(453a) Automatic Formulation and Exact Solutions to the Master Equation for Multisite Microkinetic Models in Catalysis

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 struggle to accurately describe reactions where adsorbates interact with each other and where surface diffusion is important, while rates from kMC (while accurate) lack the convenience and insight that comes from a closed-form rate expression. We introduce a novel periodic tiling approach that bridges the gap between MF-MKMs and kMC simulations. We describe a generalizable way to partition the 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 the new method for a collection of problems that are notoriously difficult for MF-MKM approaches and obtain results which are essentially indistinguishable from numerically exact KMC results. We further demonstrate capabilities which are unique advantages of the new framework, e.g. differentiation of the matrix solution for direct predictions of activation energies, reaction orders, degrees of rate control, and parameter optimization tasks in reaction engineering.