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Journal of the Chilean Chemical Society

On-line version ISSN 0717-9707

J. Chil. Chem. Soc. vol.52 no.3 Concepción Sept. 2007 


J. Chil. Chem. Soc, 52, N° 3 (2007) págs.: 1271-1275





Facultad de Ciencias Químicas Universidad de Concepción, casilla 160-C, Concepción, Chile


Interconversion reaction of I II conformers of 4-ethyl-6-methyl-1,3-dithiane (METDIT) has been studied by means of ab initio methods on the frame of MO theory. Optimized geometries at HF/6-31G** level correlate well with that found for the parent 1,3-dithianefrom an x-ray diffraction study. Both conformers possess similar bond distances, but differ in up 12° in some dihedrals. Conformer I geometry presents the larger distortion from the regular 1,3-dithiane mainly due to difference between angles κ1 and κ2 (ca. 14°). In conformer II this difference is just ca. 3°. The energetics and thermodynamics were obtained with basis sets that include diffuse, polarization functions and electronic correlations at the second-order perturbation Meller Plesset theory. Gas phase thermodynamic predicts II to be in a 98% concentration. Low and medium high polarity solvents seem to exert no influence on the conformers concentrations. Thus the I II interconversion reaction is largely displaced to II formation, both in the gas phase and solution. The calculated 1H-NMR data, i.e., chemical shifts and one-bond C-H spin-spin coupling constants are predicted on the basis of the consistent results obtained for the parent 1,3-dithiane. For both conformers reverse Perlin effect takes place at C2 and C5. The C2 - Hax and C2 - Heq bond distances are similar ( ca. 1.092 Å), whereas the C5- Heq are larger than the axial ones yielding smaller 1JC-H coupling constants.

Keywords: 4-ethyl-6-methyl-1,3-dithiane; conformational preference, NMR properties


The study and understanding the factors ruling the preferred conformation in sulfur-containing six-membered hetercycles have become an important area of research. Cyclohexane has been the model molecule to learn more about structures and reactivities of other species like 1,3-dioxane , 1,3-dithiane and 1,3-thioxane. In fact, the introduction of two heteroatoms produce important distortions in the "ideal" chair structure of cyclohexane. Thus, changes occurring in the aliphatic region of dithiane, show that this part of the molecule is less planar as compared with dioxane, thought the former is more easy distorted upon hydrogen substitution by alkyl groups than the later. Conformational analyses on substituted derivatives of these heterocycles have provided additional information on the different factors governing the preferred conformation adopted by the ring and have also allowed the understanding of some anomalous structural and spectroscopic features1-7. In fact, particular interest have been paid to chemical shift and one-bond 13C-11H spin-spin coupling constants as they allow directly to study hyperconjugation. The two-electron/two-orbital hyperconjugative interactions between an occupied high-energy donor orbital and an empty low-energy acceptor orbital, may influence conformational equilibrium and reflect the departure of the actual structure from the ideal Lewis one6. These deviations shows up themselves as geometric, electron density distribution, energies of the molecular orbitals, IR spectra and NMR properties3 changes. X-ray diffraction studies show that 2-phenyl-l,3-dithiane8 possesses a regular chair structure with angles and lengths in good agreement with the calculated values (HF/6-31G**). It is well known that hydrogen substitution distorts in a variable extent the "regular" heterocyclic ring. Energy calculations reveal that, in general, both alkyl equatorial and axial substitutions are possible and that their preferred conformation will depend on the nature, size, solvent and interaction of substituents and the sulfur lone pairs of electrons910. In the present work, we have studied conformers I and II equilibrium in trans-4-ethyl-6-methyl- 1,3-dithiane (METDIT) and see whether the calculated thermodynamic properties are consistent with the coexistence of both species as suggested by the 1H-NMR spectra11,12 or some other factors govern the interconversion reaction. We have also explored the effect of the solvent, by using PCM model13-16, on such equilibrium. If the experimental and calculated data are in agreement, the type of hypercongugative delocalization, that explain some structural and spectroscopic features could be proposed (derived from NBO analysis17). The transition state for the two conformers interconversion reaction have been found and the effect of the solvent on the activation energy also studied.


Geometry optimization of conformers I and II of METDIT were carried out at HF/6-**, MP2/6-** and B3LYP/6-** levels using Gaussian 03 series of programs18.The initial geometries were those reported previously for 1,3-dithiane4,8. The energies derived at the MP2/6-31G*//HF/6-** and MP2/6-31G*//MP2/6-** were compared in order to determine whether or not geometries needed to be calculated at a correlated level to obtain accurate energies. The AE(I - II) value of ca. 0.02 Kcal/mol, derived suggests that optimization at correlated level is not needed. Similar calculations using DFT-B3LYP functional also show that the above difference is just ca. 0.11 Kcal/mol. In fact, the largest differences in bond distances calculated at correlated and uncorrelated levels are ca. 0.009Å whereas the bond angle largest variation is ca. 2.0° for both conformers. Frequency and IR intensities were predicted at the equilibrium geometries (HF/6-31G** yielding all real frequencies so that all calculated structures are local minima. Energy calculations were carried out using a flexible basis set like 6-311+G** that includes both polarization and diffuse functions. Electron correlation at the second order Møller Plesset theory in the frozen core approximation was also included. Attempts to explore higher order Meller Plesset and QCISD using the same basis set failed due to our limited computational facilities. The calculated energies were corrected for zero point vibrational energies and enthalpies and free energy changes of interconversion were obtained from the corresponding sums of electronic and thermal enthalpies (HCORR) and free energies (GCORR), respectively. The solute-solvent interactions were calculated with the polarized continuum method (PCM )13-17 for which its capacity to reproduce solvation energies19 leads us to conclude that in general PCM behaves well, failing just in few cases. To apply PCM, the gas phase geometries were taκen since very small changes in the geometrical parameters are observed for I and II, in going from the gas phase to the solution (see table 1). In fact, optimization of all structures in several solvents show that bond distances largest variation is ca. 0.002 A, whereas bond angles vary ca. 0.3 degrees. Relative free energies in solution conformers were obtained by adding the relative free energies in the gas phase (ΔGAS) and the relative free energies of solvation (ΔΔGAS). The total free energy in solution includes both electrostatic and non-electrostatic contributions.

To obtain the theoretical 1H shifts (δ) and the one-bond 13C-1 coupling constants IJCH), the B3LYP/6-31G** geometries were obtained for all compounds studied here as well as the equilibrium geometry for TMS used as standard20. The magnetic shielding tensors were calculated at B3LYP/6-311+G*// B3LYP/66-31G** level of theory using the GIAO (Gauge-Independent Atomic Orbital) method21,22 . Chemical shifts were derived with respect to the NMR isotropic magnetic shielding tensors (in ppm) from the corresponding standard tensor (TMS = 32.1 ppm for 1H). The effect of the solvents CS2, CHC13 and DMSO (dimethtlsulfoxide) on chemical shifts and one bond spin-spin coupling constants, though initially calculated, was no further considered as the changes in either δ and IJCH are less than 0.1 ppm and 1 Hz, respectively.

In order to study the electronic structures of conformers I and II, Natural Bond Orbital (NBO) analyses were carried out on the B3LYP/6-31G** geometries and the energies of hyperconjugation interactions, the Fock (Fij) matrix element corresponding to the orbital interactions and the energies of the donor and acceptor orbitals, derived. The hyperconjugation interaction energies were obtained from the second-order perturbation approach: E(2) = -2<σ | F | σ*>2 /εσ*- εc, where the integral corresponds to the Fij. matrix element between interacting orbitals i and j whose energies are εσ and εσ*. 2 stands for the population of the donor orbital. There is good linear correlation between the second-order perturbation hyperconjugative energies and the deletion procedure23.

The transition state for the I II interconversion reaction was characterized by a frequency calculation which yielded a single imaginary frequency ( at ca. 92 cm-1) . This frequency corresponds to a ring deformation mode detected at ca. 80 cm-1 in 1,3-dithiane7. The animation, using GaussView program24, of such a mode confirm that corresponds to a ring deformation mode that conducts either to the reactant (conformer I) or the product (conformer II ). The TS I and TS II paths were followed by an intrinsic reaction coordinate (IRC) procedure25. IRC calculations lead to the conclusion that the TS connects both the reactant and the product. According to the finding of one imaginary frequency and its animation and the IRC results, we can be sure that the TS is a true one.


A) Molecular Structures

Selected structural parameters for conformers I and II are shown in table 1. To discuss the geometries of I and II, the dithiane chair has been divided into three parts (see figure 1, for atom numbering): a) the lower ( in I ) and upper (in II ) parts of the chair involving SI, C2 and S3, b) the chair middle portion including both sulfur, C4 and C6 atoms and c) the upper ( in I ) and lower (in II ) parts formed by C4, C5 and C6 atoms. In this way conformer I can be described as 5C2 chair , whereas II is clearly a 2C5 chair. The methyl group is bonded to C6 whereas the ethyl is on C4. The differences in the conformations come from the fact that in I the -CH3 group is in an equatorial position and the ethyl group is axially bound to C4. In conformer II, the reverse situation is found, i.e., the methyl is axial and the ethyl is equatorial. For both conformers, the ethyl group was rotated to see whether another configuration came out. In fact, in each case the rotation of the ethyl group by ca 10° produced the same minima. The positions of the alkyl group in I produces the regular dithiane chair to be quite distorted, whereas in II this effect is smaller and thereby the ring is noticeably less distorted. In both cases, the methyl group seems to exerts no effect on the close SI atom. Defining the torsion angles made up by the atoms involved in each side of the heterocyclic ring: κ1 = C2S1C6C5 and κ2 = C2S3C4C5, we can see that the departures of these angles from the regular dithiane (κ1 = κ2 = 57.8° ) are ca. 2 and 11.7° for I, whereas in II the deviations are ca. 3 and 0.1°, respectively. These results indicate that in I the ring is distorted in the S3 side and that conformer II remains fairly unperturbed upon alkyl substitution. Accordingly, the distortion of I implies that the sulfur atom moves up by ca. 12°. The distortion of bom conformers is not reflected in bond distances as the largest bond difference is just ca. 0.02 Å. The middle or central part of conformer I structure (measured by the dihedral S1S3C4C6) is also somewhat changed, as the S3 atom moves up ca 4.4°; SI does not vary its position appreciably. This part of II stays fairly unaltered when compared with dithiane. This same situation is observed for the lower part of this chair. In conformer I, the lower part is twisted by ca. 10° towards the S3 side. The transition state (TS) resembles I to a small extend. The ring distortion is reflected in that SI goes down and κ1 increases by ca. 19° with respect to the corresponding angle in dithiane. S3 goes up and becomes close to the plane formed by the all atoms in the ring but SI. The animation of the imaginary normal mode shows that C5, S3 and SI move up and down with rather large amplitudes. The C2H2 group simultaneously performs the same movement in such a way that conformer I is clearly "recovered". Intrinsic reaction coordinate calculations (IRC) both in the forward and reverse directions lead to the reactant and product and thereby the TS is fully characterized. Figure 2 shows the energy profile which is consistent with a single saddle point at the TS. Other saddle points in the potential energy hypersurface were not "detected" most likely due to steric effects of sulfur atoms that would produce a larger repulsion with the bulκy ethyl group leading to rather rigid structures.

B) Energetics and Thermodynamics

The conformers I II interconversion reaction energetics and thermodynamics are given in table 2. The inclusion of electron correlation at the second order Meller-Plesset theory and the 6-31G** basis set shows that the whole molecular system is stabilized by ca. 790 Kcal/mol with respect to the corresponding Hartree-Fock level. The use of a larger basis set such as 6-311G**produces the system to gain of ca. 97 Kcal/mol, whereas the inclusion of diffuse functions on the heavy atoms render a modest gain of ca. 6 Kcal/mol. When diffuse functions are added to hydrogens the stabilization of the present molecular system is negligible, i. e., ca. 1.1 Kcal/mol. According to these results the use of MP2/6-311+G**level in the calculations of the thermodynamics of the system under study is fully justified. The thermodynamics of I II interconversion reaction was calculated at the MP2/6-311+G**// HF/6-31G** level. An approximate relative % concentration of II ca. 98%, points towards a very low concentration of conformer I in the gas phase and solution, in apparent disagreement with the experimental 1H-NMR data25 obtained in CS2, CHC13 or CPC. In fact, a ΔG° of ca. -2.39 Kcal/mol indicates that the interconversion reaction is displaced to the conformer II formation. However, it is worth noting that the 1H-NMR spectra are well resolved just below the coalescence temperature (-95° C) showing the typical pattern of two AB-systems for the H-2 protons. Over Tc, the peaκs due to the A-part ( αa and ßa) are not resolved. Since our calculations were carried out in the gas phase and room temperature, the results are not strictly comparable. The NMR data would indicate that the interconversion reaction slow down enough at low temperature to observe the spectra of both conformers. The activation energy E for the forward reaction (I TS) is ca. 6.2 Kcal/mol, a value expected for a TS reactant alike. The calculations of the I II interconversion indicate that this reaction would be an exothermic process (ΔH0 -2.5 Kcal/mol) with a negligible entropy change (ΔS =-0.49 cal K-1 mol-1; ΔSexp =-0.52 e.u.). It is likely that the exothermic nature of this reaction could come from the breaκing of some important hyperconjugation interactions that stabilized the axial position of the ethyl group in I and that are lacking in II.

C) Solvent Effect

The solvent-solute interactions were obtained using PCM method. Solvents of low dielectric constants such as carbon disulfide (ε = 2.60) and CHC13 (ε = 4.90) formerly employed to obtain the 1H-NMR data11,12 were tried. High polarity solvent such as dimethylsulfoxide (DMSO, ε= 46.70) was also included but similar results were obtained. The free energy changes in solution were obtained, as usual, from ΔGoSOLN = ΔGoGAS +ΔΔGoSOLVATION. The relative free energies in solution for both conformers as well as their free energies of solvation are given in table 3. Free energies indicate that both conformers are almost equally solvated in all solvents used in the present worκ, most likely due to their similar dipole moments ( see table 3). Solvents polarities do not produce significant changes in the conformers concentration. When these results are compared with the gas phase concentrations, it can be realized that it is likely that thermodynamic and solvent polarities do not control the I II interconversion reaction and that kinetic effect might be very important in this process allowing for conformer I formation in agreements with the NMR data25. Table 4, shows the solvent effect on the activation energy for the forward reaction. Excepting DMSO, the solvent studied here are those used to obtained el NMR data11,12.

C) NMR Spectra

It has been found above ( see section B) that conformer II concentration would be ca. 98% in the gas phase and in solution. Conformer I would achieve a very small concentration. The C2-protons NMR spectra of the almost 1:1 mixture of conformers I and II would show two typical AB systems patterns. Thus, experimental spectra12 at low temperature (below Tc , i.e., ca. -95° C) reveals two quartets centered at ca. 3.70 ppm. The higher field first one, has been assigned to the coupled signals of Hαeq (II) and Hßeq (I ) whereas the downfield signals would correspond to Hαax (I) and Hßax (II). At T > Tc , the collapsed signals (not given in reference 12 ) for both α and ß protons are to be seen as a couple doublets. In fact, the δ values for the αeq and ßeq have been calculated at ca. 3.3 and 3.4 ppm, respectively. Under this condition (Tc > T ) the low filed signals were calculated at 4.6 and 4.7 ppm, The AB system showing higher intensity must corresponds to conformer I , i.e., the conformer with the equatorial methyl group. In the present worκ the NMR properties were calculated at the equilibrium geometries derived at B3LYP/6-31G(d,p) level, whereas the GIAO magnetic shielding tensors were obtained at B3LYP/6-311+G(d,p). To test the reliability of this level of theory, chemical shifts for 1,3-dithietane were calculated (see table 5) and compared with previously reported values" and the experimental data3-5. In a similar way, the one-bond 13C-11H coupling constants were derived for the parent compound. A close correspondence between the theoretical and experimental values were also found4,5. The calculated δ and 1JC-H NMR data for 1,3-dithiane correctly indicate the reverse Perlin effects at C2 and C5, and allow us to feel confident in predicting the 1H-NMR spectra of both conformers. Table 6 shows both the predicted chemical shifts and the spin-spin 13C-1H coupling constants for the conformers I and II of METDIT. The 8 values for I and II depart slightly from the corresponding values found for 1,3-dithiane, whereas variations of ca. 2-3 Hz were found for the calculated 1JC-H coupling constants at the C2 and C5 implying that spin-spin coupling constants are more sensitive to the changes occurring in the heterocyclic ring upon substitution. In both conformers the results indicate that 1JC-Hax > 1JC-Heq and thereby a "reverse Perlin" effect is operating on both C2 and C5, likewise in the parent 1,3-dithiane. Additionally, no linear correlation between coupling constants and bond distances has been found. In fact, differences of ca. 12.3 and 10.1 Hz between 1J2C-Hax and 1JC2-Heq for conformers I and II respectively, are not reflected in the axial and equatorial C2 - H bond distances where the corresponding differences is less than 0.004 Å. The C5 - He is ca. 0.004Å longer than the axial C - H bond in conformer I and ca 0. 007Å in II. The experimental data found in the parent 1,3-dithiane supports well our findings in both conformers. Alabugin6 suggests that the elongation of the equatorial bond could be explained in terms of dominant σC5 - Heq (σ*C - S two-electron/two-orbital hyperconjugation interactions. In fact, the second order perturbation energy (E(2)) for such interactions are ca. 6.79 and 6.57 Kcal/mol for I and II, respectively. The reverse interactions, i.e., σC - S Cσ*C5 - Heq are less favored (E(2)) = 2.62 and 2.92 Kcal/mol for I and II, respectively). Accordingly, the delocalization of electron density from the donor σC5 - Heq to the acceptor σ*C - S orbital is large enough to induce an elongation of the equatorial C-H bond, in both conformers, producing a weaκening of such a bond and thereby a smaller spin-spin coupling constant ( see table 6). On the other hand, it is interesting to see how conformer I is apparently stabilized by a pair of hyperconjugation interactions. Considering the main interactions derived from the NBO analysis, it can be realized that the magnitudes of σC6 - Hax → σ5 - Hax interactions in I and II are ca. 3.33 and 0.59 Kcal/mol, implying that the C4- C5-C6 group forming the upper part of the chair force the methyl group to lie equatorially. In conformer II the Ci - Hax (i= 5 or 6) bonds are not antiperiplanar and the interaction energy is not important ( 0.59 Kcal/mol). However, the σC4 - Hax σ*C5 - Hax interaction occurring in II only and completely equivalent to the interaction found in I, possesses an energy of ca. 3.67 and thereby would produce a counterbalance of the stabilizing factor found in I. The interaction of the axial ethyl group and the sulfur lone pairs of electrons910 in I can be inferred from the n s(3)σ*C4- C12 hyperconjugation interaction with a magnitude of ca.5.78 Kcal/mol. This interaction does not exist in II. On the other hand, the axial position of the methyl group in II is clearly the result of the ns(1) σ*C6 - C20 interaction with an energy of ca. 5.09 Kcal/mol and that is absent in I.


The calculations carried out on the conformers I and II of 4-ethyl-6-methyl-l,3-diethane, allow to draw some interesting conclusions:

1.- The gas phase ab initio calculations indicate that the conformers I and II posses a chair 5C2 and 2C5 ,respectively
2.- In conformer I, the position of the alkyl groups exert a strong influence in the regular structure of the 1,3-dithiane ring, whereas in II the heterocyclic ring remains fairly undistorted.
3.- Stereoelectronic effects are important in stabilizing the structure 5C2 of I.
4.- Calculations of the energies of both conformers at second order perturbation Meller- Plesset electron correlation level and employing a basis set that includes diffusion and polarization functions such as 6-311+G** are necessary for the good description of the energetics of this molecular system.
5.- The ab initio calculations indicate that conformer II would be the predominant species, in the gas phase and in low and high polarity solvents like CS2, CHC13 and DMSO
6.- It is suggested that conformer I would achieve similar concentration to conformer II at ca. -90° C due to the κinetic effect controlling the interconversion reaction.
7.- The Transition state (TS) looκs like conformer I since the methyl and ethyl groups bonded to C6 and C4, respectively remain in these positions. In fact, animation of the imaginary vibrational mode indicates that S1 is the only ring atom presenting a large departure from its original position. This reasoning is complemented with the calculated value of the Brönsted coefficient (ß) of ca. 0.45 and TS would resembles the reactant.
8.- The study of the solvent effect on the activation energy for the forward (Reactant TS) reaction shows that the activation energy does not lower appreciably in the solvents tried here.
9.- The good correlation between the calculated 1H chemical shifts and one-bond spin- spin coupling constants for 1,3-dithiane at B3LYP/6-311+G**// B3LYP/6-31G** level and the experimental data, convinced us to predict the NMR properties for conformers I and II.
10.- In both conformers a reverse Perlin effect seems to be operating at C2 and C5. C4 and C6 protons cannot be analyzed since H atoms have been replaced by either a methyl or ethyl group.


This Workwas supported by an operating grant (N°. 203.021.019-1.0) from Universidad de Concepción ,Chile.



1.      E. L Eliel, R. O. Hutchins., J. Am. Chem. Soc 91, 2703, (1969)        [ Links ]

2.      E. Juaristi, Acc. Chem. Rev. 22, 357, (1989)        [ Links ]

3.      E. Juarist, G. Cuevas, A. Vela, J. Am. Chem. Soc. 116, 5796, (1994)        [ Links ]

4.      G. Cuevas, E. Juaristi, A. Vela., J. Mol.Struct. (THEOCHEM) 418, 231, (1997)        [ Links ]

5.      G. Cuevas, E. Juaristi, A. Vela, J. Phys. Chem. 103, 932, (1999)        [ Links ]

6.      I. V. Alabugin, J. Org. Chem. 65, 3910, (2000)        [ Links ]

7.      F. Freeman, J. Le KT J. Phys. Chem. A., 107, 2908, (2003)        [ Links ]

8.      H.T. Kalff, C. Romers, Acta Cryst. 20, 490, (1966)        [ Links ]

9.      G. Apaydin, V.Aviyente, T.Varnali, M.F.Ruiz-Lopez, J. Mol. Struct. (THEOCHEM), 418, 113, (1997)        [ Links ]

10.    G. Cuevas, E. Juaristi, J. Am. Chem. Soc. 124, 13088, (2002)        [ Links ]

11.    J. Gelan, M. Anteunis, Bull. Soc, Chim, Beiges., 77, 423, (1968)        [ Links ]

12.    J. Gelan, M. Anteunis., Bull. Soc. Chim. Beiges. 78; 599,(1969)        [ Links ]

13.    J.Tomasi, M. Pérsico, Chem. Rev. 94, 2027, (1994)        [ Links ]

14.    M.T. Canees, V. Mennucci, J.Tomasi, J. Chem. Phys. 107, 3032, ( 1997)        [ Links ]

15.    V. Barone, M. Cossi, J.Tomasi, J.Chem. Phys., 107, 3210, (1997)        [ Links ]

16.    V. Barone, M. Cossi, J. Tomasi., J. Comput. Chem. 19, 404, ( 1998)        [ Links ]

17.    A.E. Reed, L.A. Curtus, F. Weinhold, Chem. Rev. 88, 899, (1988)        [ Links ]

18.    M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. N. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. NaKai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A.  J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewskki, S. Dapprich, A. D. Daniels, M. C. Strain, 0. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B.  Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian 03, Revision C.02 Gaussian, Inc., Wallingford CT, 2004.        [ Links ]

19.    J.G. Contreras, S.T. Madariaga, J. Phys. Org. Chem. 16, 47, (2003)        [ Links ]

20.    J. Foresman, A. Frisch, " Exploring Chemistry with Electronic Structure Methods", second ed., Gausian Inc., Pittsburgh, PA, 1996        [ Links ]

21.   K. Wolisky, J.F. Hilton, P. Pulay, J. Am. Chem. Soc, 112, 8251, (1990)        [ Links ]

22.    J.R. Cheeseman, G.W. Trucks, T.A. Keith, M.J. Frisch, J. Chem. Phys., 104, 5497, (1996)        [ Links ]

23.    I.V. Alabugin , T.A. Zeidan , J. Am. Chem. Soc, 124, 3175, (2002)        [ Links ]

24.    Gauss View, Revision 3.09, Gaussian Inc., Wallingford CT, 2004.        [ Links ]

25.    C.Gonzalez, H.B. Schlegel, J.Phys. Chem. 94: 5523,(1990)        [ Links ]

26.    R.A. Markus, Annu. Rev. Phys. Chem. 15, 155, (1964)        [ Links ]

27.    J.E. Leffler, J. Org. Chem., 20, 1202, (1955);         [ Links ] Science 117, 340, (1953)        [ Links ]

28.    G.S. Hammond, J. Am. Chem. Soc, 11, 334, (1955)        [ Links ]

29.    M. Sola, A. Toro-Labbe, J. Chem. Phys. A, 103, 8847, (1999)        [ Links ]

30.    F.A. Bulat, A. Toro-Labbe, J. Phys, Chem. A, 107, 3087, ( 2003)        [ Links ]


(Received 10th April 2007 - Accepted 26th June 2007)

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