catena-Poly[[bis­[3-(1H-imidazol-1-yl)-1-phenyl­propan-1-one-κN3]nickel(II)]-μ-oxalato-κ4O1,O2:O1′,O2′]

Guo, J.-H.

doi:10.1107/S1600536811049646

metal-organic compounds

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ISSN: 2056-9890

Volume 67| Part 12| December 2011| Page m1832

https://doi.org/10.1107/S1600536811049646

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catena-Poly[[bis[3-(1H-imidazol-1-yl)-1-phenylpropan-1-one-κN³]nickel(II)]-μ-oxalato-κ⁴O¹,O²:O^1′,O^2′]

Jian-Hua Guo ^a ^*

^aTianjin Key Laboratory of Structure and Performance for Functional Molecules, College of Chemistry, Tianjin Normal University, Tianjin 300387, People's Republic of China
^*Correspondence e-mail: guojianhua1998@163.com

(Received 11 November 2011; accepted 21 November 2011; online 25 November 2011)

In the title compound, [Ni(C₂O₄)(C₁₂H₁₂N₂O)₂]_n, the Ni^II atom, lying on a twofold rotation axis, is coordinated by two N atoms from two monodentate 3-(1H-imidazol-1-yl)-1-phenylpropan-1-one (L) ligands and four O atoms from two oxalate anions in a distorted octahedral geometry. The oxalate anion has a twofold rotation axis through the mid-point of the C—C bond and acts as a bridging ligand, linking the Ni^II atoms into a polymeric chain along [010]. Weak intermolecular C—H⋯O hydrogen bonds connect the chains, resulting in a three-dimensional supramolecular structure. >

Related literature

For background to the construction of metal-organic frameworks using a mixed-ligand strategy, see: Du et al. (2005 ); Tao et al. (2000 ); Ye et al. (2005 ).

Experimental

Crystal data

[Ni(C₂O₄)(C₁₂H₁₂N₂O)₂]
M_r = 547.20
Monoclinic, C 2/c
a = 15.3065 (11) Å
b = 5.6605 (4) Å
c = 27.536 (2) Å
β = 95.613 (1)°
V = 2374.3 (3) Å³
Z = 4
Mo Kα radiation
μ = 0.87 mm⁻¹
T = 296 K
0.28 × 0.22 × 0.20 mm

Data collection

Bruker APEXII CCD diffractometer
Absorption correction: multi-scan (SADABS; Sheldrick, 1996 ) T_min = 0.793, T_max = 0.845
5794 measured reflections
2105 independent reflections
1676 reflections with I > 2σ(I)
R_int = 0.043

Refinement

R[F² > 2σ(F²)] = 0.045
wR(F²) = 0.096
S = 1.02
2105 reflections
168 parameters
1 restraint
H-atom parameters constrained
Δρ_max = 0.63 e Å⁻³
Δρ_min = −0.45 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
C3—H3⋯O1ⁱ	0.93	2.46	3.290 (4)	149
C4—H4B⋯O2ⁱ	0.97	2.58	3.467 (5)	152
C10—H10⋯O2ⁱⁱ	0.93	2.42	3.318 (5)	162
Symmetry codes: (i) $[x+{\script{1\over 2}}, y-{\script{1\over 2}}, z]$ ; (ii) $[-x+{\script{3\over 2}}, -y+{\script{1\over 2}}, -z+2]$ .

Data collection: APEX2 (Bruker, 2007 ); cell refinement: SAINT (Bruker, 2007); data reduction: SAINT; 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) and DIAMOND (Brandenburg & Berndt, 1999 ); software used to prepare material for publication: SHELXTL.

Supporting information

Crystal structure: contains datablocks global, I. DOI: https://doi.org/10.1107/S1600536811049646/hy2488sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S1600536811049646/hy2488Isup2.hkl

checkCIF report

Comment top

Currently, the rational construction of new structurally defined metal-organic frameworks using a mixed-ligand strategy seems to be a marvelous success (Du et al., 2005; Tao et al., 2000; Ye et al., 2005). In our recent research, we have initiated a synthetic approach employing multicarboxylates and 3-(1H-imidazol-1-yl)-1-phenylpropan-1-one (L) upon reactions with differnent metal ions to construct new functional frameworks. To explore this series, we synthesized the title compound, a new Ni(II) complex based on the L ligand.

In the title complex (Fig. 1), the Ni^II atom, lying on a twofold rotation axis, is six-coordinated in a distorted octahedral geometry by four O atoms from two oxalate anions in the equatorial plane and two N atoms from two monodentate L ligands occupying the axial positions, with the N1—Ni1—N1ⁱ angle of 178.56 (17)° [symmetry code: (i) 1-x, y, 3/2-z]. As depicted in Fig. 2, the oxalate dianions as bridging ligands joint the Ni^II atoms into a one-dimensional polymeric [Ni(C₂O₄)]_n chain along [0 1 0]. The imidazole and benzene rings in the L ligands are not coplanar, the dihedral angel between the imidazole and benzene rings being 68.7 (2)°. Analysis of the crystal packing indicates that weak intermolecular C—H···O hydrogen bonds (Table 1) connect the chains, producing a three-dimensional supramolecular structure.

Related literature top

For background to the construction of metal-organic frameworks using a mixed-ligand strategy, see: Du et al. (2005); Tao et al. (2000); Ye et al. (2005).

Experimental top

Ni(CH₃CO₂)₂.4H₂O (24.9 mg, 0.1 mmol), 3-(1H-imidazol-1-yl)-1-phenylpropan-1-one (22.2 mg, 0.1 mmol) and oxalic acid were mixed in a CH₃CN/H₂O solution (20 ml, v/v = 1:1) with vigorous stirring for ca 30 min. The resulting solution was filtered and left to stand at room temperature. Green block crystals of the title compound suitable for X-ray analysis were obtained in 65% yield by slow evaporation of the solvent over a period of one week. Analysis, calculated for C₂₆H₂₄N₄NiO₆: C 57.07, H 4.42, N 10.24%; found: C 57.13, H 4.47, N 10.32%.

Structure description top

For background to the construction of metal-organic frameworks using a mixed-ligand strategy, see: Du et al. (2005); Tao et al. (2000); Ye et al. (2005).

Computing details top

Data collection: APEX2 (Bruker, 2007); cell refinement: SAINT (Bruker, 2007); data reduction: SAINT (Bruker, 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) and DIAMOND (Brandenburg & Berndt, 1999); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures top

	Fig. 1. The asymmetric unit of the title compound, showing the 30% probability ellipsoids. [Symmetry codes: (A) 1-x, y, 3/2-z; (B) x, -1+y, z; (C) 1-x, -1+y, 3/2-z.]
	Fig. 2. The one-dimensional structure of the title compound.

catena-Poly[[bis[3-(1H-imidazol-1-yl)-1-phenylpropan-1-one- κN³]nickel(II)]-µ-oxalato- κ⁴O¹,O²:O^1',O^2'] top

Crystal data top

[Ni(C₂O₄)(C₁₂H₁₂N₂O)₂]	F(000) = 1136
M_r = 547.20	D_x = 1.531 Mg m⁻³
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2yc	Cell parameters from 1107 reflections
a = 15.3065 (11) Å	θ = 2.9–21.3°
b = 5.6605 (4) Å	µ = 0.87 mm⁻¹
c = 27.536 (2) Å	T = 296 K
β = 95.613 (1)°	Block, colorless
V = 2374.3 (3) Å³	0.28 × 0.22 × 0.20 mm
Z = 4

Data collection top

Bruker APEXII CCD diffractometer	2105 independent reflections
Radiation source: fine-focus sealed tube	1676 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.043
φ and ω scans	θ_max = 25.0°, θ_min = 2.7°
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	h = −16→18
T_min = 0.793, T_max = 0.845	k = −6→5
5794 measured reflections	l = −32→32

Refinement top

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)] = 0.045	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.096	H-atom parameters constrained
S = 1.02	w = 1/[σ²(F_o²) + (0.0315P)² + 4.5895P] where P = (F_o² + 2F_c²)/3
2105 reflections	(Δ/σ)_max < 0.001
168 parameters	Δρ_max = 0.63 e Å⁻³
1 restraint	Δρ_min = −0.45 e Å⁻³

Crystal data top

[Ni(C₂O₄)(C₁₂H₁₂N₂O)₂]	V = 2374.3 (3) Å³
M_r = 547.20	Z = 4
Monoclinic, C2/c	Mo Kα radiation
a = 15.3065 (11) Å	µ = 0.87 mm⁻¹
b = 5.6605 (4) Å	T = 296 K
c = 27.536 (2) Å	0.28 × 0.22 × 0.20 mm
β = 95.613 (1)°

Data collection top

Bruker APEXII CCD diffractometer	2105 independent reflections
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	1676 reflections with I > 2σ(I)
T_min = 0.793, T_max = 0.845	R_int = 0.043
5794 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.045	1 restraint
wR(F²) = 0.096	H-atom parameters constrained
S = 1.02	Δρ_max = 0.63 e Å⁻³
2105 reflections	Δρ_min = −0.45 e Å⁻³
168 parameters

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

	x	y	z	U_iso*/U_eq
Ni1	0.5000	−0.13748 (10)	0.7500	0.02887 (19)
O1	0.46495 (16)	0.1678 (4)	0.79304 (9)	0.0464 (6)
O2	0.46148 (17)	0.5597 (5)	0.79161 (9)	0.0528 (7)
O3	0.8709 (3)	0.4212 (6)	0.93819 (12)	0.0912 (12)
N1	0.62123 (18)	−0.1330 (5)	0.78683 (10)	0.0388 (7)
N2	0.73701 (18)	−0.0047 (5)	0.83297 (10)	0.0400 (7)
C1	0.6893 (2)	−0.2891 (6)	0.78450 (13)	0.0418 (9)
H1	0.6865	−0.4274	0.7662	0.050*
C2	0.6534 (2)	0.0357 (7)	0.81664 (12)	0.0421 (9)
H2	0.6216	0.1666	0.8252	0.050*
C3	0.7610 (2)	−0.2127 (7)	0.81268 (13)	0.0433 (9)
H3	0.8155	−0.2863	0.8173	0.052*
C4	0.7933 (2)	0.1504 (7)	0.86521 (13)	0.0497 (10)
H4A	0.7668	0.3059	0.8657	0.060*
H4B	0.8499	0.1668	0.8525	0.060*
C5	0.8066 (3)	0.0541 (8)	0.91673 (13)	0.0591 (12)
H5A	0.7498	0.0192	0.9279	0.071*
H5B	0.8394	−0.0925	0.9166	0.071*
C6	0.8547 (3)	0.2235 (9)	0.95153 (15)	0.0573 (11)
C7	0.8814 (3)	0.1443 (9)	1.00249 (14)	0.0572 (11)
C8	0.8604 (4)	−0.0672 (11)	1.02023 (18)	0.099 (2)
H8	0.8268	−0.1721	1.0002	0.119*
C9	0.8881 (5)	−0.1321 (11)	1.06808 (19)	0.115 (2)
H9	0.8725	−0.2788	1.0797	0.138*
C10	0.9371 (3)	0.0151 (11)	1.09733 (17)	0.0782 (15)
H10	0.9546	−0.0283	1.1294	0.094*
C11	0.9609 (4)	0.2238 (12)	1.08058 (18)	0.0918 (18)
H11	0.9964	0.3247	1.1006	0.110*
C12	0.9326 (4)	0.2895 (10)	1.03341 (16)	0.0855 (17)
H12	0.9488	0.4367	1.0222	0.103*
C13	0.4784 (2)	0.3633 (6)	0.77433 (12)	0.0357 (8)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ni1	0.0301 (3)	0.0254 (3)	0.0291 (3)	0.000	−0.0074 (2)	0.000
O1	0.0468 (15)	0.0402 (14)	0.0522 (15)	0.0059 (12)	0.0044 (12)	0.0031 (11)
O2	0.0515 (16)	0.0561 (18)	0.0480 (16)	0.0131 (13)	−0.0091 (13)	−0.0136 (13)
O3	0.125 (3)	0.075 (3)	0.066 (2)	−0.038 (2)	−0.027 (2)	0.0008 (18)
N1	0.0409 (17)	0.0349 (16)	0.0391 (16)	0.0020 (14)	−0.0034 (13)	−0.0032 (14)
N2	0.0357 (17)	0.0447 (18)	0.0372 (16)	0.0003 (14)	−0.0086 (13)	−0.0031 (15)
C1	0.042 (2)	0.040 (2)	0.042 (2)	0.0066 (17)	0.0002 (17)	−0.0078 (17)
C2	0.039 (2)	0.043 (2)	0.041 (2)	0.0053 (17)	−0.0081 (17)	−0.0050 (18)
C3	0.033 (2)	0.048 (2)	0.048 (2)	0.0055 (17)	−0.0039 (17)	0.0025 (18)
C4	0.045 (2)	0.055 (2)	0.046 (2)	−0.008 (2)	−0.0118 (18)	−0.006 (2)
C5	0.065 (3)	0.060 (3)	0.048 (2)	−0.011 (2)	−0.017 (2)	−0.002 (2)
C6	0.056 (3)	0.067 (3)	0.046 (2)	−0.008 (2)	−0.007 (2)	−0.005 (2)
C7	0.053 (2)	0.073 (3)	0.042 (2)	−0.010 (2)	−0.0081 (19)	−0.010 (2)
C8	0.133 (5)	0.095 (4)	0.060 (3)	−0.046 (4)	−0.035 (3)	0.004 (3)
C9	0.169 (6)	0.106 (5)	0.062 (3)	−0.048 (5)	−0.038 (4)	0.019 (3)
C10	0.077 (3)	0.109 (4)	0.046 (3)	0.002 (3)	−0.010 (3)	−0.008 (3)
C11	0.084 (4)	0.134 (5)	0.053 (3)	−0.036 (4)	−0.014 (3)	−0.015 (3)
C12	0.093 (4)	0.110 (4)	0.050 (3)	−0.042 (3)	−0.010 (3)	−0.009 (3)
C13	0.0311 (18)	0.0335 (19)	0.0402 (19)	0.0031 (16)	−0.0089 (15)	0.0039 (17)

Geometric parameters (Å, º) top

Ni1—N1	2.026 (3)	C4—H4A	0.9700
Ni1—N1ⁱ	2.026 (3)	C4—H4B	0.9700
Ni1—O2ⁱⁱ	2.175 (3)	C5—C6	1.497 (5)
Ni1—O2ⁱⁱⁱ	2.175 (3)	C5—H5A	0.9700
Ni1—O1	2.191 (3)	C5—H5B	0.9700
Ni1—O1ⁱ	2.191 (3)	C6—C7	1.492 (6)
O1—C13	1.247 (4)	C7—C8	1.344 (7)
O2—C13	1.247 (4)	C7—C12	1.372 (6)
O3—C6	1.211 (5)	C8—C9	1.393 (7)
N1—C2	1.322 (4)	C8—H8	0.9300
N1—C1	1.372 (4)	C9—C10	1.337 (7)
N2—C2	1.334 (4)	C9—H9	0.9300
N2—C3	1.369 (4)	C10—C11	1.332 (7)
N2—C4	1.467 (4)	C10—H10	0.9300
C1—C3	1.352 (5)	C11—C12	1.380 (6)
C1—H1	0.9300	C11—H11	0.9300
C2—H2	0.9300	C12—H12	0.9300
C3—H3	0.9300	C13—C13ⁱ	1.550 (7)
C4—C5	1.515 (5)

N1—Ni1—N1ⁱ	178.56 (17)	C5—C4—H4A	109.3
N1—Ni1—O2ⁱⁱ	89.51 (10)	N2—C4—H4B	109.3
N1ⁱ—Ni1—O2ⁱⁱ	91.63 (11)	C5—C4—H4B	109.3
N1—Ni1—O2ⁱⁱⁱ	91.63 (11)	H4A—C4—H4B	108.0
N1ⁱ—Ni1—O2ⁱⁱⁱ	89.51 (11)	C6—C5—C4	112.4 (4)
O2ⁱⁱ—Ni1—O2ⁱⁱⁱ	75.98 (14)	C6—C5—H5A	109.1
N1—Ni1—O1	88.86 (10)	C4—C5—H5A	109.1
N1ⁱ—Ni1—O1	90.01 (11)	C6—C5—H5B	109.1
O2ⁱⁱ—Ni1—O1	178.36 (9)	C4—C5—H5B	109.1
O2ⁱⁱⁱ—Ni1—O1	104.07 (9)	H5A—C5—H5B	107.8
N1—Ni1—O1ⁱ	90.01 (11)	O3—C6—C7	121.2 (4)
N1ⁱ—Ni1—O1ⁱ	88.86 (10)	O3—C6—C5	120.0 (4)
O2ⁱⁱ—Ni1—O1ⁱ	104.07 (9)	C7—C6—C5	118.8 (4)
O2ⁱⁱⁱ—Ni1—O1ⁱ	178.36 (9)	C8—C7—C12	116.8 (4)
O1—Ni1—O1ⁱ	75.92 (13)	C8—C7—C6	123.8 (4)
C13—O1—Ni1	114.7 (2)	C12—C7—C6	119.4 (5)
C13—O2—Ni1^iv	115.1 (2)	C7—C8—C9	121.1 (5)
C2—N1—C1	104.8 (3)	C7—C8—H8	119.4
C2—N1—Ni1	125.9 (2)	C9—C8—H8	119.4
C1—N1—Ni1	129.1 (2)	C10—C9—C8	120.4 (6)
C2—N2—C3	107.3 (3)	C10—C9—H9	119.8
C2—N2—C4	126.1 (3)	C8—C9—H9	119.8
C3—N2—C4	126.6 (3)	C11—C10—C9	120.0 (5)
C3—C1—N1	110.2 (3)	C11—C10—H10	120.0
C3—C1—H1	124.9	C9—C10—H10	120.0
N1—C1—H1	124.9	C10—C11—C12	119.6 (5)
N1—C2—N2	111.8 (3)	C10—C11—H11	120.2
N1—C2—H2	124.1	C12—C11—H11	120.2
N2—C2—H2	124.1	C7—C12—C11	122.0 (5)
C1—C3—N2	105.9 (3)	C7—C12—H12	119.0
C1—C3—H3	127.0	C11—C12—H12	119.0
N2—C3—H3	127.0	O2—C13—O1	125.8 (3)
N2—C4—C5	111.6 (3)	O2—C13—C13ⁱ	116.9 (2)
N2—C4—H4A	109.3	O1—C13—C13ⁱ	117.3 (2)

N1—Ni1—O1—C13	91.5 (2)	C2—N2—C4—C5	105.2 (4)
N1ⁱ—Ni1—O1—C13	−87.6 (2)	C3—N2—C4—C5	−77.3 (5)
O2ⁱⁱⁱ—Ni1—O1—C13	−177.1 (2)	N2—C4—C5—C6	−173.1 (3)
O1ⁱ—Ni1—O1—C13	1.18 (18)	C4—C5—C6—O3	7.0 (7)
O2ⁱⁱ—Ni1—N1—C2	170.1 (3)	C4—C5—C6—C7	−173.5 (4)
O2ⁱⁱⁱ—Ni1—N1—C2	−114.0 (3)	O3—C6—C7—C8	175.5 (5)
O1—Ni1—N1—C2	−9.9 (3)	C5—C6—C7—C8	−4.0 (7)
O1ⁱ—Ni1—N1—C2	66.0 (3)	O3—C6—C7—C12	−6.5 (7)
O2ⁱⁱ—Ni1—N1—C1	−5.1 (3)	C5—C6—C7—C12	173.9 (5)
O2ⁱⁱⁱ—Ni1—N1—C1	70.8 (3)	C12—C7—C8—C9	1.3 (9)
O1—Ni1—N1—C1	174.9 (3)	C6—C7—C8—C9	179.3 (6)
O1ⁱ—Ni1—N1—C1	−109.2 (3)	C7—C8—C9—C10	−0.6 (11)
C2—N1—C1—C3	−0.1 (4)	C8—C9—C10—C11	−1.0 (10)
Ni1—N1—C1—C3	175.9 (2)	C9—C10—C11—C12	1.8 (9)
C1—N1—C2—N2	0.1 (4)	C8—C7—C12—C11	−0.5 (9)
Ni1—N1—C2—N2	−176.0 (2)	C6—C7—C12—C11	−178.6 (5)
C3—N2—C2—N1	−0.1 (4)	C10—C11—C12—C7	−1.1 (9)
C4—N2—C2—N1	177.8 (3)	Ni1^iv—O2—C13—O1	177.3 (3)
N1—C1—C3—N2	0.0 (4)	Ni1^iv—O2—C13—C13ⁱ	−1.6 (4)
C2—N2—C3—C1	0.1 (4)	Ni1—O1—C13—O2	178.1 (3)
C4—N2—C3—C1	−177.8 (3)	Ni1—O1—C13—C13ⁱ	−3.0 (4)

Symmetry codes: (i) −x+1, y, −z+3/2; (ii) −x+1, y−1, −z+3/2; (iii) x, y−1, z; (iv) x, y+1, z.

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C3—H3···O1^v	0.93	2.46	3.290 (4)	149
C4—H4B···O2^v	0.97	2.58	3.467 (5)	152
C10—H10···O2^vi	0.93	2.42	3.318 (5)	162

Symmetry codes: (v) x+1/2, y−1/2, z; (vi) −x+3/2, −y+1/2, −z+2.

Experimental details

Crystal data
Chemical formula	[Ni(C₂O₄)(C₁₂H₁₂N₂O)₂]
M_r	547.20
Crystal system, space group	Monoclinic, C2/c
Temperature (K)	296
a, b, c (Å)	15.3065 (11), 5.6605 (4), 27.536 (2)
β (°)	95.613 (1)
V (Å³)	2374.3 (3)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	0.87
Crystal size (mm)	0.28 × 0.22 × 0.20

Data collection
Diffractometer	Bruker APEXII CCD
Absorption correction	Multi-scan (SADABS; Sheldrick, 1996)
T_min, T_max	0.793, 0.845
No. of measured, independent and observed [I > 2σ(I)] reflections	5794, 2105, 1676
R_int	0.043
(sin θ/λ)_max (Å⁻¹)	0.595

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.045, 0.096, 1.02
No. of reflections	2105
No. of parameters	168
No. of restraints	1
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.63, −0.45

Computer programs: APEX2 (Bruker, 2007), SAINT (Bruker, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), XP in SHELXTL (Sheldrick, 2008) and DIAMOND (Brandenburg & Berndt, 1999), SHELXTL (Sheldrick, 2008).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
C3—H3···O1ⁱ	0.93	2.46	3.290 (4)	149
C4—H4B···O2ⁱ	0.97	2.58	3.467 (5)	152
C10—H10···O2ⁱⁱ	0.93	2.42	3.318 (5)	162

Symmetry codes: (i) x+1/2, y−1/2, z; (ii) −x+3/2, −y+1/2, −z+2.

References

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