The scaling relationships in the total binding energies for CH x (x = 1-4) species relative to the C atom on the 5 metal surfaces in the lowest energy sites are presented for the periodic calculations in Figure (c) and for the cluster calculations in Figure . For both the periodic and the cluster models, it can be observed in Tables S1-S5 that C and CH prefer the hollow site; CH 2 favors the bridge site in most cases and the hollow site in some cases; CH 3 prefers the bridge and ontop sites equally; CH 4 does not show any site preference. These results on preferred binding sites agree with previous works. For the periodic systems, the scaling relationships from our calculations also agree with previous works. In Figure (c), the fitted slopes (0.79, 0.52, 0.27, and 0.01) closely follow the previously suggested adsorbate valency based values of (4 x)/4 for CH x . The deviation from perfectly linear scaling relations is rather minor, where the largest mean absolute error (MAE) is 0.27 eV for the adsorption energies (that range over several eVs) and the R 2 values are all greater than 0.80.