Common features of extraordinary rate theories

We examine the capabilities and foundations of three landmark rate theories: harmonic transition state theory, classical nucleation theory, and the Marcus theory of electron transfer. Each of the three classic rate theories is widely used to predict rates and trends. They are also used "in reverse" to interpret experimental data with no computation at all. Their common foundations include a quasi-equilibrium assumption and dimensionality reduction to a physically meaningful, one-dimensional, and broadly applicable reaction coordinate. Many applications lie beyond the scope of the classic theories, so rare events research has pursued trajectory-based methods that efficiently predict accurate rate constants even when the reaction coordinate and mechanistic details are unknown. Trajectory based rare events methods achieved these ambitious goals, but (by construction) they provide rates rather than mechanistic understanding. We briefly discuss recent efforts to identify reaction coordinates, including methods which provide abstract statistically defined coordinates and those which identify physical collective variables. Finally, we note some natural synergies between existing simulation methods which might help discover simple and powerful quasi-equilibrium theories for the many applications that fall beyond the scope of the classic rate theories.