The effect of SnO2(110) supports on the geometrical and electronic properties of platinum nanoparticles

While Pt-nanoparticles supported on SnO2 exhibit improved durability, a substantial detriment is observed on the Pt-nanoparticles’ activity toward the oxygen reduction reaction. A density functional theory method is used to calculate isolated, SnO2- and graphene-supported Pt-nanoparticles. Work function difference between the Pt-nanoparticles and SnO2 leads to electron donation from the nanoparticles to the support, making the outer-shell atoms of the supported nanoparticles more positively charged compared to unsupported nanoparticles. From an electrostatic point of view, nucleophilic species tend to interact more stably with less negatively charged Pt atoms blocking the active sites for the reaction to occur, which can explain the low activity of Pt-nanoparticles supported on SnO2. Introducing oxygen vacancies and Nb dopants on SnO2 decreases the support work function, which not only reduces the charge transferred from the Pt-nanoparticles to the support but also reverses the direction of the electrons flow making the surface Pt atoms more negatively charged. A similar effect is observed when using graphene, which has a lower work function than Pt. Thus, the blocking of the active sites by nucleophilic species decreases, hence increasing the activity. These results provide a clue to improve the activity by modifying the support work function and by selecting a support material with an appropriate work function to control the charge of the nanoparticle’s surface atoms.

Resistance toward corrosion, low cost, and availability of certain metal oxides increase their suitability for the replacement of carbon-based support materials [23]. Among the many different metal oxides, tin oxide has emerged as one of the promising candidates for PEFC applications. In particular, the use of SnO 2 has resulted in a large improvement in durability when used as support for Pt-nanoparticles [22,24]. However, some mild degradation was observed due to Ostwald ripening, and low electrocatalytic activity was recognized, due to the low electrical conductivity of SnO 2 [23,25]. Theoretical and experimental results showed the preferential growth of SnO 2 films along the [110] in an oxidizing environment [26], such as the conditions at the cathode side of the PEFC. Additionally, STEM images confirmed that the lattice planes of Pt(111) were parallel to those of Nb-doped SnO 2 (110) [6], and nanostructured Sb-doped SnO 2 (110) [27,28]. The support morphology also plays an important role in the activity and stability; crystalline SnO 2 showed improved stability and higher electrochemical surface area of Pt catalyst [29]. Compared with carbon materials, the conductivity of SnO 2 limits its application as an electrode substrate material. To increase the electric conductivity and hence the activity, Pt-nanoparticles were supported on hybrid supports such as SnO 2 /C [30], SnO 2 /N-doped carbon nanotubes [29], Nb-SnO 2 containing graphitized carbon black [6], SnO 2 nanowires grown on carbon fibers [31], etc. Additionally, PtSn bimetallic nanoparticles supported on carbon-based materials promoted the oxidation of methanol [32] and ethanol [33] and exhibited enhanced lifetime [32], which led the PtSn nanoparticles to be selected as a promising catalyst for the ORR. PtSn nanoparticles and nanowires showed an increased performance; however, the decay in the mass activity for the catalysts was considerable [34]. Enhanced electrical conductivity of SnO 2 has been achieved by introducing small percentages of dopant elements [6,22,25,[35][36][37][38][39]. Specially, Nb as dopant for SnO 2 leads to increased electronic conductivity [22,39], increased electrochemical surface area [22,25], increased hydrophilicity [6], increased/decreased the stability compared to carbon black [3,6,22,25] /SnO 2 [22], increased activity toward the ORR, which was attributed to the increase in the electronic conductivity [22,25]. Although Ta-doped [38] and Sb-doped [3] SnO 2 have electrical conductivities 40 times higher than Nb-doped SnO 2 , the ORR activities of Sb-and Ta-doped SnO 2 were not correspondingly higher than Nb-doped SnO 2 . As such, no clear correlation between the conductivity of the support and the ORR activity was reached. Similarly, the effect of various dopants with different concentrations on the ORR activity was investigated and concluded that while doping SnO 2 affects the activity directly, the ambiguity between support conductivity and ORR activity still holds, as the highest activity was not obtained for Pt supported on doped SnO 2 with the highest electrical conductivity [39]. Moreover, high Pt loadings on oxidized SnO 2 , reduced SnO 2 , and graphene all showed comparable ORR. Only in the case of oxidized SnO 2 , decreasing the Pt loading led to lower ORR activity, which was attributed to stronger adsorption of oxygenated species [40]. It was shown that electronic metal-support interactions can affect the charge of the catalytically active outer surface of nanoparticles [41]. This long-range charge transfer scales with the work function difference between the support and the catalyst [41] and is also size-dependent [42]. However, theoretically, the charge transferred between the support and Pt-nanoparticles was quantified [42][43][44][45][46][47]. The effect of the charge transfer based on the work function difference between the SnO 2 supports, and Ptnanoparticles is scarce. One example is the effect of the work function difference of Sb-doped SnO 2 , Sb-doped SO 2-δ , and Pt 55 on the charge transfer [41]. To the best of our knowledge, the size dependence of the charge transfer between Pt-nanoparticles and SnO 2 supports was not carried out, and the activity of the Pt/SnO 2 systems based on the interaction with oxygenated species and its effect on the ORR as a result of the charge transfer has not been discussed.
In this work, the influence of SnO 2 on the physical and electronic properties of Pt-nanoparticles is analyzed after conducting density functional theory (DFT) calculations, showing that the support effect tends to dissipate as the size of the supported nanoparticle increases. However, for nanoparticles up to 2 nm, which is the largest Pt-nanoparticle supported on SnO 2 in this study, the support effect is still quantifiable. Moreover, the nature of the activity of the Pt-nanoparticles of different sizes supported on SnO 2 supports is discussed from an electrostatic point of view generalized by the charge transfer between the Pt-nanoparticles and different supports (reduced SnO 2 , Nb-doped SnO 2 , and graphene) as a result from their work function ( ) difference. As the outer-shell atoms of the Pt-nanoparticles become more positively charged (Pt/SnO 2 systems), nucleophilic species will interact strongly, blocking the active sites for the ORR to occur. On the other hand, Pt-nanoparticles on supports with smaller work function than SnO 2 , such as reduced SnO 2 , Nb-doped SnO 2 , and graphene, will exhibit outer-shell Pt atoms less positively charged or even negatively charged, and an increased availability of active sites as the interaction of nucleophilic species with the less positive outer-shell Pt atoms will become weaker. These results can help to explain experimental observations showing the higher activity of Pt-nanoparticles supported on reduced SnO 2 , Nb-doped SnO 2 , and graphene compared to Pt-nanoparticles supported on SnO 2 . Moreover, in this work, the difference in stability of Pt-nanoparticles supported on SnO 2 against Pt-nanoparticles supported on graphene is explained. These results show the importance of the metal-support electronic interactions to control the activity, and stability of catalysts, and at the same time, provide a clue for the tunability of the electronic structure of metal nanoparticles to improve their activity via their interaction with the support material.

Computational details
All calculations performed in this study are based on the plane wave DFT method implemented in the Vienna Ab initio Simulation Package (VASP 5.3.5) [48][49][50]. Perdew-Burke-Ernzerhof parameterization under the generalized gradient approximation (GGA) was employed as exchange-correlation functional together with the projector augmented wave method [51]. Spin-polarized calculations were performed throughout the study with a plane wave cutoff energy of 400 eV. The convergence criteria for all calculations were set until the difference in total energy between two ionic steps was less than 10 −4 eV/atom, and 10 −5 eV/atom for the self-consistent field cycles. The optimization of the face-centered cubic phase of bulk Pt and the rutile-type structure of SnO 2 was performed with 16 × 16 × 16 and 8 × 8 × 12 Monkhorst-Pack k-point meshes, respectively, for the Brillouin zone integration where all the atoms and the whole crystal volume were relaxed. After optimization, the calculated lattice parameters of bulk Pt (a = 3.966 Å) and SnO 2 (a, b = 4.763 Å, and c = 3.222 Å) were in good agreement with experimentally reported values for bulk Pt (a = 3.916 Å) [52], and SnO 2 (a, b = 4.737 Å, and c = 3.186 Å) [53]. Isolated Pt-nanoparticles (Pt n ) containing 4 (0.26 nm), 13 (0.53 nm), 55 (1.07 nm), 201 (1.70 nm), 405 (2.23 nm), 711 (2.77 nm), 807 (2.92 nm), and 2406 (4.33 nm) atoms were modeled and optimized until reaching the convergence. To avoid interaction between periodic images, the minimum distance between the boundaries of the cell and the Pt atoms was set to 6 Å, i.e., minimum 12 Å between neighbor image Pt-nanoparticles. After optimization, Pt 4 , Pt 13 , and half-spherical clusters of Pt 37 , Pt 119 , and Pt 233 that were truncated from Pt 55 , Pt 201 , and Pt 405 , respectively, were set to interact with their (111) planes parallel to those of SnO 2 (110), as it has been observed experimentally [6]. Twolayered oxygen terminated SnO 2 (110) (a single layer consists of top O, middle SnO, and bottom-O planes) was used as support for Pt 4 , Pt 13 , Pt 37 , Pt 119 , and Pt 233 nanoparticles. For the Pt n /SnO 2 systems, a minimum distance of 7.5 Å was set between the boundaries of the cell and the Pt atoms. Optimization of the isolated Pt n and Pt n /SnO 2 systems was performed at the Γ point in reciprocal space, due to the significant spatial extent of the systems, where all Pt atoms and the atoms of the top layer of SnO 2 were allowed to relax. The models employed in the calculations are shown in Fig. 1. To corroborate the difference in stability of Pt-nanoparticles on SnO 2 and directly compare the effect of graphene as support material, a single Pt atom, Pt 4 , Pt 13 , and Pt 37 nanoparticles supported on graphene were also modeled and optimized with the same conditions as the Pt-nanoparticles on SnO 2 .
Cohesive energies of isolated Pt n , E coh , adsorption energies of Pt n on support, E ads , and formation energies of supported Pt clusters, E form , were defined as: where n is the number of atoms in the nanoparticle, E Pt is the energy of a single Pt atom, E Pt n is the energy of the Pt-nanoparticle (the energies of Pt 37 , Pt 119 , and Pt 233 were obtained by a single point self-consistent field calculation after the corresponding Pt-nanoparticles were optimized and cleaved in the (111) direction), E Support is the energy of the SnO 2 or graphene slabs, and E Pt n ∕Support is the energy of the Pt-nanoparticle interacting with SnO 2 or graphene. From the definition of the cohesive, adsorption, and formation energies, negative values denote a stable Pt-Pt interaction in the unsupported Pt-nanoparticles, a stable interaction between the Pt-nanoparticles and the support, and a stable Pt-Pt interaction in the supported Pt-nanoparticles, respectively. Although a more stable interaction between Pt-nanoparticles and graphene support was reported by including dispersion corrections, a possibility of overestimation of the interaction energy was pointed out [15]. In this study, the stability of Pt-nanoparticles supported on graphene and SnO 2 was approximated without considering van der Waals interactions. Our results and conclusions about the stronger interaction of Pt-nanoparticles with SnO 2 than with graphene support agree with a previous experimental/theoretical study [6].
Reduced and Nb-doped SnO 2 supports were modeled to examine the effect of crystallographic defects such as oxygen vacancies ( V ⋅⋅ O ) and dopants on the SnO 2 work function. These supports contain 5 SnO 2 layers, symmetrically terminated to avoid artificial dipole induced between the top and bottom terminated sides of the slabs, where the atoms of the middle SnO 2 layer were kept fixed. The vacuum slab was kept to 15 Å. Reduced SnO 2 was modeled after removing an O atom from the top and the bottom layers of the stoichiometric SnO 2 slab. Once the most stable position for the V ⋅⋅ O was obtained a new O atom was subtracted from the previously reduced SnO 2 and the most stable position of the new V ⋅⋅ O was obtained. This process was repeated 6 times to obtain SnO 2-δ , where the value of δ depends on the number of V ⋅⋅ O . For the case of Nb-doped SnO 2 , it was shown that Pt/Sn 0.98 Nb 0.02 O 2 exhibits an improved ORR activity than Pt/SnO 2 [22]. Based on the size of the slab, 2% Nb doping corresponds to the symmetric substitution of one Sn atom from the top and bottom layers of stoichiometric SnO 2 . The geometry structures of SnO 2 , SnO 2-δ , and Sn 0.98 Nb 0.02 O 2 slabs are shown in Figure S1.
Work functions were determined as the difference between the plateau value of the electrostatic potential in the vacuum region and the Fermi level of the supports (stoichiometric, reduced, and Nb-doped SnO 2 ). The work function of platinum was reported to be 5.65 eV, which corresponds to the experimental value obtain photoelectrically [54]. Pt atom and Pt 4 were set to interact with the reduced and Nb-doped SnO 2 to estimate the effect of modifying the support work function on the Pt n charge. Because the work function influences the relative alignment of electronic adsorbates states and metallic surface states, substantial implications for the catalytic properties can be expected. The different work function values corresponding to SnO 2 , SnO 2-δ , and Sn 0.98 Nb 0.02 O 2 slabs are summarized in Table 1.

Geometrical features
In this section, the structural aspects of isolated Pt-nanoparticles and their dependence on size are explored. Figure 2a shows the ratio of surface sites in the outershell atoms of the isolated Pt-nanoparticles. All outershell atoms of Pt 4 and Pt 13 are located at the vertices of the nanoparticles. As the size increases, the ratio of atoms at the vertices decreases. Similarly, from Pt 55 to Pt 2406 , the percentage of edge atoms also decreases with increasing the nanoparticle size. The ratio dependency of the {100} sites on nanoparticle size is less clear. The fraction of {100} sites increases in the order Pt 201 < Pt 807 < Pt 405 < Pt 2406 < Pt 711 . Increasing the size of the nanoparticle leads to an increase in the fraction of {111} sites, which become predominant in Pt 201 or larger. Atoms at edges and vertices are of higher energy (i.e., more reactive) as they are chemically unsaturated, with a lower coordination number. The ratio of atoms with coordination numbers of 5, 6, and 7 decreases with increasing size, while the ratio of atoms with a coordination number of 12 increases.
The size dependence of the average interatomic Pt-Pt distance for different nanoparticles is shown in Fig. 2b. The average Pt-Pt distance has been studied as a function of nanoparticle size, approximated by n −1∕3 , and proved to be proportional to the effective radius of the nanoparticle and its surface-to-volume ratio [55][56][57][58]. Here, the interatomic distance increased linearly with increasing the nanoparticle size approaching the bulk Pt value of 2.823 Å, which is in good agreement with our calculated bulk value of 2.805 Å and with the experimentally reported value of 2.775 Å [59]. The overestimation of the predicted value for the interatomic Pt-Pt distance in bulk Pt compared to the experimental value (by 0.048 Å) is typically observed in DFT calculations employing GGA functionals [55], which agrees well with previous theoretical works on scaling the properties of palladium nanoparticles [45,46], copper, gold, and silver nanoparticles [57]. Although the interatomic distance averaged over all atoms scales to the bulk values, the outer-shell atoms do not exhibit a clear tendency.
Another size-dependent property is the cohesive energy of the nanoparticle. The cohesive energy is equal to the energy to divide the metal nanoparticle into isolated atoms [56,60,61]. The cohesive energy shows a linear relation with n −1/3 , gradually approaching the corresponding bulk energy as the nanoparticle size increases, as shown in Figure S2. The extrapolated Pt bulk value of the cohesive energy is − 5.66 eV/atom, in agreement with the calculated value using a bulk model consisting of 4 atoms (− 5.49 eV/ atom), as well as the experimentally reported value of − 5.84 eV/atom [62]. Underestimation of the cohesive energy with respect to the experimental bulk Pt-value is attributed to the GGA functionals because similar behavior has been observed for the cohesive energy of palladium [56] and ruthenium [63] nanoparticles. It should be noted that these values are averaged over all atoms, while different stabilities are expected to be observed for atoms in the outer-shell of each nanoparticle, depending on their degree of coordination. This is because chemically unsaturated atoms with a lower coordination number are more prone to dissolution and bond weakening induced by adsorbates than highly coordinated atoms [2,12,64].

Electronic properties
The electronic structure analysis of the isolated platinum nanoparticles is presented based on the DOS profiles in Fig. 3. This analysis can provide relevant information regarding the catalytic activity because possible changes and other features in the DOS profiles will lead to different reactivity of the nanoparticles. Figure 3a shows the size dependency of the DOS profiles of the entire Pt-nanoparticles. As the Pt-nanoparticles become smaller, a decrease in the confinement dimensions results in the energy levels becoming more discrete. The decrease in the overlapping of energy levels increases the energy separation between adjacent levels. The energy level spacings are large for Pt 4 and Pt 13 , indicating their more molecular-type character.
Increasing the number of atoms in the nanoparticle results in a continuous DOS due to the overlapping of orbitals, as in the cases of Pt 55 or larger. The same behavior has also been previously reported for copper [58], silver [58], gold [58], and Pt-nanoparticles [65]. In addition, as the Pt-nanoparticles become larger, the difference in their DOS profiles became less pronounced, as shown in Fig. 3b. Because   Fig. 3 Electronic properties of isolated Pt-nanoparticles: a partial DOS profiles of the Pt-nanoparticles, b partial DOS difference between contiguous nanoparticles, c partial DOS profiles of the outer-shell atoms of the Pt-nanoparticles the interaction of adsorbates is directly on the outer-shell atoms, the DOS profiles of only the outer-shell atoms are also shown in Fig. 3c. For smaller nanoparticles, the DOS profiles are similar for both the whole nanoparticle and the outer-shell atoms, due to a maximized surface-to-volume ratio. As the size of the Pt-nanoparticles increases, the DOS profile of the outer-shell starts to resemble that of Pt(111), correlating well with the dominance of {111} sites for the larger nanoparticles, as shown in Fig. 2a [66][67][68]. It was proved that the relationships between adsorption energy and d-band center do not account for the effect of less coordinated atoms, such as the ones located at the vertices and edges of nanoparticles, on the adsorption, especially for small cluster particles that do not expose well-defined planes [72][73][74]. Considering the experimental value of − 2.86 eV of Pt 3 Co surfaces, the calculated values of the d-band centers of the outer-shell atoms of the Pt-nanoparticles considered in this study point out to a stronger adsorption of oxygenated species; O 2− , OH − , H 2 O, H 2 O 2 , etc. (i.e., species found at the cathode environment of a PEFC), which will lead to more active sites being blocked than for the Pt 3 Co, and to a lower activity for the ORR. In Figure S3(b), the relationship between the average charge distribution at the outer-shell atoms of the Pt-nanoparticles and their average d-band center is shown. By taking into consideration this "linear" relationship, the charge per atom corresponding to the d-band center of Pt 3 Co (− 2.86 eV) can be extrapolated, i.e., − 0.0529 e/atom. Thus, as the outer-shell atoms become more negatively charged, electrostatic repulsion with oxygenated species (nucleophilic) found at the cathode environment of the PEFC will arise, decreasing their stable adsorption and their coverage, which will lead to an increase in the ORR kinetics. It should be noted that the charge distribution for the Pt 3 Co outer-shell atoms could be even more negative than the estimated value of − 0.0529 e/atom as a result of electron donation from Co atoms in the core region to Pt atoms in the surface because of the work function difference. Nevertheless, this estimated value for the charge per atom and d-band center of − 2.86 eV can be used as a "guide" for Pt-nanoparticles.

Effect of SnO 2 as support material
In this section, the influence of using a SnO 2 (110) support on the geometrical features and electronic properties of Pt-nanoparticles is discussed. Figure 4a shows the frequency distribution of Pt-Pt interatomic distances of isolated Pt-nanoparticles compared to those supported on SnO 2 . SnO 2-supported nanoparticles consisting of 4, 13, and 37 atoms exhibit significant differences in Pt-Pt distance compared to larger nanoparticles (i.e., SnO 2 -supported Pt 119 and Pt 233 ). The average interatomic Pt-Pt distance is plotted against the size of the nanoparticle in Fig. 4b. The interaction between Pt-nanoparticles and SnO 2 leads to an increase in the Pt-Pt distance compared to isolated nanoparticles. As the nanoparticle size increases, this effect decreases, showing that the support effect tends to dissipate with increasing the size of the nanoparticle. The most substantial elongation of the interatomic distance was 0.044 Å for Pt 37 /SnO 2 , which also exhibited the highest amount of atomic rearrangement. Moreover, the variations in the interparticle distance due to the interaction with SnO 2 were analyzed for the outershell atoms of the SnO 2 supported nanoparticles. Figure 4c shows the average interatomic Pt-Pt distances from the top facet to the Pt/SnO 2 interface. The most considerable variations are observed for atoms located at the triple phase boundary (TPB), i.e., the outer-shell atoms situated at the interface between Pt and SnO 2 . As the size of the nanoparticle increases, the average interatomic distance at the interface decreases, except for the case of Pt 4 , ranging from an expanded Pt-Pt distance of 2.800 Å at the Pt 13 / SnO 2 interface to a compressed Pt-Pt distance of 2.725 Å Fig. 4 Effect of SnO 2 on the Pt-Pt distance: a frequency distribution of the Pt-Pt distance of the isolated (gray bars) and supported (dark red bars) Pt-nanoparticles, b size dependence of the Pt-Pt distance of isolated Pt-nanoparticles (gray circles) and supported Pt-nanoparticles (dark red triangles), and c variation in the Pt-Pt distance of the outer-shell atoms of isolated (blue squares) and supported (red diamonds) Pt-nanoparticles at the Pt 233 /SnO 2 interface. Moreover, for the atoms at the top facets, the variations in the interatomic distance become smaller compared to the interface atoms (except for Pt 4 ), especially for the larger nanoparticles. The exception of Pt 4 can be explained by its small size and the lack of a core atom to behave as a bulk-like atom. These results show that the support effect weakens with increasing nanoparticle size and that it is localized at the metal/support interface. Similar behavior has been previously reported for spherical cuboctahedral platinum nanoparticles supported on graphene [15].

Effect of SnO 2 on the nanoparticles' electronic properties
Electron transfer is rationalized in terms of electronic equilibration between the support material and the catalyst nanoparticle. ; with increasing the diameter of the nanoparticle, more Pt atoms will be in contact with the support. These Pt atoms will be the main ones to donate electrons "shielding" the surface atoms located at the top and intermediate layers. It should be noted that even though the outer-shell atoms of the supported nanoparticles became more negatively charged with increasing the size of the nanoparticle, their charge is less negative than the outer-shell atoms of the isolated Pt-nanoparticles, as shown in Fig. 5. Thus, a stronger interaction with nucleophilic species is to be expected, which should result in blocking of the catalyst active sites, retarding the reaction kinetics.
Regarding the nanoparticle size effect, it has been reported that the oxophilicity of metal nanoparticles increases with decreasing size [75][76][77], which results in the formation PtO x [76] that have been known to be prone to dissolution during the electroreduction of O 2 [78]. In this work, the largest supported Pt-nanoparticle, Pt 233 / SnO 2 , has a size of ca. 2.11 nm. From the charge transfer analysis, Pt 233 /SnO 2 is expected to be a suitable adsorbent for oxygenated species, which will block the active sites for the ORR to occur. Our results agree and explain the low activity exhibited by Pt-nanoparticles of ca. 2 nm supported on SnO 2 [40]. Experimentally, the strong interaction of oxygenated species on Pt-nanoparticles with diameters of 2 nm supported on SnO 2 is responsible for the low ORR activity compared to those supported on glassy carbon [40]. The ORR activity increased only after extended Pt regions were formed on oxidized SnO 2 due to the large Pt loadings, where the effect of the support is minimal. Our results show a similar tendency with experimental Fig. 5 Color coding of the charge of Pt atoms, and charge distribution on the outer-shell atoms of isolated (blue squares) and supported (red diamonds) Pt-nanoparticles observations, where SnO 2 as an alternative to carbon will help to stabilize the interaction of oxygenated species on Pt-nanoparticles, blocking the active sites, and lowering ORR activity. Considering the size of the Pt-nanoparticles in this study, as the nanoparticle becomes larger, our results show that the effect of SnO 2 tends to dissipate. This tendency agrees well with previous observations from cyclic voltammograms of Pt-nanoparticles supported on Nb-doped SnO 2 , where decreasing the size of the nanoparticle led to a negative shift in the oxygen desorption peak potential indicating stronger adsorption of oxygenated species [25]. However, in the previous study [25], the Pt-nanoparticles were supported on Nb-doped SnO 2 ; thus, the interplay between the dopant and the particle size effect may have made the oxygenated species less prone to interact with Pt-nanoparticles > 2.6 nm.
Variations in the d-band centers of supported nanoparticles arising from the interaction with SnO 2 are shown in Figure S4. Because the interaction of Pt-nanoparticles with gaseous species and adsorbates will be directly on the outer-shell atoms, only the d-band centers of the outershell atoms were analyzed in this study. Only for the Pt 13 / SnO 2 , all the outer-shell Pt atoms underwent a significant downshift in their d-band centers of ca. 0.305 eV. As the size of the nanoparticle increased, the downshift in the d-band center decreased to 0.056 eV for Pt 37 /SnO 2 . Conversely, an upshift of 0.01 eV was observed for the surface atoms of Pt 119 /SnO 2 . And the outer-shell atoms of Pt 233 / SnO 2 experienced a downshift of 0.007 eV with respect to the outer-shell atoms of the isolated Pt-nanoparticles. The d-band center of the TPB atoms of Pt 13 /SnO 2 was largely downshifted by 0.672 eV. For the Pt 37 /SnO 2 , the TPB atoms' d-band center downshifted 0.098 eV. Contrarily, Pt 119 and Pt 233 experienced an upshift of 0.083 eV. It is interesting to note that the change from a downshift in the d-band center to an upshift is for nanoparticles between 37 and 119 atoms. The atoms at the top facet of the supported nanoparticles (except for the case of Pt 13 /SnO 2 ) exhibited an upshift in their d-band centers, which increases with the nanoparticle size. Additionally, the d-band centers of the layers between the TPB and the top facet became more downshifted. This downshift decreased as the size of the nanoparticle increased. According to the Hammer-Nørskov model [66][67][68], the upshift/downshift of the d-band centers will lead to stronger/weaker adsorption of oxygenated species. This effect tends to decrease with increasing the nanoparticle size on the support. A contradicting correlation is observed between the different values of the electron density distribution and the changes in the d-band centers. From the d-band center results, the large downshift of the outer-shell atoms of Pt 13 (weaker adsorption of gaseous species) is opposite to the results from the charge analysis, where the Pt 13 atoms were positively charge compared to the isolated Pt-nanoparticles. Similarly, the downshift in the d-band center experienced by the surface atoms at the layers between the top and TPB of Pt 37 , Pt 119 , and Pt 233 indicate a weaker adsorption than on the isolated Pt-nanoparticles, which is in contradiction of the results obtained from the charge analysis showing that a stronger adsorption of nucleophilic species is to be expected.

Effect of SnO 2 on nanoparticle stability
Pt-nanoparticles with small diameter supported on carbon have reduced lifetime under the operating conditions of a PEFC. The weak interaction between platinum and carbon leads to nanoparticle aggregation and detachment from the support [11]. On the other hand, Pt-nanoparticles supported on SnO 2 exhibited stronger interaction and thus greater stability, although some degradation due to Ostwald ripening has been observed [22]. In this section, the interaction strength between Pt-nanoparticles and SnO 2 is approximated by the adsorption energy. Additionally, the adsorption energy of Pt-nanoparticles on graphene is calculated and compared to SnO 2 . Figure 6a displays the Pt clusters supported on graphene. The adsorption energies for all the Pt n /SnO 2 systems are more negative; stronger interaction between the Pt n and SnO 2 , than for the Pt n / graphene systems. For both systems, increasing the size of the nanoparticle increased the total interaction with the support, as shown in Fig. 6b. On the other hand, the adsorption energy per atom in the nanoparticle decreases with increasing nanoparticle size, in agreement with a previous theoretical study [15]. The effect of the support material on the Pt-Pt interaction was estimated from their formation energies, as shown in Fig. 6c. The formation energies of all the Pt n /SnO 2 systems are more negative, and hence, they are more stable than the Pt n /graphene systems. These results are relevant because they show a destabilizing effect of graphene in Pt-Pt interaction compared to SnO 2 support. Although a previous DFT work showed the influence of the shape of isolated and carbonsupported Pt-nanoparticles against dissolution [12], the effect of graphene in the Pt-Pt interaction was not taken into consideration. While other effects such as carbon corrosion are also considered in experimental observations showing the faster degradation of Pt/graphene systems, the stronger interaction between the Pt clusters and the SnO 2 support, and the effect of SnO 2 on the Pt-Pt interaction go a long way to explaining the suppressed Pt atom dissolution, nanoparticle aggregation, and detachment. The size dependence of the formation energies shows that with increasing the nanoparticle size, more stable Pt-Pt interaction is to be expected, which is opposite to the adsorption energy per atom trend. Therefore, as the size of the nanoparticle increases, the increased Pt-Pt interaction improves nanoparticle stability. Sixth-generation density derived electrostatic, and chemical (DDEC6) atomic population analysis was conducted to compute the bond orders [79]. Individual bond orders and the sum of bond orders can help provide valuable information regarding stability and activity trends. To single out the effect of SnO 2 on the Pt-Pt interaction of the outer-shell atoms, the bond order values were computed for the isolated Pt 4 and Pt 13 nanoparticles, for the hemispherical Pt clusters, and then compared to the respective outer-shell atoms of the supported nanoparticles. The bond order values for the outershell atoms of the isolated nanoparticles become larger with increasing the size, as shown in Figure S5. Similarly, larger bond orders were observed with increasing the nanoparticle size of the supported Pt-nanoparticles. The bond order values of the outer-shell atoms of Pt 4 , Pt 13 , and Pt 37 supported on SnO 2 were smaller than the values of the outer-shell atoms of isolated Pt-nanoparticles, revealing a detrimental effect of SnO 2 in the Pt-Pt interaction. The detrimental impact dissipates for supported Pt-nanoparticles containing more than 37 atoms, i.e., Pt 119 and Pt 233 . Weakening the Pt-Pt interaction can explain the Pt mass loss due to the dissolution of PtO x as a consequence of the strong adsorption of oxygenated species [75,76].

Effect of the support work function on the charge of Pt-nanoparticles
Pt-nanoparticles supported on reduced SnO 2 [40] and Nb-doped SnO 2 [22] showed improved ORR activity compared to Pt/SnO 2 . This improved activity, in some part, can be explained in terms of perturbation of the electronic structure of the Pt catalyst driven by the new electronic equilibrium between the Pt and the reduced or doped SnO 2 affecting the charge transfer compared to SnO 2 . The formation of V ⋅⋅ O and doping SnO 2 with Nb leads to the formation of electrons, as shown in Eqs. (4) and (5). These electrons will decrease the work function of the support material (Table 1); hence, the charge redistribution on Pt/ SnO 2-δ and Pt/Sn 0.98 Nb 0.02 O 2 will be different from that on Pt/SnO 2 .
The perturbation on the work function values as a result of V ⋅⋅ O and Nb doping led to a decrease in the charge withdrawn from the Pt atom and Pt 4 supported on SnO 2-δ and Pt/Sn 0.98 Nb 0.02 O 2 . As the number of V ⋅⋅ O increased the work function decreased becoming lower than the Pt's work function; thus, electrons were donated to Pt atom and Pt 4 in line with the difference in work function, as shown in Fig. 7a. To corroborate this statement, the effect of graphene support on the charge of Pt 37 was calculated. The calculated value of graphene's work function is 4.46 eV, which is in good agreement with the experimental value of 4.60 eV [80]. The comparison between the charge of the outer-shell atoms of Pt 37 /SnO 2 , Pt 37 /graphene, and the isolated Pt-nanoparticle is shown in Fig. 7b. Upon contact, electrons will flow from the graphene support to the Ptnanoparticle in line with the work function difference between these two materials. Our results indicate that graphene is donating 0.261 electrons to the Pt 37 , which is opposite to the Pt-nanoparticles supported on SnO 2 . The charge transfer to the nanoparticle led that the outer-shell atoms of Pt 37 /graphene to exhibit a charge of − 0.039 e/ atom, which is more negative than the outer-shell atoms of Pt 37 /SnO 2 and the isolated Pt-nanoparticle, 0.007 and − 0.037 e/atom, respectively. Thus, based on electrostatic interactions, nucleophilic species will be more affine to the outer-shell atoms of the nanoparticle supported on SnO 2 Fig. 6 Effect of the support on the stability of Pt-nanoparticles: a models of the calculated Pt n /graphene structures, b adsorption energies and c formation energies of Pt-nanoparticles supported on SnO 2 (red circles) and graphene (brown asterisks) than the surface atoms of Pt 37 /graphene. Our results can be used to explain the higher activity of Pt-nanoparticles supported on reduced SnO 2 and glassy carbon compared to Pt-nanoparticles supported on SnO 2 . As the support work function decreases (effect of V ⋅⋅ O ) below the value of the work function of Pt, electrons, upon contact, will flow from the support (graphene and SnO 2-δ ) to the nanoparticle to reach a new electronic equilibrium. Thus, the electronic donation will make the surface atoms of the nanoparticle more negatively charged, which will tend to decrease the interaction of nucleophilic species. Similarly, the effect of Nb dopant showed to decrease the work function of SnO 2 . However, compared to SnO 2-δ , the influence was not as considerable; hence, there is a possibility that on the Nb-doped SnO 2 may also exist a certain percentage of V  [41]. Additionally, our results can also be used to explain the suppressed charge transfer from Pt-nanoparticles to reduced CeO 2 compared to the stoichiometric CeO 2 [42]. The lower propensity of the partially reduced ceria to accept additional electrons [42] is due to a decreased work function of the reduced support compared to the stoichiometric CeO 2 , and not just to the nucleation of Pt-nanoparticles at the defects of the reduced CeO 2 as it was stated [42]. Thus, the difference between the work function of the Pt-nanoparticles and the reduced CeO 2 support is smaller than when the Ptnanoparticles are supported on the stoichiometric CeO 2 support. Hence, a decrease in the charge withdrawn from the nanoparticles to CeO 2-δ was observed as a result of the new electronic equilibrium between the Pt and the reduced CeO 2 .
Our results match different experimental observations/tendencies; our results show that as the size of the nanoparticle decreases, there is a tendency for the nucleophilic species to interact more stably on Pt-nanoparticles supported. A similar tendency was observed for Pt-nanoparticles supported on carbon [40], glassy carbon [81], and Nb-doped SnO 2 [25]. The low activity of Pt-nanoparticles of ca. 2.0 nm supported on SnO 2 is due to the strong interaction of OH species [40], and that the OH interaction on reduced SnO 2 is weaker than on Pt/SnO 2 [40]. Additionally, our results can explain the fact that nanoparticles supported on reduced SnO 2 and Nb-doped SnO 2 exhibited increased ORR activity, which so far was related to the increased electronic conductivity due to Nb doping than the Pt/SnO 2 systems [22,25]. The experimental observations are summarized in Table S1.

Conclusions
The geometrical features and electronic properties of isolated and SnO 2 supported Pt-nanoparticles of different sizes are analyzed after conducting DFT calculations. Although for isolated Pt-nanoparticles, their electronic properties tend to converge as their size increases, the outer-shell atoms do not show such tendencies. After contact, a new equilibrium is reached between the Pt-nanoparticles and SnO 2 support, where electrons are donated from the nanoparticles to the support making the outershell atoms more oxidized than the isolated nanoparticles. On the other hand, reducing the SnO 2 work function by the presence of Nb dopant and V ⋅⋅ O , charge transfer occurs from the support to the Pt-nanoparticles. A similar effect is observed when Pt 37 is supported on graphene resulting in the outer-shell atoms to be more negatively charged than the isolated nanoparticles. From an electrostatic point of view, the interaction with nucleophilic species is expected to be stronger/weaker on less/more negatively charged Pt atoms, which leads to a change in the activity. It is observed that as the nanoparticle size increases, the support effect tends to mitigate. However, the effect of SnO 2 support is not negligible, even for Pt-nanoparticles of ca. 2.00 nm. Moreover, Pt-nanoparticles supported on SnO 2 are more stable compared to the Pt-nanoparticles supported on graphene, in agreement with experimental results. Nevertheless, the Pt-Pt interaction of the outershell atoms of Pt 4 , Pt 13 , and Pt 37 nanoparticles is weaker compared to isolated nanoparticles, while the interatomic interaction of larger size nanoparticles is slightly stronger, exhibiting a size dependence stability for nanoparticles supported on SnO 2 . This study not only highlights the importance of the metal-support electronic interactions to control the stability and activity of catalysts but also provides a clue for the tunability of the electronic structure of metal nanoparticles to improve their activity via their interaction with the support material. These results have important implications for the use of supports in catalysis, electrocatalysts, sensing devices, etc.