Accuracy of first-principles lateral interactions: Oxygen at Pd(100)

We employ a first-principles lattice-gas Hamiltonian (LGH) approach to determine the lateral interactions between O atoms adsorbed on the Pd(100) surface. With these interactions, we obtain an ordering behavior at low coverage that is in quantitative agreement with experimental data. Uncertainties in the approach arise from the finite LGH expansion and from the approximate exchange-correlation (xc) functional underlying the employed density-functional theory energetics. We carefully scrutinize these uncertainties and conclude that they primarily affect the on-site energy, which rationalizes the agreement with the experimental critical temperatures for the order-disorder transition. We also investigate the validity of the frequently applied assumption that the ordering energies can be represented by a sum of pair terms. Restricting our LGH expansion to just pairwise lateral interactions, we find that this results in effective interactions which contain spurious contributions that are of equal size, if not larger than any of the uncertainties, e.g., due to the approximate xc functional.