Reaction Coordinates and Mechanistic Hypothesis Tests

Reaction coordinates are integral to several classic rate theories that can (a) predict kinetic trends across conditions and homologous reactions, (b) extract activation parameters with a clear physical interpretation from experimental rates, and (c) enable efficient calculations of free energy barriers and rates. New trajectory-based rare events methods can provide rates directly from dynamical trajectories without a reaction coordinate. Trajectory-based frameworks can also generate ideal (but abstract) reaction coordinates such as committors and eigenfunctions of the master equation. However, rates and mechanistic insights obtained from trajectory-based methods and abstract coordinates are not readily generalized across simulation conditions or reaction families. We discuss methods for identifying physically meaningful reaction coordinates, including committor analysis, variational transition state theory, Kramers-Langer-Berezhkovskii-Szabo theory, and statistical inference methods that can use path sampling data to screen, mix, and optimize thousands of trial coordinates. Special focus is given to likelihood maximization and inertial likelihood maximization approaches.