Pierre, Sadrach2018-10-232018-10-232018-05-30Pierre_cornellgrad_0058F_10841http://dissertations.umi.com/cornellgrad:10841bibid: 10489401https://hdl.handle.net/1813/59317The accurate description of the coupled nuclear and electronic motion in large complex systems is necessary to inform the design of renewable energy devices. Treating many-body systems with exact quantum dynamics is typically intractable due to the exponential scaling of quantum mechanics. It is therefore of theoretical interest to develop accurate approximate quantum dynamics methods that are able to capture the mechanisms and varying time scales of many-body systems, while retaining the favorable linear scaling of classical methods. The focus of this dissertation is the development and application of an approximate quantum dynamics method towards elucidating mechanisms in the condensed phase. The approximate quantum dynamic method of interest is based on the path integral representation of the quantum Boltzmann distribution ~\cite{DCPW1981}. The quantum Boltzmann distribution describes the classical distribution of a "ring polymer" in an extended phase space. Mapping Variable RPMD (MV-RPMD) is an extension of RPMD that allows for the classical treatment of electronic state transitions by mapping discrete states to continuous phase-space variables and it employs classical trajectories to calculate real-time thermal correlation functions ~\cite{NA2013}. We study the condensed phase reaction dynamics of a proton-coupled electron transfer (PCET) system and an electron transfer (ET) system using MV-RPMD. We derive a more numerically stable quantum Boltzmann distribution in the MV-RPMD framework by invoking the symmetric Trotter approximation. We construct a four-state electron-proton system from a model PCET system bath model comprised of a proton double well coupled to two discrete electronic states. We establish bead convergence with significantly fewer beads than required in the original system. Further, in studying the mechanism of PCET we show that population dynamics generated from MV-RPMD trajectories can be used to accurately distinguish concerted and sequential PCET mechanisms. We verify the accuracy of PCET mechanisms predicted by MV-RPMD population dynamics by comparing against Fermi's Golden Rule and Kramers rate calculations. It is known that RPMD is an approximation to the "ImF" version of semiclassical instanton theory when used to calculate reaction rates in the deep tunneling regime ~\cite{SCA2009}. This speaks to RPMD's accuracy in approximating reaction rates within this regime. In an effort to develop a nonadiabatic rate theory in the MV-RPMD framework, we apply the method towards the calculation of an MV-RPMD instanton configuration in a model two-state system ~\cite{CAO1995} and provide preliminary results. Knowledge of the MV-RPMD instanton can provide transition state information necessary for a nonadiabatic rate calculation. In this vein, following our instanton configuration calculations, we develop three new rate expressions, in terms of flux-side thermal correlation functions(TCF), in the MV-RPMD framework .en-USStatisticsClassical MechanicsMapping Variable Ring Polymer Molecular DynamicsQuantum MechanicsComputational physicsComputational ChemistryTheoretical physicspath integralsring polymer molecular dynamicsdissertation or thesishttps://doi.org/10.7298/X4FQ9TTN