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Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890
Volume 68| Part 1| January 2012| Pages o170-o171

2,2′-[Imidazolidine-1,3-diylbis(methyl­ene)]diphenol

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 12 December 2011; accepted 13 December 2011; online 17 December 2011)

In the title mol­ecule, C17H20N2O2, the imidazolidine ring adopts a twist conformation. The mean plane through the five atoms of the imidazolidine ring makes dihedral angles of 70.18 (4) and 74.14 (4)° with the planes of the two aromatic rings. The dihedral angle between the benzene rings is 53.11 (5)°. Both phenol –OH groups form intra­molecular hydrogen bonds to the N atoms, with graph-set motif S(6). In the crystal, pairs of O—H⋯O hydrogen bonds link the mol­ecules into dimers with R44(18) ring motifs. The crystal packing is further stabilized by C—H⋯O and weak C—H⋯π inter­actions.

Related literature

For a related structure, see: Rivera et al. (2011[Rivera, A., Sadat-Bernal, J., Ríos-Motta, J., Pojarová, M. & Dušek, M. (2011). Acta Cryst. E67, o2581.]). For the preparation of the title compound, see: Rivera et al. (1993[Rivera, A., Gallo, G. I., Gayón, M. E. & Joseph-Nathan, P. (1993). Synth. Commun. 23, 2921-2929.]). For ring conformations, see Cremer & Pople (1975[Cremer, D. & Pople, J. A. (1975). J. Am. Chem. Soc. 97, 1354-1358.]). For hydrogen-bond graph-set nomenclature, see: Bernstein et al. (1995[Bernstein, J., Davis, R. E., Shimoni, L. & Chang, N. L. (1995). Angew. Chem. Int. Ed. Engl. 34, 1555-1573.]). For details of hydrogen bonding in Mannich bases, see: Koll et al. (2006[Koll, A., Karpfen, A. & Wolschann, P. (2006). J. Mol. Struct. 790, 55-64.]); Filarowski et al. (1997[Filarowski, A., Szemik-Hojniak, A., Glowiak, T. & Koll, A. (1997). J. Mol. Struct. 404, 67-74.]).

[Scheme 1]

Experimental

Crystal data
  • C17H20N2O2

  • Mr = 284.4

  • Monoclinic, P 21 /n

  • a = 9.6541 (6) Å

  • b = 9.5198 (11) Å

  • c = 16.0007 (19) Å

  • β = 97.321 (7)°

  • V = 1458.6 (3) Å3

  • Z = 4

  • Cu Kα radiation

  • μ = 0.68 mm−1

  • T = 120 K

  • 0.56 × 0.46 × 0.35 mm

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

  • Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2010[Agilent (2010). CrysAlis PRO. Agilent Technologies, Yarnton, England.]) Tmin = 0.684, Tmax = 1

  • 16045 measured reflections

  • 2592 independent reflections

  • 2323 reflections with I > 3σ(I)

  • Rint = 0.029

Refinement
  • R[F2 > 2σ(F2)] = 0.032

  • wR(F2) = 0.102

  • S = 1.84

  • 2592 reflections

  • 197 parameters

  • 2 restraints

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

  • Δρmax = 0.18 e Å−3

  • Δρmin = −0.16 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

Cg3 is the centroid of the C12–C17 benzene rings.

D—H⋯A D—H H⋯A DA D—H⋯A
O1—H1o⋯N1 0.88 (1) 1.83 (1) 2.6394 (13) 152 (2)
O2—H2o⋯N2 0.88 (1) 1.84 (1) 2.6557 (13) 154 (2)
O1—H1o⋯O1i 0.88 (1) 2.60 (2) 3.0232 (12) 111 (1)
C11—H11a⋯O1i 0.96 2.58 3.4961 (15) 159
C14—H14⋯O1ii 0.96 2.50 3.4561 (15) 172
C6—H6⋯Cg3iii 0.96 2.97 3.7868 (14) 143
C10—H10bCg3ii 0.96 2.83 3.6718 (13) 148
Symmetry codes: (i) -x+2, -y+1, -z+1; (ii) [-x+{\script{3\over 2}}, y-{\script{1\over 2}}, -z+{\script{1\over 2}}]; (iii) [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

The study of intramolecular hydrogen bonds is interesting because of the high thermodynamic and structural stability of these systems. Intramolecularly hydrogen-bonded systems with direct coupling between acid and base centers reveal properties which make them valuable materials for practical use (Koll et al., 2006). Of the various different bifunctional intramolecularly hydrogen bonded compounds, ortho-Mannich bases are of special interest due to the presence of an electronic coupling between the proton donating and proton accepting groups through the aromatic ring which potentially affords structural consequences (Filarowski et al., 1997). We report here the crystal structure analysis of the title compound, (I).

The asymmetric unit of title compound (I) contains one molecule which have no internal symmetry (Fig 1). In (I), Fig. 1, the imidazolidine ring is twisted about the N1—C8 bond as seen in the puckering parameters Q(2) = 0.4126 (12) Å and ϕ = 20.02 (17) ° (Cremer & Pople, 1975). The mean plane of imidazolidine ring defined by N2, C9 and C10 makes a dihedral angle of 67.326 (56)° and 76.528 (47)° with the two pendant aromatic rings, C1—C6 and C12—C17 respectively. The dihedral angle between the phenyl rings is 53.134 (39)°. Both N atoms serves as hydrogen-bond acceptors to the phenolic OH group forming two intramolecular O—H···N hydrogen bond with graph-set motif S(6).

The molecular packing in (I) facilitates reciprocal O1—H1···O1 and C11—H11a···O1 interactions which join two crystallographically independent molecules into a dimer (Figure 2) forming an R44(18) ring motif. The dimers are further connected via C14—H14···O1 hydrogen bonds and weak C—H···π, forming chains along [111] (Figure 3).

Related literature top

For a related structure, see: Rivera et al. (2011). For the preparation of the title compound, see: Rivera et al. (1993). For ring conformations, see Cremer & Pople (1975). For hydrogen-bond graph-set nomenclature, see: Bernstein et al. (1995). For details of hydrogen bonding in Mannich bases, see: Koll et al. (2006); Filarowski et al. (1997).

Experimental top

For the originally reported synthesis, see: Rivera et al. (1993)

Refinement top

All H atoms bonded to carbon atoms were positioned geometrically and treated as riding on their parent atoms. The hydroxyl H atoms were found in difference Fourier maps ant their coordinates were refined with a distance restraint of 0.87 Å with σ of 0.01. All H atoms were refined with displacement coefficients Uiso(H) set to 1.5Ueq(O) for hydroxyl groups and to 1.2Ueq(C) for the –CH– and CH2– groups.

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. Dimer formation of the title compound by a R44(18) ring motif.
[Figure 3] Fig. 3. Packing of the molecules of the title compound view along the b axis.
2,2'-[Imidazolidine-1,3-diylbis(methylene)]diphenol top
Crystal data top
C17H20N2O2F(000) = 608
Mr = 284.4Dx = 1.295 Mg m3
Monoclinic, P21/nCu Kα radiation, λ = 1.5418 Å
Hall symbol: -P 2ynCell parameters from 9734 reflections
a = 9.6541 (6) Åθ = 2.8–66.9°
b = 9.5198 (11) ŵ = 0.68 mm1
c = 16.0007 (19) ÅT = 120 K
β = 97.321 (7)°Block, colourless
V = 1458.6 (3) Å30.56 × 0.46 × 0.35 mm
Z = 4
Data collection top
Agilent Xcalibur
diffractometer with an Atlas (Gemini ultra Cu) detector
2592 independent reflections
Radiation source: Enhance Ultra (Cu) X-ray Source2323 reflections with I > 3σ(I)
Mirror monochromatorRint = 0.029
Detector resolution: 10.3784 pixels mm-1θmax = 67.1°, θmin = 5.1°
Rotation method data acquisition using ω scansh = 1011
Absorption correction: multi-scan
(CrysAlis PRO; Agilent, 2010)
k = 1111
Tmin = 0.684, Tmax = 1l = 1818
16045 measured reflections
Refinement top
Refinement on F2H atoms treated by a mixture of independent and constrained refinement
R[F2 > 2σ(F2)] = 0.032Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0016I2)
wR(F2) = 0.102(Δ/σ)max = 0.008
S = 1.84Δρmax = 0.18 e Å3
2592 reflectionsΔρmin = 0.16 e Å3
197 parametersExtinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974)
2 restraintsExtinction coefficient: 2300 (400)
74 constraints
Crystal data top
C17H20N2O2V = 1458.6 (3) Å3
Mr = 284.4Z = 4
Monoclinic, P21/nCu Kα radiation
a = 9.6541 (6) ŵ = 0.68 mm1
b = 9.5198 (11) ÅT = 120 K
c = 16.0007 (19) Å0.56 × 0.46 × 0.35 mm
β = 97.321 (7)°
Data collection top
Agilent Xcalibur
diffractometer with an Atlas (Gemini ultra Cu) detector
2592 independent reflections
Absorption correction: multi-scan
(CrysAlis PRO; Agilent, 2010)
2323 reflections with I > 3σ(I)
Tmin = 0.684, Tmax = 1Rint = 0.029
16045 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0322 restraints
wR(F2) = 0.102H atoms treated by a mixture of independent and constrained refinement
S = 1.84Δρmax = 0.18 e Å3
2592 reflectionsΔρmin = 0.16 e Å3
197 parameters
Special details top

Experimental. CrysAlisPro (Agilent, 2010) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.

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 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
O10.88118 (9)0.55808 (8)0.54258 (5)0.0258 (3)
O20.64185 (9)0.24108 (8)0.20085 (5)0.0266 (3)
N10.82182 (10)0.29372 (9)0.50324 (6)0.0216 (3)
N20.75183 (10)0.27736 (10)0.36014 (6)0.0230 (3)
C10.73543 (12)0.41864 (12)0.62221 (7)0.0220 (3)
C20.78452 (12)0.54925 (11)0.59766 (7)0.0223 (3)
C30.73697 (13)0.67284 (12)0.63044 (7)0.0263 (4)
C40.64267 (13)0.66779 (12)0.68865 (7)0.0286 (4)
C50.59312 (13)0.53957 (13)0.71379 (7)0.0293 (4)
C60.63913 (13)0.41633 (12)0.67971 (7)0.0260 (4)
C70.79468 (12)0.28403 (11)0.59129 (7)0.0234 (3)
C80.69700 (12)0.29649 (12)0.44015 (7)0.0234 (3)
C90.89999 (13)0.17320 (11)0.47679 (7)0.0258 (4)
C100.86888 (13)0.17560 (12)0.38032 (7)0.0261 (4)
C110.80113 (12)0.41147 (11)0.32684 (7)0.0234 (3)
C120.84082 (12)0.39145 (11)0.23931 (7)0.0220 (3)
C130.75755 (12)0.30847 (11)0.18009 (7)0.0226 (3)
C140.79084 (13)0.29425 (12)0.09837 (7)0.0260 (4)
C150.90434 (13)0.36558 (12)0.07451 (7)0.0286 (4)
C160.98804 (13)0.44846 (12)0.13217 (8)0.0282 (4)
C170.95637 (12)0.45896 (11)0.21422 (7)0.0241 (3)
H30.7696090.7618890.6126640.0316*
H40.6113030.7533940.7117890.0343*
H50.5278280.5361040.7542480.0352*
H60.6035970.3277870.6962680.0311*
H7a0.8797170.2609090.6264760.0281*
H7b0.7310880.2081420.5970160.0281*
H8a0.6374420.2188520.4495630.0281*
H8b0.6529610.3868220.440870.0281*
H9a0.8636650.088240.4979220.031*
H9b0.998060.1878510.4932440.031*
H10a0.9496310.2085980.3568720.0313*
H10b0.839350.0839540.3603220.0313*
H11a0.8805770.4449910.3636290.0281*
H11b0.7285630.4807120.3252920.0281*
H140.7351920.2351230.0586950.0312*
H150.9255460.3578380.0176850.0343*
H161.0667590.497790.1154360.0338*
H171.0155260.5140120.2544560.0289*
H1o0.8869 (16)0.4725 (11)0.5220 (9)0.0387*
H2o0.6533 (17)0.2415 (17)0.2562 (6)0.0399*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0292 (5)0.0224 (4)0.0271 (4)0.0034 (3)0.0088 (3)0.0011 (3)
O20.0273 (5)0.0291 (4)0.0231 (4)0.0045 (3)0.0026 (3)0.0035 (3)
N10.0230 (5)0.0218 (4)0.0200 (5)0.0001 (4)0.0032 (4)0.0009 (3)
N20.0263 (5)0.0222 (5)0.0209 (5)0.0016 (4)0.0047 (4)0.0017 (3)
C10.0224 (6)0.0249 (5)0.0175 (5)0.0003 (4)0.0020 (4)0.0006 (4)
C20.0217 (6)0.0264 (6)0.0179 (5)0.0008 (4)0.0010 (4)0.0003 (4)
C30.0309 (7)0.0233 (6)0.0238 (6)0.0003 (4)0.0003 (5)0.0004 (4)
C40.0315 (7)0.0281 (6)0.0257 (6)0.0049 (5)0.0012 (5)0.0054 (4)
C50.0294 (7)0.0362 (6)0.0230 (6)0.0020 (5)0.0059 (5)0.0023 (5)
C60.0280 (7)0.0280 (6)0.0217 (6)0.0028 (5)0.0030 (5)0.0010 (4)
C70.0279 (6)0.0222 (5)0.0203 (6)0.0010 (4)0.0037 (4)0.0020 (4)
C80.0237 (6)0.0249 (5)0.0218 (6)0.0022 (4)0.0036 (4)0.0013 (4)
C90.0292 (7)0.0223 (5)0.0266 (6)0.0023 (4)0.0060 (5)0.0001 (4)
C100.0309 (7)0.0220 (5)0.0258 (6)0.0012 (4)0.0057 (5)0.0023 (4)
C110.0273 (6)0.0203 (5)0.0223 (6)0.0023 (4)0.0019 (5)0.0022 (4)
C120.0261 (6)0.0183 (5)0.0214 (6)0.0030 (4)0.0024 (4)0.0007 (4)
C130.0235 (6)0.0198 (5)0.0245 (6)0.0036 (4)0.0027 (4)0.0010 (4)
C140.0309 (7)0.0248 (5)0.0217 (6)0.0053 (5)0.0013 (5)0.0023 (4)
C150.0349 (7)0.0294 (6)0.0224 (6)0.0083 (5)0.0078 (5)0.0037 (5)
C160.0292 (7)0.0250 (6)0.0313 (6)0.0036 (5)0.0079 (5)0.0057 (4)
C170.0264 (6)0.0193 (5)0.0264 (6)0.0017 (4)0.0025 (5)0.0018 (4)
Geometric parameters (Å, º) top
O1—C21.3654 (15)C7—H7b0.96
O1—H1o0.883 (11)C8—H8a0.96
O2—C131.3653 (14)C8—H8b0.96
O2—H2o0.879 (9)C9—C101.5348 (16)
N1—C71.4684 (15)C9—H9a0.96
N1—C81.4703 (14)C9—H9b0.96
N1—C91.4650 (15)C10—H10a0.96
N2—C81.4578 (15)C10—H10b0.96
N2—C101.4922 (15)C11—C121.5104 (16)
N2—C111.4849 (15)C11—H11a0.96
C1—C21.4044 (16)C11—H11b0.96
C1—C61.3890 (17)C12—C131.4050 (15)
C1—C71.5120 (16)C12—C171.3902 (17)
C2—C31.3898 (16)C13—C141.3922 (17)
C3—C41.3837 (18)C14—C151.3836 (18)
C3—H30.96C14—H140.96
C4—C51.3890 (18)C15—C161.3916 (16)
C4—H40.96C15—H150.96
C5—C61.3902 (17)C16—C171.3890 (18)
C5—H50.96C16—H160.96
C6—H60.96C17—H170.96
C7—H7a0.96
C2—O1—H1o105.3 (10)H8a—C8—H8b114.38
C13—O2—H2o104.0 (10)N1—C9—C10103.70 (9)
C7—N1—C8115.40 (9)N1—C9—H9a109.4718
C7—N1—C9112.92 (8)N1—C9—H9b109.4709
C8—N1—C9102.89 (8)C10—C9—H9a109.4712
C8—N2—C10103.93 (8)C10—C9—H9b109.4714
C8—N2—C11112.12 (9)H9a—C9—H9b114.686
C10—N2—C11111.54 (9)N2—C10—C9105.84 (9)
C2—C1—C6118.51 (10)N2—C10—H10a109.4709
C2—C1—C7120.24 (10)N2—C10—H10b109.4713
C6—C1—C7121.09 (10)C9—C10—H10a109.4712
O1—C2—C1121.18 (10)C9—C10—H10b109.4714
O1—C2—C3118.51 (10)H10a—C10—H10b112.8697
C1—C2—C3120.30 (11)N2—C11—C12110.80 (9)
C2—C3—C4120.12 (11)N2—C11—H11a109.4718
C2—C3—H3119.9399N2—C11—H11b109.4711
C4—C3—H3119.9395C12—C11—H11a109.4708
C3—C4—C5120.39 (11)C12—C11—H11b109.4713
C3—C4—H4119.8038H11a—C11—H11b108.1129
C5—C4—H4119.8053C11—C12—C13120.35 (10)
C4—C5—C6119.27 (12)C11—C12—C17121.14 (9)
C4—C5—H5120.3644C13—C12—C17118.45 (10)
C6—C5—H5120.3649O2—C13—C12121.04 (10)
C1—C6—C5121.38 (11)O2—C13—C14118.47 (10)
C1—C6—H6119.3094C12—C13—C14120.49 (11)
C5—C6—H6119.3085C13—C14—C15119.81 (10)
N1—C7—C1112.45 (9)C13—C14—H14120.0949
N1—C7—H7a109.4718C15—C14—H14120.0956
N1—C7—H7b109.4717C14—C15—C16120.58 (11)
C1—C7—H7a109.4708C14—C15—H15119.7101
C1—C7—H7b109.4707C16—C15—H15119.7107
H7a—C7—H7b106.316C15—C16—C17119.23 (11)
N1—C8—N2104.07 (9)C15—C16—H16120.3866
N1—C8—H8a109.471C17—C16—H16120.3878
N1—C8—H8b109.4708C12—C17—C16121.40 (10)
N2—C8—H8a109.4722C12—C17—H17119.2994
N2—C8—H8b109.4714C16—C17—H17119.2985
Hydrogen-bond geometry (Å, º) top
Cg3 is the centroid of the C12–C17 benzene rings.
D—H···AD—HH···AD···AD—H···A
O1—H1o···N10.88 (1)1.83 (1)2.6394 (13)152 (2)
O2—H2o···N20.88 (1)1.84 (1)2.6557 (13)154 (2)
O1—H1o···O1i0.88 (1)2.60 (2)3.0232 (12)111 (1)
C11—H11a···O1i0.962.583.4961 (15)159
C14—H14···O1ii0.962.503.4561 (15)172
C6—H6···Cg3iii0.962.973.7868 (14)143
C10—H10b···Cg3ii0.962.833.6718 (13)148
Symmetry codes: (i) x+2, y+1, z+1; (ii) x+3/2, y1/2, z+1/2; (iii) x1/2, y+1/2, z+1/2.

Experimental details

Crystal data
Chemical formulaC17H20N2O2
Mr284.4
Crystal system, space groupMonoclinic, P21/n
Temperature (K)120
a, b, c (Å)9.6541 (6), 9.5198 (11), 16.0007 (19)
β (°) 97.321 (7)
V3)1458.6 (3)
Z4
Radiation typeCu Kα
µ (mm1)0.68
Crystal size (mm)0.56 × 0.46 × 0.35
Data collection
DiffractometerAgilent Xcalibur
diffractometer with an Atlas (Gemini ultra Cu) detector
Absorption correctionMulti-scan
(CrysAlis PRO; Agilent, 2010)
Tmin, Tmax0.684, 1
No. of measured, independent and
observed [I > 3σ(I)] reflections
16045, 2592, 2323
Rint0.029
(sin θ/λ)max1)0.597
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.032, 0.102, 1.84
No. of reflections2592
No. of parameters197
No. of restraints2
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.18, 0.16

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

Hydrogen-bond geometry (Å, º) top
Cg3 is the centroid of the C12–C17 benzene rings.
D—H···AD—HH···AD···AD—H···A
O1—H1o···N10.883 (11)1.826 (11)2.6394 (13)152.2 (15)
O2—H2o···N20.878 (10)1.840 (10)2.6557 (13)153.6 (15)
O1—H1o···O1i0.883 (11)2.599 (15)3.0232 (12)110.5 (11)
C11—H11a···O1i0.96002.58003.4961 (15)159.00
C14—H14···O1ii0.96002.50003.4561 (15)172.00
C6—H6···Cg3iii0.962.973.7868 (14)143
C10—H10b···Cg3ii0.962.833.6718 (13)148
Symmetry codes: (i) x+2, y+1, z+1; (ii) x+3/2, y1/2, z+1/2; (iii) x1/2, 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 Institutional research plan No. AVOZ10100521 of the Institute of Physics and the Praemium Academiae project of the Academy of Sciences of the Czech Republic.

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Volume 68| Part 1| January 2012| Pages o170-o171
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