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ISSN: 2056-9890

1-Heptyl-1,3,6,8-tetra­aza­tri­cyclo­[4.3.1.13,8]undecan-1-ium iodide

aDepartamento de Química, Universidad Nacional de Colombia, Ciudad Universitaria, Bogotá, Colombia, and bInstitute of Physics ASCR, v.v.i., Na Slovance 2, 182 21 Praha 8, Czech Republic
*Correspondence e-mail: ariverau@unal.edu.co

(Received 31 August 2011; accepted 6 September 2011; online 14 September 2011)

The title compound C14H29N4+·I salt, was obtained by the reaction of cage adamanzane-type aminal 1,3,6,8-tetra­aza­tricyclo­[4.3.1.13,8]undecane with heptyl iodide. In the cation, the bond lengths and angles are within normal ranges, except for one N—C(ring) bond distance of 1.542 (3) Å, which is unexpectedly long compared with related compounds. In the crystal, ions are linked through C—H⋯I hydrogen bonds. The crystal studied was a non-merohedral twin with a minor twin domain of 6.56 (5)%.

Related literature

For the preparation of the title compound, see: Rivera et al. (2011[Rivera, A., Sadat-Bernal, J., Ríos-Motta, J., Dušek, M. & Palatinus, L. (2011). Chem. Cent. J. Submitted. ]). For synthetic applications of quaternary ammonium salts, see: Starks (1971[Starks, C. M. (1971). J. Am. Chem. Soc. 93, 195-199.]). For related structures, see: Betz & Klüfers (2007[Betz, R. & Klüfers, P. (2007). Acta Cryst. E63, o4279.]); Lee et al. (2011[Lee, J.-D., Han, W.-S., Suh, I.-H. & Kang, S. O. (2011). Acta Cryst. E67, o2148.]).

[Scheme 1]

Experimental

Crystal data
  • C14H29N4+·I

  • Mr = 380.3

  • Monoclinic, P 21 /n

  • a = 8.8325 (2) Å

  • b = 15.3276 (3) Å

  • c = 12.4792 (2) Å

  • β = 100.072 (2)°

  • V = 1663.41 (6) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 1.92 mm−1

  • T = 160 K

  • 0.31 × 0.24 × 0.16 mm

Data collection
  • Agilent Xcalibur diffractometer with Atlas (Gemini ultra Cu) detector

  • Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2010[Agilent (2010). CrysAlis PRO. Agilent Technologies, Yarnton, England.]) Tmin = 0.871, Tmax = 1

  • 22619 measured reflections

  • 4183 independent reflections

  • 3517 reflections with I > 3σ(I)

  • Rint = 0.031

Refinement
  • R[F2 > 2σ(F2)] = 0.027

  • wR(F2) = 0.065

  • S = 1.61

  • 4183 reflections

  • 173 parameters

  • H-atom parameters constrained

  • Δρmax = 0.53 e Å−3

  • Δρmin = −0.48 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
C2—H2a⋯I1i 0.96 2.94 3.858 (2) 161
Symmetry code: (i) [-x+{\script{1\over 2}}, y+{\script{1\over 2}}, -z+{\script{1\over 2}}].

Data collection: CrysAlis PRO (Agilent, 2010[Agilent (2010). CrysAlis PRO. Agilent Technologies, Yarnton, England.]); cell refinement: CrysAlis PRO; data reduction: CrysAlis PRO; program(s) used to solve structure: SIR2002 (Burla et al., 2003[Burla, M. C., Camalli, M., Carrozzini, B., Cascarano, G. L., Giacovazzo, C., Polidori, G. & Spagna, R. (2003). J. Appl. Cryst. 36, 1103.]); program(s) used to refine structure: JANA2006 (Petříček et al., 2006[Petříček, V., Dušek, M. & Palatinus, L. (2006). JANA2006. Institute of Physics, Praha, Czech Republic.]); molecular graphics: Diamond (Brandenburg & Putz, 2005[Brandenburg, K. & Putz, H. (2005). DIAMOND. Crystal Impact, Bonn, Germany.]); software used to prepare material for publication: JANA2006.

Supporting information


Comment top

Quaternary ammonium salts are used as phase transfer catalysts for a wide range of organic reactions involving immiscible solvent systems (Starks, 1971). Therefore, we have decided to synthesize a new series of new N-alkylated quaternary ammonium salts, based on the Menschutkin reaction (Rivera et al., 2011) of 1,3,6,8-tetraazatricyclo[4.3.1.13,8]undecane with an alkyl halide. In the present work, the structure of a new compound, 1-heptyl-1,3,6,8-tretraazatricyclo[4.3.1.13,8]undeca-1-ium iodide, is described.

The molecular geometry and the atom-numbering scheme of (I) are shown in Fig. 1. The asymetric unit of title molecule, C14H29N4+.I-, contains a 1-heptyl-1,3,6,8-tretraazatricyclo[4.3.1.13,8]undeca-1-ium cation and one iodide anion. Bond lenghts and angles in the title compound are normal, however the bond length N1—C1 [1.542 (3) Å] in the quaternary nitrogen is longer than the corresponding values observed in related structure [1.527 (3) Å] (Betz & Klüfers, 2007). In the cation, the torsion angle on the ethylene bridge is slightly distorted from the exact D2 d symmetry [N2—C5—C6—N4 torsion angle = 7.2 (4)°]. In the crystal, ions are linked by C—H···I hydrogen bonds (Figure 2), which is shorter (Table 1) than the corresponding contacts in related structure (Lee, et al., 2011).The main conformational feature is that the torsion angles in the heptyl chain are further removed from the ideal all-trans conformation, notably in C11—C12—C13—C14 fragment, which differ in the relative orientations [C—C—C—C torsion angle = 67.8 (3)°].

Related literature top

For the preparation of the title compound, see: Rivera et al. (2011). For synthetic applications of quaternary ammonium salts, see: Starks (1971). For related structures, see: Betz & Klüfers (2007); Lee et al. (2011).

Experimental top

The synthetic method has been described earlier (Rivera et al., 2011), except that heptyl idodide was used as alkylating agent. Single crystals suitable for X-ray analysis were obtained by crystallization from methanol solution. M.p. = 409–410 K. MS (ESI+): m/z 253.2441 [C7H14N4+C7H15].

Refinement top

Hydrogen atoms were placed to ideal positions and refined as riding with C–H distance 0.96 Å. The methyl H atoms were allowed to rotate freely about the adjacent C—C bonds. The isotropic atomic displacement parameters of hydrogen atoms were set to 1.2 (CH2) or 1.5 (CH3) times Ueq of the parent atom.

Structure description top

Quaternary ammonium salts are used as phase transfer catalysts for a wide range of organic reactions involving immiscible solvent systems (Starks, 1971). Therefore, we have decided to synthesize a new series of new N-alkylated quaternary ammonium salts, based on the Menschutkin reaction (Rivera et al., 2011) of 1,3,6,8-tetraazatricyclo[4.3.1.13,8]undecane with an alkyl halide. In the present work, the structure of a new compound, 1-heptyl-1,3,6,8-tretraazatricyclo[4.3.1.13,8]undeca-1-ium iodide, is described.

The molecular geometry and the atom-numbering scheme of (I) are shown in Fig. 1. The asymetric unit of title molecule, C14H29N4+.I-, contains a 1-heptyl-1,3,6,8-tretraazatricyclo[4.3.1.13,8]undeca-1-ium cation and one iodide anion. Bond lenghts and angles in the title compound are normal, however the bond length N1—C1 [1.542 (3) Å] in the quaternary nitrogen is longer than the corresponding values observed in related structure [1.527 (3) Å] (Betz & Klüfers, 2007). In the cation, the torsion angle on the ethylene bridge is slightly distorted from the exact D2 d symmetry [N2—C5—C6—N4 torsion angle = 7.2 (4)°]. In the crystal, ions are linked by C—H···I hydrogen bonds (Figure 2), which is shorter (Table 1) than the corresponding contacts in related structure (Lee, et al., 2011).The main conformational feature is that the torsion angles in the heptyl chain are further removed from the ideal all-trans conformation, notably in C11—C12—C13—C14 fragment, which differ in the relative orientations [C—C—C—C torsion angle = 67.8 (3)°].

For the preparation of the title compound, see: Rivera et al. (2011). For synthetic applications of quaternary ammonium salts, see: Starks (1971). For related structures, see: Betz & Klüfers (2007); Lee et al. (2011).

Computing details top

Data collection: CrysAlis PRO (Agilent, 2010); cell refinement: CrysAlis PRO (Agilent, 2010); data reduction: CrysAlis PRO (Agilent, 2010); program(s) used to solve structure: SIR2002 (Burla et al., 2003); program(s) used to refine structure: Jana2006 (Petříček et al., 2006); molecular graphics: Diamond (Brandenburg & Putz, 2005); software used to prepare material for publication: JANA2006 (Petříček et al., 2006).

Figures top
[Figure 1] Fig. 1. A view of (I) with the numbering scheme. Displacement ellipsoids are drawn at the 50% probability level.
[Figure 2] Fig. 2. Crystal packing of the title compound view along a axis.
1-Heptyl-1,3,6,8-tetraazatricyclo[4.3.1.13,8]undecan-1-ium iodide top
Crystal data top
C14H29N4+·IF(000) = 776
Mr = 380.3Dx = 1.518 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.7107 Å
Hall symbol: -P 2ynCell parameters from 12607 reflections
a = 8.8325 (2) Åθ = 2.9–29.2°
b = 15.3276 (3) ŵ = 1.92 mm1
c = 12.4792 (2) ÅT = 160 K
β = 100.072 (2)°Irregular shape, colourless
V = 1663.41 (6) Å30.31 × 0.24 × 0.16 mm
Z = 4
Data collection top
Agilent Xcalibur
diffractometer with Atlas (Gemini ultra Cu) detector
4183 independent reflections
Radiation source: Enhance (Mo) X-ray Source3517 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.031
Detector resolution: 10.3784 pixels mm-1θmax = 29.3°, θmin = 2.9°
Rotation method data acquisition using ω scansh = 1112
Absorption correction: multi-scan
(CrysAlis PRO; Agilent, 2010)
k = 2019
Tmin = 0.871, Tmax = 1l = 1616
22619 measured reflections
Refinement top
Refinement on F2116 constraints
R[F2 > 2σ(F2)] = 0.027H-atom parameters constrained
wR(F2) = 0.065Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0004I2)
S = 1.61(Δ/σ)max = 0.016
4183 reflectionsΔρmax = 0.53 e Å3
173 parametersΔρmin = 0.48 e Å3
0 restraints
Crystal data top
C14H29N4+·IV = 1663.41 (6) Å3
Mr = 380.3Z = 4
Monoclinic, P21/nMo Kα radiation
a = 8.8325 (2) ŵ = 1.92 mm1
b = 15.3276 (3) ÅT = 160 K
c = 12.4792 (2) Å0.31 × 0.24 × 0.16 mm
β = 100.072 (2)°
Data collection top
Agilent Xcalibur
diffractometer with Atlas (Gemini ultra Cu) detector
4183 independent reflections
Absorption correction: multi-scan
(CrysAlis PRO; Agilent, 2010)
3517 reflections with I > 3σ(I)
Tmin = 0.871, Tmax = 1Rint = 0.031
22619 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0270 restraints
wR(F2) = 0.065H-atom parameters constrained
S = 1.61Δρmax = 0.53 e Å3
4183 reflectionsΔρmin = 0.48 e Å3
173 parameters
Special details top

Refinement. The refinement was carried out against all reflections. The conventional R-factor is always based on F. The goodness of fit as well as the weighted R-factor are based on F and F2 for refinement carried out on F and F2, respectively. The threshold expression is used only for calculating R-factors etc. and it is not relevant to the choice of reflections for refinement.

The crystal studied was a non-merohedral twin with a minor twin domain of 6.56 (5)%. The overlaps of reflection between the twin domains were calculated by Jana2006 software using the twinning matrix and user- defined treshold 0.15 degs for full overlap. Due to no support for twinning in the official CIF dictionary the twinning matrix has been saved in the CIF file using special _jana_cell_twin_matrix keyword.

The program used for refinement, Jana2006, uses the weighting scheme based on the experimental expectations, see _refine_ls_weighting_details, that does not force S to be one. Therefore the values of S are usually larger than the ones from the SHELX program.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
I10.255234 (19)0.362795 (11)0.161798 (13)0.03611 (6)
N10.1652 (2)0.66563 (12)0.09078 (15)0.0265 (6)
N20.4475 (2)0.65925 (13)0.13273 (16)0.0299 (6)
N30.3065 (2)0.60189 (13)0.03990 (16)0.0314 (6)
C10.1645 (3)0.75253 (15)0.0285 (2)0.0343 (8)
C20.3103 (3)0.65513 (15)0.17770 (19)0.0285 (7)
C30.1707 (3)0.59276 (16)0.00795 (18)0.0304 (7)
C40.4444 (3)0.59596 (16)0.04572 (19)0.0321 (8)
C50.5050 (4)0.74388 (18)0.1150 (3)0.0570 (12)
C60.4250 (4)0.7963 (2)0.0231 (3)0.0625 (13)
N40.2865 (3)0.76063 (14)0.03149 (18)0.0417 (8)
C70.2995 (3)0.68432 (18)0.0992 (2)0.0406 (9)
C80.0209 (3)0.66349 (16)0.13859 (19)0.0318 (8)
C90.0031 (3)0.58651 (17)0.2112 (2)0.0362 (8)
C100.1575 (3)0.58205 (17)0.2378 (2)0.0361 (8)
C110.1784 (3)0.50740 (18)0.3136 (2)0.0376 (8)
C120.3416 (3)0.4983 (2)0.3350 (2)0.0490 (10)
C130.3676 (3)0.4201 (2)0.4036 (2)0.0543 (11)
C140.2874 (4)0.4242 (2)0.5197 (3)0.0644 (13)
H1a0.0679250.7592450.0197730.0411*
H1b0.1683630.8002940.0786230.0411*
H2a0.3123410.6997980.2318690.0343*
H2b0.306210.6004270.2145490.0343*
H3a0.1723310.5372270.0437050.0365*
H3b0.0811920.5961130.0479990.0365*
H4a0.4521990.5381550.0758020.0385*
H4b0.5349050.6025730.0135980.0385*
H5a0.6122010.7399390.1106470.0684*
H5b0.5144520.7773250.1808560.0684*
H6a0.4066090.8538910.0480840.075*
H6b0.4928830.8063210.027930.075*
H7a0.3890140.6899610.1326460.0488*
H7b0.2143780.6831070.1587380.0488*
H8a0.0119910.7167190.1775670.0381*
H8b0.0668610.6667720.0811960.0381*
H9a0.0766570.5910930.2774140.0435*
H9b0.0248420.5335480.1756990.0435*
H10a0.1812440.6362010.2698080.0433*
H10b0.2309270.5766030.1716390.0433*
H11a0.1472640.4537610.2842180.0451*
H11b0.1092580.5147720.381460.0451*
H12a0.4116440.4960680.2669360.0588*
H12b0.3702870.5505790.3688460.0588*
H13a0.4759370.4121620.401430.0651*
H13b0.3374790.3679370.3703270.0651*
H14a0.1782170.422720.522210.0966*
H14b0.3177570.3751480.5588920.0966*
H14c0.3149790.4772580.5523030.0966*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
I10.03178 (10)0.03586 (11)0.03959 (11)0.00013 (7)0.00324 (7)0.01196 (7)
N10.0256 (10)0.0264 (10)0.0269 (10)0.0031 (8)0.0033 (8)0.0015 (8)
N20.0258 (10)0.0313 (11)0.0314 (11)0.0012 (8)0.0019 (9)0.0028 (9)
N30.0340 (11)0.0326 (11)0.0276 (10)0.0013 (9)0.0050 (9)0.0032 (9)
C10.0380 (14)0.0266 (13)0.0377 (14)0.0063 (11)0.0052 (12)0.0061 (11)
C20.0283 (12)0.0314 (13)0.0245 (11)0.0047 (10)0.0006 (10)0.0018 (9)
C30.0320 (13)0.0281 (12)0.0297 (12)0.0004 (10)0.0013 (10)0.0054 (10)
C40.0310 (13)0.0315 (13)0.0342 (13)0.0049 (11)0.0068 (11)0.0007 (11)
C50.0535 (19)0.0419 (17)0.081 (2)0.0115 (15)0.0258 (18)0.0055 (16)
C60.056 (2)0.057 (2)0.076 (2)0.0098 (17)0.0148 (18)0.0051 (18)
N40.0476 (14)0.0321 (12)0.0487 (13)0.0000 (10)0.0170 (11)0.0071 (10)
C70.0456 (16)0.0481 (16)0.0287 (13)0.0058 (13)0.0076 (12)0.0075 (12)
C80.0272 (12)0.0331 (13)0.0348 (13)0.0050 (10)0.0049 (11)0.0008 (11)
C90.0341 (13)0.0379 (14)0.0366 (13)0.0017 (12)0.0060 (11)0.0039 (11)
C100.0304 (13)0.0367 (14)0.0409 (14)0.0003 (11)0.0055 (11)0.0015 (11)
C110.0344 (14)0.0394 (15)0.0379 (14)0.0011 (11)0.0035 (12)0.0021 (11)
C120.0326 (15)0.0578 (19)0.0547 (18)0.0084 (13)0.0026 (13)0.0159 (15)
C130.0458 (18)0.059 (2)0.0562 (18)0.0162 (15)0.0040 (15)0.0130 (16)
C140.058 (2)0.083 (3)0.0521 (19)0.0093 (19)0.0083 (17)0.0134 (18)
Geometric parameters (Å, º) top
N1—C11.542 (3)N4—C71.459 (4)
N1—C21.536 (3)C7—H7a0.96
N1—C31.528 (3)C7—H7b0.96
N1—C81.499 (3)C8—C91.512 (4)
N2—C21.424 (3)C8—H8a0.96
N2—C41.453 (3)C8—H8b0.96
N2—C51.424 (4)C9—C101.514 (4)
N3—C31.437 (3)C9—H9a0.96
N3—C41.476 (3)C9—H9b0.96
N3—C71.460 (3)C10—C111.517 (4)
C1—N41.421 (4)C10—H10a0.96
C1—H1a0.96C10—H10b0.96
C1—H1b0.96C11—C121.517 (4)
C2—H2a0.96C11—H11a0.96
C2—H2b0.96C11—H11b0.96
C3—H3a0.96C12—C131.515 (4)
C3—H3b0.96C12—H12a0.96
C4—H4a0.96C12—H12b0.96
C4—H4b0.96C13—C141.498 (4)
C5—C61.475 (4)C13—H13a0.96
C5—H5a0.96C13—H13b0.96
C5—H5b0.96C14—H14a0.96
C6—N41.402 (4)C14—H14b0.96
C6—H6a0.96C14—H14c0.96
C6—H6b0.96C14—C9i3.829 (4)
C1—N1—C2112.07 (17)C6—N4—C7116.3 (2)
C1—N1—C3106.73 (17)N3—C7—N4113.6 (2)
C1—N1—C8106.94 (18)N3—C7—H7a109.4709
C2—N1—C3106.25 (17)N3—C7—H7b109.4704
C2—N1—C8112.29 (18)N4—C7—H7a109.472
C3—N1—C8112.51 (18)N4—C7—H7b109.4716
C2—N2—C4111.04 (18)H7a—C7—H7b105.0122
C2—N2—C5116.9 (2)N1—C8—C9116.1 (2)
C4—N2—C5116.9 (2)N1—C8—H8a109.4708
C3—N3—C4109.67 (18)N1—C8—H8b109.4713
C3—N3—C7109.3 (2)C9—C8—H8a109.4716
C4—N3—C7112.12 (19)C9—C8—H8b109.471
N1—C1—N4113.9 (2)H8a—C8—H8b101.9387
N1—C1—H1a109.4716C8—C9—C10111.4 (2)
N1—C1—H1b109.4717C8—C9—H9a109.4711
N4—C1—H1a109.4708C8—C9—H9b109.4714
N4—C1—H1b109.4711C10—C9—H9a109.4709
H1a—C1—H1b104.657C10—C9—H9b109.4708
N1—C2—N2112.32 (19)H9a—C9—H9b107.4338
N1—C2—H2a109.4714C9—C10—C11113.1 (2)
N1—C2—H2b109.4711C9—C10—H10a109.4709
N2—C2—H2a109.4715C9—C10—H10b109.4711
N2—C2—H2b109.4706C11—C10—H10a109.4712
H2a—C2—H2b106.4595C11—C10—H10b109.4712
N1—C3—N3109.72 (19)H10a—C10—H10b105.6299
N1—C3—H3a109.4716C10—C11—C12113.7 (2)
N1—C3—H3b109.4707C10—C11—H11a109.4711
N3—C3—H3a109.471C10—C11—H11b109.4709
N3—C3—H3b109.4713C12—C11—H11a109.4715
H3a—C3—H3b109.223C12—C11—H11b109.4715
N2—C4—N3113.9 (2)H11a—C11—H11b104.9043
N2—C4—H4a109.4712C11—C12—C13114.5 (2)
N2—C4—H4b109.4712C11—C12—H12a109.471
N3—C4—H4a109.4716C11—C12—H12b109.4716
N3—C4—H4b109.471C13—C12—H12a109.4711
H4a—C4—H4b104.6525C13—C12—H12b109.4712
N2—C5—C6118.8 (3)H12a—C12—H12b103.914
N2—C5—H5a109.4717C12—C13—C14114.9 (3)
N2—C5—H5b109.4715C12—C13—H13a109.4717
C6—C5—H5a109.4709C12—C13—H13b109.4715
C6—C5—H5b109.4709C14—C13—H13a109.4714
H5a—C5—H5b98.1968C14—C13—H13b109.4712
C5—C6—N4115.1 (3)H13a—C13—H13b103.4432
C5—C6—H6a109.4709C13—C14—H14a109.4716
C5—C6—H6b109.4718C13—C14—H14b109.4709
N4—C6—H6a109.4712C13—C14—H14c109.4713
N4—C6—H6b109.4714H14a—C14—H14b109.4705
H6a—C6—H6b103.2278H14a—C14—H14c109.4719
C1—N4—C6117.1 (2)H14b—C14—H14c109.4712
C1—N4—C7112.3 (2)
C11—C12—C13—C1467.8 (4)N2—C5—C6—N47.2 (4)
Symmetry code: (i) x, y+1, z+1.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C2—H2a···I1ii0.962.943.858 (2)161
Symmetry code: (ii) x+1/2, y+1/2, z+1/2.

Experimental details

Crystal data
Chemical formulaC14H29N4+·I
Mr380.3
Crystal system, space groupMonoclinic, P21/n
Temperature (K)160
a, b, c (Å)8.8325 (2), 15.3276 (3), 12.4792 (2)
β (°) 100.072 (2)
V3)1663.41 (6)
Z4
Radiation typeMo Kα
µ (mm1)1.92
Crystal size (mm)0.31 × 0.24 × 0.16
Data collection
DiffractometerAgilent Xcalibur
diffractometer with Atlas (Gemini ultra Cu) detector
Absorption correctionMulti-scan
(CrysAlis PRO; Agilent, 2010)
Tmin, Tmax0.871, 1
No. of measured, independent and
observed [I > 3σ(I)] reflections
22619, 4183, 3517
Rint0.031
(sin θ/λ)max1)0.688
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.027, 0.065, 1.61
No. of reflections4183
No. of parameters173
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.53, 0.48

Computer programs: CrysAlis PRO (Agilent, 2010), SIR2002 (Burla et al., 2003), Jana2006 (Petříček et al., 2006), Diamond (Brandenburg & Putz, 2005), JANA2006 (Petříček et al., 2006).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C2—H2a···I1i0.962.943.858 (2)161
Symmetry code: (i) x+1/2, y+1/2, z+1/2.
 

Acknowledgements

We acknowledge the Dirección de Investigaciones, Sede Bogotá (DIB) de la Universidad Nacional de Colombia, for financial support of this work, as well as the the Institutional research plan No. AVOZ10100521 of the Institute of Physics and the project Praemium Academiae of the Academy of Science of the Czech Republic. JS-B acknowledges the Facultad de Ciencias de la Universidad Nacional de Colombia for a fellowship.

References

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