics with either acetamide or 4-nitro­phenol. Similar fusion of mixtures of acetamide and 2-nitro­phenol yields no complex similar to (III) and mixtures of acetamide and 3-nitro­phenol produce only a weak low-melting complex. The significance of this study lies in its demonstration, via graph set analysis, that some of the patterns found individually in crystalline acetamide or 4-nitro­phenol have been preserved in crystals of complex (III), while several higher order graph sets are produced in (III) due to new hydrogen bonds involving the nitro group. In particular, large hydrogen-bonded rings are formed together with helical chains.

S1. Comment

We report here the structure and graph-set analysis of the congruent 1:1 molar compound 4-nitrophenol–acetamide (1:1), (III) (m.p. 370 K), which forms eutectics with each of its two components, viz 4-nitrophenol, (I), and acetamide, (II) (Dzhelomanova et al., 1956). This molar compound crystallizes with Z' = 2 (Fig. 1) and retains some of the hydrogen-bond patterns observed in the crystal structure of the single components (Etter & MacDonald, 1990; Etter, 1990; Bernstein et al., 1995).

4-Nitrophenol, (I), has a relatively high melting point (386 K) and crystallizes in two polymorphs (Coppens & Schimdt, 1965a,b; Kulkarni et al., 1998; Wójcik & Mossakowska, 2006). The crystal structures are characterized by hydrogen bonding between hydroxyl and nitro groups of adjacent molecules, forming endless continuous chains which are described as C(8), creating a herring-bone pattern (Coppens & Schimdt, 1965a,b; Wójcik & Mossakowska, 2006).

Acetamide, (II), is also high melting (353 K) for such a simple compound and its structure is characterized by multiple N—H···O(C) bonds. This small molecule crystallizes in two forms. The more common one is the orthorhombic, which contains two molecules in the asymmetric unit (Hamilton, 1965; Jeffrey et al., 1980; Ottersen, 1975) and a more unusual rhombohedral with only one molecule in the asymmetric unit (Denne & Small, 1971; Senti & Harker, 1940). These two forms establish different hydrogen-bond patterns. The motifs in its orthorhombic form are described as C(4)C(4)DD and in the rhombohedral as C(4)C(4), reflecting the endless chains formed at the first level graph set in both forms (Bernstein et al., 1995). At the second level graph set, both forms generate ring patterns, viz. R₂²(8) in the orthorhombic form and R₆³(12) in the rhombohedral (Bernstein et al.,1995). In the orthorhombic form, the ring pattern is created through two N—H···O(C) hydrogen bonds between the two molecules present in the asymmetric unit (Bernstein et al.,1995). In the rhombohedral form, the ring is created through N—H···O(C) hydrogen bonds amongst four neighbouring acetamide molecules (Bernstein et al., 1995).

In the complex, (III), the four independent molecules present in the asymmetric unit establish six different hydrogen bonds (Fig, 1 and Table 1). These bonds have been labelled a–f to help in the assignment of the patterns formed (Etter & MacDonald, 1990; Etter, 1990; Bernstein et al., 1995). Surprisingly, although complex (III) forms six different hydrogen bonds, it only creates finite D patterns (Table 2). The D motifs, which are present in the orthorhombic form of acetamide, are retained in complex (III). In this case, bonds c and d generate identical D motifs to those observed in acetamide (Table 2). The other N—H···O(C) bond in acetamide (II) generates the C(4) motif. In complex (III) this C(4) motif is not retained because atoms H4B and H3B are hydrogen bonded, respectively, to O5ⁱⁱ and O2ⁱ, thereby establishing two new D motifs (e and f; Fig. 1).

In 4-nitrophenol, (I), a single chain is formed through O—H···O(N) hydrogen bonding between the hydroxyl H atom of one molecule and a nitro O atom of a neighbouring molecule. This pattern is not retained in the crystal structure of complex (III), in which the hydroxyl H1 and H4 atoms establish new O—H···O(C) hydrogen bonds to amide atoms O7 and O8, thereby creating two D patterns (a and b; Table 2 and Fig. 2). Thus, at the first level graph set, compound (III) is described as N₁=DDDDDD, reflecting the large number of molecules present in the unit cell.

At the second level of the graph set, more of the patterns generated in (III) are ones retained from structures seen in the individual components (I) and (II). In the orthorhombic form of the single amide component (II), dimers are formed from two N—H···O(C) bonds. This feature is retained in complex (III) and dimers are formed through bonds c and d (Fig. 1 and Table 2). Thus, the R₂²(8) ring pattern observed in complex (III) is identical to that observed in the isolated amide (II). The C(4) chains formed through N—H···O(C) hydrogen bonds between pairs of molecules in (II) (Bernstein et al., 1995) are not retained in complex (III). In the latter, the amide H atoms, which are not involved in dimer formation, instead establish hydrogen bonds with nitrophenol to create a chain of alternating (I) and (II) units. Two C₂²(12) chains are created by the pair a/f and another by the pair b/e (Fig. 2). The chains are symmetrically different and run parallel to each other along the c axis. These chains form a wave-type structure that is held together through dimers of acetamide forming a pleated sheet (Fig. 2). They are identical to the `flat' features observed in the structures of the pure components (I) and (II), but in complex (III) the chains adopt the pleated sheet form (Fig. 2). No other patterns are present at this level, therefore, the overall second level graph set for compound (III) is described as N₂ = R₂²(8)C₂²(12)C₂²(12), reflecting the rings and chains observed at this level.

The structures of the pure components (I) and (II) do not have any higher level graph sets of hydrogen-bond patterns but their complex (III) does. This pattern is formed by combining bonds a, c, b, e, d and f or a, d, b, e, c and f (Fig. 2), which combinations describe two C₅⁵(22) chains. These chains include the acetamide dimers and are better described as a chain of rings. Thus, the hydrogen-bond patterns at the sixth level graph set for complex (III) are described as N₆=C₅⁵(22)[R₂²(8)]. No other patterns were observed at higher level graph sets for complex (III).

Related literature

For related literature, see: Bernstein et al. (1995); Coppens & Schimdt (1965a, 1965b); Denne & Small (1971); Dzhelomanova et al. (1956); Etter (1990); Etter & MacDonald (1990); Hamilton (1965); Jeffrey et al. (1980); Johnstone et al. (2008); Kulkarni et al. (1998); Ottersen (1975); Senti & Harker (1940); Wójcik & Mossakowska (2006).

S2. Experimental

4-Nitrophenol and acetamide were used as provided (Aldrich and Acros). 4-Nitrophenol (5 g, 35.9 mmol) and acetamide (2.1 g, 35.9 mmol) were weighed into a conical flask. The flask was heated at 373 K until both reagents had melted. The yellow liquid was allowed to cool to room temperature and the resulting yellow solid was recrystalized as plates from toluene [m.p. 371.9– 372.9 K; literature 369 K (Dzhelomanova et al., 1956)].

S3. Refinement

All H atoms were treated as riding atoms, with C—H = 0.95 or 0.98°, N—H = 0.88Å and O—H = 0.84Å, and with U_iso(H) = kU_eq(carrier), where k = 1.2 or 1.5.

Computing details

Data collection: SMART (Bruker, 1988); cell refinement: SMART (Bruker, 1988); data reduction: SMART (Bruker, 1988); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL (Bruker, 1988); software used to prepare material for publication: SHELXTL (Bruker, 1988).

Figures

	Fig. 1. Acetamide molecules form dimers through N—H···O hydrogen bonds (c and d; dashed lines). These dimers form a three-dimensional network with 4-nitrophenol molecules through N—H···O(N), C—H···O(N) and O—H···O hydrogen bonds (a, b, e and f; dashed lines). [Symmetry codes: (i) x, -y+3/2, z+1/2; (ii) x, -y+1/2, z-1/2.]
	Fig. 2. Intercalating chains of molecules of (I) and (II) run along the c axis in complex (III). The symmetrically different chains of rings are interconnected through formation of dimers of (II). These chains create a wave-like pattern (pleated sheet).

4-nitrophenol–acetamide (1:1)

Crystal data

C6H5NO3·C2H5NO	F(000) = 832
Mr = 198.18	Dx = 1.437 Mg m^−3
Monoclinic, P21/c	Melting point: 373 K
Hall symbol: -P 2ybc	Mo Kα radiation, λ = 0.71073 Å
a = 20.370 (3) Å	Cell parameters from 11096 reflections
b = 3.7506 (6) Å	θ = 0.8–28.2°
c = 24.070 (3) Å	µ = 0.12 mm^−1
β = 94.873 (3)°	T = 100 K
V = 1832.3 (5) Å^3	Plate, yellow
Z = 8	0.5 × 0.4 × 0.1 mm

Data collection

Bruker SMART APEX diffractometer	2683 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.142
Graphite monochromator	θmax = 25.0°, θmin = 1.0°
ϕ and ω scans	h = −24→13
8627 measured reflections	k = −4→4
3239 independent reflections	l = −27→28

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)] = 0.070	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.185	H-atom parameters constrained
S = 1.08	w = 1/[σ^2(Fo^2) + (0.0863P)^2 + 1.0261P] where P = (Fo^2 + 2Fc^2)/3
3239 reflections	(Δ/σ)max < 0.001
257 parameters	Δρmax = 0.40 e Å^−3
0 restraints	Δρmin = −0.28 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
C1	0.40866 (13)	0.4034 (7)	0.36499 (12)	0.0196 (6)
C2	0.34544 (13)	0.5146 (7)	0.34218 (12)	0.0177 (6)
H2	0.3157	0.6215	0.3656	0.021*
C3	0.32704 (12)	0.4690 (7)	0.28678 (11)	0.0173 (6)
H3	0.2849	0.5461	0.2716	0.021*
C4	0.37046 (13)	0.3087 (7)	0.25257 (12)	0.0174 (6)
C5	0.43252 (13)	0.1909 (7)	0.27436 (12)	0.0174 (6)
H5	0.4614	0.0778	0.2509	0.021*
C6	0.45111 (13)	0.2396 (7)	0.32944 (12)	0.0189 (6)
H6	0.4934	0.1619	0.3442	0.023*
C7	0.09395 (13)	0.7769 (7)	0.63608 (11)	0.0172 (6)
C8	0.05236 (13)	0.8974 (7)	0.67591 (12)	0.0172 (6)
H8	0.0117	1.0088	0.6639	0.021*
C9	0.06969 (12)	0.8562 (7)	0.73151 (11)	0.0160 (6)
H9	0.0414	0.9396	0.7582	0.019*
C10	0.12932 (13)	0.6904 (7)	0.74897 (11)	0.0157 (6)
C11	0.17149 (12)	0.5698 (7)	0.71035 (11)	0.0162 (6)
H11	0.2119	0.4575	0.7228	0.019*
C12	0.15471 (12)	0.6132 (7)	0.65465 (12)	0.0169 (6)
H12	0.1837	0.5338	0.6283	0.020*
C13	0.34446 (13)	0.8232 (7)	0.52092 (11)	0.0181 (6)
C14	0.41348 (13)	0.9358 (8)	0.54068 (12)	0.0212 (6)
H14A	0.4404	0.7239	0.5498	0.032*
H14B	0.4124	1.0855	0.5740	0.032*
H14C	0.4325	1.0712	0.5112	0.032*
C15	0.15396 (13)	0.4365 (7)	0.47456 (11)	0.0180 (6)
C16	0.08455 (13)	0.3232 (8)	0.45599 (11)	0.0201 (6)
H16A	0.0652	0.2025	0.4868	0.030*
H16B	0.0852	0.1599	0.4243	0.030*
H16C	0.0581	0.5338	0.4448	0.030*
N1	0.35187 (11)	0.2638 (6)	0.19397 (10)	0.0212 (6)
N2	0.14565 (11)	0.6368 (6)	0.80801 (10)	0.0185 (5)
N3	0.29652 (11)	0.8955 (6)	0.55246 (10)	0.0213 (6)
H3A	0.2559	0.8311	0.5417	0.026*
H3B	0.3051	1.0081	0.5843	0.026*
N4	0.20141 (11)	0.3526 (6)	0.44301 (10)	0.0209 (5)
H4A	0.2422	0.4181	0.4529	0.025*
H4B	0.1923	0.2310	0.4120	0.025*
O1	0.42965 (9)	0.4481 (6)	0.41819 (8)	0.0245 (5)
H1	0.3986	0.5254	0.4357	0.037*
O2	0.29833 (9)	0.3860 (6)	0.17403 (8)	0.0259 (5)
O3	0.38951 (10)	0.1050 (6)	0.16480 (9)	0.0304 (5)
O4	0.07502 (9)	0.8246 (6)	0.58245 (8)	0.0230 (5)
H4	0.1054	0.7613	0.5631	0.035*
O5	0.19740 (9)	0.4715 (6)	0.82298 (8)	0.0259 (5)
O6	0.10815 (9)	0.7470 (6)	0.84165 (8)	0.0252 (5)
O7	0.33360 (9)	0.6632 (5)	0.47537 (8)	0.0227 (5)
O8	0.16552 (9)	0.6090 (5)	0.51875 (8)	0.0228 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C1	0.0128 (14)	0.0144 (13)	0.0315 (16)	−0.0022 (11)	0.0017 (11)	0.0016 (11)
C2	0.0101 (13)	0.0117 (13)	0.0319 (15)	0.0013 (10)	0.0058 (11)	0.0015 (11)
C3	0.0075 (13)	0.0113 (13)	0.0333 (16)	−0.0016 (10)	0.0036 (11)	0.0053 (11)
C4	0.0113 (13)	0.0097 (12)	0.0311 (15)	−0.0046 (10)	0.0013 (11)	0.0018 (11)
C5	0.0100 (13)	0.0093 (12)	0.0339 (16)	−0.0010 (10)	0.0073 (11)	0.0008 (11)
C6	0.0072 (12)	0.0154 (13)	0.0342 (16)	−0.0004 (10)	0.0017 (11)	0.0040 (12)
C7	0.0132 (14)	0.0108 (13)	0.0271 (15)	−0.0051 (10)	−0.0010 (11)	0.0003 (11)
C8	0.0081 (13)	0.0119 (13)	0.0316 (15)	−0.0003 (10)	0.0011 (11)	0.0010 (11)
C9	0.0077 (13)	0.0106 (12)	0.0310 (15)	−0.0013 (10)	0.0090 (11)	−0.0038 (11)
C10	0.0117 (13)	0.0081 (12)	0.0274 (14)	−0.0039 (10)	0.0013 (11)	−0.0002 (10)
C11	0.0069 (13)	0.0092 (12)	0.0325 (15)	−0.0025 (10)	0.0010 (11)	0.0026 (11)
C12	0.0071 (12)	0.0114 (13)	0.0328 (15)	−0.0007 (10)	0.0041 (11)	−0.0030 (11)
C13	0.0169 (14)	0.0161 (13)	0.0207 (14)	−0.0008 (11)	−0.0027 (11)	0.0045 (11)
C14	0.0139 (15)	0.0183 (14)	0.0308 (15)	−0.0021 (11)	−0.0017 (12)	0.0014 (12)
C15	0.0124 (14)	0.0187 (13)	0.0224 (14)	−0.0027 (11)	−0.0014 (11)	0.0042 (11)
C16	0.0147 (14)	0.0208 (14)	0.0247 (14)	−0.0027 (11)	0.0014 (11)	0.0006 (11)
N1	0.0148 (12)	0.0183 (12)	0.0311 (14)	−0.0018 (10)	0.0058 (10)	0.0024 (10)
N2	0.0109 (12)	0.0152 (12)	0.0299 (13)	−0.0043 (9)	0.0039 (10)	0.0005 (10)
N3	0.0156 (12)	0.0242 (13)	0.0239 (12)	−0.0021 (10)	0.0016 (10)	−0.0046 (10)
N4	0.0157 (12)	0.0223 (13)	0.0247 (12)	−0.0041 (10)	0.0010 (10)	−0.0037 (10)
O1	0.0156 (10)	0.0311 (12)	0.0268 (11)	0.0041 (9)	0.0020 (8)	−0.0014 (9)
O2	0.0154 (11)	0.0324 (12)	0.0295 (11)	0.0009 (9)	−0.0008 (8)	0.0053 (9)
O3	0.0221 (12)	0.0396 (13)	0.0305 (12)	0.0006 (10)	0.0091 (9)	−0.0072 (10)
O4	0.0136 (10)	0.0297 (11)	0.0258 (11)	0.0033 (8)	0.0021 (8)	−0.0006 (9)
O5	0.0161 (11)	0.0293 (11)	0.0321 (12)	0.0078 (9)	0.0001 (9)	0.0064 (9)
O6	0.0152 (10)	0.0346 (12)	0.0273 (11)	−0.0010 (9)	0.0098 (8)	−0.0030 (9)
O7	0.0135 (10)	0.0289 (11)	0.0257 (11)	−0.0016 (8)	0.0021 (8)	−0.0049 (9)
O8	0.0157 (10)	0.0283 (11)	0.0244 (11)	−0.0019 (8)	0.0023 (8)	−0.0044 (8)

Geometric parameters (Å, º)

C1—O1	1.326 (3)	C12—H12	0.9500
C1—C6	1.408 (4)	C13—O7	1.253 (3)
C1—C2	1.419 (4)	C13—N3	1.315 (4)
C2—C3	1.365 (4)	C13—C14	1.506 (4)
C2—H2	0.9500	C14—H14A	0.9800
C3—C4	1.395 (4)	C14—H14B	0.9800
C3—H3	0.9500	C14—H14C	0.9800
C4—C5	1.398 (4)	C15—O8	1.250 (3)
C4—N1	1.439 (4)	C15—N4	1.317 (4)
C5—C6	1.360 (4)	C15—C16	1.507 (4)
C5—H5	0.9500	C16—H16A	0.9800
C6—H6	0.9500	C16—H16B	0.9800
C7—O4	1.328 (3)	C16—H16C	0.9800
C7—C8	1.407 (4)	N1—O3	1.236 (3)
C7—C12	1.419 (4)	N1—O2	1.241 (3)
C8—C9	1.364 (4)	N2—O6	1.231 (3)
C8—H8	0.9500	N2—O5	1.249 (3)
C9—C10	1.397 (4)	N3—H3A	0.8800
C9—H9	0.9500	N3—H3B	0.8800
C10—C11	1.394 (4)	N4—H4A	0.8800
C10—N2	1.446 (4)	N4—H4B	0.8800
C11—C12	1.365 (4)	O1—H1	0.8400
C11—H11	0.9500	O4—H4	0.8400
O1—C1—C6	118.5 (2)	C11—C12—H12	120.0
O1—C1—C2	123.0 (3)	C7—C12—H12	120.0
C6—C1—C2	118.5 (3)	O7—C13—N3	121.3 (2)
C3—C2—C1	120.4 (3)	O7—C13—C14	120.1 (2)
C3—C2—H2	119.8	N3—C13—C14	118.6 (2)
C1—C2—H2	119.8	C13—C14—H14A	109.5
C2—C3—C4	119.7 (2)	C13—C14—H14B	109.5
C2—C3—H3	120.1	H14A—C14—H14B	109.5
C4—C3—H3	120.1	C13—C14—H14C	109.5
C3—C4—C5	120.9 (3)	H14A—C14—H14C	109.5
C3—C4—N1	120.1 (2)	H14B—C14—H14C	109.5
C5—C4—N1	119.0 (3)	O8—C15—N4	121.3 (2)
C6—C5—C4	119.4 (3)	O8—C15—C16	120.1 (2)
C6—C5—H5	120.3	N4—C15—C16	118.5 (2)
C4—C5—H5	120.3	C15—C16—H16A	109.5
C5—C6—C1	121.1 (2)	C15—C16—H16B	109.5
C5—C6—H6	119.4	H16A—C16—H16B	109.5
C1—C6—H6	119.4	C15—C16—H16C	109.5
O4—C7—C8	118.5 (2)	H16A—C16—H16C	109.5
O4—C7—C12	122.6 (3)	H16B—C16—H16C	109.5
C8—C7—C12	118.9 (2)	O3—N1—O2	121.7 (2)
C9—C8—C7	120.8 (2)	O3—N1—C4	119.3 (2)
C9—C8—H8	119.6	O2—N1—C4	119.0 (2)
C7—C8—H8	119.6	O6—N2—O5	122.2 (2)
C8—C9—C10	119.4 (2)	O6—N2—C10	119.7 (2)
C8—C9—H9	120.3	O5—N2—C10	118.1 (2)
C10—C9—H9	120.3	C13—N3—H3A	120.0
C11—C10—C9	120.9 (2)	C13—N3—H3B	120.0
C11—C10—N2	120.5 (2)	H3A—N3—H3B	120.0
C9—C10—N2	118.6 (2)	C15—N4—H4A	120.0
C12—C11—C10	120.0 (2)	C15—N4—H4B	120.0
C12—C11—H11	120.0	H4A—N4—H4B	120.0
C10—C11—H11	120.0	C1—O1—H1	109.5
C11—C12—C7	120.0 (3)	C7—O4—H4	109.5
O1—C1—C2—C3	178.5 (3)	C8—C9—C10—N2	−177.6 (2)
C6—C1—C2—C3	−1.2 (4)	C9—C10—C11—C12	0.0 (4)
C1—C2—C3—C4	0.7 (4)	N2—C10—C11—C12	178.2 (2)
C2—C3—C4—C5	0.6 (4)	C10—C11—C12—C7	−0.8 (4)
C2—C3—C4—N1	−179.2 (2)	O4—C7—C12—C11	−179.7 (2)
C3—C4—C5—C6	−1.2 (4)	C8—C7—C12—C11	1.0 (4)
N1—C4—C5—C6	178.5 (2)	C3—C4—N1—O3	−176.3 (2)
C4—C5—C6—C1	0.7 (4)	C5—C4—N1—O3	3.9 (4)
O1—C1—C6—C5	−179.2 (2)	C3—C4—N1—O2	3.7 (4)
C2—C1—C6—C5	0.5 (4)	C5—C4—N1—O2	−176.0 (2)
O4—C7—C8—C9	−179.7 (2)	C11—C10—N2—O6	179.5 (2)
C12—C7—C8—C9	−0.4 (4)	C9—C10—N2—O6	−2.3 (4)
C7—C8—C9—C10	−0.4 (4)	C11—C10—N2—O5	−2.0 (4)
C8—C9—C10—C11	0.6 (4)	C9—C10—N2—O5	176.3 (2)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N3—H3A···O8	0.88	2.05	2.927 (3)	172
N3—H3B···O2^i	0.88	2.21	3.036 (3)	156
N4—H4A···O7	0.88	2.11	2.976 (3)	170
N4—H4B···O5^ii	0.88	2.29	3.129 (3)	161
O1—H1···O7	0.84	1.77	2.613 (3)	176
O4—H4···O8	0.84	1.79	2.624 (3)	176

Symmetry codes: (i) x, −y+3/2, z+1/2; (ii) x, −y+1/2, z−1/2.