## 2 Theoretical Studies on Heteroatom-Mediated Metal-Support Interactions
### From Single Metal Atoms to Metal Clusters
applied periodic DFT and QUAMBO charge analysis to explore the interactions at the metal-support interface in the case of Pd nanoclusters varied in size and deposited onto carbon nanofibers with different graphitization degrees and O-functionality content. As expected, DFT calculations evidenced a significantly stronger interaction between Pd clusters and the carbon support, increasing the functionalization degree and decreasing the graphitization degree. QUAMBO analysis revealed the occurrence of charge transfer from the metal to the support, independently of particle size, for the metal atoms close to the interface, but these effects rapidly dissipated with distance from the surface. Combining these results with the information deduced from characterization experiments, the authors concluded that the Pd\({}^{\delta+}\) contributions are consistent with a partial charge localized and distributed over the first one to two atomic layers at the palladium-carbon interface, while Pd atoms in the second layer are negatively charged through a compensation effect. Transition metal-based systems are not the unique ones; their strong interactions with the support have been investigated. The confinement of Li\({}_{2}\)S and polysulfides (Li\({}_{2}\)S\({}_{\mathrm{x}}\)) on the conductive carbon host framework is an attractive challenge to be faced for the development of Li-S batteries with superior performance [70]. The Li-S battery is an emerging rechargeable device with high specific energy, whose commercialization is currently limited by some drawbacks, such as the so-called shuttle effect. The latter is related to the loss of active mass, and it can be minimized by controlling the phase evolution of S at the interface and the interactions between the conductive host framework (typically carbon-based materials) and S-containing guests. From this point of view, the introduction of N-containing functional groups in the carbon hosts is expected to improve the interaction and stabilize the S guests. To predict and rationalize the effect of N-doping on the conductive carbon host and in general in the Li-S cell, host-guest interaction has been simulated by performing DFT calculations devoted to describing the interaction between three surfaces (pristine carbon nanotubes, CNT, N\({}_{\mathrm{pyr}}\)-doped CNT, and N\({}_{\mathrm{gr}}\)-doped CNT) and several S-containing guest models (S atom and Li\({}_{2}\)S\({}_{\mathrm{x}}\) (1\(<\) x \(<\)4) clusters with high polarity and positive charged terminal Li atoms). Relaxed geometries and binding energy values revealed a comparable trend with respect to transition metals. Also in this case, S-containing species interacted more strongly with N-CNTs than pure CNT. The most stable configuration for the S-species interacting with N\({}_{\mathrm{pyr}}\) consisted of a direct bond between highly positive charged Li atoms and the electron-rich N\({}_{\mathrm{pyr}}\) center. In the case of N\({}_{\mathrm{gr}}\), S-species are adsorbed on the neighboring carbon atoms, and the nitrogen center acts only as promoter, activating carbon atoms. These promising results demonstrated that N-doping assures the anchoring and the permanent trapping of S-species, and it strengthens the host-guest interactions, thus reducing the loss of active mass. In addition, N atoms can promote electron transfer in the electrocatalytic processes. To generalize and summarize, the role of heteroatoms in mediating metal-support interaction is the result of the interplay of different electronic effects. It includes several contributions:  
1. the match between the electronic structure of the metal and that of the support
2. the number of bonds that are created with the surface atoms (carbon and heteroatoms)
3. breaking of the long-range electronic delocalization
4. local surface deformation, corrugation, and defect introduction
5. electron density redistribution and charge transfer
6. the presence of atoms near the adsorption sites that are available to saturate the eventually dangling bonds.