Invariant manifolds and rate constants in driven chemical reactions
journal contributionposted on 18.03.2019, 13:38 by Matthias Feldmaier, Philippe Schraft, Robin Bardakcioglu, Johannes Reiff, Melissa Lober, Martin Tschope, Andrej Junginger, Jorg Main, Thomas Bartsch, Rigoberto Hernandez
Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state trajectory. Here, we extend our recent methods by constructing points on the NHIM accurately even for multidimensional cases. We also advance the implementation of machine learning approaches to construct smooth versions of the NHIM from a known high-accuracy set of its points. That is, we expand on our earlier use of neural nets and introduce the use of Gaussian process regression for the determination of the NHIM. Finally, we compare and contrast all of these methods for a challenging two-dimensional model barrier case so as to illustrate their accuracy and general applicability.
The German portion of this collaborative work was partially supported by Deutsche Forschungsgemeinschaft (DFG) through Grant No. MA1639/14-1. The US portion was partially supported by the National Science Foundation (NSF) through Grant No. CHE 1700749. A.J. acknowledges the Alexander von Humboldt Foundation, Germany, for support through a Feodor Lynen Fellowship. M.F. is grateful for support from the Landesgraduiertenförderung of the Land Baden-Württemberg. This collaboration has also benefited from support by the European Union’s Horizon 2020 Research and Innovation Program under the Marie Sklodowska-Curie Grant Agreement No. 734557.
- Mathematical Sciences