| In this thesis I study the exact functional within Kohn–Sham density functional theory, and discuss its role in developing approximations and understanding their failures. In the first part, I give an overview of both the ground-state formulation of density functional theory as well as the time-dependent version. I discuss various approximations and their deficiencies in light of departures from properties of the exact functional. In the second part of the thesis, I use the density matrix renormalization group, with its ability to obtain essentially exact wavefunctions, to study strong correlation in Kohn–Sham density functional theory. Using this powerful wavefunction solver, I set up a one-dimensional model chemistry and solid-state lab. There I discover that simple one-dimensional analogs reproduce (even quantitatively) the strong correlation behavior of three-dimensional systems, like stretched H2 . This allows me to verify properties such as the exact Kohn–Sham band gap for certain extended systems. I enable calculations with the exact functional in Kohn–Sham density functional theory, and demonstrate for stretched H2 that there is no “symmetry dilemma” for the exact functional, as there are for standard approximate ones. Finally, I consider the general case of three-dimensional systems and mathematically prove that convergence is guaranteed for the exact functional, regardless of the strength of electron correlation. |
