Dielectric continuum, models

Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... 

A variety of methodologies have been implemented for the reaction field. The basic equation for the dielectric continuum model is the Poisson-Laplace equation, by which the electrostatic field in a cavity with an arbitrary shape and size is calculated, although some methods do not satisfy the equation. Because the solute s electronic strucmre and the reaction field depend on each other, a nonlinear equation (modified Schrddinger equation) has to be solved in an iterative manner. In practice this is achieved by modifying the electronic Hamiltonian or Fock operator, which is defined through the shape and size of the cavity and the description of the solute s electronic distribution. If one takes a dipole moment approximation for the solute s electronic distribution and a spherical cavity (Onsager s reaction field), the interaction can be derived rather easily and an analytical expression of theFock operator is obtained. However, such an expression is not feasible for an arbitrary electronic distribution in an arbitrary cavity fitted to the molecular shape. In this case the Fock operator is very complicated and has to be prepared by a numerical procedure. 

Equation (15) permits a straightforward analysis of dielectric continuum models of hydration that have become popular in recent decades. The dielectric model, also called the Bom approximation, for the hydration free energy of a spherical ion of radius R with a charge q at its center is... 

Archontis, G. Simonson, T., Proton binding to proteins a free energy component analysis using a dielectric continuum model, Biophys. J. 2005, 88, 3888-3904... 

This section will focus on the application of dielectric continuum models to equilibria like those described above. A special effort will be made to highlight investigations that compared two or more solvation models. We emphasize that some care must be taken to distinguish the degree to which different continuum models have been extended to account for non-electrostatic effects, since these effects may certainly play a large role in some of the equilibria under discussion. Those continuum models that consider only electrostatics are of limited applicability unless non-electrostatic effects cancel for all equilibrium contributors. 

This approximation requires that cos. This behavior in fact follows from a Debye dielectric continuum model of the solvent when it is coupled to the solute nuclear motion [21,22] and then xs would be proportional to the longitudinal dielectric relaxation time of the solvent indeed, in the context of time dependent fluorescence (TDF), the Debye model leads to such an exponential dependence of the analogue... 

We have given some highlights of a theory which combines the familiar multistate VB picture of a molecular system with a dielectric continuum model for the solvent which accounts for the solute s boundary effects — due to the presence of a van der Waals cavity which displays the solute s shape — and includes a quantum model for the electronic solvent polarization. 

The dynamics of carbon-halogen bond reductive cleavage in alkyl halides was studied by MP3 ab initio calculations, using pseudopotentials for the halogens and semidiffuse functions for the heavy atoms [104], The effect of solvent was treated by means of the ellipsoidal cavity dielectric continuum model. Both a concerted (i.e., a one-step) and a stepwise mechanism (in which an anion radical is formed at first) were... 

Even here, specific solvent effects which are not considered in the continuum theory begin to appear, most notably for hydrox-ylic solvents. However, recent work of our own suggests that it may be possible to make straightforward empirical corrections to the dielectric continuum model for such cases. 

DR. JOHN BRAUMAN (Stanford University) I have a question about the empirical correlations for quantities like charge transfer band energies versus parameters such as the Kosower Z-value. There is a very large literature of that type and there are many, many good correlations for a variety of parameters. You obtain straight lines with your simple dielectric continuum model. It seems to me, however, that one ought to be able to derive these types of relationships directly from the model. And it doesn t seem to be very helpful to say that these relationships are simply empirical and, therefore, not worth the attention. What you want to do is derive the equations and see whether they, in fact, all reduce to the same terms. 

Both the electronic couphng matrix element and the outer-sphere component of the nuclear reorientation parameter are thought to vary with donor-acceptor separation and orientation [29, 49]. It has been shown in studies of Os and Ru-ammines bridged by polyproline spacers that the distance dependence of X can be greater than that of [50]. Dielectric continuum models of solvent reorganization predict that Xg will increase with... 

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... 

Employing the Davidson-Cole model for propylene carbonate and the Cole-Cole model for propionitrile with the appropriate dielectric parameters from the literature, we have predicted C(t) for these polar aprotic solvents according to the dielectric continuum model. The agreement between the predicted and observed C(t) is not nearly as good as the alcohol examples (see below). 

The results of the SCRF models depend strongly on the radius Rx used for the definition of the spherical interface between the solute and the solvent. Unfortunately, the dielectric theory does not provide an answer for the question of which value is appropriate for this radius. Owing to the implicit assumption of the dielectric continuum models that the electron density of the solute should be essentially inside the cavity, any value of Rx below a typical van der Waals (vdW) radius would not be meaningful. On the other hand, at least at the distance of the first solvent shell, i.e., typically at two vdW radii, we should be in the dielectric continuum region. However, there is no clear rationale for the right value between these two limits other than empirical comparison of the results with experimental data. Among others, the choice of spherical cavities which correspond to the liquid molar-solute volume has proved to be successful. 

The structure of this contribution is as follows. After a brief summary of the theory of optical activity, with particular emphasis on the computational challenges induced by the presence of the magnetic dipole operator, we will focus on theoretical studies of solvent effects on these properties, which to a large extent has been done using various polarizable dielectric continuum models. Our purpose is not to give an exhaustive review of all theoretical studies of solvent effects on natural optical activity but rather to focus on a few representative studies in order to illustrate the importance of the solvent effects and the accuracy that can be expected from different theoretical methods. 

Within the dielectric continuum model, the electrostatic interactions between a probe and the surrounding molecules are described in terms of the interaction between the charges contained in the molecular cavity, and the electrostatic potential these changes experience, as a result of the polarization of the environment (the so-called reaction field). A simple expression is obtained for the case of an electric dipole, /a0, homogeneously distributed within a spherical cavity of radius a embedded in an anisotropic medium [10-12], by generalizing the Onsager model [13]. For the dipole parallel (perpendicular) to the director, the reaction field is parallel (perpendicular) to the dipole, and can be calculated as [10] ... 

Recently, the surface tensor model has been used together with the dielectric continuum model to calculate the orientational order parameters of solutes in nematic solvents [8,9,27], Figure 2.32 shows the theoretical results for anthracene and anthraquinone in nematic solvents with different dielectric anisotropy. Considering only the surface tensor contribution, positive Szz and Sxx and negative are obtained, with Szz > Sxx > Syy. This corresponds to what could be expected on the basis of the molecular shape the long axis (z) is preferentially aligned with the director, and the normal to the... 

Figure 3.26 Schematic representation of a five-zone dielectric continuum model used to calculate As for hole transfer between guanine sites (zone 1 (the solute )) in an aqueous DNA duplex [23]. The other zones refer, respectively, to other nucleobases of the DNA tt stack (zone 2) sugar-phosphate backbone (zone 3) bound water within 3 A of the surface of the DNA (zone 4) and bulk water (zone 5). The + and — charges are the simplest possible model for the net charge density change (Ap) involved in As (see Equation (3.89)). In the actual detailed calculations (see text and Equation (3.95)) multiple point-charge D and A sites were employed (figure drawn by Dr. K. Siriwong, private communication).

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