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A theoretical study of the solvent effects in ethylene oxide: Hydrofluoric acid complex using continuum and new discrete models
Journal of Molecular Structure: THEOCHEM 802 (2007) 91–97 www.elsevier.com/locate/theochem
A theoretical study of the solvent effects in ethylene oxide: Hydrofluoric acid complex using continuum and new discrete models B.G. Oliveira
a,*
, R.C.M.U. Arau´jo a, A.B. Carvalho a, M.N. Ramos b, M.Z. Hernandes c, K.R. Cavalcante d
a Departamento de Quı´mica, Universidade Federal da Paraı´ba 58036-300, Joa˜o Pessoa – PB, Brazil Departamento de Quı´mica Fundamental, Universidade Federal de Pernambuco 50739-901, Recife – PE, Brazil Departamento de Cieˆncias Farmaceˆuticas, Universidade Federal de Pernambuco 50740-521, Recife – PE, Brazil d Centro de Informa´tica, Universidade Federal de Pernambuco 50732-970, Recife – PE, Brazil
b c
Received 21 December 2005; received in revised form 1 September 2006; accepted 4 September 2006 Available online 10 September 2006
Abstract Continuum and discrete models were combined for describe the solvent effects on the hydrogen bonded complex formed by ethylene oxide and hydrofluoric acid. In terms of continuum models, we applied the self-consistent reaction field polarized continuum model to verify the behavior of the C2H4O–HF heterocyclic hydrogen bonded complex in aqueous media in comparison to the gas phase by means of several parameters, such as intermolecular distance, Gibbs free energy and dipole moment. However, as widely known that continuum models are limited for describe adequately specific interactions between solute and solvent, the new AGOA methodology supply this hindrance by determining hydration clusters around the solute molecule. Based on the analysis of the molecular electrostatic potential of the solute (C2H4O–HF), the AGOA provided hydration clusters from optimized geometry using B3LYP/6-311++G(d,p) calculations. The result obtained justifies satisfactorily the acid catalyzed open ring reactions of the ethylene oxide because the preferential nucleophilic water attack occurs on the methyl groups of the three-membered ring, whose interaction energies values had reached up to 292.0 kJ mol1. 2006 Elsevier B.V. All rights reserved. Keywords: Hydrogen complex; ACOR; Continuum; AGOA; MEP
1. Introduction The modern biochemical reveals an intimate connection between life process and the molecular structure [1]. In this context, the hydrogen bonding has been recognized as one of the most important non-covalent interactions, becoming then a fundamental key of researches in the physics, chemistry and biology [2–8]. The interest to study systems whose properties are derived from hydrogen bonding is allied undoubtedly to the several advanced techniques able to describe spectroscopy parameters [9,10] and solvent effects
*
Corresponding author. Tel.: +55 83 3321 9059. E-mail address: [email protected] (B.G. Oliveira).
0166-1280/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.09.002
[11,12], which are directly involved in the elucidation of physiochemical phenomenon and geometrical aspects [13], i.e., interaction energy and structural configurations between the solute and solvent molecules in the liquid state. In terms of heterocyclic compounds, it is well established that the chemistry of these molecules is an important focus in experimental and theoretical researches [14,15], mainly due the immense variety of reactions involving small rings, which we can cite the capacity of the ethylene oxide to interact with nucleophilic species, such as the water [16,17]. In this kind of reaction, the water molecules attack the methyl groups of the protonated ethylene oxide (1), providing the cleavage of the strained ring and the formation of the diolic compound [18–21], as presented in Fig. 1 (Reaction 1a). This reaction mechanism is so-called
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Fig. 1. ACOR reactions mechanism of the ethylene oxide (Reaction 1a) and the formation of the C2H4O–HF heterocyclic hydrogen bonded complex (Reaction 1b).
acid catalyzed open ring (ACOR) reactions and many studies have been documented about it, whose influence of the solvent (water) on the heterocyclic compound is considered an essential factor [22,23]. Thereby, the aim of this work is related to the theoretical study using continuum and new discrete models for evaluate the behavior of the solvent effect on the C2H4O–HF hydrogen complex (2) and characterize it as an intermediary precedent at the oxoniun ion in the ACOR reactions (Reaction 1b). In theoretical point of view, the first idea to evaluate the solvent effect started from dielectric model [24], which uses quantum mechanical approaches to treat the solute inserting it within a cavity molded by overlapping spheres. This approach is named as continuum model and its formalism was based on the classic works of Born [25], Onsager [26] and Kirkwood [27]. Thereby, recently other current implementations have been formulated and divulgated, such as PCM [28], COSMO [29] or SM [30] models. Although it is widely known that continuum methods have serious limitations for description of specific interactions between solute and solvent [32,33], even so Aquino et al. [31] obtained extremely satisfactory results in the study of the acetic acid dimer and some carbonyl groups through the PCM calculations. However, in general the limitation of the continuum methods to describe hydrogen bonds can be partially solved treating the solvent as individual molecules interacting with the solute through the parametric potential functions and statistical sampling techniques [34]. This proceeding is widely known by means of the Monte Carlo (MC) and Molecular Dynamics (MD) methods [35,36]. Indeed, the interactions between solute and solvent are entirely described using MC and DM and hence the inner conditions of the liquid configurations are quite deciphered [37], but these methodologies dispend great computational effort due the large number of degrees of freedom required for the solvent. In spite of this, Hernandes et al. [38] developed an alternative approach to evaluate the solvent effects on the polar solutes by generating hydration clusters. This new proce-
dure is assigned as AGOA and its implementation is established only upon the analysis of the molecular electrostatic potential (MEP) of the solute molecule, of course assuming that the electrostatic effects [39] are the most important interactions between a polar solute and water molecules. Thus, in the purpose to study the solvent effects on the C2H4O–HF heterocyclic hydrogen complex using discrete models, the use of AGOA methodology is timely and must be worthwhile, once the Lennard–Jones force fields are difficult to be determined, mainly for systems such as the C2H4O–HF hydrogen complex. Actually, even though the force field can be determined through the empirical parameters [40] or ab initio calculations [41], the computational effort used by MC and MD is normally high to study the solvent effect on the C2H4O–HF hydrogen complex. 2. Computational methods The geometry optimization of the C2H4O–HF heterocyclic hydrogen complex was carried out with the GAUSSIAN 98W [42] program using the B3LYP/6-311++G(d,p) theoretical level. The initial optimized geometry for the C2H4O–HF heterocyclic hydrogen bonded complex was processed without the solvent effects. In a further step and using the SCRF-PCM continuum model [43], the optimization was again performed to determinate the subject properties of the C2H4O–HF complex in aqueous media. In PCM approach, the values of the water dielectric constant (e) and the solution temperature used here were 78.39 and 298.15 K, respectively. Thus, the PCM model calculates the molecular free energy in solution as the sum over the electrostatic (ES), dispersion–repulsion (DR) contributions to the free energy and the cavitation energy (CAV), as can be seen in the following equation: GSOL ¼ GES þ GDR þ GCAV
ð1Þ
In terms of the new discrete model, the application of the AGOA methodology was executed using the AGOA 3.0 program [44], which takes the CUBE file obtained through
B.G. Oliveira et al. / Journal of Molecular Structure: THEOCHEM 802 (2007) 91–97
the optimized geometry of the C2H4O–HF complex in gas phase using the B3LYP/6-311++G(d,p) calculations. The CUBE file is calculated by GAUSSIAN program and contains the molecular electrostatic potential (MEP) of the solute molecule calculated within the 3D-grid that surrounds it. To build the hydration clusters, the AGOA methodology use the MEP of the solute molecule within the tridimensional grid (3D-grid) containing 203 = 8000 points with the ˚ · 20 A ˚ · 20 A ˚ , centered at the following dimensions, 20 A solute, as can be visualized in Fig. 2. We can observe that the 3D-grid involve completely the C2H4O–HF complex and the whole MEP fields can be entirely described. Thus, starting from the CUBE points and using the TIP4P model [45], the interaction between the solute and water molecules is ruled according with the following equation: Eðsolute H2 OÞ ¼ ~ lrU
ð2Þ
where ~ l is the dipolar moment of the water molecule and $U is the electrostatic potential gradient field described by finite differences in the 3D-grid points. To grants a dynamic arrangement to determinate the interaction between solute and solvent, the AGOA program has stored internally default values for the cutoff radii, which corre˚ , 2.0 A ˚, spond for H, C, N, O and F atoms, the 1.3 A ˚ ˚ ˚ 2.0 A, 2.0 A and 1.8 A values [38], respectively. After the generation of the hydration clusters, the DEWC interaction energy for each C2H4O–HF complex (solute:water) configurations can be determined as follow: DEWC ¼ ETOTAL ESOLUTE EWATER
ð3Þ
where the ETOTAL, ESOLUTE and EWATER corresponds to the single-point calculations of the solute–water dimer (C2H4O–HF), isolated solute and individual water molecule, respectively. All interaction energy values were evalu-
93
ated using the Boys and Bernardi BSSE counterpoise method [46]. Thus, we obtained the DEWC-CORR corrected interaction energy: DEWCCORR ¼ DEWC BSSE
ð4Þ
3. Results and discussion 3.1. SCRF-PCM: structure and solvation properties As already mentioned, the first objective of this work concern into describes the solvent effect on the C2H4O– HF heterocyclic hydrogen complex using the SCRF-PCM continuum model. So, Table 1 presents structural, electronic and thermodynamics properties in gas and aqueous phases using B3LYP/6-311++G(d,p) calculations. Analyzing the hydrogen bond R(OÆÆHF) in gas phase, the theoretical ˚ are in good agreement with the experiresult of 1.6623 A ˚ [47]. However, as widely known mental value of 1.70 A that the presence of the acid specie catalyze the ACOR process of the ethylene oxide [48], the R(OÆÆHF) value of ˚ in aqueous medium is really shorter in compari1.5099 A son to the result in gas phase. Under this condition, the stronger interaction in aqueous medium between the ethylene oxide and hydrofluoric acid provide a better efficiency
Table 1 lÞ, Hydrogen bond distances (R(O HF)), dipole moment increment (D~ Gibbs free energies (DG) of the C2H4O–HF heterocyclic hydrogen complex in gas and liquid phase using B3LYP/6-311++G(d,p) calculation levels Parameters
C2H4O–HF Gas
R(O HF) D~ l DG
Water a
1.6572 (1.7000) 0.4587 4.66
1.5099 1.042 14.00
˚ ); D~ R(O HF) values are given in angstro¨ns (A l values are given in Debye (D); DG values are given in kJ mol1; experimental value in parenthesis. a Ref. [47].
Fig. 2. 3D-grid of the MEP for the C2H4O–HF heterocyclic hydrogen bonded complex.
Fig. 3. Solvent accessible surface (SAS) traced out by the center of the probe representing a water solvent molecule. The solvent excluded surface (SES) is the topological boundary of the union of all possible probes that do not overlap with the molecule.
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Fig. 4. MEP isosurfaces for the C2H4O–HF heterocyclic hydrogen bonded complex. The potential energy levels are +0.5 a.u. and 0.5 a.u. for transparent and meshed isosurfaces, respectively.
of the ACOR reactions. This can be also demonstrated by means of the variation in the Gibbs energy (DG) from 4.66 kJ mol1 in gas phase up to 14 kJ mol1 in solution. In fact, the aqueous medium dispends much more energy to form the (O HF) hydrogen bond due the interactions provided by effect of the water molecules within the continuum cavity.
As well established that electrostatic potential is the main term used to determine the molecular energy of the hydrogen bonded complexes and consequently its intermolecular energy also is ruled by polarity phenomena [39], the solvent effect must furnish a pronounced distortion in the polarity on the C2H4O–HF complex. Indeed, this is demonstrated by the D~ l dipole moment increments, whose value of 1.042 D in water is larger than 0.4587 D in the gas phase. Of course that the polarity is responsible by decrease of the hydrogen bond distance, although the cluster of discrete molecules is replaced in the continuum field by Sphere Probe Balls (SPB) rolling on the van der Waals surface, making it difficult then the analysis of the Accessible Surface (SAS) and hence to get a good description of the specific interactions between the water molecules and solute, as can be seen in Fig. 3. In this insight, the main question of the continuum model is related at definition of the cavity size. In practice way, the van der Waals or Pauling radii [49] are applied for determination of the cavity size and its shape is modeled by overlapping spheres centered on the nuclei of the atoms of the solvated molecule. In a further steps, the subsequent spheres are not properly centered on the nucleus of the atoms, so the van der Waals radii are multiplied by a scale factor f = 1.2 (for aqueous solutions) obtained through the United Atom Topological Model. The scale factor is usually applied in the routine of GAUSSIAN PCM calculations and its applicability concern into minimizes the effects of the dielectric properties in the first solvation shell as the bulk of the solvent [50]. From this approach, in fact is easily observed that the specific interactions between the solute (C2H4O–HF) and the water molecules are poorly described. Thus, it is necessary to apply the AGOA meth-
Fig. 5. Hydration cluster structures on the C2H4O–HF heterocyclic hydrogen bonded complex.
B.G. Oliveira et al. / Journal of Molecular Structure: THEOCHEM 802 (2007) 91–97 95 Table 2 BSSE amounts, DEWC uncorrected and DEWC-CORR corrected hydration energies for the C2H4O–HF heterocyclic hydrogen complex using the AGOA methodology and the B3LYP/6-311++G(d,p) calculation levels Number of water molecules
1 2 3 4 5 6 7 8 9 10 11 12 13 14
C2H4O–HF DEWC / BSSE MEPmax
DEWC / BSSE MEPmin
DEWC-CORRMEPmax
DEWC-CORRMEPmin
299.4 287.8 241.8 241.8 181.3 167.4 160.3 159.7 156.8 156.8 139.5 136.7 81.3 77.6
14.7 43.2 1.9 1.9 9.0 4.8 5.6 17.2 9.9 9.9 4.2 0.7 3.9 47.1
292.0 282.2 237.4 237.4 175.6 162.4 156.0 154.1 151.2 151.2 135.5 132.3 78.4 74.0
11.4 37.9 4.8 4.8 5.7 6.3 8.3 13.8 6.2 6.2 0.6 2.4 1.1 44.1
(7.4) (5.6) (4.4) (4.4) (5.7) (5.0) (4.3) (5.6) (5.6) (5.6) (4.0) (4.4) (2.9) (3.6)
(3.3) (5.3) (2.9) (2.9) (3.3) (1.5) (2.7) (3.4) (3.7) (3.7) (3.6) (3.1) (2.8) (3.0)
All values are given in kJ mol1; BSSE values are given in parentheses.
odology to identify probable solvation sites in the C2H4O– HF heterocyclic hydrogen complex and hence simulate the ACOR reactions. 3.2. AGOA methodology: energies and hydration distances Considering the C2H4O–HF hydrogen bonded complex (2) in ACOR reactions (see Fig. 1), the solvent effects are taking into account by the application of AGOA methodology with analysis of the MEP of the solute wherein the maximum (+0.5 a.u.) and minimum (0.5 a.u.) regions are translated according to the transparent and meshed isosurfaces, respectively, see Fig. 4. Based on the gradient of the electrostatic potential and analyzing the SASA over the MEP regions [51], the AGOA methodology locates the water molecules around the solute, as can be observed in Fig. 5. In this simulation, we observed that 2 groups of 14 water molecules are aligned respectively at the maximum and minimum MEP regions of the C2H4O–HF complex. As expected, these configurations of the water molecules corroborate the experimental aspects of ACOR reactions because in the region of the maximum electrostatic potential (MEPmax) the water molecules are orientated with its oxygen atoms to interact with hydrogen atoms of the methyl groups (–CH2–), whereas in region of the minimum electrostatic potential (MEPmin) the hydrogen atoms of the water molecules are pointed toward to the fluoride atom. Physically, this panorama indicate that the dipole moment of the water molecules are oriented antiparallely toward to the MEPmax and parallely to the MEPmin (see Eq. (2)). However, according to the proposal of the Hernandes et al., AGOA not optimize the geometry of the solute, as well as not evaluate physicochemical properties inherent to the solvent effects but provides hydration clusters at low computational cost and, thereby indicate configurational aspects of the water molecules around the solute
symbolizing the effects of the first solvation shell. In this context, from single-point calculations for the whole set of AGOA configurations (see Eq. (3)), the values of the DEWC-CORR interaction energies are presented in Table 2 and graphically illustrated in Fig. 6. Considering that each DEWC value was corrected by BSSE method whose results are also gathered in parentheses in Table 2, the interaction energies on the MEPmax vary drastically in range from 74.0 kJ mol1 up to 292.0 kJ mol1. Albeit cyclic ethers such as ethylene oxide are widely known by its peculiar reactivity [52], even though these interaction energies are very high, more than any hydrogen bonding, covalent or even ionic bonds. Otherwise, the DEWC-CORR values in the MEPmin are the lowest, providing a slight stabilization to the C2H4O–HF complex. Thus, in concordance with the values of the interaction energies presented above, the greater stability for the C2H4O–HF complex within the ACOR reactions is observed really in the MEPmax region,
Fig. 6. Plot of the hydration energies for the C2H4O–HF heterocyclic hydrogen bonded complex.
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Fig. 7. Illustration of hydrogen bonded structures in the MEPmax and MEPmin generated in the AGOA procedure in and comparison with the hydration cluster shown in Fig. 5.
corroborating then energetically with the experimental behavior of ethylene oxide compound in aqueous phase [53]. Moreover, from two groups of hydration clusters by containing 14 water molecules in each one (H2O(n), with n = 1–14), the correspondent more stable configurations for both MEPmax and MEPmin are indicated by H2O(5) and H2O(10) molecules, respectively, which are featured in Fig. 7. In terms of the interaction distances of 1.61761 ˚ for the R(H H2O(5)) and R(F H2O(10)) and 2.142 A interactions in the MEPmax and MEPmin, respectively, it is clearly observed that the MEPmax is the preferential region to the attacks of the water molecules wherein the H2O(5) interacts with both Ha axial hydrogen atoms of ˚ obtained the methyl groups. So, the distance of 2.142 A by AGOA provide a less interaction of the H2O(10) with the HF specie, in other words the cleavage of the strained ring is really more pronounced by attacks of the water molecules in the MEPmax. In summary, besides to provide a good agreement of the solvent effects for the C2H4O–HF complex, AGOA is considered a flexible methodology due to the low computational cost required to generate the water clusters because only electrostatic effects are into taken account. In fact, this is a decisive point because whether apply traditional discrete methods such as MC or DM, the computational demand is extremely high due a large number of degree of freedom for the solvent. Notwithstanding, it should be emphasizes that as MEP calculations is used by AGOA, in present time its application is centered for small and medium systems because is required a considerable computational effort for the quantum calculations of the MEP for larger solute molecules. 4. Conclusions From SCRF calculations of structural, electronic and thermodynamics properties, the study of the solvation effects in the reaction step involving the interaction between the ethylene oxide and hydrofluoric acid prove that the presence of water molecules provide a stronger
interaction in the C2H4O–HF heterocyclic hydrogen bonded complex. Furthermore, using the new discrete AGOA methodology to obtain hydration clusters on the C2H4O– HF system, the analysis of the molecular electrostatic potential (MEP) indicates two important MEP fields, which correspond to the methyl (–CH2–) groups in the ethylene oxide (C2H4O), as well as the fluoride atom in the hydrofluoric acid. Thus, from clusters generated by the AGOA methodology, the DEWC-CORR hydration energies are higher for MEPmax in comparison to the MEPmin. These results are in good agreement with the experimental behavior of the acid catalyzed open ring reactions wherein the nucleophilic attack occurs through the interactions of water molecules with the methyl groups in the three-membered ring. Acknowledgements The authors gratefully acknowledge partial financial support from the Brazilian Funding agencies CAPES and CNPq. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
G. Alagona, C. Ghio, S. Monti, J. Chem. Phys. B 109 (2005) 16918. C.L. Perrin, J.B. Nielson, Ann. Rev. Phys. Chem. 48 (1997) 511. T.S. Zwier, Ann. Rev. Phys. Chem. 47 (1996) 205. B.M. Ladanyi, M.S. Skaf, Ann. Rev. Phys. Chem. 44 (1993) s135. G.A. Jeffrey, An introduction to Hydrogen Bonding, Oxford University Press, New York, 1997. P. Hobza, R. Zabradnik, Intermolecular Complexes, Elsevier Science, New York, 1988. S. Scheiner, Hydrogen Bonding: A Theoretical Perspective, Oxford University Press, Oxford, 1997. G.A. Jeffrey, W. Saeger, Hydrogen Bonding in Biological Structures, Springer, Berlin, 1991. N.S. Bayliss, E.G. McRae, J. Phys. Chem. 58 (1954) 1002. E.G. McRae, J. Phys. Chem. 61 (1957) 562. C. Reichardt, Solvent Effects in Organic Chemistry, Verlag Chemie, Weinheim, New York, 1979. S. Basu, Adv. Quantum Chem. 1 (1964) 145. V. Bertolasi, L. Nanni, P. Gilli, V. Ferretti, G. Gilli, Y.M. Issa, O.E. Sherif, New J. Chem. 18 (1994) 251.
B.G. Oliveira et al. / Journal of Molecular Structure: THEOCHEM 802 (2007) 91–97 [14] M. Torres, E.M. Lown, H.E. Gunning, O.P. Strausz, Pure Appl. Chem. 52 (1980) 1623. [15] O. Mo´, J.L.G. de Paz, M. Yanez, J. Phys. Chem. 91 (1987) 6484. [16] R. Breslow, Acc. Chem. Res. 6 (1973) 393. [17] A. Greenberg, J.F. Liebman, Strained Organic Molecules, Academic Press, New York, 1978. [18] R.E. Parker, N.E. Issacs, Chem. Rev. 59 (1959) 737. [19] M.J. Eis, J.E. Wrobel, B. Ganem, J. Am. Chem. Soc. 106 (1984) 3693. [20] M.L. Vasconcellos, D. Desmae¨le, P.R.R. Costa, J. d’Angelo, Tetrahedron Lett. 33 (1992) 4921. [21] J.E. Early, C.E. O’ Rourke, L.B. Clapp, J.D. Edwards, B.C. Lawes, J. Am. Chem. Soc. 80 (1958) 3458. [22] H. Kotsuki, T. Shimanouchi, R. Ohshima, S. Fujiwara, Tetrahedron 54 (1998) 2709. [23] C. Baylon, G. Prestat, M.-P. Heck, C. Mioskowski, Tetrahedron Lett. 41 (2000) 3833. [24] J. Tomasi, M. Persico, Chem. Rev. 94 (1994) 2027. [25] M. Born, Phys. Z 1 (1920) 45. [26] L. Onsager, J. Am. Chem. Soc. 58 (1936) 1486. [27] J. Kirkwood, J. Chem. Phys. 3 (1935) 300. [28] S. Miertus, E. Scrocco, J. Tomasi, Chem. Phys. 55 (1981) 117. [29] A. Klamt, G. Schu¨u¨rmann, J. Chem. Soc. Perkin Trans. 2 (1993) 799. [30] C.J. Cramer, D.G. Truhlar, J. Am. Chem. Soc. 113 (1991) 8305. [31] A.J.A. Aquino, D. Tunega, G. Haberhauer, M.H. Gerzabek, H. Lischka, J. Phys. Chem. A 106 (2002) 1862. [32] O. Tapia, In Molecular Interactions, John Wiley & Sons, Chichester, 1982. [33] A. Papazyan, A. Warshel, J. Chem. Phys. 107 (1997) 7975. [34] D.W. Heermann, Computer Simulation Methods in Theoretical Physics, Springer-Verlag, New York, 1990.
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[35] M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1987. [36] M.K. Kalos, P.A. Whitlock, Monte Carlo Methods, John Wiley & Sons, New York, 1986. [37] J.P. Hansen, I.R. McDonald, Theory of Simple Liquids, Academic Press, London, 1986. [38] M.Z. Hernandes, J.B.P. da Silva, R.L. Longo, J. Braz, Chem. Soc. 13 (2002) 36. [39] H. Umeyama, K. Morokuma, J. Am. Chem. Soc. 99 (1977) 1316. [40] W.L. Jorgensen, J.M. Briggs, M.L. Contreras, J. Chem. Phys. 94 (1990) 1683. [41] S. Swaminathan, R.J. Whitehead, E. Guth, D.L. Beveridge, J. Am. Chem. Soc. 99 (1977) 7817. [42] M.J. Frisch et al.; Gaussian 98W (Revision A.1), Gaussian, Inc., Pittsburgh PA, 2001. [43] J. Tomasi, B. Mennucci, R. Cammi, Chem. Rev. 105 (2005) 2999. [44] M.Z. Hernandes, AGOA v 3.0, 2004. Available from:
A theoretical study of the solvent effects in ethylene oxide: Hydrofluoric acid complex using continuum and new discrete models B.G. Oliveira
a,*
, R.C.M.U. Arau´jo a, A.B. Carvalho a, M.N. Ramos b, M.Z. Hernandes c, K.R. Cavalcante d
a Departamento de Quı´mica, Universidade Federal da Paraı´ba 58036-300, Joa˜o Pessoa – PB, Brazil Departamento de Quı´mica Fundamental, Universidade Federal de Pernambuco 50739-901, Recife – PE, Brazil Departamento de Cieˆncias Farmaceˆuticas, Universidade Federal de Pernambuco 50740-521, Recife – PE, Brazil d Centro de Informa´tica, Universidade Federal de Pernambuco 50732-970, Recife – PE, Brazil
b c
Received 21 December 2005; received in revised form 1 September 2006; accepted 4 September 2006 Available online 10 September 2006
Abstract Continuum and discrete models were combined for describe the solvent effects on the hydrogen bonded complex formed by ethylene oxide and hydrofluoric acid. In terms of continuum models, we applied the self-consistent reaction field polarized continuum model to verify the behavior of the C2H4O–HF heterocyclic hydrogen bonded complex in aqueous media in comparison to the gas phase by means of several parameters, such as intermolecular distance, Gibbs free energy and dipole moment. However, as widely known that continuum models are limited for describe adequately specific interactions between solute and solvent, the new AGOA methodology supply this hindrance by determining hydration clusters around the solute molecule. Based on the analysis of the molecular electrostatic potential of the solute (C2H4O–HF), the AGOA provided hydration clusters from optimized geometry using B3LYP/6-311++G(d,p) calculations. The result obtained justifies satisfactorily the acid catalyzed open ring reactions of the ethylene oxide because the preferential nucleophilic water attack occurs on the methyl groups of the three-membered ring, whose interaction energies values had reached up to 292.0 kJ mol1. 2006 Elsevier B.V. All rights reserved. Keywords: Hydrogen complex; ACOR; Continuum; AGOA; MEP
1. Introduction The modern biochemical reveals an intimate connection between life process and the molecular structure [1]. In this context, the hydrogen bonding has been recognized as one of the most important non-covalent interactions, becoming then a fundamental key of researches in the physics, chemistry and biology [2–8]. The interest to study systems whose properties are derived from hydrogen bonding is allied undoubtedly to the several advanced techniques able to describe spectroscopy parameters [9,10] and solvent effects
*
Corresponding author. Tel.: +55 83 3321 9059. E-mail address: [email protected] (B.G. Oliveira).
0166-1280/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.09.002
[11,12], which are directly involved in the elucidation of physiochemical phenomenon and geometrical aspects [13], i.e., interaction energy and structural configurations between the solute and solvent molecules in the liquid state. In terms of heterocyclic compounds, it is well established that the chemistry of these molecules is an important focus in experimental and theoretical researches [14,15], mainly due the immense variety of reactions involving small rings, which we can cite the capacity of the ethylene oxide to interact with nucleophilic species, such as the water [16,17]. In this kind of reaction, the water molecules attack the methyl groups of the protonated ethylene oxide (1), providing the cleavage of the strained ring and the formation of the diolic compound [18–21], as presented in Fig. 1 (Reaction 1a). This reaction mechanism is so-called
92
B.G. Oliveira et al. / Journal of Molecular Structure: THEOCHEM 802 (2007) 91–97
Fig. 1. ACOR reactions mechanism of the ethylene oxide (Reaction 1a) and the formation of the C2H4O–HF heterocyclic hydrogen bonded complex (Reaction 1b).
acid catalyzed open ring (ACOR) reactions and many studies have been documented about it, whose influence of the solvent (water) on the heterocyclic compound is considered an essential factor [22,23]. Thereby, the aim of this work is related to the theoretical study using continuum and new discrete models for evaluate the behavior of the solvent effect on the C2H4O–HF hydrogen complex (2) and characterize it as an intermediary precedent at the oxoniun ion in the ACOR reactions (Reaction 1b). In theoretical point of view, the first idea to evaluate the solvent effect started from dielectric model [24], which uses quantum mechanical approaches to treat the solute inserting it within a cavity molded by overlapping spheres. This approach is named as continuum model and its formalism was based on the classic works of Born [25], Onsager [26] and Kirkwood [27]. Thereby, recently other current implementations have been formulated and divulgated, such as PCM [28], COSMO [29] or SM [30] models. Although it is widely known that continuum methods have serious limitations for description of specific interactions between solute and solvent [32,33], even so Aquino et al. [31] obtained extremely satisfactory results in the study of the acetic acid dimer and some carbonyl groups through the PCM calculations. However, in general the limitation of the continuum methods to describe hydrogen bonds can be partially solved treating the solvent as individual molecules interacting with the solute through the parametric potential functions and statistical sampling techniques [34]. This proceeding is widely known by means of the Monte Carlo (MC) and Molecular Dynamics (MD) methods [35,36]. Indeed, the interactions between solute and solvent are entirely described using MC and DM and hence the inner conditions of the liquid configurations are quite deciphered [37], but these methodologies dispend great computational effort due the large number of degrees of freedom required for the solvent. In spite of this, Hernandes et al. [38] developed an alternative approach to evaluate the solvent effects on the polar solutes by generating hydration clusters. This new proce-
dure is assigned as AGOA and its implementation is established only upon the analysis of the molecular electrostatic potential (MEP) of the solute molecule, of course assuming that the electrostatic effects [39] are the most important interactions between a polar solute and water molecules. Thus, in the purpose to study the solvent effects on the C2H4O–HF heterocyclic hydrogen complex using discrete models, the use of AGOA methodology is timely and must be worthwhile, once the Lennard–Jones force fields are difficult to be determined, mainly for systems such as the C2H4O–HF hydrogen complex. Actually, even though the force field can be determined through the empirical parameters [40] or ab initio calculations [41], the computational effort used by MC and MD is normally high to study the solvent effect on the C2H4O–HF hydrogen complex. 2. Computational methods The geometry optimization of the C2H4O–HF heterocyclic hydrogen complex was carried out with the GAUSSIAN 98W [42] program using the B3LYP/6-311++G(d,p) theoretical level. The initial optimized geometry for the C2H4O–HF heterocyclic hydrogen bonded complex was processed without the solvent effects. In a further step and using the SCRF-PCM continuum model [43], the optimization was again performed to determinate the subject properties of the C2H4O–HF complex in aqueous media. In PCM approach, the values of the water dielectric constant (e) and the solution temperature used here were 78.39 and 298.15 K, respectively. Thus, the PCM model calculates the molecular free energy in solution as the sum over the electrostatic (ES), dispersion–repulsion (DR) contributions to the free energy and the cavitation energy (CAV), as can be seen in the following equation: GSOL ¼ GES þ GDR þ GCAV
ð1Þ
In terms of the new discrete model, the application of the AGOA methodology was executed using the AGOA 3.0 program [44], which takes the CUBE file obtained through
B.G. Oliveira et al. / Journal of Molecular Structure: THEOCHEM 802 (2007) 91–97
the optimized geometry of the C2H4O–HF complex in gas phase using the B3LYP/6-311++G(d,p) calculations. The CUBE file is calculated by GAUSSIAN program and contains the molecular electrostatic potential (MEP) of the solute molecule calculated within the 3D-grid that surrounds it. To build the hydration clusters, the AGOA methodology use the MEP of the solute molecule within the tridimensional grid (3D-grid) containing 203 = 8000 points with the ˚ · 20 A ˚ · 20 A ˚ , centered at the following dimensions, 20 A solute, as can be visualized in Fig. 2. We can observe that the 3D-grid involve completely the C2H4O–HF complex and the whole MEP fields can be entirely described. Thus, starting from the CUBE points and using the TIP4P model [45], the interaction between the solute and water molecules is ruled according with the following equation: Eðsolute H2 OÞ ¼ ~ lrU
ð2Þ
where ~ l is the dipolar moment of the water molecule and $U is the electrostatic potential gradient field described by finite differences in the 3D-grid points. To grants a dynamic arrangement to determinate the interaction between solute and solvent, the AGOA program has stored internally default values for the cutoff radii, which corre˚ , 2.0 A ˚, spond for H, C, N, O and F atoms, the 1.3 A ˚ ˚ ˚ 2.0 A, 2.0 A and 1.8 A values [38], respectively. After the generation of the hydration clusters, the DEWC interaction energy for each C2H4O–HF complex (solute:water) configurations can be determined as follow: DEWC ¼ ETOTAL ESOLUTE EWATER
ð3Þ
where the ETOTAL, ESOLUTE and EWATER corresponds to the single-point calculations of the solute–water dimer (C2H4O–HF), isolated solute and individual water molecule, respectively. All interaction energy values were evalu-
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ated using the Boys and Bernardi BSSE counterpoise method [46]. Thus, we obtained the DEWC-CORR corrected interaction energy: DEWCCORR ¼ DEWC BSSE
ð4Þ
3. Results and discussion 3.1. SCRF-PCM: structure and solvation properties As already mentioned, the first objective of this work concern into describes the solvent effect on the C2H4O– HF heterocyclic hydrogen complex using the SCRF-PCM continuum model. So, Table 1 presents structural, electronic and thermodynamics properties in gas and aqueous phases using B3LYP/6-311++G(d,p) calculations. Analyzing the hydrogen bond R(OÆÆHF) in gas phase, the theoretical ˚ are in good agreement with the experiresult of 1.6623 A ˚ [47]. However, as widely known mental value of 1.70 A that the presence of the acid specie catalyze the ACOR process of the ethylene oxide [48], the R(OÆÆHF) value of ˚ in aqueous medium is really shorter in compari1.5099 A son to the result in gas phase. Under this condition, the stronger interaction in aqueous medium between the ethylene oxide and hydrofluoric acid provide a better efficiency
Table 1 lÞ, Hydrogen bond distances (R(O HF)), dipole moment increment (D~ Gibbs free energies (DG) of the C2H4O–HF heterocyclic hydrogen complex in gas and liquid phase using B3LYP/6-311++G(d,p) calculation levels Parameters
C2H4O–HF Gas
R(O HF) D~ l DG
Water a
1.6572 (1.7000) 0.4587 4.66
1.5099 1.042 14.00
˚ ); D~ R(O HF) values are given in angstro¨ns (A l values are given in Debye (D); DG values are given in kJ mol1; experimental value in parenthesis. a Ref. [47].
Fig. 2. 3D-grid of the MEP for the C2H4O–HF heterocyclic hydrogen bonded complex.
Fig. 3. Solvent accessible surface (SAS) traced out by the center of the probe representing a water solvent molecule. The solvent excluded surface (SES) is the topological boundary of the union of all possible probes that do not overlap with the molecule.
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Fig. 4. MEP isosurfaces for the C2H4O–HF heterocyclic hydrogen bonded complex. The potential energy levels are +0.5 a.u. and 0.5 a.u. for transparent and meshed isosurfaces, respectively.
of the ACOR reactions. This can be also demonstrated by means of the variation in the Gibbs energy (DG) from 4.66 kJ mol1 in gas phase up to 14 kJ mol1 in solution. In fact, the aqueous medium dispends much more energy to form the (O HF) hydrogen bond due the interactions provided by effect of the water molecules within the continuum cavity.
As well established that electrostatic potential is the main term used to determine the molecular energy of the hydrogen bonded complexes and consequently its intermolecular energy also is ruled by polarity phenomena [39], the solvent effect must furnish a pronounced distortion in the polarity on the C2H4O–HF complex. Indeed, this is demonstrated by the D~ l dipole moment increments, whose value of 1.042 D in water is larger than 0.4587 D in the gas phase. Of course that the polarity is responsible by decrease of the hydrogen bond distance, although the cluster of discrete molecules is replaced in the continuum field by Sphere Probe Balls (SPB) rolling on the van der Waals surface, making it difficult then the analysis of the Accessible Surface (SAS) and hence to get a good description of the specific interactions between the water molecules and solute, as can be seen in Fig. 3. In this insight, the main question of the continuum model is related at definition of the cavity size. In practice way, the van der Waals or Pauling radii [49] are applied for determination of the cavity size and its shape is modeled by overlapping spheres centered on the nuclei of the atoms of the solvated molecule. In a further steps, the subsequent spheres are not properly centered on the nucleus of the atoms, so the van der Waals radii are multiplied by a scale factor f = 1.2 (for aqueous solutions) obtained through the United Atom Topological Model. The scale factor is usually applied in the routine of GAUSSIAN PCM calculations and its applicability concern into minimizes the effects of the dielectric properties in the first solvation shell as the bulk of the solvent [50]. From this approach, in fact is easily observed that the specific interactions between the solute (C2H4O–HF) and the water molecules are poorly described. Thus, it is necessary to apply the AGOA meth-
Fig. 5. Hydration cluster structures on the C2H4O–HF heterocyclic hydrogen bonded complex.
B.G. Oliveira et al. / Journal of Molecular Structure: THEOCHEM 802 (2007) 91–97 95 Table 2 BSSE amounts, DEWC uncorrected and DEWC-CORR corrected hydration energies for the C2H4O–HF heterocyclic hydrogen complex using the AGOA methodology and the B3LYP/6-311++G(d,p) calculation levels Number of water molecules
1 2 3 4 5 6 7 8 9 10 11 12 13 14
C2H4O–HF DEWC / BSSE MEPmax
DEWC / BSSE MEPmin
DEWC-CORRMEPmax
DEWC-CORRMEPmin
299.4 287.8 241.8 241.8 181.3 167.4 160.3 159.7 156.8 156.8 139.5 136.7 81.3 77.6
14.7 43.2 1.9 1.9 9.0 4.8 5.6 17.2 9.9 9.9 4.2 0.7 3.9 47.1
292.0 282.2 237.4 237.4 175.6 162.4 156.0 154.1 151.2 151.2 135.5 132.3 78.4 74.0
11.4 37.9 4.8 4.8 5.7 6.3 8.3 13.8 6.2 6.2 0.6 2.4 1.1 44.1
(7.4) (5.6) (4.4) (4.4) (5.7) (5.0) (4.3) (5.6) (5.6) (5.6) (4.0) (4.4) (2.9) (3.6)
(3.3) (5.3) (2.9) (2.9) (3.3) (1.5) (2.7) (3.4) (3.7) (3.7) (3.6) (3.1) (2.8) (3.0)
All values are given in kJ mol1; BSSE values are given in parentheses.
odology to identify probable solvation sites in the C2H4O– HF heterocyclic hydrogen complex and hence simulate the ACOR reactions. 3.2. AGOA methodology: energies and hydration distances Considering the C2H4O–HF hydrogen bonded complex (2) in ACOR reactions (see Fig. 1), the solvent effects are taking into account by the application of AGOA methodology with analysis of the MEP of the solute wherein the maximum (+0.5 a.u.) and minimum (0.5 a.u.) regions are translated according to the transparent and meshed isosurfaces, respectively, see Fig. 4. Based on the gradient of the electrostatic potential and analyzing the SASA over the MEP regions [51], the AGOA methodology locates the water molecules around the solute, as can be observed in Fig. 5. In this simulation, we observed that 2 groups of 14 water molecules are aligned respectively at the maximum and minimum MEP regions of the C2H4O–HF complex. As expected, these configurations of the water molecules corroborate the experimental aspects of ACOR reactions because in the region of the maximum electrostatic potential (MEPmax) the water molecules are orientated with its oxygen atoms to interact with hydrogen atoms of the methyl groups (–CH2–), whereas in region of the minimum electrostatic potential (MEPmin) the hydrogen atoms of the water molecules are pointed toward to the fluoride atom. Physically, this panorama indicate that the dipole moment of the water molecules are oriented antiparallely toward to the MEPmax and parallely to the MEPmin (see Eq. (2)). However, according to the proposal of the Hernandes et al., AGOA not optimize the geometry of the solute, as well as not evaluate physicochemical properties inherent to the solvent effects but provides hydration clusters at low computational cost and, thereby indicate configurational aspects of the water molecules around the solute
symbolizing the effects of the first solvation shell. In this context, from single-point calculations for the whole set of AGOA configurations (see Eq. (3)), the values of the DEWC-CORR interaction energies are presented in Table 2 and graphically illustrated in Fig. 6. Considering that each DEWC value was corrected by BSSE method whose results are also gathered in parentheses in Table 2, the interaction energies on the MEPmax vary drastically in range from 74.0 kJ mol1 up to 292.0 kJ mol1. Albeit cyclic ethers such as ethylene oxide are widely known by its peculiar reactivity [52], even though these interaction energies are very high, more than any hydrogen bonding, covalent or even ionic bonds. Otherwise, the DEWC-CORR values in the MEPmin are the lowest, providing a slight stabilization to the C2H4O–HF complex. Thus, in concordance with the values of the interaction energies presented above, the greater stability for the C2H4O–HF complex within the ACOR reactions is observed really in the MEPmax region,
Fig. 6. Plot of the hydration energies for the C2H4O–HF heterocyclic hydrogen bonded complex.
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Fig. 7. Illustration of hydrogen bonded structures in the MEPmax and MEPmin generated in the AGOA procedure in and comparison with the hydration cluster shown in Fig. 5.
corroborating then energetically with the experimental behavior of ethylene oxide compound in aqueous phase [53]. Moreover, from two groups of hydration clusters by containing 14 water molecules in each one (H2O(n), with n = 1–14), the correspondent more stable configurations for both MEPmax and MEPmin are indicated by H2O(5) and H2O(10) molecules, respectively, which are featured in Fig. 7. In terms of the interaction distances of 1.61761 ˚ for the R(H H2O(5)) and R(F H2O(10)) and 2.142 A interactions in the MEPmax and MEPmin, respectively, it is clearly observed that the MEPmax is the preferential region to the attacks of the water molecules wherein the H2O(5) interacts with both Ha axial hydrogen atoms of ˚ obtained the methyl groups. So, the distance of 2.142 A by AGOA provide a less interaction of the H2O(10) with the HF specie, in other words the cleavage of the strained ring is really more pronounced by attacks of the water molecules in the MEPmax. In summary, besides to provide a good agreement of the solvent effects for the C2H4O–HF complex, AGOA is considered a flexible methodology due to the low computational cost required to generate the water clusters because only electrostatic effects are into taken account. In fact, this is a decisive point because whether apply traditional discrete methods such as MC or DM, the computational demand is extremely high due a large number of degree of freedom for the solvent. Notwithstanding, it should be emphasizes that as MEP calculations is used by AGOA, in present time its application is centered for small and medium systems because is required a considerable computational effort for the quantum calculations of the MEP for larger solute molecules. 4. Conclusions From SCRF calculations of structural, electronic and thermodynamics properties, the study of the solvation effects in the reaction step involving the interaction between the ethylene oxide and hydrofluoric acid prove that the presence of water molecules provide a stronger
interaction in the C2H4O–HF heterocyclic hydrogen bonded complex. Furthermore, using the new discrete AGOA methodology to obtain hydration clusters on the C2H4O– HF system, the analysis of the molecular electrostatic potential (MEP) indicates two important MEP fields, which correspond to the methyl (–CH2–) groups in the ethylene oxide (C2H4O), as well as the fluoride atom in the hydrofluoric acid. Thus, from clusters generated by the AGOA methodology, the DEWC-CORR hydration energies are higher for MEPmax in comparison to the MEPmin. These results are in good agreement with the experimental behavior of the acid catalyzed open ring reactions wherein the nucleophilic attack occurs through the interactions of water molecules with the methyl groups in the three-membered ring. Acknowledgements The authors gratefully acknowledge partial financial support from the Brazilian Funding agencies CAPES and CNPq. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
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