Potential energy surface dielectric constant

It is well known that a solvent can canse dramatic changes in rates and even mechanisms of chemical reactions. Modem theoretical chemistry makes it possible to incorporate solvent effects into calcnlations of the potential energy surface in the framework of the continnnm and explicit solvent models. In the former, a solvent is represented by a homogeneous medium with a bulk dielectric constant. The second model reflects specific molecule-solvent interactions. Finally, calculations of the potential energy surface in the presence or absence of solvents can be performed at various theory levels that have been considered in detail by Zieger and Autschbach [10]. 

The potential energy of repulsion Vr depends on the size and shape of the dispersed particles, the distance between them, their surface potential To, the dielectric constant sr of the dispersing liquid, and the effectiveness thickness of the electrical double layer 1 /k (Chapter 2, Section I), where... 

Figure 2.25. Potential energy surface for the sulfoxidation of dimethyl sulfide by Cpd I (ref [122]). Barriers in parentheses incorporate the effect of a dielectric constant, e = 5.7.

The above approach neglects the modifications of the electronic structure in the surface layers. In semi-conductors and insulators, as a result of the presence of dangling bonds or due to the reduction of the Madelung potential on under-coordinated atoms, surface states appear either at the gap edges or deep in the gap. Surface electron-hole pairs have thus lower energies than in the bulk. In addition, the reduction of the Madelung potential at the surface yields an increase of the matrix elements of y in (4.2.23). Both processes enhance the surface dielectric constant. 

If a piece of metal, such as silver, is dipping into a solvent, and a positive atomic core is taken from the surface into the solvent, the ion is again surrounded by its electrostatic field but free energy has been lost by the dielectric, and a relatively small amount of work has had to be done. The corresponding potential-energy curve (Fig. 96) is therefore much less steep and has a much shallower minimum than that of Fig. 9a. For large distances d from a plane metal surface this curve is a plot of — c2/4td where t is the dielectric constant of the medium at the temperature considered The curve represents the work done in an isothermal removal of the positive core. 

The very high ionization potential and the low polarizability of the fluorine atom imply that fluorinated compounds have only weak intermolecular interactions. Thus, perfluoroalkylated compounds have very weak surface energies, dielectric constants, and refracting indexes. 

Here Vij denotes the distance between atoms i and j and g(i) the type of the amino acid i. The Leonard-Jones parameters Vij,Rij for potential depths and equilibrium distance) depend on the type of the atom pair and were adjusted to satisfy constraints derived from as a set of 138 proteins of the PDB database [18, 17, 19]. The non-trivial electrostatic interactions in proteins are represented via group-specific dielectric constants ig(i),g(j) depending on the amino-acid to which atom i belongs). The partial charges qi and the dielectric constants were derived in a potential-of-mean-force approach [20]. Interactions with the solvent were first fit in a minimal solvent accessible surface model [21] parameterized by free energies per unit area (7j to reproduce the enthalpies of solvation of the Gly-X-Gly family of peptides [22]. Ai corresponds to the area of atom i that is in contact with a ficticious solvent. Hydrogen bonds are described via dipole-dipole interactions included in the electrostatic terms... 

In this paper it is shown that the rate of deposition of Brownian particles on the collector can be calculated by solving the convective diffusion equation subject to a virtual first order chemical reaction as a boundary condition at the surface. The boundary condition concentrates the surface-particle interaction forces. When the interaction potential between the particle and the collector experiences a sufficiently high maximum (see f ig. 2) the apparent rate constant of the boundary condition has the Arrhenius form. Equations for the apparent activation energy and the apparent frequency factor are established for this case as functions of Hamaker s constant, dielectric constant, ionic strength, surface potentials and particle radius. The rate... 

The first theoretical description of the double layers assumed that the ions interact via a mean potential, which obeys the Poisson equation.2 Such a simple theory is clearly only approximate and sometimes predicts ionic concentrations in the vicinity of the surface that exceed the available volume.3 There were a number of attempts to improve the model, by accounting for the variation of the dielectric constant in the vicinity of the surface,4 for the volume-exclusion effects of the ions,5 or for additional interactions between ions and surfaces, due to the screened image force potential,6 to the van der Waals interactions of the ions7 with the system, or to the change in hydration energy when an ion approaches the interface.8... 

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