Semiclassical Origins of Density Functionals

The relation between semiclassical and density-functional approximations is clarified. Semiclassical approximations both explain and improve upon density-gradient expansions for finite systems. We derive highly accurate density and kinetic energy functionals of the potential in one dimension.

Figure 1

Cartoons of potential and Fermi energy in a simple metal (left) and molecule (right).

Figure 2

Densities for $v(x)=-80{sin}^2(2\pi x)$ for $N=4$.

Figure 3

Kinetic energy densities of Fig. 2.