Dielectric boundary

Davis, M. E., McCammon, J. A. Dielectric boundary smoothing in finite difference solutions of the poisson equation An approach to improve accuracy and convergence. J. Comp. Chem. 12 (1991) 909-912. 

A. rather complex procedure is used to determine the Born radii a values of which. calculated for each atom in the molecule that carries a charge or a partial charge. T Born radius of an afom (more correctly considered to be an effective Born radii corresponds to the radius that would return the electrostatic energy of the system accordi to the Bom equation if all other atoms in the molecule were uncharged (i.e. if the other ato only acted to define the dielectric boundary between the solute and the solvent). In Sti force field implementation, atomic radii from the OPLS force field are assigned to ec... 

Given a cavity segmentation by m segments i, of sizes s, and centered at positions fj, the dielectric surface polarization charge densities, at, and the corresponding apparent surface charges, qt = Sjffj, can be calculated from the exact dielectric boundary... 

In the previous chapter, we have seen how Born s simple and successful idea of a dielectric continuum approximation for the description of solvation effects has been developed to a considerable degree of perfection. Almost all workers in this area have been trying to obtain more efficient and more precise methods for the solution of dielectric boundary conditions combined with molecular electrostatics, but the question of the validity of Born s basic assumption has rarely been discussed. This will be done in the following sections, with a surprising result. 

To the best of our knowledge, this is the only free energy functional that can be readily introduced in an ASC implicit solvent model as it involves only surface integrals in terms of the independent polarization variable which is no longer a three-dimensional field, but instead assumes the form of a surface charge distribution on the dielectric boundary. 

In PCM, the solute is represented in terms of a charge density in a realistic model of a shaped cavity in a dielectric medium. The effects of the solute charge density and of the surface charge on the boundary with the dielectric continuum are taken into account in solving the dielectric boundary value problem, while the charge density itself is obtained... 

In order to treat the combined effects of added salt and dielectric boundaries on a manageable level, we use screened Debye-Hiickel (DH) interactions between all charges. In the presence of a dielectric interface, the Green s function can in general not be calculated in closed form [114] except for (i) a metallic substrate (with a substrate dielectric constant e =oo) and (ii) for e =0 (which is a fairly accurate approximation for a substrate with a low dielectric constant). For two unit charges at positions r and r one obtains for the total electrostatic interaction including screening and dielectric boundary effects... 

Since QMSTAT is easily adapted to this interface (remove the dielectric boundary and allow indole to translate freely), we get the same accuracy as in the bulk simulations. 

The PB equation may be solved numerically for macromolecules (for reviews, see References 36-38. The finite difference, finite element, and multigrid methods are used most commonly to solve the PB equation. Usually, this technique is performed by mapping the molecules onto a three-dimensional cubic grid. To solve the PB equation, a suitable interior relative dielectric constant and definition of the dielectric boundary should be assigned (39, 40). 

This model replaces the solute-continuum model with one in which a system of charges derived from the solute and virtual charges in the adjacent space interact in the gas phase. A set of mirror charges reflected at the dielectric boundary are created and used in the calculation of the electrostatics. 

In this approximation, the system is modeled by calculating the appropriate surface charges at the dielectric boundary. This is similar to fitting charges at atomic centers to reproduce the molecular electrostatic potential. For a quantum-mechanical equivalent, Tomasi et al. (59) introduced a charge distribution on the surface of a cavity of realistic shape to introduce... 

Pattemwise delineation must be achieved for waveguide-based devices. It should be possible to form a precise, high-quality dielectric boundary between the linear and nonlinear regions of the device and to accurately define shapes and patterns. 

Keywords Dielectric boundaries, Monte Carlo simulation, polarization charge... 

In the special case of sharp dielectric boundaries the dielectrics is separated into domains of uniform dielectric coefficients. The dielectric coefficient jumps from one value to another along a boundary. Let us denote the surface of the dielectric boundaries by B. Then the induced charge is a surface charge on the dielectric interfaces (if the induced charges around the source charges are not considered), and the volume integral in Eq. (15) becomes a surface integral over the surface B,... 

---