Large two-dimensional electronic systems: Self-consistent energies and densities at low cost

We derive a self-consistent local variant of the Thomas-Fermi approximation for (quasi-) two-dimensional (2D) systems by localizing the Hartree term. The scheme results in an explicit orbital-free representation of the electron density and energy in terms of the external potential, the number of electrons, and the chemical potential determined upon normalization. We test the method over a variety 2D nanostructures by comparing to the Kohn-Sham 2D local-density approximation (LDA) calculations up to 600 electrons. Accurate results are obtained in view of the negligible computational cost. We also assess a local upper bound for the Hartree energy.