UC Irvine

This dissertation is an accumulation of my contribution to the fundamental understanding of ensemble Density Functional Theory and finite temperature Density Functional Theory, through the use of quantum model systems. Ensemble DFT is a time-independent method to extracting excitation energies, and provides a way to extract multiple excitations. Currently this is not possible with the common approximations used in time-dependent DFT. Chapter 3 of this thesis covers ensemble DFT and verifies an exact exchange approximation that can accurately capture multiple excitations using the Hubbard model. Finite temperature DFT is often incorrectly confused with ensemble DFT, and refers to DFT at non zero temperatures. Its value comes from its applications to warm dense matter simulations. The last three chapters of this dissertation contain several projects in the hopes of improving the understanding of finite temperature DFT. In particular it generalizes the PPLB derivative discontinuity model to finite temperatures, and discusses the construction of an exact finite temperature approximation. These contributions are done with the intention on enhancing warm dense simulations.