# Optimal reaction coordinates and kinetic rates from the projected dynamics of transition paths

## TL;DR

This paper presents an algorithm that automatically identifies optimal reaction coordinates and accurately predicts kinetic rates from limited transition path data, improving molecular simulation analysis.

## Contribution

The authors introduce a Monte Carlo-based method that generates a sequence of reaction coordinates to find the optimal one minimizing the projected kinetic rate.

## Key findings

- The method accurately approximates kinetic rates in a double-well system.
- It successfully applied to complex atomistic systems involving carbon nanoparticles in water.

## Abstract

Finding optimal reaction coordinates and predicting accurate kinetic rates for activated processes are two of the foremost challenges of molecular simulations. We introduce an algorithm that tackles the two problems at once: starting from a limited number of reactive molecular dynamics trajectories (transition paths), we automatically generate with a Monte Carlo approach a sequence of different reaction coordinates that progressively reduce the kinetic rate of their projected effective dynamics. Based on a variational principle, the minimal rate accurately approximates the exact one, and it corresponds to the optimal reaction coordinate. After benchmarking the method on an analytic double-well system, we apply it to complex atomistic systems: the interaction of carbon nanoparticles of different sizes in water.