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

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ISSN: 2056-9890

Fluoren-9-one 4-toluene­sulfonyl­hydrazone: hydrogen-bonded R[{_2^2}](8) dimers are linked into sheets by ππ stacking interactions

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aSchool of Chemistry, University of St Andrews, St Andrews, Fife KY16 9ST, Scotland, bDepartment of Chemistry, University of Aberdeen, Meston Walk, Old Aberdeen AB24 3UE, Scotland, and cInstituto de Química, Departamento de Química Inorgânica, Universidade Federal do Rio de Janeiro, 21945-970 Rio de Janeiro-RJ, Brazil
*Correspondence e-mail: cg@st-andrews.ac.uk

(Received 1 March 2004; accepted 2 March 2004; online 13 March 2004)

Molecules of the title compound, C20H16N2O2S, are linked into centrosymmetric R[{_2^2}](8) dimers by paired N—H⋯O hydrogen bonds [H⋯O 2.14 Å, N⋯O 2.9951 (15) Å and N—H⋯O 164°]. Two distinct ππ stacking interactions link the dimers into chains along [10[\overline 1]] and [001], respectively, hence forming (010) sheets.

Comment

4-Toluene­sulfonyl­hydrazones, R1R2C=NNHC6H4Me, are not only important derivatives of carbonyl compounds, R1R2C=O, but are also very useful precursors of diazo compounds, R1R2CN2, (Jonczyk & Wlostowska, 1978[Jonczyk, A. & Wlostowska, J. (1978). Synth. Commun. 8, 569-572.]), as exemplified by the title compound, (I[link]) (Fig. 1[link]).

[Scheme 1]

The mol­ecules of (I[link]) are linked by paired N—H⋯O=S hydrogen bonds into centrosymmetric dimers, with the reference dimer centred at ([{1 \over 2}], [{1 \over 2}], [{1 \over 2}]) (Fig. 2[link]). The associated R[{_2^2}](8) (Bernstein et al., 1995[Bernstein, J., Davis, R. E., Shimoni, L. & Chang, N.-L. (1995). Angew. Chem. Int. Ed. Engl. 34, 1555-1573.]) motif has been observed previously in a number of sulfon­amido species (Klug, 1968[Klug, H. P. (1968). Acta Cryst. B24, 792-802.]; Blaschette et al., 1986[Blaschette, A., Wieland, E., Schomburg, D. & Adelhelm, M. (1986). Z. Anorg. Allg. Chem. 533, 7-717.]; Tremayne et al., 1999[Tremayne, M., MacLean, E. J., Tang, C. C. & Glidewell, C. (1999). Acta Cryst. B55, 1068-1074.], 2002[Tremayne, M., Seaton, C. C. & Glidewell, C. (2002). Acta Cryst. B58, 823-834.]; Kelly et al., 2002[Kelly, C. J., Skakle, J. M. S., Wardell, J. L., Wardell, S. M. S. V., Low, J. N. & Glidewell, C. (2002). Acta Cryst. B58, 94-108.]; Clark et al., 2003[Clark, J. C., McLaughlin, M. L. & Fronczek, F. R. (2003). Acta Cryst. E59, o2005-o2006.]). While there are no soft hydrogen bonds of either C—H⋯O or C—H⋯π(arene) types present in the structure of (I[link]), the dimeric aggregates are linked into sheets by two distinct ππ stacking interactions, one involving aryl rings and the other involving the fulvene portion of the fluorenone hydrazone.

The C11–C16 aryl rings of the mol­ecules at (x, y, z) and (2 − x, 1 − y, −z) are parallel, with an interplanar spacing of 3.427 (2) Å; the centroid separation is 3.725 (2) Å, corresponding to a centroid offset of 1.460 (2) Å. These two mol­ecules lie in the R[{_2^2}](8) dimers centred at ([{1 \over 2}], [{1 \over 2}], [{1 \over 2}]) and ([{3 \over 2}], [{1 \over 2}], −[{1 \over 2}]), respectively, so that propagation by inversion of this ππ interaction generates a chain of π-stacked dimers running parallel to the [10[\overline 1]] direction (Fig. 3[link]).

The fulvene-type rings (C7/C11/C16/C26/C21) of the mol­ecules at (x, y, z) and (1 − x, 1 − y, −z), which lie in the R[{_2^2}](8) dimers centred at ([{1 \over 2}], [{1 \over 2}], [{1 \over 2}]) and ([{1 \over 2}], [{1 \over 2}], −[{1 \over 2}]), respectively, are also parallel; the interplanar spacing is 3.419 (2) Å and the centroid separation is 3.451 (2) Å, corresponding to a centroid offset of only 0.473 (2) Å. Propagation by inversion of the interaction generates a second chain of π-stacked dimers, in this case running parallel to the [001] direction (Fig. 4[link]). The combination of the [001] and [10[\overline 1]] chains generates an (010) sheet.

[Figure 1]
Figure 1
The mol­ecule of (I[link]), showing the atom-labelling scheme. Displacement ellipsoids are drawn at the 30% probability level.
[Figure 2]
Figure 2
Part of the crystal structure of (I[link]), showing the formation of an R[{_2^2}](8) dimer. For the sake of clarity, H atoms bonded to C atoms have been omitted. The atoms marked with an asterisk (*) are at the symmetry position (1 − x, 1 − y, 1 − z).
[Figure 3]
Figure 3
A stereoview of part of the crystal structure of (I[link]), showing the formation of a [10[\overline 1]] chain of π-stacked dimers. For the sake of clarity, H atoms bonded to C atoms have been omitted.
[Figure 4]
Figure 4
A stereoview of part of the crystal structure of (I[link]), showing the formation of an [001] chain of π-stacked dimers. For the sake of clarity, H atoms bonded to C atoms have been omitted.

Experimental

The title compound was prepared using the published procedure of Bamford & Stevens (1952[Bamford, W. R. & Stevens, T. S. (1952). J. Chem. Soc. pp. 4735-4738.]) and it was recrystallized from ethanol [m.p. 457–460 K (decomposes); literature m.p. 453–455 K (decomposes)].

Crystal data
  • C20H16N2O2S

  • Mr = 348.41

  • Triclinic, [P\overline 1]

  • a = 7.7487 (2) Å

  • b = 10.4290 (3) Å

  • c = 11.2007 (3) Å

  • α = 71.8482 (13)°

  • β = 76.9553 (17)°

  • γ = 75.3167 (17)°

  • V = 821.34 (4) Å3

  • Z = 2

  • Dx = 1.409 Mg m−3

  • Mo Kα radiation

  • Cell parameters from 3744 reflections

  • θ = 3.1–27.5°

  • μ = 0.21 mm−1

  • T = 120 (2) K

  • Block, yellow

  • 0.48 × 0.40 × 0.26 mm

Data collection
  • Nonius KappaCCD area-detector diffractometer

  • φ scans, and ω scans with κ offsets

  • Absorption correction: multi-scan (SORTAV; Blessing, 1995[Blessing, R. H. (1995). Acta Cryst. A51, 33-37.], 1997[Blessing, R. H. (1997). J. Appl. Cryst. 30, 421-426.]) Tmin = 0.915, Tmax = 0.947

  • 6955 measured reflections

  • 3744 independent reflections

  • 3294 reflections with I > 2σ(I)

  • Rint = 0.016

  • θmax = 27.5°

  • h = −9 → 10

  • k = −13 → 13

  • l = −14 → 14

Refinement
  • Refinement on F2

  • R[F2 > 2σ(F2)] = 0.036

  • wR(F2) = 0.090

  • S = 1.06

  • 3744 reflections

  • 227 parameters

  • H-atom parameters constrained

  • w = 1/[σ2(Fo2) + (0.0355P)2 + 0.4642P] where P = (Fo2 + 2Fc2)/3

  • (Δ/σ)max < 0.001

  • Δρmax = 0.33 e Å−3

  • Δρmin = −0.49 e Å−3

Table 1
Selected geometric parameters (Å, °)

S1—C1 1.7569 (13)
S1—O1 1.4281 (10)
S1—O2 1.4448 (10)
S1—N8 1.6375 (11)
N8—N7 1.4038 (16)
N7—C7 1.2916 (18)
C7—C11 1.4803 (19)
C7—C21 1.485 (2)
C11—C16 1.403 (2)
C21—C26 1.4140 (19)
C16—C26 1.467 (2)
C11—C7—N7—N8 178.55 (11)
C7—N7—N8—S1 169.89 (9)

Table 2
Hydrogen-bonding geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N8—H8⋯O2i 0.88 2.14 2.9951 (15) 164
Symmetry code: (i) 1-x,1-y,1-z.

All H atoms were located using difference maps and subsequently treated as riding atoms, with C—H distances of 0.95 (aromatic) or 0.98 (methyl), and an N—H distance of 0.88 Å, and with Uiso(H) = 1.2Ueq(C,N), or 1.5Ueq(C) for methyl H.

Data collection: KappaCCD Server Software (Nonius, 1997[Nonius (1997). KappaCCD Server Software. Windows 3.11 Version. Nonius BV, Delft, The Netherlands.]); cell refinement: DENZO-SMN (Otwinowski & Minor, 1997[Otwinowski, Z. & Minor, W. (1997). Methods in Enzymology, Vol. 276, Macromolecular Crystallography, Part A, edited by C. W. Carter Jr & R. M. Sweet, pp. 307-326. New York: Academic Press.]); data reduction: DENZO-SMN; program(s) used to solve structure: OSCAIL (McArdle, 2003[McArdle, P. (2003). OSCAIL for Windows. Version 10. Crystallography Centre, Chemistry Department, NUI Galway, Ireland.]) and SHELXS86 (Sheldrick, 1990[Sheldrick, G. M. (1990). Acta Cryst. A46, 467-473.]); program(s) used to refine structure: OSCAIL and SHELXL97 (Sheldrick, 1997[Sheldrick, G. M. (1997). SHELXL97. University of Göttingen, Germany.]); molecular graphics: PLATON (Spek, 2003[Spek, A. L. (2003). J. Appl. Cryst. 36, 7-13.]); software used to prepare material for publication: SHELXL97 and PRPKAPPA (Ferguson, 1999[Ferguson, G. (1999). PRPKAPPA. University of Guelph, Canada.]).

Supporting information


Computing details top

Data collection: KappaCCD Server Software (Nonius, 1997); cell refinement: DENZO-SMN (Otwinowski & Minor, 1997); data reduction: DENZO-SMN; program(s) used to solve structure: OSCAIL (McArdle, 2003) and SHELXS86 (Sheldrick, 1990); program(s) used to refine structure: OSCAIL and SHELXS97 (Sheldrick, 1997); molecular graphics: PLATON (Spek, 2003); software used to prepare material for publication: SHELXL97 and PRPKAPPA (Ferguson, 1999).

Fluoren-9-one 4-toluenesulfonylhydrazone top
Crystal data top
C20H16N2O2SZ = 2
Mr = 348.41F(000) = 364
Triclinic, P1Dx = 1.409 Mg m3
Hall symbol: -P 1Mo Kα radiation, λ = 0.71073 Å
a = 7.7487 (2) ÅCell parameters from 3744 reflections
b = 10.4290 (3) Åθ = 3.1–27.5°
c = 11.2007 (3) ŵ = 0.21 mm1
α = 71.8482 (13)°T = 120 K
β = 76.9553 (17)°Block, yellow
γ = 75.3167 (17)°0.48 × 0.40 × 0.26 mm
V = 821.34 (4) Å3
Data collection top
Nonius KappaCCD area-detector
diffractometer
3744 independent reflections
Radiation source: rotating anode3294 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.016
φ scans, and ω scans with κ offsetsθmax = 27.5°, θmin = 3.1°
Absorption correction: multi-scan
(SORTAV; Blessing, 1995, 1997)
h = 910
Tmin = 0.915, Tmax = 0.947k = 1313
6955 measured reflectionsl = 1414
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)] = 0.036Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.090H-atom parameters constrained
S = 1.06 w = 1/[σ2(Fo2) + (0.0355P)2 + 0.4642P]
where P = (Fo2 + 2Fc2)/3
3744 reflections(Δ/σ)max < 0.001
227 parametersΔρmax = 0.33 e Å3
0 restraintsΔρmin = 0.49 e Å3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
S10.49758 (4)0.29627 (3)0.46935 (3)0.01486 (10)
O10.42730 (13)0.19893 (10)0.43797 (9)0.0200 (2)
O20.38541 (13)0.37025 (10)0.55813 (9)0.0191 (2)
N70.65778 (15)0.37426 (12)0.24099 (11)0.0175 (2)
N80.53735 (15)0.41975 (12)0.34037 (10)0.0170 (2)
C10.70124 (18)0.21206 (14)0.52723 (12)0.0152 (3)
C20.72736 (19)0.07160 (14)0.58536 (13)0.0190 (3)
C30.8796 (2)0.00832 (15)0.64325 (14)0.0213 (3)
C41.00559 (19)0.08295 (15)0.64246 (13)0.0198 (3)
C50.97835 (19)0.22305 (15)0.58033 (14)0.0201 (3)
C60.82650 (19)0.28867 (14)0.52338 (13)0.0192 (3)
C70.66885 (18)0.46685 (14)0.13309 (13)0.0173 (3)
C110.79401 (19)0.43389 (15)0.02076 (13)0.0203 (3)
C120.9210 (2)0.31646 (16)0.01045 (15)0.0253 (3)
C131.0248 (2)0.31484 (19)0.10839 (16)0.0313 (4)
C140.9996 (2)0.42802 (19)0.21281 (15)0.0317 (4)
C150.8723 (2)0.54628 (18)0.20293 (14)0.0278 (3)
C160.7699 (2)0.54903 (16)0.08441 (13)0.0214 (3)
C210.57250 (19)0.61144 (15)0.08941 (13)0.0184 (3)
C220.44142 (19)0.69726 (15)0.15144 (14)0.0215 (3)
C230.3761 (2)0.83030 (16)0.08245 (15)0.0264 (3)
C240.4379 (2)0.87671 (16)0.04685 (15)0.0273 (3)
C250.5645 (2)0.79084 (16)0.11100 (14)0.0253 (3)
C260.63292 (19)0.65890 (15)0.04260 (13)0.0203 (3)
C411.1667 (2)0.01449 (17)0.70916 (15)0.0280 (3)
H120.93710.23910.08220.030*
H131.11350.23550.11800.038*
H141.07130.42450.29300.038*
H150.85560.62310.27510.033*
H220.39710.66570.23960.026*
H230.28780.89040.12440.032*
H240.39270.96850.09190.033*
H250.60370.82180.20000.030*
H80.55520.49290.35550.020*
H20.64270.01960.58560.023*
H30.89790.08760.68410.026*
H51.06540.27450.57700.024*
H60.80820.38450.48230.023*
H41A1.13280.01290.79930.042*
H41B1.26420.06590.67000.042*
H41C1.20810.08000.70170.042*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.01527 (17)0.01553 (17)0.01290 (16)0.00454 (12)0.00134 (12)0.00203 (12)
O10.0209 (5)0.0209 (5)0.0208 (5)0.0083 (4)0.0036 (4)0.0055 (4)
O20.0182 (5)0.0195 (5)0.0177 (5)0.0023 (4)0.0001 (4)0.0057 (4)
N70.0174 (6)0.0213 (6)0.0156 (6)0.0056 (5)0.0013 (4)0.0068 (5)
N80.0211 (6)0.0172 (6)0.0123 (5)0.0051 (5)0.0002 (4)0.0040 (4)
C10.0158 (6)0.0170 (6)0.0120 (6)0.0024 (5)0.0014 (5)0.0041 (5)
C20.0207 (7)0.0172 (7)0.0185 (7)0.0060 (5)0.0013 (5)0.0035 (5)
C30.0232 (7)0.0162 (7)0.0204 (7)0.0020 (5)0.0024 (5)0.0013 (5)
C40.0184 (7)0.0231 (7)0.0158 (6)0.0004 (5)0.0017 (5)0.0061 (5)
C50.0179 (7)0.0223 (7)0.0222 (7)0.0056 (5)0.0027 (5)0.0077 (6)
C60.0191 (7)0.0157 (6)0.0214 (7)0.0037 (5)0.0019 (5)0.0039 (5)
C70.0169 (6)0.0236 (7)0.0148 (6)0.0088 (5)0.0021 (5)0.0062 (5)
C110.0194 (7)0.0303 (8)0.0166 (7)0.0134 (6)0.0001 (5)0.0091 (6)
C120.0237 (8)0.0294 (8)0.0271 (8)0.0099 (6)0.0009 (6)0.0124 (6)
C130.0261 (8)0.0402 (9)0.0369 (9)0.0141 (7)0.0053 (7)0.0244 (8)
C140.0332 (9)0.0482 (10)0.0236 (8)0.0243 (8)0.0089 (6)0.0199 (7)
C150.0323 (8)0.0419 (9)0.0162 (7)0.0235 (7)0.0027 (6)0.0092 (6)
C160.0228 (7)0.0317 (8)0.0155 (7)0.0163 (6)0.0013 (5)0.0069 (6)
C210.0192 (7)0.0244 (7)0.0148 (6)0.0109 (6)0.0038 (5)0.0037 (5)
C220.0221 (7)0.0260 (7)0.0172 (7)0.0065 (6)0.0042 (5)0.0049 (6)
C230.0270 (8)0.0266 (8)0.0278 (8)0.0044 (6)0.0090 (6)0.0079 (6)
C240.0326 (8)0.0249 (8)0.0263 (8)0.0088 (6)0.0146 (6)0.0000 (6)
C250.0300 (8)0.0326 (8)0.0168 (7)0.0172 (7)0.0072 (6)0.0002 (6)
C260.0216 (7)0.0296 (8)0.0142 (6)0.0153 (6)0.0033 (5)0.0038 (6)
C410.0237 (8)0.0295 (8)0.0274 (8)0.0006 (6)0.0092 (6)0.0032 (6)
Geometric parameters (Å, º) top
S1—C11.7569 (13)C22—H220.95
S1—O11.4281 (10)C23—C241.389 (2)
S1—O21.4448 (10)C23—H230.95
S1—N81.6375 (11)C24—C251.385 (2)
N8—N71.4038 (16)C24—H240.95
N7—C71.2916 (18)C25—C261.385 (2)
C11—C121.381 (2)C25—H250.95
C7—C111.4803 (19)N8—H80.88
C7—C211.485 (2)C1—C21.3876 (19)
C11—C161.403 (2)C1—C61.3911 (19)
C21—C261.4140 (19)C2—C31.390 (2)
C16—C261.467 (2)C2—H20.95
C12—C131.394 (2)C3—C41.392 (2)
C12—H120.95C3—H30.95
C13—C141.388 (3)C4—C51.393 (2)
C13—H130.95C4—C411.504 (2)
C14—C151.388 (3)C5—C61.385 (2)
C14—H140.95C5—H50.95
C15—C161.389 (2)C6—H60.95
C15—H150.95C41—H41A0.98
C21—C221.387 (2)C41—H41B0.98
C22—C231.390 (2)C41—H41C0.98
C12—C11—C16121.46 (13)N7—C7—C21133.19 (13)
C12—C11—C7130.27 (14)C11—C7—C21106.51 (12)
C16—C11—C7108.25 (13)C7—N7—N8114.54 (12)
C11—C12—C13118.00 (15)N7—N8—S1114.07 (9)
C11—C12—H12121.0N7—N8—H8116.2
C13—C12—H12121.0S1—N8—H8113.6
C14—C13—C12120.60 (16)O1—S1—O2118.82 (6)
C14—C13—H13119.7O1—S1—N8108.85 (6)
C12—C13—H13119.7O2—S1—N8102.95 (6)
C13—C14—C15121.61 (14)O1—S1—C1108.45 (6)
C13—C14—H14119.2O2—S1—C1108.17 (6)
C15—C14—H14119.2N8—S1—C1109.26 (6)
C14—C15—C16118.02 (15)C2—C1—C6121.17 (13)
C14—C15—H15121.0C2—C1—S1119.07 (10)
C16—C15—H15121.0C6—C1—S1119.55 (10)
C15—C16—C11120.29 (15)C1—C2—C3118.80 (13)
C15—C16—C26130.92 (15)C1—C2—H2120.6
C11—C16—C26108.77 (12)C3—C2—H2120.6
C22—C21—C26119.77 (13)C2—C3—C4121.18 (13)
C22—C21—C7132.65 (13)C2—C3—H3119.4
C26—C21—C7107.54 (12)C4—C3—H3119.4
C21—C22—C23118.84 (14)C3—C4—C5118.73 (13)
C21—C22—H22120.6C3—C4—C41120.79 (13)
C23—C22—H22120.6C5—C4—C41120.48 (13)
C24—C23—C22121.00 (15)C6—C5—C4121.09 (13)
C24—C23—H23119.5C6—C5—H5119.5
C22—C23—H23119.5C4—C5—H5119.5
C25—C24—C23120.84 (14)C5—C6—C1119.00 (13)
C25—C24—H24119.6C5—C6—H6120.5
C23—C24—H24119.6C1—C6—H6120.5
C26—C25—C24118.57 (14)C4—C41—H41A109.5
C26—C25—H25120.7C4—C41—H41B109.5
C24—C25—H25120.7H41A—C41—H41B109.5
C25—C26—C21120.93 (14)C4—C41—H41C109.5
C25—C26—C16130.19 (13)H41A—C41—H41C109.5
C21—C26—C16108.88 (13)H41B—C41—H41C109.5
N7—C7—C11120.27 (13)
C16—C11—C12—C130.4 (2)C12—C11—C7—C21176.23 (14)
C7—C11—C12—C13178.44 (13)C16—C11—C7—C212.00 (14)
C11—C12—C13—C140.4 (2)C22—C21—C7—N72.4 (3)
C12—C13—C14—C150.4 (2)C26—C21—C7—N7175.65 (14)
C13—C14—C15—C160.3 (2)C22—C21—C7—C11179.86 (14)
C14—C15—C16—C111.1 (2)C26—C21—C7—C112.13 (14)
C14—C15—C16—C26176.96 (14)C11—C7—N7—N8178.55 (11)
C12—C11—C16—C151.2 (2)C21—C7—N7—N83.9 (2)
C7—C11—C16—C15179.58 (12)C7—N7—N8—S1169.89 (9)
C12—C11—C16—C26177.29 (12)N7—N8—S1—O157.89 (10)
C7—C11—C16—C261.13 (15)N7—N8—S1—O2175.17 (9)
C26—C21—C22—C231.9 (2)N7—N8—S1—C160.38 (10)
C7—C21—C22—C23179.72 (14)O1—S1—C1—C227.20 (13)
C21—C22—C23—C241.1 (2)O2—S1—C1—C2102.92 (11)
C22—C23—C24—C251.0 (2)N8—S1—C1—C2145.71 (11)
C23—C24—C25—C262.1 (2)O1—S1—C1—C6158.00 (11)
C24—C25—C26—C211.3 (2)O2—S1—C1—C671.89 (12)
C24—C25—C26—C16178.06 (14)N8—S1—C1—C639.49 (12)
C22—C21—C26—C250.8 (2)C6—C1—C2—C31.7 (2)
C7—C21—C26—C25179.07 (12)S1—C1—C2—C3173.04 (10)
C22—C21—C26—C16179.79 (12)C1—C2—C3—C40.7 (2)
C7—C21—C26—C161.48 (15)C2—C3—C4—C51.1 (2)
C15—C16—C26—C251.4 (3)C2—C3—C4—C41177.93 (13)
C11—C16—C26—C25179.61 (14)C3—C4—C5—C61.9 (2)
C15—C16—C26—C21178.00 (14)C41—C4—C5—C6177.11 (13)
C11—C16—C26—C210.23 (15)C4—C5—C6—C10.9 (2)
C12—C11—C7—N75.6 (2)C2—C1—C6—C50.9 (2)
C16—C11—C7—N7176.12 (12)S1—C1—C6—C5173.81 (10)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N8—H8···O2i0.882.142.9951 (15)164
Symmetry code: (i) x+1, y+1, z+1.
 

Acknowledgements

X-ray data were collected at the EPSRC X-ray Crystallographic Service, University of Southampton, UK; the authors thank the staff for all their help and advice. JNL thanks NCR Self-Service, Dundee, for grants which have provided computing facilities for this work. JLW thanks CNPq and FAPERJ for financial support.

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