Calculation of long time classical trajectories: algorithmic treatment and applications for molecular systems

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Abstract

We study the problem of finding a path that joins a given initial state with a final one, where the evolution is governed by classical (Hamiltonian) dynamics. A new algorithm for the computation of long time transition trajectories connecting two configurations is presented. In particular, a strategy for finding transition paths between two stable basins is established. The starting point is the formulation of the equation of motion of classical mechanics in the framework of Jacobi's principle; a shortening procedure inspired by Birkhoff's method is then applied to find geodesic solutions. Numerical examples are given for Muller's potential and the collinear reaction H-2+H -> H+H-2.
Original languageEnglish
Article number124106
Number of pages11
JournalJournal of Chemical Physics
Volume130
Issue number12
Early online date23 Mar 2009
DOIs
Publication statusPublished - 28 Mar 2009

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Hamiltonians
Equations of motion
Mechanics
Trajectories
trajectories
classical mechanics
equations of motion
formulations
configurations

Keywords

  • hydrogen neutral
  • Jacobian matrices
  • hydrogen neutral atoms
  • reaction kinetics theory
  • molecules
  • atom-molecule reactions

Cite this

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abstract = "We study the problem of finding a path that joins a given initial state with a final one, where the evolution is governed by classical (Hamiltonian) dynamics. A new algorithm for the computation of long time transition trajectories connecting two configurations is presented. In particular, a strategy for finding transition paths between two stable basins is established. The starting point is the formulation of the equation of motion of classical mechanics in the framework of Jacobi's principle; a shortening procedure inspired by Birkhoff's method is then applied to find geodesic solutions. Numerical examples are given for Muller's potential and the collinear reaction H-2+H -> H+H-2.",
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