A consistent hierarchy of generalized kinetic equation approximations to the chemical master equation applied to surface catalysis

TL;DR

This paper introduces a hierarchy of approximations to the chemical master equation for surface catalysis, enabling faster simulations while maintaining accuracy, and provides evidence of convergence and efficiency in 1D and 2D models.

Contribution

The authors develop a novel hierarchy of kinetic equation approximations that efficiently models spatial correlations in surface reactions, improving computational speed and accuracy over traditional methods.

Findings

Hierarchy converges to full system behavior in numerical examples.

Lower hierarchy levels are significantly faster than kinetic Monte Carlo methods.

Low-order models effectively capture essential dynamics in 2D surface reactions.

Abstract

We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations, are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.