Thesis advisor: Udayan Mohanty / Thesis advisor: Junwei Bao / This dissertation presents the development and application of advanced theoretical techniques to address important challenges in complex biological and materials systems. We begin by investigating ion transport in metal-organic frameworks (MOFs), focusing on magnesium ion conduction in Mg-MOF-74 thin films. A novel computational approach is developed to model ion transport in the bulk MOF structure and at grain boundaries in an integrated manner. Through this, we identify strong binding at grain boundaries to be a limiting factor for magnesium ion conductivity in MOF. Next, we explore large-scale conformational rearrangements of the bacterial ribosome during protein synthesis. Molecular dynamics (MD) simulations are utilized to characterize physical pathways and energetic barriers associated with aminoacyl-tRNA accommodation, providing insight into the mechanism of tRNA proofreading by the ribosome. The dissertation also reports on the development of a quantum mechanical implicit solvation model for periodic systems, suitable for applications involving surface chemistry and crystalline materials. The developed model demonstrates significantly improved accuracy over previous methods and successfully predicts solvation effects in a wide range of molecular and surface systems. Finally, high-level theoretical calculations are employed to study the chemistry of polysulfides in magnesium-sulfur batteries. Our effort not only improves the fundamental understanding of magnesium polysulfide behavior but also lays new foundations for optimizing battery system design. Overall, this dissertation provides new tools for the development of next-generation energy storage technologies, sheds light on the elaborate mechanisms underlying fundamental biological processes, and advances the state of the art in solvation modeling for quantum chemistry calculations. / Thesis (PhD) — Boston College, 2024. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Chemistry.