# Density functional theory and pseudopotential characterizations of the electron gas in two and three dimensions

The electron gas model simplifies the many-electron problem by assuming a sea of independent electrons interacting with a positive uniform background. I have studied this model in the context of density functional theory, in both two and three dimensions A local pseudopotential was recently developed which now can be tested for its relevance to density functional theory. Using this pseudopotential, I calculated the phonon spectrum of sixteen simple metals as well as their elastic properties (bulk, Voigt and shear moduli) and found good agreement with both experiment and nonlocal pseudopotentials. Although a non-local pseudopotential may provide greater accuracy, computational simplicity and physical transparency further justify this local potential in density functional theory calculations The Kohn-Sham dielectric function epsilonks (q) used in the phonon calculations summarizes the strength of the screening of the external potential by the valence electrons. Local field corrections to the dielectric function occur by turning on exchange and correlation in epsilonks (q). I studied how local field effects influence the phonon frequencies; specifically the local density approximation (LDA), the generalized gradient approximation (GGA) and the nearly-exact levels of description were calculated Not only does insight on behavior of exchange-correlation approximations lead to the development of better functionals, but studying screening also afforded the opportunity to search for charge-density waves. I found that exchange-correlation corrections significantly reduce phonon frequencies The electron gas in two dimensions is a theoretical model now realized also in experiment within the past few decades. It is thought that this model may better describe its respective physical systems than the three-dimensional counterpart does for conduction electrons in metals. I studied how the LDA, GGA, and meta-GGA behave in the two-dimensional limit by calculating the exchange and correlation energy. This is a rigorous test of the functionals, which break down in the limit of exact two-dimensionality, but yield suitable results in the quasi-2D regime (for finite well width). A simple model based on the liquid drop also was used to calculate the exchange-correlation energy