Density Functional Studies of Spatial and On-site Strong Correlations.

摘要

This dissertation consists of two parts. In the first part, I consider density functional calculations employing a reference system of strictly-correlated electrons, and develop the corresponding adiabatic connection formula and define a "decorrelation energy". I then relate this scheme to the conventional Kohn-Sham scheme and the decorrelation energy to the conventional exchange-correlation energy. It provides an alternative perspective for understanding density functional theory and constructing approximate functionals. This scheme is particularly useful for systems with static correlation, such as stretched H2. In the second part, I consider electron transport through an Anderson junction. I show that Kohn-Sham conductance is exact at zero temperature and in the linear response regime, using the Friedel-Langreth sum rule. The Kohn-Sham potential is derived by inverting Bethe ansatz solution. I conclude that derivative discontinuity is a key feature for approximate functionals to yield accurate results at the strong correlation limit, namely the charge quantization and Kondo effect. I also analyze the successes and limitations of various approximations: smooth functionals, discontinuous functionals of the occupation, and symmetry-broken approach.