Exploring Dynamical Matching and Recrossing on a Mesa Potential Energy Surface

Abstract

Potential energy surfaces (PES) having the topographical features of a mesa, or caldera, play an important role in describing the mechanisms of many organic chemical reactions. The main geometrical characteristics of a caldera are a shallow minimum and a collection of index-1 saddles that surround the minimum region. We introduce in this work a new type of caldera PES that allows us to vary certain specific features of its landscape. We refer to these features as flatness and tilting, and we develop analytical techniques that allow us to quantify these features. We study three classes of trajectories associated with the mesa, depending on their dynamical fates: dynamical matching trajectories, that enter the flat region and exit by crossing the index-1 saddle diametrically opposite to the entrance saddle, trapped trajectories, that are permanently trapped in the mesa region, and recrossing trajectories, that enter the mesa region and exit by crossing the same index-1 saddle that they crossed to enter. We consider how flatness, tilting and total energy affect the total fraction of each of these types of trajectories for a fixed ensemble of initial conditions.