Analytic Activation Energies and Reaction Orders from Master Equation Microkinetic Modeling

Traditional mean-field microkinetic models (MF-MKMs) yield simple analytic rate expressions for multistep catalytic reactions. They help interpret observed rates and trends, test mechanistic hypotheses, and design reactors, but they cannot account for adsorbate interactions or surface diffusion. Across a wide range of situations, kinetic Monte Carlo (kMC) makes accurate predictions, but they are generated one-condition-at-a-time as estimates with statistical noise. Moreover, finite difference formulas amplify the sampling noise in derivative quantities like the overall activation energy, the reaction order, and the degree of rate control. Starting from periodic tiles that represent the catalytic surface with o(10) sites, the alternative master equation microkinetic modeling (ME-MKM) approach formulates the master equation in full microstate detail, including surface reactions, adsorption/desorption steps, adsorbate interactions, and even surface diffusion in an earlier investigation. The ME-MKM approach then directly solves the master equation (with no approximations) to predict rates that are accurate, analytic, and (as demonstrated in this work) differentiable. We develop a general ME-MKM framework to obtain derivatives of steady-state rates with respect to temperature, concentration, or other variables. We use the framework to calculate activation energies and reaction orders in two systems with adsorbate interactions: a simple A (g) + * → A* → B (g) + * process, and a more complicated process based on models of CO oxidation. For a wide range of conditions in both systems, the ME-MKM predictions match the accuracy of kMC with lower computational cost and no statistical estimation errors.