Electrostatic limit

Note that the long-range classical electrostatic limit furnishes an excellent approximation for the electrical attraction of the end groups, since these are separated far outside the range of significant exchange interactions. 

All electrochemical techniques measure charge transferred across an interface. Since charge is the measurable quantity, it is not surprising that electrochemical theory has been founded on an electrostatic basis, with chemical effects added as a perturbation. In the electrostatic limit ions are treated as fully charged species with some level of solvation. If we are to use UHV models to test theories of the double layer, we must be able to study in UHV the weakly-adsorbing systems where these ideal "electrostatic" ions could be present and where we would expect the effects of water to be most dominant. To this end, and to allow application of UHV spectroscopic methods to the pH effects which control so much of aqueous interfacial chemistry, we have studied the coadsorption of water and anhydrous HF on Pt(lll) in UHV (3). Surface spectroscopies have allowed us to follow the ionization of the acid and to determine the extent of solvation both in the layer adjacent to the metal and in subsequent layers. 

We also mention that recently a density functional approach to excited states of relativistic systems has been formulated [45], using ensembles of unequally weighted states. This formalism is restricted to the electrostatic limit and the no-sea approximation (see Section 3.2). Moreover, it remains unclear how the spontaneous emission of photons, which is possible in QED in contrast to the standard nonrelativistic many-body theory, is handled for the excited states involved. 

If one restricts oneself to the electrostatic limit of RDFT and relies on both the no-sea as well as the longitudinal approximation one arrives at the RKS-equations ... 

The theory of van der Waals (vdW) surface interactions is presented here in terms of correlation-self energies of the constituent parts involved in the interaction due to their mutual polarization in the electrostatic limit. In this description the van der Waals interactions are exhibited using the dynamic, nonlocal and inhomogeneous screening functions of the constituent parts. In regard to the van der Waals interaction of a single molecule and a substrate, this problem is substantially the same as that of the van der Waals interaction of an atom and a substrate, in which the atomic aspects of the problem are subsumed in a multipole expansion based on spatial localization of the atom/molecule. As we (and others) have treated this in detail in the past we will not discuss it further in this paper. Here, our attention will be focussed on the van der Waals interaction of an adsorbate layer with a substrate, with the dielectric properties of the adsorbate layer modeled as a two-dimensional plasma sheet, and those of the substrate modeled by a semi-infinite bulk plasma. This formulation can be easily adapted to an... 

We will be using this form of the molecule-field interaction repeatedly in this text, however, it should be kept in mind that it is an approximation on several counts. Already Eq. (3.1), an electrostatic energy expression used with a time varying field, is an approximation. Even in this electrostatic limit, Eq. (3.1) is just the first term in an infinite multipole expansion in which the higher-order terms depend on higher spatial derivatives of the electric field. 

THE NON-ELECTROSTATIC LIMIT OF CLOSED-SHELL INTERACTION BETWEEN TWO HYDROGEN ATOMS. 

Kotler and Nitzan" applied the electrostatic limit to a silver sphere coated with a dye. They found also in this case a double-peak behavior, under certain circumstances. Noteworthy, are the enhancements of the Raman scattering of up to —10", near the particle plasmon resonance. (For their model of a sphere it is at 3.5 eV but for other shapes it can be brought into the visible range). The enhancement is very weakly dependent on the distance from... 

As mentioned above, the nuclei are assumed to be fixed and are thus nothing more than sources of an external electrostatic potential in which the electrons move. If there is no magnetic field external to the molecule under consideration, and if external electric fields are time-independent, we arrive at the so-called electrostatic limit of relativistic density functional theory. Note that most molecular systems fall within this regime. In this case, one can prove the relativistic Hohen-berg-Kohn theorem using the charge density, p(r) = J f), only. This leads to a definition of an exchange-correlation functional -Exc[p( )]... 

As indicated, renormalization is necessary. Results are available to fourth order in the gradient of the density in the electrostatic limit... 

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