research communications
E)-4-methoxybenzylideneamino]propan-2-ol
of 1,3-bis[(aUniversidad Nacional de Colombia, Sede Bogotá, Facultad de Ciencias, Departamento de Química, Cra 30 No. 45-03, Bogotá, Código Postal 111321, Colombia, and bInstitut für Anorganische Chemie, J. W. Goethe-Universität Frankfurt, Max-von Laue-Strasse 7, 60438 Frankfurt/Main, Germany
*Correspondence e-mail: ariverau@unal.edu.co
The title Schiff base, C19H22N2O3, was synthesized via the condensation reaction of 1,3-diaminopropan-2-ol with 4-methoxybenzaldehyde using water as solvent. The molecule exists in an E,E conformation with respect to the C=N imine bonds and the dihedral angle between the aromatic rings is 37.25 (15)°. In the crystal, O—H⋯N hydrogen bonds link the molecules into infinite C(5) chains propagating along the a-axis direction. The packing of these chains is consolidated by C—H⋯O interactions and C—H⋯π short contacts, forming a three-dimensional network.
Keywords: crystal structure; hydrogen bonding; C—H⋯O interactions; Schiff bases.
CCDC reference: 1511139
1. Chemical context
Compounds containing the –C=N– (azomethine group) structure are known as ). are one class of the most important and fundamental unsaturated organic compounds with a C=N double bond as their characteristic chemical bond and are extensively present in natural products and many drugs (Zhu et al., 2010). The formation of underlies a discipline known as dynamic covalent chemistry (DCC), which is now used widely in the construction of exotic molecules and extended structures such as catenanes, and so on (Patil & Adimurthy, 2013). Schiff base compounds derived from 1,n-diamines play an important role in coordination chemistry and have been studied extensively for their broad range of biological activities (Sahu et al. 2012; da Silva et al., 2011; Przybylski et al. 2009; Dhar & Taploo, 1982). The common structural feature of these compounds is the presence of two azomethine groups linked by an n-methylene bridge, which can act as hydrogen-bond acceptors.
usually synthesized from the condensation of primary and active carbonyl groups (Bekdemir & Efil, 2014The title compound is interesting in that the presence of an OH group in the 1,3-diamine molecule is situated in a favorable position towards the azomethine groups to form an intramolecular hydrogen bond. Thus, one may expect that the charge distribution around the azomethine nitrogen atoms may be visibly perturbed by the presence of this type of interaction. Hence, 1,3-diaminepropan-2ol was chosen with the expectation that the presence of an OH group would result in an intramolecular hydrogen bond. The title compound was synthesized quickly and efficiently by condensation of 1,3-diamine-2-propanol and p-methoxybenzaldehyde using a simple water-mediated procedure that requires neither a catalyst nor any additive (Rivera, et al., 2016). To the best of our knowledge, no X-ray of either the uncoordinated or the coordinated title compound has been reported previously.
2. Structural commentary
The molecular structure of the title compound is illustrated in Fig. 1. The title compound exists in an E,E conformation with respect to the N1=C1 and N2=C5 azomethine bonds and the C2—N1=C1—C11 and C4—N2=C5—C21 torsion angles are 175.6 (3) and −178.3 (3)° respectively. The N1=C1 and N2=C5 distances of 1.265 (4) and 1.271 (4) Å, respectively, are consistent with C=N double bonding. The bond angles of 117.0 (3) and 117.7 (3)° around the N1 and N2 atoms confirm their sp2 character. The slight differences between N=C distances and C—N=C angles are due to the significant effect of the hydrogen bond on the geometric parameters of the nitrogen atom (N2) involved in the intermolecular hydrogen bond (see below).
The N1—C2—C3—C4 torsion angle is −64.4 (4)° and the C2—C3—C4—N2 torsion angle is 175.0 (3)°. The O1—C3—C4—N2 torsion angle is −65.3 (3)°, which has a significant role to play in the hydrogen-bonding pattern in the crystal of the title compound (see below). The two methoxy substituents are essentially coplanar with their bound benzene rings with torsion angles C17—O2—C14—C13 = 169.3 (3)° and C27—O3—C24—C23 = −172.2 (3)°.
3. Supramolecular features
Rather than the proposed intramolecular O—H⋯N hydrogen bond, adjacent molecules in the crystal of the title compound are linked by intermolecular O—H⋯N hydrogen bonds (Table 1, Fig. 2), forming an infinite zigzag C(5) chains extending along the a-axis direction. The chains are further linked to neighbouring chains through a pair of weak C—H⋯O hydrogen bonds (Table 1). Furthermore, C12—H12 and C22—H22 form weaker C—H⋯Cg (π–ring) interactions (Table 1), which connect the chains of consecutive layers, thus forming a three-dimensional supramolecular network (Fig. 2).
4. Database survey
No comparable structure of either the uncoordinated or the coordinated title compound has been found in the Cambridge Crystallographic Database.
5. Synthesis and crystallization
The title compound was prepared according to our published method (Rivera et al., 2016). The crude product was dissolved in benzene and acetonitrile was added to the solution: upon slow evaporation of the solvent, colorless plates of the title compound arose. M.p. 403 K, yield 88%.
6. Refinement
Crystal data, data collection and structure . The hydroxyl H atom was refined freely; however, the remaining H atoms were positioned geometrically and allowed to ride on their parent atoms, with d(C—H) = 0.95 Å for aromatic and azomethine atoms, d(C—H) = 0.99 Å for methylene, d(C—H) = 1.00 Å for C3—H3 and 0.98 Å for CH3 atoms. The Uiso values were constrained to be 1.5Ueq of the for methyl H atoms and 1.2Ueq for the remaining H atoms. A rotating group model was used for the methyl groups. The of the crystal chosen for data collection was indeterminate in the present refinement.
details are summarized in Table 2
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Supporting information
CCDC reference: 1511139
https://doi.org/10.1107/S2056989016016947/hb7623sup1.cif
contains datablock I. DOI:Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989016016947/hb7623Isup2.hkl
Supporting information file. DOI: https://doi.org/10.1107/S2056989016016947/hb7623Isup3.cml
Data collection: X-AREA (Stoe & Cie, 2001); cell
X-AREA (Stoe & Cie, 2001); data reduction: X-AREA (Stoe & Cie, 2001); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015); molecular graphics: XP in SHELXTL-Plus (Sheldrick, 2008); software used to prepare material for publication: SHELXL2014 (Sheldrick, 2015).C19H22N2O3 | Dx = 1.253 Mg m−3 |
Mr = 326.38 | Mo Kα radiation, λ = 0.71073 Å |
Orthorhombic, Pna21 | Cell parameters from 12316 reflections |
a = 7.9081 (3) Å | θ = 2.2–26.0° |
b = 5.8434 (3) Å | µ = 0.09 mm−1 |
c = 37.4435 (16) Å | T = 173 K |
V = 1730.27 (13) Å3 | Plate, colourless |
Z = 4 | 0.28 × 0.19 × 0.08 mm |
F(000) = 696 |
Stoe IPDS II two-circle diffractometer | 2786 reflections with I > 2σ(I) |
Radiation source: Genix 3D IµS microfocus X-ray source | Rint = 0.038 |
ω scans | θmax = 25.6°, θmin = 2.2° |
Absorption correction: multi-scan (X-AREA; Stoe & Cie, 2001) | h = −9→9 |
Tmin = 0.625, Tmax = 1.000 | k = −7→7 |
12316 measured reflections | l = −41→45 |
3084 independent reflections |
Refinement on F2 | Hydrogen site location: mixed |
Least-squares matrix: full | H atoms treated by a mixture of independent and constrained refinement |
R[F2 > 2σ(F2)] = 0.046 | w = 1/[σ2(Fo2) + (0.0961P)2] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.123 | (Δ/σ)max < 0.001 |
S = 1.01 | Δρmax = 0.15 e Å−3 |
3084 reflections | Δρmin = −0.16 e Å−3 |
224 parameters | Extinction correction: SHELXL2014 (Sheldrick, 2015), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
1 restraint | Extinction coefficient: 0.046 (8) |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
N1 | 0.5510 (4) | 0.4188 (4) | 0.44173 (8) | 0.0467 (6) | |
N2 | 0.3474 (4) | 0.4764 (4) | 0.54792 (8) | 0.0453 (6) | |
O1 | 0.7066 (3) | 0.4483 (4) | 0.53519 (7) | 0.0513 (6) | |
H1 | 0.754 (7) | 0.302 (9) | 0.5410 (13) | 0.073 (13)* | |
O2 | 0.1888 (4) | 0.4687 (4) | 0.28786 (6) | 0.0547 (6) | |
O3 | 0.0967 (3) | 0.4509 (4) | 0.71286 (7) | 0.0542 (6) | |
C1 | 0.5258 (4) | 0.5772 (6) | 0.41931 (9) | 0.0463 (7) | |
H1A | 0.5738 | 0.7234 | 0.4238 | 0.056* | |
C2 | 0.6638 (5) | 0.4706 (6) | 0.47176 (9) | 0.0518 (8) | |
H2A | 0.6906 | 0.6361 | 0.4716 | 0.062* | |
H2B | 0.7711 | 0.3856 | 0.4687 | 0.062* | |
C3 | 0.5858 (4) | 0.4072 (5) | 0.50766 (9) | 0.0461 (7) | |
H3 | 0.5540 | 0.2416 | 0.5076 | 0.055* | |
C4 | 0.4306 (4) | 0.5507 (5) | 0.51505 (9) | 0.0491 (8) | |
H4A | 0.4637 | 0.7134 | 0.5173 | 0.059* | |
H4B | 0.3507 | 0.5371 | 0.4948 | 0.059* | |
C5 | 0.3529 (4) | 0.6102 (5) | 0.57466 (9) | 0.0448 (7) | |
H5 | 0.4082 | 0.7533 | 0.5717 | 0.054* | |
C11 | 0.4253 (4) | 0.5452 (5) | 0.38653 (9) | 0.0414 (7) | |
C12 | 0.4251 (5) | 0.7189 (5) | 0.36069 (10) | 0.0477 (7) | |
H12 | 0.4806 | 0.8597 | 0.3655 | 0.057* | |
C13 | 0.3447 (4) | 0.6874 (6) | 0.32820 (9) | 0.0484 (8) | |
H13 | 0.3464 | 0.8057 | 0.3108 | 0.058* | |
C14 | 0.2617 (4) | 0.4832 (5) | 0.32098 (9) | 0.0442 (7) | |
C15 | 0.2578 (4) | 0.3105 (5) | 0.34676 (9) | 0.0436 (7) | |
H15 | 0.1994 | 0.1716 | 0.3421 | 0.052* | |
C16 | 0.3392 (4) | 0.3430 (5) | 0.37899 (8) | 0.0437 (7) | |
H16 | 0.3365 | 0.2247 | 0.3964 | 0.052* | |
C17 | 0.1278 (5) | 0.2506 (6) | 0.27655 (10) | 0.0553 (8) | |
H17A | 0.2219 | 0.1415 | 0.2758 | 0.083* | |
H17B | 0.0778 | 0.2645 | 0.2527 | 0.083* | |
H17C | 0.0420 | 0.1961 | 0.2934 | 0.083* | |
C21 | 0.2798 (4) | 0.5588 (5) | 0.60975 (9) | 0.0435 (7) | |
C22 | 0.3029 (4) | 0.7163 (5) | 0.63743 (9) | 0.0472 (7) | |
H22 | 0.3628 | 0.8540 | 0.6328 | 0.057* | |
C23 | 0.2409 (5) | 0.6766 (5) | 0.67121 (9) | 0.0499 (8) | |
H23 | 0.2581 | 0.7865 | 0.6896 | 0.060* | |
C24 | 0.1526 (4) | 0.4751 (5) | 0.67851 (9) | 0.0445 (7) | |
C25 | 0.1277 (4) | 0.3152 (5) | 0.65135 (9) | 0.0445 (7) | |
H25 | 0.0677 | 0.1776 | 0.6561 | 0.053* | |
C26 | 0.1910 (4) | 0.3579 (5) | 0.61733 (9) | 0.0455 (7) | |
H26 | 0.1734 | 0.2485 | 0.5989 | 0.055* | |
C27 | 0.0252 (5) | 0.2384 (6) | 0.72315 (10) | 0.0582 (9) | |
H27A | −0.0747 | 0.2069 | 0.7085 | 0.087* | |
H27B | −0.0079 | 0.2450 | 0.7484 | 0.087* | |
H27C | 0.1086 | 0.1163 | 0.7197 | 0.087* |
U11 | U22 | U33 | U12 | U13 | U23 | |
N1 | 0.0514 (14) | 0.0482 (13) | 0.0404 (13) | −0.0007 (12) | 0.0008 (12) | −0.0031 (12) |
N2 | 0.0506 (15) | 0.0425 (13) | 0.0429 (14) | 0.0044 (11) | −0.0030 (12) | −0.0012 (11) |
O1 | 0.0585 (14) | 0.0457 (12) | 0.0498 (13) | 0.0004 (11) | −0.0133 (11) | −0.0031 (10) |
O2 | 0.0675 (16) | 0.0507 (13) | 0.0459 (14) | 0.0031 (11) | −0.0074 (11) | 0.0050 (10) |
O3 | 0.0623 (15) | 0.0522 (13) | 0.0479 (13) | −0.0001 (11) | 0.0034 (12) | −0.0082 (10) |
C1 | 0.0470 (17) | 0.0461 (16) | 0.0459 (18) | −0.0049 (14) | 0.0055 (14) | −0.0027 (13) |
C2 | 0.0499 (18) | 0.056 (2) | 0.049 (2) | −0.0019 (14) | −0.0035 (15) | −0.0018 (14) |
C3 | 0.0507 (17) | 0.0425 (15) | 0.0451 (17) | −0.0028 (13) | −0.0076 (14) | −0.0013 (13) |
C4 | 0.0588 (18) | 0.0434 (16) | 0.0451 (18) | 0.0032 (14) | −0.0021 (14) | 0.0040 (14) |
C5 | 0.0472 (17) | 0.0373 (15) | 0.0501 (18) | 0.0021 (12) | −0.0068 (14) | 0.0020 (13) |
C11 | 0.0440 (16) | 0.0396 (16) | 0.0405 (16) | 0.0009 (12) | 0.0048 (13) | −0.0003 (12) |
C12 | 0.0526 (18) | 0.0377 (15) | 0.0529 (18) | 0.0008 (14) | 0.0095 (14) | 0.0011 (13) |
C13 | 0.0595 (19) | 0.0396 (16) | 0.0462 (19) | 0.0048 (13) | 0.0062 (14) | 0.0082 (13) |
C14 | 0.0446 (16) | 0.0453 (16) | 0.0428 (17) | 0.0074 (12) | 0.0050 (14) | 0.0021 (13) |
C15 | 0.0464 (16) | 0.0381 (16) | 0.0464 (17) | −0.0004 (13) | 0.0050 (13) | 0.0016 (12) |
C16 | 0.0482 (17) | 0.0396 (15) | 0.0432 (17) | 0.0010 (13) | 0.0043 (13) | 0.0059 (13) |
C17 | 0.0550 (19) | 0.061 (2) | 0.0503 (19) | −0.0044 (16) | −0.0028 (15) | 0.0035 (15) |
C21 | 0.0439 (16) | 0.0383 (15) | 0.0482 (18) | 0.0037 (12) | −0.0056 (13) | −0.0018 (12) |
C22 | 0.0511 (18) | 0.0375 (16) | 0.0530 (18) | −0.0005 (13) | −0.0054 (15) | −0.0027 (13) |
C23 | 0.0587 (19) | 0.0419 (15) | 0.0491 (19) | 0.0014 (15) | −0.0078 (15) | −0.0095 (13) |
C24 | 0.0453 (16) | 0.0438 (16) | 0.0444 (17) | 0.0066 (13) | −0.0016 (13) | −0.0049 (13) |
C25 | 0.0459 (16) | 0.0398 (16) | 0.0478 (17) | −0.0018 (13) | −0.0018 (14) | −0.0040 (13) |
C26 | 0.0486 (17) | 0.0400 (15) | 0.0478 (17) | 0.0019 (13) | −0.0026 (14) | −0.0082 (13) |
C27 | 0.060 (2) | 0.062 (2) | 0.0529 (19) | −0.0114 (17) | 0.0086 (17) | −0.0079 (15) |
N1—C1 | 1.265 (4) | C12—H12 | 0.9500 |
N1—C2 | 1.467 (5) | C13—C14 | 1.388 (5) |
N2—C5 | 1.271 (4) | C13—H13 | 0.9500 |
N2—C4 | 1.461 (4) | C14—C15 | 1.397 (5) |
O1—C3 | 1.426 (4) | C15—C16 | 1.381 (5) |
O1—H1 | 0.96 (5) | C15—H15 | 0.9500 |
O2—C14 | 1.370 (4) | C16—H16 | 0.9500 |
O2—C17 | 1.427 (4) | C17—H17A | 0.9800 |
O3—C24 | 1.367 (4) | C17—H17B | 0.9800 |
O3—C27 | 1.418 (4) | C17—H17C | 0.9800 |
C1—C11 | 1.474 (5) | C21—C26 | 1.397 (5) |
C1—H1A | 0.9500 | C21—C22 | 1.398 (5) |
C2—C3 | 1.525 (5) | C22—C23 | 1.376 (5) |
C2—H2A | 0.9900 | C22—H22 | 0.9500 |
C2—H2B | 0.9900 | C23—C24 | 1.396 (5) |
C3—C4 | 1.511 (5) | C23—H23 | 0.9500 |
C3—H3 | 1.0000 | C24—C25 | 1.395 (4) |
C4—H4A | 0.9900 | C25—C26 | 1.391 (5) |
C4—H4B | 0.9900 | C25—H25 | 0.9500 |
C5—C21 | 1.466 (5) | C26—H26 | 0.9500 |
C5—H5 | 0.9500 | C27—H27A | 0.9800 |
C11—C16 | 1.393 (4) | C27—H27B | 0.9800 |
C11—C12 | 1.402 (5) | C27—H27C | 0.9800 |
C12—C13 | 1.385 (5) | ||
C1—N1—C2 | 117.0 (3) | O2—C14—C15 | 124.8 (3) |
C5—N2—C4 | 117.7 (3) | C13—C14—C15 | 119.8 (3) |
C3—O1—H1 | 106 (3) | C16—C15—C14 | 119.6 (3) |
C14—O2—C17 | 117.8 (3) | C16—C15—H15 | 120.2 |
C24—O3—C27 | 118.4 (3) | C14—C15—H15 | 120.2 |
N1—C1—C11 | 123.0 (3) | C15—C16—C11 | 121.4 (3) |
N1—C1—H1A | 118.5 | C15—C16—H16 | 119.3 |
C11—C1—H1A | 118.5 | C11—C16—H16 | 119.3 |
N1—C2—C3 | 112.3 (3) | O2—C17—H17A | 109.5 |
N1—C2—H2A | 109.1 | O2—C17—H17B | 109.5 |
C3—C2—H2A | 109.1 | H17A—C17—H17B | 109.5 |
N1—C2—H2B | 109.1 | O2—C17—H17C | 109.5 |
C3—C2—H2B | 109.1 | H17A—C17—H17C | 109.5 |
H2A—C2—H2B | 107.9 | H17B—C17—H17C | 109.5 |
O1—C3—C4 | 108.6 (3) | C26—C21—C22 | 117.9 (3) |
O1—C3—C2 | 109.0 (3) | C26—C21—C5 | 123.5 (3) |
C4—C3—C2 | 110.8 (3) | C22—C21—C5 | 118.5 (3) |
O1—C3—H3 | 109.5 | C23—C22—C21 | 121.6 (3) |
C4—C3—H3 | 109.5 | C23—C22—H22 | 119.2 |
C2—C3—H3 | 109.5 | C21—C22—H22 | 119.2 |
N2—C4—C3 | 110.8 (3) | C22—C23—C24 | 120.0 (3) |
N2—C4—H4A | 109.5 | C22—C23—H23 | 120.0 |
C3—C4—H4A | 109.5 | C24—C23—H23 | 120.0 |
N2—C4—H4B | 109.5 | O3—C24—C25 | 124.8 (3) |
C3—C4—H4B | 109.5 | O3—C24—C23 | 115.7 (3) |
H4A—C4—H4B | 108.1 | C25—C24—C23 | 119.5 (3) |
N2—C5—C21 | 124.5 (3) | C26—C25—C24 | 119.8 (3) |
N2—C5—H5 | 117.8 | C26—C25—H25 | 120.1 |
C21—C5—H5 | 117.8 | C24—C25—H25 | 120.1 |
C16—C11—C12 | 118.3 (3) | C25—C26—C21 | 121.2 (3) |
C16—C11—C1 | 122.7 (3) | C25—C26—H26 | 119.4 |
C12—C11—C1 | 118.9 (3) | C21—C26—H26 | 119.4 |
C13—C12—C11 | 120.7 (3) | O3—C27—H27A | 109.5 |
C13—C12—H12 | 119.7 | O3—C27—H27B | 109.5 |
C11—C12—H12 | 119.7 | H27A—C27—H27B | 109.5 |
C12—C13—C14 | 120.2 (3) | O3—C27—H27C | 109.5 |
C12—C13—H13 | 119.9 | H27A—C27—H27C | 109.5 |
C14—C13—H13 | 119.9 | H27B—C27—H27C | 109.5 |
O2—C14—C13 | 115.4 (3) | ||
C2—N1—C1—C11 | 175.6 (3) | C13—C14—C15—C16 | −1.2 (4) |
C1—N1—C2—C3 | 129.7 (3) | C14—C15—C16—C11 | 0.2 (5) |
N1—C2—C3—O1 | 176.2 (3) | C12—C11—C16—C15 | 1.1 (5) |
N1—C2—C3—C4 | −64.4 (4) | C1—C11—C16—C15 | −174.5 (3) |
C5—N2—C4—C3 | 110.7 (3) | N2—C5—C21—C26 | −2.0 (5) |
O1—C3—C4—N2 | −65.3 (3) | N2—C5—C21—C22 | 176.6 (3) |
C2—C3—C4—N2 | 175.0 (3) | C26—C21—C22—C23 | 0.1 (5) |
C4—N2—C5—C21 | −178.3 (3) | C5—C21—C22—C23 | −178.6 (3) |
N1—C1—C11—C16 | 5.1 (5) | C21—C22—C23—C24 | 0.1 (5) |
N1—C1—C11—C12 | −170.5 (3) | C27—O3—C24—C25 | 7.6 (5) |
C16—C11—C12—C13 | −1.6 (5) | C27—O3—C24—C23 | −172.2 (3) |
C1—C11—C12—C13 | 174.3 (3) | C22—C23—C24—O3 | 179.7 (3) |
C11—C12—C13—C14 | 0.6 (5) | C22—C23—C24—C25 | −0.1 (5) |
C17—O2—C14—C13 | 169.3 (3) | O3—C24—C25—C26 | −179.8 (3) |
C17—O2—C14—C15 | −10.5 (5) | C23—C24—C25—C26 | 0.1 (5) |
C12—C13—C14—O2 | −179.0 (3) | C24—C25—C26—C21 | 0.1 (5) |
C12—C13—C14—C15 | 0.8 (5) | C22—C21—C26—C25 | −0.2 (5) |
O2—C14—C15—C16 | 178.6 (3) | C5—C21—C26—C25 | 178.4 (3) |
Cg1 and Cg2 are the centroids of the C11–C16 and C21–C26 rings, respectively. |
D—H···A | D—H | H···A | D···A | D—H···A |
O1—H1···N2i | 0.96 (5) | 1.80 (5) | 2.761 (4) | 175 (4) |
C17—H17B···O3ii | 0.98 | 2.63 | 3.447 (5) | 142 |
C27—H27B···O2iii | 0.98 | 2.65 | 3.415 (4) | 135 |
C12—H12···Cg1iv | 0.95 | 2.99 | 3.658 (4) | 129 |
C22—H22···Cg2iv | 0.95 | 2.92 | 3.628 (3) | 132 |
Symmetry codes: (i) x+1/2, −y+1/2, z; (ii) −x, −y+1, z−1/2; (iii) −x, −y+1, z+1/2; (iv) −x+1/2, y+3/2, 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 (research project No. 28427). IMC is also grateful to COLCIENCIAS for her doctoral scholarship
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