Core-extensive theories

For the core-extensive theories (i.e., with the feature (al)), there must be an explicit cluster expansion structure with respect to the core electrons, and no such cluster expansion maintained for the valence electrons. The wave-operator ft should have then either of the following forms... 

An important extension of lipid-solute interaction components [20] to membrane partitioning is provided by solute molecular structure. Spacing between polar and nonpolar regions (Fig. 8) within a solute molecule may result in significant distortion of the KpDm product across the membrane polar headgroup/lipid core interface [21], Such interactions may be responsible for deviations from projected transport predictions based on simple partitioning theory translating to deviations from predicted absorption kinetics [1],... 

Extensions of this model in which the atomic nuclei and core electrons are included by representing them by a potential function, V, in Equation (4.1) (plane wave methods) can account for the density of states in Figure 4.3 and can be used for semiconductors and insulators as well. We shall however use a different model to describe these solids, one based on the molecular orbital theory of molecules. We describe this in the next section. We end this section by using our simple model to explain the electrical conductivity of metals. 

The paper by Jungen and Atabek [10] also contains a sketch of the extension of the theory to include additional purely electronic interactions, such as the mixing of different partial waves l by the nonspherical field of the molecular core and/or interactions with core-excited Rydberg channels. This was not implemented at the time, however. 

The exact electromagnetic scattering theory of the concentric shell model was first solved by Aden and Kerker (1.) and shortly thereafter by Guttler (2). The problem has been extensively studied both theoretically and experimentally for aerosols by Kerker and co-workers and is reviewed in Kerker s book (3 ). The aerosol system had a core of relative refractive index m =2.105 and a shell of m2=1.482 corresponding to silver chloride coated with linolenic acid. The results indicated that for a smooth variation in the refractive index of the shell, the refractive index might not be sensitive to the form of the variation. 

Although the theory behind BLW is more general, a typical application of the method is the energy calculation of a specific resonance structure in the context of resonance theory. As a resonance structure is, by definition, composed of local bonds plus core and lone pairs, a bond between atoms A and B will be represented as a bonding MO strictly localized on the A and B centers, a lone pair will be an AO localized on a single center, and so on. With these restrictions on orbital extension, the SCF solution can be... 

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