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Compounds trans-tetra­aqua­dichloridocobalt(II)–piperazine-2,5-dione (1/1), [CoCl2(H2O)4]·C4H6N2O2, (I), and trans-tetra­aqua­dichloridonickel(II)–piperazine-2,5-dione (1/1), [NiCl2(H2O)4]·C4H6N2O2, (II), are isomorphous. In each structure, the metal complex and the piperazinedione unit both lie across centres of inversion in the space group P21/n. The [MCl2(H2O)4] units (M = Co or Ni) are linked by O—H...Cl hydrogen bonds into sheets of R22(8) and R42(12) rings, and these sheets are linked by the piperazinedione components via a combination of O—H...O and N—H...Cl hydrogen bonds into a three-dimensional framework. In catena-poly[[[trans-diaqua­copper(II)]-di-μ-chlorido] piperazine-2,5-dione sol­vate], {[CuCl2(H2O)2]·C4H6N2O2}n, (III), the metal ion and the piperazine unit both lie across centres of inversion in the space group I2/a. The coordination polymer forms chains of centrosymmetric [CuCl2(H2O)2] units running parallel to [010] and these are linked by the piperazinedione units into a three-dimensional framework structure. In poly[μ3-nitrato-μ2-piperazine-2,5-dione-silver(I)], [Ag(NO3)(C4H6N2O2)]n, (IV), the silver and nitrate ions lie on mirror planes in the space group Pnma, while the piperazinedione unit lies across a centre of inversion. The compound is a coordination polymer containing five-coordinate approximately square-pyramidal Ag, in which the ligating O atoms are derived from three different nitrate ligands and two different piperazinedione ligands. The ionic components form sheets in which each anion is coordinated to three different cations, and these sheets are linked into a three-dimensional framework by the organic ligands, each of which coordinates to two different Ag centres. The significance of this study lies in its demonstration of a wide variety of framework types built from a common and very simple organic component with simple metal salts.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S010827010801648X/gg3165sup1.cif
Contains datablocks global, I, II, III, IV

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S010827010801648X/gg3165Isup2.hkl
Contains datablock I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S010827010801648X/gg3165IIsup3.hkl
Contains datablock II

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S010827010801648X/gg3165IIIsup4.hkl
Contains datablock III

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S010827010801648X/gg3165IVsup5.hkl
Contains datablock IV

CCDC references: 700010; 700011; 700012; 700013

Comment top

In the structure of piperazine-2,5-dione (diketopiperazine, the cyclic anhydride derived from glycine), the molecules lie across centres of inversion. They are linked into chains of R22(8) rings (Bernstein et al., 1995) by means of N—H···O hydrogen bonds (Degeilh & Marsh, 1959; Sarangarajan et al., 2005), and these chains are themselves linked into sheets by C—H···O hydrogen bonds (Sarangarajan et al., 2005). In the hydrogen-bonded adducts formed by piperazine-2,5-dione with simple monocarboxylic acids, the same chain of R22(8) rings occurs, with the acid units pendant from it (Kartha et al., 1981; Luo & Palmore, 2002), while with dicarboxylic acids or phenolic monocarboxyic acids these chains are linked into sheets (Luo & Palmore, 2002; Sarangarajan et al., 2005). Unusually, the adduct formed with salicylic acid contains neither chains nor sheets but finite centrosymmetric aggregates of two acid molecules and one piperazinedione unit (Varughese & Kartha, 1982). Despite the substantial number of hydrogen-bonded adducts formed with organic acids, very little structural information is available for metal complexes of piperazine-2,5-dione. However, the closely-related 1,4-dimethylpiperazine-2,5-dione forms a finite encapsulation complex with aluminium tris(2,6-diphenylphenoxide (Ooi et al., 1998), and the same amide forms a one-dimensional coordination polymer with Ph2SnCl2 (Kovala-Demertzi et al., 1995). We report here the structures of four adducts, (I)–(IV) (Figs. 1–4), formed by piperazine-2.5-dione when it is co-crystallized from aqueous solutions containing simple salts of CoII, NiII, CuII and AgI.

Compounds (I) and (II) are isomorphous. In these structures, the metal atom lies at a centre of inversion in space group P21/n, selected as that at (1/2, 1/2, 1/2), and it is coordinated by two Cl and four water ligands. Within the selected asymmetric unit, the centrosymmetric piperidinedione component is linked to the neutral [M(H2O)4)Cl2] unit (M = Co or Ni) by a combination of O—H···O and N—H···Cl hydrogen bonds (Table 3), such that the organic component lies across the centre of inversion at (1/2, 0, 0) (Figs. 1 and 2). In each complex, the coordination of the metal atom has symmetry very close to D4h (4/mmm), with the bond angles subtended at the metal atoms by pairs of cis ligands all within 3° of 90°. The M—O and M—Cl distances are slightly smaller in (II) than in (I) (Table 1).

All of the O—H and N—H bonds within the structures of (I) and (II) are involved in hydrogen bonding (Table 3) and the components are thereby linked into a three-dimensional framework structure. The [M(H2O)4)Cl2] units are linked by the two independent O—H···Cl hydrogen bonds into a sheet parallel to (101) and containing both R22(8) and R42(12) rings (Fig. 5), and these inorganic sheets then linked by the organic components. This linking is most simply envisaged in terms of a chain running parallel to the [011] direction and containing alternating inorganic and organic units linked by hydrogen-bonded R22(8) rings (Fig. 6). The combination of (101) sheets and [011] chains suffices to generate the three-dimensional pillared layer structure, which could be regarded as an organic–inorganic hybrid structure. In nickel(II) chloride tetrahydrate, there are discrete [Ni(H2O)4)Cl2] units, but of cis configuration and lying in general positions. These units are linked into a complex three-dimensional framework structure by both O—H···Cl and O—H···O hydrogen bonds (Ptasiewicz-Bak et al., 1999), so that the hydrogen-bonded structure in the free hydrated chloride is quite different from that found here for the piperazinedione adduct (II).

In the Cu complex, (III), the metal atom lies on a centre of inversion in space group I2/a, selected as that at (1/4, 1/4, 1/4). It is coordinated by two water ligands and by four Cl ligands, each of which bridges two metal centres, so generating a chain of edge-fused octahedra of composition [CuCl2(H2O)2]n running parallel to the [010] direction (Fig. 3). The piperazinedione component also lies across a centre of inversion, selected as that at (1/2, 1, 1/2), so that within the selected asymmetric unit the components are linked by O—H···O and N—H···Cl hydrogen bonds (Table 3), as in compounds (I) and (II). Within the coordination polymer chain, the centrosymmetric Cu2Cl2 units contain two significantly different Cu—Cl distances (Table 1). A similar chain, with Cu—Cl distances of 2.2724 (13) and 3.1537 (14) Å, is present in benzimidazolium tetrachorocuprate [tetrachloridocuprate ?] monohydrate [Cambridge Structural Database (Allen, 2002) refcode FUTRUH; Bukowska-Strzyżewska & Skoweranda, 1987]. More frequently, however, [CuCl2(H2O)2] units are found as isolated square-planar units, as in NPYOCU (Williams et al., 1971) and TPPOCU (Dunaj-Jurco et al., 1979) or as square-planar units weakly coordinated by two further axial ligands, as in UGAYUW (Giantsidis et al., 2002). The hydrogen bonds in (III) link the reference Cu atom at (1/4, 1/4, 1/4), via the piperazinedione units centred at (0, 0, 1/2), (0, -1/2, 0), (1/2, 1/2, 0) and (1/2, 1, 1/2), respectively, to the Cu atoms at (-1/4, -1/4, 3/4), (-1/4, -5/4, -1/4), (3/4, 3/4, -1/4) and (3/4, 7/4, 3/4), so forming a sheet parallel to (211) (Fig. 7). In this manner, the reference coordination polymer chain along (1/4, y, 1/4), is directly linked to the four chains along (-1/4, y, -1/4), (-1/4, y, 3/4), (3/4, y, -1/4) and (3/4, y, 3/4), thereby generating a three-dimensional framework structure.

Complex (IV), derived from Ag[NO3], is a coordination polymer, [(DKP)Ag(NO3)]n [DKP is diketopiperazine?], containing five-coordinate Ag. The compound crystallizes in space group Pnma, and the Ag+ ions and all the atoms of the nitrate anions lie on mirror planes, while the DKP units lie across centres of inversion. For the selected asymmetric unit, in which DKP atom O12 is coordinated to Ag (Fig. 4), the DKP unit lies across the centre of inversion at (1/2, 1/2, 0), while the Ag+ and nitrate ions lie on the mirror plane at y = 1/4. The constitution of (IV) is most readily analysed in terms of the two-dimensional sub-structure built from Ag and [NO3] units only. These layers are linked by the DKP units acting as bridging ligands between pairs of Ag ions in different layers. Within the ionic layer, the Ag+ ion at (x, 1/4, z) is coordinated by O atoms from three different nitrate ions, namely atom O1 in the anion at (x, 1/4, z), atom O2 in the anion at (x, 1/4, -1 + z) and atom O3 in the anion at (-1/2 + x, 1/4, 3/2 - z) (Table 2). Propagation of these interactions then leads to the formation of an (010) sheet built from a single type of 12-membered ring (Fig. 8).

In addition to the three O ligands from within the ionic layer, the Ag+ ion at (x, 1/4, z) is also coordinated by two O atoms from two different DKP ligands, namely those at (x, y, z) and (x, 1/2 - y, z). The coordination polyhedron around the Ag+ ion is best described as a distorted square pyramid (Fig. 4) in which two of the basal Ag—O distances are significantly longer than the other pair (Table 2). The two independent O—Ag—O angles in the basal plane have values close to 90°, while the angles subtended at Ag by the axial O and one of the basal O sites range from 74.94 (6) to 114.11 (6)°. The atoms of type O12 at (x, y, z) and (x, 1/2 - y, z) form part of the DKP units centred at (1/2, 1/2, 0) and (1/2, 0, 0), respectively, so that propagation of this Ag—O interaction by reflection and inversion generates a chain running parallel to the [010] direction (Fig. 9) which serves to link all of the (010) layers into a three-dimensional coordination polymer. The three-dimensional framework is reinforced by a single N—H···O hydrogen bond.

Thus, in each of compounds (I) and (II) there is a finite [M(H2O)4Cl2] fragment, in compound (III) there is a one-dimensional coordination polymer, [CuCl2(H2O)2]n, and in compound (IV) there is a three-dimensional coordination polymer, [Ag(NO3)(C4H6N2O2]n. In (I) and (II), the formation of the three-dimensional framework is dependent upon the actions of multiple hydrogen bonds, while in compound (IV) the framework is formed by the three-dimensional coordination polymer, to the formation of which the single hydrogen bond is incidental. The three-dimensional framework in (III) is of a hybrid type, depending upon hydrogen bonds to link the one-dimensional coordination polymer chains. The organic piperazine-2,5-dione component may thus prove to be a very versatile building block for crystal structure design and construction.

Experimental top

Compounds (I)–(IV) were prepared by dissolving in water equimolar quantities of piperazine-2,5-dione and, respectively, cobalt(II) chloride hexahydrate, nickel(II) chloride tetrahydrate, copper(II) chloride dihydrate or silver nitrate. The solutions were set aside to crystallize, providing crystals of (I)–(IV) suitable for single-crystal X-ray diffraction.

Refinement top

For compounds (I), (II) and (IV, the space groups were uniquely assigned from the systematic absences as P21/n, P21/n and Pnma, respectively. For compound (III), the systematic absences permitted Cc and C2/c as possible space groups; C2/c was selected and confirmed by the refinement. Because of the very large value of β in C2/c [132.180 (3)°], the alternative setting I2/a was adopted prior to the final refinement. Compound (III) was refined as a non-merohedral twin, resulting in twin fractions of 0.469 and 0.531.

For each of (I)–(IV), all H atoms were located in difference maps and then treated as riding atoms, with C—H = 0.99, N—H = 0.88 and O—H = 0.84 or 0.90 Å, and with Uiso(H) = 1.2Ueq(C,N) or 1.5Ueq(O).

Computing details top

For all compounds, data collection: KappaCCD Server Software (Nonius, 1997); cell refinement: DENZO-SMN (Otwinowski & Minor, 1997); data reduction: DENZO-SMN (Otwinowski & Minor, 1997); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: PLATON (Spek, 2003); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008) and PRPKAPPA (Ferguson, 1999).

Figures top
[Figure 1] Fig. 1. The independent molecular components in (I), showing the atom-labelling scheme and the hydrogen bonds within the selected asymmetric unit (dashed lines). Displacement ellipsoids are drawn at the ??% probability level [Please complete] and H atoms are shown as small spheres of arbitrary radii. [Symmetry codes: (i) 1 - x, 1 - y, 1 - z; (ii) 1 - x, -y, -z.]
[Figure 2] Fig. 2. The independent molecular components in (II), showing the atom-labelling scheme and the hydrogen bonds within the selected asymmetric unit (dashed lines). Displacement ellipsoids are drawn at the ??% probability level [Please complete] and H atoms are shown as small spheres of arbitrary radii. [Symmetry codes: (i) 1 - x, 1 - y, 1 - z; (ii) 1 - x, -y, -z.]
[Figure 3] Fig. 3. The independent components in (III), showing the atom-labelling scheme together with a portion of the [CuCl2(H2O)2]n coordination polymer. Displacement ellipsoids are drawn at the 30% probabiility level and H atoms are shown as small spheres of arbitrary radii. [Symmetry codes: (i) x, -1 + y, z; (ii) x, 1 + y, z; (iii) 1/2 - x, 1/2 - y, 1/2 - z; (iv) 1/2 - x, 3/2 - y, 1/2 - z; (v) 1 - x, 2 - y, 1 - z; (vi) 1/2 - x, -1/2 - y, 1/2 - z.]
[Figure 4] Fig. 4. The independent components of adduct (IV), showing the atom-labelling scheme and the five-coordination of the Ag. Displacement ellipsoids are drawn at the 30% probability level and H atoms are shown as small spheres of arbitrary radii. [Symmetry codes: (i) x, 1/4, -1 + z); (ii) -1/2 + x, 1/4, 3/2 - z); (iii) 1 - x, 1 - y, -z; (iv) x, 1/2 - y, z.]
[Figure 5] Fig. 5. A stereoview of part of the crystal structure of (I), showing the formation of a hydrogen-bonded sheet built from [Co(H2O)4)Cl2] units only.
[Figure 6] Fig. 6. A stereoview of part of the crystal structure of (I), showing the formation of a hydrogen-bonded chain built from alternating [Co(H2O)4)Cl2] and piperazinedione units. For the sake of clarity, H atoms bonded to C atoms have been omitted.
[Figure 7] Fig. 7. A stereoview of part of the crystal structure of (III), showing the formation of a hydrogen-bonded sheet parallel to (211) formed from [CuCl2(H2O)2] and piperazinedione units.
[Figure 8] Fig. 8. Part of the crystal structure of (IV), showing the formation of a layer parallel to (010) built from silver and nitrate ions only.
[Figure 9] Fig. 9. Part of the crystal structure of (IV), showing the formation of a chain parallel to [010] consisting of cations and DKP units only. For the sake of clarity, H atoms bonded to C atoms have been omitted. Atoms marked with an asterisk (*), a hash (#), a dollar sign ($) or an ampersand (&) are at the symmetry positions (1 - x, 1 - y, -z), (x, 1/2 - y, z), (x, 3/4, z) and (1 - x, 1/2 + y, z), respectively.
(I) trans-Tetraaquadichloridocobalt(II)–piperazine-2,5-dione (1/1) top
Crystal data top
[CoCl2(H2O)4]·C4H6N2O2F(000) = 322
Mr = 316.00Dx = 1.809 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 1330 reflections
a = 9.5326 (4) Åθ = 3.8–27.5°
b = 6.6602 (2) ŵ = 1.95 mm1
c = 10.0167 (4) ÅT = 120 K
β = 114.1660 (17)°Plate, colourless
V = 580.22 (4) Å30.40 × 0.20 × 0.07 mm
Z = 2
Data collection top
Nonius KappaCCD
diffractometer
1330 independent reflections
Radiation source: Bruker Nonius FR591 rotating anode1189 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.032
Detector resolution: 9.091 pixels mm-1θmax = 27.5°, θmin = 3.8°
ϕ and ω scansh = 1212
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
k = 88
Tmin = 0.509, Tmax = 0.876l = 1213
7527 measured reflections
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.021H-atom parameters constrained
wR(F2) = 0.053 w = 1/[σ2(Fo2) + (0.020P)2 + 0.3391P]
where P = (Fo2 + 2Fc2)/3
S = 1.05(Δ/σ)max < 0.001
1330 reflectionsΔρmax = 0.44 e Å3
71 parametersΔρmin = 0.37 e Å3
0 restraintsExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
Primary atom site location: structure-invariant direct methodsExtinction coefficient: 0.0182 (19)
Crystal data top
[CoCl2(H2O)4]·C4H6N2O2V = 580.22 (4) Å3
Mr = 316.00Z = 2
Monoclinic, P21/nMo Kα radiation
a = 9.5326 (4) ŵ = 1.95 mm1
b = 6.6602 (2) ÅT = 120 K
c = 10.0167 (4) Å0.40 × 0.20 × 0.07 mm
β = 114.1660 (17)°
Data collection top
Nonius KappaCCD
diffractometer
1330 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
1189 reflections with I > 2σ(I)
Tmin = 0.509, Tmax = 0.876Rint = 0.032
7527 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0210 restraints
wR(F2) = 0.053H-atom parameters constrained
S = 1.05Δρmax = 0.44 e Å3
1330 reflectionsΔρmin = 0.37 e Å3
71 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Co10.50000.50000.50000.00843 (11)
Cl10.36781 (4)0.51301 (5)0.23198 (4)0.01167 (11)
O10.59489 (11)0.22731 (14)0.49628 (11)0.0148 (2)
O20.68877 (11)0.65237 (14)0.48809 (10)0.0129 (2)
O120.60342 (13)0.02818 (15)0.29173 (11)0.0177 (2)
N110.48079 (13)0.14996 (17)0.08559 (13)0.0131 (3)
C120.55480 (16)0.01067 (19)0.15618 (17)0.0121 (3)
C130.58539 (17)0.1785 (2)0.07207 (15)0.0146 (3)
H1A0.65520.17340.57460.022*
H1B0.58290.15010.42610.022*
H2A0.73760.71910.56430.019*
H2B0.65870.73570.41910.019*
H110.47040.24920.13880.016*
H13A0.69800.19490.10650.018*
H13B0.54410.30450.09430.018*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Co10.00921 (16)0.00771 (16)0.00769 (17)0.00058 (8)0.00276 (12)0.00047 (9)
Cl10.01405 (19)0.01107 (19)0.00752 (19)0.00048 (11)0.00200 (15)0.00086 (11)
O10.0198 (5)0.0122 (5)0.0094 (5)0.0056 (4)0.0029 (4)0.0012 (4)
O20.0147 (5)0.0121 (5)0.0108 (5)0.0013 (4)0.0038 (4)0.0003 (4)
O120.0269 (6)0.0146 (5)0.0116 (5)0.0027 (4)0.0079 (5)0.0001 (4)
N110.0181 (6)0.0112 (6)0.0117 (6)0.0025 (4)0.0077 (5)0.0027 (4)
C120.0133 (7)0.0117 (7)0.0134 (7)0.0021 (5)0.0074 (6)0.0017 (5)
C130.0218 (7)0.0126 (7)0.0113 (7)0.0043 (5)0.0086 (6)0.0006 (5)
Geometric parameters (Å, º) top
Co1—O12.0361 (9)N11—C13ii1.4534 (18)
Co1—O1i2.0361 (9)N11—H110.88
Co1—O22.1113 (9)O2—H2A0.84
Co1—O2i2.1113 (9)O2—H2B0.84
Co1—Cl12.4562 (3)C12—O121.2476 (19)
Co1—Cl1i2.4562 (3)C12—C131.4984 (19)
O1—H1A0.84C13—N11ii1.4534 (18)
O1—H1B0.84C13—H13A0.99
N11—C121.3167 (18)C13—H13B0.99
O1—Co1—O291.86 (4)C12—N11—C13ii126.05 (12)
O1i—Co1—O288.14 (4)C12—N11—H11117.0
O1—Co1—O2i88.14 (4)C13ii—N11—H11117.0
O1i—Co1—O2i91.86 (4)Co1—O2—H2A111.8
O1—Co1—Cl192.55 (3)Co1—O2—H2B110.7
O1i—Co1—Cl187.45 (3)H2A—O2—H2B105.9
O2—Co1—Cl189.37 (3)O12—C12—N11122.62 (13)
O2i—Co1—Cl190.63 (3)O12—C12—C13118.10 (12)
O1—Co1—Cl1i87.45 (3)N11—C12—C13119.27 (13)
O1i—Co1—Cl1i92.55 (3)N11ii—C13—C12114.56 (12)
O2—Co1—Cl1i90.63 (3)N11ii—C13—H13A108.6
O2i—Co1—Cl1i89.37 (3)C12—C13—H13A108.6
Co1—O1—H1A120.2N11ii—C13—H13B108.6
Co1—O1—H1B130.7C12—C13—H13B108.6
H1A—O1—H1B109.0H13A—C13—H13B107.6
C13ii—N11—C12—O12177.06 (13)O12—C12—C13—N11ii177.47 (12)
C13ii—N11—C12—C134.2 (2)N11—C12—C13—N11ii3.7 (2)
Symmetry codes: (i) x+1, y+1, z+1; (ii) x+1, y, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1A···Cl1iii0.842.353.1426 (10)158
O1—H1B···O120.841.862.6901 (14)167
O2—H2A···Cl1iv0.842.423.2302 (10)163
O2—H2B···O12v0.841.962.7834 (14)168
N11—H11···Cl10.882.383.2326 (12)164
Symmetry codes: (iii) x+1/2, y+1/2, z+1/2; (iv) x+1/2, y+3/2, z+1/2; (v) x, y+1, z.
(II) trans-Tetraaquadichloridonickel(II)–piperazine-2,5-dione (1/1) top
Crystal data top
[NiCl2(H2O)4]·C4H6N2O2F(000) = 324
Mr = 315.78Dx = 1.826 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 1315 reflections
a = 9.4844 (4) Åθ = 3.8–27.5°
b = 6.6616 (3) ŵ = 2.17 mm1
c = 9.9975 (4) ÅT = 120 K
β = 114.6290 (18)°Block, colourless
V = 574.19 (4) Å30.40 × 0.30 × 0.20 mm
Z = 2
Data collection top
Nonius KappaCCD
diffractometer
1315 independent reflections
Radiation source: Bruker Nonius FR591 rotating anode1218 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.022
Detector resolution: 9.091 pixels mm-1θmax = 27.5°, θmin = 3.8°
ϕ and ω scansh = 1212
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
k = 88
Tmin = 0.468, Tmax = 0.649l = 1212
6275 measured reflections
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.019H-atom parameters constrained
wR(F2) = 0.046 w = 1/[σ2(Fo2) + (0.0167P)2 + 0.3677P]
where P = (Fo2 + 2Fc2)/3
S = 1.06(Δ/σ)max < 0.001
1315 reflectionsΔρmax = 0.35 e Å3
71 parametersΔρmin = 0.34 e Å3
0 restraintsExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
Primary atom site location: structure-invariant direct methodsExtinction coefficient: 0.032 (2)
Crystal data top
[NiCl2(H2O)4]·C4H6N2O2V = 574.19 (4) Å3
Mr = 315.78Z = 2
Monoclinic, P21/nMo Kα radiation
a = 9.4844 (4) ŵ = 2.17 mm1
b = 6.6616 (3) ÅT = 120 K
c = 9.9975 (4) Å0.40 × 0.30 × 0.20 mm
β = 114.6290 (18)°
Data collection top
Nonius KappaCCD
diffractometer
1315 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
1218 reflections with I > 2σ(I)
Tmin = 0.468, Tmax = 0.649Rint = 0.022
6275 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0190 restraints
wR(F2) = 0.046H-atom parameters constrained
S = 1.06Δρmax = 0.35 e Å3
1315 reflectionsΔρmin = 0.34 e Å3
71 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ni10.50000.50000.50000.00809 (10)
Cl10.37016 (4)0.51186 (4)0.23679 (3)0.01131 (10)
O10.59374 (11)0.22730 (14)0.49672 (10)0.0160 (2)
O20.68915 (10)0.64843 (14)0.49002 (10)0.0128 (2)
O120.60300 (12)0.03041 (15)0.29286 (11)0.0182 (2)
N110.48200 (13)0.15055 (16)0.08636 (12)0.0128 (2)
C120.55513 (15)0.01192 (18)0.15700 (15)0.0119 (3)
C130.58485 (16)0.1796 (2)0.07224 (14)0.0146 (3)
H1A0.65190.17390.57700.024*
H1B0.58190.15250.42520.024*
H2A0.73430.71680.56670.019*
H2B0.65410.73270.42150.019*
H110.47290.25020.14000.015*
H13A0.69830.19690.10750.018*
H13B0.54270.30530.09390.018*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ni10.00879 (14)0.00747 (14)0.00677 (14)0.00066 (7)0.00200 (9)0.00034 (7)
Cl10.01365 (17)0.01068 (17)0.00688 (16)0.00055 (10)0.00159 (12)0.00093 (10)
O10.0225 (5)0.0126 (5)0.0084 (4)0.0076 (4)0.0019 (4)0.0010 (4)
O20.0136 (4)0.0122 (4)0.0107 (4)0.0011 (3)0.0030 (3)0.0009 (4)
O120.0282 (6)0.0153 (5)0.0102 (5)0.0032 (4)0.0073 (4)0.0003 (4)
N110.0186 (6)0.0104 (5)0.0106 (5)0.0024 (4)0.0073 (4)0.0027 (4)
C120.0135 (6)0.0117 (6)0.0120 (6)0.0020 (4)0.0065 (5)0.0015 (5)
C130.0221 (7)0.0120 (6)0.0116 (6)0.0055 (5)0.0090 (5)0.0017 (5)
Geometric parameters (Å, º) top
Ni1—O12.0287 (9)O2—H2B0.8399
Ni1—O1i2.0287 (9)N11—C121.3202 (17)
Ni1—O22.0869 (9)N11—C13ii1.4545 (16)
Ni1—O2i2.0869 (9)N11—H110.88
Ni1—Cl12.3971 (3)C12—O121.2459 (17)
Ni1—Cl1i2.3971 (3)C12—C131.4980 (18)
O1—H1A0.8398C13—N11ii1.4545 (16)
O1—H1B0.8399C13—H13A0.99
O2—H2A0.8399C13—H13B0.99
O1—Ni1—O291.85 (4)Ni1—O2—H2A109.6
O1i—Ni1—O288.15 (4)Ni1—O2—H2B107.5
O1—Ni1—O2i88.15 (4)H2A—O2—H2B105.1
O1i—Ni1—O2i91.85 (4)C12—N11—C13ii125.82 (11)
O1—Ni1—Cl192.29 (3)C12—N11—H11117.1
O1i—Ni1—Cl187.71 (3)C13ii—N11—H11117.1
O2—Ni1—Cl189.45 (3)O12—C12—N11122.39 (12)
O2i—Ni1—Cl190.55 (3)O12—C12—C13118.30 (11)
O1—Ni1—Cl1i87.71 (3)N11—C12—C13119.30 (12)
O1i—Ni1—Cl1i92.29 (3)N11ii—C13—C12114.72 (11)
O2—Ni1—Cl1i90.55 (3)N11ii—C13—H13A108.6
O2i—Ni1—Cl1i89.45 (3)C12—C13—H13A108.6
Ni1—O1—H1A118.8N11ii—C13—H13B108.6
Ni1—O1—H1B129.9C12—C13—H13B108.6
H1A—O1—H1B111.3H13A—C13—H13B107.6
C13ii—N11—C12—O12176.40 (13)O12—C12—C13—N11ii176.86 (12)
C13ii—N11—C12—C134.7 (2)N11—C12—C13—N11ii4.23 (19)
Symmetry codes: (i) x+1, y+1, z+1; (ii) x+1, y, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1A···Cl1iii0.842.373.1508 (10)155
O1—H1B···O120.841.872.6941 (13)167
O2—H2A···Cl1iv0.842.453.2596 (9)163
O2—H2B···O12v0.841.962.7906 (13)168
N11—H11···Cl10.882.393.2419 (11)163
Symmetry codes: (iii) x+1/2, y+1/2, z+1/2; (iv) x+1/2, y+3/2, z+1/2; (v) x, y+1, z.
(III) catena-poly[[[trans-diaquacopper(II)]-di-µ-chlorido] piperazine-2,5-dione solvate] top
Crystal data top
[CuCl2(H2O)2]·C4H6N2O2F(000) = 572
Mr = 284.58Dx = 2.032 Mg m3
Monoclinic, I2/aMo Kα radiation, λ = 0.71073 Å
Hall symbol: -I 2yaCell parameters from 1059 reflections
a = 15.224 (3) Åθ = 3.6–27.5°
b = 3.9694 (8) ŵ = 2.91 mm1
c = 15.444 (4) ÅT = 120 K
β = 94.73 (3)°Needle, blue-green
V = 930.1 (4) Å30.16 × 0.04 × 0.03 mm
Z = 4
Data collection top
Nonius KappaCCD
diffractometer
1059 independent reflections
Radiation source: Bruker Nonius FR591 rotating anode787 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.0
Detector resolution: 9.091 pixels mm-1θmax = 27.5°, θmin = 3.6°
ϕ and ω scansh = 1919
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
k = 55
Tmin = 0.654, Tmax = 0.918l = 1219
4485 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)] = 0.058Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.164H-atom parameters constrained
S = 1.09 w = 1/[σ2(Fo2) + (0.0721P)2 + 6.6393P]
where P = (Fo2 + 2Fc2)/3
1059 reflections(Δ/σ)max < 0.001
62 parametersΔρmax = 1.58 e Å3
0 restraintsΔρmin = 1.45 e Å3
Crystal data top
[CuCl2(H2O)2]·C4H6N2O2V = 930.1 (4) Å3
Mr = 284.58Z = 4
Monoclinic, I2/aMo Kα radiation
a = 15.224 (3) ŵ = 2.91 mm1
b = 3.9694 (8) ÅT = 120 K
c = 15.444 (4) Å0.16 × 0.04 × 0.03 mm
β = 94.73 (3)°
Data collection top
Nonius KappaCCD
diffractometer
1059 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
787 reflections with I > 2σ(I)
Tmin = 0.654, Tmax = 0.918Rint = 0.0
4485 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0580 restraints
wR(F2) = 0.164H-atom parameters constrained
S = 1.09Δρmax = 1.58 e Å3
1059 reflectionsΔρmin = 1.45 e Å3
62 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Cu10.25000.25000.25000.0182 (4)
Cl10.24586 (10)0.5930 (4)0.36560 (10)0.0215 (4)
O10.3780 (3)0.2422 (12)0.2634 (3)0.0205 (10)
O120.5031 (3)0.6199 (13)0.3563 (3)0.0212 (10)
N110.4258 (3)0.8700 (15)0.4572 (3)0.0195 (12)
C120.5002 (4)0.7978 (16)0.4227 (4)0.0158 (13)
C130.4159 (4)1.0630 (18)0.5352 (4)0.0186 (14)
H1A0.41110.40210.29150.031*
H1B0.41010.19480.21850.031*
H110.38050.78410.42550.023*
H13A0.38860.91730.57760.022*
H13B0.37491.25210.52070.022*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Cu10.0160 (5)0.0241 (7)0.0146 (6)0.0010 (5)0.0008 (4)0.0071 (5)
Cl10.0181 (7)0.0294 (9)0.0171 (7)0.0019 (7)0.0018 (5)0.0116 (7)
O10.0127 (19)0.029 (3)0.020 (2)0.002 (2)0.0015 (17)0.008 (2)
O120.021 (2)0.031 (3)0.011 (2)0.004 (2)0.0012 (17)0.005 (2)
N110.017 (2)0.026 (3)0.015 (3)0.006 (2)0.003 (2)0.004 (2)
C120.015 (3)0.020 (4)0.012 (3)0.002 (2)0.001 (2)0.004 (3)
C130.015 (3)0.023 (4)0.017 (3)0.001 (3)0.000 (2)0.000 (3)
Geometric parameters (Å, º) top
Cu1—O1i1.942 (4)N11—C131.446 (8)
Cu1—O11.942 (4)N11—H110.88
Cu1—Cl12.2502 (15)C12—O121.249 (8)
Cu1—Cl1i2.2502 (15)C12—C13iii1.492 (8)
Cu1—Cl1ii3.1640 (18)C13—C12iii1.492 (8)
O1—H1A0.90C13—H13A0.99
O1—H1B0.90C13—H13B0.99
N11—C121.322 (8)
O1i—Cu1—Cl188.92 (14)O12—C12—N11122.9 (6)
O1—Cu1—Cl191.08 (14)O12—C12—C13iii118.6 (5)
O1i—Cu1—Cl1i91.08 (14)N11—C12—C13iii118.4 (6)
O1—Cu1—Cl1i88.92 (14)N11—C13—C12iii114.5 (5)
Cu1—O1—H1A123.9N11—C13—H13A108.6
Cu1—O1—H1B121.7C12iii—C13—H13A108.6
H1A—O1—H1B101.6N11—C13—H13B108.6
C12—N11—C13127.0 (5)C12iii—C13—H13B108.6
C12—N11—H11110.5H13A—C13—H13B107.6
C13—N11—H11122.5
C13—N11—C12—O12177.7 (6)C12—N11—C13—C12iii2.6 (11)
C13—N11—C12—C13iii2.7 (11)
Symmetry codes: (i) x+1/2, y+1/2, z+1/2; (ii) x, y1, z; (iii) x+1, y+2, z+1.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1A···O120.901.872.737 (6)162
O1—H1B···O12iv0.901.852.735 (6)167
N11—H11···Cl10.882.313.174 (5)168
Symmetry code: (iv) x+1, y1/2, z+1/2.
(IV) silver(I) nitrate–piperazine-2.5-dione (1/1) top
Crystal data top
[Ag(NO3)]·C4H6N2O2F(000) = 552
Mr = 567.98Dx = 2.537 Mg m3
Orthorhombic, PnmaMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ac 2nCell parameters from 888 reflections
a = 9.6276 (1) Åθ = 4.1–27.6°
b = 14.7180 (2) ŵ = 2.71 mm1
c = 5.2468 (4) ÅT = 120 K
V = 743.47 (6) Å3Plate, colourless
Z = 20.42 × 0.22 × 0.12 mm
Data collection top
Nonius KappaCCD
diffractometer
888 independent reflections
Radiation source: fine-focus sealed X-ray tube826 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.041
Detector resolution: 9.091 pixels mm-1θmax = 27.6°, θmin = 4.1°
ϕ and ω scansh = 1211
Absorption correction: multi-scan
SORTAV (Blessing, 1995, 1997)
k = 1919
Tmin = 0.389, Tmax = 0.722l = 66
7016 measured reflections
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.017H-atom parameters constrained
wR(F2) = 0.044 w = 1/[σ2(Fo2) + (0.0202P)2 + 0.4734P]
where P = (Fo2 + 2Fc2)/3
S = 1.09(Δ/σ)max = 0.001
888 reflectionsΔρmax = 0.44 e Å3
68 parametersΔρmin = 0.44 e Å3
0 restraintsExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
Primary atom site location: structure-invariant direct methodsExtinction coefficient: 0.0155 (9)
Crystal data top
[Ag(NO3)]·C4H6N2O2V = 743.47 (6) Å3
Mr = 567.98Z = 2
Orthorhombic, PnmaMo Kα radiation
a = 9.6276 (1) ŵ = 2.71 mm1
b = 14.7180 (2) ÅT = 120 K
c = 5.2468 (4) Å0.42 × 0.22 × 0.12 mm
Data collection top
Nonius KappaCCD
diffractometer
888 independent reflections
Absorption correction: multi-scan
SORTAV (Blessing, 1995, 1997)
826 reflections with I > 2σ(I)
Tmin = 0.389, Tmax = 0.722Rint = 0.041
7016 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0170 restraints
wR(F2) = 0.044H-atom parameters constrained
S = 1.09Δρmax = 0.44 e Å3
888 reflectionsΔρmin = 0.44 e Å3
68 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ag10.587751 (19)0.25000.49038 (3)0.01324 (11)
O10.6353 (2)0.25000.9570 (4)0.0239 (4)
O20.81536 (18)0.25001.2012 (3)0.0161 (4)
O30.83942 (18)0.25000.7908 (4)0.0204 (4)
O120.59454 (12)0.40743 (9)0.4032 (3)0.0185 (3)
N10.7620 (2)0.25000.9817 (3)0.0107 (4)
N110.44162 (15)0.41922 (10)0.0797 (3)0.0170 (3)
C120.54788 (17)0.44853 (11)0.2160 (3)0.0139 (3)
C130.61478 (17)0.53704 (12)0.1454 (3)0.0153 (4)
H110.40140.36860.13000.020*
H13A0.60560.57930.29120.018*
H13B0.71520.52630.11780.018*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ag10.01476 (15)0.01149 (15)0.01348 (16)0.0000.00071 (6)0.000
O10.0126 (10)0.0395 (13)0.0197 (9)0.0000.0030 (7)0.000
O20.0203 (8)0.0132 (8)0.0149 (8)0.0000.0076 (7)0.000
O30.0219 (9)0.0201 (10)0.0193 (9)0.0000.0065 (8)0.000
O120.0216 (6)0.0148 (7)0.0190 (7)0.0014 (5)0.0047 (5)0.0039 (5)
N10.0136 (10)0.0066 (9)0.0119 (10)0.0000.0018 (7)0.000
N110.0179 (7)0.0124 (7)0.0207 (8)0.0042 (6)0.0028 (7)0.0058 (6)
C120.0134 (7)0.0123 (8)0.0159 (8)0.0008 (6)0.0022 (6)0.0008 (6)
C130.0158 (7)0.0150 (9)0.0153 (8)0.0034 (6)0.0011 (7)0.0026 (6)
Geometric parameters (Å, º) top
Ag1—O12.4907 (18)N11—C121.321 (2)
Ag1—O2i2.6653 (17)N11—C13iii1.451 (2)
Ag1—O3ii2.6522 (18)N11—H110.88
Ag1—O122.3627 (13)C12—O121.238 (2)
N1—O11.226 (3)C12—C131.500 (2)
N1—O31.249 (3)C13—H13A0.99
N1—O21.261 (3)C13—H13B0.99
O1—Ag1—O2i114.11 (6)C12—N11—H11117.1
O1—Ag1—O3ii74.94 (6)C13iii—N11—H11117.1
O1—Ag1—O12100.67 (3)O12—C12—N11123.44 (15)
O12—Ag1—O12iv157.45 (7)O12—C12—C13117.67 (15)
O2i—Ag1—O3ii170.95 (6)N11—C12—C13118.87 (15)
O2i—Ag1—O1282.36 (3)C12—O12—Ag1128.51 (11)
O3ii—Ag1—O1296.24 (3)N11iii—C13—C12115.20 (14)
O1—N1—O3120.58 (19)N11iii—C13—H13A108.5
O1—N1—O2120.1 (2)C12—C13—H13A108.5
O3—N1—O2119.3 (2)N11iii—C13—H13B108.5
N1—O1—Ag1106.68 (14)C12—C13—H13B108.5
C12—N11—C13iii125.86 (14)H13A—C13—H13B107.5
O12iv—Ag1—O1—N186.34 (3)C13—C12—O12—Ag1153.91 (11)
O12—Ag1—O1—N186.34 (3)O12iv—Ag1—O12—C1237.0 (2)
C13iii—N11—C12—O12178.05 (17)O1—Ag1—O12—C12162.03 (14)
C13iii—N11—C12—C133.2 (3)O12—C12—C13—N11iii178.31 (16)
N11—C12—O12—Ag127.3 (2)N11—C12—C13—N11iii2.8 (3)
Symmetry codes: (i) x, y, z1; (ii) x1/2, y+1/2, z+3/2; (iii) x+1, y+1, z; (iv) x, y+1/2, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N11—H11···O2v0.882.133.0004 (18)173
Symmetry code: (v) x1/2, y, z+3/2.

Experimental details

(I)(II)(III)(IV)
Crystal data
Chemical formula[CoCl2(H2O)4]·C4H6N2O2[NiCl2(H2O)4]·C4H6N2O2[CuCl2(H2O)2]·C4H6N2O2[Ag(NO3)]·C4H6N2O2
Mr316.00315.78284.58567.98
Crystal system, space groupMonoclinic, P21/nMonoclinic, P21/nMonoclinic, I2/aOrthorhombic, Pnma
Temperature (K)120120120120
a, b, c (Å)9.5326 (4), 6.6602 (2), 10.0167 (4)9.4844 (4), 6.6616 (3), 9.9975 (4)15.224 (3), 3.9694 (8), 15.444 (4)9.6276 (1), 14.7180 (2), 5.2468 (4)
α, β, γ (°)90, 114.1660 (17), 9090, 114.6290 (18), 9090, 94.73 (3), 9090, 90, 90
V3)580.22 (4)574.19 (4)930.1 (4)743.47 (6)
Z2242
Radiation typeMo KαMo KαMo KαMo Kα
µ (mm1)1.952.172.912.71
Crystal size (mm)0.40 × 0.20 × 0.070.40 × 0.30 × 0.200.16 × 0.04 × 0.030.42 × 0.22 × 0.12
Data collection
DiffractometerNonius KappaCCD
diffractometer
Nonius KappaCCD
diffractometer
Nonius KappaCCD
diffractometer
Nonius KappaCCD
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 2003)
Multi-scan
(SADABS; Sheldrick, 2003)
Multi-scan
(SADABS; Sheldrick, 2003)
Multi-scan
SORTAV (Blessing, 1995, 1997)
Tmin, Tmax0.509, 0.8760.468, 0.6490.654, 0.9180.389, 0.722
No. of measured, independent and
observed [I > 2σ(I)] reflections
7527, 1330, 1189 6275, 1315, 1218 4485, 1059, 787 7016, 888, 826
Rint0.0320.0220.00.041
(sin θ/λ)max1)0.6500.6510.6500.652
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.021, 0.053, 1.05 0.019, 0.046, 1.06 0.058, 0.164, 1.09 0.017, 0.044, 1.09
No. of reflections133013151059888
No. of parameters71716268
H-atom treatmentH-atom parameters constrainedH-atom parameters constrainedH-atom parameters constrainedH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.44, 0.370.35, 0.341.58, 1.450.44, 0.44

Computer programs: KappaCCD Server Software (Nonius, 1997), DENZO-SMN (Otwinowski & Minor, 1997), SHELXS97 (Sheldrick, 2008), PLATON (Spek, 2003), SHELXL97 (Sheldrick, 2008) and PRPKAPPA (Ferguson, 1999).

Selected geometric parameters (Å, º) for (IV) top
Ag1—O12.4907 (18)Ag1—O3ii2.6522 (18)
Ag1—O2i2.6653 (17)Ag1—O122.3627 (13)
O1—Ag1—O2i114.11 (6)O2i—Ag1—O3ii170.95 (6)
O1—Ag1—O3ii74.94 (6)O2i—Ag1—O1282.36 (3)
O1—Ag1—O12100.67 (3)O3ii—Ag1—O1296.24 (3)
O12—Ag1—O12iii157.45 (7)
Symmetry codes: (i) x, y, z1; (ii) x1/2, y+1/2, z+3/2; (iii) x, y+1/2, z.
Selected bond distances (Å) for compounds (I)–(III) top
Parameter(I), M = Co(II), M = Ni(III), M = Cu
M-O12.0361 (9)2.0287 (9)1.942 (4)
M-O22.1113 (9)2.0869 (9)
M-Cl2.4562 (3)2.3971 (3)2.2502 (15)
M-Cli3.1640 (18)
Symmetry code: (i) x, -1 + y, z.
Hydrogen-bond parameters (Å, °) for compounds (I)–(IV) top
D-H···AD-HH···AD···AD-H···A
(I)
O1-H1A···Cli0.842.353.1426 (10)158
O1-H1B···O120.841.862.6901 (14)167
O2-H2A···Clii0.842.423.2302 (10)163
O2-H2B···O12iii0.841.962.7834 (14)168
N11-H11···Cl10.882.383.2326 (12)164
(II)
O1-H1A···Cli0.842.373.1508 (10)155
O1-H1B···O120.841.872.6941 (13)167
O2-H2A···Clii0.842.453.2596 (9)163
O2-H2B···O12iii0.841.962.7906 (13)168
N11-H11···Cl10.882.393.2419 (11)163
(III)
N11-H11···Cl10.882.313.174 (5)168
O1-H1A···O20.901.872.736 (7)162
O1-H1B···O12iv0.901.852.735 (7)167
(IV)
N11-H11···O2v0.882.133.0004 (18)173
Symmetry codes: (i) 1/2 + x, 1/2 - y, 1/2 + z; (ii) 1/2 + x, 3/2 - y, 1/2 + z; (iii) x, 1 + y, z; (iv) 1 - x, -1/2 + y, 1/2 - z; (v) -1/2 + x, 1/2 - y, 3/2 - z.
 

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