Figure 12 Pair correlation functions of ClEH and NEH along the reaction path.

˚

are almost the same (2.258 A) in aqueous solution, whereas those in the gas phase are

˚

1.890 and 2.490 A, respectively, which is consistent with Hammond’s postulate [32]. The great stabilization of the product in aqueous solution is explained from changes

in PCFs along the reaction path, which are shown in Figure 12. The PCF of ClEH obviously illustrates the progress of hydrogen bonding along the reaction coordinate: For the reactant no peak corresponding to the ClEH interaction is observed, but a distinct peak

˚

around 2.2 A gradually appears with slight inward shifts as the reaction proceeds. In contrast, the hydrogen bond between the ammonia N and water H is observed to break.

˚

The first peak around 2.0 A corresponds to the hydrogen bonding of a water hydrogen to the lone pair electron in nitrogen. The lone pair electron participates in a new chemical bond with C of CH3Cl, and the peak disappears as the reaction proceeds. The formation of ClEH hydrogen bonds (solvation) and breaking of NEH bonds are key features in the understanding of solvent effects on the reaction mechanism.

IV. SUMMARY AND PROSPECTS

In this chapter, we have reviewed the RISM-SCF/MCSCF method, which combines electronic structure and liquid-state theories to deal with the chemistry of solutions. The ability

of the method to treat solvent effects on chemical processes has been demonstrated. Electronic structure plays a primary role in determining the structure of a molecule. However, changes in the electronic energy associated with a chemical process are comparable, in many cases, with those due to solvation in solution. This subtle balance between changes in electronic energy and in the solvation free energy sometimes causes drastic changes in the stability of chemical species, as we have seen in several examples. The solvent effect even reverses the equilibrium between a reactant and a product.

As has been repeatedly stated throughout the chapter, the theory provides good qualitative descriptions to solution chemistry in most cases, but quantitative agreement between theoretical and experimental results is only moderate. It is always possible to improve the results numberwise by tuning the molecular parameters and/or by introducing empirical parameters into either or both elements of the theory, MO and RISM. This direction, in fact, has been pursued by Gao and coworkers [33], who have shown almost perfect quantitative agreement between the theory and experiments by replacing the ab initio method by the semiempirical approach for the MO part and by adjusting the Lennard-Jones parameters of atoms. The effort should be greatly appreciated, because it could have demonstrated the capability of the combined MO and RISM method to account for experimental data at least at the same quantitative level as the continuum model descriptions. However, it will not be an ultimate goal of the combined quantum and statistical mechanics theory. The real strength of the theory lies in the fact that it does not require in principle any adjustable or empirical parameter to describe complicated solution chemistry. The theory could be or should be naturally improved by theoretical development of either or both elements of the method and by coupling them, not by adjusting or introducing empirical parameters. Since considerable efforts have been continuously devoted to improvement in both theoretical fields in chemical physics, there is no doubt that the RISM-SCF/MCSCF approach will find greater application in the future.

There are several directions conceivable to extend further the horizon of the theory. One such direction is to seek an experimental method to prove electron distributions in a molecule in solution: the partial atomic charges are an effective representation of the electron distribution. As has been described in the preceding sections, the RISM-SCF/ MCSCF method provides information on the electron distribution that is more detailed than information on the dipole moment. Therefore, if we could find a means to observe the electron distribution, it will provide more detailed information on molecular structure in solution. It will also provide a reliable tool for testing theory experimentally. One possible candidate among experimental methods to observe the electron distribution may be the NMR chemical shift, because the chemical shift is a manifestation of changes in the screening of nuclear magnetic fields due to electron clouds. It is highly desirable to establish a theory to bridge the NMR chemical shift and the RISM-SCF/MCSCF method.

In the first example of applications of the theory in this chapter, we made a point with respect to the polarizability of molecules and showed how the problem could have been handled by the RISM-SCF/MCSCF theory. However, the current level of our method has a serious limitation in this respect. The method can handle the polarizability of molecules in neat liquids or that of a single molecule in solution in a reasonable manner. But in order to be able to treat the polarizability of both solute and solvent molecules in solution, considerable generalization of the RISM side of the theory is required. When solvent molecules are situated within the influence of solute molecules, the solvent molecules are polarized differently depending on the distance from the solute molecules, and the solvent can no longer be ‘‘neat.’’ Therefore, the polarizable model developed for neat liquids is not valid. In such a case, solvent–solvent PCF should be treated under the solute

field, which is typical of in-homogeneous liquids. The density functional theory in classical theory may be the best choice for extending the theory to such a problem [34].

Nonequilibrium processes including chemical reactions present a most challenging problem in theoretical chemistry. There are two aspects to chemical reactions: the reactivity or chemical equilibrium and the reaction dynamics. The chemical equilibrium of molecules is a synonym for the free energy difference between reactant and product. Two important factors determining the chemical equilibrium in solution are the changes in electronic structure and the solvation free energy. Those quantities can be evaluated by the coupled quantum and extended RISM equations, or RISM-SCF theory. Exploration of the reaction dynamics is much more demanding. Two elements of reaction dynamics in solution must be considered: the determination of reaction paths and the time evolution along the reaction path. The reaction path can be determined most naively by calculating the free energy map of reacting species. The RISM-SCF procedure can be employed for such calculations. If the rate-determining step of the reaction is an equilibrium between the reactant and the transition state, the reaction rate can be determined from the free energy difference of the two states based on transition state theory. On the other hand, for such a reaction in which the dynamics of solvent reorganization determines the reaction rate, the time evolution along the reaction path may be described by coupling RISM and the generalized Langevin equation (GLE) in the same spirit as the Kramers theory: The time evolution along a reaction path can be viewed as a stochastic barrier crossing driven by thermal fluctuations and damped by friction. Our treatment features the microscopic treatment of solvent structure on the level of the density pair correlation functions, which distinguishes it from earlier attempts that used phenomenological solvent models. One of the prerequisites for developing such a treatment is a theory to describe liquid dynamics on the molecular level. We recently proposed a new theory based on the interaction site model in which liquid dynamics is decoupled into the collective modes of density fluctuation: the acoustic and optical modes corresponding, respectively, to transnational and rotational motion of molecules [35]. From this point of view, transport coefficients such as the friction coefficient can be realized as a response of the collective modes of the solvent to perturbations due to solute. It is the first step in developing a theory of reaction dynamics to describe stochastic barrier crossing in terms of the collective fluctuations of solvent to reacting species along a properly defined reaction coordinate.

ACKNOWLEDGMENTS

We thank all our collaborators, especially Drs. Masaaki Kawata, Kazunari Naka, Tateki Ishida, and Akihiro Morita. We are also grateful to Profs. Masaru Nakahara, Yasuhiko Kondo, and Tadashi Okuyama, who have given invaluable advice and encouragement.

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