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In the title compound, [Zn(C8H8N3S2)2], the Zn atom is coordinated by the two ligands in a tridentate manner, via the pyridyl N, the azomethine N and the thiol­ate S atom; the coordination geometry is distorted octa­hedral, with the two ligands in the mer configuration (two S atoms and two pyridyl N atoms are cis with respect to each other and the azomethine N atoms is trans). The mol­ecules are linked by C—H...S hydrogen bonds, forming a three-dimensional network structure.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536807068493/wn2230sup1.cif
Contains datablocks I, global

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536807068493/wn2230Isup2.hkl
Contains datablock I

CCDC reference: 677801

Key indicators

  • Single-crystal X-ray study
  • T = 293 K
  • Mean [sigma](C-C) = 0.006 Å
  • R factor = 0.034
  • wR factor = 0.079
  • Data-to-parameter ratio = 18.8

checkCIF/PLATON results

No syntax errors found



Alert level C PLAT062_ALERT_4_C Rescale T(min) & T(max) by ..................... 0.99 PLAT220_ALERT_2_C Large Non-Solvent C Ueq(max)/Ueq(min) ... 2.55 Ratio PLAT222_ALERT_3_C Large Non-Solvent H Ueq(max)/Ueq(min) ... 3.03 Ratio PLAT232_ALERT_2_C Hirshfeld Test Diff (M-X) Zn1 - S3 .. 6.91 su PLAT242_ALERT_2_C Check Low Ueq as Compared to Neighbors for C7 PLAT242_ALERT_2_C Check Low Ueq as Compared to Neighbors for C15 PLAT420_ALERT_2_C D-H Without Acceptor N3 - H3A ... ? PLAT420_ALERT_2_C D-H Without Acceptor N6 - H6A ... ? PLAT717_ALERT_1_C D...A Unknown or Inconsistent Label .......... SL
Alert level G REFLT03_ALERT_4_G Please check that the estimate of the number of Friedel pairs is correct. If it is not, please give the correct count in the _publ_section_exptl_refinement section of the submitted CIF. From the CIF: _diffrn_reflns_theta_max 27.13 From the CIF: _reflns_number_total 4584 Count of symmetry unique reflns 2462 Completeness (_total/calc) 186.19% TEST3: Check Friedels for noncentro structure Estimate of Friedel pairs measured 2122 Fraction of Friedel pairs measured 0.862 Are heavy atom types Z>Si present yes PLAT199_ALERT_1_G Check the Reported _cell_measurement_temperature 293 K PLAT200_ALERT_1_G Check the Reported _diffrn_ambient_temperature . 293 K PLAT860_ALERT_3_G Note: Number of Least-Squares Restraints ....... 1
0 ALERT level A = In general: serious problem 0 ALERT level B = Potentially serious problem 9 ALERT level C = Check and explain 4 ALERT level G = General alerts; check 3 ALERT type 1 CIF construction/syntax error, inconsistent or missing data 6 ALERT type 2 Indicator that the structure model may be wrong or deficient 2 ALERT type 3 Indicator that the structure quality may be low 2 ALERT type 4 Improvement, methodology, query or suggestion 0 ALERT type 5 Informative message, check

Comment top

The wide variety of biological activity exhibited by thiosemicarbazones (Kasuga et al., 2001) and Schiff bases derived from S-alkyldithiocarbazates (Akbar Ali et al., 2001) and their interesting coordination chemistry have stimulated considerable research interest in these compounds (Casas et al., 2000). Some Schiff bases of S-alkyl esters of dithiocarbazic acid and their complexes were found to display antifungal and antibacterial properties (Tarafder et al., 2003). Recently we reported the Co(II) complex of the S-containing Schiff base ligand methyl 2-pyridylmethylidenehydrazinecarbodithioate (NNS-) (Lin et al., 2007). As a part of structural studies of compounds containing the sulfur-nitrogen chelating ligand (Chen et al., 2003a,b), we report here the synthesis and structure of the compound, bis(methyl 2-pyridylmethylidenehydrazinecarbodithioato)zinc(II), Zn(NNS)2.

The Zn atom is six-coordinated by the two tridentate NNS- anions in a distorted octahedral geometry (Fig. 1). The ligands chelate the Zn(II) ion via the pyridyl N, the azomethine N, and the thiolate S atoms in a mer-configuration with four five-membered rings. The two azomethine N atoms (N2 and N5) are trans to each other, while the sulfur atoms (S1 and S3) and pyridyl N atoms (N1 and N4) are in cis positions. The two almost planar ligands [maximum deviation from their least-squares planes is 0.038 (3) Å] approach the central Zn(II) atom in an orthogonal orientation. The pyridyl ring and the two five-membered chelate rings formed by each ligand display very small dihedral angles between the planes. For each ligand, the maximum dihedral angle of 2.5 (1)° is between two neighbouring five-membered chelate rings (viz. Zn1—S1—C7—N3—N2 and Zn1—N1—C5—C6—N2).

The molecules are linked by C—H···S hydrogen bonds. As shown in Fig. 2, each molecular unit forms four acceptor/donor hydrogen bonds with four neighboring molecular units. resulting in a three-dimensional network structure.

Related literature top

For general background, see: Akbar Ali et al. (2001); Casas et al. (2000); Kasuga et al. (2001); Tarafder et al. (2003). For related structures, see: Chen et al. (2003a,b); Lin et al. (2007).

Experimental top

A solution of Zn(ClO4)2 (363 mg, 1.00 mmol) in CH3OH (20 ml) was slowly added to a solution of methyl 2-pyridylmethylidenehydrazinecarbodithioate (HNNS) (410 mg, 1.95 mmol) in CH3OH (10 ml). The resultant black-purple solution was stirred under N2 for 2 h at 323 K and then filtered. After addition of diethyl ether (20 ml), the filtrate was cooled to 253 K. A microcrystalline solid was collected after 24 h and dried under vacuum (yield: 264 mg, 55%). Brown block-shaped crystals suitable for X-ray diffraction were obtained in 2 d by slow diffusion of diethyl ether into a dilute solution of the title complex in methanol. The assigned structure was substantiated by elemental analysis; calculated for C16H16N6ZnS4: C 39.51, H 3.30, N 17.29%; found: C 39.46, H 3.38, N 17.23%.

Refinement top

All H atoms were placed in idealized positions (C—H = 0.93 or 0.97 Å), and refined in the riding-model approximation. Uiso(H) = xUeq(carrier atom), where x = 1.5 for methyl and 1.2 for all other H atoms.

Computing details top

Data collection: SMART (Bruker, 1998); cell refinement: SAINT (Bruker, 1998); data reduction: SAINT (Bruker, 1998); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL (Bruker, 1998); software used to prepare material for publication: SHELXTL (Bruker, 1998) and local programs.

Figures top
[Figure 1] Fig. 1. The molecular structure of the title compound. Dispacement ellipsoids are drawn at the 30% probability level. Hydrogen atoms have been omitted for clarity.
[Figure 2] Fig. 2. A view of the three-dimensional molecular network parallel to (010), formed by weak intermolecular C—H···S hydrogen bonds (dotted lines). Hydrogen atoms not involved in hydrogen bonds have been omitted.
Bis[methyl 2-(2-pyridylmethylidene)hydrazinecarbodithioato]zinc(II) top
Crystal data top
[Zn(C8H8N3S2)2]F(000) = 1000
Mr = 487.97Dx = 1.525 Mg m3
Orthorhombic, Pna21Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P2c-2nCell parameters from 5120 reflections
a = 18.630 (7) Åθ = 2.8–26.8°
b = 9.160 (3) ŵ = 1.56 mm1
c = 12.457 (4) ÅT = 293 K
V = 2125.8 (13) Å3Block, colorless
Z = 40.25 × 0.22 × 0.17 mm
Data collection top
Bruker SMART CCD area-detector
diffractometer
4584 independent reflections
Radiation source: fine-focus sealed tube3257 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.028
ϕ and ω scansθmax = 27.1°, θmin = 2.2°
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
h = 2313
Tmin = 0.745, Tmax = 0.777k = 1111
11500 measured reflectionsl = 1515
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)] = 0.034H-atom parameters constrained
wR(F2) = 0.079 w = 1/[σ2(Fo2) + (0.0305P)2 + 0.1243P]
where P = (Fo2 + 2Fc2)/3
S = 1.04(Δ/σ)max < 0.001
4584 reflectionsΔρmax = 0.25 e Å3
244 parametersΔρmin = 0.30 e Å3
1 restraintAbsolute structure: Flack (1983), 2122 Friedel pairs
Primary atom site location: structure-invariant direct methodsAbsolute structure parameter: 0.013 (12)
Crystal data top
[Zn(C8H8N3S2)2]V = 2125.8 (13) Å3
Mr = 487.97Z = 4
Orthorhombic, Pna21Mo Kα radiation
a = 18.630 (7) ŵ = 1.56 mm1
b = 9.160 (3) ÅT = 293 K
c = 12.457 (4) Å0.25 × 0.22 × 0.17 mm
Data collection top
Bruker SMART CCD area-detector
diffractometer
4584 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
3257 reflections with I > 2σ(I)
Tmin = 0.745, Tmax = 0.777Rint = 0.028
11500 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.034H-atom parameters constrained
wR(F2) = 0.079Δρmax = 0.25 e Å3
S = 1.04Δρmin = 0.30 e Å3
4584 reflectionsAbsolute structure: Flack (1983), 2122 Friedel pairs
244 parametersAbsolute structure parameter: 0.013 (12)
1 restraint
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
Zn10.056290 (19)0.37624 (4)0.00480 (4)0.05017 (12)
S10.06703 (6)0.16722 (11)0.12754 (9)0.0649 (3)
S20.16269 (7)0.12965 (14)0.30631 (10)0.0782 (4)
S30.15974 (5)0.33863 (11)0.11758 (9)0.0641 (3)
S40.16648 (8)0.15980 (16)0.30963 (11)0.0885 (4)
N10.05862 (16)0.6151 (3)0.0248 (2)0.0548 (9)
N20.11660 (15)0.4672 (3)0.1347 (2)0.0494 (7)
N30.14624 (17)0.3833 (4)0.2142 (2)0.0587 (8)
H3A0.17570.41720.26110.070*
N40.06136 (14)0.3920 (3)0.0321 (2)0.0527 (8)
N50.00813 (14)0.2761 (3)0.1317 (2)0.0468 (7)
N60.04532 (16)0.2141 (3)0.2144 (2)0.0563 (8)
H6A0.02520.16360.26420.068*
C10.0304 (2)0.6883 (5)0.1059 (4)0.0695 (11)
H1A0.00210.64050.15040.083*
C20.0468 (3)0.8328 (5)0.1276 (4)0.0782 (13)
H2A0.02680.88020.18640.094*
C30.0925 (3)0.9028 (5)0.0616 (4)0.0806 (13)
H3B0.10430.99980.07460.097*
C40.1219 (2)0.8307 (4)0.0255 (4)0.0708 (12)
H4A0.15320.87800.07230.085*
C50.1034 (2)0.6868 (4)0.0407 (3)0.0519 (9)
C60.13319 (19)0.6008 (4)0.1282 (3)0.0540 (9)
H6B0.16380.64310.17830.065*
C70.1259 (2)0.2492 (5)0.2121 (3)0.0513 (10)
C80.2232 (3)0.2385 (6)0.3797 (5)0.123 (2)
H8A0.24610.18010.43370.185*
H8B0.25890.27760.33200.185*
H8C0.19760.31720.41330.185*
C90.0957 (2)0.4483 (5)0.1153 (4)0.0715 (11)
H9A0.06950.49840.16700.086*
C100.1684 (2)0.4357 (5)0.1283 (4)0.0832 (14)
H10A0.19060.47780.18760.100*
C110.2080 (2)0.3619 (5)0.0549 (4)0.0846 (15)
H11A0.25730.35210.06320.102*
C120.1735 (2)0.3019 (5)0.0324 (4)0.0729 (12)
H12A0.19930.25190.08480.087*
C130.09986 (19)0.3174 (4)0.0405 (3)0.0529 (9)
C140.05961 (18)0.2558 (4)0.1289 (3)0.0543 (9)
H14A0.08260.20260.18240.065*
C150.1136 (2)0.2385 (4)0.2107 (3)0.0535 (10)
C160.1042 (3)0.0692 (7)0.3960 (4)0.131 (2)
H16A0.12980.02230.45330.197*
H16B0.07810.00270.35580.197*
H16C0.07130.13930.42530.197*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Zn10.0438 (2)0.0553 (2)0.0514 (2)0.00346 (17)0.0087 (2)0.0044 (2)
S10.0754 (7)0.0579 (6)0.0615 (6)0.0133 (5)0.0076 (6)0.0041 (5)
S20.0750 (8)0.0874 (9)0.0721 (7)0.0010 (6)0.0107 (6)0.0295 (6)
S30.0393 (5)0.0865 (7)0.0665 (6)0.0000 (5)0.0002 (5)0.0022 (6)
S40.0793 (9)0.0942 (9)0.0921 (9)0.0049 (7)0.0400 (8)0.0142 (7)
N10.0497 (16)0.0497 (16)0.065 (3)0.0043 (15)0.0092 (15)0.0022 (14)
N20.0492 (16)0.053 (2)0.0462 (16)0.0006 (14)0.0097 (14)0.0008 (15)
N30.0558 (19)0.071 (2)0.0496 (18)0.0080 (16)0.0192 (15)0.0006 (16)
N40.0441 (16)0.0578 (18)0.056 (2)0.0011 (14)0.0030 (14)0.0111 (14)
N50.0418 (17)0.0534 (17)0.0451 (15)0.0013 (13)0.0030 (14)0.0051 (14)
N60.057 (2)0.065 (2)0.0474 (17)0.0068 (15)0.0047 (15)0.0106 (15)
C10.066 (3)0.073 (3)0.070 (3)0.007 (2)0.016 (2)0.002 (2)
C20.097 (3)0.068 (3)0.070 (3)0.021 (2)0.008 (3)0.011 (2)
C30.101 (4)0.058 (3)0.083 (3)0.007 (3)0.005 (3)0.009 (2)
C40.080 (3)0.057 (2)0.076 (4)0.004 (2)0.002 (2)0.005 (2)
C50.051 (2)0.044 (2)0.060 (2)0.0033 (17)0.0019 (17)0.0037 (16)
C60.056 (2)0.052 (2)0.055 (2)0.0081 (17)0.0097 (19)0.0076 (18)
C70.051 (2)0.058 (3)0.045 (2)0.0007 (19)0.0046 (16)0.0083 (18)
C80.119 (4)0.148 (5)0.103 (4)0.015 (4)0.053 (4)0.024 (4)
C90.060 (3)0.079 (3)0.076 (3)0.000 (2)0.003 (2)0.026 (3)
C100.066 (3)0.089 (3)0.095 (3)0.001 (2)0.026 (3)0.032 (3)
C110.047 (2)0.093 (4)0.114 (4)0.004 (2)0.018 (3)0.023 (3)
C120.048 (2)0.090 (3)0.080 (3)0.019 (2)0.002 (2)0.016 (2)
C130.039 (2)0.060 (2)0.059 (2)0.0024 (17)0.0026 (17)0.0065 (18)
C140.045 (2)0.069 (2)0.049 (2)0.0080 (17)0.0058 (19)0.0063 (18)
C150.051 (2)0.056 (3)0.054 (2)0.0061 (19)0.0101 (19)0.0152 (17)
C160.158 (6)0.146 (5)0.090 (4)0.045 (4)0.054 (4)0.052 (4)
Geometric parameters (Å, º) top
Zn1—N52.130 (3)C1—H1A0.9300
Zn1—N22.139 (3)C2—C31.346 (7)
Zn1—N12.219 (3)C2—H2A0.9300
Zn1—N42.223 (3)C3—C41.384 (6)
Zn1—S12.4584 (13)C3—H3B0.9300
Zn1—S32.4814 (13)C4—C51.376 (5)
S1—C71.697 (4)C4—H4A0.9300
S2—C71.744 (4)C5—C61.456 (5)
S2—C81.761 (5)C6—H6B0.9300
S3—C151.710 (4)C8—H8A0.9600
S4—C151.735 (4)C8—H8B0.9600
S4—C161.786 (6)C8—H8C0.9600
N1—C11.321 (5)C9—C101.368 (5)
N1—C51.339 (4)C9—H9A0.9300
N2—C61.264 (4)C10—C111.356 (6)
N2—N31.370 (4)C10—H10A0.9300
N3—C71.286 (5)C11—C121.377 (6)
N3—H3A0.8600C11—H11A0.9300
N4—C91.323 (5)C12—C131.384 (5)
N4—C131.341 (4)C12—H12A0.9300
N5—C141.276 (4)C13—C141.447 (5)
N5—N61.365 (4)C14—H14A0.9300
N6—C151.293 (4)C16—H16A0.9600
N6—H6A0.8600C16—H16B0.9600
C1—C21.385 (6)C16—H16C0.9600
N5—Zn1—N2173.15 (11)C5—C4—C3117.7 (4)
N5—Zn1—N1107.46 (11)C5—C4—H4A121.1
N2—Zn1—N174.43 (11)C3—C4—H4A121.1
N5—Zn1—N474.61 (10)N1—C5—C4122.9 (4)
N2—Zn1—N4112.15 (11)N1—C5—C6115.4 (3)
N1—Zn1—N488.90 (11)C4—C5—C6121.7 (4)
N5—Zn1—S1101.26 (8)N2—C6—C5118.6 (3)
N2—Zn1—S177.89 (8)N2—C6—H6B120.7
N1—Zn1—S1150.43 (8)C5—C6—H6B120.7
N4—Zn1—S192.05 (8)N3—C7—S1128.7 (3)
N5—Zn1—S377.11 (8)N3—C7—S2118.1 (3)
N2—Zn1—S396.37 (9)S1—C7—S2113.2 (2)
N1—Zn1—S391.11 (8)S2—C8—H8A109.5
N4—Zn1—S3150.32 (8)S2—C8—H8B109.5
S1—Zn1—S3102.17 (4)H8A—C8—H8B109.5
C7—S1—Zn195.42 (14)S2—C8—H8C109.5
C7—S2—C8104.2 (2)H8A—C8—H8C109.5
C15—S3—Zn195.79 (13)H8B—C8—H8C109.5
C15—S4—C16104.6 (2)N4—C9—C10122.6 (4)
C1—N1—C5117.7 (3)N4—C9—H9A118.7
C1—N1—Zn1128.3 (3)C10—C9—H9A118.7
C5—N1—Zn1113.2 (2)C11—C10—C9120.0 (4)
C6—N2—N3119.4 (3)C11—C10—H10A120.0
C6—N2—Zn1117.2 (2)C9—C10—H10A120.0
N3—N2—Zn1122.7 (2)C10—C11—C12118.6 (4)
C7—N3—N2113.8 (3)C10—C11—H11A120.7
C7—N3—H3A123.1C12—C11—H11A120.7
N2—N3—H3A123.1C11—C12—C13118.6 (4)
C9—N4—C13117.9 (3)C11—C12—H12A120.7
C9—N4—Zn1128.5 (3)C13—C12—H12A120.7
C13—N4—Zn1113.0 (2)N4—C13—C12122.3 (4)
C14—N5—N6117.5 (3)N4—C13—C14115.8 (3)
C14—N5—Zn1117.2 (2)C12—C13—C14122.0 (4)
N6—N5—Zn1124.6 (2)N5—C14—C13118.5 (3)
C15—N6—N5113.6 (3)N5—C14—H14A120.8
C15—N6—H6A123.2C13—C14—H14A120.8
N5—N6—H6A123.2N6—C15—S3127.7 (3)
N1—C1—C2123.1 (4)N6—C15—S4117.5 (3)
N1—C1—H1A118.5S3—C15—S4114.8 (2)
C2—C1—H1A118.5S4—C16—H16A109.5
C3—C2—C1118.4 (4)S4—C16—H16B109.5
C3—C2—H2A120.8H16A—C16—H16B109.5
C1—C2—H2A120.8S4—C16—H16C109.5
C2—C3—C4120.2 (4)H16A—C16—H16C109.5
C2—C3—H3B119.9H16B—C16—H16C109.5
C4—C3—H3B119.9
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C2—H2A···Sli0.932.943.715 (3)142
C12—H12A···S3ii0.932.793.526 (4)138
Symmetry codes: (i) x+1/2, y+1/2, z; (ii) x1/2, y+1/2, z.

Experimental details

Crystal data
Chemical formula[Zn(C8H8N3S2)2]
Mr487.97
Crystal system, space groupOrthorhombic, Pna21
Temperature (K)293
a, b, c (Å)18.630 (7), 9.160 (3), 12.457 (4)
V3)2125.8 (13)
Z4
Radiation typeMo Kα
µ (mm1)1.56
Crystal size (mm)0.25 × 0.22 × 0.17
Data collection
DiffractometerBruker SMART CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 1996)
Tmin, Tmax0.745, 0.777
No. of measured, independent and
observed [I > 2σ(I)] reflections
11500, 4584, 3257
Rint0.028
(sin θ/λ)max1)0.642
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.034, 0.079, 1.04
No. of reflections4584
No. of parameters244
No. of restraints1
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.25, 0.30
Absolute structureFlack (1983), 2122 Friedel pairs
Absolute structure parameter0.013 (12)

Computer programs: SMART (Bruker, 1998), SAINT (Bruker, 1998), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), SHELXTL (Bruker, 1998) and local programs.

Selected geometric parameters (Å, º) top
Zn1—N52.130 (3)Zn1—N42.223 (3)
Zn1—N22.139 (3)Zn1—S12.4584 (13)
Zn1—N12.219 (3)Zn1—S32.4814 (13)
N5—Zn1—N2173.15 (11)N1—Zn1—S1150.43 (8)
N5—Zn1—N1107.46 (11)N4—Zn1—S192.05 (8)
N2—Zn1—N174.43 (11)N5—Zn1—S377.11 (8)
N5—Zn1—N474.61 (10)N2—Zn1—S396.37 (9)
N2—Zn1—N4112.15 (11)N1—Zn1—S391.11 (8)
N1—Zn1—N488.90 (11)N4—Zn1—S3150.32 (8)
N5—Zn1—S1101.26 (8)S1—Zn1—S3102.17 (4)
N2—Zn1—S177.89 (8)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C2—H2A···Sli0.9302.9353.715 (3)142.34
C12—H12A···S3ii0.9302.7853.526 (4)137.53
Symmetry codes: (i) x+1/2, y+1/2, z; (ii) x1/2, y+1/2, z.
 

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