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

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ISSN: 2056-9890

Tris{2-[(2-amino­benzyl­­idene)amino]­ethyl}amine

aLaboratorio de Química Industrial, CELAES, Facultad de Ciencias Químicas, UANL, Pedro de Alba s/n, 66451 San Nicolás de los Garza, NL, Mexico, and bDEP Facultad de Ciencias Químicas, UANL, Guerrero y Progreso S/N, Col. Treviño, 64570 Monterrey, NL, Mexico
*Correspondence e-mail: sylvain_bernes@hotmail.com

(Received 20 October 2010; accepted 27 October 2010; online 6 November 2010)

The title Schiff base, C27H33N7, is a tripodal amine displaying C3 symmetry, with the central tertiary N atom lying on the threefold crystallographic axis. The N—CH2—CH2—N conformation of the pendant arms is gauche [torsion angle = 76.1 (3)°], which results in a claw-like mol­ecule, with the terminal aniline groups wrapped around the symmetry axis. The lone pair of the apical N atom is clearly oriented inwards towards the cavity, and should thus be chemically inactive. The amine NH2 substituents lie in the plane of the benzene ring to which they are bonded. With such an arrangement, one amine H atom forms an S(6) motif through a weak N—H⋯N hydrogen bond with the imine N atom, while the other is engaged in an inter­molecular N—H⋯π contact involving the benzene ring of a neighbouring mol­ecule related by inversion. The benzene rings also participate in an intra­molecular C—H⋯π contact of similar strength. In the crystal structure, mol­ecules are separated by empty voids (ca 5% of the crystal volume), although the crystal seems to be unsolvated.

Related literature

For applications of polyamines as metal extracta­nts, see: Wenzel (2008[Wenzel, M. (2008). PhD thesis, TU Dresden, Germany.]); Bernier et al. (2009[Bernier, N., Carvalho, S., Li, F., Delgado, R. & Félix, V. (2009). J. Org. Chem. 74, 4819-4827.]); Galbraith et al. (2006[Galbraith, S. G., Lindoy, L. F., Tasker, P. A. & Plieger, P. G. (2006). Dalton Trans. pp. 1134-1136.]). For other applications, see: Zibaseresht & Hartshorn (2005[Zibaseresht, R. & Hartshorn, R. M. (2005). Dalton Trans. pp. 3898-3908.]); Mercs et al. (2008[Mercs, L., Neels, A. & Albrecht, M. (2008). Dalton Trans. pp. 5570-5576.]). For similar C3 tripodal structures, see: Weibel et al. (2002[Weibel, N., Charbonnière, L. J. & Ziessel, R. F. (2002). J. Org. Chem. 67, 7876-7879.]); Işıklan et al. (2010[Işıklan, M., Pramanik, A., Fronczek, F. R. & Hossain, M. A. (2010). Acta Cryst. E66, o2739-o2740.]); McKee et al. (2006[McKee, V., Morgan, G. G. & Nelson, J. (2006). Acta Cryst. E62, o3747-o3749.]); Glidewell et al. (2005[Glidewell, C., Low, J. N., Skakle, J. M. S. & Wardell, J. L. (2005). Acta Cryst. C61, o75-o77.]). The software used for analysis of the empty voids in the crystal structure was SQUEEZE in PLATON (Spek, 2009[Spek, A. L. (2009). Acta Cryst. D65, 148-155.]).

[Scheme 1]

Experimental

Crystal data
  • C27H33N7

  • Mr = 455.60

  • Trigonal, [R \overline 3]

  • a = 13.1075 (18) Å

  • c = 25.985 (6) Å

  • V = 3866.3 (12) Å3

  • Z = 6

  • Mo Kα radiation

  • μ = 0.07 mm−1

  • T = 300 K

  • 0.40 × 0.40 × 0.18 mm

Data collection
  • Siemens P4 diffractometer

  • 6668 measured reflections

  • 1507 independent reflections

  • 838 reflections with I > 2σ(I)

  • Rint = 0.033

  • 2 standard reflections every 98 reflections intensity decay: 2%

Refinement
  • R[F2 > 2σ(F2)] = 0.058

  • wR(F2) = 0.176

  • S = 1.81

  • 1507 reflections

  • 110 parameters

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

  • Δρmax = 0.51 e Å−3

  • Δρmin = −0.21 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

Cg is the centroid of the benzene ring.

D—H⋯A D—H H⋯A DA D—H⋯A
N12—H12A⋯N4 0.92 (3) 2.02 (3) 2.700 (3) 129 (2)
N12—H12BCgi 0.86 (3) 2.70 (3) 3.430 (2) 143 (3)
C7—H7ACgii 0.93 2.71 3.494 (3) 143
Symmetry codes: (i) [x-y+{\script{1\over 3}}, x-{\script{1\over 3}}, -z+{\script{2\over 3}}]; (ii) -y+2, x-y+1, z.

Data collection: XSCANS (Siemens, 1996[Siemens (1996). XSCANS. Siemens Analytical X-ray Instruments Inc., Madison, Wisconsin, USA.]); cell refinement: XSCANS; data reduction: XSCANS; 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: Mercury (Macrae et al., 2006[Macrae, C. F., Edgington, P. R., McCabe, P., Pidcock, E., Shields, G. P., Taylor, R., Towler, M. & van de Streek, J. (2006). J. Appl. Cryst. 39, 453-457.]); software used to prepare material for publication: SHELXL97.

Supporting information


Comment top

Recently, the research line of receptors with the ability to extract metal salts has grown in relevance, because of the harmful effects that anions and cations have in health and the environment. A class of such receptors includes polyamines, in which cations and anions are found in separate sites in a zwitterionic form of the ligand. As a consequence, the efficiency for solvent extraction of metal salts may be modulated trough pH adjustment (Wenzel, 2008). In these compounds, the metal ion coordinates in the deprotonated moiety, while the anion is associated to the protonated pendant groups (Bernier et al., 2009; Galbraith et al., 2006). The Schiff base condensation is a useful route to obtain polyamines including suitable structural characteristics in order to act as polytopic ligands. Some recent reports highlighted important applications of this type of compounds (Zibaseresht & Hartshorn, 2005; Mercs et al., 2008).

We report herein on the synthesis (Fig. 1) and crystal structure of a new Schiff base, which, we hope, will allow to bond both cations and anions, depending on the pH. The molecule (Fig. 2) is a tripodal tertiary amine NR3 where R contains imine functionality. The tripodal N atom is placed on a 3-fold axis in a trigonal cell (C3 point symmetry). The pendant arms R are gauche, as reflected by torsion angle N1—C2—C3—N4, 76.1 (3)°, and the lone pair on N1 is directed toward the cavity formed by the arms. Similar arrangements giving claw-like molecules were observed in related tertiary amines, although in less symmetric Laue groups (e.g. Weibel et al., 2002; Işıklan et al., 2010). In some instances, closely related tripodal NR3 molecules approximate the C3 symmetry but with R arms lying in a plane rather than forming a closed cavity (McKee et al., 2006). Glidewell et al. (2005) showed that the molecular conformation for this class of amines is determined mainly by direction-specific intra- and intermolecular interactions. In the case of the title amine, NH2 groups in the aniline moieties are engaged in both intra and intermolecular interactions: H12A forms a weak hydrogen bond with the imine atom N4, while H12B affords an intermolecular N—H···π contact, also of limited strength. The last significant contact is intramolecular: the C7—H7 aromatic group gives a C—H···π contact with the next arm in the molecule.

As mentioned, all non bonding contacts are rather weak. As a consequence, molecules are not densely packed in the crystal, and voids of ca 60 Å3 are available for solvent insertion. However, attempts to include non-diffracting solvent in the structural model using SQUEEZE (Spek, 2009) were unsuccessful. The chemical formula was thus left as unsolvated.

Related literature top

For applications of polyamines as metal extractants, see: Wenzel (2008); Bernier et al. (2009); Galbraith et al. (2006). For other applications, see: Zibaseresht & Hartshorn (2005); Mercs et al. (2008). For similar C3 tripodal structures, see: Weibel et al. (2002); Işıklan et al. (2010); McKee et al. (2006); Glidewell et al. (2005). The software used for analysis of the empty voids in the crystal structure was SQUEEZE in PLATON (Spek, 2009).

Experimental top

To a dissolution of 2-nitrobenzaldehyde (0.020 mol) in ethanol (60 ml), were added 11.114 g (0.20 mol) of iron, 90 µl of hydrochloric acid and 15 ml of distilled water. Immediately the mixture was refluxed for 90 min. The mixture was filtered off using Hyfo supercell, and the solvent was distilled, affording a yellow oil (Fig. 1, IL). In order to obtain the title molecule (I), a dissolution of 2.414 g of IL in 20 ml of methanol and 1060 µl of tris(2-aminoethyl)amine (TREN) were stirred at room temperature for 30 min, affording a yellow solid, (I), which was filtered off and recrystallized from acetonitrile. Suitable crystals were obtained as pale-yellow blocks by slow evaporation of an acetone solution at 298 K. m.p. 416–417 K; analysis found (calc. for C27H33N7): C 71.02 (71.18%), H 7.82 (7.30%), N 22.40 (21.52%); IR RTA: 3437, 3237 (NH νas and νs), 1635 (CN δs), 1588 (NH δs), 749 cm-1 (NH δs). 1H NMR (200 MHz, CDCl3): δ, p.p.m.: 2.92 (6H, t, H2C—N), 3.69 (6H, t, H2CN), 6.34 (6H, s, H2NAr), 6.62 (6H, c, Ar), 6.88 (3H, dd, Ar), 7.12 (3H, td, Ar), 8.17 (3H, s, Ar).

Refinement top

Amine H atoms H12A and H12B were found in a difference map and refined with free coordinates. Other H atoms were placed in idealized positions and refined as riding to their parent C atoms, with bond lengths fixed to 0.97 (methylene) or 0.93 Å (aromatic). Isotropic displacement parameters for H atoms were calculated as Uiso(H) = 1.2Ueq(carrier atom). A set of 21 reflections with Fo << Fc (probably because of a diffractometer instability) were omitted in least-squares refinement.

Structure description top

Recently, the research line of receptors with the ability to extract metal salts has grown in relevance, because of the harmful effects that anions and cations have in health and the environment. A class of such receptors includes polyamines, in which cations and anions are found in separate sites in a zwitterionic form of the ligand. As a consequence, the efficiency for solvent extraction of metal salts may be modulated trough pH adjustment (Wenzel, 2008). In these compounds, the metal ion coordinates in the deprotonated moiety, while the anion is associated to the protonated pendant groups (Bernier et al., 2009; Galbraith et al., 2006). The Schiff base condensation is a useful route to obtain polyamines including suitable structural characteristics in order to act as polytopic ligands. Some recent reports highlighted important applications of this type of compounds (Zibaseresht & Hartshorn, 2005; Mercs et al., 2008).

We report herein on the synthesis (Fig. 1) and crystal structure of a new Schiff base, which, we hope, will allow to bond both cations and anions, depending on the pH. The molecule (Fig. 2) is a tripodal tertiary amine NR3 where R contains imine functionality. The tripodal N atom is placed on a 3-fold axis in a trigonal cell (C3 point symmetry). The pendant arms R are gauche, as reflected by torsion angle N1—C2—C3—N4, 76.1 (3)°, and the lone pair on N1 is directed toward the cavity formed by the arms. Similar arrangements giving claw-like molecules were observed in related tertiary amines, although in less symmetric Laue groups (e.g. Weibel et al., 2002; Işıklan et al., 2010). In some instances, closely related tripodal NR3 molecules approximate the C3 symmetry but with R arms lying in a plane rather than forming a closed cavity (McKee et al., 2006). Glidewell et al. (2005) showed that the molecular conformation for this class of amines is determined mainly by direction-specific intra- and intermolecular interactions. In the case of the title amine, NH2 groups in the aniline moieties are engaged in both intra and intermolecular interactions: H12A forms a weak hydrogen bond with the imine atom N4, while H12B affords an intermolecular N—H···π contact, also of limited strength. The last significant contact is intramolecular: the C7—H7 aromatic group gives a C—H···π contact with the next arm in the molecule.

As mentioned, all non bonding contacts are rather weak. As a consequence, molecules are not densely packed in the crystal, and voids of ca 60 Å3 are available for solvent insertion. However, attempts to include non-diffracting solvent in the structural model using SQUEEZE (Spek, 2009) were unsuccessful. The chemical formula was thus left as unsolvated.

For applications of polyamines as metal extractants, see: Wenzel (2008); Bernier et al. (2009); Galbraith et al. (2006). For other applications, see: Zibaseresht & Hartshorn (2005); Mercs et al. (2008). For similar C3 tripodal structures, see: Weibel et al. (2002); Işıklan et al. (2010); McKee et al. (2006); Glidewell et al. (2005). The software used for analysis of the empty voids in the crystal structure was SQUEEZE in PLATON (Spek, 2009).

Computing details top

Data collection: XSCANS (Siemens, 1996); cell refinement: XSCANS (Siemens, 1996); data reduction: XSCANS (Siemens, 1996); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: Mercury (Macrae et al., 2006); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. Synthetic route for the title compound.
[Figure 2] Fig. 2. ORTEP-like view of the title molecule, with displacement ellipsoids at the 30% probability level. H atoms have been omitted for clarity, and only the asymmetric unit is completely labeled. Other atoms are generated by symmetry codes A: 2 - y, 1 + x - y, z and B: 1 - x + y, 2 - x, z.
2-[({2-[bis(2-{[(2- aminophenyl)methylidene]amino}ethyl)amino]ethyl}imino)methyl]aniline top
Crystal data top
C27H33N7Dx = 1.174 Mg m3
Mr = 455.60Melting point: 416 K
Trigonal, R3Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -R 3Cell parameters from 70 reflections
a = 13.1075 (18) Åθ = 4.8–12.3°
c = 25.985 (6) ŵ = 0.07 mm1
V = 3866.3 (12) Å3T = 300 K
Z = 6Prism, yellow
F(000) = 14640.40 × 0.40 × 0.18 mm
Data collection top
Siemens P4
diffractometer
Rint = 0.033
Radiation source: fine-focus sealed tubeθmax = 25.0°, θmin = 2.0°
Graphite monochromatorh = 1315
ω scansk = 1515
6668 measured reflectionsl = 3030
1507 independent reflections2 standard reflections every 98 reflections
838 reflections with I > 2σ(I) intensity decay: 2%
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.058H atoms treated by a mixture of independent and constrained refinement
wR(F2) = 0.176 w = 1/[σ2(Fo2) + (0.05P)2]
where P = (Fo2 + 2Fc2)/3
S = 1.81(Δ/σ)max < 0.001
1507 reflectionsΔρmax = 0.51 e Å3
110 parametersΔρmin = 0.21 e Å3
0 restraintsExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
0 constraintsExtinction coefficient: 0.0057 (9)
Primary atom site location: structure-invariant direct methods
Crystal data top
C27H33N7Z = 6
Mr = 455.60Mo Kα radiation
Trigonal, R3µ = 0.07 mm1
a = 13.1075 (18) ÅT = 300 K
c = 25.985 (6) Å0.40 × 0.40 × 0.18 mm
V = 3866.3 (12) Å3
Data collection top
Siemens P4
diffractometer
Rint = 0.033
6668 measured reflections2 standard reflections every 98 reflections
1507 independent reflections intensity decay: 2%
838 reflections with I > 2σ(I)
Refinement top
R[F2 > 2σ(F2)] = 0.0580 restraints
wR(F2) = 0.176H atoms treated by a mixture of independent and constrained refinement
S = 1.81Δρmax = 0.51 e Å3
1507 reflectionsΔρmin = 0.21 e Å3
110 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
N11.00001.00000.17108 (11)0.0773 (10)
C20.9753 (3)0.8840 (2)0.15415 (9)0.0952 (9)
H2A1.00680.89040.11980.114*
H2B0.89060.83220.15240.114*
C31.0266 (3)0.8305 (3)0.18909 (10)0.0990 (10)
H3A1.02870.76630.17140.119*
H3B1.10690.88920.19780.119*
N40.95737 (19)0.78635 (19)0.23590 (8)0.0821 (7)
C51.0077 (2)0.8295 (2)0.27831 (10)0.0741 (7)
H5A1.08620.88910.27760.089*
C60.9507 (2)0.79175 (19)0.32820 (9)0.0680 (7)
C71.0149 (2)0.8459 (2)0.37218 (10)0.0825 (8)
H7A1.09330.90450.36880.099*
C80.9669 (3)0.8163 (3)0.42032 (11)0.0985 (9)
H8A1.01200.85400.44920.118*
C90.8505 (3)0.7297 (3)0.42536 (10)0.0915 (9)
H9A0.81650.70960.45790.110*
C100.7853 (3)0.6738 (2)0.38354 (10)0.0820 (8)
H10A0.70730.61470.38790.098*
C110.8319 (2)0.7026 (2)0.33419 (9)0.0696 (7)
N120.7651 (2)0.6450 (2)0.29267 (9)0.0958 (8)
H12A0.792 (3)0.670 (3)0.2599 (10)0.115*
H12B0.692 (3)0.597 (3)0.2993 (11)0.115*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
N10.0863 (15)0.0863 (15)0.0592 (18)0.0432 (8)0.0000.000
C20.116 (2)0.101 (2)0.0686 (14)0.0545 (18)0.0064 (14)0.0093 (14)
C30.118 (2)0.098 (2)0.0928 (18)0.0631 (19)0.0324 (16)0.0059 (15)
N40.0836 (15)0.0817 (14)0.0848 (14)0.0442 (12)0.0142 (12)0.0027 (11)
C50.0668 (15)0.0620 (14)0.0941 (17)0.0327 (12)0.0095 (13)0.0063 (13)
C60.0648 (15)0.0560 (13)0.0840 (16)0.0307 (12)0.0009 (12)0.0046 (11)
C70.0821 (17)0.0684 (16)0.0913 (18)0.0333 (14)0.0097 (14)0.0050 (13)
C80.121 (3)0.094 (2)0.0859 (18)0.058 (2)0.0204 (18)0.0012 (16)
C90.112 (2)0.094 (2)0.0842 (18)0.063 (2)0.0122 (16)0.0217 (16)
C100.0820 (17)0.0778 (17)0.0947 (18)0.0463 (14)0.0110 (15)0.0148 (14)
C110.0679 (15)0.0647 (14)0.0832 (15)0.0384 (13)0.0025 (13)0.0001 (13)
N120.0638 (14)0.1025 (18)0.1008 (16)0.0263 (13)0.0001 (13)0.0157 (14)
Geometric parameters (Å, º) top
N1—C21.455 (3)C6—C111.413 (3)
N1—C2i1.455 (3)C7—C81.366 (4)
N1—C2ii1.455 (3)C7—H7A0.9300
C2—C31.498 (4)C8—C91.379 (4)
C2—H2A0.9700C8—H8A0.9300
C2—H2B0.9700C9—C101.350 (4)
C3—N41.454 (3)C9—H9A0.9300
C3—H3A0.9700C10—C111.389 (3)
C3—H3B0.9700C10—H10A0.9300
N4—C51.264 (3)C11—N121.356 (3)
C5—C61.454 (3)N12—H12A0.92 (3)
C5—H5A0.9300N12—H12B0.86 (3)
C6—C71.386 (3)
C2—N1—C2i111.28 (14)C7—C6—C5119.0 (2)
C2—N1—C2ii111.28 (14)C11—C6—C5123.1 (2)
C2i—N1—C2ii111.28 (14)C8—C7—C6122.3 (3)
N1—C2—C3112.9 (2)C8—C7—H7A118.8
N1—C2—H2A109.0C6—C7—H7A118.8
C3—C2—H2A109.0C7—C8—C9118.9 (3)
N1—C2—H2B109.0C7—C8—H8A120.5
C3—C2—H2B109.0C9—C8—H8A120.5
H2A—C2—H2B107.8C10—C9—C8120.7 (3)
N4—C3—C2110.9 (2)C10—C9—H9A119.7
N4—C3—H3A109.5C8—C9—H9A119.7
C2—C3—H3A109.5C9—C10—C11121.5 (3)
N4—C3—H3B109.5C9—C10—H10A119.2
C2—C3—H3B109.5C11—C10—H10A119.2
H3A—C3—H3B108.1N12—C11—C10120.6 (2)
C5—N4—C3118.0 (2)N12—C11—C6120.7 (2)
N4—C5—C6124.1 (2)C10—C11—C6118.7 (2)
N4—C5—H5A117.9C11—N12—H12A120.7 (19)
C6—C5—H5A117.9C11—N12—H12B115 (2)
C7—C6—C11117.9 (2)H12A—N12—H12B123 (3)
C2i—N1—C2—C383.1 (3)C6—C7—C8—C90.1 (4)
C2ii—N1—C2—C3152.1 (3)C7—C8—C9—C100.9 (4)
N1—C2—C3—N476.1 (3)C8—C9—C10—C111.1 (4)
C2—C3—N4—C5119.7 (3)C9—C10—C11—N12179.7 (2)
C3—N4—C5—C6178.2 (2)C9—C10—C11—C60.6 (3)
N4—C5—C6—C7179.8 (2)C7—C6—C11—N12178.9 (2)
N4—C5—C6—C110.3 (4)C5—C6—C11—N121.6 (3)
C11—C6—C7—C80.3 (4)C7—C6—C11—C100.1 (3)
C5—C6—C7—C8179.1 (2)C5—C6—C11—C10179.3 (2)
Symmetry codes: (i) y+2, xy+1, z; (ii) x+y+1, x+2, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N12—H12A···N40.92 (3)2.02 (3)2.700 (3)129 (2)
N12—H12B···Cgiii0.86 (3)2.70 (3)3.430 (2)143 (3)
C7—H7A···Cgi0.932.713.494 (3)143
Symmetry codes: (i) y+2, xy+1, z; (iii) xy+1/3, x1/3, z+2/3.

Experimental details

Crystal data
Chemical formulaC27H33N7
Mr455.60
Crystal system, space groupTrigonal, R3
Temperature (K)300
a, c (Å)13.1075 (18), 25.985 (6)
V3)3866.3 (12)
Z6
Radiation typeMo Kα
µ (mm1)0.07
Crystal size (mm)0.40 × 0.40 × 0.18
Data collection
DiffractometerSiemens P4
Absorption correction
No. of measured, independent and
observed [I > 2σ(I)] reflections
6668, 1507, 838
Rint0.033
(sin θ/λ)max1)0.594
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.058, 0.176, 1.81
No. of reflections1507
No. of parameters110
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.51, 0.21

Computer programs: XSCANS (Siemens, 1996), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), Mercury (Macrae et al., 2006).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N12—H12A···N40.92 (3)2.02 (3)2.700 (3)129 (2)
N12—H12B···Cgi0.86 (3)2.70 (3)3.430 (2)143 (3)
C7—H7A···Cgii0.932.713.494 (3)142.6
Symmetry codes: (i) xy+1/3, x1/3, z+2/3; (ii) y+2, xy+1, z.
 

Acknowledgements

The authors thank the Facultad de Ciencias Químicas (UANL, Mexico) and PAICyT (project number IT164–09) for financial support.

References

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