Computing reaction paths of a bifurcation reaction: an action wave-front-based perspective

Abstract

Application of Hamilton–Jacobi (HJ) equation to reaction systems which involve energy barrier(s) leading to the product is relatively new. Such problems are described by a new class of HJ equation, called the generalised HJ equation. This new HJ equation renders an anisotropic propagation for the wave front. In this paper, we describe the adaptation of the fast marching method (FMM) and the generalised HJ equation to understand a new class of reaction process where the energy barrier does not lead to the product; instead, a new class of states are detected along the reaction path of such reactions. These states are valley-ridge inflection point, branching point and potential energy ridge. Such reactions are characterised as bifurcation reactions. We have identified a new classical wave front, called the reaction action front (RAF) which distinctly separates the reaction system into a reactant zone and a product zone connected by a third zone, called ‘neck’. The RAF is an important tool to understand the bifurcation reaction and the associated reaction paths. We have also introduced a convenient way to compute the reaction path force (RPF) using the FMM. The RPF for a bifurcation reaction significantly differs from the reactions with energy barrier, and so, the RPF provides vital information about the occurrence of branching of a path. The method has been tested for the isomerisation reaction of methoxy radical (H₃C) to hydroxymethylene radical (H₂ĊOH).

Keywords:

• bifurcation reaction
• potential energy surface
• valley-ridge inflection
• Hamilton–Jacobi, eikonal equation
• wave front
• reaction path
• reaction action surface
• reaction path force

Acknowledgements

This research is supported by grants from NSF-NPURC and NSF-SD-EPSCoR.