As seen earlier in Fig. , CH x binds weaker and weaker to the 5 metal surfaces as the number of hydrogen atoms in the adsorbate increases. This is expected on the ground of lowering valency of the adsorbates. In this work, a new metric -effective Mayer "bond order" between the adsorbate and metal surface -is computed according to Eq. 13 and shown in Figure for cases of hollow-site adsorption.