This is mathematically identical to the prior approach (Eq. ( )), with the difference being that the enthalpies of adsorbed species, rather than gas-phase species, are used as references. For the construction of the stoichiometry matrix M, we refer the reader to Section 4.2.2. Since the approach connects the DFT data with the ATcT, it is possible to replace all DFT energies of gas-phase species with accurate ∆ f H form the ATcT to achieve thermodynamic consistency. The resulting enthalpy diagram using this approach is shown in Fig. . Similar to the previous method, this approach does not affect the reaction enthalpies of surface steps since it uses an atomic reference basis set. However, all adsorption/desorption reaction enthalpies are changed except for the reference species. In the previous approach, the adsorption enthalpies of CH 4 , H 2 , and H 2 O were fixed at the DFT values. The difference in this approach is that the adsorption enthalpies of CO, H 2 , and O 2 correspond now to experimental values (see Fig. ). This adjustment leads to noticeable changes in the adsorption enthalpies of some species. The biggest change occurs for the adsorption of CO 2 , which changes from strongly exothermic to mildly endothermic. Typically, CO 2 binds only weakly through physisorption on the Pt(111) surface 196 . Using gas-phase reference ∆ f H indicates that the CO 2 binds strongly to the surface in disagreement with experiments. Mhadeshwar et al. also describe the use of the experimental ∆ f H of adsorbates as a basis set to reference the DFT energies to the global thermochemical network, thereby ensuring thermodynamic consistency of the reaction mechanism with known adsorption enthalpies.