Topological Methods for Searching Barriers and Reaction Paths

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Abstract
We present a family of algorithms for the fast determination of reaction paths and barriers in phase space and the computation of the corresponding rates. The method requires that reaction times be large compared to the microscopic time, irrespective of the origin—energetic, entropic, cooperative—of the time scale separation. It lends itself to temperature cycling as in simulated annealing and to activation-relaxation routines. The dynamics is ultimately based on supersymmetry methods used years ago to derive Morse theory. Thus, the formalism automatically incorporates all relevant topological information.
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