Effects ofd-band shape on the surface reactivity of transition-metal alloys

The $d$-band shape of a metal site, governed by the local geometry and composition of materials, plays an important role in determining trends of the surface reactivity of transition-metal alloys. We discuss this phenomenon using the chemisorption of various adsorbates such as C, N, O, and their hydrogenated species on Pd bimetallic alloys as an example. For many alloys, the $d$-band center, even with consideration of the $d$-band width and $\mathit{sp}$ electrons, can not describe variations in reactivity from one surface to another. We investigate the effect of the $d$-band shape, represented by higher moments of the $d$ band, on the local electronic structure of adsorbates, e.g., energy and filling of adsorbate-metal antibonding states. The upper $d$-band edge ${\ensuremath{\varepsilon}}_{u}$, defined as the highest peak position of the Hilbert transform of the density of states projected onto $d$ orbitals of an active metal site, is identified as an electronic descriptor for the surface reactivity of transition metals and their alloys, regardless of variations in the $d$-band shape. The utilization of the upper $d$-band edge with scaling relations enables a considerable reduction of the parameter space in search of improved alloy catalysts and further extends our understanding of the relationship between the electronic structure and chemical reactivity of metal surfaces.