Topological methods for searching barriers and reaction paths

TL;DR

This paper introduces a family of algorithms leveraging topological methods to efficiently identify reaction pathways and energy barriers in phase space, applicable across various timescale origins and compatible with techniques like simulated annealing.

Contribution

It develops a novel topological framework based on supersymmetry and Morse theory for rapid reaction path and barrier computation, unifying different timescale origins.

Findings

Algorithms effectively determine reaction paths and barriers.

Applicable to diverse timescale origins and temperature cycling.

Incorporates topological information automatically.

Abstract

We present a family of algorithms for the fast determination of reaction paths and barriers in phase space and the computation of the corresponding rates. The method requires the reaction times be large compared to the microscopic time, irrespective of the origin - energetic, entropic, cooperative - of the timescale separation. It lends itself to temperature cycling as in simulated annealing and to activation-relaxation routines. The dynamics is ultimately based on supersymmetry methods used years ago to derive Morse theory. Thus, the formalism automatically incorporates all relevant topological information.