Invariant Manifolds and Rate Constants in Driven Chemical Reactions

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.Comment: 28 pages, 13 figures, table of contents figur

Influence of external driving on decays in the geometry of the LiCN isomerization

The framework of transition state theory relies on the determination of a geometric structure identifying reactivity. It replaces the laborious exercise of following many trajectories for a long time to provide chemical reaction rates and pathways. In this paper, recent advances in constructing this geometry even in time-dependent systems are applied to the LiCN $\rightleftharpoons$ LiNC isomerization reaction, driven by an external field. We obtain decay rates of the reactant population close to the transition state by exploiting local properties of the dynamics of trajectories in and close to it. We find that the external driving has a large influence on these decay rates when compared to the non-driven isomerization reaction. This, in turn, provides renewed evidence for the possibility of controlling chemical reactions, like this one, through external time-dependent fields.Comment: Main article has 11 pages, 6 figures. Supplemental material has 4 pages, 1 figur

Mean first-passage times for solvated LiCN isomerization at intermediate to high temperatures

The following article appeared in The Journal of Chemical Physics 156 (2022): 034103 and may be found at https://aip.scitation.org/doi/full/10.1063/5.0065090The behavior of a particle in a solvent has been framed using stochastic dynamics since the early theory of Kramers. A particle in a chemical reaction reacts slower in a diluted solvent because of the lack of energy transfer via collisions. The flux-over-population reaction rate constant rises with increasing density before falling again for very dense solvents. This Kramers turnover is observed in this paper at intermediate and high temperatures in the backward reaction of the LiNC ⇌ LiCN isomerization via Langevin dynamics and mean first-passage times (MFPTs). It is in good agreement with the Pollak-Grabert-Hänggi (PGH) reaction rates at lower temperatures. Furthermore, we find a square root behavior of the reaction rate at high temperatures and have made direct comparisons of the methods in the intermediate- and high-temperature regimes, all suggesting increased ranges in accuracy of both the PGH and MFPT approache

Invariant manifolds and rate constants in driven chemical reactions

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

Description of PT-symmetric Bose-Einstein condensates with a four-well potential using the Bogoliubov-backreaction method

Nicht-hermitesche Hamiltonoperatoren mit PT-Symmetrie erlauben die elegante Beschreibung offener Quantensysteme. Die Arbeit untersucht die Realisierung eines PT-symmetrischen Zweimuldensystems durch die Einbettung in ein hermitesches Viermuldensystem mithilfe der Bogoliubov-Backreaction-Methode