- Email: [email protected]
Parametrization of the PCM model for calculating solvation free energy of anions in dimethyl sulfoxide solutions
8 April 2002
Chemical Physics Letters 355 (2002) 543–546 www.elsevier.com/locate/cplett
Parametrization of the PCM model for calculating solvation free energy of anions in dimethyl sulfoxide solutions Josefredo R. Pliego Jr., Jose M. Riveros
*
Instituto de Quımica, Universidade de S~ ao Paulo, Caixa Postal 26077, CEP 05513-970 S~ ao Paulo, SP, Brazil Received 28 January 2002
Abstract We report the first parametrization of a continuum model for the solvation of anions in DMSO solution. The present parameters used in conjunction with the PCM method predict the solvation free energy of 21 anions in DMSO solution with an average error of 1:2 kcal mol1 , and a S.D. for the average error of only 2:2 kcal mol1 . This low value of the S.D. shows that the present parametrization is capable of predicting accurate differences of the solvation free energies in DMSO solution and is reliable for modeling liquid phase chemical reactions. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Chemical properties of ions and molecules in the liquid phase are intrinsically related to solute– solvent interactions, and these interactions must be properly addressed in theoretical studies of chemical reactions in order to make reliable predictions. Approximate models that treat the solute by quantum mechanics and the solvent as a dielectric continuum surrounding the solute cavity are extensively used nowadays in the modeling of liquid phase chemical processes and properties [1–6].
*
Corresponding author. Fax: +55-11-3091-3888. E-mail addresses: [email protected] (J.R. Pliego [email protected] (J.M. Riveros).
Jr.),
Continuum models are practical and introduce several important properties of solute–solvent interactions, such as: (a) the dielectric constant of the solvent; (b) the charge distribution in the solute; and (c) the size and form of the solute cavity. The first property is intrinsic to the solvent, while the other two properties depend on the specific continuum model. However, a reliable continuum model must make use of an accurate charge distribution and a physically correct shape for the cavity. On the other hand, the size of the cavity must be empirically defined and nonelectrostatic terms need to be included in order to reproduce experimental solvation free energy data. This empirical determination of the size of the cavity is due to the simplified treatment of the solvent, considered to be a dielectric continuum. As a matter of fact, it has been shown that in continuum
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 3 7 7 - 9
544
J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 355 (2002) 543–546
models the cavity of the solute is intrinsically related to each specific solvent [7]. Thus, a scale factor must be applied to the cavity in order to obtain a physically meaningful solute–solvent interaction. Continuum models and parametrization for aqueous solutions have been developed by several groups [8–22]. More recently, parametrizations were extended to nonaqueous media [23–29]. A good example is the SM5.42R model of Cramer and Truhlar that has been extensively parametrized for several solvents [24]. Likewise, Orozco et al. [17] have parametrized the Miertus–Scroco– Tomasi model for water, carbon tetrachloride [29], chloroform [28] and octanol [23]. In all these works, only solvation free energy of neutral solutes in water and organic solvents, and ions in water, were used in the parametrization procedure. As a consequence, no parametrization is presently available for any of the continuum models to predict accurate and consistent DGsolv of ions in organic solvents. For example, the experimental solvation free energy of the hydroxide ion in dimethyl sulfoxide (DMSO) is 79 kcal mol1 , while a calculation using the SM5.42R/HF/6-31G* method predicts 105 kcal mol1 , amounting to an error of 26 kcal mol1 ! One important reason for the lack of parametrization is the fact that solvation data for organic ions in organic solvents is very scarce. However, we have recently reported for the first time the solvation free energy of several organic ions in DMSO solution [30] as an extension of our previous work on solvation of ions in aqueous solution [31]. Now, these important data open the possibility to make an adequate parametrization of the PCM model [12] to treat anions in DMSO. Thus, the present work reports the first parametrization of a continuum model for the solvation of anions in dimethyl sulfoxide solutions.
2. Ab initio calculations and parametrization procedure Geometries for the anions used in the present work were obtained by full optimization at the HF/6-31+G(d,p) level of theory, and the stationary points confirmed as minima by harmonic frequency calculations. The polarizable continuum model (PCM) implemented in the GA M E S S program [32] was used for the parametrization. We have adopted the integral equation formalism (IEF) routines in the PCM calculation [33] as well as the charge renormalization correction. The PCM calculations were carried using the HF/ 6-31+G(d,p) wavefunction. Only electrostatic contributions were included. This can be justified in the present work because the solvation of ions is greatly dominated by electrostatic interactions. The determination of atomic radii was based on the deviation between theoretical and experimental solvation free energy. We have tried to maintain the same atomic radii internally stored in the GA M E S S program while varying the scale factor (f). Once a good scale factor was obtained, the atomic radius of some atoms such as Br and I were modified in order to decrease the error between theoretical and experimental DGsolv values. We have found that f ¼ 1:35 yields a very good correlation between theoretical and experimental data. On the whole, 21 anions were used in the parametrization process.
3. Results and discussion The atomic radii used in the parametrization are shown in Table 1 and the solvation free energy of the anions are given in Table 2. The theoretical values for DGsolv , obtained by the procedure outlined in this report, are compared with the
Table 1 Atomic radii optimized for DMSO solutiona H
F
O
N
C
S
Cl
Br
I
1.20
1.40
1.50
1.60
1.70
1.85
1.81
1.88
2.05
a
In Angstroms. Scale factor f ¼ 1:35.
J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 355 (2002) 543–546 Table 2 Solvation free energy of anions in DMSO solutiona DGsolv ðexpÞb
DGsolv ðPCMÞ
F Cl Br I OH CH3 O EtO ðCH3Þ2 CHO ðCH3Þ3 CO PhO AcO CH3 COCH 2 CH3 CONH CH3 SOCH2 NH 2 CN N 3 CH2 CN PhNH PhS PhCH 2
)82.6 )65.0 )62.1 )57.4 )79.0 )72.1 )67.6 )63.7 )59.4 )56.7 )62.7 )61.4 )59.2 )57.6 )74.3 )58.0 )65.6 )57.2 )55.3 )54.9 )50.9
)84.9 )65.3 )62.2 )57.1 )81.8 )71.0 )68.1 )65.6 )63.3 )57.0 )64.7 )61.3 )62.4 )60.1 )76.8 )64.2 )60.3 )59.0 )55.7 )55.9 )51.8
)2.3 )0.3 )0.1 0.3 )2.8 1.1 )0.5 )1.9 )3.9 )0.3 )2.0 0.1 )3.2 )2.5 )2.5 )6.2 5.3 )1.8 )0.4 )1.0 )0.9
Average error S.D.
– –
– –
)1.2 2.2
Ion
a b
Error
Units of kcal mol1 . Experimental data taken from [30].
experimental values in Fig. 1. The correlation between the two sets of values can be fitted by a straight line of unit slope. As can be observed, the
Fig. 1. Correlation between our theoretical values and experimental values of solvation free energy of anions in DMSO solution. Units of kcal mol1 .
545
present parametrization produces very good solvation free energy values in close agreement with experimental data. The average error is 1:2 kcal mol1 , while the S.D. of the average error is 2:2 kcal mol1 . Only two species display a high deviation ð>5 kcal mol1 Þ from experimental data, namely N 3 and CN . The errors have opposite signals and it is not possible to improve these results by changing the radius of nitrogen. Furthermore, for other species containing nitrogen such as NH 2, CH2 CN and PhNH good agreement is obtained between the theoretical DGsolv and experimental data. For species with charge on oxygen, good correlation between theory and experiment was also obtained. This is a point that deserves particular attention because for aqueous solution it is not possible to obtain a unique radius for oxygen that yields such good fitting. As an example, Orozco and Luque [17] have calculated DGsolv for OH , NO 2 and NO 3 using several values of the scale parameter. It is noticeable from their report that it is not possible to use a unique oxygen radius to predict theoretical values of DGsolv in good agreement with the experimental data for these three ions. The flaw of pure continuum models to describe the solvation of ions in aqueous solution in a homogeneous form, using fixed atomic radii, is evident from our recent work [34]. The theoretical solvation free energies for 14 ions calculated using the SM5.42R, PCM or IPCM methods display a S.D. 8 kcal mol1 from the average error. However, when some solvent molecules are explicitly included to interact with the solutes, and the resulting clusters solvated by the dielectric continuum, the S.D. decreases to 2:9 kcal mol1 . This behavior in aqueous solution is in marked contrast with dimethyl sulfoxide solutions where the S.D. is only 2:2 kcal mol1 using a pure continuum model. The source of this discrepancy can be attributed to the specific interactions (hydrogen bond) present in aqueous solution, and absent in the solvation of anions in DMSO. The situation is different when we use the present parametrization to calculate the DGsolv of cations in DMSO. Taking NHþ 4 as an example, the theoretical DGsolv is 70 kcal mol1 while the experimental DGsolv is 89 kcal mol1 , an error of 19 kcal mol1 . In this case, the deviation can be attributed to the strong hydrogen bond present
546
J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 355 (2002) 543–546
between the NH4 ion and the dimethyl sulfoxide molecules. Thus, the present parametrization can be used to study anions and neutral molecules in DMSO, but it is not adequate for cations capable of forming strong hydrogen bonds with DMSO molecules. In these cases, the use of the cluster-continuum model [34] may be an adequate strategy.
4. Conclusion Solvation free energies for 21 anions in DMSO solution were used in the present parametrization of the PCM model. The obtained cavities are able to predict DGsolv of the 21 anions with an average error of 1:2 kcal mol1 and a S.D. for the average error of only 2:2 kcal mol1 . These results suggest that the proposed parametrization should be a reliable approach for modeling chemical reactions in DMSO solutions.
Acknowledgements The present work was supported by the S~ao Paulo Science Foundation (FAPESP) and the Brazilian Research Council (CNPq).
References [1] I.M. Cuccovia, M.A. Silva, H.M.C. Ferraz, J.R. Pliego Jr., J.M. Riveros, H. Chaimovich, J. Chem. Soc., Perkin Trans. 2 (2000) 1896. [2] I. Massova, P.A. Kollman, J. Phys. Chem. B 103 (1999) 8628. [3] D.J. Tantillo, K.N. Houk, J. Org. Chem. 64 (1999) 3066. [4] C. Gonzalez, A. Restrepo-Cossio, M. Marquez, K.B. Wiberg, M. De Rosa, J. Phys. Chem. A 102 (1998) 2732. [5] C.J. Cramer, D.G. Truhlar, Chem. Rev. 99 (1999) 2161. [6] J. Tomasi, M. Persico, Chem. Rev. 94 (1994) 2027. [7] G. Hummer, L.R. Pratt, A.E. Garcia, J. Phys. Chem. A 102 (1998) 7885. [8] A. Cheng, S.A. Best, K.M. Merz Jr., C.H. Reynolds, J. Mol. Graphics Mod. 18 (2000) 273.
[9] P.F.B. Goncßalves, P.R. Livotto, Chem. Phys. Lett. 304 (1999) 438. [10] D. Qiu, P.S. Shenkin, F.P. Hollinger, W.C. Still, J. Phys. Chem. A 101 (1997) 3005. [11] J.B. Foresman, T.A. Keith, K.B. Wiberg, J. Snoonian, M.J. Frisch, J. Phys. Chem. 100 (1996) 16098. [12] M. Cossi, V. Barone, R. Cammi, J. Tomasi, Chem. Phys. Lett. 255 (1996) 327. [13] C.C. Chambers, G.D. Hawkins, C.J. Cramer, D.G. Truhlar, J. Phys. Chem. 100 (1996) 16385. [14] K.B. Wiberg, P.R. Rablen, D.J. Rush, T.A. Keith, J. Am. Chem. Soc. 117 (1995) 4261. [15] K.B. Wiberg, T.A. Keith, M.J. Frisch, M. Murcko, J. Phys. Chem. 99 (1995) 9072. [16] E.V. Stefanovich, T.N. Truong, Chem. Phys. Lett. 244 (1995) 65. [17] M. Orozco, F.J. Luque, Chem. Phys. 182 (1994) 237. [18] V. Mohan, M.E. Davis, J.A. McCammon, B.M. Pettit, J. Phys. Chem. 96 (1992) 6428. [19] C.J. Cramer, D.G. Truhlar, Science 256 (1992) 213. [20] W.C. Still, A. Tempczyk, R.C. Hawley, T. Hendrickson, J. Am. Chem. Soc. 112 (1990) 6127. [21] S. Miertus, J. Tomasi, Chem. Phys. 65 (1982) 239. [22] S. Miertus, E. Scrocco, J. Tomasi, Chem. Phys. 55 (1981) 117. [23] C. Curutchet, M. Orozco, F.J. Luque, J. Comput. Chem. 22 (2001) 1180. [24] J. Li, T. Zhu, G.D. Hawkins, P. Winget, D.A. Liotard, C.J. Cramer, D.G. Truhlar, Theor. Chem. Acc. 103 (1999) 9. [25] J. Li, G.D. Hawkins, C.J. Cramer, D.G. Truhlar, Chem. Phys. Lett. 288 (1998) 293. [26] D.J. Giesen, G.D. Hawkins, D.A. Liotard, C.J. Cramer, D.G. Truhlar, Theor. Chem. Acc. 98 (1997) 85. [27] D. Sitkoff, N. Ben-Tal, B. Honig, J. Phys. Chem. 100 (1996) 2744. [28] F.J. Luque, Y. Zhang, C. Aleman, M. Bachs, J. Gao, M. Orozco, J. Phys. Chem. 100 (1996) 4269. [29] F.J. Luque, M. Bachs, C. Aleman, M. Orozco, J. Comput. Chem. 17 (1996) 806. [30] J.R. Pliego Jr., J.M. Riveros, Phys. Chem. Chem. Phys. (in press). [31] J.R. Pliego Jr., J.M. Riveros, Chem. Phys. Lett. 332 (2000) 597. [32] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, J.A. Montgomery Jr., J. Comput. Chem. 14 (1993) 1347. [33] E. Cances, B. Mennucci, J. Tomasi, J. Chem. Phys. 107 (1997) 3032. [34] J.R. Pliego Jr., J.M. Riveros, J. Phys. Chem. A 105 (2001) 7241.
Chemical Physics Letters 355 (2002) 543–546 www.elsevier.com/locate/cplett
Parametrization of the PCM model for calculating solvation free energy of anions in dimethyl sulfoxide solutions Josefredo R. Pliego Jr., Jose M. Riveros
*
Instituto de Quımica, Universidade de S~ ao Paulo, Caixa Postal 26077, CEP 05513-970 S~ ao Paulo, SP, Brazil Received 28 January 2002
Abstract We report the first parametrization of a continuum model for the solvation of anions in DMSO solution. The present parameters used in conjunction with the PCM method predict the solvation free energy of 21 anions in DMSO solution with an average error of 1:2 kcal mol1 , and a S.D. for the average error of only 2:2 kcal mol1 . This low value of the S.D. shows that the present parametrization is capable of predicting accurate differences of the solvation free energies in DMSO solution and is reliable for modeling liquid phase chemical reactions. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Chemical properties of ions and molecules in the liquid phase are intrinsically related to solute– solvent interactions, and these interactions must be properly addressed in theoretical studies of chemical reactions in order to make reliable predictions. Approximate models that treat the solute by quantum mechanics and the solvent as a dielectric continuum surrounding the solute cavity are extensively used nowadays in the modeling of liquid phase chemical processes and properties [1–6].
*
Corresponding author. Fax: +55-11-3091-3888. E-mail addresses: [email protected] (J.R. Pliego [email protected] (J.M. Riveros).
Jr.),
Continuum models are practical and introduce several important properties of solute–solvent interactions, such as: (a) the dielectric constant of the solvent; (b) the charge distribution in the solute; and (c) the size and form of the solute cavity. The first property is intrinsic to the solvent, while the other two properties depend on the specific continuum model. However, a reliable continuum model must make use of an accurate charge distribution and a physically correct shape for the cavity. On the other hand, the size of the cavity must be empirically defined and nonelectrostatic terms need to be included in order to reproduce experimental solvation free energy data. This empirical determination of the size of the cavity is due to the simplified treatment of the solvent, considered to be a dielectric continuum. As a matter of fact, it has been shown that in continuum
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 3 7 7 - 9
544
J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 355 (2002) 543–546
models the cavity of the solute is intrinsically related to each specific solvent [7]. Thus, a scale factor must be applied to the cavity in order to obtain a physically meaningful solute–solvent interaction. Continuum models and parametrization for aqueous solutions have been developed by several groups [8–22]. More recently, parametrizations were extended to nonaqueous media [23–29]. A good example is the SM5.42R model of Cramer and Truhlar that has been extensively parametrized for several solvents [24]. Likewise, Orozco et al. [17] have parametrized the Miertus–Scroco– Tomasi model for water, carbon tetrachloride [29], chloroform [28] and octanol [23]. In all these works, only solvation free energy of neutral solutes in water and organic solvents, and ions in water, were used in the parametrization procedure. As a consequence, no parametrization is presently available for any of the continuum models to predict accurate and consistent DGsolv of ions in organic solvents. For example, the experimental solvation free energy of the hydroxide ion in dimethyl sulfoxide (DMSO) is 79 kcal mol1 , while a calculation using the SM5.42R/HF/6-31G* method predicts 105 kcal mol1 , amounting to an error of 26 kcal mol1 ! One important reason for the lack of parametrization is the fact that solvation data for organic ions in organic solvents is very scarce. However, we have recently reported for the first time the solvation free energy of several organic ions in DMSO solution [30] as an extension of our previous work on solvation of ions in aqueous solution [31]. Now, these important data open the possibility to make an adequate parametrization of the PCM model [12] to treat anions in DMSO. Thus, the present work reports the first parametrization of a continuum model for the solvation of anions in dimethyl sulfoxide solutions.
2. Ab initio calculations and parametrization procedure Geometries for the anions used in the present work were obtained by full optimization at the HF/6-31+G(d,p) level of theory, and the stationary points confirmed as minima by harmonic frequency calculations. The polarizable continuum model (PCM) implemented in the GA M E S S program [32] was used for the parametrization. We have adopted the integral equation formalism (IEF) routines in the PCM calculation [33] as well as the charge renormalization correction. The PCM calculations were carried using the HF/ 6-31+G(d,p) wavefunction. Only electrostatic contributions were included. This can be justified in the present work because the solvation of ions is greatly dominated by electrostatic interactions. The determination of atomic radii was based on the deviation between theoretical and experimental solvation free energy. We have tried to maintain the same atomic radii internally stored in the GA M E S S program while varying the scale factor (f). Once a good scale factor was obtained, the atomic radius of some atoms such as Br and I were modified in order to decrease the error between theoretical and experimental DGsolv values. We have found that f ¼ 1:35 yields a very good correlation between theoretical and experimental data. On the whole, 21 anions were used in the parametrization process.
3. Results and discussion The atomic radii used in the parametrization are shown in Table 1 and the solvation free energy of the anions are given in Table 2. The theoretical values for DGsolv , obtained by the procedure outlined in this report, are compared with the
Table 1 Atomic radii optimized for DMSO solutiona H
F
O
N
C
S
Cl
Br
I
1.20
1.40
1.50
1.60
1.70
1.85
1.81
1.88
2.05
a
In Angstroms. Scale factor f ¼ 1:35.
J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 355 (2002) 543–546 Table 2 Solvation free energy of anions in DMSO solutiona DGsolv ðexpÞb
DGsolv ðPCMÞ
F Cl Br I OH CH3 O EtO ðCH3Þ2 CHO ðCH3Þ3 CO PhO AcO CH3 COCH 2 CH3 CONH CH3 SOCH2 NH 2 CN N 3 CH2 CN PhNH PhS PhCH 2
)82.6 )65.0 )62.1 )57.4 )79.0 )72.1 )67.6 )63.7 )59.4 )56.7 )62.7 )61.4 )59.2 )57.6 )74.3 )58.0 )65.6 )57.2 )55.3 )54.9 )50.9
)84.9 )65.3 )62.2 )57.1 )81.8 )71.0 )68.1 )65.6 )63.3 )57.0 )64.7 )61.3 )62.4 )60.1 )76.8 )64.2 )60.3 )59.0 )55.7 )55.9 )51.8
)2.3 )0.3 )0.1 0.3 )2.8 1.1 )0.5 )1.9 )3.9 )0.3 )2.0 0.1 )3.2 )2.5 )2.5 )6.2 5.3 )1.8 )0.4 )1.0 )0.9
Average error S.D.
– –
– –
)1.2 2.2
Ion
a b
Error
Units of kcal mol1 . Experimental data taken from [30].
experimental values in Fig. 1. The correlation between the two sets of values can be fitted by a straight line of unit slope. As can be observed, the
Fig. 1. Correlation between our theoretical values and experimental values of solvation free energy of anions in DMSO solution. Units of kcal mol1 .
545
present parametrization produces very good solvation free energy values in close agreement with experimental data. The average error is 1:2 kcal mol1 , while the S.D. of the average error is 2:2 kcal mol1 . Only two species display a high deviation ð>5 kcal mol1 Þ from experimental data, namely N 3 and CN . The errors have opposite signals and it is not possible to improve these results by changing the radius of nitrogen. Furthermore, for other species containing nitrogen such as NH 2, CH2 CN and PhNH good agreement is obtained between the theoretical DGsolv and experimental data. For species with charge on oxygen, good correlation between theory and experiment was also obtained. This is a point that deserves particular attention because for aqueous solution it is not possible to obtain a unique radius for oxygen that yields such good fitting. As an example, Orozco and Luque [17] have calculated DGsolv for OH , NO 2 and NO 3 using several values of the scale parameter. It is noticeable from their report that it is not possible to use a unique oxygen radius to predict theoretical values of DGsolv in good agreement with the experimental data for these three ions. The flaw of pure continuum models to describe the solvation of ions in aqueous solution in a homogeneous form, using fixed atomic radii, is evident from our recent work [34]. The theoretical solvation free energies for 14 ions calculated using the SM5.42R, PCM or IPCM methods display a S.D. 8 kcal mol1 from the average error. However, when some solvent molecules are explicitly included to interact with the solutes, and the resulting clusters solvated by the dielectric continuum, the S.D. decreases to 2:9 kcal mol1 . This behavior in aqueous solution is in marked contrast with dimethyl sulfoxide solutions where the S.D. is only 2:2 kcal mol1 using a pure continuum model. The source of this discrepancy can be attributed to the specific interactions (hydrogen bond) present in aqueous solution, and absent in the solvation of anions in DMSO. The situation is different when we use the present parametrization to calculate the DGsolv of cations in DMSO. Taking NHþ 4 as an example, the theoretical DGsolv is 70 kcal mol1 while the experimental DGsolv is 89 kcal mol1 , an error of 19 kcal mol1 . In this case, the deviation can be attributed to the strong hydrogen bond present
546
J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 355 (2002) 543–546
between the NH4 ion and the dimethyl sulfoxide molecules. Thus, the present parametrization can be used to study anions and neutral molecules in DMSO, but it is not adequate for cations capable of forming strong hydrogen bonds with DMSO molecules. In these cases, the use of the cluster-continuum model [34] may be an adequate strategy.
4. Conclusion Solvation free energies for 21 anions in DMSO solution were used in the present parametrization of the PCM model. The obtained cavities are able to predict DGsolv of the 21 anions with an average error of 1:2 kcal mol1 and a S.D. for the average error of only 2:2 kcal mol1 . These results suggest that the proposed parametrization should be a reliable approach for modeling chemical reactions in DMSO solutions.
Acknowledgements The present work was supported by the S~ao Paulo Science Foundation (FAPESP) and the Brazilian Research Council (CNPq).
References [1] I.M. Cuccovia, M.A. Silva, H.M.C. Ferraz, J.R. Pliego Jr., J.M. Riveros, H. Chaimovich, J. Chem. Soc., Perkin Trans. 2 (2000) 1896. [2] I. Massova, P.A. Kollman, J. Phys. Chem. B 103 (1999) 8628. [3] D.J. Tantillo, K.N. Houk, J. Org. Chem. 64 (1999) 3066. [4] C. Gonzalez, A. Restrepo-Cossio, M. Marquez, K.B. Wiberg, M. De Rosa, J. Phys. Chem. A 102 (1998) 2732. [5] C.J. Cramer, D.G. Truhlar, Chem. Rev. 99 (1999) 2161. [6] J. Tomasi, M. Persico, Chem. Rev. 94 (1994) 2027. [7] G. Hummer, L.R. Pratt, A.E. Garcia, J. Phys. Chem. A 102 (1998) 7885. [8] A. Cheng, S.A. Best, K.M. Merz Jr., C.H. Reynolds, J. Mol. Graphics Mod. 18 (2000) 273.
[9] P.F.B. Goncßalves, P.R. Livotto, Chem. Phys. Lett. 304 (1999) 438. [10] D. Qiu, P.S. Shenkin, F.P. Hollinger, W.C. Still, J. Phys. Chem. A 101 (1997) 3005. [11] J.B. Foresman, T.A. Keith, K.B. Wiberg, J. Snoonian, M.J. Frisch, J. Phys. Chem. 100 (1996) 16098. [12] M. Cossi, V. Barone, R. Cammi, J. Tomasi, Chem. Phys. Lett. 255 (1996) 327. [13] C.C. Chambers, G.D. Hawkins, C.J. Cramer, D.G. Truhlar, J. Phys. Chem. 100 (1996) 16385. [14] K.B. Wiberg, P.R. Rablen, D.J. Rush, T.A. Keith, J. Am. Chem. Soc. 117 (1995) 4261. [15] K.B. Wiberg, T.A. Keith, M.J. Frisch, M. Murcko, J. Phys. Chem. 99 (1995) 9072. [16] E.V. Stefanovich, T.N. Truong, Chem. Phys. Lett. 244 (1995) 65. [17] M. Orozco, F.J. Luque, Chem. Phys. 182 (1994) 237. [18] V. Mohan, M.E. Davis, J.A. McCammon, B.M. Pettit, J. Phys. Chem. 96 (1992) 6428. [19] C.J. Cramer, D.G. Truhlar, Science 256 (1992) 213. [20] W.C. Still, A. Tempczyk, R.C. Hawley, T. Hendrickson, J. Am. Chem. Soc. 112 (1990) 6127. [21] S. Miertus, J. Tomasi, Chem. Phys. 65 (1982) 239. [22] S. Miertus, E. Scrocco, J. Tomasi, Chem. Phys. 55 (1981) 117. [23] C. Curutchet, M. Orozco, F.J. Luque, J. Comput. Chem. 22 (2001) 1180. [24] J. Li, T. Zhu, G.D. Hawkins, P. Winget, D.A. Liotard, C.J. Cramer, D.G. Truhlar, Theor. Chem. Acc. 103 (1999) 9. [25] J. Li, G.D. Hawkins, C.J. Cramer, D.G. Truhlar, Chem. Phys. Lett. 288 (1998) 293. [26] D.J. Giesen, G.D. Hawkins, D.A. Liotard, C.J. Cramer, D.G. Truhlar, Theor. Chem. Acc. 98 (1997) 85. [27] D. Sitkoff, N. Ben-Tal, B. Honig, J. Phys. Chem. 100 (1996) 2744. [28] F.J. Luque, Y. Zhang, C. Aleman, M. Bachs, J. Gao, M. Orozco, J. Phys. Chem. 100 (1996) 4269. [29] F.J. Luque, M. Bachs, C. Aleman, M. Orozco, J. Comput. Chem. 17 (1996) 806. [30] J.R. Pliego Jr., J.M. Riveros, Phys. Chem. Chem. Phys. (in press). [31] J.R. Pliego Jr., J.M. Riveros, Chem. Phys. Lett. 332 (2000) 597. [32] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, J.A. Montgomery Jr., J. Comput. Chem. 14 (1993) 1347. [33] E. Cances, B. Mennucci, J. Tomasi, J. Chem. Phys. 107 (1997) 3032. [34] J.R. Pliego Jr., J.M. Riveros, J. Phys. Chem. A 105 (2001) 7241.