Bifurcations and phase-space structures in KCN molecular system

TL;DR

This paper investigates how phase-space structures of the KCN molecular system evolve with vibrational energy, revealing the transition from regular to mixed dynamics and the role of invariant manifolds, using Lagrangian descriptors and bifurcation theory.

Contribution

It introduces a detailed analysis of phase-space evolution in KCN using Lagrangian descriptors and confirms bifurcation theory predictions with invariant manifold computations.

Findings

Phase space transitions from regular to mixed dynamics with increasing energy.

Invariant manifolds govern the system's dynamics near energetic barriers.

Bifurcation theory accurately predicts phase-space structure changes.

Abstract

In this work, we analyze the evolution of the phase-space structures of KCN molecular system as a function of the vibrational energy using Lagrangian descriptors. For low energies, the motion is mostly regular around the absolute minimum of the potential energy surface. As the energy increases, the phase space combines regions with regular and chaotic motion, a difference that is well captured by the Lagrangian descriptors. We show that the dynamics is mostly governed by the invariant manifolds of the stretch periodic orbits located at the top of one of the energetic barriers of the system. Furthermore, we show a perfect agreement between the bifurcation theory and the differences observed in the phase-space structures as the vibrational energy is modified. The accuracy of our calculations is also assessed by explicit comparison with the invariant manifolds computed using linear dynamics.