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

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Bis(3-aza­niumylpyridin-1-ium) hexa­chloridostannate(IV) dichloride

aInstitut für Anorganische Chemie und Strukturchemie, Lehrstuhl II: Material- und Strukturforschung, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany
*Correspondence e-mail: reissg@hhu.de

(Received 4 March 2013; accepted 11 March 2013; online 16 March 2013)

The asymmetric unit of the title compound, (C5H8N2)2[SnCl6]Cl2, consists of one 3-aza­niumylpyridin-1-ium dication and one chloride ion in a general position and a hexa­chloridostannate(IV) dianion lying about a centre of inversion. The [SnCl6]2− anion exhibits almost perfect octa­hedral geometry. The 3-aza­niumylpyridin-1-ium and chloride ions are connected via medium–strong charge-supported N—H⋯Cl hydrogen bonds, forming undulating layers in the (110) plane. The [SnCl6]2− ions are located between these layers and occupy cavities formed by two facing layer puckers.

Related literature

For related 3-aza­niumylpyridin-1-ium salts, see: Ali et al. (2008[Ali, B. F., Al-Far, R. H. & Haddad, S. F. (2008). Acta Cryst. E64, m751-m752.]); Kapoor et al. (2012[Kapoor, I. P. S., Kapoor, M., Singh, G., Singh, U. P. & Goel, N. (2012). J. Mol. Struct. 1012, 62-72.]); Rao et al. (2011[Rao, A. S., Baruah, U. & Das, S. K. (2011). Inorg. Chim. Acta, 372, 206-212.]); Sarma et al. (2012[Sarma, M., Chatterjee, T. & Das, S. K. (2012). RSC Adv. 2, 3920-3926.]); Willett et al. (1988[Willett, R., Place, H. & Middleton, M. (1988). J. Am. Chem. Soc. 110, 8639-8650.]). For related hexa­halogenido­metalate salts, see: Reiss (1998[Reiß, G. J. (1998). Acta Cryst. C54, 1489-1491.], 2002[Reiß, G. J. (2002). Acta Cryst. E58, m47-m50.]); Reiss & Helmbrecht (2012[Reiss, G. J. & Helmbrecht, C. (2012). Acta Cryst. E68, m1402-m1403.]). For spectroscopy of hexa­chloridostannate(IV) salts, see: Brown et al. (1970[Brown, T. L., McDugle, W. G. Jr & Kent, L. G. (1970). J. Am. Chem. Soc. 92, 3645-3653.]); Ouasri et al. (2001[Ouasri, A., Elyoubi, M. S. D., Guedira, T., Rhandour, A., Mhiri, T. & Daoud, A. (2001). Spectrochim. Acta Part A, 57, 2593-2598.]). For graph-set theory and its applications, see: Bernstein et al. (1995[Bernstein, J., Davis, R. E., Shimoni, L. & Chang, N.-L. (1995). Angew. Chem. Int. Ed. Engl. 34, 1555-1573.]); Etter et al. (1990[Etter, M. C., MacDonald, J. C. & Bernstein, J. (1990). Acta Cryst. B46, 256-262.]).

[Scheme 1]

Experimental

Crystal data
  • (C5H8N2)2[SnCl6]Cl2

  • Mr = 594.56

  • Orthorhombic, P b c a

  • a = 11.9379 (3) Å

  • b = 10.3704 (3) Å

  • c = 16.7018 (5) Å

  • V = 2067.70 (10) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 2.27 mm−1

  • T = 290 K

  • 0.14 × 0.12 × 0.06 mm

Data collection
  • Oxford Diffraction Xcalibur Eos diffractometer

  • Absorption correction: multi-scan (CrysAlis PRO; Oxford Diffraction, 2009[Oxford Diffraction (2009). CrysAlis PRO. Oxford Diffraction Ltd, Yarnton, England.]) Tmin = 0.853, Tmax = 1.000

  • 30476 measured reflections

  • 2364 independent reflections

  • 1875 reflections with I > 2σ(I)

  • Rint = 0.038

Refinement
  • R[F2 > 2σ(F2)] = 0.020

  • wR(F2) = 0.044

  • S = 1.06

  • 2364 reflections

  • 138 parameters

  • All H-atom parameters refined

  • Δρmax = 0.26 e Å−3

  • Δρmin = −0.22 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N1—H11⋯Cl1 0.94 (2) 2.23 (3) 3.135 (2) 161 (2)
N1—H12⋯Cl2i 0.91 (3) 2.48 (3) 3.343 (2) 160 (2)
N1—H13⋯Cl1ii 0.92 (3) 2.19 (3) 3.104 (2) 176 (2)
N2—H2⋯Cl1iii 0.86 (2) 2.21 (2) 3.055 (2) 167 (2)
Symmetry codes: (i) [x, -y+{\script{1\over 2}}, z+{\script{1\over 2}}]; (ii) [-x+{\script{1\over 2}}, y+{\script{1\over 2}}, z]; (iii) [-x+1, y+{\script{1\over 2}}, -z+{\script{1\over 2}}].

Data collection: CrysAlis PRO (Oxford Diffraction, 2009[Oxford Diffraction (2009). CrysAlis PRO. Oxford Diffraction Ltd, Yarnton, England.]); cell refinement: CrysAlis PRO; data reduction: CrysAlis PRO; 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: DIAMOND (Brandenburg, 2012[Brandenburg, K. (2012). DIAMOND. Crystal Impact GbR, Bonn, Germany.]); software used to prepare material for publication: publCIF (Westrip, 2010[Westrip, S. P. (2010). J. Appl. Cryst. 43, 920-925.]).

Supporting information


Comment top

Only a limited number of 3-azaniumylpyridin-1-ium containing compounds has structurally been characterized so far. The majority of these are salts consisting of halogenidometalate anions such as [BiCl6]3- (Rao et al., 2011), [CuCl4]2- (Willett et al., 1988), [CuBr4]2- (Willett et al., 1988) and [HgBr4]2- (Ali et al., 2008). Furthermore, the dinitrate (Kapoor et al., 2012) and some complex crown ether compounds (Sarma et al., 2012) have been reported. This study on (C5H8N2)2[SnCl6]Cl2 is part of our long standing interest on the principles of arrangement of simple hexahalogenidometalate salts (dipH = diisopropylaminium): (dipH)2[SiF6] (Reiss, 1998); (dipH)2[IrCl6] (Reiss, 2002); (dipH)2[SnCl6] (Reiss & Helmbrecht, 2012).

The asymmetric unit of the title compound, (C5H8N2)2[SnCl6]Cl2, consists of one 3-azaniumylpyridin-1-ium dication and one chloride ion in general positions and the hexachloridostannate(IV) dianion lying on a centre of inversion (Fig. 1). The C–N and C–C bond lengths and angles of the cation are within the expected ranges. The [SnCl6]2- dianion exhibits a nearly perfect octahedral coordination sphere with Sn–Cl bond lengths ranging from 2.4162 (5) to 2.4242 (5) Å and bond angles between 88.03 (2) and 91.97 (2)°. The 3-azaniumylpyridin-1-ium dications and chloride ions are connected by medium strong, charge supported hydrogen bonds (Table 1) forming layers in the [110] plane. The characteristic hydrogen bonding motif is a 18-membered, wavy ring, which is classified as a third level graph-set R63(18) (Etter et al., 1990; Fig. 2). In addition to that, the second level graph-set descriptors C21(4) and C21(7) represent the chains, bridging the dications and chloride ions along [010] and [100], respectively. Thereby, the NH3+ group as well as the NH+ group of the 3-azaniumylpyridin-1-ium dication acts as a hydrogen bond donor. D···A distances for the NH3+ group range from 3.104 (2) to 3.343 (2) Å and for the NH+ group a D···A distance of 3.055 (2) Å is found. The [SnCl6]2- dianions are located in cavities between the layers, connected to the 3-azaniumylpyridin-1-ium dications by weak hydrogen bonds (Table 1) between two of their chlorido ligands and neighbouring NH3+groups (Fig. 3). The Raman-active bands (ν1, ν2, ν4 and ν5) of the [SnCl6]2- dianion appear in the Raman spectrum of the title compound (C5H8N2)2[SnCl6]Cl2 (Brown et al., 1970; Ouasri et al., 2001).

Related literature top

For related 3-azaniumylpyridin-1-ium salts, see: Ali et al. (2008); Kapoor et al. (2012); Rao et al. (2011); Sarma et al. (2012); Willett et al. (1988). For related hexahalogenidometalate salts, see: Reiss (1998, 2002); Reiss & Helmbrecht (2012). For spectroscopy of hexachloridostannate(IV) salts, see: Brown et al. (1970); Ouasri et al. (2001). For graph-set theory and its applications, see: Bernstein et al. (1995); Etter et al. (1990).

Experimental top

The title compound, (C5H8N2)2[SnCl6]Cl2, was prepared by dissolving 0.47 g (5.0 mmol) 3-aminopyridine and 0.65 g (2.5 mmol) tin(IV) chloride in 10 ml of concentrated (37%) hydrochloric acid. Within two to three days under ambient conditions colourless, rod-shaped crystals were obtained by slow evaporation of the solvent. The Raman spectrum was measured using a Bruker MULTIRAM spectrometer (Nd:YAG-Laser at 1064 nm; RT-InGaAs-detector); 4000–70 cm-1: 3082(w), 3049(w), 2954(vw), 1646(w), 1625(w), 1502(w), 1231(w), 1188(w), 1046(m), 1030(m), 815(w), 627(w), 537(w), 324(vs; ν1, Sn–Cl), 241 (m, br; ν2, Sn–Cl), 172 (s; ν4, Sn–Cl), 158 (s; ν5, Sn–Cl), 98 (m; most likely a lattice mode). - IR spectroscopic data were recorded on a Digilab FT3400 spectrometer using a MIRacle ATR unit (Pike Technologies); 4000–560 cm-1: 3458(w), 3364(w), 3245(w), 3187(w), 3080(s), 3066(s), 3008(m), 2952(m), 2880(m), 2773(vs), 2739(vs), 2687(s), 2604(s), 2542(vs), 1892(w, br), 1644(w), 1624(w), 1556(s), 1499(s), 1472(w), 1380(m), 1318(m), 1131(m), 1123(m), 1092(w), 1009(w), 998(w), 941(w), 890(w), 798(m), 673(m), 625(w). - Elemental analyses (C, H, N) were performed with a HEKA-Tech Euro EA3000 instrument; SnCl8N4C10H16 (594.60): calcd. C 20.20, H 2.71, N 9.42; found C 20.38, H 2.54, N 9.34.

Refinement top

All hydrogen atoms were identified in difference syntheses and refined freely with individual Uiso(H) values.

Computing details top

Data collection: CrysAlis PRO (Oxford Diffraction, 2009); cell refinement: CrysAlis PRO (Oxford Diffraction, 2009); data reduction: CrysAlis PRO (Oxford Diffraction, 2009); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2012); software used to prepare material for publication: publCIF (Westrip, 2010).

Figures top
[Figure 1] Fig. 1. The asymmetric unit of the title compound plus the symmetry-related chlorido ligands completing the hexachloridostannate(IV) dianion (displacement ellipsoids are drawn at the 50% probability level; hydrogen atoms are drawn as spheres with arbitrary radii; symmetry code: -x, -y, -z).
[Figure 2] Fig. 2. View on a hydrogen bonded layer of 3-azaniumylpyridin-1-ium dications and chloride anions in the [110] plane (graph-set descriptors R63(18), C21(4) and C21(7) are indicated with green, red and blue numbers; symmetry code: ' 0.5 - x, 0.5 + y, z, '' 1 - x, 0.5 + y, 0.5 - z).
[Figure 3] Fig. 3. View along [110] on the title structure. Showing the hydrogen bonded layers consisting of 3-azaniumylpyridin-1-ium and chloride ions (parallel to ab at c = 1/4, 3/4) with the [SnCl6]2- dianions (parallel to ab at c = 0, 1/2, 1) located in cavities between them.
Bis(3-azaniumylpyridin-1-ium) hexachloridostannate(IV) dichloride top
Crystal data top
(C5H8N2)2[SnCl6]Cl2F(000) = 1160
Mr = 594.56Dx = 1.910 Mg m3
Orthorhombic, PbcaMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ac 2abCell parameters from 11374 reflections
a = 11.9379 (3) Åθ = 3.6–33.9°
b = 10.3704 (3) ŵ = 2.27 mm1
c = 16.7018 (5) ÅT = 290 K
V = 2067.70 (10) Å3Block, colourless
Z = 40.14 × 0.12 × 0.06 mm
Data collection top
Oxford Diffraction Xcalibur Eos
diffractometer
2364 independent reflections
Radiation source: fine-focus sealed tube1875 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.038
Detector resolution: 16.2711 pixels mm-1θmax = 27.5°, θmin = 3.6°
ω scansh = 1515
Absorption correction: multi-scan
(CrysAlis PRO; Oxford Diffraction, 2009)
k = 1313
Tmin = 0.853, Tmax = 1.000l = 2121
30476 measured reflections
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)] = 0.020Hydrogen site location: difference Fourier map
wR(F2) = 0.044All H-atom parameters refined
S = 1.06 w = 1/[σ2(Fo2) + (0.0162P)2 + 0.6462P]
where P = (Fo2 + 2Fc2)/3
2364 reflections(Δ/σ)max < 0.001
138 parametersΔρmax = 0.26 e Å3
0 restraintsΔρmin = 0.22 e Å3
Crystal data top
(C5H8N2)2[SnCl6]Cl2V = 2067.70 (10) Å3
Mr = 594.56Z = 4
Orthorhombic, PbcaMo Kα radiation
a = 11.9379 (3) ŵ = 2.27 mm1
b = 10.3704 (3) ÅT = 290 K
c = 16.7018 (5) Å0.14 × 0.12 × 0.06 mm
Data collection top
Oxford Diffraction Xcalibur Eos
diffractometer
2364 independent reflections
Absorption correction: multi-scan
(CrysAlis PRO; Oxford Diffraction, 2009)
1875 reflections with I > 2σ(I)
Tmin = 0.853, Tmax = 1.000Rint = 0.038
30476 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0200 restraints
wR(F2) = 0.044All H-atom parameters refined
S = 1.06Δρmax = 0.26 e Å3
2364 reflectionsΔρmin = 0.22 e Å3
138 parameters
Special details top

Experimental. CrysAlisPro, Oxford Diffraction Ltd., Version 1.171.34.44 Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.

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
N10.28997 (16)0.5670 (2)0.35522 (13)0.0399 (4)
H110.262 (2)0.496 (2)0.3270 (14)0.059 (8)*
H120.257 (2)0.574 (2)0.4040 (16)0.076 (9)*
H130.273 (2)0.639 (2)0.3256 (14)0.060 (8)*
C10.41111 (17)0.55437 (19)0.36189 (11)0.0308 (4)
C20.4574 (2)0.4437 (2)0.39366 (14)0.0433 (5)
H2A0.4103 (19)0.381 (2)0.4093 (13)0.048 (7)*
C30.5719 (2)0.4332 (2)0.39775 (15)0.0511 (6)
H3A0.603 (2)0.364 (2)0.4159 (14)0.061 (8)*
C40.6373 (2)0.5311 (3)0.37014 (14)0.0472 (6)
H4A0.712 (2)0.529 (2)0.3692 (14)0.060 (8)*
N20.58917 (16)0.63570 (19)0.33931 (10)0.0395 (4)
H20.630 (2)0.695 (2)0.3187 (14)0.061 (8)*
C50.47825 (17)0.65048 (19)0.33392 (12)0.0335 (5)
H5A0.4526 (16)0.7277 (19)0.3111 (11)0.033 (5)*
Cl10.25614 (5)0.31396 (5)0.25548 (3)0.04263 (13)
Sn10.00000.00000.00000.02235 (6)
Cl20.14393 (4)0.16245 (5)0.01538 (3)0.04262 (13)
Cl30.14685 (4)0.15423 (5)0.02721 (3)0.04332 (13)
Cl40.00932 (5)0.04893 (7)0.14177 (3)0.05529 (16)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
N10.0356 (11)0.0370 (11)0.0470 (11)0.0016 (9)0.0044 (9)0.0035 (10)
C10.0342 (11)0.0297 (10)0.0285 (9)0.0009 (9)0.0042 (8)0.0031 (8)
C20.0491 (14)0.0340 (12)0.0469 (13)0.0021 (11)0.0031 (11)0.0082 (11)
C30.0556 (17)0.0417 (14)0.0559 (15)0.0141 (13)0.0052 (12)0.0085 (12)
C40.0357 (13)0.0564 (15)0.0493 (13)0.0017 (12)0.0005 (11)0.0078 (12)
N20.0384 (11)0.0414 (11)0.0388 (10)0.0095 (9)0.0066 (8)0.0026 (8)
C50.0391 (14)0.0288 (10)0.0327 (10)0.0016 (9)0.0045 (8)0.0004 (8)
Cl10.0474 (3)0.0329 (2)0.0476 (3)0.0018 (2)0.0113 (2)0.0002 (2)
Sn10.01879 (9)0.02282 (9)0.02543 (9)0.00037 (7)0.00169 (7)0.00180 (6)
Cl20.0341 (3)0.0371 (3)0.0566 (3)0.0133 (2)0.0059 (2)0.0094 (2)
Cl30.0334 (3)0.0338 (3)0.0627 (3)0.0120 (2)0.0084 (2)0.0002 (2)
Cl40.0572 (4)0.0802 (4)0.0285 (3)0.0001 (3)0.0011 (3)0.0142 (3)
Geometric parameters (Å, º) top
N1—C11.456 (3)C4—H4A0.90 (3)
N1—H110.94 (2)N2—C51.336 (3)
N1—H120.91 (3)N2—H20.86 (2)
N1—H130.92 (3)C5—H5A0.938 (19)
C1—C51.362 (3)Sn1—Cl3i2.4162 (5)
C1—C21.380 (3)Sn1—Cl32.4162 (5)
C2—C31.373 (4)Sn1—Cl2i2.4200 (5)
C2—H2A0.90 (2)Sn1—Cl22.4200 (5)
C3—C41.361 (4)Sn1—Cl42.4242 (5)
C3—H3A0.86 (2)Sn1—Cl4i2.4242 (5)
C4—N21.331 (3)
C1—N1—H11108.4 (16)C5—N2—H2117.0 (17)
C1—N1—H12111.5 (17)N2—C5—C1118.4 (2)
H11—N1—H12111 (2)N2—C5—H5A116.7 (12)
C1—N1—H13109.8 (15)C1—C5—H5A124.9 (13)
H11—N1—H13107 (2)Cl3i—Sn1—Cl3180.00 (3)
H12—N1—H13109 (2)Cl3i—Sn1—Cl2i91.968 (19)
C5—C1—C2120.3 (2)Cl3—Sn1—Cl2i88.032 (19)
C5—C1—N1119.49 (19)Cl3i—Sn1—Cl288.032 (19)
C2—C1—N1120.1 (2)Cl3—Sn1—Cl291.968 (19)
C3—C2—C1119.0 (2)Cl2i—Sn1—Cl2180.00 (3)
C3—C2—H2A123.4 (15)Cl3i—Sn1—Cl490.68 (2)
C1—C2—H2A117.7 (15)Cl3—Sn1—Cl489.32 (2)
C4—C3—C2119.7 (2)Cl2i—Sn1—Cl489.46 (2)
C4—C3—H3A119.5 (17)Cl2—Sn1—Cl490.54 (2)
C2—C3—H3A120.8 (17)Cl3i—Sn1—Cl4i89.32 (2)
N2—C4—C3119.4 (2)Cl3—Sn1—Cl4i90.68 (2)
N2—C4—H4A116.1 (16)Cl2i—Sn1—Cl4i90.54 (2)
C3—C4—H4A124.5 (16)Cl2—Sn1—Cl4i89.46 (2)
C4—N2—C5123.2 (2)Cl4—Sn1—Cl4i180.00 (5)
C4—N2—H2119.7 (17)
Symmetry code: (i) x, y, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H11···Cl10.94 (2)2.23 (3)3.135 (2)161 (2)
N1—H12···Cl2ii0.91 (3)2.48 (3)3.343 (2)160 (2)
N1—H13···Cl1iii0.92 (3)2.19 (3)3.104 (2)176 (2)
N2—H2···Cl1iv0.86 (2)2.21 (2)3.055 (2)167 (2)
Symmetry codes: (ii) x, y+1/2, z+1/2; (iii) x+1/2, y+1/2, z; (iv) x+1, y+1/2, z+1/2.

Experimental details

Crystal data
Chemical formula(C5H8N2)2[SnCl6]Cl2
Mr594.56
Crystal system, space groupOrthorhombic, Pbca
Temperature (K)290
a, b, c (Å)11.9379 (3), 10.3704 (3), 16.7018 (5)
V3)2067.70 (10)
Z4
Radiation typeMo Kα
µ (mm1)2.27
Crystal size (mm)0.14 × 0.12 × 0.06
Data collection
DiffractometerOxford Diffraction Xcalibur Eos
diffractometer
Absorption correctionMulti-scan
(CrysAlis PRO; Oxford Diffraction, 2009)
Tmin, Tmax0.853, 1.000
No. of measured, independent and
observed [I > 2σ(I)] reflections
30476, 2364, 1875
Rint0.038
(sin θ/λ)max1)0.650
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.020, 0.044, 1.06
No. of reflections2364
No. of parameters138
H-atom treatmentAll H-atom parameters refined
Δρmax, Δρmin (e Å3)0.26, 0.22

Computer programs: CrysAlis PRO (Oxford Diffraction, 2009), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), DIAMOND (Brandenburg, 2012), publCIF (Westrip, 2010).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H11···Cl10.94 (2)2.23 (3)3.135 (2)161 (2)
N1—H12···Cl2i0.91 (3)2.48 (3)3.343 (2)160 (2)
N1—H13···Cl1ii0.92 (3)2.19 (3)3.104 (2)176 (2)
N2—H2···Cl1iii0.86 (2)2.21 (2)3.055 (2)167 (2)
Symmetry codes: (i) x, y+1/2, z+1/2; (ii) x+1/2, y+1/2, z; (iii) x+1, y+1/2, z+1/2.
 

Acknowledgements

We thank E. Hammes and P. Roloff for technical support. We acknowledge the support for the publication fee by the `Lehrförderfond' of the Heinrich-Heine-Universität Düsseldorf.

References

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