The Nature of Reactive and Non-reactive Trajectories for a Three Dimensional Caldera Potential Energy Surface

TL;DR

This paper applies the method of periodic orbit dividing surfaces to a three-dimensional Caldera potential energy surface, revealing complex trajectory behaviors, homoclinic intersections, and dynamical matching phenomena crucial for understanding organic reaction dynamics.

Contribution

It introduces the use of periodic orbit dividing surfaces in a non-integrable 3D Hamiltonian system, analyzing trajectory types and homoclinic intersections in the Caldera potential.

Findings

Identified four types of trajectory behavior in the 3D Caldera potential.

Discovered two trajectory types unique to three dimensions due to homoclinic intersections.

Detected and described dynamical matching as a key reaction mechanism.

Abstract

We used for the first time the method of periodic orbit dividing surfaces in a non-integrable Hamiltonian system with three degrees of freedom. We have studied the structure of these four dimensional objects in the five dimensional phase space. This method enabled us to detect the reactive and non-reactive trajectories in a three dimensional Caldera potential energy surface. We distinguished four distinct types of trajectory behavior. Two of the types of trajectories could only occur in a three dimensional Caldera potential energy surface and not in a two dimensional surface, and we have shown that this is a result of homoclinic intersections. These homoclinic intersections were analyzed with the method of Lagrangian descriptors. Finally, we were able to detect and describe the phenomenon of dynamical matching in the three dimensional Caldera potential energy surface, which is an important mechanism for understanding the reaction dynamics of organic molecules.