Electron Density for Jellium

The electron density distribution, along with other properties of the metal, shows an oscillatory dependence on the width of the metal slab. These oscillations correspond to the inclusion of one additional occupied eigenstate. For narrow slabs (about 20 A wide), these oscillations can be significant. For example, the potential drop across the Hg-vacuum interface oscillates by about 0.1 volt. For the results considered here, a slab width of 64 A was used giving rise to oscillations of only 0.01 volt. As the width of the slab increases furthei the semiinfinite limit of the potential drop is approached.  

Several structural properties are typically monitored to characterize water in these systems. Some of these are the density distribution of water molecules with respect to the surface, surface area per water molecule, the root-mean-square displacements from the optimal surface positions for corrugated surfaces, angular distributions of the dipolar and O—H bond vectors with respect to the surface normal, and moments of the angular distributions. Most of these characterize the water structure with reference to the metal surface. In contrast, the radial distribution function, number of nearest neighbors per molecule, and number of hydrogen bonds per molecule are used to characterize water-water interactions. 

It is tempting to try to estimate the characteristic density for water within the first peak of the water density profile. Such estimations are difficult, however, because this layer is significantly narrower than the diameter of a water molecule (roughly 2.8 A) and the density varies rapidly over this range, making the results somewhat ill-defined. Instead, it is more appropriate to estimate the 

To condense the information contained in the angular distributions of the dipoles to a more manageable form, it is common to calculate order parameters such as 

The radial distribution function, g(r), is the ratio of the density distribution of a type of site / at a given distance from a given type of site i, to the average density of site / in the system. A more technical definition, which allows the binning of this function into discrete intervals of r, is  

---