Simultaneous estimation of free energies and rates using forward flux sampling and mean first passage times

In this work, a method is proposed to simultaneously compute the transition rate constant and the free energy profile of a rare event along an order parameter connecting two well-defined regions of phase space. The method employs a forward flux sampling technique in combination with a mean first passage time approach to estimate the steady state probability and mean first passage times. These quantities are fitted to a Markovian model that allows the estimation of the free energy along the chosen order parameter. The proposed technique is first validated with two test systems (an Ising model and a model potential energy surface) and then used to study the solid-phase homogeneous nucleation of selected polyhedral particles.