Pitfalls of choosing an order parameter for rare event calculations

摘要

The mechanism of rare events in complex systems can be found by sampling dynamical paths thatconnect stable states. To calculate a rate using transition paths, an order parameter is required todescribe the progress of the reaction and to distinguish the initial and final states. In this work, wecompare two implementations of transition path sampling for Langevin paths, one for which pathsare sampled in configuration space and the other in the space of the random variables that describethe thermostat. These two approaches are found to give different rates for the rearrangement of aseven-particle cluster despite the fact that both are formally exact. The difference is understood interms of how efficiently the methbds sample states along the order parameter.The more efficientapproach takes the system to unexpected states that are allowed by a poor choice of order parameter.While transition path sampling is formally correct, we show how mistakes can be made when thesystem escapes to unknown states along an order parameter represented in terms of collectivevariables.