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The crystal structure of the title thia­zolecarb­oxy­lic acid derivative, C6H7NO2S, (I), has been determined from single-crystal X-ray analysis at 100 K. In the crystal packing, an inter­play of O—H...N and C—H...O hydrogen bonds connects the mol­ecules to form C(6)R22(8) polymeric chains, which are further linked via weak C—H...O hydrogen bonds into a two-dimensional supra­molecular framework. The relative contributions of different inter­actions to the Hirshfeld surface in (I) and a few related thia­zolecarb­oxy­lic acid derivatives indicate that the H...H, N...H and O...H contacts can account for about 50–70% of the total Hirshfeld surface area in this class of compound.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S010827011204142X/cu3014sup1.cif
Contains datablocks I, global

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S010827011204142X/cu3014Isup2.hkl
Contains datablock I

cml

Chemical Markup Language (CML) file https://doi.org/10.1107/S010827011204142X/cu3014Isup3.cml
Supplementary material

CCDC reference: 914654

Comment top

Non-covalent molecular interactions, in particular hydrogen bonds, play an important role in the field of crystal engineering (Desiraju, 1996). It is well known that electronegative atoms such as N and O can form strong hydrogen bonds, D—H···A (where D is a donor and A an acceptor), with an estimated interaction energy in the range of 15–60 kJ mol-1 (Aburaya et al., 2008). These hydrogen bonds often lead to the self-assembly of molecules, whereby supramolecular structures are built from a relatively small building block or synthon with simple aromatic functionalities. In recent decades, moderately strong hydrogen bonds (energy range 4–15 kJ mol-1) and weaker interactions (usually 4 kJ mol-1), such as C—H···O, C/N—H···π and S···S interactions, have also received much attention due to their ability to form supramolecular motifs in molecular solids (Desiraju, 2011; Arunan et al., 2011). These interactions are individually weaker and geometrically less well defined, but their combined effect can be just as important as that of strong interactions (Desiraju & Steiner, 1999). In order to improve the reliability of studies of weak intermolecular interactions, accurate positions for the H atoms in the molecule are necessary, and consequently the X-ray structure analysis should be carried out using a high-quality data set collected at a sufficiently low temperature. In this context, the small molecule methylthiazolecarboxylic acid [Should this not refer to 2,4-dimethylthiazole-5-carboxylic acid?], possessing O—H and C—H donors and a carboxyl CO acceptor, constitutes an ideal structural component with a rigid core. A search of the Cambridge Structural Database (CSD, Version 5.33, November 2011 release; Allen, 2002) for simple aromatic thiazolecarboxylic acids returned only 5 hits (excluding duplicate structure determinations), with refcodes BETKUH (Curtis et al., 2004; CCDC No. 237120), BUFMEV (Quan et al., 2009; CCDC No. 751282), IYULUJ (Fong et al., 2004; CCDC No. 219844), JEVCOD (Chen et al., 2007; CCDC No. 638357) and ONOHEF (Rossin et al., 2011; CCDC No. 781928) (see scheme). In order to analyse the role of intermolecular O—H···N and C—H···O hydrogen bonds in building any possible supramolecular assembly, the structural characterization of 2,4-dimethylthiazole-5-carboxylic acid, (I), has now been undertaken at 100 K. An investigation of the close intermolecular interactions in (I) and in some related thiazolecarboxylic acid derivatives via Hirshfeld surface analysis is also presented.

The molecule of (I) (Fig. 1), containing a thiazole ring (S1/C1/C2/N1/C3), is essentially planar, with r.m.s. fits of the atomic positions (excluding atom C6) of 0.011 Å; the exocyclic methyl atom C6 deviates from the least-squares plane through atoms S1/C1–C5/N1/O1/O2 by 0.087 (2) Å. The C1—S1 [1.7231 (10) Å] and C3—S1 [1.7148 (11) Å] bond lengths indicate single-bond character (Allen et al., 1987). The C3—N1 [1.3180 (13) Å] and C2—N1 [1.3874 (13) Å] (Table 1) distances agree well with the mean values for CN [1.31 Å] and C—N [1.38 Å] bond lengths based on 193 –Csp2N—Csp2– fragments obtained using Mogul (Bruno et al., 2004) for a search of the CSD for related organic compounds. The lengthening of the C1—C2 bond [1.3748 (13) Å] in (I) compared with the average Csp2(cyclic)Csp2(cyclic) distance of 1.35 Å calculated using 52770 organic structures in the CSD is a consequence of extended π-conjugation between the thiazole ring and the carboxylic acid fragment.

In the crystal structure of (I), a combination of O—H···N and C—H···O hydrogen bonds and an S···S interaction (Table 2) generates a supramolecular framework. Considering the criteria X···A < 3.0 Å, H···A < 2.2 Å and 150 < X—H···A < 180°, the observed O—H···N interaction in (I) can be classified as a strong hydrogen bond (Desiraju & Steiner, 1999), whereas the corresponding C—H···O interactions can be termed weak hydrogen bonds (Desiraju & Steiner, 1999) on the basis of the criteria 3.0 < X···A < 3.5 Å, 2.2 < H···A < 2.8 Å and 120 < X—H···A < 180°. The O1—H1···N1(x + 1, -y + 3/2, z - 1/2) and C6—H6A···O2(x - 1, -y + 3/2, z + 1/2) hydrogen bonds connect the molecules of (I) into an R22(8) graph-set dimer (Bernstein et al., 1995). Adjacent R22(8) rings (marked A in Fig. 2) are linked to form a one-dimensional C11(6)R22(8) polymeric chain running along the [201] direction. Further linking of parallel chains via intermolecular C5—H5A···O2(x - 1, y, z) and C6—H6B···O2(x, -y + 3/2, z + 1/2) hydrogen bonds generates two R32(10) and R33(15) rings, labelled B and C, respectively, in Fig. 3. The resulting molecular assembly can be visualized as a two-dimensional framework built from edge-fused ABCABC– synthons (Fig. 4). Additional reinforcement within the framework is provided by a non-bonded S···S interaction with an interatomic separation of 3.4685 (5) Å. Similar S···S interactions have been reported for related sulfur-containing compounds (Ksiazek et al., 2009).

The Hirshfeld surface (Spackman & Jayatilaka, 2009) and associated two-dimensional fingerprint plot (Spackman & McKinnon, 2002) for (I) were calculated using CrystalExplorer (Wolff et al., 2007) and are illustrated in Fig. 4. The dominant interactions between the carboxylic acid OH group and the thiazole ring N atom can be seen in the Hirshfeld surface as bright-red areas marked a and b in Fig. 4(a). The pale-red spots labelled c, d, e and f are due to C—H···O interactions (Fig. 4a). Other visible spots in Fig. 4(a) correspond to H···S and S···S contacts. In the corresponding two-dimensional fingerprint plot (Fig. 4b), two pairs of sharp spikes labelled a and b, and c and d, are characteristic of a cyclic hydrogen-bonded R22(8) synthon. The difference between the lengths of the outer pair of spikes, a and b, in the region 1.7 < de + di < 2.7 Å, and the inner pair of spikes, c and d, in the region 2.2 < de + di < 2.7 Å, is a consequence of different types of hydrogen bonds (O—H···N and C—H···O) involved in building the R22(8) synthon. The upper spikes a and c (Fig. 4b) represent the donor spikes (carboxylic acid and methyl H atoms interacting with the N atom of the thiazole ring and the O atom of the COOH group), and the lower spikes b and d the acceptor spikes (thiazole N and carboxylic acid O atoms interacting with the H atoms of the COOH and CH3 fragments). The wings (Fig. 4b, marked with black circles) in the (di, de) regions of (1.9 Å, 1.2 Å) and (1.2 Å, 1.9 Å) are attributable to the S···H interactions. The density of points in the (di, de) regions of (1.7 Å, 1.7 Å), marked g in the fingerprint plot (Fig. 4b), indicates the presence of S···S contacts.

The relative contributions of different interactions to the Hirshfeld surface were calculated for (I) and for a few thiazolecarboxylic acid derivatives (Fig. 5) retrieved from the CSD. Due to differences in the number and type of substituents on the thiazolecarboxylic acid core in the structures used in Fig. 5, they are not directly comparable across the compounds, but it offers some insight into the effect of different substituents on the thiazolecarboxylic acid backbone. The H···H, N···H and O···H contacts contribute about 50–70% of the Hirshfeld surface area in (I) (65.1%), BETKUH (62.7%), IYULUZ (66.5%), JEVCOD (52.3%) and ONOHEF (52.7%); the remaining contributions were distributed among the S···H, C···H, C···C, C···N and C···O interactions. With an additional CH3 substitution at the thiazole ring 4-position in (I) compared with IYULUJ, the contribution of the S···H contacts to the Hirshfeld surface increases significantly, from 1.4% in IYULUJ to 13.6% in (I), with a corresponding decrease in the N···H interactions, from 13.1% in IYULUJ to 7.3% in (I). Although (I) and BUFMEV differ only in terms of substitution at the thiazole 4-position [CH3 in (I) and CF3 in BUFMEV], the contributions of various contacts to the Hirshfeld surfaces of the two compounds are widely different. In BUFMEV, intermolecular contacts involving F atoms can account for 52.4% of the Hirshfeld surface area, while the corresponding contribution of H···H, N···H and O···H contacts combinedr is only 26.5%. The variation in the contributions of different interactions to the Hirshfeld surfaces of BUFMEV and other compounds used in Fig. 5 is a consequence of differences in the stereoelectronic properties of C—H and C—F bonds, due to the highly polar nature of the latter (O'Hagan, 2008).

Related literature top

For related literature, see: Aburaya et al. (2008); Allen (2002); Allen et al. (1987); Arunan et al. (2011); Bernstein et al. (1995); Bruker (2007); Bruno et al. (2004); Chen et al. (2007); Curtis et al. (2004); Desiraju (1996, 2011); Desiraju & Steiner (1999); Fong et al. (2004); Ksiazek et al. (2009); O'Hagan (2008); Quan et al. (2009); Rossin et al. (2011); Sheldrick (2005, 2007); Spackman & Jayatilaka (2009); Spackman & McKinnon (2002); Wolff et al. (2007).

Experimental top

The title compound, 2,4-dimethylthiazole-5-carboxylic acid, (I), was purchased from Aldrich (CAS No. 53137-27-2) and used without further purification. Good quality colourless single crystals were obtained from a solution in methanol by slow evaporation at room temperature (300 K).

Refinement top

The crystal was twinned and the twin matrix was determined using the program CELL_NOW (Sheldrick, 2005), with the second domain being rotated with respect to the first by 179.9° about the reciprocal axis (1.000 -0.003 0.993). The twin law to convert hkl from the first to the second domain was (0.518 0.001 0.485/ -0.006 -1.000 0.000/ 1.507 -0.001 -0.518). Data processing carried out using both orientation matrices using SAINT (Bruker, 2007) resulted in 14967 reflections. The data were merged (Rint = 0.055) and a multi-scan absorption correction was applied using TWINABS (Sheldrick, 2007). The twin fraction refined to a value of 0.435 (2). H atoms, located from difference Fourier maps, were refined with isotropic displacement parameters.

Computing details top

Data collection: APEX2 (Bruker, 2007); cell refinement: SAINT and XPREP (Bruker, 2007); data reduction: SAINT and XPREP (Bruker, 2007); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997), DIAMOND (Brandenburg, 1999) and Mercury (Macrae et al., 2008); software used to prepare material for publication: PLATON (Spek, 2009) and PARST (Nardelli, 1995).

Figures top
[Figure 1] Fig. 1. An ORTEP view of (I) showing the atom numbering scheme. Displacement ellipsoids are drawn at the 40% probability level and H atoms are shown as spheres with radii scaled to their Uiso.
[Figure 2] Fig. 2. The hydrogen bonds (dashed lines) forming a one-dimensional C11(6)R22(8) polymeric chain running along the [201] direction in (I). H atoms not participating in the chain formation have been omitted for clarity. [Symmetry codes: (i) x + 1, -y + 3/2, z - 1/2; (iii) x - 1, -y + 3/2, z + 1/2] [Atoms are not uniquely labelled and labels are too small - please revise]
[Figure 3] Fig. 3. Part of the crystal structure of (I), showing the formation of the two-dimensional framework with fused R22(8) (denoted A), R32(10) (denoted B) and R33(15) (denoted C) rings. Dashed lines indicate hydrogen bonds. [Symmetry codes: (i) x + 1, -y + 3/2, z - 1/2; (ii) x - 1, y, z; (iii) x - 1, -y + 3/2, z + 1/2; (iv) x, -y + 3/2, z + 1/2] [Atoms N1i are not unique - please revise (with larger labels)]
[Figure 4] Fig. 4. (a) The Hirshfeld surfaces and (b) two-dimensional fingerprint plots for (I).
[Figure 5] Fig. 5. The relative contributions of various intermolecular contacts to the Hirshfeld surface area in (I) and in related structures retrieved from the CSD.
2,4-Dimethyl-1,3-thiazole-5-carboxylic acid top
Crystal data top
C6H7NO2SF(000) = 328
Mr = 157.19Dx = 1.526 Mg m3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P2ybcCell parameters from 998 reflections
a = 4.8120 (3) Åθ = 3.5–49.9°
b = 14.3729 (7) ŵ = 0.40 mm1
c = 9.9178 (5) ÅT = 100 K
β = 94.037 (2)°Plate, colourless
V = 684.24 (6) Å30.60 × 0.55 × 0.12 mm
Z = 4
Data collection top
Bruker Kappa APEXII CCD area-detector
diffractometer
2299 independent reflections
Radiation source: fine-focus sealed tube2237 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.000
ω and ϕ scansθmax = 30.0°, θmin = 2.5°
Absorption correction: multi-scan
(TWINABS; Sheldrick, 2007)
h = 66
Tmin = 0.794, Tmax = 0.953k = 200
2299 measured reflectionsl = 135
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)] = 0.032Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.091All H-atom parameters refined
S = 1.09 w = 1/[σ2(Fo2) + (0.0563P)2 + 0.1582P]
where P = (Fo2 + 2Fc2)/3
2299 reflections(Δ/σ)max = 0.001
120 parametersΔρmax = 0.40 e Å3
0 restraintsΔρmin = 0.25 e Å3
Crystal data top
C6H7NO2SV = 684.24 (6) Å3
Mr = 157.19Z = 4
Monoclinic, P21/cMo Kα radiation
a = 4.8120 (3) ŵ = 0.40 mm1
b = 14.3729 (7) ÅT = 100 K
c = 9.9178 (5) Å0.60 × 0.55 × 0.12 mm
β = 94.037 (2)°
Data collection top
Bruker Kappa APEXII CCD area-detector
diffractometer
2299 independent reflections
Absorption correction: multi-scan
(TWINABS; Sheldrick, 2007)
2237 reflections with I > 2σ(I)
Tmin = 0.794, Tmax = 0.953Rint = 0.000
2299 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0320 restraints
wR(F2) = 0.091All H-atom parameters refined
S = 1.09Δρmax = 0.40 e Å3
2299 reflectionsΔρmin = 0.25 e Å3
120 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
S10.45810 (5)0.619635 (16)0.00899 (3)0.01593 (10)
O10.78973 (17)0.72378 (5)0.16442 (8)0.01835 (17)
O20.66108 (19)0.86916 (5)0.10973 (9)0.02072 (18)
N10.15541 (18)0.71303 (6)0.16100 (9)0.01456 (18)
C10.4659 (2)0.73920 (7)0.00279 (10)0.0143 (2)
C20.2919 (2)0.77796 (7)0.08597 (10)0.01405 (19)
C30.2247 (2)0.62707 (7)0.13147 (11)0.0153 (2)
C40.6463 (2)0.78554 (7)0.09681 (10)0.01511 (19)
C50.2407 (3)0.87877 (7)0.11043 (13)0.0185 (2)
C60.1226 (2)0.54277 (7)0.20076 (12)0.0188 (2)
H10.889 (5)0.7486 (15)0.220 (2)0.046 (5)*
H5A0.057 (5)0.8942 (14)0.089 (2)0.050 (6)*
H5B0.275 (5)0.8936 (12)0.196 (2)0.043 (5)*
H5C0.356 (5)0.9172 (15)0.059 (2)0.058 (6)*
H6A0.040 (4)0.5538 (13)0.240 (2)0.039 (5)*
H6B0.256 (5)0.5241 (14)0.270 (2)0.048 (6)*
H6C0.097 (4)0.4920 (11)0.147 (2)0.034 (5)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.01682 (16)0.01415 (14)0.01783 (16)0.00063 (8)0.00839 (11)0.00104 (8)
O10.0180 (4)0.0197 (4)0.0187 (4)0.0007 (3)0.0106 (3)0.0006 (3)
O20.0221 (4)0.0175 (3)0.0237 (4)0.0013 (3)0.0092 (3)0.0020 (3)
N10.0140 (4)0.0154 (4)0.0148 (4)0.0002 (3)0.0054 (3)0.0005 (3)
C10.0146 (5)0.0140 (4)0.0146 (5)0.0007 (3)0.0039 (3)0.0007 (3)
C20.0132 (4)0.0150 (4)0.0142 (4)0.0001 (3)0.0032 (3)0.0005 (3)
C30.0140 (4)0.0170 (4)0.0155 (5)0.0000 (3)0.0054 (4)0.0007 (3)
C40.0131 (4)0.0191 (4)0.0134 (4)0.0006 (3)0.0031 (3)0.0005 (3)
C50.0221 (6)0.0143 (5)0.0198 (5)0.0011 (3)0.0060 (4)0.0016 (3)
C60.0203 (5)0.0151 (4)0.0222 (5)0.0011 (4)0.0090 (4)0.0013 (4)
Geometric parameters (Å, º) top
C1—S11.7231 (10)C2—C51.4924 (13)
C3—S11.7148 (11)C3—C61.4932 (14)
C4—O11.3339 (12)C5—H5A0.92 (2)
O1—H10.84 (2)C5—H5B0.88 (2)
C4—O21.2112 (13)C5—H5C0.96 (2)
C2—N11.3874 (13)C6—H6A0.91 (2)
C3—N11.3180 (13)C6—H6B0.95 (2)
C1—C21.3748 (13)C6—H6C0.906 (18)
C1—C41.4766 (13)
C1—S1—C390.25 (5)O1—C4—C1111.42 (9)
C4—O1—H1112.9 (15)C2—C5—H5A111.3 (13)
C2—N1—C3112.00 (9)C2—C5—H5B111.7 (12)
C2—C1—C4129.28 (9)H5A—C5—H5B106.0 (19)
C2—C1—S1110.09 (7)C2—C5—H5C111.5 (14)
C4—C1—S1120.61 (8)H5A—C5—H5C108.8 (18)
C1—C2—N1113.80 (9)H5B—C5—H5C107.3 (18)
C1—C2—C5127.76 (9)C3—C6—H6A112.2 (12)
N1—C2—C5118.44 (9)C3—C6—H6B109.7 (13)
N1—C3—C6124.18 (9)H6A—C6—H6B107.0 (18)
N1—C3—S1113.85 (8)C3—C6—H6C114.8 (12)
C6—C3—S1121.92 (8)H6A—C6—H6C107.9 (17)
O2—C4—O1124.80 (9)H6B—C6—H6C104.8 (17)
O2—C4—C1123.77 (9)
C3—S1—C1—C20.11 (8)C2—N1—C3—C6176.78 (10)
C3—S1—C1—C4178.83 (9)C2—N1—C3—S10.65 (12)
C4—C1—C2—N1179.05 (10)C1—S1—C3—N10.45 (9)
S1—C1—C2—N10.22 (11)C1—S1—C3—C6177.05 (10)
C4—C1—C2—C50.13 (18)C2—C1—C4—O21.27 (18)
S1—C1—C2—C5178.71 (10)S1—C1—C4—O2179.99 (9)
C3—N1—C2—C10.56 (13)C2—C1—C4—O1178.52 (10)
C3—N1—C2—C5178.47 (10)S1—C1—C4—O10.20 (12)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1···N1i0.84 (2)1.88 (2)2.7108 (11)170 (2)
C5—H5A···O2ii0.92 (2)2.67 (2)3.4220 (17)139.6 (18)
C6—H6A···O2iii0.91 (2)2.41 (2)3.2640 (14)155.7 (16)
C6—H6B···O2iv0.95 (2)2.69 (2)3.3413 (16)126.4 (16)
Symmetry codes: (i) x+1, y+3/2, z1/2; (ii) x1, y, z; (iii) x1, y+3/2, z+1/2; (iv) x, y+3/2, z+1/2.

Experimental details

Crystal data
Chemical formulaC6H7NO2S
Mr157.19
Crystal system, space groupMonoclinic, P21/c
Temperature (K)100
a, b, c (Å)4.8120 (3), 14.3729 (7), 9.9178 (5)
β (°) 94.037 (2)
V3)684.24 (6)
Z4
Radiation typeMo Kα
µ (mm1)0.40
Crystal size (mm)0.60 × 0.55 × 0.12
Data collection
DiffractometerBruker Kappa APEXII CCD area-detector
diffractometer
Absorption correctionMulti-scan
(TWINABS; Sheldrick, 2007)
Tmin, Tmax0.794, 0.953
No. of measured, independent and
observed [I > 2σ(I)] reflections
2299, 2299, 2237
Rint0.000
(sin θ/λ)max1)0.704
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.032, 0.091, 1.09
No. of reflections2299
No. of parameters120
H-atom treatmentAll H-atom parameters refined
Δρmax, Δρmin (e Å3)0.40, 0.25

Computer programs: APEX2 (Bruker, 2007), SAINT and XPREP (Bruker, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 1997), DIAMOND (Brandenburg, 1999) and Mercury (Macrae et al., 2008), PLATON (Spek, 2009) and PARST (Nardelli, 1995).

Selected geometric parameters (Å, º) top
C1—S11.7231 (10)C2—N11.3874 (13)
C3—S11.7148 (11)C3—N11.3180 (13)
C4—O11.3339 (12)C1—C21.3748 (13)
C4—O21.2112 (13)
C1—S1—C390.25 (5)C2—N1—C3112.00 (9)
C2—C1—C4—O21.27 (18)S1—C1—C4—O10.20 (12)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1···N1i0.84 (2)1.88 (2)2.7108 (11)170 (2)
C5—H5A···O2ii0.92 (2)2.67 (2)3.4220 (17)139.6 (18)
C6—H6A···O2iii0.91 (2)2.41 (2)3.2640 (14)155.7 (16)
C6—H6B···O2iv0.95 (2)2.69 (2)3.3413 (16)126.4 (16)
Symmetry codes: (i) x+1, y+3/2, z1/2; (ii) x1, y, z; (iii) x1, y+3/2, z+1/2; (iv) x, y+3/2, z+1/2.
 

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