Charge excess functional theory

CHARGE DISTRIBUTIONS IN METALLIC ALLOYS A CHARGE EXCESS FUNCTIONAL THEORY APPROACH... 

The wavefunctions from the Density Functional Theory calculations on calcium on DP7 indicate that calcium-doped DP7 accommodates a bipolaron-like defect, with two excess electrons per DP7. In the modelling of an isolated molecule with two negative charges, two new occupied states appear above the HOMO of the pristine molecule42. When the calcium counter-ion is included, however, the electrostatic interaction of the Ca2+-ion with DP72- leads to the stabilization of the two new states, so that the lower state (the HOMO-1 for Ca on DP7) lies at the same energy as the HOMO of... 

In the last decade order N electronic structure calculations [1, 2] made possible the study of large supercells containiug from 100 to 1000 atoms. Namely Faulkner, Wang and Stocks [2,3] have shown that simple linear laws, the so called qV relations, link the local charge excesses and the local Madelung potentials in metallic alloys. These qV linear laws have been obtained from the numerical analysis of data produced by Locally Self-consistent Multiple Scattering (LSMS) [1] calculations, while their formal derivation within the density functional theory has not yet been obtained. As a matter of fact, the above laws can be considered to hold at least within the approximations underlying I/SMS calculations, i.e. the l/ocal Density and the muffin-tin approximations. 

While the homogeneous effective crystal, the coherent" medium of the CPA theory, let us call it C, is electroneutral, the two impurity Green s functions lead to net charge excesses, q and in the sites occupied by the A and B impurities. On behalf of Eq. (4), these charge excesses satisfy the condition,... 

Figure 2.10 Schematic representation of the variation of the excess, or nett, surface charge density as a function of the distance away from the electrode surface, according to the Gouy-Chapman theory. The distance of nearest approach of the ions, with their associated solvation...

It is not necessary to consider spheres only. For any particular system the dielectric-response functions and excess ion densities can be measured or formulated as functions of the size, shape, and charge of the suspended particles as well as from ionic properties of the bathing solution. It is a separate procedure to compute the excess numbers Tv from mean-field theory. They are used here as given quantities. 

This is Kirkwood s expression for the chemical potential. To use it, one needs the pair correlation function as a function of the coupling parameter k as well as its spatial dependence. For instance, if k is the charge on a selected ion in an electrolyte, the excess chemical potential follows from a theory that provides the dependence of g(i j2 charge and the distance r 2- This method of calculating the chemical potential... 

Fig. 5. Relative surface excesses of Li ( ) and Cl (o) ions as functions of the surface charge density in aqueous phase at the interface between 0.1 mol dm TBATPB nitrobenzene solution and 0.1 mol dm LiCl aqueous solution. The solid lines are the theoretical curves based on the Gouy-Chapman theory (the right-hand sides of Eq. (14)). The dashed lines are the theoretical curves shifted by — 3 X 10 12molcm" for correction of (Eq. (10))...

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