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.