Binary Approach to Ternary Cluster Expansions: NO-O-Vacancy System on Pt(111)

Cluster expansions (CEs) provide an exact framework for representing the configurational energy of interacting adsorbates at a surface. Coupled with Monte Carlo methods, they can be used to predict both equilibrium and dynamic processes at surfaces. In this work, we propose a three binary -to-single-ternary (TBST) fitting procedure, in which a ternary CE is approximated as a linear combination of the three binary CEs (O-vac, NO- vac, and NO-O) obtained by fitting to the three binary legs. We first construct a full ternary CE by fitting to a database of density functional theory (DFT) computed energies of configurations across a full range of adsorbate configurations and then construct a second ternary using the TBST approach. We compare two approaches for the NO-O vacancy system on the (111) surface of Pt, a system of relevance to the catalytic oxidation of NO. We find that the TBST model matches the ternary CE to within 0.018 eV/site across a wide range of configurations. Further, surface coverages and NO oxidation rates extracted from Monte Carlo simulations show that the two models are qualitatively consistent over the range of conditions of practical interest.