metal-organic compounds\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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ISSN: 2056-9890

Poly[bis­­[μ2-2-(2-pyridylmethyl­amino)ethane­sulfonato]cadmium(II)]

aDepartment of Chemistry, Luoyang Normal University, Luoyang, Henan 471022, People's Republic of China
*Correspondence e-mail: dzx6281@126.com

(Received 5 November 2009; accepted 18 November 2009; online 21 November 2009)

The title compound [Cd(C8H11N2O3S)2]n, is a two-dimensional coordination polymer based on a Cd2+ atom and deprotonated 2-(2-pyridylmethyl­amino)ethanesulfonic acid (Hpmt). The complex has mol­ecular symmetry Ci as a consequence of the CdII being located on an inversion centre. Two N atoms of each pmt ligand coordinate to the Cd2+ ion and its sulfonate O atom bonds to an adjacent Cd2+ ion. 24-membered (–Cd—N—C—C—S—O–)4 rings are formed between neighbouring Cd2+ ions; these are inter­connected, forming a two-dimensional layer structure. In respect to stereogenic amino N atom and the inversion symmetry of the complex, the compound is a 1:1 racemate. The crystal packing is stabilized by inter­molecular N—H⋯O hydrogen bonds and further connected by ππ stacking inter­actions between the pyridyl rings [average inter­planar distance and centroid–centroid separation = 3.582 (1) and 3.634 (1)Å, respectively], forming a three-dimensional supra­molecular architecture.

Related literature

For different coordination modes of the pmt ligand in complexes derived from Hpmt, see: Du & Zhang (2009[Du, Z.-X. & Zhang, G.-Y. (2009). Acta Cryst. E65, m706.]); Li et al. (2006[Li, J.-X., Jiang, Y.-M. & Li, H.-Y. (2006). Acta Cryst. E62, m2984-m2986.], 2007a[Li, J.-X., Jiang, Y.-M. & Wang, J.-G. (2007a). Acta Cryst. E63, m213-m215.],b[Li, J.-X., Jiang, Y.-M. & Wang, J.-G. (2007b). Acta Cryst. E63, m601-m603.], 2008a[Li, J.-X., Jiang, Y.-M. & Chen, M.-J. (2008a). J. Coord. Chem. 61, 1765-1773.],b[Li, J.-X., Jiang, Y.-M. & Lian, B.-R. (2008b). J. Chem. Crystallogr. 38, 711-715.]); Liao et al. (2007[Liao, B.-L., Li, J.-X. & Jiang, Y.-M. (2007). Acta Cryst. E63, m1974.]).

[Scheme 1]

Experimental

Crystal data
  • [Cd(C8H11N2O3S)2]

  • Mr = 542.90

  • Monoclinic, P 21 /c

  • a = 8.8982 (8) Å

  • b = 14.0206 (12) Å

  • c = 7.9040 (7) Å

  • β = 103.579 (1)°

  • V = 958.52 (15) Å3

  • Z = 2

  • Mo Kα radiation

  • μ = 1.40 mm−1

  • T = 291 K

  • 0.22 × 0.16 × 0.12 mm

Data collection
  • Bruker APEXII CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Sheldrick, 1996[Sheldrick, G. M. (1996). SADABS. University of Göttingen, Germany.]) Tmin = 0.749, Tmax = 0.849

  • 5691 measured reflections

  • 2178 independent reflections

  • 2008 reflections with I > 2σ(I)

  • Rint = 0.011

Refinement
  • R[F2 > 2σ(F2)] = 0.019

  • wR(F2) = 0.049

  • S = 1.03

  • 2178 reflections

  • 133 parameters

  • H-atom parameters constrained

  • Δρmax = 0.48 e Å−3

  • Δρmin = −0.38 e Å−3

Table 1
Selected bond lengths (Å)

Cd1—N1 2.2853 (14)
Cd1—O2i 2.3496 (14)
Cd1—N2 2.3979 (15)
Symmetry code: (i) [-x+1, y-{\script{1\over 2}}, -z+{\script{1\over 2}}].

Table 2
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N2—H2⋯O3ii 0.91 2.26 3.089 (2) 152
Symmetry code: (ii) [x, -y+{\script{1\over 2}}, z+{\script{1\over 2}}].

Data collection: APEX2 (Bruker, 2004[Bruker (2004). APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 2004[Bruker (2004). APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); molecular graphics: SHELXTL (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); software used to prepare material for publication: SHELXTL.

Supporting information


Comment top

In the previous literatures, several complexes derived from Hpmt have been reported. Among them, pmt- ligand displays different coordination modes, such as tridentate chelate (Du & Zhang, 2009; Li et al., 2006, 2008a; Liao et al., 2007), µ2 bridge(Li et al., 2007a, 2008b) and µ3 bridge (Li et al., 2007b). In this paper, we describe another new complex of pmt-, (I), Figure 1.

Compound 1 is a two-dimensional coordination polymer and the repeating unit comprises one Cd2+ ion and two pmt- ligands(Fig. 1, Table 1). Cd2+ ion situates on a centre of symmetry and is six-coordinated with four N atoms from two pmt- ligands along with two sulfonate O atoms belonging to another two ligands, showing a distorted octahedral geometry (Table 1). The four N atoms from two pmt- ligands define the equatorial plane with the Cd centre located in the plane, and two O atoms are at the axial positions with O2A—Cd1—O2B angle of just 180°[Symmetry codes: (A)1 - x, -1/2 + y, 0.5 - z; (B)x, 0.5 - y, -1/2 + z]. Each pmt- plays as a µ2 bridge to connect two Cd2+ ions and each Cd2+ ion links four pmt- ligands, forming an infinite two-dimensional layer structure with (4, 4) topology (Figure 2). The network is based on (Cd(pmt))4 rhombus, a 24-membered metal-ligand ring (–Cd—N—C—C—S—O–)4 formed by four pmt- and four quadruply connected Cd2+ ions. The edge Cd···Cd distance of the rhombus is 8.048 (3)Å and the Cd···Cd separations through the diagonal of the rhombus are 7.904 (2)Å and 14.021 (1) Å, respectively (Figure 2).

The two-dimensional layer is stabilized by intermolecular N—H···O hydrogen bonds (Figure 3 & Table 2). The interlayers are further connected by π-π stacking interactions of parallel pyridine rings of adjacent layers. The interplanar average distance and ringcentroid separation distance are 3.582 (1)Å and 3.634 (1) Å, respectively. Thus, the three-dimensional supramolecular architecture of (I) is formed (Figure 4).

Related literature top

For different coordination modes of the pmt- ligand in complexes derived from Hpmt, see: Du & Zhang (2009); Li et al. (2006, 2007a,b, 2008a,b); Liao et al. (2007).

Experimental top

The ligand Hpmt was prepared according to the method of Li et al., 2006. A water solution (5 ml) of ligand Hpmt (2 mmol, 0.432 g) was added dropwise to a solution of CdCl2. 2.5H2O (0.228 g, 1.0 mmol) in methanol (8 ml), then the obtained mixture was stirred at 333 K for 3 h. After that, the mixture was basified with KOH (1 mol/l) to a pH of 7.5–8.0 and continued stirring for another 4 h, filtrated. Two weeks later, colourless claviform crystals were grown from the filtrate by slow evaporation. Analysis, found: C 35.40, H 4.02, N 10.36, S 11.36%; C16H22CdN4O6S2 requires: C 35.36, H 4.05, N 10.31, S 11.42%. IR (KBr, ν, cm-1): 771.2[γ(CC—H)], 745.7(γCH2); 1188.3, 1157.4, 1040.6(ν SO3-); 1607.7, 1571.7(ν CC + ν CN); 3266.2(ν N—H). CCDC 614219.

Refinement top

H atoms bonded to C were positioned geometrically with C—H distance of 0.93–0.97 Å, and treated as riding atoms, with Uiso(H)=1.2Ueq(C). The N—H hydrogen atom was located in a difference Fourier map and refined isotropically.

Computing details top

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT (Bruker, 2004); 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 coordination of Cd2+ ion of (I) with the atom-numbering scheme. Displacement ellipsoids drawn at the 30% probability level. H atoms have been omitted. [Symmetry codes: (A)1 - x, -1/2 + y, 0.5 - z; (B)x, 0.5 - y, -1/2 + z; (C)1 - x, -y, -z; (D)1 - x, 1/2 + y, 0.5 - z]
[Figure 2] Fig. 2. The two-dimensional layer structure of (I). H atoms have been omitted.
[Figure 3] Fig. 3. The hydrogen bonding interactions in (I)(dashed lines) projected in the plane bc. H atoms on C atoms have been omitted.
[Figure 4] Fig. 4. Packing diagram for (I), showing π-π stacking as dashed lines in the plane ab. H atoms on C have been deleted.
Poly[bis[µ2-2-(2-pyridylmethylamino)ethanesulfonato]cadmium(II)] top
Crystal data top
[Cd(C8H11N2O3S)2]F(000) = 548
Mr = 542.90Dx = 1.881 Mg m3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 3852 reflections
a = 8.8982 (8) Åθ = 2.4–28.2°
b = 14.0206 (12) ŵ = 1.40 mm1
c = 7.9040 (7) ÅT = 291 K
β = 103.579 (1)°Claviform, colourless
V = 958.52 (15) Å30.22 × 0.16 × 0.12 mm
Z = 2
Data collection top
Bruker APEXII CCD area-detector
diffractometer
2178 independent reflections
Radiation source: fine-focus sealed tube2008 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.011
ϕ and ω scansθmax = 27.5°, θmin = 2.4°
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
h = 711
Tmin = 0.749, Tmax = 0.849k = 1815
5691 measured reflectionsl = 1010
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.019Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.049H-atom parameters constrained
S = 1.03 w = 1/[σ2(Fo2) + (0.0237P)2 + 0.5977P]
where P = (Fo2 + 2Fc2)/3
2178 reflections(Δ/σ)max < 0.001
133 parametersΔρmax = 0.48 e Å3
0 restraintsΔρmin = 0.38 e Å3
Crystal data top
[Cd(C8H11N2O3S)2]V = 958.52 (15) Å3
Mr = 542.90Z = 2
Monoclinic, P21/cMo Kα radiation
a = 8.8982 (8) ŵ = 1.40 mm1
b = 14.0206 (12) ÅT = 291 K
c = 7.9040 (7) Å0.22 × 0.16 × 0.12 mm
β = 103.579 (1)°
Data collection top
Bruker APEXII CCD area-detector
diffractometer
2178 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
2008 reflections with I > 2σ(I)
Tmin = 0.749, Tmax = 0.849Rint = 0.011
5691 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0190 restraints
wR(F2) = 0.049H-atom parameters constrained
S = 1.03Δρmax = 0.48 e Å3
2178 reflectionsΔρmin = 0.38 e Å3
133 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
Cd10.50000.00000.00000.02456 (7)
S10.33469 (5)0.35013 (3)0.12343 (6)0.02701 (10)
O10.17221 (17)0.35246 (12)0.0384 (2)0.0474 (4)
O20.36412 (18)0.38778 (10)0.30088 (18)0.0382 (3)
O30.43417 (19)0.39430 (11)0.0247 (2)0.0446 (4)
N10.72897 (17)0.05064 (11)0.05239 (19)0.0265 (3)
N20.60386 (17)0.11240 (10)0.22587 (19)0.0260 (3)
H20.57770.09290.32500.031*
C10.7692 (2)0.04398 (15)0.2058 (2)0.0342 (4)
H10.70610.00960.29570.041*
C20.9010 (2)0.08650 (17)0.2341 (3)0.0409 (5)
H2A0.92750.08000.34060.049*
C30.9923 (2)0.13852 (18)0.1025 (3)0.0456 (5)
H31.08050.16880.11960.055*
C40.9522 (2)0.14571 (16)0.0561 (3)0.0393 (5)
H41.01340.18050.14680.047*
C50.8193 (2)0.10009 (13)0.0778 (2)0.0270 (4)
C60.7732 (2)0.10068 (13)0.2504 (2)0.0289 (4)
H6A0.80520.04130.31110.035*
H6B0.82600.15250.32170.035*
C70.5616 (2)0.21429 (13)0.1977 (2)0.0301 (4)
H7A0.60540.23950.10550.036*
H7B0.60480.24990.30310.036*
C80.3876 (2)0.22747 (12)0.1489 (2)0.0289 (4)
H8A0.34350.19960.23860.035*
H8B0.34510.19400.04090.035*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Cd10.02285 (10)0.02064 (10)0.03077 (10)0.00396 (6)0.00747 (7)0.00131 (7)
S10.0320 (2)0.0237 (2)0.0260 (2)0.00119 (16)0.00802 (17)0.00138 (16)
O10.0355 (8)0.0447 (9)0.0561 (10)0.0066 (6)0.0011 (7)0.0040 (7)
O20.0547 (9)0.0275 (7)0.0328 (7)0.0018 (6)0.0109 (6)0.0074 (6)
O30.0567 (9)0.0389 (8)0.0447 (8)0.0005 (7)0.0249 (7)0.0101 (7)
N10.0246 (7)0.0267 (8)0.0287 (7)0.0016 (6)0.0071 (6)0.0000 (6)
N20.0295 (7)0.0237 (7)0.0263 (7)0.0002 (6)0.0098 (6)0.0002 (6)
C10.0332 (10)0.0393 (11)0.0309 (9)0.0007 (8)0.0092 (8)0.0007 (8)
C20.0353 (10)0.0545 (13)0.0375 (10)0.0039 (9)0.0178 (9)0.0075 (10)
C30.0289 (10)0.0554 (14)0.0563 (14)0.0057 (9)0.0176 (9)0.0085 (11)
C40.0274 (9)0.0428 (11)0.0468 (12)0.0094 (8)0.0071 (8)0.0037 (9)
C50.0234 (8)0.0245 (8)0.0324 (9)0.0015 (6)0.0052 (7)0.0018 (7)
C60.0271 (9)0.0294 (9)0.0277 (8)0.0013 (7)0.0018 (7)0.0015 (7)
C70.0336 (9)0.0217 (8)0.0361 (9)0.0005 (7)0.0103 (8)0.0035 (7)
C80.0332 (9)0.0226 (8)0.0316 (9)0.0006 (7)0.0089 (7)0.0056 (7)
Geometric parameters (Å, º) top
Cd1—N12.2853 (14)C1—C21.380 (3)
Cd1—N1i2.2853 (14)C1—H10.9300
Cd1—O2ii2.3496 (14)C2—C31.370 (3)
Cd1—O2iii2.3497 (14)C2—H2A0.9300
Cd1—N22.3979 (15)C3—C41.385 (3)
Cd1—N2i2.3979 (15)C3—H30.9300
S1—O11.4447 (15)C4—C51.390 (3)
S1—O31.4496 (15)C4—H40.9300
S1—O21.4635 (14)C5—C61.514 (2)
S1—C81.7821 (18)C6—H6A0.9700
O2—Cd1iv2.3497 (14)C6—H6B0.9700
N1—C51.341 (2)C7—C81.516 (3)
N1—C11.346 (2)C7—H7A0.9700
N2—C71.481 (2)C7—H7B0.9700
N2—C61.483 (2)C8—H8A0.9700
N2—H20.9100C8—H8B0.9700
N1—Cd1—N1i180N1—C1—H1118.9
N1—Cd1—O2ii89.37 (5)C2—C1—H1118.9
N1i—Cd1—O2ii90.63 (5)C3—C2—C1118.77 (19)
N1—Cd1—O2iii90.63 (5)C3—C2—H2A120.6
N1i—Cd1—O2iii89.37 (5)C1—C2—H2A120.6
O2ii—Cd1—O2iii179.999 (1)C2—C3—C4119.59 (19)
N1—Cd1—N274.13 (5)C2—C3—H3120.2
N1i—Cd1—N2105.87 (5)C4—C3—H3120.2
O2ii—Cd1—N283.89 (5)C3—C4—C5119.02 (19)
O2iii—Cd1—N296.11 (5)C3—C4—H4120.5
N1—Cd1—N2i105.87 (5)C5—C4—H4120.5
N1i—Cd1—N2i74.13 (5)N1—C5—C4121.17 (17)
O2ii—Cd1—N2i96.11 (5)N1—C5—C6116.99 (15)
O2iii—Cd1—N2i83.89 (5)C4—C5—C6121.80 (17)
N2—Cd1—N2i180.0N2—C6—C5111.41 (14)
O1—S1—O3114.25 (10)N2—C6—H6A109.3
O1—S1—O2111.86 (9)C5—C6—H6A109.3
O3—S1—O2111.57 (9)N2—C6—H6B109.3
O1—S1—C8106.47 (9)C5—C6—H6B109.3
O3—S1—C8107.12 (9)H6A—C6—H6B108.0
O2—S1—C8104.88 (9)N2—C7—C8111.36 (15)
S1—O2—Cd1iv146.26 (9)N2—C7—H7A109.4
C5—N1—C1119.27 (16)C8—C7—H7A109.4
C5—N1—Cd1114.90 (11)N2—C7—H7B109.4
C1—N1—Cd1125.37 (13)C8—C7—H7B109.4
C7—N2—C6109.95 (14)H7A—C7—H7B108.0
C7—N2—Cd1118.81 (11)C7—C8—S1111.93 (12)
C6—N2—Cd1103.10 (10)C7—C8—H8A109.2
C7—N2—H2108.2S1—C8—H8A109.2
C6—N2—H2108.2C7—C8—H8B109.2
Cd1—N2—H2108.2S1—C8—H8B109.2
N1—C1—C2122.17 (19)H8A—C8—H8B107.9
O1—S1—O2—Cd1iv124.02 (16)Cd1—N1—C1—C2171.82 (15)
O3—S1—O2—Cd1iv5.3 (2)N1—C1—C2—C31.1 (3)
C8—S1—O2—Cd1iv120.97 (16)C1—C2—C3—C41.3 (3)
O2ii—Cd1—N1—C571.71 (12)C2—C3—C4—C50.3 (3)
O2iii—Cd1—N1—C5108.29 (12)C1—N1—C5—C41.0 (3)
N2—Cd1—N1—C512.12 (12)Cd1—N1—C5—C4171.65 (15)
N2i—Cd1—N1—C5167.88 (12)C1—N1—C5—C6176.72 (16)
O2ii—Cd1—N1—C1116.16 (16)Cd1—N1—C5—C610.6 (2)
O2iii—Cd1—N1—C163.84 (16)C3—C4—C5—N10.9 (3)
N2—Cd1—N1—C1160.01 (16)C3—C4—C5—C6176.77 (19)
N2i—Cd1—N1—C119.99 (16)C7—N2—C6—C580.67 (18)
N1—Cd1—N2—C790.73 (12)Cd1—N2—C6—C546.99 (15)
N1i—Cd1—N2—C789.27 (12)N1—C5—C6—N242.0 (2)
O2ii—Cd1—N2—C7178.19 (12)C4—C5—C6—N2140.29 (18)
O2iii—Cd1—N2—C71.81 (12)C6—N2—C7—C8172.59 (14)
N1—Cd1—N2—C631.13 (10)Cd1—N2—C7—C854.25 (18)
N1i—Cd1—N2—C6148.87 (10)N2—C7—C8—S1177.53 (12)
O2ii—Cd1—N2—C659.95 (10)O1—S1—C8—C7166.69 (13)
O2iii—Cd1—N2—C6120.05 (10)O3—S1—C8—C744.07 (16)
C5—N1—C1—C20.0 (3)O2—S1—C8—C774.60 (15)
Symmetry codes: (i) x+1, y, z; (ii) x+1, y1/2, z+1/2; (iii) x, y+1/2, z1/2; (iv) x+1, y+1/2, z+1/2.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N2—H2···O3v0.912.263.089 (2)152
Symmetry code: (v) x, y+1/2, z+1/2.

Experimental details

Crystal data
Chemical formula[Cd(C8H11N2O3S)2]
Mr542.90
Crystal system, space groupMonoclinic, P21/c
Temperature (K)291
a, b, c (Å)8.8982 (8), 14.0206 (12), 7.9040 (7)
β (°) 103.579 (1)
V3)958.52 (15)
Z2
Radiation typeMo Kα
µ (mm1)1.40
Crystal size (mm)0.22 × 0.16 × 0.12
Data collection
DiffractometerBruker APEXII CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 1996)
Tmin, Tmax0.749, 0.849
No. of measured, independent and
observed [I > 2σ(I)] reflections
5691, 2178, 2008
Rint0.011
(sin θ/λ)max1)0.649
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.019, 0.049, 1.03
No. of reflections2178
No. of parameters133
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.48, 0.38

Computer programs: APEX2 (Bruker, 2004), SAINT (Bruker, 2004), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), SHELXTL (Sheldrick, 2008).

Selected geometric parameters (Å, º) top
Cd1—N12.2853 (14)Cd1—N22.3979 (15)
Cd1—O2i2.3496 (14)
N1—Cd1—N1ii180O2i—Cd1—N283.89 (5)
N1—Cd1—O2i89.37 (5)O2iii—Cd1—N296.11 (5)
N1—Cd1—N274.13 (5)N1—Cd1—N2ii105.87 (5)
Symmetry codes: (i) x+1, y1/2, z+1/2; (ii) x+1, y, z; (iii) x, y+1/2, z1/2.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N2—H2···O3iv0.912.263.089 (2)151.5
Symmetry code: (iv) x, y+1/2, z+1/2.
 

Acknowledgements

This work was supported financially by the National Natural Science Foundation of China (No. 20771054).

References

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