Development of Molecular Dynamics Approaches for Charge Transfer and Quantum Dynamics

Molecular dynamics (MD) is a computational method used for exploring the motion of a variety of atomic and molecular systems, ranging from model atoms moving in a simple potential to the complicated movements of proteins. This dissertation covers two distinct research projects, which are linked in their use of molecular dynamics as a foundational modeling tool. In the first project, a multidimensional form of Marcus theory is used to explore charge transfer reactions, particularly proton-coupled electron transfer (PCET) reactions. In the second project, quantum dynamics are approximated using ring polymer molecular dynamics (RPMD).;Marcus theory, the subject of the first project, is often used to calculate reaction rates in charge transfer reactions such as electron and proton transfer. Multiple charge transfer reactions can be modeled using a multidimensional form of Marcus theory, where each dimension has its own reaction coordinate. For computational studies of Marcus theory, the extension to multiple dimensions can greatly increase the time needed to simulate systems. Fortunately, it is often possible to reduce multidimensional Marcus theory to a simpler, one-dimensional formalism. This dissertation rigorously derives one such method and examines the conditions under which the simplifications are valid. The method involves choosing a particular single reaction coordinate that is a linear combination of the standard Marcus theory reaction coordinates. A procedure for finding accurate transition state energies (which are essential for calculating reaction rates) is described and applied to a two-dimensional model of proton-coupled electron transfer. The results of the reduced one-dimensional system are in excellent agreement with the original multidimensional system based on both analytic calculations and numerical simulations.;The second project involves ring polymer molecular dynamics (RPMD), where quantum dynamics are approximated by replacing a quantum particle with a ring of harmonically-coupled, classical "beads," each of which are treated using classical molecular dynamics. In traditional RPMD each quantum degree of freedom has n beads, while the classical degrees of freedom each have a single bead (the mixed quantum-classical method). In this work, a scheme that allows each quantum degree of freedom to have a different number of beads (or equivalently, a different number of time slices) is derived. The benefits of the new scheme include faster convergence compared to full quantization and greater accuracy compared to both classical and the standard mixed quantum-classical methods. The new scheme is used to model systems of coupled high- and low-frequency oscillators, and convergence of quantum mechanical observables with fully quantum results is demonstrated. Computational cost estimates are provided and indicate that the new scheme is most efficient in cases where there are relatively few fully quantum degrees of freedom. In this case, the computational cost of the simulation will scale with the number of beads on the least quantized degrees of freedom. Finally, we show that the new mixed-bead scheme is analogous to multiple time step molecular dynamics, which could yield insight into further refinement and extension of the scheme.