In Fig. , The RuO2 and TaO2 O*-systems show a large magnitude of the 0 th order ICOHP, indicating a strong covalent metal-adsorbate bonding. The 0 th order ICOHP values therefore differ among the systems, increasing from weakly to strongly adsorbed systems. Note that in the clean slabs (Figure ), the 0 th order average ICOHP is automatically equal to zero due to the absence of the metal-adsorbate axial(2) bond. Next, there is a large change from 0 th order to 1 st order except for TiO₂, which has d 0 character, and was discussed already in the previous section. Although the three systems belong to different adsorption energy regions, the average values of the expansion always approach the corresponding ICOHP of the bulk, where the differences between the systems are small. An alternative approach can be used to enhance the differences by considering the difference in ICOHP sums between the O*-adsorbed systems and corresponding clean slabs, labeled as ΔICOHP, as shown in Figure . We can see that the trend in adsorption energies is well reproduced by the considering ΔICOHP, particularly when going to higher orders. Similar to Figure , we observe a large jump from 0 th order to 1 st order here as well, suggesting that the 1 st order ΔICOHP vastly underestimates the change in covalent bond formation in adsorption. The ΔICOHP is well converged at 3 rd order and beyond. Direct comparison of ΔICOHP with the O* adsorption energies (alternate y-axis) indicates accurate linear correlation of this new descriptor.