Positive charge background

The jellium model for the surface electronic structure of free-electron metals was introduced by Bardeen (1936) for a treatment of the surface potential. In the jellium model, the lattice of positively charged cores is replaced by a uniform positive charge background, which drops abruptly to zero at the... 

In the bulk, the charge density of electrons n equals in magnitude the charge density of the uniform positive charge background +, thus to preserve charge neutrality. The only parameter in the jellium model, r,, is the same as in the Sommerfeld theory of free-electron metals. 

Fig. 4.3. Position of the image plane in the jellium model. The surface potential of an electron in the jellium model is calculated using the local-density approximation. By fitting the numerically calculated surface potential with the classical image potential, Eq. (4.7), the position of the image plane is obtained as a function of r, and z. The results show that the classical image potential is accurate down to about 3 bohrs from the boundary of the uniform positive charge background. For metals used in STM, r, 2 — 3 bohr, zo 0.9 bohr. (Reproduced from Appelbaum and Hamann, 1972, with permission.

A rigorous electro-nuclear separability scheme has been examined. Therein, an equivalent positive charge background replaces the nuclear configuration space the coordinates of which form, in real space, the -space. Diabatic potential energy hypersurfaces for isomers of ethylene in -space were calculated by adapting standard quantum chemical packages. 

At this point one needs to remember that electrons are not completely independent particles, moving randomly in a positively charged background. They are a charged species and as such, they also interact with the positive ions (nucleus)... 

Experiments show that the values for the double layer capacity at single crystal metal surfaces depend on the nature of the metal. This indicates that the metal surface cannot be considered as a perfect conductor, as was done in classical theories. It is well known that an overspill of metal electrons can occur at the boundary of a metal with vacuum. A similar overspill expected at a metal-solution interface would alter the double layer capacity by an amount depending on the type of metal. Models have been constructed in which the metal is represented by an electronic plasma in a uniformly, positively charged background, which is known as the jellium model [81,82]. The inclusion of the electron overspill into the integral equation theories of the electric double layer has been performed basically with the HAB model. 

In general, the presence of the impurity atom induces a strong perturbation of the electronic cloud of an alkali cluster. The different nature of the impurity can be accounted for by a simple extension of the jellium model. The foreign atom is assumed to be at the cluster centre, and both subsystems - impurity and host - are characterized by different ionic densities in a jellium-like description. The following positive-charge background is then assumed ... 

At low densities, Wigner supposed that the electrons would become localized and form a regular lattice. The electron lattice is a close-packed structure such as fee or hep, in which electrons vibrate around their equilibrium positions. This lattice is immersed in a positive charged background. 

Clusters of alkali metals and especially of sodium are the most studied of all. From the theoretical point of view, sodium is the one most amenable to treatments with simple models. The free-electron behavior known for the bulk phase has suggested that jellium-like models could also be suitable for small-size aggregates. By means of these models, in fact, a large variety of measurable properties have been calculated. This in turn has allowed the approximations used to be tested at several levels [121]. Two comprehensive and very instructive reviews have been dedicated to both experimental and theoretical approaches to simple metal clusters with an emphasis on phenomenological aspects and jellium or jellium-derived models [4, 5]. Here we shall report on DFT calculations that go beyond the assumption of a homogeneous, positively charged background. 

FIGURE 22. Surface charge density Ap of a metal, induced by a weak external electric field. X = 0 denotes the edge of the positive-charge background, = Wigner-Seitz radius. After Ref. 67. 

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