## 2 Theoretical Studies on Heteroatom-Mediated Metal-Support Interactions
### Predicting the Effect of Heteroatom-Mediated SMSI on the Catalytic Performances
#### 2.4.1 Effects on Molecule Adsorption and Metal Cluster Shape  
The adsorption of reactant on the metal surface is the first step of a catalytic cycle, occurring on supported transition metal nanoparticles. The description of the formation of a chemical bond between a surface and a molecule can be performed in terms of a d-band model. According to this model, the bond formation at a transition metal surface is the result of the interaction between the valence states of the adsorbate molecule and the S and D states of the transition metal surface. The interaction of valence states with the S states of the metal produces a shift and broadening of the adsorbate. These renormalized valence states interact with the metal D states, thus generating separate bonding and antibonding states. The strength of the bond is determined by the relative occupancy of these states. The filling of antibonding states results in a bond weakening, which is a function of the energy of the antibonding states relative to the Fermi level. The higher the antibonding states are in energy relative to the Fermi level, the lower their filling degree, and the stronger the bond. Since D antibonding states are always above the D states, the evaluation of the D state energy (the center of the D band) relative to the Fermi level can give a rough idea of the bond strength. Consequently, the variation in the position of the metal D band induced by heteroatom mediated metal-support interaction will affect the strength of the adsorbate bonding. [PERSON] et al. [71] compared the adsorption of H\({}_{2}\) on transition metal (TM) supported on boron and pyridine-like nitrogen-doped graphenes. The binding energies were similar for adsorption on TM/N-graphene and TM/B-graphene with values slightly smaller than the one on TM/graphene. The number of maximal H\({}_{2}\) adsorption is lower for TM/N-graphene compared to B-doped and pristine graphene. These trends can be explained considering that upon H\({}_{2}\) adsorption, electrons are transferred from metal D orbitals to the antibonding state of H\({}_{2}\) (backdonation). As described in the previous section, the interaction between transition metals and doped surfaces is stronger than the interaction with undoped surfaces. Consequently, when metals are supported on N or B-containing graphene, their back-donation ability is reduced, and then the H\({}_{2}\)-metal binding is weakened. The adsorption and decomposition of formic acid have been studied on transition metal (Pt, Pd, Ru) NPs supported on nitrogen-doped graphene. The interaction with a couple of edged pyridinic nitrogen atoms was the most energetically favorable, and promoted the formic acid decomposition to CO\({}_{2}\) and H\({}_{2}\) (except in the case of Ru). The easy decomposition of formic acid is favored by the proximity of a formed adsorbed hydrogen atom and a hydrogen atom of the carboxyl fragment, which are directed toward each other. This is an ideal configuration for the formation of hydrogen and CO\({}_{2}\) molecules [72]. The position of the D-band is a fundamental parameter to describe the adsorption of molecules on metal surfaces, since it can be correlated with the adsorbate binding energy. However, this is not always true. [PERSON] et al. [73] demonstrated that a direct correlation between the D-band center and the adsorption energy of H\({}_{2}\) and CO is not applicable in the case of Pt nanoparticles supported on nitrogen-doped graphene. Otherwise, in these cases, an affordable correlation has been disclosed between the D-band center and the difference in the averaged adsorption energies between H\({}_{2}\) and CO, \(\Delta\)Ead = Ead(CO) \(-\) Ead(H\({}_{2}\)). Authors also reported the weakened adsorption strength on Pt NPs supported on doped graphene. This difference in adsorption energy was more pronounced for CO adsorption than H\({}_{2}\), and it is a consequence of the strong metal-support interactions.