Figure 8 Pair correlation functions between X (in HX) and H (in solvent water) for a series of hydrogen halides.

gies of the halide anions. The characteristic behavior of hydrogen fluoride as a weak acid is explained in terms of the enhanced stability of the nondissociated form of the molecule in aqueous solution due to the extra hydrogen bonding with solvent. From these modern theoretical considerations, one can say that Pauling’s heuristic argument seems to be correct in a qualitative sense.

F. Tautomerization in Formamide*

Solvent effects on chemical equilibria and reactions have been an important issue in physical organic chemistry. Several empirical relationships have been proposed to characterize systematically the various types of properties in protic and aprotic solvents. One of the simplest models is the continuum reaction field characterized by the dielectric constant, ε, of the solvent, which is still widely used. Taft and coworkers [30] presented more sophisticated solvent parameters that can take solute–solvent hydrogen bonding and polarity into account. Although this parameter has been successfully applied to rationalize experimentally observed solvent effects, it seems still far from satisfactory to interpret solvent effects on the basis of microscopic information of the solute–solvent interaction and solvation free energy.

Among many examples of the solvent effects on chemical equilibria and reactions, the solvent effect on tautomerization has been one of the most extensively studied. Experi-

* This discussion is based on Ref. 29.

mentally, it is known that such equilibrium constants depend sensitively on the solvent polarity in solution. Tautomerization in formamide has been studied to obtain the microscopic solvation structure around the solute and to find a relationship between the empirical relation (Taft’s parameter) and microscopic information given by ab initio theory.

The empirical parameters derived by Taft and coworkers are well known as a measure of the hydrogen-bonding abilities of solvents. For aprotic solvents, β parameters indicate the strength of hydrogen bonding. On the other hand, the height of the first peak in PCFs around solute hydrogen, which are obtained from the RISM-SCF calculation, also represent the strength of hydrogen bonding. As shown in Figure 9, Taft’s β parameters are actually well correlated to the calculated well depth of the hydrogen bonding corresponding to the logarithm of the height of the first peak in the PCFs. The figures give a microscopic explanation for the origin of the empirical solvent parameters representing the ability of a solvent to form hydrogen bonds.

Figure 10 presents a correlation between the solvation energy computed by the RISM-SCF method and the Onsager–Kirkwood parameter, (ε 1)/(2ε 1), which is a typical parameter empirically derived from the macroscopic parameter ε. If the parameters are good, all the solvation energies must lie on a straight line. One can see that the irregularity of the solvation free energy in acetonitrile is remarkable for both tautomers. Considering the situation that the present theory reproduces well the experimentally derived hydrogen bonding strengths, the irregularity observed here clearly demonstrates the breakdown of the continuum solvation model.

G.The SN2 Reaction*

Chemical reactions are undoubtedly the most important issue in theoretical chemistry, where electronic structure plays an essential role. However, as will be demonstrated in this section, solvent effects also often play a crucial role in the mechanism of a chemical reaction in solution.

The Menshutkin-type SN2 reaction in aqueous solution,

NH3 CH3Cl → NH3CH3 Cl

is a prototype reaction in quantum chemistry that requires treatment of the solvent effect, and substantial computational studies have been reported based on the dielectric continuum model and QM/MM method.

A free energy profile along the reaction path is constructed by taking the difference of the CECl and CEN distances as the reaction coordinate (see Fig. 11). Although this reaction is found by the Hartree-Fock method to be endothermic in the gas phase by 106.3 kcal/mol, it becomes exothermic in aqueous solution by 27.8 kcal/mol with a barrier height of 17.7 kcal/mol. The barrier height in aqueous solution computed by the MP2 method (not shown) is slightly higher, 20.9 kcal/mol, but the global feature of the energy surfaces is not affected by taking the electron correlation into account.

It is interesting that the molecular structure in the transition state is also subject to a solvent effect. Compared to the gas phase, the solute molecular geometry at the transition state shifts toward the reactant side in aqueous solution; the CEN and CECl distances

* This discussion is based on Ref. 31.

Figure 10 Solvation free energy versus the Onsager–Kirkwood parameter (ε 1)/(2ε 1).

Figure 11 Potential energy and potential of mean force of the Menshutkin reaction. The dashed line is for reaction in the gas phase, and the solid line for reaction in aqueous solution.