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ISSN: 2056-9890

Cyclo­hexane-1,4-dicarb­­oxy­lic acid–pyridinium-4-olate (1/1)

aFacultad de Ingenieria Mochis, Universidad Autónoma de Sinaloa, Fuente Poseidón y Prol. A. Flores S/N, CP 81223, C.U. Los Mochis, Sinaloa, México, and bCentro de Investigaciones Químicas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, CP 62210, Cuernavaca, Morelos, México
*Correspondence e-mail: cenriqueza@yahoo.com.mx

(Received 9 March 2013; accepted 19 March 2013; online 28 March 2013)

In the title adduct, C5H5NO·C8H12O4, the heterocycle exists in its zwitterionic form. The cyclo­hexane ring exhibits a chair conformation with the carb­oxy­lic acid groups in equatorial and axial orientations. In the crystal, mol­ecules are linked through charge-assisted O—H⋯O, N+—H⋯O and N+—H⋯O hydrogen bonds, and an additional series of C—H⋯O contacts, giving a pleated two-dimensional hydrogen-bonded network parallel to (-204).

Related literature

For reports on supra­molecular crystal engineering and potential applications of co-crystals, see: Desiraju (1995[Desiraju, G. R. (1995). Angew. Chem. Int. Ed. 34, 2311-2327.]); Simon & Bassoul (2000[Simon, J. & Bassoul, P. (2000). In Design of Molecular Materials: Supramolecular Engineering. Berlin: Wiley-VCH.]); Weyna et al. (2009[Weyna, D. R., Shattock, T., Vishweshwar, P. & Zaworotko, M. J. (2009). Cryst. Growth Des. 9, 1106-1123.]); Aakeröy et al. (2010[Aakeröy, C. B., Champness, N. R. & Janiak, C. (2010). CrystEngComm, 12, 22-43.]); Yan et al. (2012[Yan, D., Delori, A., Lloyd, G. O., Patel, B., Friscic, T., Day, G. M., Bucar, D. K., Jones, W., Lu, J., Wei, M., Evans, D. G. & Duan, X. (2012). CrystEngComm, 14, 5121-5123.]). For related structures, see: Bhogala et al. (2005[Bhogala, B. R., Basavoju, S. & Nangia, A. (2005). CrystEngComm, 7, 551-562.]); Shattock et al. (2008[Shattock, T. R., Arora, K. K., Vishweshwar, P. & Zaworotko, M. J. (2008). Cryst. Growth Des. 8, 4533-4545.]); Yu (2012[Yu, C.-H. (2012). Acta Cryst. E68, o1989.]).

[Scheme 1]

Experimental

Crystal data
  • C5H5NO·C8H12O4

  • Mr = 267.28

  • Monoclinic, P 21 /c

  • a = 11.749 (2) Å

  • b = 11.618 (2) Å

  • c = 10.8010 (19) Å

  • β = 115.383 (2)°

  • V = 1332.0 (4) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.10 mm−1

  • T = 293 K

  • 0.50 × 0.43 × 0.24 mm

Data collection
  • Bruker SMART CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Sheldrick, 1996[Sheldrick, G. M. (1996). SADABS. University of Göttingen, Germany.]) Tmin = 0.95, Tmax = 0.98

  • 12552 measured reflections

  • 2345 independent reflections

  • 2229 reflections with I > 2σ(I)

  • Rint = 0.041

Refinement
  • R[F2 > 2σ(F2)] = 0.072

  • wR(F2) = 0.161

  • S = 1.02

  • 2345 reflections

  • 181 parameters

  • 3 restraints

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

  • Δρmax = 0.20 e Å−3

  • Δρmin = −0.27 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
O1—H1′⋯O5 0.84 1.82 2.638 (3) 165
O3—H3′⋯O5i 0.84 1.76 2.594 (2) 175
N1—H1⋯O4ii 0.84 2.29 2.921 (3) 132
N1—H1⋯O5iii 0.84 2.39 3.038 (3) 134
C1—H1A⋯O2iv 0.98 2.67 3.625 (4) 162
C11—H11⋯O2iii 0.93 2.62 3.420 (5) 143
C12—H12⋯O4ii 0.93 2.47 3.014 (4) 117
Symmetry codes: (i) [x+1, -y+{\script{1\over 2}}, z+{\script{1\over 2}}]; (ii) -x+1, -y, -z+1; (iii) [-x, y-{\script{1\over 2}}, -z+{\script{1\over 2}}]; (iv) [x, -y+{\script{1\over 2}}, z-{\script{1\over 2}}].

Data collection: SMART (Bruker, 2000[Bruker (2000). SMART. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT-Plus-NT (Bruker, 2001[Bruker (2001). SAINT-Plus-NT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT-Plus-NT; program(s) used to solve structure: SHELXTL-NT (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXTL-NT; molecular graphics: ORTEP-3 (Farrugia, 2012[Farrugia, L. J. (2012). J. Appl. Cryst. 45, 849-854.]) and Mercury (Macrae et al. 2008[Macrae, C. F., Bruno, I. J., Chisholm, J. A., Edgington, P. R., McCabe, P., Pidcock, E., Rodriguez-Monge, L., Taylor, R., van de Streek, J. & Wood, P. A. (2008). J. Appl. Cryst. 41, 466-470.]); software used to prepare material for publication: publCIF (Westrip, 2010)[Westrip, S. P. (2010). J. Appl. Cryst. 43, 920-925.].

Supporting information


Comment top

The engineering of novel materials via non-covalent synthesis has developed as a very attractive and potential area of research because of its importance in biological systems, molecular recognition (Simon et al., 2000; Aakeröy et al., 2010), pharmaceutical chemistry (Weyna et al., 2009) and materials chemistry (Yan et al., 2012). Aromatic carboxylic acids form reliable supramolecular synthons for the construction of novel organic networks by hydrogen bonding and π-π interactions (Desiraju, 1995), and numerous studies have focused on hydrogen bonding between carboxylic acids and pyridine derivatives (Bhogala et al., 2005; Shattock et al. 2008; Yu, 2012). Herein, we report on the solid-state structure of a 1:1 co-crystal formed between cyclohexane-1,4-dicarboxylic acid and pyridin-4-ol. The molecular components of the title compound are shown in Fig. 1. The asymmetric unit contains one cyclohexane-1,4-dicarboxylic acid and one pyridin-4-ol molecule in the zwitterionic form. The cyclohexane ring exhibits a chair conformation with the carboxylic groups in equatorial and axial orientation, as denoted by the C7—C1—C2—C3 [-177.7 (2)°] and C8—C4—C5—C6 [75.7 (3)°] torsion angles, respectively. In the crystal, the molecular entities are linked through charge-assisted O—H···O-, N+—H···O- and N+—H···O hydrogen bonds and an additional series of C—H···O contacts to give a pleated two-dimensional hydrogen-bonded network parallel to (-204) (Fig. 2, Table 1).

Related literature top

For reports on supramolecular crystal engineering and potential applications of co-crystals, see: Desiraju (1995); Simon & Bassoul (2000); Weyna et al. (2009); Aakeröy et al. (2010); Yan et al. (2012). For related structures, see: Bhogala et al. (2005); Shattock et al. (2008); Yu (2012).

Experimental top

C5H5NO.C8H12O4 was prepared from a solution of C5H5NO (0.05 g, 0.53 mmol) and C8H12O4 (0.09 g, 0.53 mmol) in CH3OH (5 ml), which was stirred for a few minutes at room temperature, giving a clear transparent solution. After evaporation of the solvent, colorless crystals suitable for single-crystal X-ray diffraction had formed in about 51% yield. IR (KBr): 3471, 3276, 3131, 3092, 2937, 2863, 1709, 1632, 1576, 1509, 1416, 1364, 1331, 1316, 1229, 1170, 1001 cm-1.

Refinement top

H atoms were found in difference Fourier maps. Carbon-bound hydrogen atoms were placed in idealized positions using a riding models with constrained distances of 0.97 Å (R2CH2), 0.98 Å (R3CH) and 0.93 Å (Csp2H). Coordinates for hydrogens bound to oxygen and nitrogen were refined. Uiso(H) values were set to either 1.2Ueq or 1.5Ueq (OH, NH) of the attached atom.

Computing details top

Data collection: SMART (Bruker, 2000); cell refinement: SAINT-Plus-NT (Bruker, 2001); data reduction: SAINT-Plus-NT (Bruker, 2001); program(s) used to solve structure: SHELXTL-NT (Sheldrick, 2008); program(s) used to refine structure: SHELXTL-NT (Sheldrick, 2008); molecular graphics: ORTEP-3 (Farrugia, 2012) and Mercury (Macrae et al. 2008); software used to prepare material for publication: publCIF (Westrip, 2010).

Figures top
[Figure 1] Fig. 1. The molecular structures of the components in the title compound, showing displacement ellipsoids drawn at the 30% probability level.
[Figure 2] Fig. 2. View down the c-axis of the two-dimensional hydrogen-bonded supramolecular network formed through O—H···O-, N+—H···O- and N+—H···O and C—H···O interactions.
Cyclohexane-1,4-dicarboxylic acid–pyridinium-4-olate (1/1) top
Crystal data top
C5H5NO·C8H12O4F(000) = 568
Mr = 267.28Dx = 1.333 Mg m3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 5484 reflections
a = 11.749 (2) Åθ = 2.6–27.4°
b = 11.618 (2) ŵ = 0.10 mm1
c = 10.8010 (19) ÅT = 293 K
β = 115.383 (2)°Rectangular prism, yellow
V = 1332.0 (4) Å30.50 × 0.43 × 0.24 mm
Z = 4
Data collection top
Bruker SMART CCD area-detector
diffractometer
2345 independent reflections
Radiation source: fine-focus sealed tube2229 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.041
ϕ and ω scansθmax = 25.0°, θmin = 1.9°
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
h = 1313
Tmin = 0.95, Tmax = 0.98k = 1313
12552 measured reflectionsl = 1212
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)] = 0.072Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.161H atoms treated by a mixture of independent and constrained refinement
S = 1.02 w = 1/[σ2(Fo2) + (0.0623P)2 + 1.4075P]
where P = (Fo2 + 2Fc2)/3
2345 reflections(Δ/σ)max < 0.001
181 parametersΔρmax = 0.20 e Å3
3 restraintsΔρmin = 0.27 e Å3
Crystal data top
C5H5NO·C8H12O4V = 1332.0 (4) Å3
Mr = 267.28Z = 4
Monoclinic, P21/cMo Kα radiation
a = 11.749 (2) ŵ = 0.10 mm1
b = 11.618 (2) ÅT = 293 K
c = 10.8010 (19) Å0.50 × 0.43 × 0.24 mm
β = 115.383 (2)°
Data collection top
Bruker SMART CCD area-detector
diffractometer
2345 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
2229 reflections with I > 2σ(I)
Tmin = 0.95, Tmax = 0.98Rint = 0.041
12552 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0723 restraints
wR(F2) = 0.161H atoms treated by a mixture of independent and constrained refinement
S = 1.02Δρmax = 0.20 e Å3
2345 reflectionsΔρmin = 0.27 e Å3
181 parameters
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
O10.2230 (2)0.1930 (2)0.0632 (2)0.0663 (6)
H1'0.162 (2)0.198 (4)0.085 (4)0.099*
O20.3186 (2)0.3059 (3)0.2412 (3)0.0898 (9)
O30.8439 (2)0.3327 (2)0.3413 (2)0.0733 (7)
H3'0.901 (3)0.324 (4)0.4210 (17)0.110*
O40.7984 (2)0.15562 (19)0.3701 (2)0.0805 (8)
C10.4258 (2)0.2522 (2)0.1037 (2)0.0420 (6)
H1A0.38920.25390.00330.050*
C20.5129 (3)0.3552 (2)0.1563 (3)0.0489 (7)
H2A0.46470.42560.12460.059*
H2B0.55100.35550.25570.059*
C30.6155 (3)0.3511 (3)0.1063 (3)0.0556 (8)
H3A0.67180.41600.14420.067*
H3B0.57730.35830.00730.067*
C40.6915 (3)0.2400 (3)0.1470 (3)0.0497 (7)
H40.74280.23740.09550.060*
C50.6058 (3)0.1347 (3)0.1039 (3)0.0557 (8)
H5A0.56830.12830.00480.067*
H5B0.65590.06620.14160.067*
C60.5018 (3)0.1405 (2)0.1514 (3)0.0485 (7)
H6A0.53840.13630.25060.058*
H6B0.44600.07510.11520.058*
C70.3195 (3)0.2542 (2)0.1453 (3)0.0471 (6)
C80.7822 (2)0.2371 (2)0.2978 (3)0.0442 (6)
N10.0308 (3)0.0636 (2)0.3628 (3)0.0590 (7)
H10.041 (4)0.115 (2)0.421 (3)0.088*
O50.01175 (16)0.18473 (15)0.09311 (18)0.0470 (5)
C90.0146 (2)0.1065 (2)0.1791 (2)0.0384 (6)
C100.0764 (3)0.0194 (2)0.1462 (3)0.0495 (7)
H100.14440.01850.06030.059*
C110.0659 (3)0.0638 (2)0.2390 (4)0.0609 (8)
H110.12660.12130.21590.073*
C120.1179 (3)0.0179 (3)0.4004 (3)0.0584 (8)
H120.18360.01650.48800.070*
C130.1124 (3)0.1029 (2)0.3127 (3)0.0497 (7)
H130.17400.15990.34100.060*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0561 (13)0.0868 (16)0.0593 (13)0.0227 (12)0.0280 (11)0.0188 (12)
O20.0729 (16)0.130 (2)0.0779 (16)0.0249 (15)0.0433 (14)0.0510 (16)
O30.0722 (15)0.0658 (14)0.0532 (13)0.0221 (12)0.0005 (11)0.0129 (11)
O40.1024 (19)0.0580 (14)0.0471 (12)0.0139 (13)0.0003 (12)0.0119 (11)
C10.0442 (14)0.0476 (15)0.0296 (12)0.0022 (11)0.0115 (11)0.0003 (11)
C20.0532 (16)0.0370 (14)0.0506 (15)0.0012 (12)0.0166 (13)0.0067 (12)
C30.0529 (16)0.0624 (18)0.0448 (15)0.0094 (14)0.0146 (13)0.0164 (13)
C40.0479 (15)0.0695 (19)0.0349 (13)0.0017 (14)0.0207 (12)0.0011 (13)
C50.0569 (17)0.0591 (18)0.0447 (15)0.0045 (14)0.0157 (13)0.0176 (13)
C60.0550 (16)0.0374 (14)0.0483 (15)0.0063 (12)0.0175 (13)0.0069 (12)
C70.0480 (15)0.0490 (16)0.0400 (14)0.0005 (12)0.0146 (12)0.0019 (12)
C80.0437 (14)0.0500 (16)0.0386 (13)0.0008 (12)0.0174 (11)0.0004 (12)
N10.0757 (18)0.0480 (15)0.0647 (17)0.0093 (13)0.0411 (15)0.0138 (12)
O50.0441 (10)0.0454 (10)0.0432 (10)0.0014 (8)0.0109 (8)0.0082 (8)
C90.0411 (13)0.0345 (13)0.0403 (13)0.0048 (10)0.0182 (11)0.0015 (10)
C100.0450 (15)0.0467 (16)0.0554 (16)0.0027 (12)0.0202 (13)0.0062 (13)
C110.0667 (19)0.0407 (16)0.088 (2)0.0111 (14)0.0458 (19)0.0066 (15)
C120.0672 (19)0.0558 (18)0.0488 (16)0.0103 (16)0.0217 (14)0.0081 (14)
C130.0517 (15)0.0439 (15)0.0449 (14)0.0043 (12)0.0125 (12)0.0001 (12)
Geometric parameters (Å, º) top
O1—C71.310 (3)C4—H40.9800
O1—H1'0.8400 (10)C5—C61.516 (4)
O2—C71.201 (3)C5—H5A0.9700
O3—C81.299 (3)C5—H5B0.9700
O3—H3'0.8400 (11)C6—H6A0.9700
O4—C81.189 (3)C6—H6B0.9700
C1—C71.498 (4)N1—C121.324 (4)
C1—C21.518 (4)N1—C111.333 (4)
C1—C61.534 (4)N1—H10.8400 (10)
C1—H1A0.9800O5—C91.289 (3)
C2—C31.518 (4)C9—C101.403 (4)
C2—H2A0.9700C9—C131.408 (4)
C2—H2B0.9700C10—C111.359 (4)
C3—C41.524 (4)C10—H100.9300
C3—H3A0.9700C11—H110.9300
C3—H3B0.9700C12—C131.351 (4)
C4—C81.517 (4)C12—H120.9300
C4—C51.525 (4)C13—H130.9300
C7—O1—H1'112 (3)H5A—C5—H5B107.8
C8—O3—H3'110 (3)C5—C6—C1111.2 (2)
C7—C1—C2113.0 (2)C5—C6—H6A109.4
C7—C1—C6110.6 (2)C1—C6—H6A109.4
C2—C1—C6109.8 (2)C5—C6—H6B109.4
C7—C1—H1A107.7C1—C6—H6B109.4
C2—C1—H1A107.7H6A—C6—H6B108.0
C6—C1—H1A107.7O2—C7—O1122.0 (3)
C3—C2—C1110.7 (2)O2—C7—C1125.7 (3)
C3—C2—H2A109.5O1—C7—C1112.3 (2)
C1—C2—H2A109.5O4—C8—O3122.4 (2)
C3—C2—H2B109.5O4—C8—C4124.3 (3)
C1—C2—H2B109.5O3—C8—C4113.3 (2)
H2A—C2—H2B108.1C12—N1—C11121.6 (3)
C2—C3—C4112.4 (2)C12—N1—H1116 (3)
C2—C3—H3A109.1C11—N1—H1122 (3)
C4—C3—H3A109.1O5—C9—C10123.0 (2)
C2—C3—H3B109.1O5—C9—C13121.1 (2)
C4—C3—H3B109.1C10—C9—C13115.8 (2)
H3A—C3—H3B107.9C11—C10—C9120.6 (3)
C8—C4—C3112.5 (2)C11—C10—H10119.7
C8—C4—C5112.2 (2)C9—C10—H10119.7
C3—C4—C5111.2 (2)N1—C11—C10120.5 (3)
C8—C4—H4106.8N1—C11—H11119.8
C3—C4—H4106.8C10—C11—H11119.8
C5—C4—H4106.8N1—C12—C13120.6 (3)
C6—C5—C4112.6 (2)N1—C12—H12119.7
C6—C5—H5A109.1C13—C12—H12119.7
C4—C5—H5A109.1C12—C13—C9120.9 (3)
C6—C5—H5B109.1C12—C13—H13119.6
C4—C5—H5B109.1C9—C13—H13119.6
C7—C1—C2—C3177.7 (2)C6—C1—C7—O179.7 (3)
C6—C1—C2—C358.2 (3)C3—C4—C8—O4136.9 (3)
C1—C2—C3—C456.6 (3)C5—C4—C8—O410.5 (4)
C2—C3—C4—C874.5 (3)C3—C4—C8—O344.6 (3)
C2—C3—C4—C552.4 (3)C5—C4—C8—O3170.9 (2)
C8—C4—C5—C675.7 (3)O5—C9—C10—C11177.2 (2)
C3—C4—C5—C651.4 (3)C13—C9—C10—C111.8 (4)
C4—C5—C6—C154.4 (3)C12—N1—C11—C101.2 (4)
C7—C1—C6—C5177.2 (2)C9—C10—C11—N10.3 (4)
C2—C1—C6—C557.4 (3)C11—N1—C12—C131.1 (5)
C2—C1—C7—O222.5 (4)N1—C12—C13—C90.5 (4)
C6—C1—C7—O2101.1 (3)O5—C9—C13—C12177.1 (3)
C2—C1—C7—O1156.7 (2)C10—C9—C13—C121.9 (4)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1···O50.841.822.638 (3)165
O3—H3···O5i0.841.762.594 (2)175
N1—H1···O4ii0.842.292.921 (3)132
N1—H1···O5iii0.842.393.038 (3)134
C1—H1A···O2iv0.982.673.625 (4)162
C11—H11···O2iii0.932.623.420 (5)143
C12—H12···O4ii0.932.473.014 (4)117
Symmetry codes: (i) x+1, y+1/2, z+1/2; (ii) x+1, y, z+1; (iii) x, y1/2, z+1/2; (iv) x, y+1/2, z1/2.

Experimental details

Crystal data
Chemical formulaC5H5NO·C8H12O4
Mr267.28
Crystal system, space groupMonoclinic, P21/c
Temperature (K)293
a, b, c (Å)11.749 (2), 11.618 (2), 10.8010 (19)
β (°) 115.383 (2)
V3)1332.0 (4)
Z4
Radiation typeMo Kα
µ (mm1)0.10
Crystal size (mm)0.50 × 0.43 × 0.24
Data collection
DiffractometerBruker SMART CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 1996)
Tmin, Tmax0.95, 0.98
No. of measured, independent and
observed [I > 2σ(I)] reflections
12552, 2345, 2229
Rint0.041
(sin θ/λ)max1)0.595
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.072, 0.161, 1.02
No. of reflections2345
No. of parameters181
No. of restraints3
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.20, 0.27

Computer programs: SMART (Bruker, 2000), SAINT-Plus-NT (Bruker, 2001), SHELXTL-NT (Sheldrick, 2008), ORTEP-3 (Farrugia, 2012) and Mercury (Macrae et al. 2008), publCIF (Westrip, 2010).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1'···O50.841.822.638 (3)165
O3—H3'···O5i0.841.762.594 (2)175
N1—H1···O4ii0.842.292.921 (3)132
N1—H1···O5iii0.842.393.038 (3)134
C1—H1A···O2iv0.982.673.625 (4)162
C11—H11···O2iii0.932.623.420 (5)143
C12—H12···O4ii0.932.473.014 (4)117
Symmetry codes: (i) x+1, y+1/2, z+1/2; (ii) x+1, y, z+1; (iii) x, y1/2, z+1/2; (iv) x, y+1/2, z1/2.
 

Acknowledgements

This work was supported financially by the Universidad Autónoma de Sinaloa (PROFAPI 2012/049).

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