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Molecule- and particle-based simulations provide the tools to test, inmicroscopic detail, the validity of classical nucleation theory. In thisendeavour, determining nucleation mechanisms and rates for phase separationrequires an appropriately defined reaction coordinate to describe thetransformation of an out-of-equilibrium parent phase, for which myriad optionsare available to the simulator. In this article, we describe the application ofthe variational approach to Markov processes (VAMP) to quantify the suitabilityof reaction coordinates to study crystallisation from supersaturated colloidsuspensions. Our analysis indicates that collective variables (CVs) thatcorrelate with the number of particles in the condensed phase, the systempotential energy and approximate configurational entropy often feature as themost appropriate order parameters to quantitatively describe thecrystallisation process. We apply time-lagged independent component analysis toreduce high-dimensional reaction coordinates constructed from these CVs tobuild Markov State Models (MSMs), which indicate that two barriers separate asupersaturated fluid phase from crystals in the simulated environment. The MSMsprovide consistent estimates for crystal nucleation rates, regardless of thedimensionality of the order parameter space adopted; however, the two-stepmechanism is only consistently evident from spectral clustering of the MSMs inhigher dimensions. As the method is general and easily transferable, thevariational approach we adopt could provide a useful framework to studycontrols for crystal nucleation.

A Variational Approach to Assess Reaction Coordinates for Two-Step Crystallisation