Speeding up the Detection of Adsorbate Lateral Interactions in Graph-Theoretical Kinetic Monte Carlo Simulations

Kinetic Monte Carlo (KMC) has become an indispensable tool in heterogeneous catalyst discovery, but realistic simulations remain computationally demanding on account of the need to capture complex and long-range lateral interactions between adsorbates. The Zacros software package (https://zacros.org) adopts a graph-theoretical cluster expansion (CE) framework that allows such interactions to be computed with a high degree of generality and fidelity. This involves solving a series of subgraph isomorphism problems in order to identify relevant interaction patterns in the lattice. In an effort to reduce the computational burden, we have adapted two well-known subgraph isomorphism algorithms, namely, VF2 and RI, for use in KMC simulations and implemented them in Zacros. To benchmark their performance, we simulate a previously established model of catalytic NO oxidation, treating the O* lateral interactions with a series of progressively larger CEs. For CEs with long-range interactions, VF2 and RI are found to provide impressive speedups relative to simpler algorithms. RI performs best, giving speedups reaching more than 150× when combined with OpenMP parallelization. We also simulate a recently developed methane cracking model, showing that RI offers significant improvements in performance at high surface coverages.