Dielectric continuum processes

One of the models that has had considerable success for predicting solvation processes of dipoles in non-hydrogen-bonded solvents is the dielectric continuum model [5,14]. In this model, the amount of solvation will depend on the dipole density— that is, the molar concentration and strength of dipoles. While the position of the absorption maximum is not directly related to the energy of solvation that a molecule experiences, one would expect the two to be very strongly correlated. However, for the three different... 

A nowadays more easily applicable framework to treat local field effects in optical processes involving pure liquids or solutions has been discussed at length elsewhere in this book, and it consists in resorting to dielectric continuum solvation models. In the last pages of this section some application of such models the study of birefringences in condensed phases will be briefly discussed. 

The mutual polarization process between the solute and the polarizable medium is obtained by solving a system of two coupled equations, i.e., the QM Schrodinger equation for the solute in presence of the polarized dielectric, and the electrostatic Poisson equation for the dielectric medium in presence of the charge distribution (electrons and nuclei) of the solute. The solute occupies a molecular shaped cavity within the dielectric continuum, whose polarization is represented by an apparent surface charge (ASC) density spread on the cavity surface. The solute-solvent interaction is then represented by a QM operator, the solvent reaction potential operator, Va, corresponding to the electrostatic interaction of the solute electrons and nuclei with the ASC density of the solvent. 

It was recently shown (Ratner and Levine, 1980) that the Marcus cross-relation (62) can be derived rigorously for the case that / = 1 by a thermodynamic treatment without postulating any microscopic model of the activation process. The only assumptions made were (1) the activation process for each species is independent of its reaction partner, and (2) the activated states of the participating species (A, [A-], B and [B ]+) are the same for the self-exchange reactions and for the cross reaction. Note that the following assumptions need not be made (3) applicability of the Franck-Condon principle, (4) validity of the transition-state theory, (5) parabolic potential energy curves, (6) solvent as a dielectric continuum and (7) electron transfer is... 

Experimental tests of the dielectric continuum model based on variations of the solvent medium are, unfortunately, quite limited these are summarized in Sect. 4.5. It is nonetheless useful to examine the physical basis of eqn. (19) in order to ascertain the likelihood of its applicability. An enlightening derivation of eqn. (19) involves treating the formation of the transition state in terms of a hypothetical two-step charging process [31b, 40]. First, the charge of the reactant Ox is slowly adjusted to an appropriate value so that the solvent molecules are polarized to an extent identical to that for the transition state (step 1). Second, the charge is readjusted to that of the reactant sufficiently rapidly so that the solvent orientation remains unaltered (step 2), thereby yielding the non-equilibrium solvent polarization appropriate to the transition state. 

The charge is assumed to be uniformly distributed on the surface of the sphere. Such an ion is transferred from vacuum, with a relative dielectric permittivity equal to 1, to the solvent, which is considered to be a structureless dielectric continuum characterized by the static dielectric permittivity, This transfer may be divided into two processes the transfer of a noncharged sphere from vacuum to continuum and the charging (to ne) of the transferred sphere. 

The irreversible dehydration process indicates that the underlying dielectric continuum approach used in the anisotropic primitive model does not hold. Further numerical simulations are presently imdertaken at the atomic scale in the frame of the polarized ion model (so-called shell model ) in order to give a better description of Tobennorite dehydration/rehydration and cohesive property of cement [24]. 

Another field where dielectric continuum models are extensively used is the statistical mechanical study of many particle systems. In the past decades, computer simulations have become the most popular statistical mechanical tool. With the increasing power of computers, simulation of full atomistic models became possible. However, creating models of full atomic detail is still problematic from many reasons (1) computer resources are still unsatisfactory to obtain simulation results for macroscopic quantities that can be related to experiments (2) unknown microscopic structures (3) uncertainties in developing intermolecular potentials (many-body correlations, quantum-corrections, potential parameter estimations). Therefore, creating continuum models, which process is sometimes called coarse graining in this field, is still necessary. 

These calculations illustrate two aspects of the role of hydrogen-bonding solvents in proton transfer processes. On the one hand they catalyze these processes by forming proton conduits between donor and acceptor atoms, and on the other they provide a dielectric medium that stabilizes ionic or highly polar intermediates. Representation of the solvent by a dielectric continuum cannot account for this dual role. To treat the transfer process adequately, it will be necessary to introduce a primary shell of discrete solvent molecules into the calculations. 

Light-induced processes are described quite differently in molecular photochemistry and solid-state photophysics. In photochemistry one is used to an atomistic picture in which the arrangement of the atoms in the structure of a single molecule determines the electronic levels and thus the photochemical behavior. In contrast, the electronic levels of a solid are determined by the infinite periodicity of the atomic sequence in the crystal lattice. This leads to a basic concept according to which the solid can be treated as a dielectric continuum. Atomistic irregularities in the crystalline structure, such as lattice defects or impurities, are treated as perturbations of the spatially independent states in the energy bands. 

On the other hand, the reactions of esters with amines generate the aminolysis products. A theoretical study " on ester aminolysis reaction mechanisms in aqueous solution shows that the formation of a tetrahedral zwitterionic intermediate (Scheme 9.3) plays a key role in the aminolysis process. The rate-determining step is the formation or breakdown of such an intermediate, depending on the pH of the medium. Stepwise and concerted processes have been studied by using computation methods. Static and dynamic solvent effects have been analyzed by using a dielectric continuum model in the first case and molecular dynamics simulations together with the QM/MM method in the second case. The results show that a zwitterionic structure is always formed in the reaction path although its lifetime appears to be quite dependent on solvent dynamics. 

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