Density Functional Theory for Two-Dimensional Homogeneous Materials

We study Density Functional Theory models for systems which are translationally invariant in some directions, such as a homogeneous 2-d slab the 3-d space. show how different terms of energy modified and we derive reduced equations remaining directions. In Thomas–Fermi model, prove that there is perfect screening, provide decay estimates electronic density away from slab. Kohn–Sham models, Pauli principle replaced by penalization term energy. Hartree–Fock model particular, resulting well-posed, give properties minimizer.