Molecular Theory of Solvation (Understanding Chemical Reactivity)

Book Preface

In most of the past century, the study of solvent effect on chemicalprocesses in solution has been dominated by continuum models which has been established during the 19th century. The Onsager reaction field and the Born model of ion hydration are good examples. The Onsager reaction field has been widely employed in the interpretation of solvatochromism. The Born model of ion hydration has been incorporated in the Marcus theory for electron-transfer reactions to realize the solvent reorganization energy. It has been recently generalized to explain the solvent effect on the electronic structure in solution. The generalized version of the Born model and the Poisson-Boltzmann equation have been applied also to biomolecules, i.e., protein as well as nucleic acids, in water. The model and theory are enjoying the status of standard machinery for evaluating the electrostatics which play an essential role in chemical reactions and the conformational stability of protein, which are two of the most important topics in theoretical chemistry. The success of those theories lies on rather general laws of physics: the long-range nature of the electrostatic interaction, which makes the mean-field treatment reasonably good, and the central limiting theorem, which ensures a Gaussian character for solvent fluctuations. Owing to their generality, such models can be characterized by just a few parameters, such as dielectric constant and viscosity. However, the generality of the theory is sometimes of an unwelcome nature for chemistry, which should be able to distinguish a chemical element from other elements. The continuum theory may never be able to distinguish ethanol from acetonitrile, which have similar dielectric constants. A common maneuver to be employed in such cases to incorporate chemical specificity is to use an adjective, “effective”, e.g., “effective” radii, as boundary conditions for solving the continuum equations. Unfortunately, effective quantities so obtained for different physical processes conflict with each other, sometimes seriously, leading to vain a “religious war”. Broadly distributed values assigned to the size of ions, such as the Stokes radii of hydrodynamic equations and the Born radii of hydration free energy, are the best examples of serious drawback of the model shows up in some biological applications. One of the most dramatic events which proteins exhibit in solutions is so called ”cold denaturation,” that is, some protein denatures with decreasing temperature. The phenomenon is believed to be caused by a hydrophobic effect. The continuum model will never be able to explain the phenomenon even in the level of the ”effective” description.

Molecular simulations, i.e., the molecular dynamics and the Monte Carlo methods, have become an invaluable tool for studying liquids and solutions during the last few decades. Those methods have been widely employed to explore the phase-space or the configuration space of the liquid system to acquire observables as an average of mechanical quantities over the space. So, it is capable of accounting for chemical specificity of the system from its most elementary level. However, this merit turns into a defect in some applications. Exploring the phase-space from the most elementary process requires a large amount of computation, and it often ends up with wandering around a rather limited region of the space, not to mention the infamous non-Ergodic trap. Naive use of the method may lead to results which are either entirely wrong or are unscientific. While the method is expected generally to provide a good account for quantities related to short wavelength and large frequency, it become more and more troublesome as the wavelength becomes greater and the frequency becomes smaller.

In this book we present the third choice for describing the solvation phenomena in solutions. The method relies on the statistical mechanics applied to the liquid state of matter, especially on the RISM theory, an integral equation theory of molecular liquids. As will be described briefly in Chapter 1, the liquid state theory has been developed over the period of the past century, and has now reached the point at which almost the entire spectrum of chemistry in solution can be faithfully reproduced, at least in a qualitatively reliable manner: from ions to biomolecules, and from equilibrium to non-equilibrium. The theory isfree from such adjectives as “effective”, since it is thoroughly based on the first principle, or Hamiltonian, of the system. There is no necessity for concerns about the limited sampling of the phase space, because it explores the entire phase-space in principle by means of the statistical mechanics. Of course, the theory involves some approximations, and is never be perfect, as is the case in any meaningful theory. The best part of the theory is that the approximation involved is unambiguous, which means it can be improved not by waiting for the development ofthe computer, but by grinding the human brain. However, the theory, by itself, is not enough to describe a variety of chemistry occurring in solutions. Our strategy for exploring chemistry in solutions is to combine the RISMtheory with other methodologies well established in theoretical physics and chemistry.