New Solid-State Table: Estimating d-Band Characteristics for Transition Metal Atoms
Nilay İnoğlu and John R. Kitchin, “New solid-state table: estimating d-band characteristics for transition metal atoms”, Molecular Simulation 36(7-8), 633-638 (2010). https://doi.org/10.1080/08927022.2010.481794
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.
Question
In the d-band model, the center and width of the surface d band govern how strongly a transition metal surface binds adsorbates, and both respond to strain and ligand effects when metals are alloyed. Computing these quantities with density functional theory for every candidate surface is expensive. Earlier work had shown that the d-band width is proportional to a tight-binding interatomic matrix element, written in Harrison’s form with a characteristic d-orbital length for each element. Harrison’s lengths, however, were fitted to experimental data and do not reproduce DFT-computed d-band properties. The paper asks whether a set of DFT-derived characteristic lengths can turn the matrix-element relation into a fast predictive model for the d-band width (and hence center) of bulk atoms, clean surfaces and alloy surfaces (İnoğlu 2010).
Approach
The authors performed DFT calculations with DACAPO (ultrasoft pseudopotentials, 340 eV plane-wave cutoff, PW91 functional) on bulk unit cells and on four-layer 2x2 slabs of the (111), (100) and (110) facets, with the top two layers relaxed. The d-band center and width were taken as the first moment and the square root of the second moment of the atom-projected d density of states about the Fermi level. For each metal they strained the bulk lattice constant by up to about 0.08 Å (roughly 6.5% in volume) and found that the d-band width varies linearly with the inverse fifth power of the nearest-neighbor distance. From the slope and intercept of this line they extracted, for each metal, a characteristic orbital length rd and a residual width Wo (the nonzero width of an isolated atom-projected band). These parameters, for Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt and Au, make up the new solid-state table. The width of atom i is then estimated as Wo plus a sum over nearest neighbors j of (rd,i rd,j)(3/2) divided by dij5. Ligand effects enter through the rd of the neighbors, and strain enters through the distances. For surface atoms, a facet-specific constant beta was added to account for charge redistribution and relaxation, fitted separately for noble metals and other transition metals (İnoğlu 2010).
Key findings
The fitted rd values increase down each group, from about 2.4 to 2.7 for the 3d metals to about 3.7 to 3.9 for Ir, Pt and Au (the table does not state units in the extracted text). With these parameters the model reproduced DFT d-band widths of bulk atoms and of the (111), (100) and (110) surfaces of Cu, Rh, Pd, Ag, Ir, Pt and Au with an average error of about 2%; the worst case was Cu(110) at about 9% (İnoğlu 2010).
For surface alloys made by replacing one of four surface atoms of Pd(111) with Fe, Co, Ni, Ru, Rh, Ag, Ir, Pt or Au (25% surface impurity), the estimated widths agreed with DFT to an average error below 2.5%, with Co giving the largest error of about 6%. Impurities further right and down the periodic table broadened the d band of neighboring Pd atoms more, which the authors attribute mainly to the larger size of those atoms; 5d impurities should therefore make Pd surfaces less reactive. Smaller 3d impurities narrowed the Pd band and pushed its center toward the Fermi level, an effect the authors describe as electronic strain, since the Pd d orbitals are effectively under-coordinated (İnoğlu 2010).
The model was then applied to all overlayer/host combinations of the 11 metals, following the database of Greeley and Nørskov. For a fixed host, overlayers further right or lower in the periodic table had wider estimated bands, with Ag overlayers the widest. Plotting the estimated widths against DFT d-band centers from that database for Ni-, Pd- and Ir-hosted structures gave reasonable linear correlations with slopes near -1, as a rectangular band model predicts; deviations were traced to the need to guess interatomic distances. The authors note that surface alloy stability was not considered (İnoğlu 2010).
Significance
The paper turns the earlier matrix-element explanation of strain and ligand effects into a quantitative, transferable tool: with a single table of per-element parameters and a geometry, one can estimate d-band widths and, through the width-center correlation, d-band centers without new DFT calculations. The authors propose it for rapid screening of alloy surfaces, with sulfur-tolerant Pd-based hydrogen separation membranes named as an intended application to be combined with atomistic thermodynamics of segregation (İnoğlu 2010).