(377g) Overcoming the Compromise between Accuracy and Efficiency in Modelling Catalytic Kinetics

Modelling catalytic kinetics is indispensable for the design of reactors and chemical processes. Currently, the majority of kinetic models are formulated as ordinary differential equations (ODEs) that employ mean-field (MF) approximations, thereby omitting spatial correlations and the inherent stochasticity in reaction occurrence. However, correlations do arise from slow diffusion in tandem with 2-site reactions, or from adsorbate-adsorbate lateral interactions, and have previously been shown to markedly affect the observed kinetics. In addition, stochasticity has been demonstrated to induce complexity in the behavior of chemical systems, such as noise-induced transitions or oscillations. Such effects can be captured by kinetic Monte Carlo (KMC) approaches, which provide a discrete-space continuous-time stochastic formulation, but at a significant computational expense. It is therefore of interest to develop computational methods that compete with KMC in terms of accuracy, but incur a low computational expense, preferably comparable to that of MF.

In this study, we develop such computational methods based on statistical mechanical approaches. We first discuss the treatment of lateral interactions in the context of the Bethe-Peierls and Kikuchi approximations, adapted for use in chemical kinetics. The key idea behind these methods is embedding a progressively larger (but finite) cluster of explicitly treated sites, into a continuum field of adsorbates. A single-site cluster gives rise to the MF approximation, whereas larger clusters can lead to higher accuracy, but only if appropriate correction terms are introduced and solved-for self-consistently. For capturing stochasticity, we use a system size expansion method to coarse-grain the chemical master equation into the Fokker-Planck formalism and the corresponding stochastic differential equation (SDE) for the adsorbate coverage. We discuss complications in numerically solving this SDE, arising from the coverage being bounded between 0 and 1, and demonstrate that the use of appropriate SDE formulations (Skorokhod problem) and corresponding numerical schemes can effectively tackle these issues. We further demonstrate the accuracy and efficiency of our methods in prototype systems, but also on a model for NO oxidation and NO₂ reduction incorporating first nearest neighbor lateral interactions. We finally discuss broader impacts in the context of employing such approximations in multiscale modelling frameworks.