Reaction rate calculation with time-dependent invariant manifolds
journal contributionposted on 10.09.2014 by Thomas Bartsch, F. Revuelta, R.M. Benito, F. Borondo
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The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in particular if the reactive system is exposed to the influence of a heat bath. As an efficient alternative, we propose here to compute invariant surfaces in the phase space of the reactive system that separate reactive from nonreactive trajectories. The location of these invariant manifolds depends both on time and on the realization of the driving force exerted by the bath. These manifolds allow the identification of reactive trajectories simply from their initial conditions, without the need of any further simulation. In this paper, we show how these invariant manifolds can be calculated, and used in a formally exact reaction rate calculation based on perturbation theory for any multidimensional potential coupled to a noisy environment.
This work has been supported by the MCINN (Spain) under projects MTM2009-14621 and CONSOLIDER 2006-32 (i-Math). F.R. gratefully acknowledges a doctoral fellowship the UPM and the hospitality of the members of the School of Mathematics at Loughborough University, where part of this work was done.
- Mathematical Sciences