(121k) Metadynamics with Non-Differentiable Collective Variables

In this work, we propose hybrid Monte Carlo Metadynamics (hybrid-MCMetaD), a new hybrid algorithm that combines hybrid MC (hybrid-MC) and Well-Tempered Metadynamics. hybrid-MCMetaD retains the strengths of both hybrid-MC and metadynamics while allowing for the utilization of a wider range of collective variables (CVs), further enhancing its flexibility and applicability.

We demonstrate the use of hybrid-MCMetaD with various examples of rare events including condensation of the argon system, two-step crystallization of a DLVO colloidal suspension, and the crystallization processes of a nearly-hard sphere system and a nearly-hard bipyramid system. By taking advantage of hybrid-MC, which uses MD to propose trial moves that are then accepted or rejected using Monte Carlo, we are able to bias the transitions along non-differentiable CVs for all the systems, which would otherwise be unfeasible with conventional molecular dynamics simulations or conventional hybrid-MC. Enabled by metadynamics, we observed significant acceleration of the phase transitions and calculated free energy barriers using the hybrid-MCMetaD simulation data. For the nearly-hard bipyramid system whose crystallization is primarily driven by entropy, we report the free energy surface for the first time. We also report the free energy surface of the hard shape system whose crystallization is driven solely by entropy, by using Hard Particle Metadynamics (HPMetaD) instead of hybrid-MCMetaD. Through our case studies, we demonstrate that our hybrid-MCMetaD and HPMetaD schemes reduce the complexity of using metadynamics and increase its accessibility. We believe the hybrid-MCMetaD and HPMetaD algorithms will stimulate greater interest in and foster broader applications of metadynamics, providing new insights into both soft and hard particle systems.