On Sampling Minimum Energy Path

Sampling the minimum energy path (MEP) between two minima of a system is often hindered by the presence of an energy barrier separating the two metastable states. As a consequence, direct sampling based on molecular dynamics or Markov Chain Monte Carlo methods becomes inefficient, the crossing of the energy barrier being associated to a rare event. Augmented sampling methods based on the definition of collective variables or reaction coordinates allow us to circumvent this limitation at the price of an arbitrary choice of the dimensionality reduction algorithm. We couple the statistical sampling techniques, namely, metadynamics and invertible neural networks, with autoencoders so as to gradually learn the MEP and the collective variable at the same time. Learning is achieved through a succession of two steps: statistical sampling of the most probable path between the two minima and redefinition of the collective variable from the updated data points. The prototypical Mueller potential with nearly orthogonal minima is employed to demonstrate the ability of such coupling to unravel a complex MEP.