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Reactivity Boundaries to Separate the Fate of a Chemical Reaction Associated with an Index-two saddle

Reactivity boundaries that divide the destination and the origin of trajectories are of crucial importance to reveal the mechanism of reactions. We investigate whether such reactivity boundaries can be extracted for higher index saddles in terms of a nonlinear canonical transformation successful for index-one saddles by using a model system with an index-two saddle. It is found that the true reactivity boundaries do not coincide with those extracted by the transformation taking into account a nonlinearity in the region of the saddle even for small perturbations, and the discrepancy is more pronounced for the less repulsive direction of the index-two saddle system. The present result indicates an importance of the global properties of the phase space to identify the reactivity boundaries, relevant to the question of what reactant and product are in phase space, for saddles with index more than one.