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A novel neutral polymer, {[Co2(C7H3NO4)2(H2O)4]·2H2O}n, was hydro­thermally synthesized using pyridine-2,5-di­car­box­yl­ate (2,5-PDC2−) as the organic linker. It features a two-dimensional layer structure constructed from one-dimensional {[Co(2,5-PDC)2]2−}n chains interlinked by [Co(H2O)4]+ units. The two CoII cations occupy special positions, sitting on inversion centres. Each 2,5-PDC2− anion chelates to one CoII cation via the pyridine N atom and an O atom of the adjacent carboxyl­ate group, and links to two other CoII cations in a bridging mode via the O atoms of the other carboxyl­ate group. In this way, the 2,5-PDC2− ligand connects three neighbouring CoII centres to form a two-dimensional network. The two-dimensional undulating layers are linked by extensive hydrogen bonds to form a three-dimensional supra­molecular structure, with the uncoordinated solvent mol­ecules occupying the inter­lamellar region.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S2053229614003696/bg3170sup1.cif
Contains datablocks I, global

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2053229614003696/bg3170Isup2.hkl
Contains datablock I

CCDC reference: 987642

Introduction top

In recent years, considerable attention has been paid to the area of crystal engineering of metal–organic frameworks (MOFs) in view of their potential applications in adsorption, luminescence, magnetism and catalysis, as well as their intriguing structural diversity (Chen et al., 2011; Li et al., 1999; Mulfort & Hupp, 2007; Zhang et al., 2010). The rational choice of appropriate organic linkers is an important issue for the design and synthesis of predi­cta­ble MOFs. In addition, several important factors also influence the construction of molecular structures, such as the choice of metal ions, pH value, temperature and solvent (Qin et al., 2010). 2,5-Pyridinedi­carb­oxy­lic acid (2,5-H2PDC) contains both carboxyl­ate and pyridine N-donors, giving the ligand more coordination modes, and it is an efficient ligand for the construction of MOFs (Xie et al., 2007). Some polymeric structures of 2,5-PDC2- complexes with transition and lanthanide metals have been reported, in which the 2,5-PDC2- ligand shows not only a strong chelating ability but also a bridging tendency to form various structures (Chuang et al., 2007; Kumagai et al., 2008; Liang et al., 2000; Sun et al., 2012; Shi et al., 2011; Xia et al., 2013; Xu et al., 2004). In this paper, we present the title two-dimensional polymeric compound, viz. {[Co2(2,5-PDC)2(H2O)4].2H2O}n, (I), which is composed of one-dimensional {[Co(2,5-PDC)2]2-}n chains linked by [Co(H2O)4]2+ units.

Experimental top

Synthesis and crystallization top

A mixture of Co(NO3)2.6H2O (0.057 g, 0.2 mmol), 2,5-H2PDC (0.025 g, 0.15 mmol) and H2O–alcohol (5 ml, 2:3 v/v) was stirred for 30 min and then sealed in an 18 ml Teflon-lined autoclave. The mixture was heated for 5 d at 433 K under autogenous pressure and then slowly cooled to room temperature to give dark-red block-shaped crystals of (I) (yield ca 38%, based on Co). Analysis, calculated for C7H9CoNO7 (%): C 30.23, H 3.26, N 5.04; found: C 30.01, H 3.72, N 4.97. The IR spectrum in the range 400–4000 cm-1 was recorded on KBr pellets using an Avatar 360 FT–IR ESP (Nicolet).

Refinement top

Crystal data, data collection and structure refinement details are summarized in Table 1. The water H atoms were located in difference Fourier maps and refined with restrained O—H and H···H distances of 0.820 (1) and 1.35 (1) Å, respectively. The remaining H atoms were placed geometrically and refined as riding, with C—H = 0.93 Å and Uiso(H) = 1.2Ueq(C).

Results and discussion top

Single-crystal analysis reveals that the structure of (I) consists of an extended two-dimensional layer constructed by two different CoII centres bridged by 2,5-pyridinedi­carboxyl­ate (2,5-PDC2-) ligands. The asymmetric unit contains one 2,5-PDC2- ligand, two CoII cations lying on symmetry centres, two coordinated aqua groups and one solvent water molecule. As shown in Fig. 1, the coordination environment of atom Co1 is well described as a small distorted o­cta­hedron, in which the two 2,5-PDC2- ligands are bonded to the Co1 metal centre in a κ2N,O2 mode, forming the equatorial plane, and two carboxyl­ate O atoms from another two 2,5-PDC2- ligands occupy the axial sites. Atom Co2 is also six-coordinated in a distorted o­cta­hedral environment with a CoO6 core: two carboxyl­ate O atoms from two different 2,5-PDC2- ligands occupy the axial positions and four O atoms from the aqua ligands reside in the equatorial plane. Both atoms Co1 and Co2 occupy special positions, sitting on inversion centres at (0, 3/2, 1/2) and (1/2, 1/2, 0), respectively. The Co—N [2.113 (2) Å] and Co—O [2.310 (3)–2.499 (3) Å [not valid distances; please revise]] bond lengths (Table 2) are comparable with those of other 2,5-PDC2- chelated cobalt complexes (Shi et al., 2011; Humphrey & Wood, 2004; Tian et al., 2005; Xie et al., 2007; Wang et al., 2008).

The 2,5-PDC2- ligands are deprotonated in (I). Each 2,5-PDC2- anion chelates to one CoII cation via an N atom and an O atom of the adjacent carboxyl­ate group, and links to two other CoII cations via the other carboxyl­ate group in a bridging mode. In this way, each 2,5-PDC2- ligand joins three neighbouring CoII cations to form a two-dimensional network (Fig. 2). The structure of (I) could also be described as Co1 centres bridged by 2,5-PDC2- ligands to form a twisted-pair-like one-dimensional chain; these chains are further connected by Co2 centres to construct the layer structure.

The two-dimensional layers are further linked by intricate inter­layer hydrogen bonding to constitute the three-dimensional supra­molecular structure, as shown in Fig. 3. A hydrogen bond formed between atom O5 of one coordinated aqua molecule of Co2 in one layer and uncoordinated carboxyl­ate atom O1 in an adjacent layer serves mainly to extend the structural dimension. An intra­layer hydrogen bond between atom O6 of the other coordinated aqua group of Co2 and coordinated carboxyl­ate atom O3 of Co1 helps to stabilize the structure. It is worth noting that the isolated solvent molecule acts not only as a hydrogen-bond donor for two O atoms (O1 and O3) of two carboxyl­ate groups, but also as hydrogen-bond acceptor for two O atoms (O5 and O6) of two coordinated water molecules, to form four hydrogen bonds simultaneously. The uncoordinated water molecule serves as a space-filling unit here and contributes to the stabilization of the crystal structure by hydrogen bonding. Relevant bond lengths and angles are listed in Table 2.

The strong broad bands in the range 3100–3400 cm-1 in the IR spectrum of (I) (Fig. 4a) can be assigned to the O—H stretching vibration of the coordinated and solvent water molecules. The strong bands characteristic of carboxyl­ate groups at 1628 and 1584 cm-1 for anti­symmetric stretching, and at 1394 and 1362 cm-1 for symmetric stretching, can also be observed (Xie et al., 2007). The weak peak at 1666 cm-1 can be assigned to the vibration of the CN group of the pyridine ring.

The thermogravimetric (TG) curve of (I) displays three weight-loss steps (see Fig. 4b). The first weight loss of 20.0% occurs between 433 and 528 K and corresponds to the exclusion of three water molecules (calculated 19.4%). The second weight loss of 52.9% in the temperature range 623–728 K might be due to the release of the 2,5-PDC2- ligands (calculated 53.7%) and the final product (27.1%) should be assumed to be CoO (calculated 26.9%).

Related literature top

For related literature, see: Chen et al. (2011); Chuang et al. (2007); Humphrey & Wood (2004); Kumagai et al. (2008); Li et al. (1999); Liang et al. (2000); Mulfort & Hupp (2007); Qin et al. (2010); Shi et al. (2011); Sun et al. (2012); Tian et al. (2005); Wang et al. (2008); Xia et al. (2013); Xie et al. (2007); Xu et al. (2004); Zhang et al. (2010).

Computing details top

Data collection: CrystalClear (Rigaku, 2002); cell refinement: CrystalClear (Rigaku, 2002); data reduction: CrystalClear (Rigaku, 2002); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. The asymmetric unit of (I), shown with 50% probability displacement ellipsoids. H atoms bonded to C atoms have been omitted for clarity. [Symmetry code: (i) -x, -y + 3, -z + 1; (ii) -x, -y + 2, -z + 1; (iii) x, y + 1, z; (iv) -x + 1, -y + 1, -z; (v) x, y - 1, z.]
[Figure 2] Fig. 2. A perspective view of the two-dimensional layer structure in (I). All H atoms have been omitted for clarity. [Please provide a revised version with no Co1/Co2 labels]
[Figure 3] Fig. 3. A view of the packing of (I), with hydrogen-bonding interactions shown as dashed lines.
[Figure 4] Fig. 4. (a) The IR spectrum and (b) the TG curve of (I).
Poly[[tetraaquabis(µ3-pyridine-2,5-dicarboxylato-κ4N,O2:O5:O5')dicobalt(II)] dihydrate] top
Crystal data top
[Co2(C7H3NO4)2(H2O)4]·2H2OV = 463.99 (15) Å3
Mr = 556.16Z = 1
Triclinic, P1F(000) = 282
Hall symbol: -P 1Dx = 1.990 Mg m3
a = 7.3088 (19) ÅMo Kα radiation, λ = 0.71073 Å
b = 7.3343 (11) Åθ = 2.2–25.5°
c = 10.0658 (14) ŵ = 1.87 mm1
α = 87.759 (11)°T = 293 K
β = 71.037 (14)°Prism, red
γ = 66.135 (14)°0.30 × 0.20 × 0.15 mm
Data collection top
Rigaku Mercury CCD area-detector
diffractometer
1726 independent reflections
Radiation source: fine-focus sealed tube1451 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.021
Detector resolution: 14.6306 pixels mm-1θmax = 25.5°, θmin = 2.2°
ω scansh = 28
Absorption correction: multi-scan
(CrystalClear; Rigaku, 2002)
k = 88
Tmin = 0.565, Tmax = 1.000l = 1112
1898 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)] = 0.031H atoms treated by a mixture of independent and constrained refinement
wR(F2) = 0.085 w = 1/[σ2(Fo2) + (0.0525P)2 + 0.228P]
where P = (Fo2 + 2Fc2)/3
S = 1.02(Δ/σ)max < 0.001
1726 reflectionsΔρmax = 0.45 e Å3
167 parametersΔρmin = 0.50 e Å3
9 restraintsExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
Primary atom site location: structure-invariant direct methodsExtinction coefficient: 0.089 (6)
Crystal data top
[Co2(C7H3NO4)2(H2O)4]·2H2Oγ = 66.135 (14)°
Mr = 556.16V = 463.99 (15) Å3
Triclinic, P1Z = 1
a = 7.3088 (19) ÅMo Kα radiation
b = 7.3343 (11) ŵ = 1.87 mm1
c = 10.0658 (14) ÅT = 293 K
α = 87.759 (11)°0.30 × 0.20 × 0.15 mm
β = 71.037 (14)°
Data collection top
Rigaku Mercury CCD area-detector
diffractometer
1726 independent reflections
Absorption correction: multi-scan
(CrystalClear; Rigaku, 2002)
1451 reflections with I > 2σ(I)
Tmin = 0.565, Tmax = 1.000Rint = 0.021
1898 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0319 restraints
wR(F2) = 0.085H atoms treated by a mixture of independent and constrained refinement
S = 1.02Δρmax = 0.45 e Å3
1726 reflectionsΔρmin = 0.50 e Å3
167 parameters
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
N10.1713 (4)1.1859 (3)0.4846 (2)0.0145 (5)
Co10.00001.50000.50000.0153 (2)
Co20.50000.50000.00000.0166 (2)
O10.2349 (4)1.2645 (3)0.8085 (2)0.0297 (5)
O1W0.1790 (5)1.0990 (4)1.0537 (3)0.0437 (7)
H1A0.239 (7)1.093 (6)0.9685 (10)0.066*
H1B0.231 (7)0.984 (2)1.073 (4)0.066*
O20.0981 (3)1.4796 (3)0.6682 (2)0.0217 (5)
O30.2844 (3)0.5277 (3)0.3544 (2)0.0196 (5)
O40.3336 (3)0.7205 (3)0.1803 (2)0.0208 (5)
O50.2453 (4)0.5843 (4)0.0716 (3)0.0352 (6)
H5B0.139 (4)0.688 (3)0.062 (4)0.053*
H5C0.234 (6)0.500 (4)0.116 (4)0.053*
O60.4199 (4)0.2847 (3)0.1156 (2)0.0277 (5)
H6A0.333 (4)0.258 (6)0.095 (3)0.042*
H6B0.359 (5)0.335 (5)0.1980 (13)0.042*
C10.2165 (4)1.1321 (4)0.6043 (3)0.0147 (6)
C20.2884 (5)0.9358 (4)0.6342 (3)0.0179 (6)
H2A0.31940.90240.71690.021*
C30.3139 (4)0.7880 (4)0.5383 (3)0.0183 (6)
H3A0.35530.65540.55840.022*
C40.2770 (4)0.8409 (4)0.4128 (3)0.0141 (6)
C50.2067 (4)1.0424 (4)0.3894 (3)0.0148 (6)
H5A0.18361.07840.30470.018*
C60.1794 (5)1.3044 (4)0.7027 (3)0.0167 (6)
C70.3003 (4)0.6853 (4)0.3072 (3)0.0151 (6)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
N10.0176 (12)0.0112 (11)0.0144 (11)0.0059 (9)0.0052 (9)0.0018 (9)
Co10.0237 (3)0.0086 (3)0.0135 (3)0.0053 (2)0.0080 (2)0.00166 (19)
Co20.0220 (3)0.0132 (3)0.0142 (3)0.0080 (2)0.0045 (2)0.0012 (2)
O10.0497 (15)0.0215 (11)0.0256 (12)0.0119 (11)0.0263 (11)0.0046 (9)
O1W0.0667 (19)0.0252 (13)0.0282 (13)0.0118 (13)0.0117 (13)0.0034 (10)
O20.0357 (12)0.0117 (10)0.0214 (11)0.0084 (9)0.0159 (9)0.0015 (8)
O30.0278 (11)0.0108 (10)0.0180 (10)0.0087 (8)0.0039 (8)0.0004 (8)
O40.0302 (11)0.0147 (10)0.0146 (10)0.0079 (9)0.0056 (9)0.0002 (8)
O50.0289 (13)0.0247 (12)0.0519 (16)0.0028 (10)0.0226 (12)0.0103 (11)
O60.0393 (14)0.0246 (12)0.0182 (11)0.0177 (11)0.0023 (10)0.0025 (9)
C10.0138 (13)0.0150 (14)0.0148 (13)0.0052 (11)0.0050 (11)0.0009 (11)
C20.0222 (15)0.0159 (14)0.0153 (14)0.0049 (12)0.0100 (12)0.0030 (11)
C30.0209 (15)0.0106 (13)0.0219 (15)0.0042 (12)0.0086 (12)0.0030 (11)
C40.0127 (13)0.0117 (13)0.0141 (13)0.0039 (11)0.0008 (10)0.0021 (10)
C50.0159 (13)0.0133 (13)0.0131 (13)0.0054 (11)0.0034 (11)0.0023 (10)
C60.0218 (14)0.0161 (14)0.0159 (14)0.0100 (12)0.0082 (11)0.0026 (11)
C70.0142 (13)0.0119 (13)0.0162 (13)0.0033 (11)0.0038 (11)0.0025 (10)
Geometric parameters (Å, º) top
N1—C51.338 (3)O2—C61.267 (3)
N1—C11.353 (3)O3—C71.267 (3)
N1—Co12.113 (2)O3—Co1v2.202 (2)
Co1—O22.021 (2)O4—C71.257 (3)
Co1—O2i2.021 (2)O5—H5B0.8199 (11)
Co1—N1i2.113 (2)O5—H5C0.8200 (11)
Co1—O3ii2.202 (2)O6—H6A0.8200 (11)
Co1—O3iii2.202 (2)O6—H6B0.8199 (11)
Co2—O5iv2.067 (2)C1—C21.377 (4)
Co2—O52.067 (2)C1—C61.516 (4)
Co2—O62.086 (2)C2—C31.393 (4)
Co2—O6iv2.086 (2)C2—H2A0.9300
Co2—O42.1431 (19)C3—C41.385 (4)
Co2—O4iv2.1431 (19)C3—H3A0.9300
O1—C61.243 (3)C4—C51.393 (4)
O1W—H1A0.8200 (11)C4—C71.510 (4)
O1W—H1B0.8200 (11)C5—H5A0.9300
C5—N1—C1118.8 (2)O4—Co2—O4iv180.00 (8)
C5—N1—Co1129.86 (18)H1A—O1W—H1B104.9 (12)
C1—N1—Co1110.38 (17)C6—O2—Co1115.85 (17)
O2—Co1—O2i180.000 (1)C7—O3—Co1v127.77 (18)
O2—Co1—N180.06 (8)C7—O4—Co2125.86 (17)
O2i—Co1—N199.94 (8)Co2—O5—H5B134 (2)
O2—Co1—N1i99.94 (8)Co2—O5—H5C120 (2)
O2i—Co1—N1i80.06 (8)H5B—O5—H5C106.0 (12)
N1—Co1—N1i180.000 (1)Co2—O6—H6A114 (3)
O2—Co1—O3ii86.62 (8)Co2—O6—H6B106 (3)
O2i—Co1—O3ii93.38 (8)H6A—O6—H6B105.0 (12)
N1—Co1—O3ii89.47 (8)N1—C1—C2122.2 (2)
N1i—Co1—O3ii90.53 (8)N1—C1—C6114.8 (2)
O2—Co1—O3iii93.38 (8)C2—C1—C6122.9 (2)
O2i—Co1—O3iii86.62 (8)C1—C2—C3118.8 (3)
N1—Co1—O3iii90.53 (8)C1—C2—H2A120.6
N1i—Co1—O3iii89.47 (8)C3—C2—H2A120.6
O3ii—Co1—O3iii180.000 (1)C4—C3—C2119.2 (3)
O5iv—Co2—O5180.0C4—C3—H3A120.4
O5iv—Co2—O687.66 (10)C2—C3—H3A120.4
O5—Co2—O692.34 (10)C3—C4—C5118.6 (2)
O5iv—Co2—O6iv92.34 (10)C3—C4—C7120.7 (2)
O5—Co2—O6iv87.66 (10)C5—C4—C7120.6 (2)
O6—Co2—O6iv180.00 (11)N1—C5—C4122.2 (2)
O5iv—Co2—O485.06 (9)N1—C5—H5A118.9
O5—Co2—O494.94 (9)C4—C5—H5A118.9
O6—Co2—O492.31 (8)O1—C6—O2124.8 (3)
O6iv—Co2—O487.69 (8)O1—C6—C1118.3 (2)
O5iv—Co2—O4iv94.94 (9)O2—C6—C1116.9 (2)
O5—Co2—O4iv85.06 (9)O4—C7—O3124.9 (2)
O6—Co2—O4iv87.69 (8)O4—C7—C4118.3 (2)
O6iv—Co2—O4iv92.31 (8)O3—C7—C4116.8 (2)
Symmetry codes: (i) x, y+3, z+1; (ii) x, y+2, z+1; (iii) x, y+1, z; (iv) x+1, y+1, z; (v) x, y1, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1W—H1A···O10.82 (1)2.00 (2)2.691 (3)141 (4)
O1W—H1B···O4vi0.82 (1)2.16 (1)2.954 (3)165 (4)
O5—H5B···O1Wii0.82 (1)2.19 (1)2.981 (4)163 (3)
O5—H5C···O1vii0.82 (1)1.91 (1)2.719 (3)167 (4)
O6—H6A···O1Wvii0.82 (1)2.05 (1)2.840 (4)161 (4)
O6—H6B···O30.82 (1)1.94 (2)2.701 (3)154 (3)
Symmetry codes: (ii) x, y+2, z+1; (vi) x, y, z+1; (vii) x, y1, z1.

Experimental details

Crystal data
Chemical formula[Co2(C7H3NO4)2(H2O)4]·2H2O
Mr556.16
Crystal system, space groupTriclinic, P1
Temperature (K)293
a, b, c (Å)7.3088 (19), 7.3343 (11), 10.0658 (14)
α, β, γ (°)87.759 (11), 71.037 (14), 66.135 (14)
V3)463.99 (15)
Z1
Radiation typeMo Kα
µ (mm1)1.87
Crystal size (mm)0.30 × 0.20 × 0.15
Data collection
DiffractometerRigaku Mercury CCD area-detector
diffractometer
Absorption correctionMulti-scan
(CrystalClear; Rigaku, 2002)
Tmin, Tmax0.565, 1.000
No. of measured, independent and
observed [I > 2σ(I)] reflections
1898, 1726, 1451
Rint0.021
(sin θ/λ)max1)0.606
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.031, 0.085, 1.02
No. of reflections1726
No. of parameters167
No. of restraints9
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.45, 0.50

Computer programs: CrystalClear (Rigaku, 2002), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), DIAMOND (Brandenburg, 1999).

Selected geometric parameters (Å, º) top
Co1—O22.021 (2)Co2—O52.067 (2)
Co1—N1i2.113 (2)Co2—O62.086 (2)
Co1—O3ii2.202 (2)Co2—O42.1431 (19)
O2—Co1—N180.06 (8)O5—Co2—O692.34 (10)
O2—Co1—O3ii86.62 (8)O5—Co2—O494.94 (9)
N1—Co1—O3ii89.47 (8)O6—Co2—O492.31 (8)
Symmetry codes: (i) x, y+3, z+1; (ii) x, y+2, z+1.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1W—H1A···O10.8200 (11)2.00 (2)2.691 (3)141 (4)
O1W—H1B···O4iii0.8200 (11)2.155 (10)2.954 (3)165 (4)
O5—H5B···O1Wii0.8199 (11)2.189 (11)2.981 (4)163 (3)
O5—H5C···O1iv0.8200 (11)1.914 (9)2.719 (3)167 (4)
O6—H6A···O1Wiv0.8200 (11)2.052 (14)2.840 (4)161 (4)
O6—H6B···O30.8199 (11)1.942 (15)2.701 (3)154 (3)
Symmetry codes: (ii) x, y+2, z+1; (iii) x, y, z+1; (iv) x, y1, z1.
 

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