Multisite Microkinetic Models in Catalysis: Automatic Formulation and Direct Solutions of the Master Equation

Accurate kinetic models are crucial for catalyst development efforts. Tremendous progress has been made with existing mean-field microkinetic models (MF-MKMs) and kinetic Monte Carlo (kMC) simulations. However, MF-MKMs cannot accurately describe reactions where adsorbates interact with each other or where surface diffusion is important, whereas kMC (while accurate) lacks the convenience and insight that comes from a closed-form rate expression. We introduce a master equation microkinetic modeling (ME-MKM) approach that bridges the gap between MF-MKMs and kMC simulations. We describe a generalizable way to partition a surface into linear periodic tiles, to automate the formulation of the master equation including adsorption, reaction, diffusion, and desorption steps (with adsorbate interactions of any strength), and to exactly solve the master equation. We demonstrate this method for examples that are notoriously difficult for MF-MKMs and obtain results which are essentially indistinguishable from numerically exact kMC results. We also demonstrate (using kMC data) that the analytic ME-MKM rate expression can be used “in reverse” to accurately estimate rate parameters and adsorbate interactions from data.