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The asymmetric unit of the title compound, poly[{μ4-4-[(car­boxyl­atometh­yl)sulfan­yl]benzoato}(N,N-dimethyl­form­am­ide)­zinc], [Zn(C9H6O4S)(C3H7NO)]n, consists of one crystallographically independent ZnII cation, one 4-[(car­boxyl­atometh­yl)sulfan­yl]benzoate (L2−) ligand and one coordinated dimethyl­formamide (DMF) mol­ecule. The zinc ion is coordinated by five O atoms from four separate L2− ligands and one DMF mol­ecule, and the ZnO5 unit displays a distorted square-based-pyramidal geometry. Two ZnO5 units form a binuclear zinc–tetra­carboxyl­ate paddlewheel cluster, and these are bridged by L2− ligands to generate an inter­secting helical chain (Zn2+ ions as nodes), which is composed of right-handed (P) and left-handed (M) helices. Weak C—H...O hydrogen bonds extend the one-dimensional coordinated chain into a weakly bound three-dimensional supra­molecular architecture.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270111032811/em3043sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270111032811/em3043Isup2.hkl
Contains datablock I

CCDC reference: 851732

Comment top

The design and synthesis of metal–organic coordination polymers have attracted great interest in recent years, not only for their structural diversity and intriguing molecular topologies, but also for their potential as a new class of solid-state materials applied in the fields of separation, catalysis, gas storage and drug delivery (Kitagawa & Uemura, 2005; Dincă & Long, 2008; Choi & Suh, 2004). To construct such materials, judicious selection of bridging ligands is one of the various factors to be taken into account. Flexible ligands have been extensively explored in coordination chemistry and crystal engineering because of their numerous conformations and coordination modes observed in the coordination process (Ma et al., 2008; Zhang et al., 2008). In this contribution, we choose a new flexible ligand, 4-[(carboxylatomethyl)sulfanyl]benzoate (L2-), as a bridging ligand to synthesize the coordination polymers. Herein we report a new binuclear ZnII polymer with paddlewheel building units and intersecting helical chains (Zn2+ ions as nodes), which is composed of P- (right-) and M-(left-)handed helices.

In the structure of (I) (Fig. 1, Table 1), the Zn2+ centre adopts a five-coordinated mode with a distorted square-based-pyramidal geometry (ZnO5) via binding to one axial dimethylformamide (DMF) oxygen atom and four oxygen atoms from four different CO2- groups of L2- ligands in the basal plane. The four carboxylate O atoms [O1, O2i, O3, O4i; symmetry code: (i) -x + 1, -y + 2, -z] are coplanar with an r.m.s. deviation of 0.0139 (14) Å . Each L2- ligand bridges four different Zn2+ ions, via bridging carboxylate groups at each end of the ligand molecule, to form a one-dimensional coordination polymer. The two Zn2+ centres are bridged by four carboxylate groups from different L2- ligands in a synsyn bidentate mode, forming a paddlewheel secondary building unit (SBU). The intradimer Zn···Zn separation is 2.9186 (11) Å, within the nomal range found in other reported structures with the same paddlewheel core [Zn2O2(O2CR)4] (Zhou et al., 2000; Kwak et al., 2009). A dramatic, almost perpendicular, twist between the two carboxylate groups in the L2- ligand is observed, with a dihedral angle of 87.1 (4)° (Fig. 1).

In (I), each paddlewheel unit connects to two neighbouring paddlewheel clusters via bridging L2- anions, which adopt a bridging tetradentate mode. It should be emphasized that because of the orientation of the carboxylate coordination sites and flexibility of the L2- ligand, the quadrate rings in the one-dimensional chain are highly distorted. Interestingly, these quadrate rings are interlinked by sharing the Zn2+ ions to form an intersecting helical chain, in which P- and M-handed helices can be distinguished (Fig. 2). Obviously, the twist of the L2- ligand is responsible for the formation of the helical chain.

To date, only a few stuctures with the same paddlewheel core [Zn4O2(O2CR)4] [Zn2?] have been reported. These are the zero-dimensional Lantern-type [Zn2(O2CCF3)6]2- ions (Demirhan et al., 2002); the zero-dimensional dinuclear [Zn2(Indo)4(DMA)2].2DMA [IndoH = 1-(4-chlorobenzoyl)-5-methoxy-2-methyl-1H-indole-3-acetic acid and DMA = N,N-dimethylacetamide; Zhou et al., 2000]; the zero-dimensional overall 'figure-of-eight' shape [Zn2(C18H12N2O4S3)2(C3H7NO)2] (Wang et al., 2009); the two-dimensional square-grid motif {[Zn2(C8H4O2)2(H2O)2].2C4H9NO}n (Lv & Ng, 2007); the one-dimensional zigzag chain [Zn2(O2CPh)4(H2O)2][Zn(O2CPh)2(bpe)]n, (II) [bpe = 1,2-bis(4-pyridyl)ethane; Kwak et al., 2009]; the two-dimensional layer structure [Zn2(C8H4O4)2(C2H6OS)2].5C2H6OS (Yang et al., 2005); the three-dimensional (3,24)-connected metal–organic framework [Zn24(L)8(H2O)24]n {L = 5,5',5''-[benzene-1,3,5-triyltris(carbonylimino)]tris-1,3-benzenedicarboxylic acid; Zou et al., 2008}; the three-dimensional twofold interpenetrating polyhedral metal–organic framework {[Zn3(BTPCA)2(H2O)3].py.3DMSO}n with a primitive cubic network [BTPCA = 1,1',1''-(benzene-1,3,5-triyl)tripiperidine-4-carboxylic acid, py = ?, DMSO = dimethyl sulfoxide?; Zhao et al., 2009]. The chain structure of complex (I) is quite different from that of complex (II), which consists of mononuclear Zn(O2CC6H5)2 units bridged by a bpe ligand to form a one-dimensional zigzag chain. Importantly, such an example of the coexistence of a binuclear ZnII-tetracarboxylate paddlewheel cluster and intersecting P- and M-handed helical chains is unique, to the best of our knowledge.

Another interesting feature of complex (I) is the non-covalent interactions (Table 2). In the landmark study by Desiraju (1996), C—H···O contacts occur within certain distance (2.30 < d < 2.84 Å, 3.18 < D < 3.60 Å) and angle (122< θ < 160°) ranges. There are weak C—H···O hydrogen bonds between two L2- ligands [C9···O3iv; symmetry code: (iv) -x, -y + 2, -z] as well as between two DMF molecules [C12···O5v; symmetry code: (v) -x + 1/2, y-1/2, -z+1/2] which link the one-dimensional helical chains to generate a weakly bound three-dimensional supramolecular architecture as depicted in Fig. 3.

Related literature top

For related literature, see: Choi & Suh (2004); Demirhan et al. (2002); Dincă & Long (2008); Kitagawa & Uemura (2005); Kwak et al. (2009); Lv & Ng (2007); Ma et al. (2008); Wang et al. (2009); Yang et al. (2005); Zhang et al. (2008); Zhao et al. (2009); Zhou et al. (2000); Zou et al. (2008).

Experimental top

All reagents and solvents employed were commercially available and used as received without further purification. A mixture of Zn(NO3)2.6H2O (60 mg, 0.2 mmol), H2L (42 mg, 0.2 mmol) and DMF (10 ml) was sealed in a 25 ml stainless steel reactor with Teflon liner and directly heated to 348 K for 4 d, and then cooled to room temperature. The crystals were washed with methanol to give complex (I) in about 45% yield (based on the H2L ligand).

Refinement top

The hydrogen atoms were positioned geometrically and included in the refinement using a riding model [C—H = 0.96 Å (CH3), 0.97 Å (CH2), 0.93Å (CH) and Uiso(H) = 1.2Ueq(parent atom)].

Computing details top

Data collection: SMART (Bruker, 2001); cell refinement: SMART (Bruker, 2001); data reduction: SAINT-Plus (Bruker, 2001); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2008) and ORTEP-3 (Farrugia, 1997); software used to prepare material for publication: PLATON (Spek, 2009).

Figures top
[Figure 1] Fig. 1. The structure of (I), showing the atom-numbering scheme. Displacement ellipsoids are drawn at the 30% probability level. All H atoms have been omitted for clarity. [Symmetry codes: (i) -x+1, -y+2, -z; (ii) x, y-1, z; (iii) -x+1, -y+1, -z.]
[Figure 2] Fig. 2. View of intersecting helical chains in (I) comprised of P- and M-handed helices with Zn2+ ions as nodes.
[Figure 3] Fig. 3. View of the the weak C—H···O hydrogen-bonding interactions between adjacent chains generating a three-dimensional supramolecular network. Dashed lines indicate hydrogen bonds and polyhedra represent ZnO5 groups.
poly[{µ4-4-[(carboxyatomethyl)sulfanyl]benzoato}(N,N- dimethylformamide)zinc] top
Crystal data top
[Zn(C9H6O4S)(C3H7NO)]F(000) = 712
Mr = 348.66Dx = 1.704 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 2096 reflections
a = 7.873 (3) Åθ = 2.2–26.8°
b = 10.225 (3) ŵ = 1.98 mm1
c = 17.006 (6) ÅT = 298 K
β = 97.014 (4)°Block, colourless
V = 1358.7 (8) Å30.35 × 0.34 × 0.24 mm
Z = 4
Data collection top
Bruker SMART APEX II CCD
diffractometer
2402 independent reflections
Radiation source: fine-focus sealed tube1855 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.032
ϕ and ω scansθmax = 25.0°, θmin = 2.3°
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
h = 99
Tmin = 0.544, Tmax = 0.648k = 912
5851 measured reflectionsl = 2015
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)] = 0.037Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.091H-atom parameters constrained
S = 1.00 w = 1/[σ2(Fo2) + (0.0468P)2 + 0.359P]
where P = (Fo2 + 2Fc2)/3
2402 reflections(Δ/σ)max = 0.001
183 parametersΔρmax = 0.65 e Å3
0 restraintsΔρmin = 0.50 e Å3
Crystal data top
[Zn(C9H6O4S)(C3H7NO)]V = 1358.7 (8) Å3
Mr = 348.66Z = 4
Monoclinic, P21/nMo Kα radiation
a = 7.873 (3) ŵ = 1.98 mm1
b = 10.225 (3) ÅT = 298 K
c = 17.006 (6) Å0.35 × 0.34 × 0.24 mm
β = 97.014 (4)°
Data collection top
Bruker SMART APEX II CCD
diffractometer
2402 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
1855 reflections with I > 2σ(I)
Tmin = 0.544, Tmax = 0.648Rint = 0.032
5851 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0370 restraints
wR(F2) = 0.091H-atom parameters constrained
S = 1.00Δρmax = 0.65 e Å3
2402 reflectionsΔρmin = 0.50 e Å3
183 parameters
Special details top

Experimental. 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
Zn10.44726 (5)0.98040 (4)0.07850 (2)0.02767 (15)
N10.3960 (4)0.7560 (3)0.27221 (18)0.0398 (8)
O10.3840 (4)0.8147 (2)0.01288 (16)0.0459 (7)
O20.4537 (3)0.8424 (2)0.10938 (16)0.0428 (7)
O30.2300 (3)1.0709 (3)0.02693 (15)0.0388 (6)
O40.3076 (3)1.0928 (3)0.09457 (15)0.0415 (7)
O50.3739 (3)0.9127 (3)0.17854 (14)0.0350 (6)
S10.02332 (13)1.27397 (10)0.15567 (6)0.0387 (3)
C10.3909 (5)0.7776 (4)0.0567 (2)0.0347 (9)
C20.3150 (5)0.6466 (3)0.0796 (2)0.0320 (9)
C30.2695 (6)0.5616 (4)0.0231 (2)0.0465 (11)
H30.29350.58380.03020.056*
C40.1891 (6)0.4441 (4)0.0433 (2)0.0451 (11)
H40.16170.38750.00390.054*
C50.1495 (4)0.4109 (3)0.1225 (2)0.0302 (8)
C60.2003 (5)0.4932 (4)0.1797 (2)0.0349 (9)
H60.17860.47000.23290.042*
C70.2829 (5)0.6092 (4)0.1588 (2)0.0338 (9)
H70.31760.66310.19790.041*
C80.2065 (5)1.1074 (3)0.0442 (2)0.0308 (8)
C90.0339 (4)1.1706 (4)0.0700 (2)0.0328 (9)
H9A0.00211.22200.02610.039*
H9B0.05071.10180.08050.039*
C100.4246 (5)0.8026 (4)0.2037 (2)0.0368 (9)
H100.48600.75140.17180.044*
C110.3021 (6)0.8301 (5)0.3251 (3)0.0617 (14)
H11A0.27730.91560.30330.092*
H11B0.36970.83800.37580.092*
H11C0.19700.78590.33120.092*
C120.4597 (7)0.6270 (5)0.2993 (3)0.0736 (16)
H12A0.51750.58700.25900.110*
H12B0.36530.57300.30980.110*
H12C0.53790.63660.34690.110*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Zn10.0316 (3)0.0281 (3)0.0245 (2)0.00339 (18)0.00857 (18)0.00144 (18)
N10.0414 (19)0.045 (2)0.0337 (18)0.0073 (16)0.0081 (16)0.0103 (16)
O10.0620 (19)0.0329 (16)0.0432 (17)0.0125 (14)0.0084 (15)0.0106 (13)
O20.0482 (17)0.0312 (16)0.0502 (17)0.0127 (13)0.0107 (15)0.0025 (13)
O30.0353 (15)0.0439 (17)0.0371 (16)0.0003 (12)0.0041 (12)0.0087 (12)
O40.0338 (15)0.0519 (18)0.0401 (16)0.0082 (13)0.0098 (13)0.0055 (13)
O50.0415 (15)0.0377 (17)0.0277 (14)0.0003 (13)0.0121 (12)0.0075 (12)
S10.0440 (6)0.0309 (6)0.0381 (6)0.0064 (5)0.0077 (5)0.0012 (4)
C10.027 (2)0.030 (2)0.047 (2)0.0013 (17)0.0045 (18)0.0051 (19)
C20.031 (2)0.026 (2)0.039 (2)0.0027 (16)0.0076 (18)0.0004 (16)
C30.069 (3)0.043 (3)0.027 (2)0.015 (2)0.003 (2)0.0047 (18)
C40.071 (3)0.034 (2)0.031 (2)0.019 (2)0.007 (2)0.0035 (18)
C50.033 (2)0.024 (2)0.033 (2)0.0001 (16)0.0017 (17)0.0005 (16)
C60.038 (2)0.037 (2)0.029 (2)0.0021 (18)0.0016 (17)0.0010 (17)
C70.040 (2)0.029 (2)0.034 (2)0.0042 (18)0.0095 (18)0.0027 (17)
C80.035 (2)0.019 (2)0.039 (2)0.0080 (16)0.0056 (19)0.0027 (17)
C90.031 (2)0.026 (2)0.041 (2)0.0037 (16)0.0038 (18)0.0007 (17)
C100.036 (2)0.042 (3)0.035 (2)0.0087 (19)0.0097 (18)0.0001 (19)
C110.075 (3)0.077 (4)0.037 (2)0.012 (3)0.021 (3)0.008 (2)
C120.084 (4)0.065 (4)0.074 (4)0.002 (3)0.017 (3)0.036 (3)
Geometric parameters (Å, º) top
Zn1—O12.056 (3)C3—C41.382 (5)
Zn1—O2i2.017 (3)C3—H30.9300
Zn1—O32.045 (3)C4—C51.388 (5)
Zn1—O4i2.057 (3)C4—H40.9300
Zn1—O51.987 (2)C5—C61.382 (5)
Zn1—Zn1i2.9188 (11)C6—C71.379 (5)
N1—C101.304 (5)C6—H60.9300
N1—C111.446 (5)C7—H70.9300
N1—C121.465 (6)C8—C91.520 (5)
O1—C11.250 (4)C9—H9A0.9700
O2—C11.263 (4)C9—H9B0.9700
O3—C81.258 (4)C10—H100.9300
O4—C81.247 (4)C11—H11A0.9600
O5—C101.252 (4)C11—H11B0.9600
C1—C21.498 (5)C11—H11C0.9600
S1—C91.794 (4)C12—H12A0.9600
C5—S1ii1.769 (4)C12—H12B0.9600
C2—C31.375 (5)C12—H12C0.9600
C2—C71.393 (5)
O5—Zn1—O2i103.50 (11)C5—C4—H4120.2
O5—Zn1—O3102.08 (10)C6—C5—C4119.0 (3)
O2i—Zn1—O388.95 (11)C6—C5—S1ii117.2 (3)
O5—Zn1—O195.82 (11)C4—C5—S1ii123.6 (3)
O2i—Zn1—O1160.39 (11)C7—C6—C5120.6 (4)
O3—Zn1—O190.32 (11)C7—C6—H6119.7
O5—Zn1—O4i97.23 (10)C5—C6—H6119.7
O2i—Zn1—O4i88.02 (11)C6—C7—C2120.7 (3)
O3—Zn1—O4i160.63 (10)C6—C7—H7119.7
O1—Zn1—O4i86.19 (12)C2—C7—H7119.7
O5—Zn1—Zn1i167.45 (8)O4—C8—O3126.4 (4)
O2i—Zn1—Zn1i88.32 (8)O4—C8—C9118.4 (3)
O3—Zn1—Zn1i82.07 (8)O3—C8—C9115.2 (3)
O1—Zn1—Zn1i72.18 (8)C8—C9—S1115.8 (3)
O4i—Zn1—Zn1i78.72 (7)C8—C9—H9A108.3
C10—N1—C11121.4 (4)S1—C9—H9A108.3
C10—N1—C12121.4 (4)C8—C9—H9B108.3
C11—N1—C12117.2 (4)S1—C9—H9B108.3
C1—O1—Zn1136.7 (3)H9A—C9—H9B107.4
C1—O2—Zn1i117.4 (2)O5—C10—N1123.5 (4)
C8—O3—Zn1124.3 (2)O5—C10—H10118.3
C8—O4—Zn1i128.3 (2)N1—C10—H10118.3
C10—O5—Zn1119.4 (2)N1—C11—H11A109.5
C5iii—S1—C9103.83 (17)N1—C11—H11B109.5
O1—C1—O2125.3 (4)H11A—C11—H11B109.5
O1—C1—C2117.1 (3)N1—C11—H11C109.5
O2—C1—C2117.6 (3)H11A—C11—H11C109.5
C3—C2—C7118.0 (3)H11B—C11—H11C109.5
C3—C2—C1120.9 (4)N1—C12—H12A109.5
C7—C2—C1121.1 (3)N1—C12—H12B109.5
C2—C3—C4121.8 (4)H12A—C12—H12B109.5
C2—C3—H3119.1N1—C12—H12C109.5
C4—C3—H3119.1H12A—C12—H12C109.5
C3—C4—C5119.7 (4)H12B—C12—H12C109.5
C3—C4—H4120.2
O5—Zn1—O1—C1179.8 (4)O2—C1—C2—C712.8 (5)
O2i—Zn1—O1—C19.7 (6)C7—C2—C3—C42.1 (6)
O3—Zn1—O1—C178.1 (4)C1—C2—C3—C4175.7 (4)
O4i—Zn1—O1—C182.9 (4)C2—C3—C4—C51.3 (7)
Zn1i—Zn1—O1—C13.5 (4)C3—C4—C5—C63.7 (6)
O5—Zn1—O3—C8166.3 (3)C3—C4—C5—S1ii171.7 (3)
O2i—Zn1—O3—C890.1 (3)C4—C5—C6—C72.7 (6)
O1—Zn1—O3—C870.3 (3)S1ii—C5—C6—C7173.0 (3)
O4i—Zn1—O3—C89.1 (5)C5—C6—C7—C20.7 (6)
Zn1i—Zn1—O3—C81.6 (3)C3—C2—C7—C63.1 (6)
O2i—Zn1—O5—C10126.8 (3)C1—C2—C7—C6174.7 (3)
O3—Zn1—O5—C10141.4 (3)Zn1i—O4—C8—O35.6 (5)
O1—Zn1—O5—C1049.8 (3)Zn1i—O4—C8—C9176.9 (2)
O4i—Zn1—O5—C1037.1 (3)Zn1—O3—C8—O41.4 (5)
Zn1i—Zn1—O5—C1033.2 (5)Zn1—O3—C8—C9179.1 (2)
Zn1—O1—C1—O23.1 (6)O4—C8—C9—S123.8 (4)
Zn1—O1—C1—C2175.6 (3)O3—C8—C9—S1158.4 (3)
Zn1i—O2—C1—O10.6 (5)C5iii—S1—C9—C869.4 (3)
Zn1i—O2—C1—C2179.2 (2)Zn1—O5—C10—N1173.4 (3)
O1—C1—C2—C311.8 (5)C11—N1—C10—O50.2 (6)
O2—C1—C2—C3169.4 (4)C12—N1—C10—O5179.4 (4)
O1—C1—C2—C7165.9 (3)
Symmetry codes: (i) x+1, y+2, z; (ii) x, y1, z; (iii) x, y+1, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C9—H9B···O3iv0.972.503.365 (4)148
C12—H12B···O5v0.962.523.476 (6)172
Symmetry codes: (iv) x, y+2, z; (v) x+1/2, y1/2, z+1/2.

Experimental details

Crystal data
Chemical formula[Zn(C9H6O4S)(C3H7NO)]
Mr348.66
Crystal system, space groupMonoclinic, P21/n
Temperature (K)298
a, b, c (Å)7.873 (3), 10.225 (3), 17.006 (6)
β (°) 97.014 (4)
V3)1358.7 (8)
Z4
Radiation typeMo Kα
µ (mm1)1.98
Crystal size (mm)0.35 × 0.34 × 0.24
Data collection
DiffractometerBruker SMART APEX II CCD
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 2003)
Tmin, Tmax0.544, 0.648
No. of measured, independent and
observed [I > 2σ(I)] reflections
5851, 2402, 1855
Rint0.032
(sin θ/λ)max1)0.595
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.037, 0.091, 1.00
No. of reflections2402
No. of parameters183
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.65, 0.50

Computer programs: SMART (Bruker, 2001), SAINT-Plus (Bruker, 2001), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), DIAMOND (Brandenburg, 2008) and ORTEP-3 (Farrugia, 1997), PLATON (Spek, 2009).

Selected bond lengths (Å) top
Zn1—O12.056 (3)Zn1—O51.987 (2)
Zn1—O2i2.017 (3)S1—C91.794 (4)
Zn1—O32.045 (3)C5—S1ii1.769 (4)
Zn1—O4i2.057 (3)
Symmetry codes: (i) x+1, y+2, z; (ii) x, y1, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C9—H9B···O3iii0.972.503.365 (4)148
C12—H12B···O5iv0.962.523.476 (6)172
Symmetry codes: (iii) x, y+2, z; (iv) x+1/2, y1/2, z+1/2.
 

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