Orbital-free energy functional for electrons in two dimensions

We derive a nonempirical, orbital-free density functional for the total energy of interacting electrons in two dimensions. The functional consists of a local formula for the interaction energy, where we follow the lines introduced by Parr for three-dimensional systems [R. G. Parr, J. Phys. Chem. 92, 3060 (1988)], and the Thomas-Fermi approximation for the kinetic energy. The freedom from orbitals and from the Hartree integral makes the proposed approximation numerically highly efficient. The total energies obtained for confined two-dimensional systems are in a good agreement with the standard local-density approximation within density-functional theory and considerably more accurate than the Thomas-Fermi approximation.

Figure 1

(Color online) Relative error in the total energy calculated with our functional (filled circles) and with the Thomas-Fermi approximation (open circles) for a six-electron parabolic quantum dot as a function of the density parameter $r_s$.

Figure 2

(Color online) Relative error in the total energy calculated with our functional (filled symbols) and with the Thomas-Fermi approximation (open symbols) for rectangular quantum slabs with $N=12,\dots ,200$ as a function of the density parameter $r_s$.