Figure 4 Free energy surfaces of triiodide ion in various solutions. Contours correspond to isoenergy lines of 1kBT, 2kBT, and 3kBT, respectively.

in the figure, contributions from ∆T pKw,δµ and ∆T pKvacw,elec are very large, but they compensate for each other. The final temperature dependence of pKw is determined by an interplay of several contributions with different physical origins. It is also interesting that the temperature dependence is dominated by ∆T pKw,reorg after the compensation for the largest contributions. The theoretical results for temperature dependence of the ionic product show fairly good agreement with experiments and also demonstrate the importance of polarization effects.

C. Solvatochromism*

The molecular properties of the triiodide ion (I3 ) in polar liquids have been studied by many techniques, motivated in part by the expected strong coupling between the solute I3 electronic structure and the environment. Interestingly, Raman and resonance Raman spectra in several solvents show a weak band corresponding to the antisymmetrical stretch mode, which is expected to be symmetry-forbidden [19], whereas the infrared spectra of many triiodide complexes with cations were also reported to show a band corresponding to the symmetrical stretching mode, which again should be symmetry-forbidden. Ab initio MO calculations for the solvated triiodide ion had been impracticable because of the difficulties in dealing with the character of the solvation, which is strongly coupled with solute electronic structure.

Computed free energy surfaces of the triiodide ion in its ground state in acetonitrile, methanol, and aqueous solution are presented in Figure 4, in which the two IEI bond

* This discussion is based on Ref. 18.

lengths (R1 and R2) are taken as coordinates. Note that the free energy surface in solution does not correspond to the potential energy surface but governs the relative population of different structures in solution. It would be misleading to estimate vibrational frequencies from the curvature of the surfaces. Contours in the figures represent isoenergy lines of 1 kBT at room temperature, 298.15 K, showing how large a population of triiodide ions exists in the different structures. The free energy profiles in solution strongly depend on the solvent. The profiles in acetonitrile solution are very localized and similar to those in the gas phase, consistent with resonance Raman experimental results in which the symme- try-forbidden band does not appear. The free energy surface in aqueous solution is markedly different and indicates a dramatically enhanced probability of structures with lower symmetry. The observation of nominally symmetry-forbidden bands in vibrational spectra is attributed to these species.

D.Conformational Equilibrium*

The acidity or basicity of organic acids and bases such as carboxylic acid and amines is governed by many factors: solvent, substitution, conformation, and so forth. Among those factors, the effect of conformational change is of special interest in terms of its significance in biological systems. In bimolecular systems such as protein, the acidity or basicity of related functional groups depends sensitively upon the molecular conformations; due to such sensitivity, the property is sometimes exploited to detect the conformational change of protein [21].

A prototype of such phenomena can be seen in even the simplest carboxylic acid, acetic acid (CH3CHOOH). Acidity is determined by the energy or free energy difference between the dissociated and nondissociated forms, whose energetics usually depend significantly on their conformation, e.g., the syn/anti conformational change of the carboxylate group in the compound substantially affects the acid–base equilibrium. The coupled conformation and solvent effects on acidity is treated in Ref. 20.

Potential and potential of mean force curves along the torsional angle θ (HEOECEC) is illustrated in Figure 5. In the gas phase the syn-acetic acid (θ 180°) is more stable than the anti conformer by 6.9 kcal/mol, and the barrier height of rotation between these conformers is estimated as 13.2 kcal/mol. In aqueous solution, the calculated free energy difference is significantly reduced to 1.7 kcal/mol. The rotational barrier also becomes lower than that in the gas phase, 10.3 kcal/mol. The reduction of the free energy gap indicates that the pKa difference between the two conformers is drastically changed from 5.1 to 1.2 on transferring from the gas phase to aqueous solution at room temperature.

Stabilization of the syn conformer in the gas phase is explained rather intuitively in terms of the extra stabilization due to increased interactions between the H atom in the OH group and the O atom in CCO group. As one can see in Figure 5, the extra stabilization in the anti conformer in aqueous solution arises from the solvation energy, especially at the carbonyl oxygen site.

The change in the electronic redistribution on transferring the molecule from the gas phase to aqueous solution is another interesting issue. Analysis of the computed Mulliken charge population demonstrates a substantial change on the hydrogen and oxygen in

* This discussion is based on Ref. 20.

Figure 5 Calculated potential and potential of mean force of acetic acid along the torsional angle of θ(HEOECEC). The left-hand side shows the total energies and the components, and the righthand side shows the decomposed ∆µ into the site.

the OH group: for the anti-conformer, the partial charges are altered from 0.355 (H) and0.428 (O) to 0.377 (H) and 0.434 (O) upon transfering from the gas to the aqueous solution phases, and for the syn conformer, from 0.373 (H) and 0.463 (O) to 0.395 (H) and 0.476 (O), respectively. One can notice that the character of the proton increases on the hydrogen in the OH group when it is immersed into aqueous solution. (Note that these values are evaluated at the optimized geometry in aqueous solution. Geometrical changes from the gas to aqueous phases should also contribute to the modification of the electron density.)

E.Acid–Base Equilibrium

In this section, we review three studies on the coupled substitution and solvent effects on basicity and acidity.

1. Basicity of the Methylamines in Aqueous Solution*

Basicity and acidity are fundamental and familiar concepts in chemistry and biochemistry. Quantum chemistry has provided a theoretical understanding of the phenomena as far as the gas phase in concerned. However, it is known that in solution reactivity is seriously affected by solvents. One example of such a well-known phenomenon is that the basicity

* This discussion is based on Ref. 22 and Ref. 23.

cule and Ereorg), solvation energy (∆ ) described above, and kinetic contributions evaluated from the elementary statistical mechanics of ideal systems. The contribution from solute itself, ∆∆G298s (solute), exhibits similar monotonic behavior with the gas phase result (∆∆Gg298), which is in good agreement with the experimental data. The difference between ∆∆Gs298(solute) and ∆∆Gg298 is due essentially to the electron reorganization energy. The solvation free energy ∆∆G298s (solvent) shows the monotonic increase with successive methyl substitution. The sum of the two contributions produces an inversion in the overall free energy change ∆∆Gs298, which is in qualitative accord with the experimental result.

2. Acidities of Haloacetic Acids in Aqueous Solution*

Another example is the acidities of a series of carboxylic acids. It is known that the substitution effect on these compounds also depends on the environment. The behavior of the halo-substituted acetic acids is one of the prototype problems for the solvent effect on acidity: The order in strength of the haloacetic acids in the gas phase is

CH3COOH CH2FCOOH CH2ClCOOH CH2BrCOOH

whereas in aqueous solution it is drastically altered [27] to

CH3COOH CH2FCOOH CH2ClCOOH CH2BrCOOH

The observed acidities in the gas phase are interpreted in terms of the negative induction effect of the halo substituents; however, the microscopic picture of the solvent effects in addition to such induction effects of the solute have not been clarified.

Procedures to compute acidities are essentially similar to those for the basicities discussed in the previous section. The acidities in the gas phase and in solution can be calculated as the free energy changes ∆Gg and ∆Gs upon proton release of the isolated and solvated molecules, respectively. To discuss the relative strengths of acidity in the gas and aqueous solution phases, we only need the magnitude of ∆Gg and ∆Gs for haloacetic acids relative to those for acetic acids. Thus the free energy calculations for acetic acid, haloacetic acids, and each conjugate base are carried out in the gas phase and in aqueous solution.

In Figure 7, ∆Gs and its components, ∆Gs(solute) and ∆Gs(solvent), are plotted. ∆Gs(solute) contributes to the increase in the net free energy upon proton release or to the acidity, which is similar to ∆Gg in the gas phase. ∆Gs(solvent) is positive relative to acetic acid and contributes to hinder the proton release and to decrease the acidity. The net increase in ∆Gs(solvent) from the fluoro derivative to the chloro derivative is caused by the greater destabilization of the negative ions compared to that of the neutral molecules. The essential difference between the ionic and neutral species lies in the electrostatic interactions, which play an important role in determining the order of the acidities in solution. The inversion in the acidities from the fluoro substitution to the chloro substitution is due to the greater increase in the electrostatic contribution in the solvation free energy compared to the decrease in the contribution from the change in the solute electronic structure. As shown in Figure 7, agreement with respect to the relative order in acidity is obtained in aqueous solution as well as in the gas phase.

* This discussion is based on Ref. 25 and Ref. 26.

Figure 7 Free energy changes of halo-substituted carboxyl acid in aqueous solution upon deprotonation referred to acetic acid.

3. Acid Strength of the Hydrogen Halides in Aqueous Solution*

It is known that the order of acidity of hydrogen halides (HX, where X F, Cl, Br, I) in the gas phase can be successfully predicted by quantum chemical considerations, namely, F Cl Br I. However, in aqueous solution, whereas hydrogen chloride, bromide, and iodide completely dissociate in aqueous solutions, hydrogen fluoride shows a small dissociation constant. This phenomenon is explained by studying free energy changes associated with the chemical equilibrium HX H2O s X H3O in the solution phase for a series of hydrogen halides. In this study, the species in the equilibrium reaction, HX, X , H2O, and H3O , are regarded as ‘‘solute’’ in the infinitely dilute solution. Thus the free energy difference in aqueous solution can be obtained in terms of the free energy difference associated with the reaction in vacuo and solvation free energy.

Figure 8 shows the PCF between the halogen site in HX and the hydrogen site in

˚

solvent water. The fluoride shows a distinct peak at 1.82 A. There is no corresponding peak in the other XEH correlation functions. From other PCFs and geometrical considerations, we can conclude that hydrogen bonds between solute hydrogen and solvent oxygen are strong and are found in all the hydrogen halides and that only hydrogen fluoride forms a distinct FEH (solvent water) hydrogen bond. The liquid structure around HF is expected to be markedly different from those around the other hydrogen halides.

The free energy difference is mainly governed by the subtle balance of the two energetic components, the formation energies of hydrogen halides and the solvation ener-

* This discussion is based on Ref. 28.