## 2 Theoretical Studies on Heteroatom-Mediated Metal-Support Interactions
### Metal Single-Atom Adsorption on Doped Carbon Surfaces  
Among the several functionalizations, the substitution of carbon atoms with nitrogen or boron has received great attention. In the case of substitutional B doping, a carbon atom is replaced by an atom with one less electron; consequently, sharp and localized states below the Fermi level (i.e., in the valence band) are generated. The electronic structure modifications induced by nitrogen doping are more complex, and they depend on the possible bonding configurations for N in graphitic networks, as detailed below. [PERSON] et al. [57] provided a deep insight into the adsorption of Pt and Ru atoms onto isolated B and N-doped graphene surfaces. C\({}_{18}\), C\({}_{16}\)B\({}_{2}\), and C\({}_{16}\)N\({}_{2}\) were selected as the carbon structural models for the adsorption of metal species respectively on pristine, B-doped and N-doped graphene. In addition, the co-presence of boron and nitrogen (co-doping) with different connections (heteroatom-carbon or heteroatom-heteroatom bonds) was also investigated. According to DFT calculations, the incorporation of boron atoms in the graphene lattice produces a lowering of the Fermi energy (from \(-2.25\) eV to \(-3.43\) eV) and a consequent increase in the work function from 4.31 eV to 5.43 eV. Looking at the projected density of states (PDOS) for the p-orbital (Figure 3), a lower  
Figure 2: Effect of the introduction of a heteroatom on metal nanoparticles and the carbon support. Fermi energy implies an augmented number of states (bonding and antibonding states) close to the Fermi energy and the appearance of more antibonding empty states above the Fermi level, which can help in minimizing the antibonding repulsions during the adsorption of metal species on the surface. In other words, a strong hybridization between the platinum d-orbitals and boron p-orbitals occurs. The essential consequence is the strengthening of the interaction between the B-doped surface and metal atoms. Computed values for binding energy of both Pt and Ru atoms confirmed this hypothesis, since the highest values are associated with the adsorption on boron-modified surfaces. In the presence of nitrogen atoms, the increased Fermi energy (\(-1.27\) eV) and the lower work function (3.37 eV) lead to the presence of fewer antibonding empty states close to the Fermi energy, and thus to a weakening of the interaction between metal and the nitrogen atoms. However, although the hybridization between the nitrogen p-orbital and platinum d-orbital is very weak, the presence of nitrogen atoms can result in an enhancement of the interaction with Pt compared to undoped surfaces. The promotion effect of nitrogen can be ascribed to the activation of the neighboring carbon atoms, whose reciprocal \(\pi\)-\(\pi\) interactions are weakened by the lower electron delocalization induced by the close proximity of nitrogen atoms with large electron affinity [58]. An analogous effect can be envisaged in defective carbon surfaces, where the presence of curvature, vacancies, or edges produces a disruption of the delocalized electronic structure of the graphene surface. Consequently, the actual interaction energy is often the balance between electronic effects deriving from both doping and local geometric strain. As an example,  
Figure 3: Projected density of states (PDOS) of different doped and undoped graphene models. The Fermi energy is adjusted to zero. Reprinted with permission from reference [57]. Copyright 2008 American Chemical Society. comparing the Pt adsorption energy on doped single-walled carbon nanotubes B(N)-SWCNT(6,6) and B(N)-SWCNT(8,0), in the former system, a more moderate enhancement was unveiled compared to the SWCNT(8,0), which was probably due to the reduced curvature in SWCNT(6,6) [59]. In the co-doped surfaces, the effect of nitrogen and boron doping are mixed; therefore, the interaction of Pt and Ru results stronger close to boron atoms and weaker close to nitrogen atoms.