Exploring long range dynamics using neural network potentials: From recrossing coefficients to roaming

Abstract

Accurate determination of the rate coefficients and branching ratios for the various channels in a barrierless reaction process are critical for reliable mechanistic predictions, but they are often treated approximately due to several substantial challenges. The gold standard for computing rate constants of barrierless reactions is variable reaction coordinate transition state theory (VRC-TST), with accuracies approaching those of experimental measurements. However, the statistical assumptions that provide the basis for VRC-TST may not adequately describe certain dynamical effects, such as transition state recrossing fractions, especially for reactions with multiple bottlenecks, and roaming pathways. Although these processes can be adequately described with rigid-body trajectory simulations, doing so requires a sufficiently accurate potential energy surface (PES). Direct trajectory simulations come at a huge computational cost, requiring up to millions of single point energy evaluations and are thus unfeasible for the vast majority of chemical reactions. In this work we investigate whether it is possible to determine a PES suitable for trajectory simulations using a novel machine learning approach that exploits ab-initio calculations to feed a physics-inspired neural network (PHINN) architecture. The main result of this work is that the PHINN PES is sufficiently accurate not only to carry out VRC-TST simulations, but also to perform trajectory simulations, thus opening the path to the systematic use of trajectory simulations to study the kinetics of barrierless reactions. The developed framework is validated via a study of formaldehyde decomposition, providing roaming fractions in agreement with existing studies. After validation, the PHINN is employed to compute temperature-dependent recrossing coefficients for the recombination reactions between CH₃ + H and NH₂ + CH₃, providing in the latter case a framework for validating the accuracy of two-state transition state theory. The developed computational approach is then used to study the long-range recombination roaming dynamics between H and phenoxy radical, providing site-specific branching fractions among the three possible addition sites.

Novelty and significance statement

In this work, we demonstrate for the first time that rate constants and roaming fluxes can be computed using trajectory simulations combined with neural network potential energy surfaces, enabling new approaches to reaction kinetics. We present a robust framework to (i) compute temperature-dependent recrossing coefficients, (ii) assess the accuracy of 2-state transition state theory, and (iii) determine roaming branching fractions, which are extremely difficult to evaluate accurately with existing methods. These advances are critical for improving the understanding of barrierless reactions, typically involving radical–radical recombination, which are prevalent in fuel oxidation, pyrolysis, and pollutant formation kinetic mechanisms. The systems studied range from hydrocarbons, including aromatic species, to amino radicals. Therefore, this work provides an important new tool for accelerating and improving the accuracy of theoretical rate constant predictions, representing a key asset for the combustion community.