An algorithm for computing phase space structures in chemical reaction dynamics using Voronoi tessellation

An efficient sampling algorithm is proposed for computing reactive islands, which consist of intersections of reactive trajectories and a Poincaré surface of section (PSOS), and are characterized by the number of times the reactive trajectories intersect the PSOS before/after reactions take place. The boundaries of reactive islands are series of intersections of cylindrical stable and unstable invariant manifolds emanated from a normally hyperbolic invariant manifold located, typically, nearby a rank-one potential energy saddle, which forms “reactivity boundaries”. The reactive islands structures enable us to predict the fate of trajectories. The proposed algorithm estimates regions of reactive islands on the PSOS as a Voronoi diagram constructed from the set of labeled intersections of computed molecular dynamics trajectories. The algorithm iteratively refines the boundaries of the estimated reactive islands efficiently, by computing trajectories of which initial condition is sampled from the estimated boundaries of reactive islands in the Voronoi diagram of the previous iteration step. The efficiency of the proposed algorithm is scrutinized, compared with random sampling algorithm and using a two-degrees of freedom Hamiltonian system of a double well potential, and further possible extensions of the proposed algorithm are addressed.