Density Functional Theory (DFT) is an effective and popular approach to the quantum many-body problem. DFT is exact but, in practice, the exchange-correlation contribution to the total energy must be approximated. Because of the demand for higher accuracy in applications, the modeling and understanding of this exchange-correlation density functional is an important area of research and is the focus of this thesis. First, a DFT is developed for a one-dimensional contact interaction. Then, the focus returns to the Coulomb-interacting problem. Uniform density scaling relationships are generalized to spin-scaling relationships. The adiabatic connection is considered at both strong and weak interaction limits. In the strong limit, the strictly-correlated electron hypothesis is tested. In the weak limit, the accuracy of exact-exchange DFT as applied to large gap solids is examined.
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