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

Abstract

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.

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“…We consider pair interactions between any combination of sites up to distances that correspond to the third nearest neighor (NN) shell at Pd(100), as well as the most compact manybody interactions in form of trio interactions between any three site combination within a second NN shell distance. Judging from our preceding systematic analysis of lateral interactions at the extended Pd(100) surface [11] we are confident that this truncated LGH covers the ordering behavior at the accuracy level of interest to this study, and we will comment on this accuracy level and steps to further validate the truncation below.…”

“…In preceding work exactly the same computational setup [10] was validated and used to systematically investigate the on-surface adsorption of oxygen at Pd(100) [11] and the series of Pd(11N ) vicinals (with N = 3, 5, 7), which exhibit (111) FIG. 1: Schematic view of a Pd(100) surface with (111) steps.…”

“…In all cases such interaction energies differed by less than 20 meV and we verified that choosing either or the other value did not affect any of the conclusions presented below. Due to the large mass mismatch between O and Pd, the vibrational contribution to the LGH parameters can be approximately considered through its leading term which arises from the change of the O 2 gas-phase stretch frequency to the O-substrate stretch mode [11]. Extensive test calculations for various ordered configurations involving all five adsorption sites revealed only a small coverage-dependence of this term, which is correspond-ingly modeled as constant shifts of the five on-site energies by the zero point energy changes computed in the low-coverage limit.…”

“…[11]. In brief, we determine those on-site energies and interactions influenced by the (111) step from large supercell calculations for the Pd(117) vicinal, and those of undisturbed terrace sites from calculations for the lowindex Pd(100) surface.…”

“…A first indication for the reliability of the resulting LGH expansion comes from the computed leave-one-out cross validation score [11,13,14] of 29 meV / adatom, which provides a measure for the average accuracy with which the truncated LGH can predict the energetics of adatom configurations not included in the fitting procedure. The consistency of the expansion procedure is furthermore reflected by the similarity of equivalent LGH parameters that can be independently determined by fitting to the low-index or the vicinal DFT data.…”