Transition State Theory for dissipative systems without a dividing surface

TL;DR

This paper develops a new rate theory for dissipative systems that avoids the problematic dividing surface assumption of traditional transition state theory, providing an exact and surface-independent rate formula.

Contribution

It introduces a geometric structure in phase space that unambiguously identifies reactive trajectories in dissipative systems, leading to a new exact rate calculation method.

Findings

Derived a surface-independent rate formula for dissipative systems.

Identified a geometric phase space structure for reactive trajectories.

Validated the new rate formula in systems near energetic barriers.

Abstract

Transition State Theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when the reactive system is coupled to an environment. The calculations made in this way then overestimate the reaction rate and the results depend critically on the choice of the dividing surface. In this Letter, we study the phase space of a stochastically driven system close to an energetic barrier in order to identify the geometric structure unambiguously determining the reactive trajectories, which is then incorporated in a simple rate formula for reactions in condensed phase that is both independent of the dividing surface and exact.