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

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ISSN: 2056-9890
Volume 65| Part 3| March 2009| Pages m255-m256

1,3-Benzo­thia­zolium tetra­chlorido­aurate(III) tetra­hydro­furan solvate

aDepartment of Chemistry, University of Stellenbosch, Private Bag X1, Matieland, South Africa
*Correspondence e-mail: lianger@sun.ac.za

(Received 26 January 2009; accepted 29 January 2009; online 6 February 2009)

In the crystal structure of the title ionic compound (C7H6NS)[AuCl4]·C4H8O, the [AuCl4] anion shows a typical square-planar geometry. Numerous weak C—H⋯Cl hydrogen bonds between [AuCl4] and the 1,3-benzothia­zolium units form layers comprised of 24-membered rings in which hydrogen-bonded tetra­hydro­furan (THF) solvent mol­ecules are accommodated. C—H⋯Cl inter­actions between THF and [AuCl4] from adjacent layers result in bilayers. These are further stabilized by ππ inter­actions between the thia­zole and benzene rings [centroid–centroid distance = 3.971 (3) Å], resulting in the formation of a three-dimensional supra­molecular assembly.

Related literature

For background, see: Hagos et al. (2008[Hagos, T. K., Nogai, S. D., Dobrzańska, L. & Cronje, S. (2008). Acta Cryst. E64, m1357.]). For related compounds, see: Huynh et al. (2006[Huynh, H. V., Meier, N., Pape, T. & Hahn, F. E. (2006). Organometallics, 25, 3012-3018.]); Yen et al. (2006[Yen, S. K., Koh, L. L., Hahn, F. E., Huynh, H. V. & Hor, T. S. A. (2006). Organometallics, 25, 5105-5112.], 2008[Yen, S. K., Koh, L. L., Huynh, H. V. & Hor, T. S. A. (2008). Dalton Trans. pp. 699-706.]). For bond-length data, see Adé et al. (2004[Adé, A., Cerrada, E., Contel, M., Laguna, M., Merino, P. & Tejero, T. (2004). J. Organomet. Chem. 689, 1788-1795.]); Asaji et al. (2004[Asaji, T., Akiyama, E., Tajima, F., Eda, K., Hashimoto, M. & Furukawa, Y. (2004). Polyhedron, 23, 1605-1611.]); Makotchenko et al. (2006[Makotchenko, E. V., Baidina, I. A. & Naumov, D. Yu. (2006). J. Struct. Chem. 47, 499-503.]). For related literature, see: Brammer et al. (2001[Brammer, L., Bruton, E. A. & Sherwood, P. (2001). Cryst. Growth Des. 1, 277-290.]).

[Scheme 1]

Experimental

Crystal data
  • (C7H6NS)[AuCl4]·C4H8O

  • Mr = 547.06

  • Triclinic, [P \overline 1]

  • a = 7.3213 (7) Å

  • b = 10.3498 (10) Å

  • c = 11.8783 (12) Å

  • α = 99.331 (1)°

  • β = 107.579 (1)°

  • γ = 104.483 (2)°

  • V = 802.75 (14) Å3

  • Z = 2

  • Mo Kα radiation

  • μ = 9.95 mm−1

  • T = 100 (2) K

  • 0.30 × 0.20 × 0.10 mm

Data collection
  • Bruker APEX CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Sheldrick, 1997[Sheldrick, G. M. (1997). SADABS. University of Göttingen, Germany.]) Tmin = 0.101, Tmax = 0.371

  • 4957 measured reflections

  • 3504 independent reflections

  • 3325 reflections with I > 2σ(I)

  • Rint = 0.013

Refinement
  • R[F2 > 2σ(F2)] = 0.027

  • wR(F2) = 0.064

  • S = 1.05

  • 3504 reflections

  • 175 parameters

  • 1 restraint

  • H atoms treated by a mixture of independent and constrained refinement

  • Δρmax = 2.27 e Å−3

  • Δρmin = −1.00 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N6—H6⋯O14 0.86 (5) 1.87 (5) 2.728 (5) 177 (6)
C5—H5⋯Cl2i 0.95 2.65 3.588 (5) 170
C8—H8⋯Cl4 0.95 2.93 3.447 (5) 116
C9—H9⋯Cl4 0.95 3.00 3.498 (5) 114
C10—H10⋯Cl2ii 0.95 2.96 3.541 (6) 121
C11—H11⋯Cl2ii 0.95 2.90 3.498 (5) 122
C11—H11⋯Cl3ii 0.95 2.77 3.639 (5) 154
C15—H15B⋯Cl1iii 0.99 3.02 3.922 (6) 153
C18—H18A⋯Cl4iii 0.99 2.91 3.547 (6) 123
Symmetry codes: (i) x+1, y+1, z+1; (ii) x+1, y, z+1; (iii) -x+1, -y+1, -z+1.

Data collection: SMART (Bruker, 2001[Bruker (2001). SMART. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 2002[Bruker (2002). 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: X-SEED (Barbour 2001[Barbour, L. J. (2001). J. Supramol. Chem. 1, 189-191.]); software used to prepare material for publication: SHELXL97.

Supporting information


Comment top

During the course of ongoing studies on the reactions of gold(III) compounds with heterocycles, we have isolated the title ionic compound (I) with a structure resembling that of a 1,3-dimesitylimidazolinium tetrachloro-gold(III) dichloromethane solvate reported earlier (Hagos et al. 2008). The asymmetric unit (Fig. 1) consists of a 1,3-benzothiazolium cation, a tetrachloro-gold(III) anion and a tetrahydrofuran molecule. The structural parameters associated with the 1,3-benzothiazolium moiety agree well with reported values, see for example 3-(2-propenyl)-1,3-benzothiazolium bromide (Huynh et al. 2006), N-benzyl-1,3-benzothiazolium bromide (Yen et al. 2006) and 3-n-propyl-1,3-benzothiazolium bromide monohydrate (Yen et al. 2008). The anionic part displays a typical square-planar geometry around Au and the Au—Cl distances compare well with previously reported values (Adé et al., 2004; Asaji et al., 2004; Makotchenko et al., 2006). All Cl atoms of [AuCl4]- complex participate in the formation of weak C—H···Cl hydrogen bonds (Table 1). Atoms Cl2, Cl3 and Cl4 interact with the 1,3-benzothiazolium cation forming layers consisting of R56(24) rings in which tetrahydrofuran molecules are incorporated by forming hydrogen bonds O6—H6···N14 with a distance of 2.728 (5) Å (Fig. 2). Further C—H···Cl interactions between THF and [AuCl4]- from neighbouring layers (C15—H15B···Cl1 and C18—H18A···Cl4) form pillar-like connections between them, leading to the formation of bilayers. The latter are propagated along [100] by π-π interactions between thiazole and benzene rings [symmetry operation: 1 - x, 1 - y, 2 - z, centroid-centroid distance = 3.971 (3) Å], resulting in a three-dimensional assembly (Fig. 3).

Related literature top

For background, see: Hagos et al. (2008). For related compounds, see: Huynh et al. (2006); Yen et al. (2006, 2008). For bond-length data, see Adé et al. (2004); Asaji et al. (2004); Makotchenko et al. (2006). For related literature, see: Brammer et al. (2001).

Experimental top

1,3-Benzothiazole (0.10 g, 0.76 mmol) in acetonitrile (5 ml) was treated with HAuCl4.4H2O (0.31 g, 0.76 mmol) in water (5 ml) at room temperature (2.5 h). The reaction mixture was stripped of solvent and extracted with a mixture of dichloromethane and THF (1:1, 150 ml). Then the solvent was removed under reduced pressure to yield a yellow residue. Orange crystals suitable for single-crystal X-ray analysis were obtained from a THF solution layered with n-pentane at 253 K.

Refinement top

H6 atom (for NH) was located in a difference map and refined with a restrained N—H distance of 0.86 (5) Å, and with Uiso(H) = 1.2Ueq(N). The remaining H atoms were positioned geometrically, with C—H = 0.95 and 0.99 Å for aromatic and methylene H, respectively, and constrained to ride on their parent atoms with Uiso(H) = 1.2Ueq(C). The highest peak and deepest hole in the final difference Fourier map are located at 0.88 Å and 0.95 Å from atom Au1, respectively.

Computing details top

Data collection: SMART (Bruker, 2001); cell refinement: SAINT (Bruker, 2002); data reduction: SAINT (Bruker, 2002); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: X-SEED (Barbour 2001); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. The molecular structure of the title molecule, with the atom-numbering scheme. Displacement ellipsoids are drawn at the 50% probability level.
[Figure 2] Fig. 2. Capped-stick representation showing the formation of layers consisting of R56(24) rings (shown in black). Dashed orange lines represent C—H···Cl hydrogen bonds.
[Figure 3] Fig. 3. Representation of the bilayers (red-green) with pillar-like connections (yellow dashed lines) extended in the third dimension by π-π interactions (blue dashed lines) viewed down [010].
1,3-Benzothiazolium tetrachloridoaurate(III) tetrahydrofuran solvate top
Crystal data top
(C7H6NS)[AuCl4]·C4H8OZ = 2
Mr = 547.06F(000) = 516
Triclinic, P1Dx = 2.263 Mg m3
Hall symbol: -P 1Mo Kα radiation, λ = 0.71073 Å
a = 7.3213 (7) ÅCell parameters from 3347 reflections
b = 10.3498 (10) Åθ = 2.4–28.1°
c = 11.8783 (12) ŵ = 9.95 mm1
α = 99.331 (1)°T = 100 K
β = 107.579 (1)°Block, orange
γ = 104.483 (2)°0.30 × 0.20 × 0.10 mm
V = 802.75 (14) Å3
Data collection top
Bruker APEX CCD area-detector
diffractometer
3504 independent reflections
Radiation source: fine-focus sealed tube3325 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.013
ω scansθmax = 28.3°, θmin = 2.4°
Absorption correction: multi-scan
(SADABS; Sheldrick, 1997)
h = 99
Tmin = 0.101, Tmax = 0.371k = 1313
4957 measured reflectionsl = 1415
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)] = 0.027Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.064H atoms treated by a mixture of independent and constrained refinement
S = 1.05 w = 1/[σ2(Fo2) + (0.0432P)2 + 0.5801P]
where P = (Fo2 + 2Fc2)/3
3504 reflections(Δ/σ)max < 0.001
175 parametersΔρmax = 2.27 e Å3
1 restraintΔρmin = 1.00 e Å3
Crystal data top
(C7H6NS)[AuCl4]·C4H8Oγ = 104.483 (2)°
Mr = 547.06V = 802.75 (14) Å3
Triclinic, P1Z = 2
a = 7.3213 (7) ÅMo Kα radiation
b = 10.3498 (10) ŵ = 9.95 mm1
c = 11.8783 (12) ÅT = 100 K
α = 99.331 (1)°0.30 × 0.20 × 0.10 mm
β = 107.579 (1)°
Data collection top
Bruker APEX CCD area-detector
diffractometer
3504 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1997)
3325 reflections with I > 2σ(I)
Tmin = 0.101, Tmax = 0.371Rint = 0.013
4957 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0271 restraint
wR(F2) = 0.064H atoms treated by a mixture of independent and constrained refinement
S = 1.05Δρmax = 2.27 e Å3
3504 reflectionsΔρmin = 1.00 e Å3
175 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
Au10.00874 (2)0.215338 (16)0.234396 (14)0.01707 (7)
Cl10.03040 (19)0.00191 (12)0.22763 (11)0.0318 (3)
Cl20.26390 (17)0.12764 (11)0.05577 (10)0.0235 (2)
Cl30.00788 (18)0.43396 (11)0.24088 (10)0.0249 (2)
Cl40.27948 (17)0.29983 (13)0.41246 (10)0.0287 (2)
C50.6777 (7)0.7714 (5)0.9404 (4)0.0215 (9)
H50.69920.86780.96290.026*
N60.5448 (6)0.6896 (4)0.8362 (3)0.0207 (8)
H60.477 (7)0.718 (5)0.778 (4)0.025*
C70.5351 (7)0.5514 (4)0.8204 (4)0.0178 (8)
C80.4115 (7)0.4415 (5)0.7204 (4)0.0233 (9)
H80.31660.45410.65170.028*
C90.4313 (8)0.3142 (5)0.7244 (4)0.0276 (10)
H90.34870.23700.65710.033*
C100.5711 (8)0.2954 (5)0.8257 (5)0.0276 (10)
H100.58110.20560.82540.033*
C110.6940 (7)0.4035 (5)0.9253 (4)0.0231 (9)
H110.78880.39030.99360.028*
C120.6738 (6)0.5330 (4)0.9220 (4)0.0182 (8)
S130.80728 (17)0.68998 (12)1.03100 (10)0.0219 (2)
O140.3180 (5)0.7755 (3)0.6536 (3)0.0219 (7)
C150.3808 (7)0.9178 (5)0.6497 (4)0.0227 (9)
H15B0.52160.94680.65200.027*
H15A0.37150.97910.71950.027*
C160.2358 (8)0.9226 (5)0.5300 (5)0.0286 (10)
H16B0.29551.00140.50090.034*
H16A0.10680.92860.53720.034*
C170.2060 (9)0.7850 (5)0.4458 (5)0.0335 (12)
H17A0.07460.75340.37720.040*
H17B0.31590.79180.41270.040*
C180.2116 (7)0.6889 (5)0.5298 (4)0.0241 (9)
H18B0.07260.63520.51980.029*
H18A0.28300.62360.51080.029*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Au10.01437 (9)0.01940 (10)0.01510 (9)0.00527 (6)0.00270 (6)0.00332 (6)
Cl10.0340 (7)0.0253 (6)0.0289 (6)0.0156 (5)0.0022 (5)0.0042 (5)
Cl20.0220 (5)0.0200 (5)0.0205 (5)0.0076 (4)0.0028 (4)0.0022 (4)
Cl30.0284 (6)0.0196 (5)0.0221 (5)0.0062 (4)0.0045 (4)0.0038 (4)
Cl40.0211 (5)0.0370 (6)0.0194 (5)0.0097 (5)0.0013 (4)0.0004 (5)
C50.025 (2)0.019 (2)0.023 (2)0.0104 (18)0.0086 (19)0.0063 (18)
N60.0214 (19)0.0210 (19)0.0190 (18)0.0094 (16)0.0037 (15)0.0059 (15)
C70.017 (2)0.020 (2)0.016 (2)0.0064 (17)0.0048 (17)0.0062 (17)
C80.024 (2)0.025 (2)0.015 (2)0.0063 (19)0.0024 (18)0.0030 (18)
C90.034 (3)0.020 (2)0.020 (2)0.007 (2)0.002 (2)0.0006 (18)
C100.034 (3)0.021 (2)0.026 (2)0.013 (2)0.005 (2)0.0068 (19)
C110.025 (2)0.021 (2)0.022 (2)0.0102 (19)0.0023 (18)0.0085 (18)
C120.014 (2)0.020 (2)0.017 (2)0.0045 (17)0.0016 (16)0.0039 (17)
S130.0206 (5)0.0221 (5)0.0177 (5)0.0071 (4)0.0009 (4)0.0025 (4)
O140.0250 (17)0.0173 (15)0.0198 (16)0.0060 (13)0.0031 (13)0.0058 (12)
C150.025 (2)0.020 (2)0.024 (2)0.0075 (19)0.0089 (19)0.0080 (18)
C160.035 (3)0.025 (2)0.028 (3)0.013 (2)0.009 (2)0.010 (2)
C170.041 (3)0.027 (3)0.025 (3)0.007 (2)0.005 (2)0.007 (2)
C180.023 (2)0.025 (2)0.020 (2)0.0081 (19)0.0012 (18)0.0032 (18)
Geometric parameters (Å, º) top
Au1—Cl42.2733 (11)C11—C121.390 (6)
Au1—Cl12.2835 (12)C11—H110.9500
Au1—Cl22.2850 (11)C12—S131.741 (4)
Au1—Cl32.2864 (11)O14—C151.443 (5)
C5—N61.310 (6)O14—C181.450 (5)
C5—S131.686 (4)C15—C161.513 (6)
C5—H50.9500C15—H15B0.9900
N6—C71.392 (6)C15—H15A0.9900
N6—H60.86 (5)C16—C171.525 (7)
C7—C81.387 (6)C16—H16B0.9900
C7—C121.398 (6)C16—H16A0.9900
C8—C91.368 (7)C17—C181.518 (7)
C8—H80.9500C17—H17A0.9900
C9—C101.402 (7)C17—H17B0.9900
C9—H90.9500C18—H18B0.9900
C10—C111.373 (7)C18—H18A0.9900
C10—H100.9500
Cl4—Au1—Cl190.14 (4)C11—C12—S13128.7 (3)
Cl4—Au1—Cl2179.27 (4)C7—C12—S13110.4 (3)
Cl1—Au1—Cl289.16 (4)C5—S13—C1290.5 (2)
Cl4—Au1—Cl389.45 (4)C15—O14—C18109.0 (3)
Cl1—Au1—Cl3179.07 (4)O14—C15—C16104.8 (4)
Cl2—Au1—Cl391.25 (4)O14—C15—H15B110.8
N6—C5—S13114.0 (3)C16—C15—H15B110.8
N6—C5—H5123.0O14—C15—H15A110.8
S13—C5—H5123.0C16—C15—H15A110.8
C5—N6—C7114.4 (4)H15B—C15—H15A108.9
C5—N6—H6124 (4)C15—C16—C17101.8 (4)
C7—N6—H6121 (4)C15—C16—H16B111.4
C8—C7—N6127.8 (4)C17—C16—H16B111.4
C8—C7—C12121.4 (4)C15—C16—H16A111.4
N6—C7—C12110.8 (4)C17—C16—H16A111.4
C9—C8—C7117.5 (4)H16B—C16—H16A109.3
C9—C8—H8121.3C18—C17—C16102.9 (4)
C7—C8—H8121.3C18—C17—H17A111.2
C8—C9—C10121.4 (5)C16—C17—H17A111.2
C8—C9—H9119.3C18—C17—H17B111.2
C10—C9—H9119.3C16—C17—H17B111.2
C11—C10—C9121.7 (4)H17A—C17—H17B109.1
C11—C10—H10119.2O14—C18—C17106.7 (4)
C9—C10—H10119.2O14—C18—H18B110.4
C10—C11—C12117.2 (4)C17—C18—H18B110.4
C10—C11—H11121.4O14—C18—H18A110.4
C12—C11—H11121.4C17—C18—H18A110.4
C11—C12—C7120.9 (4)H18B—C18—H18A108.6
S13—C5—N6—C70.3 (5)N6—C7—C12—C11178.5 (4)
C5—N6—C7—C8179.6 (5)C8—C7—C12—S13179.4 (4)
C5—N6—C7—C120.3 (5)N6—C7—C12—S130.1 (5)
N6—C7—C8—C9178.7 (5)N6—C5—S13—C120.2 (4)
C12—C7—C8—C90.5 (7)C11—C12—S13—C5178.6 (4)
C7—C8—C9—C100.0 (8)C7—C12—S13—C50.0 (4)
C8—C9—C10—C110.1 (9)C18—O14—C15—C1624.2 (5)
C9—C10—C11—C120.2 (8)O14—C15—C16—C1737.1 (5)
C10—C11—C12—C70.6 (7)C15—C16—C17—C1835.6 (5)
C10—C11—C12—S13179.0 (4)C15—O14—C18—C171.1 (5)
C8—C7—C12—C110.8 (7)C16—C17—C18—O1422.0 (5)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N6—H6···O140.86 (5)1.87 (5)2.728 (5)177 (6)
C5—H5···Cl2i0.952.653.588 (5)170
C8—H8···Cl40.952.933.447 (5)116
C9—H9···Cl40.953.003.498 (5)114
C10—H10···Cl2ii0.952.963.541 (6)121
C11—H11···Cl2ii0.952.903.498 (5)122
C11—H11···Cl3ii0.952.773.639 (5)154
C15—H15B···Cl1iii0.993.023.922 (6)153
C18—H18A···Cl4iii0.992.913.547 (6)123
Symmetry codes: (i) x+1, y+1, z+1; (ii) x+1, y, z+1; (iii) x+1, y+1, z+1.

Experimental details

Crystal data
Chemical formula(C7H6NS)[AuCl4]·C4H8O
Mr547.06
Crystal system, space groupTriclinic, P1
Temperature (K)100
a, b, c (Å)7.3213 (7), 10.3498 (10), 11.8783 (12)
α, β, γ (°)99.331 (1), 107.579 (1), 104.483 (2)
V3)802.75 (14)
Z2
Radiation typeMo Kα
µ (mm1)9.95
Crystal size (mm)0.30 × 0.20 × 0.10
Data collection
DiffractometerBruker APEX CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 1997)
Tmin, Tmax0.101, 0.371
No. of measured, independent and
observed [I > 2σ(I)] reflections
4957, 3504, 3325
Rint0.013
(sin θ/λ)max1)0.666
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.027, 0.064, 1.05
No. of reflections3504
No. of parameters175
No. of restraints1
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)2.27, 1.00

Computer programs: SMART (Bruker, 2001), SAINT (Bruker, 2002), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), X-SEED (Barbour 2001).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N6—H6···O140.86 (5)1.87 (5)2.728 (5)177 (6)
C5—H5···Cl2i0.952.653.588 (5)170
C8—H8···Cl40.952.933.447 (5)116
C9—H9···Cl40.953.003.498 (5)114
C10—H10···Cl2ii0.952.963.541 (6)121
C11—H11···Cl2ii0.952.903.498 (5)122
C11—H11···Cl3ii0.952.773.639 (5)154
C15—H15B···Cl1iii0.993.023.922 (6)153
C18—H18A···Cl4iii0.992.913.547 (6)123
Symmetry codes: (i) x+1, y+1, z+1; (ii) x+1, y, z+1; (iii) x+1, y+1, z+1.
 

Acknowledgements

The authors thank the National Research Foundation of South Africa and the University of Stellenbosch for financial support.

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Volume 65| Part 3| March 2009| Pages m255-m256
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