Advanced Computational Methods for Ground and Excited States to Study Complex Systems

The real-time time-dependent density functional theory (rt-TDDFT) approach, which is complementary to the more traditional linear-response TDDFT (lr-TDDFT), propagates the electron density in real time for studying the ground and excited states. Researchers use rt-TDDFT to study electron dynamics in real time. Moreover, rt-TDDFT can treat nonlinear effects, which is especially useful for experimentalists studying external field effects in complex systems. This dissertation presents computational methods for studying a complex system's ground and excited states. We start with ground state calculations, via density functional theory (DFT), for studies on Cyclodextrins as a catalyst, binary compound convex hull, and transition states. Then we go into ground state studies with nuclear motion using the Born-Oppenheimer Molecular Dynamics. An application of lr-TDDFT on TiSe$_{2}$ follows this. We transition to excited state studies by introducing our rt-TDDFT formalism. We validate the implementation with benchmark tests for essential elements. Finally, we demonstrate our implementation capabilities and apply them to practical systems. The first application simulates the attosecond transient absorption spectroscopy for charge transfer and polarization switching in BaTiO$_{3}$. The second application involves molecular dynamics, a nonlinear process, for photo-induced degradation mechanisms of perfluorooctanoic acid (PFOA). By explicitly accounting for non-adiabatic excited-state interactions in solvated PFOA, we show that these photo-induced excitations enable a charge-transfer process that polarizes the C\textendash F bond, resulting in a dynamic dissociation on a femtosecond time scale. Ultimately, this dissertation emphasizes the importance of quantum simulations for studying excited states of molecular and extended systems