Pitfalls of choosing an order parameter for rare event calculations

The mechanism of rare events in complex systems can be found by sampling dynamical paths that connect stable states. To calculate a rate using transition paths, an order parameter is required to describe the progress of the reaction and to distinguish the initial and final states. In this work, we compare two implementations of transition path sampling for Langevin paths, one for which paths are sampled in configuration space and the other in the space of the random variables that describe the thermostat. These two approaches are found to give different rates for the rearrangement of a seven-particle cluster despite the fact that both are formally exact. The difference is understood in terms of how efficiently the methods sample states along the order parameter. The more efficient approach 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 the system escapes to unknown states along an order parameter represented in terms of collective variables.