## 2 Theoretical Studies on Heteroatom-Mediated Metal-Support Interactions  
### Basic Concepts for Understanding Heteroatom Mediated Metal-Support Interactions  
The deposition of metal nanoparticles or clusters onto the surface of carbon support generates an interface accompanied by a local electrostatic potential perturbation. The entity of this perturbation reflects the strength of the interactions between metal and support atoms at the interface, and it is strictly related to the electronic structures of these two actors [51]. The electronic structure of solids is usually described in terms of electronic bands. The nature and width of the electronic bands can be evaluated considering the density of states (DOS), which are defined as the number of allowed electron states per volume at a given energy. Two parameters related to DOS are of paramount importance for understanding metal-support interactions: the Fermi level and the work function. The Fermi level (E\({}_{\text{F}}\)) is an energy state having a 50% probability of being filled, and it coincides with the electrochemical potential of electrons in the solid. The position of the Fermi level with respect to the D-band is an indicator of the D unoccupied density. The work function, \(\Phi\), is the minimum energy that must be furnished to the metal system to extract an electron from the Fermi level, E\({}_{\text{F}}\), and transport it at infinite distance, when the metal surface is electrically neutral. According to the metal-semiconductor boundary-layer theory, when two phases are contacted, the thermodynamic equilibrium is attained. The equilibrium condition requires that the electrochemical potential and then the Fermi energy level of the electrons of the two solids is the same at the interface. The equalization of Fermi levels implies charge transfers across the interface from one material to the other, whose direction can be predicted from the analysis of the electronic structures. In cases where the work function of the electrons of the metal is larger than in the support, electrons will migrate from the support to the metal, until the Fermi level at the interface is equilibrated, and vice versa. This flow of charge sets up a partial positive charge on the support in the proximity of the interface, and an induced negative charge on the surface of the metal. Moreover, in the presence of the charge at the interface, the rehybridization of electron orbitals occurs, leading to changes in the D-band population and in the density of states at the Fermi level. These phenomena are at the basis of the metal-support interactions of the electronic type.  
The introduction of heteroatoms in the support framework causes electron relocalization and local variations in the density of states of the support (LDOS, local density of states), thus producing an increase or decrease of the work function. This modification unavoidably influences the charge transfer,  
Figure 1: Strong metal–support interaction: electronic, geometric, and dispersion effects.  
the hybridization between the electron states of the metal and those of the support, and definitively the metal-support interactions (Figure 2).  
Theoretical simulations are a valuable technique to explore the phenomena occurring at metal-support interface. Binding energy, atomic distances, and relaxed geometries are useful descriptors can be derived from density functional theory (DFT). Molecular dynamics simulations based on a generic force field have been implemented to obtain information on the mobility of adsorbed metal species. Molecular orbital analysis provides a useful indication of the electron density and charge distribution.