Path collective variables without paths

TL;DR

This paper presents a novel method to construct one-dimensional collective variables for rare transition studies without prior path information, using Fisher's linear discriminant analysis based on system fluctuations.

Contribution

It introduces a new approach to generate collective variables without needing path data, applicable to diverse systems, enhancing free energy barrier crossing simulations.

Findings

Effective in simulating silver iodide freezing

Successfully applied to Diels-Alder reaction

No prior path information required

Abstract

We introduce a method to obtain one-dimensional collective variables for studying rarely occurring transitions between two metastable states separated by a high free energy barrier. No previous information, not even approximated, on the path followed during the transition is needed. The only requirement is to know the fluctuations of the system while in the two metastable states. With this information in hand we build the collective variable using a modified version of Fisher's linear discriminant analysis. The usefulness of this approach is tested on the metadynamics simulation of two representative systems. The first is the freezing of silver iodide into the superionic $\alpha$-phase, the second is the study of a classical Diels Alder reaction. The collective variable works very well in these two diverse cases.