Optimizing Nucleus Size Metrics for Liquid-Solid Nucleation from Transition Paths of Near-Nanosecond Duration

We determine the mechanism for the liquid-solid phase transition in the Lennard-Jones fluid close to coexistence with aimless shooting and likelihood maximization. The reaction coordinate for this process is a product of a structural descriptor and the size of the nascent solid nucleus and is quantitatively verified with the committor probability histogram test. This study identifies the first accurate scalar reaction coordinate for the liquid-solid nucleation process in Lennard-Jonesium, which will likely extend to nucleation processes in other spherically symmetric fluids. On the basis of our results, we propose a structural correction factor for the commonly cited nucleus size reaction coordinate from classical nucleation theory that enables connection of simulation data to stochastic models of nucleation kinetics. In addition, we show that aimless shooting is able to obtain reasonable acceptance rates for transitions with highly diffusive characteristics, which has been problematic for transition path sampling methods for diffusive processes such as nucleation and macromolecular transitions.