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2,2,7,7,12,12,17,17-Octa­methyl-21,22,23,24-tetra­thia-2,7,12,17-tetra­germa­penta­cyclo­[16.2.1.13,6.18,11.113,16]tetra­cosa-3,5,8,10,13,15,18,20-octa­ene

aLaboratoire Hétérochimie Fondamentale et Appliquée, UMR CNRS 5069, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9, France, and bUniversité de Toulouse, UPS, Institut de Chimie de Toulouse FR2599, 118 route de Narbonne, 31062 Toulouse Cedex 9, France
*Correspondence e-mail: castel@chimie.ups-tlse.fr

(Received 27 November 2012; accepted 4 December 2012; online 12 December 2012)

The title compound, [Ge4(CH3)8(C4H2S)4], crystallizes with one-half mol­ecule in the asymmetric unit, the whole mol­ecule being generated by inversion symmetry. The dihedral angle between adjacent thio­phene rings is 72.84 (14)°. In the crystal, mol­ecules are linked by C—H⋯π inter­actions, leading to the formation of chains along [100].

Related literature

For a review concerning aryl- and heteroaryl­germanes, see: Spivey & Diaper (2003[Spivey, A. C. & Diaper, C. M. (2003). Sci. Synth. 5, 149-157.]). For syntheses and structures of heteroaryl­germanes, see: Hockemeyer, Castel et al. (1997[Hockemeyer, J., Castel, A., Riviere, P., Satgé, J., Ryder, K. G., Drury, A., Davey, A. P. & Blau, W. J. (1997). Appl. Organomet. Chem. 11, 513-521.]); Barrau et al. (1997[Barrau, J., Rima, G., Akkari, A. & Satgé, J. (1997). Inorg. Chim. Acta, 260, 11-15.]); König & Rödel (1997[König, B. & Rödel, M. (1997). Chem. Ber. 130, 421-423.]). For properties of heteroaryl­germanes, see: Hockemeyer, Valentin et al. (1997[Hockemeyer, J., Valentin, B., Castel, A., Riviere, P., Satgé, J., Cardin, C. J. & Teixeira, S. (1997). Main Group Met. Chem. 20, 775-781.]). For a description of the Cambridge Structural Database, see: Allen (2002[Allen, F. H. (2002). Acta Cryst. B58, 380-388.]).

[Scheme 1]

Experimental

Crystal data
  • [Ge4(CH3)8(C4H2S)4]

  • Mr = 739.22

  • Monoclinic, P 21 /c

  • a = 6.6211 (4) Å

  • b = 12.6668 (7) Å

  • c = 18.3413 (11) Å

  • β = 90.698 (4)°

  • V = 1538.14 (16) Å3

  • Z = 2

  • Mo Kα radiation

  • μ = 4.15 mm−1

  • T = 193 K

  • 0.20 × 0.06 × 0.02 mm

Data collection
  • Bruker APEXII diffractometer

  • Absorption correction: multi-scan (SADABS; Bruker, 2006[Bruker (2006). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]) Tmin = 0.741, Tmax = 0.922

  • 34763 measured reflections

  • 4222 independent reflections

  • 3102 reflections with I > 2σ(I)

  • Rint = 0.065

Refinement
  • R[F2 > 2σ(F2)] = 0.030

  • wR(F2) = 0.064

  • S = 1.01

  • 4222 reflections

  • 149 parameters

  • H-atom parameters constrained

  • Δρmax = 0.44 e Å−3

  • Δρmin = −0.37 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

Cg1 is the centroid of the S1/C3–C6 ring.

D—H⋯A D—H H⋯A DA D—H⋯A
C10—H10⋯Cg1i 0.95 2.82 3.606 (4) 141
Symmetry code: (i) x+1, y, z.

Data collection: APEX2 (Bruker, 2006[Bruker (2006). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: APEX2 and SAINT (Bruker, 2006[Bruker (2006). APEX2, SAINT and SADABS. 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: SHELXTL (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); software used to prepare material for publication: SHELXTL and publCIF (Westrip, 2010[Westrip, S. P. (2010). J. Appl. Cryst. 43, 920-925.]).

Supporting information


Comment top

Calix[4]thiophenes, sulfur-based analogues of calixarenes are of great importance for their uses in supramolecular chemistry. On the other hands, various hetero-calix[4]thiophenes in which group 14 atoms such as Si, Ge and Sn replace carbon atoms in the cyclic backbone have been prepared and characterized. However, to the best of our knowledge, no crystallographic data concerning germa-calixarene derivatives has far been reported so far (Cambridge Structural Database, V5.33, last update Aug. 2012; Allen, 2002).

The asymmetric unit of the title compound contains one half-molecule, the other half being related by a crystallographic inversion center (Fig. 1). In the asymmetric unit, the dihedral angle between adjacent thiophene rings is 72.84 (14)°. It is noteworthy that a C–H···π interaction between the hydrogen H10 and the π cloud of the thiophene ring S1/C3—C6 is observed giving stacks of the title compound along the a axis (Table 1 and Fig.2).

Related literature top

For a review concerning aryl- and heteroarylgermanes, see: Spivey & Diaper (2003). For syntheses and structures of heteroarylgermanes, see: Hockemeyer, Castel et al. (1997); Barrau et al. (1997); Koenig & Roedel (1997). For properties of heteroarylgermanes, see: Hockemeyer, Valentin et al. (1997). For a description of the Cambridge Structural Database, see: Allen (2002).

Experimental top

The title compound was prepared according to the following procedure:

In a first step, to a solution of thiophene (5.09 g, 60 mmol) and TMEDA (9.10 ml, 60 mmol) in dry diethyl ether (150 ml) was added a solution of n-BuLi (37.50 ml, 60 mmol, 1.6 M in hexanes). The mixture was stirred for 2 h at room temperature. A solution of Me2GeCl2 (5.20 g, 30 mmol) in dry diethyl ether (30 ml) was added slowly, the mixture was stirred for an additional 2 h. The reaction mixture was then filtered and the solvents removed by evaporation under reduced pressure. The residue was distillated to afford Me2Ge(C4H3S)2 (4.90 g, 61% yield).

In a second step, to a solution of Me2Ge(C4H3S)2 (2.69 g, 10 mmol) and TMEDA (3.0 ml, 20 mmol) in dry pentane (150 ml) cooled to 193 K was slowly added a solution of n-BuLi (12.50 ml, 20 mmol, 1.6 M in hexanes). The mixture was allowed to rise to room temperature and stirred for 2 h. To the formed precipitate in suspension was slowly added at 233 K a solution of Me2GeCl2 (1.75 g, 10 mmol) in dry pentane (50 ml). The mixture was allowed to rise to room temperature and stirred for 1h, and one additional hour at reflux. The reaction mixture was filtered and the solvents removed by evaporation under reduced pressure. The solid was washed by pentane. Crystals of the title compound were obtained by slow evaporation of a solution in CH2Cl2. Both the intermediate and the title compound were fully characterized, and spectroscopic and other data are available in the archived CIF.

Refinement top

All the H atoms were included in calculated positions and treated as riding atoms: C—H = 0.95 Å (aromatic), and 0.98 Å (methyl) with Uiso(H) = 1.2Ueq(aromatic) and Uiso(H) = 1.5Ueq(methyl).

Structure description top

Calix[4]thiophenes, sulfur-based analogues of calixarenes are of great importance for their uses in supramolecular chemistry. On the other hands, various hetero-calix[4]thiophenes in which group 14 atoms such as Si, Ge and Sn replace carbon atoms in the cyclic backbone have been prepared and characterized. However, to the best of our knowledge, no crystallographic data concerning germa-calixarene derivatives has far been reported so far (Cambridge Structural Database, V5.33, last update Aug. 2012; Allen, 2002).

The asymmetric unit of the title compound contains one half-molecule, the other half being related by a crystallographic inversion center (Fig. 1). In the asymmetric unit, the dihedral angle between adjacent thiophene rings is 72.84 (14)°. It is noteworthy that a C–H···π interaction between the hydrogen H10 and the π cloud of the thiophene ring S1/C3—C6 is observed giving stacks of the title compound along the a axis (Table 1 and Fig.2).

For a review concerning aryl- and heteroarylgermanes, see: Spivey & Diaper (2003). For syntheses and structures of heteroarylgermanes, see: Hockemeyer, Castel et al. (1997); Barrau et al. (1997); Koenig & Roedel (1997). For properties of heteroarylgermanes, see: Hockemeyer, Valentin et al. (1997). For a description of the Cambridge Structural Database, see: Allen (2002).

Computing details top

Data collection: APEX2 (Bruker, 2006); cell refinement: APEX2 and SAINT (Bruker, 2006); data reduction: SAINT (Bruker, 2006); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008) and publCIF (Westrip, 2010).

Figures top
[Figure 1] Fig. 1. The molecular structure of the title molecule, with the atom numbering. The displacement ellipsoids are drawn at the 50% probability level. H atoms have been omitted for clarity. [Symmetry code: (A) -x + 1, -y + 1, -z + 1]
[Figure 2] Fig. 2. A partial view of the crystal packing of the title compound, showing the C—H··· π interactions (dashed lines; see Table 1 for details). H atoms not involved in these interactions have been omitted for clarity.
2,2,7,7,12,12,17,17-Octamethyl-21,22,23,24-tetrathia-2,7,12,17- tetragermapentacyclo[16.2.1.13,6.18,11.113,16]tetracosa- 3,5,8,10,13,15,18,20-octaene top
Crystal data top
[Ge4(CH3)8(C4H2S)4]F(000) = 736
Mr = 739.22Dx = 1.596 Mg m3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 5690 reflections
a = 6.6211 (4) Åθ = 3.1–24.2°
b = 12.6668 (7) ŵ = 4.15 mm1
c = 18.3413 (11) ÅT = 193 K
β = 90.698 (4)°Plate, colourless
V = 1538.14 (16) Å30.20 × 0.06 × 0.02 mm
Z = 2
Data collection top
Bruker APEXII
diffractometer
4222 independent reflections
Radiation source: fine-focus sealed tube3102 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.065
phi and ω scansθmax = 29.4°, θmin = 2.2°
Absorption correction: multi-scan
(SADABS; Bruker, 2006)
h = 99
Tmin = 0.741, Tmax = 0.922k = 1717
34763 measured reflectionsl = 2525
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)] = 0.030Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.064H-atom parameters constrained
S = 1.01 w = 1/[σ2(Fo2) + (0.0251P)2 + 0.5305P]
where P = (Fo2 + 2Fc2)/3
4222 reflections(Δ/σ)max = 0.001
149 parametersΔρmax = 0.44 e Å3
0 restraintsΔρmin = 0.37 e Å3
Crystal data top
[Ge4(CH3)8(C4H2S)4]V = 1538.14 (16) Å3
Mr = 739.22Z = 2
Monoclinic, P21/cMo Kα radiation
a = 6.6211 (4) ŵ = 4.15 mm1
b = 12.6668 (7) ÅT = 193 K
c = 18.3413 (11) Å0.20 × 0.06 × 0.02 mm
β = 90.698 (4)°
Data collection top
Bruker APEXII
diffractometer
4222 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2006)
3102 reflections with I > 2σ(I)
Tmin = 0.741, Tmax = 0.922Rint = 0.065
34763 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0300 restraints
wR(F2) = 0.064H-atom parameters constrained
S = 1.01Δρmax = 0.44 e Å3
4222 reflectionsΔρmin = 0.37 e Å3
149 parameters
Special details top

Experimental. Spectroscopic data for the intermediate: M.p.= 363 - 364 K/0.25 mm Hg. 1H NMR (300 MHz in CDCl3) δ, p.p.m.: 7.71–7.64 (m, 2H), 7.36–7.31 (m, 2H), 7.31–7.34 (m, 2H), 0.85 (s, 6H). 13C NMR (75 MHz in CDCl3) δ, p.p.m.: 138.1, 133.9, 130.4, 128.1, -0.1. MS (EI, 70 eV) m/z= 270 (M+.). UV: λ max= 235 nm, log ε= 1.41. IR (Nujol, cm-1): 3100, 3073, 2976, 2907, 1497, 1402, 1214, 1080, 974, 848, 831, 807, 746, 704. Anal. Found: C, 44.62; H, 4.57. Calc. for C10H12S2Ge: C, 44.68; H, 4.47.

Spectroscopic data for the title compound: M.p.: 389 - 390 K(dec.). 1H NMR (300 MHz in CDCl3) δ, p.p.m.: 7.31 (s, 8H), 0.78 (s, 24H). 13C NMR (75 MHz in CDCl3) δ, p.p.m.: 143.6, 134.9, 1.2. MS (EI, 70 eV) m/z= 740 (M+.). UV: λ max= 247 nm, log ε = 4.6. IR (Nujol, cm-1): 2960, 2915, 1643, 1490, 1406, 1270, 1240, 1200, 985, 953, 836, 802, 738. Anal. Found: C, 38.85; H, 4.42. Calc. for C24H32S4Ge4: C, 39.00; H, 4.33.

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
Ge10.09401 (4)0.22725 (2)0.492665 (15)0.02782 (8)
Ge20.54568 (4)0.48911 (2)0.256324 (15)0.02951 (8)
S10.37473 (10)0.38100 (5)0.39987 (3)0.03005 (15)
S20.62663 (10)0.65368 (6)0.38758 (4)0.03257 (16)
C10.1957 (4)0.2081 (2)0.48350 (16)0.0387 (7)
H1A0.25950.27580.47140.058*
H1B0.24900.18200.52970.058*
H1C0.22510.15690.44480.058*
C20.2337 (5)0.0964 (2)0.51710 (17)0.0461 (8)
H2A0.21280.04500.47780.069*
H2B0.18000.06790.56260.069*
H2C0.37840.11030.52320.069*
C30.1957 (4)0.2830 (2)0.40179 (14)0.0295 (6)
C40.1417 (4)0.2561 (2)0.33170 (15)0.0366 (7)
H40.04440.20330.32030.044*
C50.2455 (4)0.3148 (2)0.27812 (15)0.0346 (6)
H50.22390.30490.22730.042*
C60.3792 (4)0.3868 (2)0.30595 (13)0.0281 (5)
C70.7184 (5)0.4178 (3)0.18768 (17)0.0544 (9)
H7A0.79900.47010.16150.082*
H7B0.63510.37790.15280.082*
H7C0.80860.36930.21400.082*
C80.3709 (5)0.5915 (2)0.20864 (18)0.0535 (9)
H8A0.29600.63080.24550.080*
H8B0.27560.55480.17620.080*
H8C0.45280.64050.18020.080*
C90.7126 (4)0.5572 (2)0.32987 (13)0.0274 (5)
C100.9108 (4)0.5395 (3)0.34415 (18)0.0493 (8)
H100.98870.48890.31860.059*
C110.9916 (4)0.6038 (3)0.40107 (18)0.0525 (9)
H111.12860.60030.41690.063*
C120.8553 (4)0.6707 (2)0.43070 (14)0.0291 (6)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ge10.02892 (14)0.02620 (14)0.02832 (15)0.00283 (11)0.00068 (11)0.00038 (11)
Ge20.03170 (15)0.03462 (16)0.02218 (14)0.00246 (12)0.00042 (11)0.00054 (12)
S10.0324 (3)0.0329 (4)0.0247 (3)0.0058 (3)0.0027 (3)0.0015 (3)
S20.0283 (3)0.0388 (4)0.0305 (4)0.0048 (3)0.0027 (3)0.0058 (3)
C10.0322 (14)0.0451 (17)0.0386 (16)0.0069 (13)0.0029 (12)0.0004 (13)
C20.0519 (18)0.0328 (16)0.053 (2)0.0011 (14)0.0074 (15)0.0035 (14)
C30.0300 (13)0.0257 (13)0.0330 (14)0.0012 (11)0.0004 (11)0.0011 (11)
C40.0399 (15)0.0337 (15)0.0362 (16)0.0078 (12)0.0001 (13)0.0090 (12)
C50.0393 (15)0.0384 (15)0.0261 (14)0.0031 (12)0.0010 (12)0.0068 (12)
C60.0275 (12)0.0310 (14)0.0260 (13)0.0034 (11)0.0025 (10)0.0016 (11)
C70.0522 (19)0.074 (2)0.0372 (18)0.0103 (18)0.0156 (15)0.0179 (17)
C80.059 (2)0.0482 (19)0.053 (2)0.0040 (16)0.0258 (17)0.0174 (16)
C90.0295 (13)0.0307 (13)0.0221 (13)0.0006 (11)0.0026 (10)0.0021 (10)
C100.0350 (15)0.0518 (19)0.061 (2)0.0096 (14)0.0035 (15)0.0294 (16)
C110.0293 (15)0.058 (2)0.070 (2)0.0078 (14)0.0124 (15)0.0270 (18)
C120.0280 (12)0.0285 (14)0.0307 (14)0.0006 (11)0.0004 (11)0.0005 (11)
Geometric parameters (Å, º) top
Ge1—C12i1.935 (3)C3—C41.373 (4)
Ge1—C31.938 (3)C4—C51.417 (4)
Ge1—C11.939 (3)C4—H40.9500
Ge1—C21.948 (3)C5—C61.366 (3)
Ge2—C71.935 (3)C5—H50.9500
Ge2—C91.936 (2)C7—H7A0.9800
Ge2—C61.936 (3)C7—H7B0.9800
Ge2—C81.939 (3)C7—H7C0.9800
S1—C31.718 (3)C8—H8A0.9800
S1—C61.725 (3)C8—H8B0.9800
S2—C121.714 (2)C8—H8C0.9800
S2—C91.718 (3)C9—C101.354 (4)
C1—H1A0.9800C10—C111.424 (4)
C1—H1B0.9800C10—H100.9500
C1—H1C0.9800C11—C121.356 (4)
C2—H2A0.9800C11—H110.9500
C2—H2B0.9800C12—Ge1i1.935 (3)
C2—H2C0.9800
C12i—Ge1—C3108.81 (11)C5—C4—H4123.3
C12i—Ge1—C1108.00 (11)C6—C5—C4114.1 (2)
C3—Ge1—C1108.94 (11)C6—C5—H5122.9
C12i—Ge1—C2108.88 (12)C4—C5—H5122.9
C3—Ge1—C2109.81 (12)C5—C6—S1109.0 (2)
C1—Ge1—C2112.32 (13)C5—C6—Ge2129.9 (2)
C7—Ge2—C9108.94 (12)S1—C6—Ge2120.97 (14)
C7—Ge2—C6109.73 (13)Ge2—C7—H7A109.5
C9—Ge2—C6107.11 (10)Ge2—C7—H7B109.5
C7—Ge2—C8111.90 (15)H7A—C7—H7B109.5
C9—Ge2—C8110.41 (12)Ge2—C7—H7C109.5
C6—Ge2—C8108.64 (12)H7A—C7—H7C109.5
C3—S1—C694.08 (13)H7B—C7—H7C109.5
C12—S2—C994.39 (12)Ge2—C8—H8A109.5
Ge1—C1—H1A109.5Ge2—C8—H8B109.5
Ge1—C1—H1B109.5H8A—C8—H8B109.5
H1A—C1—H1B109.5Ge2—C8—H8C109.5
Ge1—C1—H1C109.5H8A—C8—H8C109.5
H1A—C1—H1C109.5H8B—C8—H8C109.5
H1B—C1—H1C109.5C10—C9—S2109.0 (2)
Ge1—C2—H2A109.5C10—C9—Ge2127.2 (2)
Ge1—C2—H2B109.5S2—C9—Ge2123.75 (14)
H2A—C2—H2B109.5C9—C10—C11113.7 (3)
Ge1—C2—H2C109.5C9—C10—H10123.2
H2A—C2—H2C109.5C11—C10—H10123.2
H2B—C2—H2C109.5C12—C11—C10114.0 (2)
C4—C3—S1109.4 (2)C12—C11—H11123.0
C4—C3—Ge1128.7 (2)C10—C11—H11123.0
S1—C3—Ge1121.86 (14)C11—C12—S2108.9 (2)
C3—C4—C5113.3 (2)C11—C12—Ge1i126.73 (19)
C3—C4—H4123.3S2—C12—Ge1i124.31 (14)
Symmetry code: (i) x+1, y+1, z+1.
Hydrogen-bond geometry (Å, º) top
Cg1 is the centroid of the S1/C3–C6 ring.
D—H···AD—HH···AD···AD—H···A
C10—H10···Cg1ii0.952.823.606 (4)141
Symmetry code: (ii) x+1, y, z.

Experimental details

Crystal data
Chemical formula[Ge4(CH3)8(C4H2S)4]
Mr739.22
Crystal system, space groupMonoclinic, P21/c
Temperature (K)193
a, b, c (Å)6.6211 (4), 12.6668 (7), 18.3413 (11)
β (°) 90.698 (4)
V3)1538.14 (16)
Z2
Radiation typeMo Kα
µ (mm1)4.15
Crystal size (mm)0.20 × 0.06 × 0.02
Data collection
DiffractometerBruker APEXII
Absorption correctionMulti-scan
(SADABS; Bruker, 2006)
Tmin, Tmax0.741, 0.922
No. of measured, independent and
observed [I > 2σ(I)] reflections
34763, 4222, 3102
Rint0.065
(sin θ/λ)max1)0.691
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.030, 0.064, 1.01
No. of reflections4222
No. of parameters149
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.44, 0.37

Computer programs: APEX2 (Bruker, 2006), APEX2 and SAINT (Bruker, 2006), SAINT (Bruker, 2006), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), SHELXTL (Sheldrick, 2008) and publCIF (Westrip, 2010).

Hydrogen-bond geometry (Å, º) top
Cg1 is the centroid of the S1/C3–C6 ring.
D—H···AD—HH···AD···AD—H···A
C10—H10···Cg1i0.952.823.606 (4)141.0
Symmetry code: (i) x+1, y, z.
 

Acknowledgements

This work was supported financially by the Centre National de la Recherche Scientifique (CNRS), by Université Paul Sabatier (UPS) and by the Agence Nationale de la Recherche (ANR-08-CSOG-00). GC is grateful to the ANR for a PhD grant.

References

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