  We derive a non-empirical, 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.
