(521dt) Non-Mean Field Approaches for Surface Catalysis: Analytical Description of Adsorbate-Adsorbate Interactions

Theoretical studies of heterogeneous catalytic reactions routinely utilize microkinetic models, which are powerful tools for rationalizing experimentally observed reaction rates, effective activation barriers, and reaction orders in terms of the corresponding elementary steps. Such models generally rely on the mean-field assumption, where the configurational entropy of adsorbates on the surface is taken to be that of a random distribution of molecules on a lattice. This simplification, in turn, often allows the development of analytical rate expressions with straightforward physical interpretations. However, interactions and spatial correlations between the adsorbates, which are common in many catalytic systems, cause significant deviation from the mean field configurational entropy, limiting the accuracy of this assumption. Previous efforts to correct this approximation have either been purely numerical, resulting in the loss of analytical rate equations, or have employed spatially averaged binding energy correction factors, which have limited ability to capture contributions which arise because of local configurations deviating from the average.

To address the above limitations, we present a compact strategy to incorporate adsorbate-adsorbate interactions as activity coefficient correction factors to the mean field microkinetic expressions on FCC (100) surfaces. To derive the activity coefficients, we utilize Bethe-Peierls approximations to the grand canonical partition function, based on the Cluster Variational Method, assuming pairwise nearest neighbor interactions. Under the assumption of a single Most Abundant Surface Intermediates, we demonstrate how this formalism can be generalized to (semi)analytically describe multiple reactive intermediates adsorbed simultaneously. We further demonstrate how this analysis can be extended to describe the physics of transition states for monomolecular combination reactions, which commonly adapt bidentate geometries, simultaneously occupying two neighboring sites. The successfully preserved analytical form of these activities permits direct incorporation into microkinetic rate expressions.