Uncertainty and figure selection for DFT based cluster expansions for oxygen adsorption on Au and Pt (111) surfaces

We utilise two-dimensional cluster expansions in order to extend a small density functional theory (DFT) database of oxygen adsorption energies on Au and Pt (111) surfaces to explore a wide range of configurational space in larger unit cells than can be conveniently examined by DFT. We calculate adsorption energies and heats of formation for all configurations of up to 15 adsorption sites using the cluster expansions. We show how the cluster expansion adsorption energies obey the configurational correlation previously observed for the DFT results. The ramifications of figure selection are considered and the use of cross-validation scores to weigh figure sets and determine predictive power is examined. Finally, we show that there are only a small number of structural motifs needed to describe the most relevant structures in the phase diagram on these metals.