Chemical reactions, mass transport in solids, protein folding, and nucleation in first-order phase transitions are examples of processes characterized by multiple, long-lived states. Transitions from one (meta)stable state to another are rare and brief, making them difficult to resolve experimentally. And yet the short transition paths contain valuable structural and dynamic information that governs the lifetimes of the stable states. Transition state theory provides a valuable framework for analyzing rare events, provided that an exact dividing surface with no-recrossing can be found. Direct simulation of rare events processes are complicated by the long waiting times for a transition to spontaneously occur. Simulation methods that introduce a bias decrease the waiting time but also risk altering the mechanism. The reactive flux correlation function provides a two-step recipe for computing rates from simulation using an approximate dividing surface, but may miss important details about the physical reaction mechanism. Transition path sampling (TPS) was developed specifically to sample unbiased dynamical reactive trajectories and in combination with likelihood maximization provides an optimized reaction coordinate model.

We present new, simple TPS methods that reduce the computational expense of simulating rare events over existing methods. We apply these methods to study rare events in condensed phases and analyze the resulting data with likelihood maximization. The mechanism for vacancy migration in a single domain crystal by activated hops is examined. We find that accurately locating the donor and acceptor sites has a dramatic effect on identifying the mechanism. We next investigate the role of water in ion-pair dissociation, uncovering two solvent mechanisms that influence ion-pair transition states. The resulting dividing surface does not eliminate recrossing, so we present a test for the existence of a no-recrossing surface. It is revealed that an exact dividing surface does not exist for ion-pair dissociation. We discuss the ramifications for transition state theory, Grote-Hynes theory and the relationship between them.