Construction of model dielectric functions for two- and three-dimensional electron liquids from density functionals

摘要

The Thomas-Fermi (TF) approximation for the static dielectric function of a three-dimensional (3D) electron liquid can be derived by minimizing the TF local-density approximation for the kinetic-energy functional. Here we show that this connection between energy functional and model dielectric functions is not an artifact, but a general paradigm. Four examples are worked out in detail, by calculating the model dielectric functions that follow, respectively, from (ⅰ) exchange corrections to TF theory in 3D, i.e., TF-Dirac theory, (ⅱ) further correlation corrections to TF-Dirac theory in 3D, (ⅲ) TF theory in two dimensions (2D), and (ⅳ) exchange corrections to TF theory in 2D. Each of these cases has certain interesting features, revealing connections between independent many-body methods, that are discussed in some detail. As a by-product of these inves- tigations we also find that a common textbook statement about the long-wavelength (k → 0) limit of the random-phase approximation is not fully correct.