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Acta Cryst. (2008). E64, m609    [ doi:10.1107/S1600536808008325 ]

Bis[4-(4-methoxyphenyl)-4H-1,2,4-triazole-[kappa]N1]bis(thiocyanato-[kappa]N)zinc(II)

Y. Zuo

Abstract top

In the title complex, [Zn(NCS)2(C9H9N3O)2], the ZnII ion is coordinated by two N atoms from the NCS- anions and two N atoms from two 4-(4-methoxyphenyl)-4H-1,2,4-triazole ligands in a slightly distorted tetrahedral geometry. Three intermolecular weak hydrogen-bonding contacts of the types C-H...N, C-H...S and C-H...O are observed in the crystal structure.

Comment top

The organic ligands, 1,2,4-triazole and its derivatives continue to attract considerable attention due to the luminescent, magnetic, and electronic properties of their complexes and the potential application in material science (Yin et al., 2007; Zhou, et al., 2007; Han et al., 2006). On the other hand, 1,2,4-triazole and its derivatives combine the coordination geometry of both pyrazole and imidazole with regard to the arrangement and coordination of their three heteroatoms. Compared with the chelating to the metal centers with the nitrogen atom in the 1,2-positions (Thomann et al., 1994), it is familiar that the nitrogen atom serve as the solo coordinated atom (Ling & Zhang, 2007). In order to explore furthur the coordination chemistry of the 4-(4-methoxyphenyl)-4H-1,2,4-triazole system (hereafter abbreviated as L), the title complex was synthesized.

The coordination geometry of the ZnII ion is a slightly distorted tetrahedron, in which each ZnII ion is coordinated to two nitrogen atoms from the NCS- anions and two nitrogen atoms from two ligands L. (Fig. 1). The separations of Zn—N range from 1.923 (6) to 2.009 (5)Å (Table 1), which is close to the corresponding distances in the 4-coordinated Zn compound (2.050 (4)Å and 2.023 (4) Å) reported previously (Han et al., 2006), while the average distance of Zn—N is 2.162 (2)Å in the 6-coordinated (Ling & Zhang, 2007) and 2.065 (2)Å in the 5-coordinated (Yin et al., 2007) compounds, respectively. The bond angles around ZnII ions vary between 102.2 (2)° and 116.4 (2)°. The central ZnII ion, is coordinated with the L ligands in the 1-position, which is the common coordination mode (Ling & Zhang, 2007) of 1,2,4-Triazole and its derivatives, differently from that in the 1,2-position (Thomann et al., 1994). As the important structural parameters, the dihedral angles between the triazole and phenyl rings of the two L ligands are distinct, that of C1—N3—C3—C8 is equal to 39.2 (9)°, while the value of C10—N6—C12—C17 is 93.8 (8)°. With regard to the two trans thiocyanato NCS- anions, the group is almost linear with an N7—C19—S1 angle of 178.8 (8)° and N8—C20—S2 angle of 178.1 (7)°. The connection between Zn atoms and NCS groups are bent with a C20—N8—Zn1 angle of 168.1 (6)°, and a C19—N7—Zn1 angle of 160.9 (6)° (Zhao et al., 2002). Three intermoleular hydrogen bonding contacts of the type C—H···N, C—H···S and C—H···O are observed in the title structure (Table 2).

Related literature top

For related literature, see: Han et al. (2006); Ling & Zhang (2007); Thomann et al. (1994); Yin et al. (2007); Zhao et al. (2002); Zhou et al. (2007).

Experimental top

The compound was synthesized under hydrothermal conditions. A mixture of L (L=4-(1,2,4-triazol)-1-methoxy-benzene) (0.3 mmol, 0.045 g), ZnSO4˙7H2O (0.1 mmol, 0.029 g), KSCN (0.2 mmol, 0.019 g) and water (10 mL) was placed in a 25 mL acid digestion bomb and heated at 160° for two days, then equably cooled to room temperature for three days. After washed by 5 ml water for twice, colorless block crystals of the title compound were obtained.

Refinement top

The H atoms (methyl) on the ligands were allowed to ride on their parent atoms with C—H distances of 0.96Å and Uiso(H)=1.5Ueq(C), and the rest C—H distances of 0.93Å and Uiso(H)=1.2Ueq(C). All of the non-hydrogen atoms were refined anisotropically.

Computing details top

Data collection: SMART (Bruker, 1998); cell refinement: SAINT (Bruker, 1999); data reduction: SAINT (Bruker, 1999); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. The ORTEP plot of the title complex, showing 30% probability displacement ellipsoids and the atom-numbering schemes. H atoms have been omitted for clarity.
Bis[4-(4-methoxyphenyl)-4H-1,2,4-triazole-κN1]bis(thiocyanato-κN)zinc(II) top
Crystal data top
[Zn(NCS)2(C9H9N3O)2]F000 = 1088
Mr = 531.91Dx = 1.473 Mg m−3
Monoclinic, P21/nMo Kα radiation
λ = 0.71073 Å
a = 7.812 (3) ÅCell parameters from 713 reflections
b = 17.111 (6) Åθ = 2.6–21.1º
c = 18.201 (6) ŵ = 1.23 mm−1
β = 99.726 (6)ºT = 293 (2) K
V = 2398.0 (15) Å3Block, colorless
Z = 40.16 × 0.12 × 0.10 mm
Data collection top
Bruker SMART CCD area-detector
diffractometer		4932 independent reflections
Radiation source: fine-focus sealed tube2127 reflections with I > 2σ(I)
Monochromator: graphiteRint = 0.121
T = 293(2) Kθmax = 26.5º
φ and O scansθmin = 1.6º
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)		h = −9→9
Tmin = 0.700, Tmax = 0.884k = −21→14
13731 measured reflectionsl = −22→18
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)] = 0.067H-atom parameters constrained
wR(F2) = 0.158  w = 1/[σ2(Fo2) + (0.0555P)2]
where P = (Fo2 + 2Fc2)/3
S = 0.97(Δ/σ)max = 0.001
4932 reflectionsΔρmax = 0.39 e Å−3
300 parametersΔρmin = −0.33 e Å−3
Primary atom site location: structure-invariant direct methodsExtinction correction: none
Crystal data top
[Zn(NCS)2(C9H9N3O)2]V = 2398.0 (15) Å3
Mr = 531.91Z = 4
Monoclinic, P21/nMo Kα
a = 7.812 (3) ŵ = 1.23 mm−1
b = 17.111 (6) ÅT = 293 (2) K
c = 18.201 (6) Å0.16 × 0.12 × 0.10 mm
β = 99.726 (6)º
Data collection top
Bruker SMART CCD area-detector
diffractometer		4932 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)		2127 reflections with I > 2σ(I)
Tmin = 0.700, Tmax = 0.884Rint = 0.121
13731 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.067300 parameters
wR(F2) = 0.158H-atom parameters constrained
S = 0.97Δρmax = 0.39 e Å−3
4932 reflectionsΔρmin = −0.33 e Å−3
Special details top

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
Zn10.36832 (9)1.10583 (5)0.05909 (4)0.0434 (3)
N10.2576 (6)1.0131 (3)0.0996 (3)0.0448 (14)
N20.2447 (7)1.0191 (4)0.1742 (3)0.0506 (15)
N30.1960 (6)0.8971 (4)0.1360 (3)0.0417 (13)
O10.0331 (6)0.5821 (3)0.1525 (2)0.0495 (12)
C10.2292 (7)0.9405 (4)0.0785 (3)0.0393 (16)
H10.23170.92160.03070.047*
C20.2083 (9)0.9483 (5)0.1939 (4)0.055 (2)
H20.19270.93460.24180.066*
C30.1559 (8)0.8147 (4)0.1374 (3)0.0364 (15)
C40.2212 (8)0.7714 (4)0.1995 (3)0.0436 (17)
H40.29490.79430.23910.052*
C50.1762 (8)0.6938 (4)0.2023 (3)0.0429 (17)
H50.21790.66460.24470.051*
C60.0701 (8)0.6587 (4)0.1433 (3)0.0383 (16)
C70.0088 (8)0.7023 (4)0.0807 (3)0.0462 (18)
H7−0.06100.67910.04000.055*
C80.0506 (8)0.7795 (4)0.0784 (3)0.0467 (18)
H80.00730.80890.03640.056*
C9−0.0628 (8)0.5413 (4)0.0903 (4)0.060 (2)
H9A−0.17520.56490.07670.090*
H9B−0.07620.48760.10350.090*
H9C−0.00140.54400.04890.090*
N40.6037 (6)1.1085 (3)0.1237 (3)0.0423 (13)
N50.7566 (7)1.1233 (4)0.0996 (3)0.0586 (18)
N60.8049 (6)1.1152 (3)0.2222 (3)0.0421 (14)
O21.1582 (6)1.1055 (3)0.5135 (2)0.0655 (14)
C100.6367 (8)1.1026 (4)0.1966 (3)0.0464 (16)
H100.55411.09120.22640.056*
C110.8730 (9)1.1266 (5)0.1594 (4)0.065 (2)
H110.99021.13590.15920.078*
C120.8924 (7)1.1139 (4)0.2991 (3)0.0385 (15)
C130.8962 (8)1.1802 (4)0.3406 (3)0.0474 (18)
H130.84101.22530.32020.057*
C140.9835 (8)1.1797 (4)0.4138 (4)0.0509 (18)
H140.98601.22460.44290.061*
C151.0660 (7)1.1130 (4)0.4433 (3)0.0436 (16)
C161.0579 (8)1.0461 (4)0.4010 (4)0.0505 (18)
H161.11141.00070.42140.061*
C170.9708 (8)1.0461 (4)0.3285 (4)0.0462 (18)
H170.96511.00090.29990.055*
C181.1740 (10)1.1722 (5)0.5603 (4)0.080 (3)
H18A1.22791.21380.53720.120*
H18B1.24401.15950.60740.120*
H18C1.06081.18840.56810.120*
S10.1894 (3)1.35631 (13)0.11268 (10)0.0765 (7)
N70.2543 (7)1.2013 (4)0.0874 (3)0.0527 (16)
C190.2283 (9)1.2663 (5)0.0986 (3)0.0445 (18)
S20.3020 (3)1.10216 (14)−0.19983 (10)0.0796 (7)
N80.3645 (7)1.0978 (4)−0.0466 (3)0.0619 (17)
C200.3357 (8)1.1003 (4)−0.1112 (4)0.0500 (17)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Zn10.0453 (4)0.0419 (5)0.0414 (4)0.0001 (5)0.0025 (3)0.0030 (4)
N10.045 (3)0.045 (4)0.045 (3)−0.001 (3)0.007 (3)−0.003 (3)
N20.070 (4)0.047 (4)0.036 (3)−0.003 (3)0.012 (3)−0.007 (3)
N30.051 (3)0.045 (4)0.029 (3)−0.001 (3)0.008 (2)−0.001 (3)
O10.062 (3)0.040 (3)0.046 (3)−0.008 (2)0.006 (2)0.001 (2)
C10.041 (4)0.043 (5)0.033 (4)0.000 (3)0.006 (3)−0.009 (3)
C20.073 (5)0.055 (6)0.039 (4)−0.002 (4)0.013 (4)−0.005 (4)
C30.041 (4)0.032 (4)0.037 (4)0.005 (3)0.010 (3)0.000 (3)
C40.047 (4)0.051 (5)0.031 (4)−0.007 (4)0.000 (3)−0.009 (3)
C50.044 (4)0.048 (5)0.036 (4)0.000 (3)0.004 (3)0.011 (3)
C60.033 (3)0.043 (5)0.041 (4)−0.002 (3)0.011 (3)−0.002 (3)
C70.052 (4)0.047 (5)0.035 (4)−0.014 (4)−0.007 (3)−0.007 (3)
C80.059 (4)0.043 (5)0.033 (4)−0.009 (4)−0.004 (3)0.012 (3)
C90.061 (5)0.050 (5)0.068 (5)−0.010 (4)0.006 (4)−0.019 (4)
N40.037 (3)0.052 (4)0.039 (3)0.003 (3)0.007 (2)0.008 (3)
N50.046 (3)0.087 (5)0.043 (3)−0.005 (3)0.009 (3)0.009 (3)
N60.037 (3)0.049 (4)0.039 (3)−0.003 (3)0.006 (3)0.000 (3)
O20.071 (3)0.070 (4)0.048 (3)0.003 (3)−0.012 (2)−0.011 (3)
C100.042 (4)0.052 (5)0.045 (4)−0.002 (4)0.007 (3)0.000 (4)
C110.045 (4)0.099 (7)0.052 (5)−0.012 (4)0.012 (4)0.006 (5)
C120.033 (3)0.046 (5)0.039 (4)0.001 (3)0.009 (3)−0.003 (4)
C130.048 (4)0.048 (5)0.046 (4)0.008 (4)0.008 (4)0.008 (4)
C140.058 (5)0.041 (5)0.053 (4)0.003 (4)0.006 (4)−0.009 (4)
C150.039 (3)0.049 (5)0.043 (4)−0.009 (4)0.006 (3)−0.006 (4)
C160.057 (4)0.040 (5)0.050 (4)0.013 (4)−0.004 (4)0.006 (4)
C170.045 (4)0.040 (5)0.053 (5)0.009 (4)0.008 (3)−0.011 (4)
C180.072 (5)0.100 (8)0.059 (5)0.011 (5)−0.010 (4)−0.018 (5)
S10.128 (2)0.0453 (13)0.0492 (12)0.0171 (13)−0.0041 (12)−0.0014 (10)
N70.060 (4)0.050 (4)0.045 (3)0.003 (3)−0.001 (3)−0.001 (3)
C190.053 (4)0.048 (5)0.030 (4)−0.005 (4)0.000 (3)0.005 (4)
S20.1267 (18)0.0637 (15)0.0433 (11)−0.0087 (14)−0.0001 (12)−0.0048 (11)
N80.065 (4)0.070 (5)0.048 (4)0.004 (4)0.003 (3)0.001 (4)
C200.054 (4)0.038 (4)0.055 (5)0.001 (4)0.001 (4)−0.001 (4)
Geometric parameters (Å, °) top
Zn1—N81.923 (6)N4—C101.312 (7)
Zn1—N71.970 (6)N4—N51.365 (6)
Zn1—N12.005 (5)N5—C111.296 (7)
Zn1—N42.009 (5)N6—C101.336 (7)
N1—C11.309 (8)N6—C111.354 (7)
N1—N21.382 (7)N6—C121.450 (7)
N2—C21.308 (8)O2—C151.363 (7)
N3—C11.344 (7)O2—C181.417 (8)
N3—C21.361 (8)C10—H100.9300
N3—C31.445 (8)C11—H110.9300
O1—C61.359 (7)C12—C131.360 (9)
O1—C91.430 (7)C12—C171.377 (8)
C1—H10.9300C13—C141.391 (8)
C2—H20.9300C13—H130.9300
C3—C81.375 (8)C14—C151.374 (9)
C3—C41.376 (8)C14—H140.9300
C4—C51.378 (9)C15—C161.375 (9)
C4—H40.9300C16—C171.379 (8)
C5—C61.379 (8)C16—H160.9300
C5—H50.9300C17—H170.9300
C6—C71.379 (8)C18—H18A0.9600
C7—C81.364 (9)C18—H18B0.9600
C7—H70.9300C18—H18C0.9600
C8—H80.9300S1—C191.598 (8)
C9—H9A0.9600N7—C191.155 (8)
C9—H9B0.9600S2—C201.591 (7)
C9—H9C0.9600N8—C201.160 (7)
N8—Zn1—N7112.9 (2)H9B—C9—H9C109.5
N8—Zn1—N1112.1 (2)C10—N4—N5107.9 (5)
N7—Zn1—N1108.5 (2)C10—N4—Zn1126.4 (4)
N8—Zn1—N4116.4 (2)N5—N4—Zn1125.5 (4)
N7—Zn1—N4103.8 (2)C11—N5—N4105.4 (5)
N1—Zn1—N4102.2 (2)C10—N6—C11103.4 (5)
C1—N1—N2108.8 (5)C10—N6—C12127.6 (5)
C1—N1—Zn1134.9 (5)C11—N6—C12129.0 (5)
N2—N1—Zn1114.2 (4)C15—O2—C18117.8 (6)
C2—N2—N1104.9 (5)N4—C10—N6110.7 (6)
C1—N3—C2104.5 (6)N4—C10—H10124.6
C1—N3—C3128.5 (5)N6—C10—H10124.6
C2—N3—C3127.0 (6)N5—C11—N6112.6 (6)
C6—O1—C9117.9 (5)N5—C11—H11123.7
N1—C1—N3109.9 (6)N6—C11—H11123.7
N1—C1—H1125.0C13—C12—C17121.3 (6)
N3—C1—H1125.0C13—C12—N6119.1 (6)
N2—C2—N3111.9 (6)C17—C12—N6119.7 (6)
N2—C2—H2124.0C12—C13—C14119.3 (6)
N3—C2—H2124.0C12—C13—H13120.4
C8—C3—C4119.7 (6)C14—C13—H13120.4
C8—C3—N3121.1 (6)C15—C14—C13120.0 (6)
C4—C3—N3119.2 (6)C15—C14—H14120.0
C3—C4—C5119.2 (6)C13—C14—H14120.0
C3—C4—H4120.4O2—C15—C14125.7 (7)
C5—C4—H4120.4O2—C15—C16114.3 (7)
C4—C5—C6121.0 (6)C14—C15—C16120.0 (6)
C4—C5—H5119.5C15—C16—C17120.2 (6)
C6—C5—H5119.5C15—C16—H16119.9
O1—C6—C7125.0 (6)C17—C16—H16119.9
O1—C6—C5115.9 (6)C12—C17—C16119.2 (6)
C7—C6—C5119.2 (6)C12—C17—H17120.4
C8—C7—C6119.9 (6)C16—C17—H17120.4
C8—C7—H7120.1O2—C18—H18A109.5
C6—C7—H7120.1O2—C18—H18B109.5
C7—C8—C3121.0 (6)H18A—C18—H18B109.5
C7—C8—H8119.5O2—C18—H18C109.5
C3—C8—H8119.5H18A—C18—H18C109.5
O1—C9—H9A109.5H18B—C18—H18C109.5
O1—C9—H9B109.5C19—N7—Zn1161.0 (6)
H9A—C9—H9B109.5N7—C19—S1178.8 (7)
O1—C9—H9C109.5C20—N8—Zn1168.1 (6)
H9A—C9—H9C109.5N8—C20—S2178.1 (7)
N8—Zn1—N1—C124.0 (7)N7—Zn1—N4—N5−108.5 (5)
N7—Zn1—N1—C1149.4 (6)N1—Zn1—N4—N5138.7 (5)
N4—Zn1—N1—C1−101.4 (6)C10—N4—N5—C11−0.9 (8)
N8—Zn1—N1—N2−175.1 (4)Zn1—N4—N5—C11174.2 (5)
N7—Zn1—N1—N2−49.7 (4)N5—N4—C10—N61.8 (8)
N4—Zn1—N1—N259.5 (4)Zn1—N4—C10—N6−173.2 (4)
C1—N1—N2—C2−0.1 (7)C11—N6—C10—N4−1.9 (8)
Zn1—N1—N2—C2−165.9 (4)C12—N6—C10—N4−180.0 (6)
N2—N1—C1—N30.5 (7)N4—N5—C11—N6−0.3 (9)
Zn1—N1—C1—N3162.2 (4)C10—N6—C11—N51.4 (9)
C2—N3—C1—N1−0.7 (7)C12—N6—C11—N5179.4 (6)
C3—N3—C1—N1179.2 (5)C10—N6—C12—C13−86.6 (8)
N1—N2—C2—N3−0.4 (7)C11—N6—C12—C1395.8 (8)
C1—N3—C2—N20.7 (7)C10—N6—C12—C1793.7 (8)
C3—N3—C2—N2−179.3 (6)C11—N6—C12—C17−83.8 (9)
C1—N3—C3—C8−39.2 (9)C17—C12—C13—C141.1 (10)
C2—N3—C3—C8140.7 (6)N6—C12—C13—C14−178.5 (5)
C1—N3—C3—C4142.3 (6)C12—C13—C14—C150.6 (10)
C2—N3—C3—C4−37.7 (9)C18—O2—C15—C14−1.2 (9)
C8—C3—C4—C5−1.6 (9)C18—O2—C15—C16179.4 (6)
N3—C3—C4—C5176.9 (5)C13—C14—C15—O2178.7 (6)
C3—C4—C5—C61.4 (9)C13—C14—C15—C16−1.9 (10)
C9—O1—C6—C76.3 (9)O2—C15—C16—C17−179.0 (6)
C9—O1—C6—C5−174.3 (5)C14—C15—C16—C171.6 (10)
C4—C5—C6—O1−179.4 (5)C13—C12—C17—C16−1.4 (10)
C4—C5—C6—C70.1 (9)N6—C12—C17—C16178.2 (5)
O1—C6—C7—C8178.2 (6)C15—C16—C17—C120.1 (10)
C5—C6—C7—C8−1.3 (9)N8—Zn1—N7—C19−71.6 (17)
C6—C7—C8—C31.1 (10)N1—Zn1—N7—C19163.5 (16)
C4—C3—C8—C70.4 (10)N4—Zn1—N7—C1955.3 (17)
N3—C3—C8—C7−178.0 (6)Zn1—N7—C19—S1105 (36)
N8—Zn1—N4—C10−169.6 (6)N7—Zn1—N8—C20−29 (3)
N7—Zn1—N4—C1065.7 (6)N1—Zn1—N8—C2093 (3)
N1—Zn1—N4—C10−47.1 (6)N4—Zn1—N8—C20−149 (3)
N8—Zn1—N4—N516.2 (6)Zn1—N8—C20—S2180 (100)
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
C1—H1···N5i0.932.513.438 (8)177
C7—H7···S1ii0.932.863.735 (6)158
C10—H10···O1iii0.932.423.265 (8)151
Symmetry codes: (i) −x+1, −y+2, −z; (ii) −x, −y+2, −z; (iii) −x+1/2, y+1/2, −z+1/2.
Table 1
Selected geometric parameters (Å, °) top
Zn1—N81.923 (6)N4—N51.365 (6)
Zn1—N71.970 (6)S1—C191.598 (8)
Zn1—N12.005 (5)N7—C191.155 (8)
Zn1—N42.009 (5)S2—C201.591 (7)
N1—N21.382 (7)N8—C201.160 (7)
N8—Zn1—N7112.9 (2)N7—Zn1—N4103.8 (2)
N8—Zn1—N1112.1 (2)N1—Zn1—N4102.2 (2)
N7—Zn1—N1108.5 (2)N7—C19—S1178.8 (7)
N8—Zn1—N4116.4 (2)N8—C20—S2178.1 (7)
Table 2
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
C1—H1···N5i0.932.513.438 (8)177
C7—H7···S1ii0.932.863.735 (6)158
C10—H10···O1iii0.932.423.265 (8)151
Symmetry codes: (i) −x+1, −y+2, −z; (ii) −x, −y+2, −z; (iii) −x+1/2, y+1/2, −z+1/2.
references
References top

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