Orbitalwise Coordination Number for Predicting Adsorption Properties of Metal Nanocatalysts

We present the orbitalwise coordination number ${\mathrm{CN}}^{\alpha }$ ($\alpha =s$ or $d$) as a reactivity descriptor for metal nanocatalysts. With the noble metal Au ($5d^{10}6s^1$) as a specific case, the ${\mathrm{CN}}^s$ computed using the two-center $s$-electron hopping integrals to neighboring atoms provides an accurate and robust description of the trends in CO and O adsorption energies on extended surfaces terminated with different facets and nanoparticles of varying size and shape, outperforming existing bond-counting methods. Importantly, the ${\mathrm{CN}}^s$ has a solid physiochemical basis via a direct connection to the moment characteristics of the projected density of states onto the $s$ orbital of a Au adsorption site. Furthermore, the ${\mathrm{CN}}^s$ shows promise as a viable descriptor for predicting adsorption properties of Au alloy nanoparticles with size-dependent lattice strains and coinage metal ligands.

Figure 1

Adsorption energies of the atop CO on Au nanoparticles and extended surfaces described by (a) the generalized coordination number $\overline{\mathrm{CN}}$ [11], and (b) the orbitalwise coordination number ${\mathrm{CN}}^s$ computed using the two-center $s$-electron hopping integrals. Linear regression lines (dashed) and related statistics are also given.

Figure 2

(a) Density of states projected onto the $s$ orbital of surface Au atoms on the terrace, step, and kink atoms of the ${\mathrm{Au}}_{201}$ nanoparticle, and (b) the relationship between ${ϵ}_s^{*}$ and the ${\mathrm{CN}}^s$ for various surface atoms of extended Au surfaces and nanoparticles. The dashed line is the least-square fit; the sold line is the theoretical correlation, corresponding to Eq. (3).

Figure 3

Description of adsorption energies of atomic O on hollow sites of Au nanoparticles by the orbitalwise coordination number ${\mathrm{CN}}^s$. Related statistics of the linear regression are shown.

Figure 4

The prediction of CO and O adsorption energies on a series of $M@\mathrm{Au}$ ($M=\mathrm{Cu}$ or Ag) core-shell nanoparticles (38, 79, and 201 atoms) using the ${\mathrm{CN}}^s$ as a reactivity descriptor and theoretical relationships developed from pure Au nanocatalysts.