Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S2053229613034347/sk3520sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S2053229613034347/sk3520Isup2.hkl |
CCDC reference: 978268
Supramolecular assembly of metal–organic coordination frameworks has attracted increasing attention due to the fascinating structures of these frameworks, as well as their potential applications in materials science (Batten & Robson, 1998; Pan et al., 2004; Zhang et al., 2010; Zhong et al., 2011). The polycarboxylate ligands, such as benzene-1,2,4,5-tetracarboxylate acid (Fabelo et al., 2008), benzene-1,2,3,4-tetracarboxylate acid (Zhang et al., 2010), benzene-1,2,4-tricarboxylate acid (Wang et al., 2006), benzene-1,3,5-tricarboxylate acid (Hao et al., 2012) and cyclohexane-1,3,5-tricarboxylate acid (Lill & Cahill, 2006), have been widely applied in constructing interesting coordination polymers, owing to the fact that the carboxylate group may bind to metal ions in various coordination modes and different directions. The crystal engineering of coordination frameworks based on imidazole-containing multidentate ligands has recently received much attention, for example, 1,3,5-tris(imidazol-1-yl)benzene (Su et al., 2010), 1,3,5-tris(imidazol-1-ylmethyl)-2,4,6-trimethylbenzene (Zhao et al., 2004), 1,2,4,5-tetrakis(imidazol-1-ylmethyl)benzene (Hua et al., 2010), 1,3,5-tris(imidazol-1-ylmethyl)benzene (Xu et al., 2009), 1,3-bis(imidazol-1-yl)-5-(imidazol-1-ylmethyl)benzene (Fan et al., 2003) and 2,4,6-tris[4-(imidazol-1-ylmethyl)phenyl]-1,3,5-triazine (Wan et al., 2004) complexes with suitable metal salts have been synthesized and characterized. We have focused our attention on the synthesis of transition metal coordination polymers with mixed polycarboxylate and imidazole-containing multidentate ligands. We report here the crystal structure of the title three-dimensional ZnII polymeric compound with mixed 1,3,5-tris(imidazol-1-ylmethyl)benzene (timb) and cyclohexane-1,3,5-tricarboxylate (chtca) ligands, {[Zn3(chtca)2(timb)2].6H2O}n, (I).
ZnSO4.7H2O (0.1 mmol), 1,3,5-tris(imidazol-1-ylmethyl)benzene (0.1 mmol), cyclohexane-1,3,5-tricarboxylic acid (0.1 mmol) and water (4.0 ml) were mixed and placed in a thick Pyrex tube, which was sealed and heated to 398 K for 72 h. The tube was then left to cool to ambient temperature [Rephrasing OK?], whereupon colourless block-shaped crystals of (I) were obtained. Analysis, found: C 47.31, H 5.01, N 12.17%; calculated for C54H66N12O18Zn3: C 47.40, H 4.83, N 12.29%.
C-bound H atoms were positioned geometrically and allowed to ride on their parent atoms, with C—H = 0.93–0.98 Å and Uiso(H) = 1.2Ueq(C). Water H atoms were either located in difference density Fourier maps or placed in calculated positions so as to form a reasonable hydrogen-bond network, as far as possible. Initially, their positions were refined with tight restraints on the O—H and H···H distances [0.82 (1) and 1.35 (1) Å, respectively] in order to ensure a reasonable geometry. They were then constrained to ride on their parent O atoms, with Uiso(H) = 1.5Ueq(O). One carboxylate group of a cyclohexane-1,3,5-carboxylate ligand is disordered over two positions and was refined as two COO- groups with site occupancies of 0.800 (6) and 0.200 (6).
The asymmetric unit of (I) (Fig. 1) contains two crystallographically independent ZnII centres, one in a general position and one on a twofold crystallographic axis, both with a distorted tetrahedral ZnN2O2 environment. Each ZnII cation is coordinated by two N atoms from two different tripodal timb ligands and two O atoms from two individual chtca ligands. Atom Zn1 is coordinated by atoms N2, N4ii, O1 and O4i, and Zn2 is surrounded by atoms N6i, N6iv, O6 and O6iii (see Fig. 1 and Table 2 for symmetry codes). The Zn1—N and Zn1—O bond lengths may be compared with the Zn2—N and Zn1—O bond lengths. The N—Zn1—N and O—Zn1—O angles are different from those observed around Zn2 [Values removed to avoid duplication - OK?] (Fig. 1 and Table 2). The slight difference in the Zn—O coordination distances around the two Zn atoms may be attributed to the different degree of distortion around them.
The two monodetentate carboxylate groups of the chtca ligand link two Zn1 atoms to generate a one-dimensional ···Zn–chtca–Zn··· zigzag chain running parallel to the b axis. The remaining carboxylate group of the chtca ligand connects with the Zn2 centre, leading to a two-dimensional layered structure extending parallel to the (201) plane, with approximate Zn···Zn separations of 10.01 (Zn1···Zn1i), 8.70 (Zn1···Zn2), 18.30 (Zn2···Zn2viii) and 16.35 Å (Zn2···Zn2ix). Within the sheets there are 48-membered macrocyclic rings composed of six chtca ligands and six Zn atoms through Zn—O coordination bonds (Fig. 2). The dihedral angles between each pair of the three coordinating COO- groups of the chtca ligand are 68.6 (3) (O1/C25/O2 and O3/C26/O4), 27.9 (3) (O1/C25/O2 and O5/C27/O6) and 70.3 (5)° (O3/C26/O4 and O5/C27/O6). One carboxylate group of the chtca ligand (O3/C26/O4) is disordered over two positions and was refined with occupancies of 0.800 (6) and 0.200 (6).
The timb ligand, with cis, trans and trans substituent conformations, coordinates to three ZnII centres (two Zn1 and one Zn2), with approximate metal–metal distances (Zn···Zn) of 12.79 (Zn1···Zn1ii), 11.41 (Zn2x···Zn1ii) and 7.25 Å (Zn2x···Zn1), which are evidently different from that observed in the methyl-substituted timb–zinc compound (Zhao et al., 2004). The dihedral angles between the least-squares plane of the timb ligand and those of the coordinated terminal imidazole groups are 77.8 (1) (N1/C12/N2/C11/C10), 68.0 (1) (N3/C15/N4/C14/C13) and 78.0 (1)° (N5/C18/N6/C17/C16). The three planes of the terminal imidazole ring of the timb ligand are oriented with respect to each other at 86.7 (1) (N1/C12/N2/C11/C10 and N3/C15/N4/C14/C13), 75.9 (1) (N1/C12/N2/C11/C10 and N5/C18/N6/C17/C16) and 34.2 (2)° (N3/C15/N4/C14/C13 and N5/C18/N6/C17/C16), which are different from the values found in a previously reported zinc compound (Zhao et al., 2004).
The two timb ligands adopt a face-to-face orientation and are joined together by five ZnII centres (four Zn1 and one Zn2), giving rise to a one-dimensional screw double chain along the [101] direction (Fig. 3). It is noteworthy that these double chains and the above-mentioned two-dimensional sheets intersect each other, resulting in a three-dimensional porous structure (Fig. 4).
Analysis of the crystal packing of (I) shows that the solvent water molecules reside in the porous metal–organic framework via classical intermolecular O—H···O hydrogen-bonding interactions involving the carboxylate groups of the chtca ligands (Table 3 and Fig. 4).
Data collection: CrystalClear (Rigaku, 2007); cell refinement: CrystalClear (Rigaku, 2007); data reduction: CrystalClear (Rigaku, 2007); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: XP in SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).
Fig. 1. The asymmetric unit of (I), showing the atom-numbering scheme.
Displacement ellipsoids are drawn at the 30% probability level. Dashed lines
represent intermolecular O—H···O interactions. All C-bound H atoms have been
omitted for clarity. [Symmetry codes: (i) -x + 1/2, y + 1/2,
-z + 1/2; (ii) x + 1/2, -y + 1/2, z + 1/2; (iii)
-x + 1, y, -z + 3/2; (iv) x + 1/2, y + 1/2,
z + 1.] Fig. 2. The two-dimensional polymeric layer in (I), viewed down the a axis. The 48-membered macrocyclic ring is illustrated. The timb ligand, water molecules and H atoms of the chtca ligand have been omitted for clarity. [Symmetry codes: (i) -x + 1/2, y + 1/2, -z + 1/2; (iii) -x + 1, y, -z + 3/2; (vii) -x + 1/2, y - 1/2, -z + 1/2; (viii) x, y + 1, z; (ix) x - 1/2, y + 1/2, z - 1.] Fig. 3. The one-dimensional double-chain structure of (I), along the [101] direction. The chtca ligand and water molecules have been omitted for clarity. [Symmetry codes: (ii) x + 1/2, -y + 1/2, z + 1/2; (x) -x + 1, -y + 1, -z + 1.] Fig. 4. The three-dimensional structure of (I), involving two-dimensional layers (blue, green and purple) and one-dimensional double chains (red), viewed down the b axis, showing interactions between adjacent chains and complex cations. Hydrogen bonds are represented by dashed lines. All C-bound H atoms have been omitted for clarity. |
[Zn3(C18H18N6)2(C9H9O6)2]·6H2O | F(000) = 2832 |
Mr = 1367.30 | Dx = 1.538 Mg m−3 |
Monoclinic, C2/c | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -C 2yc | Cell parameters from 6396 reflections |
a = 25.3826 (8) Å | θ = 2.5–27.4° |
b = 18.3013 (5) Å | µ = 1.29 mm−1 |
c = 15.0344 (5) Å | T = 223 K |
β = 122.244 (1)° | Block, colourless |
V = 5906.9 (3) Å3 | 0.30 × 0.20 × 0.15 mm |
Z = 4 |
Rigaku Mercury CCD area-detector diffractometer | 7340 independent reflections |
Radiation source: fine-focus sealed tube | 5783 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.022 |
Detector resolution: 28.5714 pixels mm-1 | θmax = 28.3°, θmin = 1.5° |
ω scans | h = −33→32 |
Absorption correction: multi-scan (REQAB; Jacobson, 1998) | k = −23→24 |
Tmin = 0.782, Tmax = 1.000 | l = −9→20 |
21212 measured reflections |
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.036 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.098 | H-atom parameters constrained |
S = 1.06 | w = 1/[σ2(Fo2) + (0.0492P)2 + 2.9442P] where P = (Fo2 + 2Fc2)/3 |
7340 reflections | (Δ/σ)max = 0.001 |
421 parameters | Δρmax = 0.62 e Å−3 |
36 restraints | Δρmin = −0.43 e Å−3 |
[Zn3(C18H18N6)2(C9H9O6)2]·6H2O | V = 5906.9 (3) Å3 |
Mr = 1367.30 | Z = 4 |
Monoclinic, C2/c | Mo Kα radiation |
a = 25.3826 (8) Å | µ = 1.29 mm−1 |
b = 18.3013 (5) Å | T = 223 K |
c = 15.0344 (5) Å | 0.30 × 0.20 × 0.15 mm |
β = 122.244 (1)° |
Rigaku Mercury CCD area-detector diffractometer | 7340 independent reflections |
Absorption correction: multi-scan (REQAB; Jacobson, 1998) | 5783 reflections with I > 2σ(I) |
Tmin = 0.782, Tmax = 1.000 | Rint = 0.022 |
21212 measured reflections |
R[F2 > 2σ(F2)] = 0.036 | 36 restraints |
wR(F2) = 0.098 | H-atom parameters constrained |
S = 1.06 | Δρmax = 0.62 e Å−3 |
7340 reflections | Δρmin = −0.43 e Å−3 |
421 parameters |
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. |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Zn1 | 0.209200 (11) | 0.438330 (12) | 0.09148 (2) | 0.03888 (8) | |
Zn2 | 0.5000 | 0.379001 (17) | 0.7500 | 0.03712 (9) | |
O1 | 0.25408 (7) | 0.39896 (8) | 0.23844 (13) | 0.0502 (4) | |
O1W | 0.10266 (8) | 0.20522 (11) | 0.11883 (14) | 0.0665 (5) | |
H1WA | 0.1319 | 0.2325 | 0.1336 | 0.100* | |
H1WB | 0.0956 | 0.2070 | 0.1661 | 0.100* | |
O2 | 0.19061 (8) | 0.30946 (10) | 0.14750 (13) | 0.0608 (5) | |
O2W | 0.45616 (18) | 0.14046 (15) | 0.7925 (2) | 0.1439 (13) | |
H2WA | 0.4918 | 0.1546 | 0.8153 | 0.216* | |
H2WB | 0.4318 | 0.1750 | 0.7684 | 0.216* | |
O3W | 0.35098 (17) | −0.0338 (2) | 0.2209 (3) | 0.1549 (14) | |
H3WA | 0.3275 | −0.0235 | 0.2410 | 0.232* | |
H3WB | 0.3559 | −0.0782 | 0.2205 | 0.232* | |
O3 | 0.31544 (13) | 0.06600 (12) | 0.3318 (2) | 0.0615 (8) | 0.800 (6) |
O3' | 0.2919 (5) | 0.0530 (5) | 0.5084 (10) | 0.066 (4) | 0.200 (6) |
O4 | 0.27076 (13) | 0.03843 (14) | 0.4191 (4) | 0.0630 (11) | 0.800 (6) |
O4' | 0.2747 (7) | 0.0503 (7) | 0.3505 (9) | 0.064 (5) | 0.200 (6) |
O5 | 0.41330 (10) | 0.28182 (11) | 0.70841 (14) | 0.0711 (5) | |
O6 | 0.43413 (8) | 0.34540 (10) | 0.60920 (12) | 0.0559 (4) | |
N1 | 0.01644 (8) | 0.42389 (9) | −0.06275 (14) | 0.0387 (4) | |
N2 | 0.11558 (8) | 0.43952 (9) | −0.00249 (14) | 0.0399 (4) | |
N3 | −0.17058 (8) | 0.18462 (10) | −0.45415 (14) | 0.0424 (4) | |
N4 | −0.24325 (9) | 0.11298 (10) | −0.46554 (16) | 0.0494 (5) | |
N5 | −0.04348 (8) | 0.05094 (9) | −0.11977 (14) | 0.0377 (4) | |
N6 | −0.04119 (8) | −0.04597 (9) | −0.20339 (14) | 0.0404 (4) | |
C1 | −0.05257 (9) | 0.31760 (10) | −0.13575 (17) | 0.0394 (5) | |
C2 | −0.08144 (9) | 0.31404 (11) | −0.24506 (18) | 0.0421 (5) | |
H2A | −0.0950 | 0.3567 | −0.2846 | 0.063* | |
C3 | −0.09000 (9) | 0.24764 (11) | −0.29475 (16) | 0.0384 (4) | |
C4 | −0.06947 (9) | 0.18399 (11) | −0.23431 (16) | 0.0378 (4) | |
H4A | −0.0739 | 0.1393 | −0.2671 | 0.045* | |
C5 | −0.04270 (9) | 0.18622 (10) | −0.12683 (16) | 0.0355 (4) | |
C6 | −0.03433 (9) | 0.25378 (11) | −0.07837 (16) | 0.0379 (4) | |
H6A | −0.0161 | 0.2558 | −0.0059 | 0.045* | |
C7 | −0.04076 (10) | 0.39016 (11) | −0.0800 (2) | 0.0485 (6) | |
H7A | −0.0758 | 0.4226 | −0.1220 | 0.058* | |
H7B | −0.0370 | 0.3828 | −0.0130 | 0.058* | |
C8 | −0.12300 (11) | 0.24252 (13) | −0.41316 (17) | 0.0485 (5) | |
H8A | −0.1426 | 0.2890 | −0.4444 | 0.058* | |
H8B | −0.0929 | 0.2321 | −0.4324 | 0.058* | |
C9 | −0.02313 (11) | 0.11857 (11) | −0.05905 (17) | 0.0436 (5) | |
H9A | 0.0219 | 0.1181 | −0.0134 | 0.052* | |
H9B | −0.0402 | 0.1207 | −0.0148 | 0.052* | |
C10 | 0.02043 (11) | 0.47979 (13) | −0.11864 (19) | 0.0528 (6) | |
H10A | −0.0125 | 0.5062 | −0.1724 | 0.063* | |
C11 | 0.08133 (11) | 0.48925 (13) | −0.08077 (19) | 0.0512 (6) | |
H11A | 0.0978 | 0.5243 | −0.1042 | 0.061* | |
C12 | 0.07455 (10) | 0.40118 (11) | 0.00575 (18) | 0.0424 (5) | |
H12A | 0.0847 | 0.3631 | 0.0532 | 0.051* | |
C13 | −0.17828 (15) | 0.12976 (16) | −0.5202 (2) | 0.0716 (8) | |
H13A | −0.1570 | 0.1236 | −0.5544 | 0.086* | |
C14 | −0.22282 (17) | 0.08571 (18) | −0.5270 (3) | 0.0838 (11) | |
H14A | −0.2375 | 0.0433 | −0.5672 | 0.101* | |
C15 | −0.21013 (10) | 0.17239 (12) | −0.42341 (19) | 0.0459 (5) | |
H15A | −0.2139 | 0.2025 | −0.3773 | 0.055* | |
C16 | −0.10301 (11) | 0.02342 (12) | −0.1757 (2) | 0.0506 (6) | |
H16A | −0.1378 | 0.0422 | −0.1782 | 0.061* | |
C17 | −0.10086 (10) | −0.03610 (12) | −0.2263 (2) | 0.0510 (6) | |
H17A | −0.1346 | −0.0660 | −0.2700 | 0.061* | |
C18 | −0.00843 (9) | 0.00763 (11) | −0.13935 (16) | 0.0372 (4) | |
H18A | 0.0339 | 0.0146 | −0.1111 | 0.045* | |
C19 | 0.25828 (9) | 0.29043 (10) | 0.33223 (17) | 0.0400 (5) | |
H19A | 0.2271 | 0.2916 | 0.3516 | 0.048* | |
C20 | 0.26628 (11) | 0.21048 (11) | 0.31258 (19) | 0.0521 (6) | |
H20A | 0.2271 | 0.1921 | 0.2542 | 0.063* | |
H20B | 0.2971 | 0.2071 | 0.2932 | 0.063* | |
C21 | 0.28638 (10) | 0.16433 (11) | 0.4071 (2) | 0.0506 (6) | |
H21A | 0.2538 | 0.1669 | 0.4234 | 0.061* | |
C22 | 0.34694 (10) | 0.19285 (11) | 0.50283 (18) | 0.0457 (5) | |
H22A | 0.3571 | 0.1641 | 0.5642 | 0.055* | |
H22B | 0.3807 | 0.1874 | 0.4908 | 0.055* | |
C23 | 0.34084 (10) | 0.27337 (11) | 0.52354 (17) | 0.0395 (4) | |
H23A | 0.3082 | 0.2758 | 0.5396 | 0.047* | |
C24 | 0.31853 (10) | 0.32010 (10) | 0.42588 (16) | 0.0383 (4) | |
H24A | 0.3119 | 0.3698 | 0.4402 | 0.046* | |
H24B | 0.3504 | 0.3212 | 0.4089 | 0.046* | |
C25 | 0.23249 (9) | 0.33541 (11) | 0.23277 (17) | 0.0409 (5) | |
C26 | 0.29175 (16) | 0.0835 (2) | 0.3814 (5) | 0.0426 (8) | 0.800 (6) |
C26' | 0.2853 (6) | 0.0848 (8) | 0.4302 (15) | 0.042 (3) | 0.200 (6) |
C27 | 0.39983 (10) | 0.30130 (11) | 0.61991 (17) | 0.0413 (5) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Zn1 | 0.03507 (13) | 0.03259 (13) | 0.04489 (15) | 0.00156 (9) | 0.01859 (11) | 0.00365 (10) |
Zn2 | 0.04412 (19) | 0.03156 (17) | 0.03036 (17) | 0.000 | 0.01630 (14) | 0.000 |
O1 | 0.0551 (9) | 0.0350 (8) | 0.0465 (9) | −0.0012 (7) | 0.0177 (8) | 0.0060 (7) |
O1W | 0.0547 (10) | 0.0871 (13) | 0.0557 (11) | −0.0159 (9) | 0.0281 (9) | −0.0084 (10) |
O2 | 0.0528 (10) | 0.0612 (10) | 0.0437 (9) | −0.0127 (8) | 0.0092 (8) | 0.0056 (8) |
O2W | 0.209 (4) | 0.0795 (17) | 0.120 (2) | 0.048 (2) | 0.073 (3) | 0.0434 (17) |
O3W | 0.165 (3) | 0.174 (3) | 0.184 (4) | 0.027 (3) | 0.132 (3) | 0.033 (3) |
O3 | 0.0736 (18) | 0.0421 (12) | 0.0721 (17) | 0.0068 (11) | 0.0412 (14) | −0.0035 (11) |
O3' | 0.070 (6) | 0.045 (5) | 0.077 (8) | −0.015 (4) | 0.035 (6) | 0.009 (5) |
O4 | 0.0571 (15) | 0.0282 (14) | 0.117 (4) | −0.0022 (11) | 0.056 (2) | −0.0008 (15) |
O4' | 0.065 (8) | 0.035 (6) | 0.047 (7) | 0.001 (5) | −0.001 (6) | −0.008 (5) |
O5 | 0.1017 (15) | 0.0645 (11) | 0.0406 (10) | −0.0027 (11) | 0.0335 (10) | 0.0030 (9) |
O6 | 0.0533 (9) | 0.0702 (11) | 0.0385 (9) | −0.0208 (8) | 0.0207 (8) | −0.0098 (8) |
N1 | 0.0365 (9) | 0.0280 (8) | 0.0444 (10) | −0.0018 (6) | 0.0167 (8) | −0.0039 (7) |
N2 | 0.0385 (9) | 0.0327 (8) | 0.0417 (10) | −0.0027 (7) | 0.0167 (8) | 0.0017 (7) |
N3 | 0.0428 (9) | 0.0442 (10) | 0.0338 (9) | −0.0096 (8) | 0.0162 (8) | 0.0022 (8) |
N4 | 0.0498 (11) | 0.0461 (10) | 0.0517 (12) | −0.0132 (8) | 0.0267 (9) | −0.0067 (9) |
N5 | 0.0433 (9) | 0.0325 (8) | 0.0369 (9) | 0.0068 (7) | 0.0211 (8) | 0.0047 (7) |
N6 | 0.0404 (9) | 0.0335 (8) | 0.0440 (10) | 0.0038 (7) | 0.0203 (8) | 0.0012 (7) |
C1 | 0.0305 (9) | 0.0332 (10) | 0.0498 (12) | −0.0038 (8) | 0.0183 (9) | −0.0065 (9) |
C2 | 0.0362 (10) | 0.0331 (10) | 0.0484 (12) | −0.0054 (8) | 0.0168 (9) | 0.0040 (9) |
C3 | 0.0349 (10) | 0.0387 (10) | 0.0365 (11) | −0.0078 (8) | 0.0156 (9) | 0.0023 (9) |
C4 | 0.0421 (11) | 0.0324 (9) | 0.0356 (10) | −0.0036 (8) | 0.0185 (9) | −0.0029 (8) |
C5 | 0.0337 (9) | 0.0344 (10) | 0.0363 (10) | 0.0019 (8) | 0.0174 (8) | 0.0003 (8) |
C6 | 0.0334 (9) | 0.0404 (10) | 0.0359 (11) | −0.0006 (8) | 0.0158 (8) | −0.0056 (9) |
C7 | 0.0390 (11) | 0.0378 (11) | 0.0671 (16) | −0.0042 (9) | 0.0274 (11) | −0.0137 (11) |
C8 | 0.0482 (12) | 0.0510 (13) | 0.0381 (11) | −0.0172 (10) | 0.0174 (10) | 0.0054 (10) |
C9 | 0.0536 (12) | 0.0397 (11) | 0.0333 (11) | 0.0077 (9) | 0.0203 (10) | 0.0000 (9) |
C10 | 0.0459 (12) | 0.0446 (12) | 0.0467 (13) | 0.0023 (10) | 0.0105 (10) | 0.0108 (10) |
C11 | 0.0494 (13) | 0.0454 (12) | 0.0476 (13) | −0.0049 (10) | 0.0184 (11) | 0.0124 (10) |
C12 | 0.0398 (11) | 0.0328 (10) | 0.0473 (13) | 0.0007 (8) | 0.0183 (10) | 0.0054 (9) |
C13 | 0.092 (2) | 0.0764 (19) | 0.0719 (19) | −0.0347 (16) | 0.0611 (18) | −0.0289 (16) |
C14 | 0.112 (3) | 0.082 (2) | 0.088 (2) | −0.0521 (19) | 0.074 (2) | −0.0472 (18) |
C15 | 0.0457 (12) | 0.0425 (11) | 0.0490 (13) | −0.0082 (9) | 0.0249 (10) | −0.0063 (10) |
C16 | 0.0417 (12) | 0.0435 (12) | 0.0702 (16) | 0.0051 (9) | 0.0322 (12) | 0.0052 (11) |
C17 | 0.0408 (12) | 0.0399 (11) | 0.0670 (16) | −0.0023 (9) | 0.0253 (11) | −0.0001 (11) |
C18 | 0.0354 (10) | 0.0388 (10) | 0.0352 (10) | 0.0046 (8) | 0.0173 (9) | 0.0021 (8) |
C19 | 0.0381 (10) | 0.0299 (9) | 0.0441 (12) | 0.0005 (8) | 0.0166 (9) | 0.0032 (9) |
C20 | 0.0415 (11) | 0.0335 (10) | 0.0513 (14) | 0.0020 (9) | 0.0047 (10) | −0.0078 (10) |
C21 | 0.0386 (11) | 0.0275 (10) | 0.0721 (16) | −0.0012 (8) | 0.0203 (11) | 0.0035 (10) |
C22 | 0.0431 (11) | 0.0298 (10) | 0.0498 (13) | 0.0003 (8) | 0.0151 (10) | 0.0053 (9) |
C23 | 0.0415 (11) | 0.0350 (10) | 0.0409 (11) | −0.0014 (8) | 0.0212 (9) | 0.0017 (9) |
C24 | 0.0421 (11) | 0.0287 (9) | 0.0395 (11) | −0.0039 (8) | 0.0187 (9) | 0.0005 (8) |
C25 | 0.0365 (10) | 0.0387 (10) | 0.0436 (12) | 0.0032 (8) | 0.0187 (9) | 0.0034 (9) |
C26 | 0.0269 (15) | 0.0316 (18) | 0.051 (3) | 0.0011 (12) | 0.0088 (17) | −0.0012 (18) |
C26' | 0.030 (6) | 0.026 (7) | 0.048 (9) | 0.000 (4) | 0.005 (6) | −0.002 (6) |
C27 | 0.0508 (12) | 0.0351 (10) | 0.0365 (11) | 0.0044 (9) | 0.0223 (10) | −0.0029 (9) |
Zn1—O4i | 1.930 (3) | C2—H2A | 0.9300 |
Zn1—O1 | 2.0032 (16) | C3—C4 | 1.396 (3) |
Zn1—N2 | 2.0152 (17) | C3—C8 | 1.513 (3) |
Zn1—N4ii | 2.0439 (19) | C4—C5 | 1.379 (3) |
Zn1—O4'i | 2.178 (13) | C4—H4A | 0.9300 |
Zn2—O6 | 1.9692 (15) | C5—C6 | 1.393 (3) |
Zn2—O6iii | 1.9692 (15) | C5—C9 | 1.509 (3) |
Zn2—N6iv | 2.0619 (17) | C6—H6A | 0.9300 |
Zn2—N6i | 2.0619 (17) | C7—H7A | 0.9700 |
O1—C25 | 1.269 (2) | C7—H7B | 0.9700 |
O1W—H1WA | 0.8203 | C8—H8A | 0.9700 |
O1W—H1WB | 0.8206 | C8—H8B | 0.9700 |
O2—C25 | 1.243 (3) | C9—H9A | 0.9700 |
O2W—H2WA | 0.8202 | C9—H9B | 0.9700 |
O2W—H2WB | 0.8200 | C10—C11 | 1.343 (3) |
O3W—H3WA | 0.8201 | C10—H10A | 0.9300 |
O3W—H3WB | 0.8231 | C11—H11A | 0.9300 |
O3—C26 | 1.225 (6) | C12—H12A | 0.9300 |
O3'—C26' | 1.24 (2) | C13—C14 | 1.347 (4) |
O4—C26 | 1.267 (6) | C13—H13A | 0.9300 |
O4—Zn1v | 1.930 (3) | C14—H14A | 0.9300 |
O4'—C26' | 1.25 (2) | C15—H15A | 0.9300 |
O4'—Zn1v | 2.178 (13) | C16—C17 | 1.346 (3) |
O5—C27 | 1.237 (3) | C16—H16A | 0.9300 |
O6—C27 | 1.259 (3) | C17—H17A | 0.9300 |
N1—C12 | 1.337 (3) | C18—H18A | 0.9300 |
N1—C10 | 1.362 (3) | C19—C25 | 1.516 (3) |
N1—C7 | 1.468 (3) | C19—C24 | 1.523 (3) |
N2—C12 | 1.315 (3) | C19—C20 | 1.528 (3) |
N2—C11 | 1.370 (3) | C19—H19A | 0.9800 |
N3—C15 | 1.329 (3) | C20—C21 | 1.490 (3) |
N3—C13 | 1.351 (3) | C20—H20A | 0.9700 |
N3—C8 | 1.472 (3) | C20—H20B | 0.9700 |
N4—C15 | 1.312 (3) | C21—C26' | 1.500 (17) |
N4—C14 | 1.373 (3) | C21—C22 | 1.532 (3) |
N4—Zn1vi | 2.0439 (19) | C21—C26 | 1.553 (5) |
N5—C18 | 1.336 (3) | C21—H21A | 0.9800 |
N5—C16 | 1.374 (3) | C22—C23 | 1.531 (3) |
N5—C9 | 1.459 (3) | C22—H22A | 0.9700 |
N6—C18 | 1.314 (3) | C22—H22B | 0.9700 |
N6—C17 | 1.374 (3) | C23—C27 | 1.513 (3) |
N6—Zn2vii | 2.0619 (17) | C23—C24 | 1.523 (3) |
C1—C6 | 1.377 (3) | C23—H23A | 0.9800 |
C1—C2 | 1.399 (3) | C24—H24A | 0.9700 |
C1—C7 | 1.512 (3) | C24—H24B | 0.9700 |
C2—C3 | 1.382 (3) | ||
O4i—Zn1—O1 | 114.34 (14) | C11—C10—H10A | 126.8 |
O4i—Zn1—N2 | 101.30 (11) | N1—C10—H10A | 126.8 |
O1—Zn1—N2 | 122.76 (7) | C10—C11—N2 | 109.7 (2) |
O4i—Zn1—N4ii | 99.28 (10) | C10—C11—H11A | 125.1 |
O1—Zn1—N4ii | 100.47 (7) | N2—C11—H11A | 125.1 |
N2—Zn1—N4ii | 116.76 (8) | N2—C12—N1 | 111.42 (19) |
O1—Zn1—O4'i | 91.3 (3) | N2—C12—H12A | 124.3 |
N2—Zn1—O4'i | 99.8 (4) | N1—C12—H12A | 124.3 |
N4ii—Zn1—O4'i | 125.0 (5) | C14—C13—N3 | 106.7 (2) |
O6—Zn2—O6iii | 143.60 (11) | C14—C13—H13A | 126.7 |
O6—Zn2—N6iv | 106.24 (7) | N3—C13—H13A | 126.7 |
O6iii—Zn2—N6iv | 97.83 (7) | C13—C14—N4 | 109.5 (2) |
O6—Zn2—N6i | 97.83 (7) | C13—C14—H14A | 125.2 |
O6iii—Zn2—N6i | 106.24 (7) | N4—C14—H14A | 125.2 |
N6iv—Zn2—N6i | 96.49 (10) | N4—C15—N3 | 112.3 (2) |
C25—O1—Zn1 | 106.53 (14) | N4—C15—H15A | 123.8 |
H1WA—O1W—H1WB | 109.0 | N3—C15—H15A | 123.8 |
H2WA—O2W—H2WB | 110.1 | C17—C16—N5 | 106.26 (19) |
H3WA—O3W—H3WB | 111.9 | C17—C16—H16A | 126.9 |
C26—O4—Zn1v | 112.9 (4) | N5—C16—H16A | 126.9 |
C26'—O4'—Zn1v | 101.1 (13) | C16—C17—N6 | 109.6 (2) |
C27—O6—Zn2 | 108.13 (14) | C16—C17—H17A | 125.2 |
C12—N1—C10 | 107.11 (18) | N6—C17—H17A | 125.2 |
C12—N1—C7 | 125.89 (19) | N6—C18—N5 | 111.64 (18) |
C10—N1—C7 | 126.80 (19) | N6—C18—H18A | 124.2 |
C12—N2—C11 | 105.29 (18) | N5—C18—H18A | 124.2 |
C12—N2—Zn1 | 128.68 (15) | C25—C19—C24 | 114.24 (16) |
C11—N2—Zn1 | 125.44 (14) | C25—C19—C20 | 111.19 (19) |
C15—N3—C13 | 106.90 (19) | C24—C19—C20 | 110.42 (17) |
C15—N3—C8 | 125.36 (19) | C25—C19—H19A | 106.9 |
C13—N3—C8 | 127.4 (2) | C24—C19—H19A | 106.9 |
C15—N4—C14 | 104.6 (2) | C20—C19—H19A | 106.9 |
C15—N4—Zn1vi | 123.22 (17) | C21—C20—C19 | 111.8 (2) |
C14—N4—Zn1vi | 129.44 (17) | C21—C20—H20A | 109.3 |
C18—N5—C16 | 106.95 (18) | C19—C20—H20A | 109.3 |
C18—N5—C9 | 125.87 (18) | C21—C20—H20B | 109.3 |
C16—N5—C9 | 126.92 (18) | C19—C20—H20B | 109.3 |
C18—N6—C17 | 105.51 (18) | H20A—C20—H20B | 107.9 |
C18—N6—Zn2vii | 120.58 (14) | C20—C21—C26' | 137.0 (8) |
C17—N6—Zn2vii | 133.90 (16) | C20—C21—C22 | 111.36 (18) |
C6—C1—C2 | 119.12 (18) | C26'—C21—C22 | 104.2 (5) |
C6—C1—C7 | 119.8 (2) | C20—C21—C26 | 109.5 (3) |
C2—C1—C7 | 121.1 (2) | C22—C21—C26 | 112.4 (2) |
C3—C2—C1 | 120.59 (19) | C20—C21—H21A | 107.8 |
C3—C2—H2A | 119.7 | C26'—C21—H21A | 82.4 |
C1—C2—H2A | 119.7 | C22—C21—H21A | 107.8 |
C2—C3—C4 | 119.05 (19) | C26—C21—H21A | 107.8 |
C2—C3—C8 | 121.29 (19) | C23—C22—C21 | 111.06 (17) |
C4—C3—C8 | 119.63 (19) | C23—C22—H22A | 109.4 |
C5—C4—C3 | 121.15 (19) | C21—C22—H22A | 109.4 |
C5—C4—H4A | 119.4 | C23—C22—H22B | 109.4 |
C3—C4—H4A | 119.4 | C21—C22—H22B | 109.4 |
C4—C5—C6 | 118.77 (18) | H22A—C22—H22B | 108.0 |
C4—C5—C9 | 123.07 (18) | C27—C23—C24 | 113.73 (17) |
C6—C5—C9 | 118.14 (18) | C27—C23—C22 | 111.36 (17) |
C1—C6—C5 | 121.25 (19) | C24—C23—C22 | 111.74 (18) |
C1—C6—H6A | 119.4 | C27—C23—H23A | 106.5 |
C5—C6—H6A | 119.4 | C24—C23—H23A | 106.5 |
N1—C7—C1 | 110.64 (17) | C22—C23—H23A | 106.5 |
N1—C7—H7A | 109.5 | C19—C24—C23 | 111.37 (16) |
C1—C7—H7A | 109.5 | C19—C24—H24A | 109.4 |
N1—C7—H7B | 109.5 | C23—C24—H24A | 109.4 |
C1—C7—H7B | 109.5 | C19—C24—H24B | 109.4 |
H7A—C7—H7B | 108.1 | C23—C24—H24B | 109.4 |
N3—C8—C3 | 110.65 (17) | H24A—C24—H24B | 108.0 |
N3—C8—H8A | 109.5 | O2—C25—O1 | 121.4 (2) |
C3—C8—H8A | 109.5 | O2—C25—C19 | 119.44 (19) |
N3—C8—H8B | 109.5 | O1—C25—C19 | 119.20 (19) |
C3—C8—H8B | 109.5 | O3—C26—O4 | 124.2 (5) |
H8A—C8—H8B | 108.1 | O3—C26—C21 | 122.5 (4) |
N5—C9—C5 | 113.22 (17) | O4—C26—C21 | 113.3 (5) |
N5—C9—H9A | 108.9 | O3'—C26'—O4' | 121.5 (17) |
C5—C9—H9A | 108.9 | O3'—C26'—C21 | 131.6 (14) |
N5—C9—H9B | 108.9 | O4'—C26'—C21 | 107 (2) |
C5—C9—H9B | 108.9 | O5—C27—O6 | 120.6 (2) |
H9A—C9—H9B | 107.7 | O5—C27—C23 | 119.8 (2) |
C11—C10—N1 | 106.4 (2) | O6—C27—C23 | 119.53 (19) |
O4i—Zn1—O1—C25 | 175.14 (15) | Zn1vi—N4—C15—N3 | 162.91 (15) |
N2—Zn1—O1—C25 | 51.98 (16) | C13—N3—C15—N4 | −0.1 (3) |
N4ii—Zn1—O1—C25 | −79.58 (15) | C8—N3—C15—N4 | −173.7 (2) |
O4'i—Zn1—O1—C25 | 154.5 (5) | C18—N5—C16—C17 | 0.4 (3) |
O6iii—Zn2—O6—C27 | 52.96 (14) | C9—N5—C16—C17 | 174.7 (2) |
N6iv—Zn2—O6—C27 | −76.42 (16) | N5—C16—C17—N6 | −0.4 (3) |
N6i—Zn2—O6—C27 | −175.56 (15) | C18—N6—C17—C16 | 0.1 (3) |
O4i—Zn1—N2—C12 | −147.8 (2) | Zn2vii—N6—C17—C16 | −178.52 (17) |
O1—Zn1—N2—C12 | −18.9 (2) | C17—N6—C18—N5 | 0.2 (2) |
N4ii—Zn1—N2—C12 | 105.60 (19) | Zn2vii—N6—C18—N5 | 179.04 (13) |
O4'i—Zn1—N2—C12 | −116.8 (4) | C16—N5—C18—N6 | −0.4 (2) |
O4i—Zn1—N2—C11 | 22.1 (2) | C9—N5—C18—N6 | −174.73 (18) |
O1—Zn1—N2—C11 | 151.01 (18) | C25—C19—C20—C21 | −175.07 (18) |
N4ii—Zn1—N2—C11 | −84.5 (2) | C24—C19—C20—C21 | 57.0 (3) |
O4'i—Zn1—N2—C11 | 53.1 (4) | C19—C20—C21—C26' | 159.3 (11) |
C6—C1—C2—C3 | −1.8 (3) | C19—C20—C21—C22 | −56.8 (3) |
C7—C1—C2—C3 | 177.69 (19) | C19—C20—C21—C26 | 178.3 (2) |
C1—C2—C3—C4 | 0.1 (3) | C20—C21—C22—C23 | 54.7 (3) |
C1—C2—C3—C8 | 177.98 (19) | C26'—C21—C22—C23 | −149.9 (9) |
C2—C3—C4—C5 | 2.0 (3) | C26—C21—C22—C23 | 177.9 (3) |
C8—C3—C4—C5 | −175.93 (19) | C21—C22—C23—C27 | 178.29 (19) |
C3—C4—C5—C6 | −2.3 (3) | C21—C22—C23—C24 | −53.3 (3) |
C3—C4—C5—C9 | 176.43 (19) | C25—C19—C24—C23 | 178.59 (17) |
C2—C1—C6—C5 | 1.6 (3) | C20—C19—C24—C23 | −55.2 (2) |
C7—C1—C6—C5 | −177.92 (18) | C27—C23—C24—C19 | −178.64 (18) |
C4—C5—C6—C1 | 0.4 (3) | C22—C23—C24—C19 | 54.2 (2) |
C9—C5—C6—C1 | −178.35 (19) | Zn1—O1—C25—O2 | −1.2 (3) |
C12—N1—C7—C1 | −71.4 (3) | Zn1—O1—C25—C19 | 178.98 (15) |
C10—N1—C7—C1 | 102.7 (3) | C24—C19—C25—O2 | 166.6 (2) |
C6—C1—C7—N1 | 97.1 (2) | C20—C19—C25—O2 | 40.8 (3) |
C2—C1—C7—N1 | −82.4 (2) | C24—C19—C25—O1 | −13.5 (3) |
C15—N3—C8—C3 | 43.2 (3) | C20—C19—C25—O1 | −139.3 (2) |
C13—N3—C8—C3 | −129.1 (3) | Zn1v—O4—C26—O3 | 8.6 (7) |
C2—C3—C8—N3 | −131.9 (2) | Zn1v—O4—C26—C21 | −169.7 (2) |
C4—C3—C8—N3 | 46.1 (3) | C20—C21—C26—O3 | 42.9 (4) |
C18—N5—C9—C5 | 99.6 (2) | C26'—C21—C26—O3 | −162.1 (13) |
C16—N5—C9—C5 | −73.6 (3) | C22—C21—C26—O3 | −81.4 (5) |
C4—C5—C9—N5 | −8.4 (3) | C20—C21—C26—O4 | −138.8 (4) |
C6—C5—C9—N5 | 170.28 (18) | C26'—C21—C26—O4 | 16.2 (9) |
C12—N1—C10—C11 | −0.6 (3) | C22—C21—C26—O4 | 96.9 (4) |
C7—N1—C10—C11 | −175.6 (2) | Zn1v—O4'—C26'—O3' | −10 (2) |
N1—C10—C11—N2 | 0.6 (3) | Zn1v—O4'—C26'—C21 | 170.7 (7) |
C12—N2—C11—C10 | −0.4 (3) | C20—C21—C26'—O3' | −163.3 (10) |
Zn1—N2—C11—C10 | −172.21 (17) | C22—C21—C26'—O3' | 51.2 (18) |
C11—N2—C12—N1 | 0.0 (3) | C26—C21—C26'—O3' | 161 (2) |
Zn1—N2—C12—N1 | 171.48 (14) | C20—C21—C26'—O4' | 15 (2) |
C10—N1—C12—N2 | 0.4 (3) | C22—C21—C26'—O4' | −130.1 (11) |
C7—N1—C12—N2 | 175.47 (19) | C26—C21—C26'—O4' | −20.3 (10) |
C15—N3—C13—C14 | 0.0 (3) | Zn2—O6—C27—O5 | −5.6 (3) |
C8—N3—C13—C14 | 173.4 (3) | Zn2—O6—C27—C23 | 172.99 (15) |
N3—C13—C14—N4 | 0.2 (4) | C24—C23—C27—O5 | 159.9 (2) |
C15—N4—C14—C13 | −0.3 (4) | C22—C23—C27—O5 | −72.7 (3) |
Zn1vi—N4—C14—C13 | −161.4 (2) | C24—C23—C27—O6 | −18.6 (3) |
C14—N4—C15—N3 | 0.2 (3) | C22—C23—C27—O6 | 108.7 (2) |
Symmetry codes: (i) −x+1/2, y+1/2, −z+1/2; (ii) x+1/2, −y+1/2, z+1/2; (iii) −x+1, y, −z+3/2; (iv) x+1/2, y+1/2, z+1; (v) −x+1/2, y−1/2, −z+1/2; (vi) x−1/2, −y+1/2, z−1/2; (vii) x−1/2, y−1/2, z−1. |
D—H···A | D—H | H···A | D···A | D—H···A |
O1W—H1WA···O2 | 0.82 | 1.98 | 2.790 (2) | 169 |
O1W—H1WB···O5viii | 0.82 | 2.03 | 2.844 (3) | 174 |
O2W—H2WB···O5 | 0.82 | 2.10 | 2.830 (3) | 148 |
O2W—H2WA···O2Wiii | 0.82 | 2.59 | 3.102 (8) | 122 |
O3W—H3WA···O3 | 0.82 | 2.26 | 2.921 (4) | 139 |
O3W—H3WB···O2Wix | 0.82 | 2.45 | 3.005 (5) | 126 |
Symmetry codes: (iii) −x+1, y, −z+3/2; (viii) −x+1/2, −y+1/2, −z+1; (ix) x, −y, z−1/2. |
Experimental details
Crystal data | |
Chemical formula | [Zn3(C18H18N6)2(C9H9O6)2]·6H2O |
Mr | 1367.30 |
Crystal system, space group | Monoclinic, C2/c |
Temperature (K) | 223 |
a, b, c (Å) | 25.3826 (8), 18.3013 (5), 15.0344 (5) |
β (°) | 122.244 (1) |
V (Å3) | 5906.9 (3) |
Z | 4 |
Radiation type | Mo Kα |
µ (mm−1) | 1.29 |
Crystal size (mm) | 0.30 × 0.20 × 0.15 |
Data collection | |
Diffractometer | Rigaku Mercury CCD area-detector diffractometer |
Absorption correction | Multi-scan (REQAB; Jacobson, 1998) |
Tmin, Tmax | 0.782, 1.000 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 21212, 7340, 5783 |
Rint | 0.022 |
(sin θ/λ)max (Å−1) | 0.667 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.036, 0.098, 1.06 |
No. of reflections | 7340 |
No. of parameters | 421 |
No. of restraints | 36 |
H-atom treatment | H-atom parameters constrained |
Δρmax, Δρmin (e Å−3) | 0.62, −0.43 |
Computer programs: CrystalClear (Rigaku, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), XP in SHELXTL (Sheldrick, 2008), SHELXTL (Sheldrick, 2008).
Zn1—O4i | 1.930 (3) | Zn2—O6 | 1.9692 (15) |
Zn1—O1 | 2.0032 (16) | Zn2—O6iii | 1.9692 (15) |
Zn1—N2 | 2.0152 (17) | Zn2—N6iv | 2.0619 (17) |
Zn1—N4ii | 2.0439 (19) | Zn2—N6i | 2.0619 (17) |
O4i—Zn1—O1 | 114.34 (14) | O6—Zn2—O6iii | 143.60 (11) |
N2—Zn1—N4ii | 116.76 (8) | N6iv—Zn2—N6i | 96.49 (10) |
Symmetry codes: (i) −x+1/2, y+1/2, −z+1/2; (ii) x+1/2, −y+1/2, z+1/2; (iii) −x+1, y, −z+3/2; (iv) x+1/2, y+1/2, z+1. |
D—H···A | D—H | H···A | D···A | D—H···A |
O1W—H1WA···O2 | 0.82 | 1.98 | 2.790 (2) | 169 |
O1W—H1WB···O5v | 0.82 | 2.03 | 2.844 (3) | 174 |
O2W—H2WB···O5 | 0.82 | 2.10 | 2.830 (3) | 148 |
O2W—H2WA···O2Wiii | 0.82 | 2.59 | 3.102 (8) | 122 |
O3W—H3WA···O3 | 0.82 | 2.26 | 2.921 (4) | 139 |
O3W—H3WB···O2Wvi | 0.82 | 2.45 | 3.005 (5) | 126 |
Symmetry codes: (iii) −x+1, y, −z+3/2; (v) −x+1/2, −y+1/2, −z+1; (vi) x, −y, z−1/2. |