Jellium coupling

The ionic profile of the metal was modeled as a step function, since it was anticipated that it would be much narrower than the electronic profile, and the distance dx from this step to the beginning of the water monolayer, which reflects the interaction of metal ions and solvent molecules, was taken as the crystallographic radius of the metal ions, Rc. Inside the metal, and out to dl9 the relative dielectric constant was taken as unity. (It may be noted that these calculations, and subsequent ones83 which couple this model for the metal with a model for the interface, take the position of the outer layer of metal ion cores to be on the jellium edge, which is at variance with the usual interpretation in terms of Wigner-Seitz... 

The screened susceptibility x(q, m z, z ) appearing in equation (23) is a smooth function of the spatial coordinates that interpolates from zero very far from the surface to the bulk value. It contains the spectrum of the single-pai ticle and collective modes and their coupling. This coupling, known as Landau-damping, depends on distance and it is the only channel that allows decaying of a collective mode in the jellium theory. Surface plasmons of parallel momentum q different from zero are Landau-damped but bulk plasmons cannot decay into electron-hole pairs below a critical frequency in this linear theory. Collective modes can show up in electron emission spectra [28,29] because they are coupled to electron-hole pairs. 

These results, in turn, then formed the basis for the non-jellium part of the jel-lium model in [73]. Berkowitz [52-54] and later Zhu and Philpott [55] and Spohr [56] followed the approach by Steele [93] and Fourier-expanded the lattice sum of all (pairwise) interactions between the atoms in the solid and one molecule or ion in the liquid. Only the lowest order corrugation terms are kept in the expansion but in principle the summation can be extended to any desired accuracy. The procedure is adequate as long as there is no substantial coupling between liquid and metal motions that could influence the liquid structure and relaxation phenomena. Spohr [56] used a corrugated Morse potential for the oxygen-metal interactions and an exponentially repulsive potential for the hydrogen metal interactions in the form... 

An alternative description of the metal that can be profitably coupled to the continuum electrostatic approach is given by the jellium model. In this model, the valence electrons of the conductor are treated as an interacting electron gas in the neutralizing background of the averaged distribution of the positive cores (some discreteness in this core distribution may be introduced to describe atomic motions). The jellium is described at the quantum level by the Density Functional Theory (DFT) and it represents a solid bridge between classical and full QM descriptions of such interfaces further improvements of the jellium which introduce a discrete nature of the lattice are now often used. ... 

We start with the simplest model of the interface, which consists of a smooth charged hard wall near a ionic solution that is represented by a collection of charged hard spheres, all embedded in a continuum of dielectric constant c. This system is fairly well understood when the density and coupling parameters are low. Then we replace the continuum solvent by a molecular model of the solvent. The simplest of these is the hard sphere with a point dipole[32], which can be treated analytically in some simple cases. More elaborate models of the solvent introduce complications in the numerical discussions. A recently proposed model of ionic solutions uses a solvent model with tetrahedrally coordinated sticky sites. This model is still analytically solvable. More realistic models of the solvent, typically water, can be studied by computer simulations, which however is very difficult for charged interfaces. The full quantum mechanical treatment of the metal surface does not seem feasible at present. The jellium model is a simple alternative for the discussion of the thermodynamic and also kinetic properties of the smooth interface [33, 34, 35, 36, 37, 38, 39, 40]. 

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