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In the title compound, C20H16N2O5, both of the 1-acetyl­isatin (1-acetyl-1H-indole-2,3-dione) moieties are planar and form a dihedral angle of 74.1 (1)°. Weak intermolecular hydrogen bonds and C—H...π interactions stabilize the packing in the crystal.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270101017875/da1206sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270101017875/da1206Isup2.hkl
Contains datablock I

CCDC reference: 180159

Comment top

Derivatives of 1H-indole-2,3-dione (isatin) are of interest due to their biological activities (Bieck et al., 1993) and wide use as synthetic precursors (Popp, 1975; Shvekhgeimer, 1996). Xue's group has intensively investigated the photoinduced reactions of the isatin derivatives in order to further explore the scope of their photochemistry (Xue et al., 2000; 2001). The title compound, (I), is the sole product of the photoreaction of 1-acetylisatin and dibenzoylmethane. We have undertaken an X-ray crystal structure analysis of (I) to confirm the biindole structure and to establish the steric configuration of the two chiral carbon atoms.

Scheme I

The bond lengths and bond angles observed in (I) are within normal values (Table 1). The values for the two 1-acetylisatin moieties agree with each other and are comparable with those of the previously studied related structure (Zukerman-Schpector et al., 1992). Each of the 1-acetylisatin moieties are almost planar, with maximum deviations of 0.028 (2) Å (C7) and -0.066 (1) Å (C9). The dihedral angles between the heterocyclic and benzene rings are 1.7 (1) and 4.1 (1)°. The two acetyl groups are twisted by 8.3 (1) and 14.7 (1)° from their attached isatin planes, and the two 1-acetylisatin moieties form a dihedral angle of 74.1 (1)°. The ketone atoms O2 and O3 are essentially coplanar with their attached isatin groups, with maximum deviations of 0.032 (1) and 0.127 (1) Å, respectively. Atoms C8 and C9 are chiral centers.

Although intramolecular interactions between the acetyl O1 and O4 atoms and the indole-H atoms [H5A···O4 2.3295, C5···O4 2.863 (2) Å, C5A—H5A···O4 116°; H12A···O1 2.3095, C12···O1 2.855 (2) Å, C12—H12A···O1 117°] can be viewed as closed six-membered rings of O4—C17—N1—C6—C5—H5A and O1—C19—N2—C11—C12—H12A, the planarity of both of the 1-acetylisatin moieties is mostly due to conjugation of N—C and C=O bonds. Atom O4 is also involved in a weak intermolecular O—H···O hydrogen bond, and atom O2 facilitates a bifurcated intermolecular weak C—H···O hydrogen bond (Table 2). These intermolecular hydrogen bonds interconnect the molecules into a three dimensional molecular arrangement (Fig. 2). Intermolecular C—H···π interactions are observed for C18—H18A···π(A)i [(i) 2 - x,2 - y,-z, H···π 2.785 Å, C···π 3.570 (2) Å, C—H···π 139°] and C18—H18A···π(B)ii [(ii) 1 - x,2 - y,-z, H···π 3.187 Å, C···π 3.846 (2) Å, C—H···π 127°], where A and B denote the center of gravity of the two benzene rings of the isatin moieties. The intermolecular hydrogen bonds and C—H···π interactions stabilize the molecular packing.

Experimental top

The title compound was prepared by the photoinduced reaction of a benzene solution (40 ml) of 1-acetylisatin (0.05 M) in an excess of dibenzoylmethane with Pyrex-filtered light from a medium-pressure mercury lamp. The reaction was carried out under a constant nitrogen purge. After irradiation, the solvent was removed in vacuo and the residue was separated by column chromatography with petroleum spirit/ethyl acetate as eluent. The title compound was obtained as the sole product and was recrystallized from an acetone/petroleum ether mixture.

Refinement top

After checking their presence in the difference map, all H atoms were geometrically fixed and allowed to ride on the parent C atoms.

Computing details top

Data collection: SMART (Siemens, 1996); cell refinement: SAINT (Siemens, 1996); data reduction: SAINT; program(s) used to solve structure: SHELXTL (Sheldrick, 1997); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL, PARST (Nardelli, 1995) and PLATON (Spek, 1990).

Figures top
[Figure 1] Fig. 1. The structure of (I) showing 50% probability displacement ellipsoids and the atom-numbering scheme.
[Figure 2] Fig. 2. Packing diagram of the title structure (I) viewed down the b axis. The dashed lines denote the weak intermolecular hydrogen bonds.
1,1'-diacetyl-3-hydroxy-1,1',3,3'-tetrahydro-3,3'-bisindole-2,2'-dione top
Crystal data top
C20H16N2O5Dx = 1.383 Mg m3
Mr = 364.35Melting point: 425K K
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
a = 10.2447 (1) ÅCell parameters from 8056 reflections
b = 10.3416 (1) Åθ = 2.1–28.3°
c = 16.9848 (2) ŵ = 0.10 mm1
β = 103.482 (1)°T = 293 K
V = 1749.89 (3) Å3Block, colourless
Z = 40.40 × 0.36 × 0.32 mm
F(000) = 760
Data collection top
Siemens SMART CCD area detector
diffractometer
4186 independent reflections
Radiation source: fine-focus sealed tube2872 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.071
Detector resolution: 8.33 pixels mm-1θmax = 28.2°, θmin = 2.1°
ω scansh = 1313
Absorption correction: empirical (using intensity measurements)
SADABS (Sheldrick, 1996)
k = 1310
Tmin = 0.961, Tmax = 0.968l = 2222
11650 measured reflections
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.053Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.138H-atom parameters constrained
S = 0.92 w = 1/[σ2(Fo2) + (0.0647P)2]
where P = (Fo2 + 2Fc2)/3
4186 reflections(Δ/σ)max < 0.001
246 parametersΔρmax = 0.21 e Å3
0 restraintsΔρmin = 0.30 e Å3
Crystal data top
C20H16N2O5V = 1749.89 (3) Å3
Mr = 364.35Z = 4
Monoclinic, P21/nMo Kα radiation
a = 10.2447 (1) ŵ = 0.10 mm1
b = 10.3416 (1) ÅT = 293 K
c = 16.9848 (2) Å0.40 × 0.36 × 0.32 mm
β = 103.482 (1)°
Data collection top
Siemens SMART CCD area detector
diffractometer
4186 independent reflections
Absorption correction: empirical (using intensity measurements)
SADABS (Sheldrick, 1996)
2872 reflections with I > 2σ(I)
Tmin = 0.961, Tmax = 0.968Rint = 0.071
11650 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0530 restraints
wR(F2) = 0.138H-atom parameters constrained
S = 0.92Δρmax = 0.21 e Å3
4186 reflectionsΔρmin = 0.30 e Å3
246 parameters
Special details top

Experimental. The data collection covered over a hemisphere of reciprocal space by a combination of three sets of exposures; each set had a different ϕ angle (0, 88 and 180°) for the crystal and each exposure of 10 s covered 0.3° in ω. The crystal-to-detector distance was 4 cm and the detector swing angle was -35°. Crystal decay was monitored by repeating fifty initial frames at the end of data collection and analysing the intensity of duplicate reflections, and was found to be negligible.

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 (Å2) top
xyzUiso*/Ueq
O10.31295 (14)0.52762 (14)0.03210 (8)0.0632 (4)
O20.60067 (11)0.80810 (12)0.05176 (6)0.0452 (3)
O30.72325 (12)1.08574 (12)0.01751 (8)0.0500 (3)
O41.06736 (12)0.88071 (13)0.12001 (7)0.0539 (4)
O50.67471 (11)1.01219 (12)0.15358 (7)0.0441 (3)
H5A0.74881.04210.15370.066*
N10.87171 (12)0.91177 (13)0.02826 (7)0.0334 (3)
N20.43969 (12)0.70124 (12)0.04652 (7)0.0316 (3)
C10.77762 (14)0.80929 (15)0.09308 (9)0.0344 (3)
C20.76833 (18)0.71839 (18)0.15415 (11)0.0478 (4)
H2A0.69800.72100.20000.057*
C30.8667 (2)0.6231 (2)0.14517 (12)0.0579 (5)
H3A0.86250.56130.18540.069*
C40.97040 (19)0.61993 (19)0.07692 (12)0.0557 (5)
H4A1.03510.55540.07200.067*
C50.98113 (17)0.71046 (18)0.01507 (11)0.0467 (4)
H5B1.05130.70720.03080.056*
C60.88320 (14)0.80589 (15)0.02442 (9)0.0340 (3)
C70.75740 (14)0.98635 (16)0.00787 (9)0.0334 (3)
C80.68700 (14)0.92212 (15)0.08918 (9)0.0316 (3)
C90.54206 (14)0.88879 (14)0.08615 (8)0.0296 (3)
H9A0.49870.96980.07660.036*
C100.53475 (14)0.79807 (15)0.01683 (9)0.0314 (3)
C110.38959 (14)0.71884 (14)0.13248 (8)0.0309 (3)
C120.29013 (17)0.64997 (16)0.18539 (10)0.0433 (4)
H12A0.24880.57890.16800.052*
C130.25490 (18)0.69128 (18)0.26512 (10)0.0485 (5)
H13A0.18740.64760.30150.058*
C140.31670 (18)0.79519 (17)0.29239 (10)0.0450 (4)
H14A0.29190.81940.34660.054*
C150.41626 (15)0.86367 (17)0.23860 (9)0.0379 (4)
H15A0.45820.93410.25630.045*
C160.45174 (14)0.82509 (14)0.15827 (8)0.0299 (3)
C170.96249 (15)0.94156 (17)0.10180 (9)0.0395 (4)
C180.92867 (19)1.0452 (2)0.15434 (11)0.0551 (5)
H18A0.83901.03240.16090.083*
H18B0.93461.12790.12970.083*
H18C0.99051.04230.20630.083*
C190.38605 (17)0.61266 (17)0.00105 (10)0.0412 (4)
C200.4213 (2)0.6294 (2)0.09094 (11)0.0610 (6)
H20A0.40450.71720.10410.091*
H20B0.51460.60970.11170.091*
H20C0.36760.57220.11480.091*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0673 (9)0.0564 (9)0.0606 (9)0.0230 (7)0.0041 (7)0.0072 (7)
O20.0399 (6)0.0632 (8)0.0259 (5)0.0066 (5)0.0059 (5)0.0002 (5)
O30.0392 (7)0.0468 (7)0.0579 (8)0.0062 (5)0.0010 (6)0.0190 (6)
O40.0328 (6)0.0674 (9)0.0526 (8)0.0023 (6)0.0082 (5)0.0069 (6)
O50.0340 (6)0.0529 (7)0.0414 (6)0.0044 (5)0.0007 (5)0.0127 (5)
N10.0236 (6)0.0413 (7)0.0325 (6)0.0009 (5)0.0004 (5)0.0001 (6)
N20.0312 (6)0.0311 (7)0.0289 (6)0.0012 (5)0.0002 (5)0.0016 (5)
C10.0279 (7)0.0410 (9)0.0344 (8)0.0010 (6)0.0076 (6)0.0007 (7)
C20.0424 (9)0.0579 (12)0.0427 (9)0.0038 (8)0.0093 (8)0.0128 (8)
C30.0585 (12)0.0559 (12)0.0630 (12)0.0088 (9)0.0218 (10)0.0179 (10)
C40.0509 (11)0.0476 (11)0.0714 (14)0.0156 (8)0.0195 (10)0.0003 (10)
C50.0373 (9)0.0469 (10)0.0538 (10)0.0098 (7)0.0067 (8)0.0074 (8)
C60.0289 (7)0.0368 (9)0.0364 (8)0.0013 (6)0.0076 (6)0.0028 (7)
C70.0233 (7)0.0383 (9)0.0365 (8)0.0014 (6)0.0026 (6)0.0025 (7)
C80.0269 (7)0.0358 (8)0.0298 (7)0.0003 (6)0.0021 (6)0.0001 (6)
C90.0245 (7)0.0342 (8)0.0272 (7)0.0012 (6)0.0001 (5)0.0022 (6)
C100.0254 (7)0.0376 (8)0.0288 (7)0.0025 (6)0.0016 (6)0.0028 (6)
C110.0305 (7)0.0303 (8)0.0278 (7)0.0053 (6)0.0016 (6)0.0026 (6)
C120.0472 (9)0.0349 (9)0.0399 (9)0.0046 (7)0.0058 (7)0.0024 (7)
C130.0518 (10)0.0456 (10)0.0369 (9)0.0033 (8)0.0128 (8)0.0083 (8)
C140.0479 (10)0.0519 (11)0.0275 (8)0.0068 (8)0.0068 (7)0.0019 (7)
C150.0356 (8)0.0439 (9)0.0306 (8)0.0021 (7)0.0003 (6)0.0029 (7)
C160.0248 (6)0.0341 (8)0.0276 (7)0.0048 (6)0.0005 (5)0.0028 (6)
C170.0289 (8)0.0520 (10)0.0346 (8)0.0116 (7)0.0008 (6)0.0079 (7)
C180.0536 (11)0.0696 (13)0.0369 (9)0.0121 (10)0.0001 (8)0.0082 (9)
C190.0369 (8)0.0412 (9)0.0436 (9)0.0020 (7)0.0055 (7)0.0077 (7)
C200.0693 (13)0.0724 (14)0.0420 (10)0.0116 (11)0.0148 (9)0.0107 (10)
Geometric parameters (Å, º) top
O1—C191.206 (2)C7—C81.551 (2)
O2—C101.2072 (16)C8—C91.537 (2)
O3—C71.1978 (19)C9—C161.5040 (19)
O4—C171.221 (2)C9—C101.521 (2)
O5—C81.4197 (18)C9—H9A0.9800
O5—H5A0.8200C11—C121.388 (2)
N1—C171.4065 (19)C11—C161.391 (2)
N1—C71.4169 (19)C12—C131.385 (2)
N1—C61.436 (2)C12—H12A0.9300
N2—C101.4059 (19)C13—C141.381 (3)
N2—C191.414 (2)C13—H13A0.9300
N2—C111.4419 (18)C14—C151.394 (2)
C1—C21.387 (2)C14—H14A0.9300
C1—C61.394 (2)C15—C161.386 (2)
C1—C81.502 (2)C15—H15A0.9300
C2—C31.393 (3)C17—C181.487 (3)
C2—H2A0.9300C18—H18A0.9600
C3—C41.378 (3)C18—H18B0.9600
C3—H3A0.9300C18—H18C0.9600
C4—C51.392 (3)C19—C201.495 (2)
C4—H4A0.9300C20—H20A0.9600
C5—C61.390 (2)C20—H20B0.9600
C5—H5B0.9300C20—H20C0.9600
C8—O5—H5A109.5O2—C10—N2126.31 (14)
C17—N1—C7125.03 (14)O2—C10—C9125.22 (13)
C17—N1—C6125.94 (13)N2—C10—C9108.47 (12)
C7—N1—C6108.95 (12)C12—C11—C16121.49 (14)
C10—N2—C19125.83 (13)C12—C11—N2128.70 (15)
C10—N2—C11109.06 (12)C16—C11—N2109.73 (12)
C19—N2—C11124.48 (13)C13—C12—C11117.34 (16)
C2—C1—C6120.89 (14)C13—C12—H12A121.3
C2—C1—C8128.63 (14)C11—C12—H12A121.3
C6—C1—C8110.47 (13)C14—C13—C12122.18 (15)
C1—C2—C3118.44 (17)C14—C13—H13A118.9
C1—C2—H2A120.8C12—C13—H13A118.9
C3—C2—H2A120.8C13—C14—C15119.89 (15)
C4—C3—C2120.35 (17)C13—C14—H14A120.1
C4—C3—H3A119.8C15—C14—H14A120.1
C2—C3—H3A119.8C16—C15—C14118.87 (16)
C3—C4—C5121.91 (17)C16—C15—H15A120.6
C3—C4—H4A119.0C14—C15—H15A120.6
C5—C4—H4A119.0C15—C16—C11120.20 (13)
C6—C5—C4117.61 (16)C15—C16—C9130.23 (14)
C6—C5—H5B121.2C11—C16—C9109.24 (12)
C4—C5—H5B121.2O4—C17—N1118.21 (16)
C5—C6—C1120.81 (15)O4—C17—C18122.28 (15)
C5—C6—N1129.20 (15)N1—C17—C18119.51 (15)
C1—C6—N1109.98 (13)C17—C18—H18A109.5
O3—C7—N1126.33 (14)C17—C18—H18B109.5
O3—C7—C8125.01 (14)H18A—C18—H18B109.5
N1—C7—C8108.57 (13)C17—C18—H18C109.5
O5—C8—C1114.85 (12)H18A—C18—H18C109.5
O5—C8—C9105.08 (11)H18B—C18—H18C109.5
C1—C8—C9116.05 (13)O1—C19—N2119.16 (15)
O5—C8—C7110.15 (12)O1—C19—C20122.50 (17)
C1—C8—C7102.01 (12)N2—C19—C20118.34 (15)
C9—C8—C7108.59 (11)C19—C20—H20A109.5
C16—C9—C10103.19 (12)C19—C20—H20B109.5
C16—C9—C8119.13 (12)H20A—C20—H20B109.5
C10—C9—C8112.74 (11)C19—C20—H20C109.5
C16—C9—H9A107.0H20A—C20—H20C109.5
C10—C9—H9A107.0H20B—C20—H20C109.5
C8—C9—H9A107.0
C6—C1—C2—C30.3 (2)C7—C8—C9—C1058.88 (16)
C8—C1—C2—C3178.55 (16)C19—N2—C10—O212.5 (2)
C1—C2—C3—C40.1 (3)C11—N2—C10—O2176.31 (14)
C2—C3—C4—C50.1 (3)C19—N2—C10—C9167.92 (13)
C3—C4—C5—C60.3 (3)C11—N2—C10—C93.25 (16)
C4—C5—C6—C10.6 (2)C16—C9—C10—O2174.33 (14)
C4—C5—C6—N1178.31 (15)C8—C9—C10—O244.5 (2)
C2—C1—C6—C50.6 (2)C16—C9—C10—N25.24 (15)
C8—C1—C6—C5179.21 (14)C8—C9—C10—N2135.07 (13)
C2—C1—C6—N1178.49 (14)C10—N2—C11—C12176.41 (16)
C8—C1—C6—N10.08 (17)C19—N2—C11—C125.1 (2)
C17—N1—C6—C51.2 (2)C10—N2—C11—C160.31 (16)
C7—N1—C6—C5178.06 (16)C19—N2—C11—C16171.63 (13)
C17—N1—C6—C1177.84 (13)C16—C11—C12—C130.1 (2)
C7—N1—C6—C10.97 (17)N2—C11—C12—C13176.32 (15)
C17—N1—C7—O31.7 (3)C11—C12—C13—C141.1 (3)
C6—N1—C7—O3175.16 (16)C12—C13—C14—C151.3 (3)
C17—N1—C7—C8178.49 (13)C13—C14—C15—C160.3 (2)
C6—N1—C7—C81.59 (16)C14—C15—C16—C110.7 (2)
C2—C1—C8—O558.3 (2)C14—C15—C16—C9171.93 (15)
C6—C1—C8—O5120.10 (14)C12—C11—C16—C150.9 (2)
C2—C1—C8—C964.7 (2)N2—C11—C16—C15177.85 (13)
C6—C1—C8—C9116.85 (14)C12—C11—C16—C9173.20 (14)
C2—C1—C8—C7177.45 (16)N2—C11—C16—C93.79 (16)
C6—C1—C8—C70.98 (16)C10—C9—C16—C15178.73 (15)
O3—C7—C8—O552.9 (2)C8—C9—C16—C1555.4 (2)
N1—C7—C8—O5123.94 (13)C10—C9—C16—C115.46 (15)
O3—C7—C8—C1175.25 (16)C8—C9—C16—C11131.28 (14)
N1—C7—C8—C11.55 (15)C7—N1—C17—O4169.04 (14)
O3—C7—C8—C961.7 (2)C6—N1—C17—O47.3 (2)
N1—C7—C8—C9121.49 (13)C7—N1—C17—C1810.7 (2)
O5—C8—C9—C1662.16 (16)C6—N1—C17—C18172.87 (14)
C1—C8—C9—C1665.88 (17)C10—N2—C19—O1174.21 (15)
C7—C8—C9—C16179.99 (12)C11—N2—C19—O115.9 (2)
O5—C8—C9—C10176.72 (12)C10—N2—C19—C206.5 (2)
C1—C8—C9—C1055.25 (16)C11—N2—C19—C20163.35 (16)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O5—H5A···O4i0.822.002.799 (2)164
C9—H9A···O2ii0.982.593.564 (2)176
C13—H13A···O2iii0.932.493.143 (2)128
Symmetry codes: (i) x+2, y+2, z; (ii) x+1, y+2, z; (iii) x1/2, y+3/2, z1/2.

Experimental details

Crystal data
Chemical formulaC20H16N2O5
Mr364.35
Crystal system, space groupMonoclinic, P21/n
Temperature (K)293
a, b, c (Å)10.2447 (1), 10.3416 (1), 16.9848 (2)
β (°) 103.482 (1)
V3)1749.89 (3)
Z4
Radiation typeMo Kα
µ (mm1)0.10
Crystal size (mm)0.40 × 0.36 × 0.32
Data collection
DiffractometerSiemens SMART CCD area detector
diffractometer
Absorption correctionEmpirical (using intensity measurements)
SADABS (Sheldrick, 1996)
Tmin, Tmax0.961, 0.968
No. of measured, independent and
observed [I > 2σ(I)] reflections
11650, 4186, 2872
Rint0.071
(sin θ/λ)max1)0.666
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.053, 0.138, 0.92
No. of reflections4186
No. of parameters246
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.21, 0.30

Computer programs: SMART (Siemens, 1996), SAINT (Siemens, 1996), SAINT, SHELXTL (Sheldrick, 1997), SHELXTL, PARST (Nardelli, 1995) and PLATON (Spek, 1990).

Selected geometric parameters (Å, º) top
O2—C101.2072 (16)C1—C61.394 (2)
O3—C71.1978 (19)C1—C81.502 (2)
O5—C81.4197 (18)C7—C81.551 (2)
N1—C71.4169 (19)C8—C91.537 (2)
N1—C61.436 (2)C9—C161.5040 (19)
N2—C101.4059 (19)C9—C101.521 (2)
N2—C111.4419 (18)
C7—N1—C6108.95 (12)C1—C8—C9116.05 (13)
C10—N2—C11109.06 (12)O5—C8—C7110.15 (12)
C1—C8—C9—C1665.88 (17)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O5—H5A···O4i0.822.00232.799 (2)164
C9—H9A···O2ii0.982.58653.564 (2)176
C13—H13A···O2iii0.932.48573.143 (2)128
Symmetry codes: (i) x+2, y+2, z; (ii) x+1, y+2, z; (iii) x1/2, y+3/2, z1/2.
 

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