Transition path sampling (TPS) leverages a Monte Carlo algorithm to sample the TPE starting from a single reactive trajectory that connects reactants and products. In the context of homogeneous nucleation, this trajectory connects a supersaturated solution to a solution containing a crystal particle. This initial reactive trajectory is often generated using biased sampling techniques. New trajectories are then sampled by implementing a shooting algorithm. While multiple shooting algorithms exist, a typical approach consists of perturbing a configuration sampled by the initial reactive trajectory i.e., by slightly modifying the momenta, thus generating a new trajectory via a backward and forward propagation in time. If the new trajectory, proceeding through the set of configurations 𝑥 in 𝑛 steps, connects reactants and products, it is accepted with a path weight that depends on the equilibirum phase space probability density of the initial point in the trajectory 𝜌(𝑥 0 ) as: