A fivefold interpenetrating diamond-oid three-dimensional metal–organicframework constructed from benzene-1,4-diacetic acid and flexible triazolederivatives: poly[[(l2-benzene-1,4-di-acetato-j2O:O){l2-1,4-bis[(1H-1,2,4-triazol-1-yl)methyl]benzene-j2N4:N4000}-zinc(II)] monohydrate]

Hong Shen

City Vocational College of Jiangsu, Jiangsu Open University, Nanjing 210036,

People’s Republic of China

Correspondence e-mail: shnju@hotmail.com

Received 8 September 2013

Accepted 9 December 2013

In the title mixed-ligand metal–organic polymeric compound,

{[Zn(C10H8O4)(C12H14N6)]�H2O}n, the asymmetric unit con-

tains a divalent ZnII cation lying on a twofold axis, one half of

a fully deprotonated benzene-1,4-diacetate (PBEA) ligand,

one half of a 1,4-bis[(1H-1,2,4-triazol-1-yl)methyl]benzene

(BTX) ligand and a water molecule, also lying on a twofold

axis. Each ZnII centre is surrounded by two O-donor atoms

from monodentate carboxylate groups belonging to two

different PBEA2� ligands and by two triazole N-donor atoms

from two different BTX ligands. Single-crystal X-ray diffrac-

tion analysis revealed that the compound has a fivefold

interpenetrating diamondoid three-dimensional metal–

organic framework.

Keywords: crystal structure; metal–organic framework; MOFs;fivefold interpenetrating diamondoid framework; benzene-1,4-diacetic acid; 1,4-bis[(1H-1,2,4-triazol-1-yl)methyl]benzene.

1. Introduction

Considerable effort has been focused on the rational design

and synthesis of coordination polymers and this field remains

intensely active, not only owing to the fascinating structural

diversity of these materials but also because of their potential

applications in many fields, such as ion-exchange compounds,

heterogeneous catalysts, optical devices and magnets, and in

gas storage (An et al., 2010; Han & Goddard, 2007; Krishna,

2012; Laguna et al., 2010; Wu et al., 2005). It is well known that

the structure of a coordination polymer depends on many

factors in the self-assembly process, such as the geometry of

the central metal ions, the organic ligands, the counter-ions,

the solvents, the temperature, the reaction conditions and so

on (Cook et al., 2013; Paz et al., 2012). Among these para-

meters, the nature of the organic ligands is a key factor that

influences the network structure of a coordination polymer. In

this regard, flexible ligands coordinating to metal centres may

bend or rotate to adopt different conformations, and often

form novel coordination polymers.

Flexible bidentate N-donor ligands, such as bis(imidazole)

and bis(triazole) ligands, are widely used for constructing

coordination polymers because such flexible ligands can rotate

freely to meet the requirements of the coordination geometry

of the metal atom on the basis of their –CH2– spacer (Meng et

al., 2004; Peng et al., 2006; Wang, Tao et al., 2012; Wang, Tao et

al., 2013; Yu et al., 2011). Taking these factors into consid-

eration, we explored the self-assembly of ZnII, benzene-1,4-

diacetic acid (H2PBEA) and 1,4-bis[(1H-1,2,4-triazol-1-yl)-

methyl]benzene (BTX) under hydrothermal conditions, and

obtained the title novel three-dimensional coordination

polymer, {[Zn(PBEA)(BTX)]�H2O}n, (I), the crystal structure

of which is reported herein.

2. Experimental

2.1. Synthesis and crystallization

A mixture of Zn(NO3)2�6H2O (0.0297 g, 0.100 mmol),

H2PBEA (0.0390 g, 0.200 mmol), BTX (0.0240 g, 0.100 mmol)

and NaOH (0.00800 g, 0.200 mmol) in H2O (10 ml) was sealed

in a 16 ml Teflon-lined stainless steel container and heated at

393 K for 72 h. After cooling to room temperature, colourless

block-shaped crystals of (I) were collected by filtration and

washed several times with water and ethanol (yield 37.1%,

based on BTX). Elemental analysis for C22H22N6O5Zn:

C 51.22, H 4.30, N 16.29%; found: C 51.32, H 4.31, N 16.31%.

2.2. Refinement

Crystal data, data collection and structure refinement

details are summarized in Table 1. C-bound H atoms were

placed in calculated positions and treated using a riding-model

approximation, with C—H = 0.93 (triazole and benzene) or

0.97 A (methylene) and Uiso(H) = 1.2Ueq(C). Water H atoms

were located in difference Fourier maps and refined as riding,

with Uiso(H) = 1.2Ueq(O).

metal-organic compounds

28 # 2014 International Union of Crystallography doi:10.1107/S2053229613033305 Acta Cryst. (2014). C70, 28–30

Acta Crystallographica Section C

Structural Chemistry

ISSN 2053-2296

3. Results and discussion

X-ray crystallography reveals that (I) crystallizes in the

centrosymmetric monoclinic space group C2/c, with an

asymmetric unit consisting of a divalent ZnII cation lying on a

twofold axis, one half of a centrosymmetric fully deprotonated

PBEA2� ligand, one half of a centrosymmetric BTX ligand

and a water molecule, also lying on a twofold axis. As shown in

Fig, 1, each ZnII centre is surrounded by two O-donor atoms

from monodentate carboxylate groups belonging to two

different PBEA2� ligands [Zn1—O1 = 1.9340 (18) A] and two

triazole N-donor atoms from two different BTX ligands

[Zn1—N1 = 2.021 (2) A]. The distortion of the tetrahedron

can be indicated by the calculated value of the �4 parameter;

for a perfect square-planar geometry, �4 = 0, and a perfect

tetrahedral geometry is described when �4 = 1 (Yang et al.,

2007). In (I), the calculated value of the �4 parameter for atom

Zn1 is 0.84, showing that the tetrahedral geometry is not

perfect but distorted. The Zn—N and Zn—O bond lengths are

comparable with those reported for other zinc compounds

(Wang, Kan et al., 2013; Zhu et al., 2013), and the bond angles

around the Zn atoms are in the range 98.44 (11)–121.04 (8)�.

In (I), the BTX ligand exhibits an anti conformation, with a

dihedral angle between the planes of the triazole and benzene

rings of 99.1 (2)�. The Zn1 atoms are connected into zigzag

{[Zn(BTX)]2+}n cationic chains by BTX ligands (Fig. 2)

arranged parallel to the [201] crystal direction, with a Zn� � �Zn

contact distance through the BTX ligands of 14.6438 (18) A.

As for the PBEA2� ligand, the dihedral angle between the

symmetry-unique carboxylate group and its corresponding

benzene ring is 95.3 (1)�. Furthermore, adjacent {[Zn-

(BTX)]2+}n cationic chains are conjoined into a three-dimen-

sional [Zn(PBEA)(BTX)]n coordination polymer by bridging

PBEA2� ligands that bridge pairs of Zn atoms with a Zn� � �Zn

contact distance of 13.2341 (18) A (Fig. 3).

A further insight into the nature of this intricate framework

can be obtained using topological analysis. Topologically, if the

Zn1 atoms can be considered as 4-connected nodes, and the

BTX ligands and PBEA anions are viewed as linkers, the

three-dimensional framework of (I) can be simplified to a

three-dimensional diamondoid topological network with a

total Schlafli symbol of 66 (Zhang et al., 2013). In (I), the

Zn� � �Zn� � �Zn angles range from 76.8 to 158.1�, representing a

significant distortion from the ideal tetrahedral angle of 109.5�

found in diamond. There is a large hexagonal channel in (I)

which allows each net to be penetrated by other four inde-

pendent nets, generating a fivefold interpenetrating three-

dimensional architecture (Fig. 4). To the best of our knowl-

metal-organic compounds

Acta Cryst. (2014). C70, 28–30 Hong Shen � [Zn(C10H8O4)(C12H14N6)]�H2O 29

Table 1Experimental details.

Crystal dataChemical formula [Zn(C10H8O4)(C12H14N6)]�H2OMr 515.85Crystal system, space group Monoclinic, C2/cTemperature (K) 296a, b, c (A) 14.824 (2), 17.755 (2), 9.8630 (14)� (�) 118.615 (2)V (A3) 2278.9 (5)Z 4Radiation type Mo K�� (mm�1) 1.13Crystal size (mm) 0.21 � 0.19 � 0.17

Data collectionDiffractometer Bruker SMART CCD area-detector

diffractometerAbsorption correction Multi-scan (SADABS; Bruker, 2000)Tmin, Tmax 0.790, 0.826No. of measured, independent and

observed [I > 2�(I)] reflections8145, 2103, 1740

Rint 0.044(sin �/�)max (A�1) 0.606

RefinementR[F 2 > 2�(F 2)], wR(F 2), S 0.036, 0.082, 1.06No. of reflections 2103No. of parameters 155H-atom treatment H-atom parameters constrained�max, �min (e A�3) 0.32, �0.32

Computer programs: SMART (Bruker, 2000), SAINT (Bruker, 2000), SHELXTL(Sheldrick, 2008), SHELXL97 (Sheldrick, 2008) and DIAMOND (Brandenburg,1999).

Figure 1The asymmetric unit of (I), showing the atom-numbering scheme.Displacement ellipsoids are drawn at the 30% probablity level.[Symmetry code: (i) �x, y, �z + 1

2.]

Figure 2A view of the zigzag {[Zn(BTX)]2+}n cationic chain in (I).

edge, a fivefold interpenetrating diamondoid MOF with mixed

organic ligands is relatively rare (Fu et al., 2002; Kongshaug &

Fjellvag, 2002; Li et al., 2004; Wei et al., 2012; Wang, Xu et al.,

2012). It is noteworthy that the interpenetration mode belongs

to class Ia, fivefold interpenetration, and the translational

degree of interpenetration (Zt) of the structure is 5, which

means that the overall network structure can be categorized

into five topologically equivalent three-dimensional subsets

related by the translation vector [001]. The distance between

interpenetrating subsets is 9.8630 (14) A.

An analysis with PLATON (Spek, 2009) suggests that the

unligated water molecules occupy a solvent-accessible inci-

pient space comprising 2.9% of the unit-cell volume. In

addition, there are intermolecular hydrogen bonds between

the water molecules and PBEA2� anions (Table 2) which

further stabilize the three-dimensional architecture of (I).

Supplementary data for this paper are available from the IUCr electronicarchives (Reference: QS3033). Services for accessing these data aredescribed at the back of the journal.

References

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R.-Q. (2002). Eur. J. Inorg. Chem. pp. 2730–2735.Han, S. S. & Goddard, W. A. (2007). J. Am. Chem. Soc. 129, 8422–8423.Kongshaug, K. O. & Fjellvag, H. J. (2002). J. Solid State Chem. 166, 213–218.Krishna, R. (2012). Chem. Soc. Rev. 41, 3099–3118.Laguna, A., Lasanta, T., Lopezde-Luzuriaga, J. M., Monge, M., Naumov, P. &

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Des. 6, 994–998.Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122.Spek, A. L. (2009). Acta Cryst. D65, 148–155.Wang, W., Kan, W.-Q., Yang, J. & Ma, J.-F. (2013). CrystEngComm, 15, 3824–

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metal-organic compounds

30 Hong Shen � [Zn(C10H8O4)(C12H14N6)]�H2O Acta Cryst. (2014). C70, 28–30

Figure 3A view of the three-dimensional framework of (I).

Figure 4A schematic representation of the fivefold interpenetrating three-dimensional diamondoid framework of (I).

Table 2Hydrogen-bond geometry (A, �).

D—H� � �A D—H H� � �A D� � �A D—H� � �A

C2—H2� � �O3i 0.93 2.54 3.428 (3) 159C1—H1� � �N2ii 0.93 2.59 3.301 (3) 134C1—H1� � �O2iii 0.93 2.56 3.270 (3) 134O3—H3D� � �O2i 0.85 2.07 2.911 (3) 170O3—H3C� � �O2iv 0.85 2.07 2.911 (3) 170

Symmetry codes: (i) �xþ 12;�yþ 1

2;�z; (ii) x;�yþ 1; zþ 12; (iii) �x; y;�zþ 1

2; (iv)x þ 1

2;�yþ 12; zþ 1

2.

supplementary materials

sup-1Acta Cryst. (2014). C70, 28-30

supplementary materials

Acta Cryst. (2014). C70, 28-30 [doi:10.1107/S2053229613033305]

A fivefold interpenetrating diamondoid three-dimensional metal–organic

framework constructed from benzene-1,4-diacetic acid and flexible triazole

derivatives: poly[[(µ2-benzene-1,4-diacetato-κ2O:O){µ2-1,4-bis[(1H-1,2,4-

triazol-1-yl)methyl]benzene-κ2N4:N4′}zinc(II)] monohydrate]

Hong Shen

Computing details

Data collection: SMART (Bruker, 2000); cell refinement: SAINT (Bruker, 2000); data reduction: SAINT (Bruker, 2000);

program(s) used to solve structure: SHELXTL (Sheldrick, 2008); program(s) used to refine structure: SHELXL97

(Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for

publication: SHELXTL (Sheldrick, 2008).

Poly[[(µ2-benzene-1,4-diacetato-κ2O:O){µ2-1,4-bis[(1H-1,2,4-triazol-1-yl)methyl]benzene-κ2N4:N4′}zinc(II)]

monohydrate]

Crystal data

[Zn(C10H8O4)(C12H14N6)]·H2OMr = 515.85Monoclinic, C2/cHall symbol: -C 2yca = 14.824 (2) Åb = 17.755 (2) Åc = 9.8630 (14) Åβ = 118.615 (2)°V = 2278.9 (5) Å3

Z = 4

F(000) = 1064Dx = 1.503 Mg m−3

Mo Kα radiation, λ = 0.71073 ÅCell parameters from 2832 reflectionsθ = 2.3–22.8°µ = 1.13 mm−1

T = 296 KBlock, colourless0.21 × 0.19 × 0.17 mm

Data collection

Bruker SMART CCD area-detector diffractometer

Radiation source: fine-focus sealed tubeGraphite monochromatorφ and ω scansAbsorption correction: multi-scan

(SADABS; Bruker, 2000)Tmin = 0.790, Tmax = 0.826

8145 measured reflections2103 independent reflections1740 reflections with I > 2σ(I)Rint = 0.044θmax = 25.5°, θmin = 1.9°h = −17→17k = −21→21l = −11→11

supplementary materials

sup-2Acta Cryst. (2014). C70, 28-30

Refinement

Refinement on F2

Least-squares matrix: fullR[F2 > 2σ(F2)] = 0.036wR(F2) = 0.082S = 1.062103 reflections155 parameters0 restraintsPrimary atom site location: structure-invariant

direct methods

Secondary atom site location: difference Fourier map

Hydrogen site location: inferred from neighbouring sites

H-atom parameters constrainedw = 1/[σ2(Fo

2) + (0.0359P)2 + 1.0515P] where P = (Fo

2 + 2Fc2)/3

(Δ/σ)max < 0.001Δρmax = 0.32 e Å−3

Δρmin = −0.32 e Å−3

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

x y z Uiso*/Ueq Occ. (<1)

Zn1 0.0000 0.32102 (2) 0.2500 0.02966 (15)O1 −0.06448 (16) 0.24987 (11) 0.0819 (2) 0.0517 (5)O2 −0.09822 (18) 0.33641 (12) −0.0958 (2) 0.0601 (6)N1 0.10571 (15) 0.39532 (12) 0.2580 (2) 0.0326 (5)N2 0.19119 (18) 0.47834 (14) 0.1929 (3) 0.0478 (6)N3 0.21812 (16) 0.48481 (13) 0.3447 (3) 0.0395 (6)C2 0.1228 (2) 0.42483 (17) 0.1454 (3) 0.0433 (7)H2 0.0887 0.4083 0.0434 0.052*C1 0.16708 (19) 0.43533 (15) 0.3809 (3) 0.0367 (6)H1 0.1733 0.4294 0.4787 0.044*C3 0.2945 (2) 0.54076 (18) 0.4423 (4) 0.0547 (9)H3A 0.2938 0.5449 0.5399 0.066*H3B 0.2764 0.5895 0.3919 0.066*C4 0.4012 (2) 0.51942 (18) 0.4725 (3) 0.0454 (7)C5 0.4475 (2) 0.45430 (19) 0.5490 (4) 0.0530 (8)H5 0.4123 0.4226 0.5827 0.064*C6 0.4547 (2) 0.56539 (18) 0.4227 (4) 0.0532 (8)H6 0.4249 0.6097 0.3699 0.064*C7 −0.1040 (2) 0.27247 (17) −0.0576 (3) 0.0369 (6)C8 −0.1606 (3) 0.21106 (19) −0.1745 (3) 0.0645 (10)H8A −0.1132 0.1696 −0.1550 0.077*H8B −0.2154 0.1925 −0.1563 0.077*C9 −0.2066 (2) 0.23223 (15) −0.3426 (3) 0.0420 (7)C11 −0.1488 (2) 0.23107 (18) −0.4178 (3) 0.0529 (8)H11 −0.0796 0.2182 −0.3631 0.063*C10 −0.3087 (2) 0.25139 (16) −0.4278 (3) 0.0498 (8)

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sup-3Acta Cryst. (2014). C70, 28-30

H10 −0.3498 0.2525 −0.3801 0.060*O3 0.5000 0.0855 (2) 0.2500 0.0775 (10)H3D 0.5265 0.1135 0.2084 0.093* 0.50H3C 0.4736 0.1135 0.2916 0.093* 0.50

Atomic displacement parameters (Å2)

U11 U22 U33 U12 U13 U23

Zn1 0.0293 (2) 0.0326 (3) 0.0232 (2) 0.000 0.00951 (17) 0.000O1 0.0675 (14) 0.0458 (13) 0.0222 (10) −0.0056 (10) 0.0057 (10) −0.0037 (9)O2 0.0936 (17) 0.0429 (14) 0.0381 (12) −0.0182 (12) 0.0269 (12) −0.0068 (10)N1 0.0310 (11) 0.0386 (13) 0.0279 (12) −0.0015 (10) 0.0139 (10) −0.0022 (10)N2 0.0535 (15) 0.0544 (17) 0.0399 (15) −0.0091 (13) 0.0259 (12) 0.0022 (12)N3 0.0369 (12) 0.0408 (14) 0.0457 (14) −0.0101 (10) 0.0238 (11) −0.0096 (11)C2 0.0406 (16) 0.055 (2) 0.0315 (16) −0.0092 (14) 0.0153 (13) −0.0012 (14)C1 0.0355 (14) 0.0450 (18) 0.0330 (15) −0.0053 (13) 0.0191 (13) −0.0069 (13)C3 0.0524 (19) 0.050 (2) 0.070 (2) −0.0226 (16) 0.0360 (17) −0.0253 (17)C4 0.0433 (16) 0.050 (2) 0.0477 (18) −0.0225 (15) 0.0254 (15) −0.0203 (15)C5 0.0524 (19) 0.061 (2) 0.057 (2) −0.0250 (17) 0.0350 (17) −0.0084 (17)C6 0.0561 (19) 0.050 (2) 0.057 (2) −0.0165 (16) 0.0293 (17) −0.0068 (16)C7 0.0376 (15) 0.0403 (18) 0.0267 (15) −0.0064 (13) 0.0105 (12) −0.0030 (13)C8 0.093 (3) 0.050 (2) 0.0246 (17) −0.0244 (19) 0.0072 (17) 0.0000 (15)C9 0.0549 (18) 0.0326 (16) 0.0217 (14) −0.0159 (14) 0.0049 (13) −0.0049 (12)C11 0.0375 (16) 0.061 (2) 0.0406 (18) −0.0019 (15) 0.0030 (14) 0.0038 (16)C10 0.056 (2) 0.053 (2) 0.0391 (18) −0.0070 (16) 0.0220 (16) −0.0035 (14)O3 0.112 (3) 0.073 (2) 0.067 (2) 0.000 0.057 (2) 0.000

Geometric parameters (Å, º)

Zn1—O1 1.9340 (18) C4—C6 1.382 (4)Zn1—O1i 1.9340 (18) C5—C6ii 1.383 (4)Zn1—N1i 2.021 (2) C5—H5 0.9300Zn1—N1 2.021 (2) C6—C5ii 1.383 (4)O1—C7 1.275 (3) C6—H6 0.9300O2—C7 1.212 (3) C7—C8 1.515 (4)N1—C1 1.321 (3) C8—C9 1.507 (4)N1—C2 1.357 (3) C8—H8A 0.9700N2—C2 1.302 (3) C8—H8B 0.9700N2—N3 1.357 (3) C9—C11 1.376 (4)N3—C1 1.315 (3) C9—C10 1.377 (4)N3—C3 1.467 (3) C11—C10iii 1.377 (4)C2—H2 0.9300 C11—H11 0.9300C1—H1 0.9300 C10—C11iii 1.377 (4)C3—C4 1.511 (4) C10—H10 0.9300C3—H3A 0.9700 O3—H3D 0.8499C3—H3B 0.9700 O3—H3C 0.8499C4—C5 1.372 (4)

O1—Zn1—O1i 98.44 (11) C5—C4—C3 121.4 (3)

supplementary materials

sup-4Acta Cryst. (2014). C70, 28-30

O1—Zn1—N1i 109.71 (8) C6—C4—C3 120.5 (3)O1i—Zn1—N1i 121.04 (8) C4—C5—C6ii 121.6 (3)O1—Zn1—N1 121.04 (8) C4—C5—H5 119.2O1i—Zn1—N1 109.71 (8) C6ii—C5—H5 119.2N1i—Zn1—N1 98.49 (12) C4—C6—C5ii 120.2 (3)C7—O1—Zn1 120.17 (18) C4—C6—H6 119.9C1—N1—C2 103.1 (2) C5ii—C6—H6 119.9C1—N1—Zn1 124.57 (17) O2—C7—O1 124.5 (3)C2—N1—Zn1 131.69 (18) O2—C7—C8 122.2 (2)C2—N2—N3 103.1 (2) O1—C7—C8 113.3 (2)C1—N3—N2 109.8 (2) C9—C8—C7 116.9 (3)C1—N3—C3 129.6 (2) C9—C8—H8A 108.1N2—N3—C3 120.6 (2) C7—C8—H8A 108.1N2—C2—N1 113.9 (2) C9—C8—H8B 108.1N2—C2—H2 123.1 C7—C8—H8B 108.1N1—C2—H2 123.1 H8A—C8—H8B 107.3N3—C1—N1 110.1 (2) C11—C9—C10 117.5 (3)N3—C1—H1 125.0 C11—C9—C8 121.2 (3)N1—C1—H1 125.0 C10—C9—C8 121.2 (3)N3—C3—C4 111.4 (2) C9—C11—C10iii 121.3 (3)N3—C3—H3A 109.3 C9—C11—H11 119.3C4—C3—H3A 109.3 C10iii—C11—H11 119.3N3—C3—H3B 109.3 C11iii—C10—C9 121.2 (3)C4—C3—H3B 109.3 C11iii—C10—H10 119.4H3A—C3—H3B 108.0 C9—C10—H10 119.4C5—C4—C6 118.2 (3) H3D—O3—H3C 108.6

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

Hydrogen-bond geometry (Å, º)

D—H···A D—H H···A D···A D—H···A

C2—H2···O3iv 0.93 2.54 3.428 (3) 159C1—H1···N2v 0.93 2.59 3.301 (3) 134C1—H1···O2i 0.93 2.56 3.270 (3) 134O3—H3D···O2iv 0.85 2.07 2.911 (3) 170O3—H3C···O2vi 0.85 2.07 2.911 (3) 170

Symmetry codes: (i) −x, y, −z+1/2; (iv) −x+1/2, −y+1/2, −z; (v) x, −y+1, z+1/2; (vi) x+1/2, −y+1/2, z+1/2.