In order to capture the longer-range surface effects due to adsorption, we have generalized approach by further expanding the ICOHP sum values beyond the active site into the multiple orders. We consider expansion to whole surface slab, starting from active site ICOHP to nearest neighbors, second-nearest neighbors, etc. This is schematically shown in a hierarchical order in Figure . This expansion is defined as follows: the 0 th order encompasses only the adsorbate bond; the 1 st order includes all bonds around the immediate active site; the 2 nd order incorporates all the bonds of the active site and its nearest neighbors; and the 3 rd order extends to include all the bonds of the next-nearest neighbors along with the 2 nd order, etc. To compare the values, we consider the average value per bond, where the ICOHP sum is divided by the total number of bonds included in the overall sum, labeled a <ICOHP> thereafter.