Tight-Binding Models
Tight-binding models describe the electronic structure of solids in terms of hopping (interatomic matrix) elements between localized atomic orbitals on neighboring atoms. In Harrison’s formulation these matrix elements depend on characteristic orbital radii and interatomic distance through simple power laws, so band widths and related properties can be estimated from geometry and a small table of parameters instead of a full electronic-structure calculation. See also d-Band model, Strain and ligand effects and Coverage-dependent adsorption.
Tight-binding estimates of coverage-dependent d-band widths (2010)
İnoğlu and Kitchin fit Harrison-style matrix-element expressions to DFT d-band widths (defined as the root second moment of the d band) for Cu, Rh, Pd, Ag, Ir, Pt and Au, adding facet-specific constants for surface relaxation and a coverage-proportional term for metal-adsorbate orbital overlap (İnoğlu 2010). The metal-metal term scales as the inverse fifth power of distance, while the fitted metal-adsorbate term scales as the inverse 5/2 power, and the resulting parameter table reproduces DFT widths for clean and covered surfaces with average error below 5 percent. Summary: inoglu2010.
A DFT-parameterized solid-state table for d-band widths (2010)
In a companion paper, İnoğlu and Kitchin replaced Harrison’s experimentally fitted d-orbital lengths with values fitted to DFT: for 11 late transition metals they obtained a characteristic d-orbital length rd and a residual width Wo from the linear dependence of DFT bulk d-band widths on the inverse fifth power of the nearest-neighbor distance (İnoğlu 2010). The d-band width of any atom is then Wo plus a nearest-neighbor sum of (rd,i rd,j)(3/2)/dij5, with a facet-specific correction for surface atoms, so strain enters through the distances and ligand effects through the neighbors’ orbital lengths. This solid-state table reproduced DFT widths of bulk atoms and low-index surfaces with about 2% average error (9% worst case, Cu(110)) and was used to estimate d-band widths, and from them d-band centers, of surface impurity and overlayer alloys without new DFT calculations. Summary: inouglu2010.