The role of vdW interactions in coverage dependent adsorption energies of atomic adsorbates on Pt(111) and Pd(111)
Hari Thirumalai and John R. Kitchin, “The role of vdW interactions in coverage dependent adsorption energies of atomic adsorbates on Pt(111) and Pd(111)”, Surface Science 650, 196-202 (2016). https://doi.org/10.1016/j.susc.2015.10.001
This summary was written by a language model from the paper and has not been checked line by line. Rely on the published paper for details.
Note on the source text: the extraction drops the fraction glyphs, so coverages appear as “14 ML”, “12 ML” and “34 ML”; from context these are 1/4, 1/2 and 3/4 ML. The ordering of effective nuclear charges is also partly garbled. No tables of numerical adsorption energies are given in the text; the results are presented in figures.
Question
Coverage-dependent adsorption energies of atomic adsorbates on late transition metals had been studied extensively with GGA functionals such as PBE, which describe van der Waals (vdW) forces poorly. At high coverage, long-range interactions between neighboring adsorbates could plausibly matter. The paper asks how much vdW interactions contribute to the adsorption energies of atoms on Pt(111) and Pd(111), how that contribution changes with coverage and adsorbate identity, and whether including it alters the coverage trends and site correlations found earlier with PBE (Thirumalai 2016).
Approach
Calculations used VASP with PAW potentials and the BEEF-vdW functional, which combines GGA exchange, LDA and PBE correlation, and a vdW-DF2-type nonlocal correlation term. Surfaces were four-layer 2x2 (111) slabs (bottom two layers fixed) with 6 Å of vacuum on each side, a 520 eV cutoff and a 12x12x1 k-point mesh. BEEF-vdW lattice constants from a stabilized jellium equation of state were 3.9934 Å for Pt and 3.9791 Å for Pd, somewhat larger than the experimental values. Seven adsorbates (C, N, O, S, F, Cl, Br) were placed in hollow and atop sites at 1/4, 1/2, 3/4 and 1 ML, with energies referenced to the isolated gas-phase atoms. Two quantities were extracted: the BEEF error ensemble, giving a one-standard-deviation (68%) error bar on each adsorption energy, and the vdW contribution, computed with the same reaction-energy expression applied only to the nonlocal correlation energy. The authors note this nonlocal term includes some double counting of correlation. Adsorption energies were compared in a parity plot with earlier PBE results from Xu and Kitchin (Thirumalai 2016).
Key findings
On hollow sites of both metals the adsorption energies still weaken linearly with coverage, and the ensemble error bars show the trend is statistically meaningful: for example, binding at 1 ML is weaker than at 1/4 ML with high confidence. On atop sites there is no clear linear trend and the error bars at different coverages overlap substantially, so those energies look roughly coverage independent (Thirumalai 2016).
BEEF-vdW binds the adsorbates less strongly than PBE, especially at low coverage, and the gap narrows with coverage until the two nearly agree at very high coverage. The authors caution that PBE is known to overbind, so the differences are not a physical vdW effect but show that quantitative coverage trends depend on the functional. They rationalize weaker binding with effective medium theory and bond-order arguments: attractive vdW interactions with neighbors supply part of an adsorbate’s optimal embedding density, so it needs less from the surface and its bond to the metal weakens (Thirumalai 2016).
The vdW contribution generally becomes more attractive as adsorbates are added, and more so for the larger, more polarizable atoms S, Cl and Br. Sulfur has the largest contribution on hollow sites, bromine exceeds chlorine, and fluorine has the smallest. O and N adlayers on hollow sites show a nearly constant vdW term, attributed to screening by the metal, while C, N and O on atop sites show a sharper increase with coverage. F and Cl started in Pt(111) hollow sites but relaxed to atop sites, in contrast to earlier reports of hollow-site adatoms. Hollow and atop sites gave nearly the same vdW magnitudes, which suggests the vdW term depends mainly on the adsorbate rather than the surface, and it correlates with the adsorbate’s effective nuclear charge (Thirumalai 2016).
Significance
The work gives theory-based statistical support, through the BEEF-vdW error ensemble, for the linear coverage dependence of hollow-site adsorption energies that is often assumed in kinetic models. It also shows that dispersion contributions grow with coverage and scale with adsorbate size and polarizability, so trends computed with plain GGA functionals may change when vdW is included (Thirumalai 2016).