Accelerating Electron Dynamics Simulation with Moment Propagation Theory and Improving DFT with Local Hybrid Functionals

This senior honors thesis consists of three major research projects that I have undertaken in my undergraduate studies at the University of North Carolina at Chapel Hill. The first project describes a novel development of the theory of moment propagation such that the moments of the position operator are used as a concise description of the probability density to perform quantum dynamics in the single-particle description. The second part of this thesis leverages the machine learning techniques for efficiently performing electron dynamics in real systems via the moment propagation theory.&nbsp;<br />The third project describes my most recent work on improving a key approximation in density functional theory by implementing the exact exchange energy density for a so-called local hybrid functional.