Electrostatic penetration term

The penetration contribution to the electrostatic potential at R, is evaluated by application of the general expression of Eq. (8.49) for per for the spherical density (lt = ml = 0). The point-charge term, proportional to 1/Rfj-, must subsequently be subtracted. Due to the rapid decrease of the penetration terms with increasing R j, convergence is quickly achieved. For spherically averaged Hartree-Fock atom densities, inclusion of penetration terms for atoms within 10 A of the point under consideration is more than adequate. 

Note that in Spackman (1986b), the energy is subdivided in contributions labeled as electrostatic, penetration, repulsion, and dispersive terms. The first two of these are due to electrostatic interactions. 

The multipole part can efficiently be estimated from the distributed multipole analysis191. In this way the electrostatic penetration contribution is obtained. One may note that the accuracy of the electrostatic term can be increased by keeping the penetration part from Eq. (1-184), and replacing the Hartree-Fock distributed multipole moments by some correlated, e.g. MP2 moments. Finally, the intramonomer correlation term and the dispersion energy can be evaluated from the expression,... 

And even when the convergence is rapid, the multipole expansion is not a complete representation of the true electrostatic energy, as it neglects the effects of overlap of the charge distributions of the two molecules in question [12,14], sometimes referred to as a penetration term. Fortunately, the latter complicating effect dies off exponentially with intermolecular separation [15], adding to the validity of the multipole expansion at sufficient spacing. 

Figure 3.5 Charge penetration in base stacking for the GGiCC base pair step [at 35° Twist and 0.28 A Siide] as a function of Rise, the vertical separation between the base pairs. The difference between the distributed multipole analysis [DMA) value for electrostatics and the quantum mechanical symmetry-adapted perturbation theory [SAPTO/jun-cc-pVDZ) value for electrostatics may be taken as a measure of the charge penetration term. The DMA analysis includes terms up through order 5 [32pole-chai e, hexadecapole-dipole, octopole-quadrupole). Charge penetration rapidly increases in magnitude for smaller intermolecular distances.

Table 13J. The table pertains to two molecules in their eleetronie ground states. For each pair of molecules a short characteristic of their electrostatic, induction and dispersion interactions is given. It consists of the sign of the corresponding interaction type (the minus sign means attraction, the plus sign means repulsion and 0 corresponds to the absence of such an interaction, the penetration terms have been neglected)...

Thus a synthetic cation- (anion-) selective membrane consists of a dense polyanion (cation) matrix soaked with solvent carrying the counterions. These latter are electrostatically attracted to the fixed charges of the matrix and remain confined to it unless they are replaced by (exchanged with) some other counterions of a low molecular electrolyte dissolved in an aqueous solvent surrounding and penetrating the membrane. A porous bulk material with high counterion capacity of the type described herein is termed ion-exchanger. 

The electrostatic term can further be decomposed into the multipole and penetration components,... 

The anisotropies of the electrostatic (e 0 ), SCF-deformation (AEj ) and perturbation induction ( r) terms are quite similar and qualitatively reciprocal to the anisotropy of the HL-exchange energy, see Fig.4.A. s0) is reduced for this complex to the penetration part only and has no long range component. . r, which includes the interaction of the quadrupole and higher CO2 moments with induced moments of Ar (restrained by overlap effects and... 

It includes the interactions of distributed multipole moments Q (up to a quadrupole) labeled t and u. The T matrix provides the Coulomb energy appropriate for particular multipoles and includes the distance between sites a and b and their relative orientations. The short range (penetration) component of the electrostatic energy, in a manner similar to the Ar-CC>2 case, can be absorbed into the exchange repulsion term. 

Here E, D, and P represent, respectively, the electric field, electric induction (or displacement), and electric polarization vectors P (D - )/4x. The integration must be carried out over all space penetrated by the electrostatic field. Equation (5.6.1), while correct, is awkward in several respects. First, there is the need to integrate over all space, including the region outside the system of interest. In the presence of a medium, the electric lines of force not only are present within the specimen, but also bulge out in all directions away from the system these effects must be included in (5.6.1). Second, there is a tendency in the literature to associate the first term in (5.6.1b) with the establishment of the electric field in free space, and the second term with the reaction of the medium to the electric field. This is wrong The quantity D is subject to direct experimental control because it is linked by Maxwell s equation to the presence of free charges by contrast, E is in part a reaction field that also includes the... 

In Chapter 1, we have discussed the potential and charge of hard particles, which colloidal particles play a fundamental role in their interfacial electric phenomena such as electrostatic interaction between them and their motion in an electric field [1 ]. In this chapter, we focus on the case where the particle core is covered by an ion-penetrable surface layer of polyelectrolytes, which we term a surface charge layer (or, simply, a surface layer). Polyelectrolyte-coated particles are often called soft particles [3-16]. It is shown that the Donnan potential plays an important role in determining the potential distribution across a surface charge layer. Soft particles serve as a model for biocolloids such as cells. In such cases, the electrical double layer is formed not only outside but also inside the surface charge layer Figure 4.1 shows schematic representation of ion and potential distributions around a hard surface (Fig. 4.1a) and a soft surface (Fig. 4.1b). 

For particle cleanup cyclones, impact separators, fabric and fiber filters, granular beds, and electrostatic percipitators for low-temperature gas cleaning have been widely used in the industry. However, for hot gas filtration with ceramic filters, the long-term durability, alkali corrosion, cleanability, thermal shock, and particulate penetration into filter media has been recognized as major concerns. Traditional bag filters are sensitive to high ten erature and hot particles, electrostatic percipitators have a relatively high cost of installation in smaller plants and multi-cyclone cleaners are not sufficiently efficient to meet the new purification demands. 

Surface complexation models (SCM s) provide a rational interpretation of the physical and chemical processes of adsorption and are able to simulate adsorption in complex geochemical systems. Chemical reactions at the solid-solution interface are treated as surface complexation reactions analogous to the formation of complexes in solution. Each reaction is defined in terms of a mass action equation and an equilibrium constant. The activities of adsorbing ions are modified by a coulombic term to account for the energy required to penetrate the electrostatic-potential field extending away from the surface. Detailed information on surface complexation theory and the models that have been developed, can be found in (Stumm et al., 1976 ... 

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