Correlations in Coverage-Dependent Atomic Adsorption Energies on Pd(111)
John R. Kitchin, “Correlations in Coverage-Dependent Atomic Adsorption Energies on Pd(111)”, Physical Review B 79(20), 205412 (2009). https://doi.org/10.1103/physrevb.79.205412
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Question
Adsorption energies on metal surfaces usually depend on how many adsorbates are already present, and because reaction and dissociation barriers often track adsorption energies, coverage effects can make kinetic parameters themselves coverage dependent. Earlier work from the same group had found that the coverage dependence of atomic oxygen on Pt(111) and Au(111) could be explained through adsorbate-induced changes in surface electronic structure, and that this led to correlations between the two metals (Miller 2009). This paper asks whether the same picture extends to other atomic adsorbates, specifically C, N and O in fcc hollow sites of Pd(111), and whether the coverage-dependent energies of different adsorbates are correlated with one another (Kitchin 2009).
Approach
The calculations use plane-wave DFT in DACAPO with Vanderbilt ultrasoft pseudopotentials and the PW91 functional, on four-layer Pd(111) slabs (bottom two layers fixed at the computed bulk lattice constant of 3.92 Å, versus 3.88 Å experimentally) with about 10 Å of vacuum. Each adsorption energy was converged to within 0.02 eV/adsorbate with respect to plane-wave cutoff and k-point sampling, and energies are referenced to spin-polarized gas-phase atoms. Twenty fcc-site configurations per adsorbate span coverages from 0.2 to 1 ML. The surface Pd d band is analyzed through the atom-projected density of states, with the d-band center taken as the first moment, the width as the square root of the second moment, and the fractional filling from integration up to the Fermi level. To test functional sensitivity, energies were also recomputed non-self-consistently with VWN (LDA), PBE, revPBE and RPBE using the frozen PW91 densities (Kitchin 2009).
Key findings
For the most stable configurations the adsorption energy weakens roughly linearly with coverage over a range of nearly 1.5 eV between about 0.2 and 1 ML, with binding strength generally ordered C > N > O. The sensitivity to coverage also follows this order: the fitted slopes are 2.49 eV/ML for C, 1.88 eV/ML for N and 1.29 eV/ML for O. Two carbon configurations near 0.8 ML are outliers because the surface reconstructed substantially and incorporated carbon (Kitchin 2009).
The surface d band broadens with coverage while its fractional filling stays nearly constant (about 0.91 to 0.95 across the cases shown), so the d-band center must drop. Across all configurations the d-band width and center are strongly correlated, consistent with a rectangular band model at fixed filling; some loss of d electrons at the highest coverages is noted but the author argues charge transfer is not needed to explain the trends. The d-band center falls approximately linearly with coverage for each adsorbate, and weaker adsorption accompanies lower d-band centers. Carbon sits closest to the surface, overlaps most with the Pd d orbitals and perturbs the electronic structure most, while oxygen shows little change in adsorbate height with coverage (Kitchin 2009).
Because each adsorbate perturbs the d band in a similar way, the energies of C and N in a given configuration are nearly linear functions of the energy of O in the same configuration (configurational correlations), with fitted slopes of roughly 1.95 for C and 1.45 for N as read from the figure labels. Deviations trace to the reconstructed carbon structures and to small displacements from ideal fcc sites. The correlations persist with all four alternative functionals, with most points within 50 meV of a linear fit; the reconstructed C structures deviate by about 250 meV only with LDA. Subtracting the intercept and dividing by the slope collapses all C and N data onto a single line against O, with deviations below 100 meV/adsorbate in nearly every case, a result the author calls a principle of corresponding adsorption states. Two calculations, for example at 0.25 and 1 ML, would then suffice to predict coverage-dependent energies of another adsorbate (Kitchin 2009).
Significance
The work offers an electronic-structure explanation of coverage dependence (adsorbate-induced d-band broadening and down-shift at constant filling) as an alternative to pairwise repulsion or bonding-competition pictures, and it shows that the configurational correlations first seen for O on Pt and Au generalize to other adsorbates. It connects coverage effects to the single-coverage scaling relations reported by Abild-Pedersen and co-workers, suggesting those relations should hold at other coverages too. The author limits the expectation to geometrically similar configurations with a common d-mediated bonding mechanism, excluding cases with dipole interactions, hydrogen bonding, dimer formation, or metals without participating d orbitals (Kitchin 2009).