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Heterogeneous nucleation is the dominant form of liquid-to-solid transition in na- ture. Although molecular simulations are most uniquely suited to study nucleation, the waiting time to observe even a single nucleation event can easily exceed current computational capabilities. Therefore, there exists an imminent need for methods that enable computationally fast and feasible studies of heterogeneous nucleation. Seeding is a technique that has proven successful at dramatically expanding the range of computationally accessible nucleation rates in simulation studies of ho- mogeneous crystal nucleation. In this paper, we introduce a new seeding method for heterogeneous nucleation called Rigid Seeding (RSeeds). Crystalline seeds are treated as pseudo-rigid bodies and simulated on a surface with metastable liquid above its melting temperature. This allows the seeds to adapt to the surface and identify favorable seed–surface configurations, which is necessary for reliable predictions of crystal polymorphs that form and the corresponding heterogeneous nucle- ation rates. We demonstrate and validate RSeeds for heterogeneous ice nucleation on a flexible self-assembled monolayer surface, a mineral surface based on kaolinite, and two model surfaces. RSeeds predicts the correct ice polymorph, exposed crystal plane, and rotation on the surface. RSeeds is semiquantitative and can be used to estimate the critical nucleus size and nucleation rate when combined with classical nucleation theory. We demonstrate that RSeeds can be used to evaluate nucleation rates spanning many orders of magnitude. 

Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of the so-called rare events that are characterized by transitions between metastable states separated by sizable free energy barriers. Their practical application, in particular to ever more complex molecular systems, is, however, not entirely trivial. Focusing on replica exchange transition interface sampling (RETIS) and forward flux sampling (FFS), we discuss a range of analysis tools that can be used to assess the quality and convergence of such simulations, which is crucial to obtain reliable results. The basic ideas of a step-wise evaluation are exemplified for the study of nucleation in several systems with different complexities, providing a general guide for the critical assessment of RETIS and FFS simulations. 

Molecular simulations are a powerful tool in the study of crystallization and polymorphic transitions yielding detailed information of transformation mechanisms with high spatiotemporal resolution. How- ever, characterizing various crystalline and amorphous phases as well as sampling nucleation events and structural transitions remain extremely challenging tasks. The integration of machine learning with molecular simulations has the potential of unprecedented advancement in the area of crystal nucleation and growth. In this article, we discuss recent progress in the analysis and sampling of structural trans- formations aided by machine learning and the resulting potential future directions opening in this area.