Hybrid Monte Carlo metadynamics (hybridMC-MetaD)

We propose the powerful integration of the Hybrid Monte Carlo (hybridMC) algorithm and well-tempered metadynamics. This new algorithm, hybridMC-MetaD, enhances the flexibility and applicability of metadynamics by allowing for the utilization of a wider range of collective variables (CVs), namely non-differentiable CVs. We demonstrate the usage of hybridMC-MetaD through five examples of rare events in molecular dynamics (MD) simulations, including a rare transition in a model potential system, condensation of the argon system, crystallization in a nearly hard sphere system, a nearly hard bipyramid system, and a colloidal suspension. By taking advantage of hybridMC, which combines MD and MC, we are able to bias the transitions along non-differentiable CVs for all five cases, which would be unfeasible with conventional MD simulations. Enabled by metadynamics, we observed significant acceleration of the phase transitions and calculated free energy barriers using the hybridMC-MetaD 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. Through our case studies, we show that our hybridMC-MetaD scheme reduces the complexity of using metadynamics and increases its accessibility. We believe the hybridMC-MetaD algorithm will stimulate greater interest in and foster broader applications of metadynamics.