Dielectric inhomogeneous

The interface is, from a general point of view, an inhomogeneous dielectric medium. The effects of a dielectric permittivity, which need not be local and which varies in space, on the distribution of charged particles (ions of the electrolyte), were analyzed and discussed briefly by Vorotyntsev.78 Simple models for the system include, in addition to the image-force interaction, a potential representing interaction of ions with the metal electrons. 

E. F. Kuester and D. C. Chang, Propagation, attenuation and dispersion characteristics of inhomogeneous dielectric slab waveguides, IEEE Trans Microwave Theory Tech. 23, 98-106 (1975). 

Source Equation numbers are for formulae derived in V. A. Parsegian and G. H. Weiss, "On van der Waals interactions between macroscopic bodies having inhomogeneous dielectric susceptibilities," J. Colloid Interface Sci., 40, 35-41 (1972). 

According to Jorgensen and Judd, hypersensitivity may occur due to pseudoquadrupole transitions [66]. Consequently an ion embedded in an inhomogeneous dielectric would exhibit hypersensitive behavior. These normally weak electric quadrupole transitions are probably intensified and become hypersensitive transitions. Hypersensitivity can also occur in symmetries of spherical harmonics (Ymk, with k = 1) which form totally symmetrical representations. Thus this permits their inclusion in the crystal field potential. 

The difference between the electrostatic effect calculated using the bulk dielectric constant and that calculated taking account of local structural factors is sometimes called dielectric saturation, although it has been suggested that a better phrase would be inhomogeneous dielectric constant. We refer to the sum of these first-hydration-shell effects as the CDS term, representing structural rearrangements that entail cavitation, dispersion, and solvent disposition. 

Application in Monte Carlo simulations of inhomogeneous dielectric systems... 

Graf, P., Nitzan, A., Kurnikova, M.G., Coalson, R.D. A dynamic lattice Monte Carlo model of ion transport in inhomogeneous dielectric environments Method and implementation. J. Phys. Chem. B 2000,104,12324-38. 

In the case of an inhomogeneous dielectric, serving as a boundary or an intermediate layer, onesided difference operators have to be reformulated in order to circumvent possible instabilities. The key concept for these amendments, which lies on the efficient analysis of [20,23], presumes an explicit (2, 4) FDTD approach in the homogeneous areas of the computational space and... 

However, neither the inhomogeneous dielectric mechanism nor its equivalent, the dynamic-coupling mechanism, makes allowance for the polarizability of the outer shells of the rare-earth or actinide ion. For an external quadrupole field to penetrate to the f electrons, we must include a screening factor (1- o ) the same factor must be introduced if we take the point of view of dynamic coupling and ask what reduction the quadrupole field of the f electrons experiences as it penetrates out to the ligands. For a... 

Work is being carried out in collaboration with Dr. W.T. Carnall in an effort to connect hypersensitivity to the structures of the crystal lattices where it is exhibited. The mechanism based on an inhomogeneous dielectric leads to an expression for the intensities of hypersensitive lines that is proportional to (12)... 

Some correlation can be established between and hypersensitivity. Thus, for a nearly planar molecule Ndl, we find is roughly 6, while for the crystal NdCl, it is only 0.9. Intense hypersensitive transitions occur in the molecule but not in the crystal. Jowever, the pyramidal Ndl produces an electric field at the Nd site, while the crystal does not so the intensity correlation does not establish the predominance of the inhomogeneous-dielectric mechanism. The issue is further clouded by the vibronic contributions that undoubtedly occur in the molecule. 

In these expressions, p is an arbitrary coefficient that measures the strength of the electric-field mechanism compared to qne based on an inhomogeneous dielectric. The values of CK can be worked out once the polar angles of any one of the three igands is specified. For example, ell - cos. The components for which M = 1 are mixed with those for which M = T 2 in C v symmetry, but if the relative mixtures are known (as they could be from Zeeman-effect data), a measurement of the three intensities would, in principle, determine p and also check the expressions above for consistency. 

We have recently started to explore a type of calculations in which DFT treatment of the quantum mechanical (QM) site is combined with either continuum electrostatics treatment of the protein, or with microscopic molecular mechanics/dynamics treatment of the protein, or with a combined molecular mechanics and continuum electrostatics treatment of the protein in a truly multiscale type of calculations. All these calculations have a spirit of QM/MM (quantum mechanics combined with molecular mechanics) method, which is currently in wide use in protein calculations. The DFT and the solvation energy calculations are performed in a self-consistent way. The work aims at both improving the QM part of p/ calculations and the MM or electrostatic part, in which of the protein dielectric properties are involved. In these studies, an efficient procedure has been developed for incorporating inhomogeneous dielectric models of the proteins into self-consistent DFT calculations, in which the polarization field of the protein is efficiently represented in the region of the QM system by using spherical harmonics and singular value decomposition techniques [41,42]. 

Figure 4 Schematic of a solvation energy calculation. The initial state treats the solute in a homogeneous dielectric material with both solvent and solute dielectric coefficients set to solute value Ep. The final state involves an inhomogeneous dielectric coefficient with solute value Ep and bulk solvent value Ej.

AGi is the solvation energy of the isolated ions (i.e., at infinite distance). This is the energy of transferring each ion from a homogeneous dielectric p to an inhomogeneous dielectric with constants p and Ej. 

Figure 5 Thermodynamic cycle illustrating the standard numerical procedure for calculating the energy of two solutes at distance R. When R is varied, this method can construct a potential of mean force. The steps are (1) association of solutes in a medium with a homogeneous dielectric, (2) transfer of the isolated solutes from a homogeneous dielectric into solution with an inhomogeneous dielectric, (3) association of the solutes in a medium with an inhomogeneous dielectric, and (4) transfer of the associated solutes from a homogeneous dielectric into solution with an inhomogeneous dielectric.

MULTI- AND INHOMOGENEOUS DIELECTRIC LAYERS LAYER-BY-LAYER ETCHING... 

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