The Dynamical Significance of Valley-Ridge Inflection Points

Abstract

In this paper we demonstrate that valley-ridge inflection (VRI) points of a potential energy surface (PES) have a dynamical influence on the fate of trajectories of the underlying Hamiltonian system. These points have attracted the attention of chemists in the past decades when studying selectivity problems in organic chemical reactions whose energy landscape exhibits a post-transition-state bifurcation in the region between two sequential saddles without an intervening energy minimum. To address the dynamical significance of valley-ridge inflection points, we construct a symmetric potential energy function that allows us to move the location of the VRI point while keeping the locations and energies of the critical points fixed. In this setup, we carry out a parametric study of the dynamical behavior of ensembles of trajectories in terms of the energy of the chemical system and the position of the VRI point. Our analysis reveals that the location of the VRI point controls the fraction of trajectories that recross the high energy saddle region of the PES without entering either of the potential wells that are separated by the low energy saddle.

arXiv comment14 pages, 9 figures

References in corpus (5)

• The Effect of Focusing and Caustics on Exit Phenomena in Systems Lacking Detailed Balance
• Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valley-ridge inflection points
• Phase Space Analysis of the Dynamics on a Potential Energy Surface with an Entrance Channel and Two Potential Wells
• The Phase Space Mechanism for Selectivity in a Symmetric Potential Energy Surface with a Post-Transition-State Bifurcation
• Tuning the Branching Ratio in a Symmetric Potential Energy Surface with a Post-Transition State Bifurcation using External Time Dependence