Transition states and dynamical bottlenecks in the Li-NC <-> Li-CN isomerizing reaction with the Lagrangian betweenness

Abstract

We study the vibrational dynamics that is responsible for Li-NC <-> Li-CN isomerization reaction using the Lagrangian betweenness, a tool recently developed to identify dynamical bottlenecks in the context of oceanographic transport. Following the spirit of the betweenness-centrality metric, which efficiently identifies the nodes that act as bottlenecks in complex networks, the Lagrangian betweenness is similarly capable to identify bottlenecks in dynamical systems. On the one hand, in this paper we show the ability of the Lagrangian betweenness to identify transition states, which are short-lived states that are formed at the top of the energetic barrier that the system must surpass in order to transition the reaction from the (initial) reactants to the (final) products. On the other hand, we also demonstrate that the Lagrangian betweenness is also able to identify other dynamical bottlenecks, and phase-space invariant structures such as manifolds, chains of islands and invariant tori, which are also responsible for the intricate vibrational dynamics of the system.