Dielectric continuum models chemical reactions

Another example of a process in which a charge is moved across an interface is interfacial electron transfer reactions. As in the case of ion transfer, experimental data on electron transfer across liquid-liquid interfaces are very limited. For this process, however, there exists a theoretical framework developed within a dielectric continuum model,which built on the fundamental theory of electron transfer in bulk media. Computer simulations, which complement experiments and theory, have not yet dealt with chemically realistic systems but, instead, considered idealized molecules to test the basic assumptions of the continuum model. 

Including electronic interactions increases the complexity of the problem enormously, such that the number of atoms to be included typically ranges from 10-100, depending on the methodology chosen. The more accurate the treatment, the more computationally costly the calculation will be. This implies that quantum chemical calculations are generally performed on small model systems, usually in a vacuum or surrounded by a dielectric continuum that mimics bulk solution effects. Based on studies of, e.g., several alternative reaction mechanisms or properties of different... 

From a computational view point, chemical reactions in solution present a yet not solved challenge. On one hand, some of the solvent effects can be approximated as if the solute molecule would be in a continuum with a given dielectric characterization of the liquid, and this view point has been pioneered by Bom [1], later by Kirkwood [2] and Onsager [3] and even later by many computational quantum chemists [4-9], On the other hand, the continuum model fails totally when one is interested in the specific... 

When structural and dynamical information about the solvent molecules themselves is not of primary interest, the solute-solvent system may be made simpler by modeling the secondary subsystem as an infinite (usually isotropic) medium characterized by the same dielecttic constant as the bulk solvent, that is, a dielectric continuum. Theoretical interpretation of chemical reaction rates has a long history already. Until recently, however, only the chemical reactions of systems containing a few atoms in the gas phase could be studied using molecular quantum mechanics due to computational expense. Fortunately, very important advances have been made in the power of computer-simulation techniques for chemical reactions in the condensed phase, accompanied by an impressive progress in computer speed (Gonzalez-Lafont et al., 1996). 

Solvent effects can significantly influence the function and reactivity of organic molecules.1 Because of the complexity and size of the molecular system, it presents a great challenge in theoretical chemistry to accurately calculate the rates for complex reactions in solution. Although continuum solvation models that treat the solvent as a structureless medium with a characteristic dielectric constant have been successfully used for studying solvent effects,2,3 these methods do not provide detailed information on specific intermolecular interactions. An alternative approach is to use statistical mechanical Monte Carlo and molecular dynamics simulation to model solute-solvent interactions explicitly.4 8 In this article, we review a combined quantum mechanical and molecular mechanical (QM/MM) method that couples molecular orbital and valence bond theories, called the MOVB method, to determine the free energy reaction profiles, or potentials of mean force (PMF), for chemical reactions in solution. We apply the combined QM-MOVB/MM method to... 

In the empirical valence bond (EVB) model [304, 349, 370] a fairly small number of VB functions is used to fit a VB model of a chemical reaction path the parameterisation of these functions is carried out to reproduce experimental or ab initio MO data. The simple EVB Hamiltonian thus calibrated for a model reaction in solution can subsequently be used in the description of the enzyme-ligand complex. One of the most ingenious attributes of the EVB model is that the reduction of the number of VB resonance structures included in the model does not introduce serious errors, as would happen in an ab initio VB formulation, due to the parameterisation of the VB framework which ensures the reproduction of the experimental or other information used. This computationally efficient approach has been extensively used with remarkable success [305, 306, 371, 379] A similar method presented by Kim and Hymes [380] considers a non-equilibrium coupling between the solute and the solvent, the latter being treated as a dielectric continuum. 

In the continuum solvent distribution models, Vei is evaluated by resorting to the description of the solvent as a dielectric medium. This medium may be modeled in many different ways, being the continuous methods quite flexible. We shall consider the simplest model only, i.e. an infinite linear isotropic dielectric, characterized by a scalar dielectric constant e. The interested reader can refer to a recent review (Tomasi and Persico, 1994) for the literature regarding more detailed and more specialistic models. However, the basic model we are considering here is sufficient to treat almost all chemical reactions occurring in bulk homogeneous solutions. 

Relatively few theoretical studies have been devoted to the nitration of aromatics in solution. The main reason stems from the difficulty of treating solute-solvent interactions within a quantum chemical framework. Although it is in principle possible to represent the solvent explicitly, such a procedure is generally not applicable, since a very large number of solvent molecules are needed to get an accurate representation of the PES for a solution reaction. This is particularly true for reactions involving ions or zwitterions. The most common approach for representing the solvent in quantum chemical calculations is instead by a dielectric continuum approach, such as the polarizable continuum model (PCM) [57]. This type of approach can be combined with a few explicit solvent molecules in cases where the solvent is expected to play an active role in bond breaking or bond formation [58]. 

The hybrid methods which combine quantum-mechanical (QM) and classical descriptions are surely one of the mostly well-suited strategies in this context. Two main families of hybrid methods can be defined according to the model used to describe the classical part of the system. Either continuum or atomistic formulations can be introduced where, in the first case, the classical subsystem is described as a dielectric medium while, in the second case, a Molecular Mechanics (MM) formulation is generally adopted. While QM/continuum methods have been largely and successfully applied to molecular solutes in liquid solutions [2-5], QM/MM formulations have been more often used in the field of structured (biological) environments [6-10] even if the study of chemical reaction dynamics in solution represents another important field of applications of the method [11, 12]. 

The RPH concept has been used by Lee and Hynes to develop a model for the description of chemical reactions in polar solvents where the solvent is treated as a polarizable continuum characterized by its dielectric constant. The progress of the reaction from reactants to products is described by a single coordinate Xrc (ignoring any other internal molecular modes), which is chosen on the basis of chemical intuition rather than rigorous definition. For example, in the case of the ionic dissociation AB -> A+ -f B the reaction coordinate Xrc is simply the distance between atoms A and B. 

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, e, 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 infomation of the solute-solvent interaction and solvation free energy. 

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