Reactivity Boundaries to Separate the Fate of a Chemical Reaction Associated with Multiple Saddles

TL;DR

This paper generalizes the concept of reactivity boundaries to complex reaction pathways involving multiple saddle points, demonstrating their existence and utility in understanding reaction mechanisms beyond simple index-one saddle cases.

Contribution

It introduces a broader definition of reactivity boundaries applicable to reactions with higher index saddles and multiple saddle points, supported by numerical analysis of a proton exchange in H+5.

Findings

Reactivity boundaries exist even in complex saddle configurations.

Reactivity boundaries can predict effective initial conditions for reactions.

The method reveals detailed reaction mechanisms in multi-saddle systems.

Abstract

Reactivity boundaries that divide the origin and destination of trajectories are crucial of importance to reveal the mechanism of reactions, which was recently found to exist robustly even at high energies for index-one saddles [Phys. Rev. Lett. 105, 048304 (2010)]. Here we revisit the concept of the reactivity boundary and propose a more general definition that can involve a single reaction associated with a bottleneck made up of higher index saddles and/or several saddle points with different indices, where the normal form theory, based on expansion around a single stationary point, does not work. We numerically demonstrate the reactivity boundary by using a reduced model system of the $H^+_5$ cation where the proton exchange reaction takes place through a bottleneck made up of two index-two saddle points and two index-one saddle points. The cross section of the reactivity boundary in the reactant region of the phase space reveals which initial conditions are effective in making the reaction happen, and thus sheds light on the reaction mechanism.