Configurational Correlations in the Coverage Dependent Adsorption Energies of Oxygen Atoms on Late Transition Metal fcc(111) Surfaces
Spencer D. Miller, Nilay İnoğlu and John R. Kitchin, “Configurational correlations in the coverage dependent adsorption energies of oxygen atoms on late transition metal fcc(111) surfaces”, The Journal of Chemical Physics 134(10), 104709 (2011). https://doi.org/10.1063/1.3561287
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Question
Oxygen adsorption on late transition metal surfaces weakens as coverage rises, and earlier work had traced this to adsorbate-induced changes in the surface d band. That work also found that the adsorption energies of the same oxygen configurations on Au(111) and Pt(111) were linearly related, a relationship called the configurational correlation (Miller 2009). Because those results came from a few metals, this paper asks whether a single, consistently computed data set across many late transition metals shows that the d-band mediated mechanism and the configurational correlation are general, and what sets the slope of the correlation for each metal (Miller et al. 2011).
Approach
The authors used DACAPO with the PW91 GGA functional and ultrasoft Vanderbilt pseudopotentials on four-layer fcc(111) slabs of Rh, Ir, Pd, Pt, Cu, Ag and Au, with the bottom two layers fixed. Computed lattice constants range from 3.68 Å (Cu) to 4.19 Å (Au). Twenty oxygen configurations, using only fcc hollow sites in cells of one to five sites and coverages up to 1 ML, were computed on every metal with a 350 eV cutoff and a 12 × 12 × 1 k-point grid for the p(1 × 1) cell (equal density for larger cells). Adsorption energies are per oxygen atom relative to a gas-phase O atom. The surface d band was analyzed with atom-projected densities of states, taking the d-band center as the first moment and the width as the square root of the second moment about the Fermi level. The study covers only chemisorbed oxygen, so the authors note that it applies directly only where surface oxides do not form or are kinetically hindered, which for Ag and Au in particular is a narrow window (Miller et al. 2011).
Key findings
On all seven surfaces the oxygen adsorption energy becomes less favorable roughly linearly with coverage. Taking Pd(111) as the example, the surface d band widens with coverage while the number of d electrons stays about constant (with a slight decrease suggesting a little charge transfer to oxygen), so the d-band center moves down. For every metal the d-band center and width are linearly related, as a rectangular band model at fixed filling predicts. On Rh, Ir, Pd and Pt the adsorption energy is roughly linear in the d-band center, consistent with the Hammer-Nørskov model. On the filled-d-shell metals Cu, Ag and Au, where Pauli repulsion could alter the picture, the linear trend still appears, with coefficients of determination of 0.71 for Cu and Au but only 0.30 for Ag (Miller et al. 2011).
Plotting each configuration’s energy on Rh, Ir, Pt, Cu, Ag and Au against the same configuration on Pd(111) gives linear configurational correlations for all six metals. The mean absolute fit error is below 22 meV/O for Ir, Pt and Rh, close to the roughly 20 meV/O convergence of the calculations, but larger for the noble metals: 55 meV/O for Ag and Au and 120 meV/O for Cu. Relaxed Cu structures showed strong reconstruction, with some surface Cu atoms lifting out of the plane, so they were no longer geometrically similar to the Pd structures. When Cu, Ag and Au were recomputed with atoms fixed at the relaxed Pd positions scaled by the lattice constant ratio, the errors fell to 24 meV/O for Au, 46 meV/O for Ag and 65 meV/O for Cu. The correlation is therefore between configurations, not coverages, and requires geometric similarity (Miller et al. 2011).
The slopes relative to Pd were fit by an empirical model in which the slope scales inversely with the characteristic d-orbital radius of the metal and with the cube of its fractional d-band filling, each relative to Pd, times a fitted constant of 0.976. Model and DFT slopes agree within 0.1 for all metals, for example 1.69 versus 1.61 for Cu, 1.36 versus 1.38 for Ag and 0.87 versus 0.87 for Pt. Higher d filling gives a steeper slope, meaning adsorption weakens faster as more oxygen is added (Miller et al. 2011).
Significance
The paper establishes, with one consistent set of calculations, that d-band mediated coverage dependence and the configurational correlation it produces are general to oxygen on late transition metal (111) surfaces, extending the Au/Pt and Pd results to seven metals. It also shows the main limit of the correlation (reconstruction breaks geometric similarity, most strongly on Cu) and links the correlation slope to simple d-band properties, so coverage effects on one metal can in principle be estimated from another (Miller et al. 2011).