Dielectric interaction energies

A problem of molecular-shaped SCRF models is the absence of an analytical solution for the reaction field. One line of development was the search for an approximate expression for the dielectric interaction energy of a solute in a molecular-shaped cavity, without the need for explicit calculation of the solvent polarization. These models were summarized as generalized Born (GB) approximations [22,30]. The most popular of these models... 

The dielectric interaction energy density is simply given by y > . For an applied electric field along they axis, for example, in the plane of the smectic layer, the interaction energy is given by... 

Li) he so-called distance-dependent dielectric models. The simplest implementation of a dis-i.iiice-dependent dielectric is to make the relative permittivity proportional to the distance. Tine interaction energy between two charges qi and qj then becomes ... 

Polarizability Attraction. AU. matter is composed of electrical charges which move in response to (become electrically polarized in) an external field. This field can be created by the distribution and motion of charges in nearby matter. The Hamaket constant for interaction energy, A, is a measure of this polarizability. As a first approximation it may be computed from the dielectric permittivity, S, and the refractive index, n, of the material (15), where is the frequency of the principal electronic absorption... 

It should be noted that, if the medium between the particle and substrate is something other than vacuum and possesses a dielectric constant e, the interaction energy in Eq. 68 is reduced by a factor of Eq. 68, which relates the interaction energy between permanent electric dipoles and their separation distances is known as the Keesom effect. 

In the Born equation, the ion solvent interaction energy is determined only by one physical parameter of the solvent, i.e., the dielectric constant. However, since actual ion-solvent interactions include specific interactions such as the charge-transfer interaction or hydrogen bonds, it is natural to think that the Born equation should be insufficient. It is well known that the difference in the behavior of an ion in different solvents is not often elucidated in terms of the dielectric constant. 

Coulomb s law describes the charge-charge interaction energy (Equation 15). It is used in MM3 for the calculation of two charges interacting with one another. This term is used to calculate ionic interactions. The variables qA and qB are the formal charges on atoms A and B, respectively. The distance between the two atoms is r, and the dielectric constant is D. 

Here the atoms in the system are numbered by i, j, k, l = 1,..., N. The distance between two atoms i, j is ry, q is the (partial) charge on an atom, 6 is the angle defined by the coordinates (i, j, k) of three consecutive atoms, and 4> is the dihedral angle defined by the positions of four consecutive atoms, e0 is the dielectric permittivity of vacuum, n is the dihedral multiplicity. The potential function, as given in equation (6), has many parameters that depend on the atoms involved. The first term accounts for Coulombic interactions. The second term is the Lennard-Jones interaction energy. It is composed of a strongly repulsive term and a van der Waals-like attractive term. The form of the repulsive term is chosen ad hoc and has the function of defining the size of the atom. The Ay coefficients are a function of the van der Waals radii of the... 

To answer this question, let us first consider a neutral molecule that is usually said to be polar if it possesses a dipole moment (the term dipolar would be more appropriate)1 . In solution, the solute-solvent interactions result not only from the permanent dipole moments of solute or solvent molecules, but also from their polarizabilities. Let us recall that the polarizability a of a spherical molecule is defined by means of the dipole m = E induced by an external electric field E in its own direction. Figure 7.1 shows the four major dielectric interactions (dipole-dipole, solute dipole-solvent polarizability, solute polarizability-solvent dipole, polarizability-polarizability). Analytical expressions of the corresponding energy terms can be derived within the simple model of spherical-centered dipoles in isotropically polarizable spheres (Suppan, 1990). These four non-specific dielectric in-... 

Another type of ternary electrolyte system consists of two solvents and one salt, such as methanol-water-NaBr. Vapor-liquid equilibrium of such mixed solvent electrolyte systems has never been studied with a thermodynamic model that takes into account the presence of salts explicitly. However, it should be recognized that the interaction parameters of solvent-salt binary systems are functions of the mixed solvent dielectric constant since the ion-molecular electrostatic interaction energies, gma and gmc, depend on the reciprocal of the dielectric constant of the solvent (Robinson and Stokes, (13)). Pure component parameters, such as gmm and gca, are not functions of dielectric constant. Results of data correlation on vapor-liquid equilibrium of methanol-water-NaBr and methanol-water-LiCl at 298.15°K are shown in Tables 9 and 10. 

These points indicate that the continuum theory expression of the free energy of activation, which is based on the Born solvation equation, has no relevance to the process of activation of ions in solution. The activation of ions in solution should involve the interaction energy with the solvent molecules, which depends on the structure of the ions, the solvent, and their orientation, and not on the Born charging energy in solvents of high dielectric constant (e.g., water). Consequently, the continuum theory of activation, which depends on the Born equation,fails to correlate (see Fig. 1) with experimental results. Inverse correlations were also found between the experimental values of the rate constant for an ET reaction in solvents having different dielectric constants with those computed from the continuum theory expression. Continuum theory also fails to explain the well-known Tafel linearity of current density at a metal electrode. ... 

The energy involves electronic energy s°, solvent interaction energy Ep, and the image interaction energy e, . The distance-dependent effective solvent dielectric constant k(x), which appears in the image term, was taken as... 

Coarse-grained molecular d5mamics simulations in the presence of solvent provide insights into the effect of dispersion medium on microstructural properties of the catalyst layer. To explore the interaction of Nation and solvent in the catalyst ink mixture, simulations were performed in the presence of carbon/Pt particles, water, implicit polar solvent (with different dielectric constant e), and ionomer. Malek et al. developed the computational approach based on CGMD simulations in two steps. In the first step, groups of atoms of the distinct components were replaced by spherical beads with predefined subnanoscopic length scale. In the second step, parameters of renormalized interaction energies between the distinct beads were specified. 

The double layer interaction energy is given In terms of the eluant dielectric constant e by (37). 

Dipole-dipole interaction energies are proportional to the product of the dipole moments, and /H2, divided by the product of the dielectric constant D and the sixth power of the distance between the dipoles. 

Dipole-induced dipole interaction energies are proportional to the product of the square of the dipole moment and the polarizability a of the atom/group with which the ion interacts, divided by the product of the square of dielectric constant D and the sixth power of the distance between the dipole and the polarizable group. Dispersion interactions have energies that are proportional to the product of polarizabilities i and 2. divided by the sixth power of the distance between two polarizable atoms (or groups of atoms). 

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