Phase space conduits for reaction in multidimensional systems: HCN isomerization in three dimensions

Area of Science:

• Chemical Dynamics
• Theoretical Chemistry
• Chemical Physics

Background:

• Classical reaction dynamics are governed by phase space structures.
• Understanding these structures is crucial for predicting reaction pathways.
• Existing methods often rely on assumptions that may not hold universally.

Purpose of the Study:

• To present a general, algorithmic theory for computing phase space structures.
• To identify and compute global phase space transition pathways for reactions.
• To provide a framework for understanding reaction dynamics without prior assumptions.

Main Methods:

• Development of a general theory for computing phase space structures.
• Construction of a minimal flux dividing surface as a "surface of no return."
• Computation of global phase space transition pathways using normally hyperbolic invariant manifolds (NHIMs) and their associated stable/unstable manifolds.

Main Results:

• The theory enables computation of phase space structures for systems with arbitrary degrees of freedom.
• Identified transition pathways are enclosed by NHIM manifolds.
• Methods are provided to compute homoclinic and heteroclinic orbits related to NHIMs, explaining global recrossings and transport.
• Demonstrated that phase space analysis is essential and cannot be inferred from configuration space.

Conclusions:

• The presented theory offers a robust method for analyzing and quantifying reaction dynamics in phase space.
• The findings challenge certain routine assumptions in global dynamics studies.
• The framework can be extended to incorporate quantum effects for a more complete picture.