Conformational Equilibrium of 1,2-Dichloroethane in Water

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J. Phys. Chem. B 2006, 110, 16018-16025

Conformational Equilibrium of 1,2-Dichloroethane in Water: Comparison of PCM and RISM-SCF Methods Jin Yong Lee,†,‡ Norio Yoshida,† and Fumio Hirata*,†,§ Department of Theoretical Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan, Department of Fundamental Molecular Science, The Graduate UniVersity for AdVanced Studies, Okazaki 444-8585, Japan, and Department of Chemistry, Institute of Basic Science, Sungkyunkwan UniVersity, Suwon, 440-746, Korea ReceiVed: February 1, 2006; In Final Form: May 23, 2006

The RISM-SCF and polarizable continuum model (PCM) approaches have been applied to study the conformational equilibrium of 1,2-dichloroethane (DCE) in water. Both the electron correlation effect and basis sets play an important role in the relative energies of the gauche and trans conformers in gas and solution phases. Both PCM and RISM-MP2 methods resulted in a consistent trend with the previous experimental and theoretical studies that the population of the gauche conformer increases in going from the gas phase to the aqueous solution. However, the PCM treatment could not describe the solvent effect completely in that the sign of the relative free energy of the gauche and trans forms is opposite to the most recent experimental and theoretical data, while the RISM-MP2 gives the right sign in the free energy difference. We found that the larger excess chemical potential gain (by ca. -4.1 kcal/mol) for the gauche conformer is large enough to result in the gauche preference of DCE in water, though it has to compensate for more solute reorganization energy (∼1.6 kcal/mol) and overcome the energy difference (∼1.6 kcal/mol) in the gas phase. The radial distribution functions between DCE and the nearest water shows that the electrostatic repulsion between chlorine and oxygen atoms is higher in the trans conformer than in the gauche one, while the attractive interaction between chlorine and hydrogen of water is higher in the gauche conformer.

I. Introduction Molecular conformational equilibrium by internal rotation is a central and classical concept in the structural chemistry of biomolecules1 and smaller flexible compounds,2 and plays an important role in the chemical reactivity.3-5 The internal rotation through the multiple bonds6,7 (double or triple bond) is well understood by the chemical bonding theory, especially by the molecular orbital theory, in the textbook knowledge. However, the internal rotation through the single bonds is still waiting for more in-depth explanations. For example, in the gas phase, it has been often believed that the trans preference of ethane is due to the steric effects. However, the structural preference of the simplest single bond system, ethane, was recently reported to be mainly attributed to the hyperconjugation.8 Nowadays, one of the most challenging problems is to describe the conformations of a protein that is composed of many amino acids. Through the peptide bonds between amino acids, there are a number of internal rotations through the single bonds. In particular, the solvent molecules can have a great influence on such conformational preferences in proteins,9-11 and thus it is very important to describe the solvent effects in liquids and solutions. To date, the most widely used treatment for the solvent effect has been the simple dielectric continuum model.12-14 However, such a treatment fails to account for the detailed molecular * Address correspondence to this author. Phone: +81-564-55-7314. Fax: +81-564-53-4660. E-mail: [email protected]. † Institute for Molecular Science. ‡ Sungkyunkwan University. § The Graduate University for Advanced Studies.

nature of the solvent. The explicit incorporation of model solvent molecules surrounding a solute molecule can provide in principle an accurate means for considering such solvent effects by molecular dynamics (MD) and Monte Carlo (MC) techniques.15-17 However, such techniques demand a lot of computational cost, and the results severely depend on the potential functions employed. Another very efficient way to include the solvent effect is the so-called reference interaction site model (RISM) integral equations, which were derived by Chandler and Anderson18 and extended by Hirata and Rossky.19 The RISM integral equation has been successfully applied to many liquids and polar solvent systems.20-22 The extended RISM formalism includes the direct site-site interactions of solute-solvent and solvent-solvent and gives a tremendous computational efficiency. However, even in RISM formalism, we cannot avoid some problem in describing the molecular property of the solute in solution when the solute itself bears a quantum mechanical nature. Accordingly, there are many so-called QM/MM studies which adapt quantum mechanical treatment of a solute and classical treatment of solvent molecules.23-25 But, this method no doubt demands a large computational cost, and is limited in its applications. During the past decade, a new theoretical method, RISMSCF, has been proposed, developed, and successfully applied to calculate the molecular properties of a solute in solutions.26-28 This method is basically an ab initio method combining with the RISM formalism in the statistical mechanics of the molecular liquids. The advantage of the RISM-SCF method is not only to save computational cost, but also to maintain the molecular quantum mechanical nature of the solute molecule keeping the local solute-solvent site-site interactions such as hydrogen

10.1021/jp0606762 CCC: $33.50 © 2006 American Chemical Society Published on Web 07/26/2006

Conformational Equilibrium of 1,2-Dichloroethane in Water bonding. The quantum mechanical level of theory for describing the solute molecule can be properly chosen.29 1,2-Dichloroethane (DCE) is a prototype of flexible small molecules that have been extensively studied.30-34 The DCE shows a large dipole moment variation between its conformational minima, gauche and trans. The dipole moment of DCE in the gas phase was reported to be 3.12 and 0 D for the gauche and trans conformer, respectively.35 According to the textbooks, the trans preference of DCE in the gas phase over the gauche arises from the steric effect, which is basically exchange and Coulombic repulsion. However, in the liquid phase or polar solvent media, due to the dipole moment of the gauche conformer, the gauche conformer can be more stabilized than the trans form due to the dipole-dipole interactions with neighboring gauche species (in liquid) or polar solvent molecules (in solutions). The conformational equilibria in solution are of particular importance because most of the biological systems of interest are in solution media.1 Despite a number of theoretical and experimental studies, the conformational equilibrium of DCE has not yet been determined.32-34,36-41 To fully understand the conformational equilibrium of DCE in solution, we first should obtain more accurate data by both the experiment and theory. It was pointed out that the variation in experimental values of the gauche-trans free energy difference is substantial in many cases. Jorgensen pointed out several points about the possible reasons for such discrepancies.32 One is the misassignments of bands and the occurrence of overlapping bands in the IR and Raman spectra.42 Another source of error results from the fact that the ∆E values are mostly obtained via van’t Hoff plots from the temperature dependence of the equilibrium constant.43 However, in the liquid or solution phase ∆E (or ∆H) should not be constant since the solvation energy difference between the conformers should diminish with increasing temperature. Despite such an extensive study, there still seems to be variation in the experimental and theoretical data.44-48 The reason may be because the free energy difference between the two conformations is so subtle that the current experimental technique may not resolve the difference. Thus, the physical origin of such a tendency should be clarified. However, to date, such clarification can be made only by a theoretical study. This problem involves not only equilibrium between the two particular conformations, but also their distribution along the reaction coordinates, in this case, the dihedral angle. Along the reaction coordinates, the molecule changes its state not only in terms of the solvation free energy, but also in terms of the electronic structure. Furthermore, those two effects are correlated with each other. In this respect, the problem has to be solved self-consistently in terms of both the electronic structure and the solvation. Thus, it is very important to find free energy changes by a different method and to compare them with recent experimental and theoretical data. In this study, we investigate the conformational equilibrium of 1,2-dichloroethane in water by adapting the RISM-SCF method and polarizable continuum model (PCM) treatment for the solvent effect. II. Basic RISM-SCF Equation Here, we briefly show only the equations which are conceptually important and will be used to discuss our results. The detailed equations and explanations are available in our previous articles.26-29 The total free energy (G) of the solute in solvent is defined as the sum of the energy of the solute molecule in its isolated condition (Eiso), solute reorganization energy (Ereorg), and the excess chemical potential (∆µ):

J. Phys. Chem. B, Vol. 110, No. 32, 2006 16019

G ) Eiso + Ereorg + ∆µ

(1)

Each term has the following meaning

ˆ 0|Ψgas〉 Eiso ) 〈Ψgas|H

(2)

Ereorg ) Eelec uu - Eiso

(3)

ˆ 0|Ψsolv〉 Eelec uu ) 〈Ψsolv|H

(4)

ˆ 0 are the wave function and Hamiltonian of where Ψgas and H the isolated molecules, and Ψsolv is the wave function of the solvated molecule. The solute reorganization energy represents the reorganization energy associated with the relaxation or distortion of the electronic cloud and molecular geometry of the solute molecule in solution. For the solvation free energy (excess chemical potential) term, we adopted the free energy derived from the hypernetted-chain (HNC) closure relation by Singer and Chandler,49

F ∆µ ) 4π β R∈solute β∈solvent 1 2 1 hRβ (r) - cRβ(r) - hRβ(r)cRβ(r) r2 dr (5) 2 2

∑

∫

[

∑

]

where cRβ and hRβ are the direct and total correlation functions, respectively. These definitions allowed us to define the Lagrangian of the system as a function of the correlation functions hRβ, cRβ, and tRβ ()hRβ - cRβ), as well as the MO coefficient. (See eq 8 of ref 29.) Variations with respect to the functions yield the definition of HNC closure, RISM equation, and solvated Fock matrix element:

hRβ(r) ) e[-βuRβ(r)+tRβ(r)] - 1

∑ωRR′/cR′β/χββ′(r) Fij ) 〈φi|H ˆ 0 + F∑∫uˆ Rβ(r)(hRβ(r) + 1) dr|φj〉 hRβ(r) ) F-1

(6) (7) (8)

Rβ

where ωRR′, χββ′, and φij are the intramolecular correlation function, the sum of solvent intramocular correlation funcion and solvent total correlation function, and the basis set of solute wave function. uˆ Rβ is defined as follows

uR,βes )

∑ij γij〈φi|uˆ Rβ|φj〉

(9)

where uR,βes is the electrostatic interaction potential between solute site R and solvent site β. uR,β of eq 6 is a sum of the electrostatic interaction uR,βes and Lennard-Jones interaction potential. We can determine the solvent distribution around the solute molecule and the solute electronic structure in solution simultaneously by solving eqs 6-9. III. Computational Detail To study the conformational equilibrium of DCE in water, we first carried out ab initio calculations for DCE in the gas phase. To obtain the energy profile along the dihedral angle of Cl-C-C-Cl, we optimized the geometries at the fixed dihedral angles in the range of 60-300° starting at 60°. The dihedral angles between -60° and 60° are not included because the potential barrier is quite high in that region.23,31,32 To include solvent effect, we used two different approaches, PCM and RISM, to pinpoint the contribution of continuum medium and

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TABLE 1: LJ Potential Parameters and Charges for Atom Sites of DCE and Water Used for RISM-HF and RISM-MP2 of Atom Sites of DCE and Solvent Water center water O H DCE C Cl H

σ (Å)

 (kcal/mol)

q (e+)

3.166 1.000

0.1554 0.056

-0.8476 0.4238

3.816 3.896 2.974

0.086 0.265 0.0157

direct site-site interactions. For the gas phase and PCM calculations, we carried out Hartree-Fock (HF), Mo¨ller-Plesset second order perturbation (MP2), and density functional theory with three-parametrized Lee-Yang-Parr exchange correlation functional (B3LYP) theory calculations using various basis sets, 6-311G, 6-311G**, 6-311+G**, cc-pvDZ, cc-pvTZ, aug-ccpvDZ, and aug-cc-pvTZ. These calculations were performed with a suite of Gaussian 03 programs.50 It is of crucial importance to use fast and reliable procedures for the continuum solvent description, and the family of PCM algorithms has become a sort of standard for this kind of calculation thanks to their accuracy and flexibility. The most commonly used PCM version performs a reaction field calculation by using the IEF-PCM model51-53 with the integral equation formulism.51,53-55 The model of Chipman56 is closely related to this earlier model.57 In PCM, the solute is placed in a cavity formed by interlocking spheres, centered on solute atoms or atomic groups, and several sets of radii can be used. This is an important parameter, since the computed energies and properties depend critically on the cavity size. Recently, Cossi et al. recommended the use of the united atom topological model, where hydrogen atoms are enclosed on the same sphere of the heavy atom they are bound to, and the sphere radii are set according to the atomic number, the charge, and the hybridization of the atom, possibly corrected for the first neighbors’ effect.58,59 Thus, we used the united atom topological model for the atomic groups radii of DCE, 2.325 and 1.973 Å for CH2 and Cl, respectively. The RISM-HF and RISM-MP2 methods were implemented into the GAMESS package for the electronic structure calculations. In the following text, the RISM-SCF denotes both RISMHF and RISM-MP2. In RISM-SCF calculations, we do not need to assign the solute charges as parameters because the electrostatic potential will be derived based on the electron densities of the solute. 6-311G, 6-311G**, and 6-311+G** basis sets were used for the RISM-SCF calculations. The RISM-SCF calculations were carried out at 298.15 K and a solvent density of 0.03334 molecule/Å3 ()0.9974 g/cm3), using 1024 grids with a width of 0.05 Å. In the RISM-SCF theory, Lennard-Jones (LJ) potential was employed as a short range interaction between solute and solvent to represent electron exchange repulsion and/ or charge transfer. These treatments were essentially justified in previous work.60,61 For the potential parameters of DCE, the OPLS LJ parameters62 for C and H and the AMBER LJ parameters63 for Cl were employed (Table 1). For the solvent water molecules, we employed the SPC/E parameters64 for O, and added hydrogen LJ parameters to perform the RISM calculations because the SPC/E model has no hydrogen LJ parameters. We fixed the geometry of solvent water molecules with an OH distance of 1.0 Å and an H-O-H angle of 109.27°. We do not need to specify the effective point charges on the solute site as potential parameters because the effective charges can be generated in the RISM-SCF calculations.

TABLE 2: Calculated Energy Differences (∆Et/g ) Egauche Etrans) of DCE in the Gas Phase at Various Basis Sets basis sets 6-311G 6-311G** 6-311+G** ccpvDZ aug-ccpvDZ ccpvTZ aug-ccpvTZ exptl a

HF

B3LYP

MP2/FC

2.24 2.01 1.93 1.79 1.51 1.51 1.87 1.58 1.44 1.82 1.53 1.42 2.03 1.68 1.51 1.89 1.63 1.36 1.89 1.60 1.30 1.20,a 1.26 ( 0.09,b1.27 ( 0.04c

MP2/Full 1.91 1.49 1.44 1.43 1.54 1.32 1.21

Reference 43. b Reference 38. c Reference 48.

IV. Results and Discussion We first calculated the energies of DCE in the gas phase as a function of the Cl-C-C-Cl dihedral angle in HF, B3LYP, MP2 levels of theory using various basis sets. The dihedral angle of the gauche conformer is around 70°, which is consistent with previous results.2,23 This is due to the fact that the steric repulsion between Cl and Cl is larger than that between Cl and H. The relative energies (denoted as ∆Et/g ) Egauche - Etrans) of gauche and trans conformers are listed in Table 2. In Table 2, each row entails the electron correlation effect at the given basis sets, while each column implicates the basis set effect at the given level of theory. It should be addressed that both the electron correlation and basis set play an important role in obtaining more accurate relative energy. For example, for the largest basis sets (aug-cc-pVTZ), the ∆Et/g is 1.89 kcal/mol at the HF level, while it reduces to 1.30 and 1.21 kcal/mol at MP2/FC (MP2 calculations with core orbitals frozen) and MP2/Full (MP2 calculations without core orbitals frozen), respectively. The MP2 results with enough diffusive and polarization functions are in excellent agreement with the experimental value of 1.27 kcal/ mol, which was obtained by Wiberg et al.48 using the corrections of Capelli et al.47 On the other hand, from the MP2/Full results with 6-311G, 6-311G**, and 6-311+G** basis sets, it is clearly shown that the diffusive and polarization functions in the basis sets play a significant role too. This is consistent with the finding that the inclusion of higher angular momentum functions, that is, polarization functions, is required to obtain a reasonable energy difference, and the smaller basis sets gave energy differences too large.2,34 Our calculation also shows that very large basis sets should be used to accurately describe the internal rotation along the single bond, and the electron correlation effect as well. In the present study, the energy is not corrected for the zero-point vibrations, because in the earlier study the zero-point energy (ZPE) difference was very small, 0.04 kcal/mol, between the gauche and trans conformers.2 As pointed out by Jorgensen, in experiment, it is not easy to quantify the free energy difference for the conformational equilibria of the flexible molecules in solution by the interpretation of the spectra due to several factors. As a matter of fact, many different experimental data show different numbers.38,44,47,48 The antisymmetric C-Cl stretching band of the trans conformer and the symmetric C-Cl stretching band for the gauche conformer have been used to estimate the free energy difference because those two bands are well separated at 727 and 669 cm-1, and the symmetric C-Cl band of the trans conformer is IR inactive by the symmetry.65 The free energy difference relies on the following relationship:

∆Gt/g ) RT ln

2CT 2τGAT ) RT ln CG τ TA G

(10)

Conformational Equilibrium of 1,2-Dichloroethane in Water

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TABLE 3: Calculated Energy Differences (∆Gt/g ) GGauche Gtrans) of DCE for Solution in Water at Various Basis Sets basis sets PCM treatment 6-311G 6-311G** 6-311+G** ccpvDZ aug-ccpvDZ ccpvTZ aug-ccpvTZ RISM-SCF method 6-311G 6-311G** 6-311+G** expt recent calcns

HF 0.16 0.29 0.33 0.33 0.52 0.47 0.50 -0.58 -0.56 -0.74 -0.02,a -0.22b (in acetonitrile) -0.25c, -0.28 to -0.31d, -0.62e

B3LYP MP2/FC MP2/Full 0.12 0.09 0.15 0.22 0.32 0.32 0.31

0.33 0.38 0.28 0.27 0.22 0.17 0.09

0.32 0.36 0.27 0.27 0.25 0.14 0.01 -0.33 -0.44 -0.79

a

This is the experimental value obtained by Kato et al. (Reference 55) using the corrections of Capeli et al. (Reference 47). b Reference 48. c Reference 46. d Reference 45. e Reference 23.

where C is the concentration, A is the IR absorbance or Raman activity, and τ is the absorption coefficient () of IR spectroscopy or the scattering cross section (σ) of Raman spectroscopy. For a long time, the ∆Gt/g values were obtained from the absorbance ratio for the asymmetric C-Cl stretching band of the trans conformer and symmetric mode of the gauche conformer (AT/ AG) assuming that the τG/τT value is constant. Accordingly, Wiberg et al.48 reported that the ∆Gt/g value of DCE is -0.22 kcal/mol in acetonitrile from the experimental AT/AG value and calculated τG/τT value for the asymmetric C-Cl mode of the trans and the symmetric mode of the gauche conformer. However, Cappelli et al.47 pointed out that the discrepancy of the τG/τT value is larger when the asymmetric C-Cl mode of the trans and the symmetric mode of the gauche conformer are used than when the asymmetric C-Cl modes of both the trans and gauche conformer are used. Thus, they suggested that it is more precise to use the τG/τT value from the asymmetric C-Cl stretching bands of both the trans and gauche conformers. By adapting this idea and using the experimental value of Wiberg et al.,48 they reported the ∆Gt/g value of DCE in water as 0.15 kcal/mol.47 Similarly, taking many published experimental data, they reported modified data and found that most of the ∆Gt/g values were positive, which implies that trans is more favored in various solvents such as hexane, ethers, THF, acetone, and acetonitrile. But, when the most recent experimental data for the DCE in water by Kato et al.66 were used, and corrected by using the corrections of Capelli et al.,47 the ∆Gt/g value changed to -0.02 kcal/mol. In all theoretical and experimental cases, it is obvious that the population of the gauche conformer increases as the medium changes from gas to solution or condensed phase. Our calculated free energy (∆Gt/g) variations between the gauche and trans conformers of DCE in water are listed in Table 3, and Figure 3 shows the free energy variations for rotation about the C-C bond of DCE in the gas phase and solution (PCM and RISM-MP2). As in the gas phase, the ∆Gt/g values from the PCM treatment at the MP2 level with the aug-cc-pVTZ basis set do not support the gauche preference of DCE in water: the ∆Gt/gvalue is still a positive 0.006 kcal/mol. Nevertheless, the trend of ∆Gt/g in going from gas to solution is consistent with experimental results. The ∆∆Gt/g value, defined as (∆Gt/g in solution) - (∆Gt/g in gas), is -1.21 kcal/ mol at the MP2/aug-cc-pVTZ calculation with the PCM model. The more negative the ∆∆Gt/g value is, the more gauche form

Figure 1. Free energy profiles for rotation about the C-C bond of DCE from the MP2/aug-cc-pVTZ for gas phase (dotted line with open circles) and MP2/aug-cc-pVTZ with PCM (solid line with solid triangles) and MP2/6-311+G** with RISM methods (solid line with solid circles) in water.

is populated in the solution phase compared with the gas phase population. In PCM treatment, the solute molecule can be polarized due to the field generated by the surrounding solvent medium. But the solvent is treated as a continuum medium, and this may cause some errors. This problem can be overcome by treating the solvent molecules explicitly. Our ultimate concern is the molecular properties of the solute in solvent, thus, the solvent molecules are described explicitly and classically. On the other hand, for the solute, the molecule can be described either classically as in MD/MC or quantum mechanically as in QM/MM. The classical treatment of solute has been successful in many applications, especially in liquids. However, for the study of internal rotation along the single bond like DCE, the intrinsic quantum mechanical nature of the solute would be critical. In fact, recent gas phase study about the internal rotation of ethane reported the opposite interpretation to the commonly accepted reasoning on the rotational barrier.8 On the basis of such a background, recently developed RISM-SCF can meet the requirement for the calculations of molecular properties in solution. The ∆Gt/g values obtained from the RISM-SCF calculations at the HF level are -0.58, -0.56, and -0.74 kcal/mol with 6-311G, 6-311G**, and 6-311+G** basis sets, respectively, while those at the MP2 level are -0.33, -0.44, and -0.79 kcal/ mol. The negative values of RISM-SCF calculations are consistent with the solution experimental value of -0.02 kcal/ mol obtained by Kato et al.66 using the correction of Capelli et al.47 The sign of the ∆Gt/g value would be critical when the flexible conformational equilibrium is considered to be critical, for example, in the case of chain molecules where there are a number of internal rotations through the single bonds. It seems that, in the experimental data, it is inevitable to have some errors due to the assumption of constant τG/τT value in all cases. In another experiment, the ∆Gt/g values of DCE were obtained to be -0.14 and -0.22 kcal/mol in acetone and acetonitrile, respectively.48 The dielectric constants of acetone and acetonitrile are 20.7 and 36.0, respectively. Considering the gauche preference of DCE is generally more pronounced in more polar solvent, our RISM-SCF result in water (dielectric constant is 78) is in better agreement with this experiment. Madurga and Vilaseca reported the ∆Gt/g values of -0.25 kcal/mol46 and

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TABLE 4: Contributions of Excess Chemical Potential and Solute Reorganization to the Solvation Free Energy Obtained by Different Calculationsa RISM-HF/6-311G RISM-HF/6-311G** RISM-HF/6-311+G** RISM-MP2/6-311G RISM-MP2/6-311G** RISM-MP2/6-311+G**

∆Eiso

∆(∆µ)

∆Ereorg

∆G

2.25 1.79 1.87 1.91 1.49 1.63

-4.13 -3.31 -3.99 -4.18 -3.14 -4.08

1.30 0.96 1.38 1.93 1.21 1.62

-0.58 -0.56 -0.74 -0.33 -0.44 -0.83

a Energies are in kcal/mol, and ∆Q denote Qgauche - Qtrans, where Q is any energy term of Eiso, ∆µ, Ereorg, and G.

Figure 3. Free energy variation for the C-C rotation of DCE at different levels of calculations in solution: RISM-HF/6-311G (dotted line with open triangles), RISM-HF/6-311G** (dotted line with open squares), RISM-HF/6-311+G** (dotted line with open circles), RISMMP2/6-311G (solid line with solid triangles), RISM-MP2/6-311G** (solid line with solid squares), and RISM-MP2/6-311+G** (solid line with solid circles).

Figure 2. Contributions of solute reorganization energy (Ereorg; solid line with open triangles) and excess chemical potential (∆µ; dotted line with open diamonds) to the total free energy in solution (solid line with solid circles) for the C-C rotation of DCE. The dotted lines with open circles and open squares are for the isolated gas phase and Ereorg + ∆µ, respectively.

-0.28 to -0.31 kcal/mol45 by the free energy perturbation method through the MC simulations using all-atom OPLS parameters for the DCE and TIP4P water model. Recent QM/ MM calculations using CM1A charges by Kaminski and Jorgensen resulted in ∆Gt/g values of -0.33 and -0.62 kcal/ mol in acetonitril and water.23 Our RISM-SCF calculation, which requires much less computational cost, results in good agreement with the QM/MM results. The advanced recent computational treatments including our present study clearly show the negative ∆Gt/g value. However, it should be mentioned that the high level quantum mechanical treatment by the PCM model could describe the solvent effect to a certain extent on the conformational equilibrium and the trend is consistent in going from the gas to solution. We investigated the contribution of the solute reorganization energy and the excess chemical potential to the total free energy difference, which causes the gauche preference in solution, and the results are listed in Table 4. Figure 2 shows the free energy profiles for rotation about the C-C bond of DCE in water obtained from the RISM-MP2 calculations with the 6-311+G** basis set. More solute reorganization energy is required for the gauche conformer than the trans conformer by ∼1.6 kcal/mol. The solute reorganization energy is the energy required for the solute molecule to rearrange the geometry and electron cloud according to the environmental solvent molecules. However, the excess chemical potential gives more stabilization energy to the gauche conformer than the trans form by ∆∆µ (∆µg ∆µt) ≈ -4.1 kcal/mol. By summing these two values, the

gauche conformer has energetically more benefit than the trans one by solvation by ∼2.4 kcal/mol. In the isolated gas phase, the gauche conformer is higher in energy by 1.6 kcal/mol at the MP2/6-311+G** level. Consequently, the net free energy of the gauche conformer is lower than that of the trans by ∼0.8 kcal/mol. From the comparison of the results by PCM and RISM treatments, it may be concluded that the excess chemical potential due to the solvent molecules can be reasonably described by including the site-site direct interaction, but not by the polarizable continuum model (PCM) treatment. The importance of the direct site-site interactions between the solute and solvent molecules was previously invoked.38 Nevertheless, the PCM treatment gives a good agreement in the trend of free energy changes (∆∆G ) ∆Gsol - ∆Ggas) in going from the gas phase to solvent media as previously used successfully, thus, it can be usefully applied to many properties of molecules in solution except for cases such as internal rotation of DCE. The contribution of excess chemical potential and solute reorganization energy with RISM methods at HF and MP2 levels of theory with 6-311G, 6-311G**, and 6-311+G** basis sets is compared. The total free energies are in the range of -0.33 to -0.83 kcal/mol and negative in all cases, and the values are in good agreement with the recently published value by Jorgensen23 and Vilaseca.45,46 Thus, we hope that by incorporating the RISM method into the quantum electronic structure theory the solvation free energy can be well described even by the HF level of theory with a basis set of medium size. Figure 3 shows the free energy variation for the C-C rotation of DCE in water at different levels of RISM-SCF calculations. As mentioned above, all the levels of calculations resulted in the free energy difference in the range of -0.33 to -0.83 kcal/ mol. However, a little conformational shift is noticed in the RISM-MP2 calculations with the 6-311+G** basis set. Apparently, the minimum energy conformer seems to have the dihedral angle of ∼70° except for RISM-MP2/6-311+G** where the minimum energy conformer shifts to a slightly lower angle, 6070°, which is consistent with the finding from the AOC results by Jorgensen23 that the dihedral angle is 70° in the gas phase and 65° in water. The solvation free energy resulting the gauche preference in water can be related to the difference of the microsolvation

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J. Phys. Chem. B, Vol. 110, No. 32, 2006 16023

Figure 4. Radial distribution functions of DCE in water: between Cl of DCE and O of water (a), Cl of DCE and H of water (b), C of DCE and O of water (c), C of DCE and H of water (d), and H of DCE and O of water (e).

structures between the gauche and trans conformers. Figure 4a-d represents the radial distribution functions (RDF), g(r), between Cl of DCE and O of water, Cl of DCE and H of water, C of DCE and O of water, and C of DCE and H of water, respectively. Figure 4a clearly shows the difference of the RDF in the first peak, which shows the average population having the interatomic distance ∼3.45 Å between Cl of DCE and O of the water molecules in the first hydration shell. The population of the first peak for the trans conformer is a bit larger than that for the gauche as seen in Figure 4a. Since the charges of Cl and O are negative, the electrostatic interaction between them is purely repulsive. Thus, the trans conformer may be more repulsive than the gauche conformer. Reversely, as seen in Figure 4b, the population of the first peak of the RDF between Cl of DCE and H of water is larger in the gauche conformer than in the trans one, and the interaction between these sites is purely attractive. These differences of the RDFs are due to the change of the effective charge on the solute atoms. In the case of 6-311+G**, the effective charge on the solute chlorine atoms is -0.19 and -0.21 for the gauche and trans conformers, respectively. The four hydrogen atoms are all equivalent in the trans form, while there are two different types of hydrogen

atoms, antiperiplanar (Hap) and synclinal (Hsc) with respect to the chlorine atoms, in the gauche conformer as seen in the inset of Figure 4e. The effective point charge on the hydrogen is 0.23 for Hap and 0.22 for Hsc, while it is 0.17 for the hydrogen atoms in the trans form. On the other hand, for the Hap in the gauche conformer, the first peak of the RDF between H of DCE and O of water is significantly higher than that for any other cases (trans form or Hsc in the gauche) as seen in Figure 4e. It mainly originates from the tendency to minimize the steric hindrance effects. This increase of the first peak of RDF of Hap results in the gauche preference of DCE in water through the attractive electrostatic interactions between Hap and oxygen atoms of water. Although the difference of the charge on the solute carbon atom is quite large, -0.26 for the gauche and -0.13 for the trans, the influence of RDF is only a little due to the steric hindrance and other intramolecular atoms as seen in Figure 4c,d. As a whole, the gauche preference of DCE in water is derived from the stabilization by the excess chemical potential, and this is well reflected in the solvation structures. The other RDFs show similar behavior though the difference between the trans and gauche forms is marginal.

16024 J. Phys. Chem. B, Vol. 110, No. 32, 2006 V. Conclusion We investigated the conformational equilibrium of 1,2dichloroethane in water by the RISM-SCF method and polarizable continuum model (PCM). The gas phase energy difference between the trans and gauche conformers is quite dependent on both the electron correlation effect and basis sets. The PCM treatment at the MP2 level with the aug-cc-pVTZ basis set does not support the gauche preference of DCE in water, though the free energies of the trans and gauche conformers are virtually equivalent with the ∆Gt/g value of 0.01 kcal/mol. Nevertheless, the trend of ∆Gt/g in going from the gas to solution is consistent with the experimental results. Our RISM-SCF calculation that requires much less computational cost results in the negative ∆Gt/g value and shows a good agreement with the previous QM/ MM results. Incorporated with the RISM method, both the HF and MP2 theory in all the basis sets used have resulted in a free energy difference in the range of -0.33 to -0.83 kcal/ mol. We also investigated the contribution of the solute reorganization energy and the excess chemical potential to the solvation free energy that causes the gauche preference in solution. More solute reorganization energy is required for the gauche conformer to be accustomed with the surrounding solvent molecules than the trans conformer by ∼1.6 kcal/mol. However, the excess chemical potential gives more stabilization energy to the gauche conformer by ∆∆µ (∆µg - ∆µt) ≈ -4.1 kcal/mol. The preference toward the gauche conformer in water based on the free energy difference is also implied from the repulsive interaction between the chlorine atom of DCE and the oxygen atom of water and the attractive interaction between the chlorine atom of DCE and the hydrogen atom of water, and this energetics is well reflected in the radial distribution functions in the trans and gauche conformers. Acknowledgment. Numerical calculations were partly carried out in the Research Center for Computational Science, Institutes of Natural Science. This work is supported by the Grant-in-Aid for Scientific Research on Priority Area of “Water and Biomolecules” from the Ministry of Education in Japan, Culture, Sports, Science and Technology (MONBUKAGAKUSHO). We are also grateful to the support by the grant from The Next Generation Supercomputing Project, Nanoscience Program, MEXT, Japan. J.Y.L. gratefully acknowledges the Faculty Research Fund, Sungkyunkwan University, 2005. This research is supported also by the “Japan-Korea Basic Scientific Cooperation Program”. References and Notes (1) Soriano, A.; Silla, E.; Tun˜o´n, I. J. Phys. Chem. B 2003, 107, 6234. (2) Wiberg, K. B.; Murcko, M. A. J. Phys. Chem. 1987, 91, 3616. (3) Mizushima, S. Structure of Molecules and Internal Rotations; Academic: New York, 1954. (4) (a) Abraham, M. H. Prog. Phys. Org. Chem. 1974, 11, 1. (b) Sheppard, N. AdV. Spectrosc. 1959, 1, 288. (c) Lowe, J. P. Prog. Phys. Org. Chem. 1969, 6, 1. (5) (a) Amis, E. S.; Hinton, J. F. SolVent Effects on Chemical Phenomena; Academic: New York, 1973. (b) Reichardt, C. In SolVent Effects in Organic Chemistry; Verlag Chemie: Weinhein, Germany, 1979. (6) Wiberg, K. B.; Martin, E. J. J. Am. Chem. Soc. 1985, 107, 5053. (7) Wiberg, K. B. J. Am. Chem. Soc. 1986, 108, 5817. (8) Pophristic, V.; Goodman, L. Nature 2001, 411, 565. (9) (a) Gao, Y. Q.; Yang, W.; Karplus, M. Cell 2005, 123, 195. (b) Krivov, S. V.; Karplus, M. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 14766. (c) Vitkup, D.; Ringe, D.; Petsko, G. A.; Karplus, M. Nature Struct. Biol. 2000, 7, 34. (10) (a) Dobson, C. M. Nature 2003, 426, 884. (b) Lindorff-Larsen, K.; Best, R. B.; De Pristo, M. A.; Dobson, C. M.; Vendruscolo, M. Nature 2005, 433, 129.

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