Path Integral Dynamics Methods for Simulating Quantum Processes in Multi-Electron, Condensed-Phase Systems

Understanding the mechanisms and timescales of charge and energy transfer processes in large, complex molecular systems is an essential step towards the rational design of a wide variety of renewable energy technologies. Unfortunately, the quantum mechanical nature of these reactions, where nuclear motions mediate transitions between electronic states, makes them infeasible to simulate exactly in many-body systems because of the scaling limitations of exact quantum dynamics methods. Developing approximate quantum dynamics methods capable of efficiently, yet accurately describing quantum processes in high-dimensional systems is, therefore, an ongoing effort in the field of theoretical chemistry and the focus of this dissertation. The two methods we discuss here are based on the imaginary-time path integral formulation of the quantum Boltzmann distribution that allows quantum degrees of freedom to be represented by classical ``ring polymers" in an extended phase space. Specifically, these methods are versions of the promising ring polymer molecular dynamics (RPMD) method for approximating quantum real-time thermal correlation functions using classical ring polymer trajectories. The first method we discuss, mean field (MF)-RPMD, extends the original RPMD formulation to multi-electron systems and describes nuclear dynamics on an average potential energy surface. We show how a novel implementation of this method for rate calculations yields accurate electron transfer rate constants across a wide range of parameter regimes. The second method we describe, mapping variable (MV)-RPMD, captures electronic state transitions using only classical MD trajectories by employing an exact mapping from discrete electronic states to classical phase-space variables. In order to use this method to study photochemistry, we derive a function in the MV-RPMD framework that reports on electronic state populations as a function of time, and we introduce a constraint protocol to initialize an MV-RPMD simulation to a particular electronic state. We numerically demonstrate the accuracy of this population function and constraint technique in the context of model systems undergoing electronic state transmission/reflection and photodissociation