LAUSR

We present the orbitalwise coordination number CN^{α} (α=s or d) as a reactivity descriptor for metal nanocatalysts. With the noble metal Au (5d^{10}6s^{1}) as a specific case, the 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 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 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.