Pt nanoparticles under oxidizing conditions – implications of particle size, adsorption sites and oxygen coverage on stability

Platinum nanoparticles are efficient catalysts for different reactions, such as oxidation of carbon and nitrogen monoxides. Adsorption and interaction of oxygen with the nanoparticle surface, taking place under reaction conditions, determine not only the catalytic efficiency but also the stability of the nanoparticles against oxidation. In this study, platinum nanoparticles in oxygen environment are investigated by systematic screening of initial nanoparticle–oxygen configurations and employing density functional theory and a thermodynamics-based approach. The structures formed at low oxygen coverages are described by adsorption of atomic oxygen on the nanoparticles whereas at high coverages oxide-like species are formed. The relative stability of adsorption configurations at different oxygen coverages, including the phase of fully oxidized nanoparticles, is investigated by constructing p–T phase diagrams for the studied systems.


Introduction
Transition metals, such as platinum (Pt), are widely known for their catalytic performance in both oxidizing and reducing reactions and have been widely applied industrially for hydrocarbon oxidation, 1 for abatement of automobile exhaust gases, 2,3 in fuel cells 4 and in catalytic reforming. 5 The use of metallic nanoparticles as catalysts is motivated not only by their large active surface area but also by their special catalytic properties due to their particular size, shape and structure. For catalyst design, control over these latter variables implies the ability to manipulate the catalytic activity by introducing specic facets, edges and corners in the structure of the nanoparticles, which is essential for optimizing the activity and selectivity. 6 Many industrially relevant catalytic reactions, relying on late transition metals as catalysts, oen proceed in oxygen-rich operating conditions or involve oxygen as a reacting species on the surface of a metal catalyst. Acquiring a fundamental understanding of the nature of the interaction between metal surfaces and oxygen is key to explain the role of oxygen in a number of important catalytic chemical processes. 7 Metal-oxygen interactions are manifested in the formation of different metal-oxygen surface states, such as surface-adsorbed atomic oxygen, surface oxide lms, and even bulk metal oxides, for many metallic catalysts. 7 Thereby atomic and molecular oxygen adsorption is regarded as oxygen activation for subsequent oxidation reactions on the catalyst surface and the reactivity of the catalyst is oen represented as a function of the oxygen adsorbate coverage. A modeling study of small nanoparticles of different metals has shown that oxygen activation is enhanced substantially at active sites with low coordination numbers 8 that raises the question about the stability of these sites against oxidation. Dissociation of molecular oxygen on the truncated octahedron platinum nanoparticles with 38, 79 and 116 atoms 9,10 has been investigated using density functional theory (DFT) whereby it has been shown that barrierless oxygen dissociation occurs on the (111) facet accompanied by signicant surface distortion. A preference for the edge bridge sites for atomic oxygen adsorption and an increase of the adsorption energy with atomic oxygen coverage have been found in a DFT study of cuboctahedral nanoparticles with 55, 147 and 309 atoms. 11 Adsorption energy of atomic oxygen enters different scaling relations that, in combination with microkinetic modeling, enable prediction of the rates of various catalytic reactions 12 involving this species.
When oxygen interacts with a metal surface, different oxide lms can be formed depending on the partial pressure, temperature, and orientation of the metal surface. Numerous experimental and DFT studies have characterized oxide formation on different Pt surfaces, [13][14][15][16][17][18] on the Pd(111) [18][19][20] and the Cu(111) surface. 21 Pressure-temperature phase diagrams have been constructed for the extended Cu(111)-O 21 and Pt(111)-O 15 surface systems based on DFT data, as well as for extended Pd surfaces and Pd nanoparticles by using molecular dynamics. 22 In all these studies surface oxide formation has been considered. 15,21,22 CO oxidation on the surface of small Pt nanoparticles is known to accompany oscillatory behavior under realistic conditions and results in a change of the catalytic activity. 23,24 This phenomenon would have consequences for the exhaust gas catalysis. 25,26 Some of the hypotheses to explain this oscillatory behavior suggest cyclic oxidation-reduction 24,27 and reversible surface phase transitions of Pt surfaces. 28 There has been disagreement concerning whether the surface or subsurface Pt oxides are active. 18,[29][30][31][32] For example, Boubnov et al. 23 have found that low-coordinated surface Pt sites on small Pt nanoparticles (nm) are oxidized at temperatures higher than 135 C and become inactive for the CO oxidation.
A comprehensive ab initio study of adsorption of atomic oxygen will be therefore very useful to scrutinize these hypotheses by giving more insight and understanding of the oxygennanoparticle interactions. The produced data will enable the construction of phase diagrams of relevant Pt nanoparticles in oxygen environment to nd the most stable oxygen adsorption congurations under experimental conditions and the limits of stability against formation of Pt oxide nanoparticles. To this end, we employ DFT to study atomic oxygen adsorption on four different Pt nanoparticles addressing all possible adsorption sites. To investigate the effect of oxygen coverage on the nanoparticles, aer screening congurations with different occupied adsorption sites for different numbers of adsorbed oxygen atoms, we compute the oxygen adsorption energy. We determine how the adsorption energy depends on nanoparticle size, type and coordination number of the occupied adsorption sites and oxygen coverage. Using an approximation of the free energy based on the adsorption energies computed by DFT, 33,34 we construct the p-T phase diagrams for all four nanoparticles. The phase diagrams allow us to examine the most stable adsorption congurations with varying the pressure and temperature and to nd the conditions for which the metallic nanoparticles are not oxidized. In addition, structural reorganization of surface Pt atoms under increasing oxygen coverage will be detected and discussed.

Methods
The computations and data analyses in this work have been performed using FireWorks 35 and the Atomic Simulation Environment (ASE). 36

Structural models and DFT calculations
All DFT calculations have been performed using the Vienna ab initio simulation package (VASP) code 37,38 with spin polarization. The core electrons have been described by using projector augmented wave (PAW) potentials. 39 The wave functions (orbitals) of the valence electrons have been expanded using plane waves with an energy cutoff of 450 eV. The Perdew-Burke-Ernzerhof (PBE) 40 generalized gradient approximation has been used to describe the exchange-correlation functional. The latter has been widely used for metallic systems 21,41,42 including platinum nanoparticles. We expect that all adsorption energies will become somewhat higher when using the RPBE 43 or PBE-vdW. 44 However, the focus of this study is on the relative stability of the adsorbed species rather than on providing high-accuracy reference data or accuracy assessment of different charge density functionals.
The initial nanoparticle structures have been constructed from bulk fcc Pt with the experimental lattice constant of 3.92Å corresponding to a nearest-neighbor distance of 2.77Å. To be able to use the plane-wave VASP code for non-periodic Pt nanoparticles, the latter have been modelled in cubic cells with three-dimensional periodic boundary conditions. To ensure that the interactions between neighboring periodic images are negligible, a vacuum region along each of the three directions has been added so that the distance between two nearest surface atoms in neighboring images is at least 16Å. The rst Brillouin zone has been sampled by the gamma point only. Unconstrained geometry optimizations have been performed using the conjugate gradient algorithm until the maximum force on any atom was below 0.01 eVÅ À1 and the electronic relaxation has been converged within 10 À6 eV. The rst-order Methfessel-Paxton smearing method 45 with smearing width of 0.2 eV has been used.
For the adsorption energies discussed in Sections 3.1 and 3.2, the O 2 energy has been calculated with the same DFT parameters outlined above. The O 2 energy used in the freeenergy diagrams in Section 3.3 has been corrected to compensate for the strongly overestimated O 2 binding energy using a GGA density functional that has been reported e.g. in ref. 21 and in the references therein. First, the O 2 dissociation energy has been calculated using the "hard" PAW pseudopotential with a kinetic energy cutoff of 900 eV and a Gaussian smearing parameter of 0.005 eV. Then, the zero-point energy (787.380 cm À1 ) 46 has been subtracted from the experimental dissociation energy (493.687 kJ mol À1 ). 47 Finally, the correction is found as the difference of the DFT-calculated O 2 dissociation energy and the experimental O 2 dissociation energy. The correction to the O 2 energy obtained is 0.460 eV per atom that is in good agreement with the difference of 0.48 eV per atom reported in a similar DFT study. 21 The Pt slabs, used in Section 3.1 to model the (111) and (100) extended surfaces on fcc Pt, have been constructed from bulk fcc Pt with a lattice constant of 3.92Å by including three Pt layers in all space directions, i.e. using a 3 Â 3 supercell. In the z direction, that is perpendicular to the slab surface, a vacuum layer of 12Å has been included to both the top and the bottom slab surfaces. The adsorbed oxygen atoms have been added to the top layer in z direction. The positions of the atoms in the bottom layer in z direction have been kept xed during relaxation performed using a Monkhorst-Pack k-point grid with (5, 5, 1) divisions. A similar slab model has been used elsewhere. [48][49][50] Different PtO 2 nanoparticles have been constructed from the most stable b-PtO 2 bulk structure (orthorhombic, space group Pnnm) 51 following this procedure: (1) repeat the atoms in the primitive cell along all cell vectors; (2) remove Pt and O atoms that are the most distant from the structure centroid and have the lowest coordination numbers so that the number of dangling bonds is minimized and the stoichiometry of PtO 2 is maintained; (3) repeat step (2) until the target size is reached. By varying the parameters of the algorithm several different nanoparticles for each size have been obtained. The structures of these nanoparticles have been fully relaxed using Gaussian smearing of 0.05 eV until the difference between the energies of two subsequent ionic relaxation steps was less than 10 À4 eV per Pt atom and the largest norm of the forces acting on the nuclei aer the last ionic relaxation step was 0.05 eVÅ À1 . For each nanoparticle size the structure with the lowest total energy has been selected and its total energy has been used in the phase diagrams in Section 3.3. It is noted that we have not performed global optimization but a local relaxation of several different nanoparticles of the same size. The relaxed structures of the lowest-energy PtO 2 nanoparticles are available in the ESI. † The generalized coordination number 52,53 has been used to describe the various individual adsorption sites on the Pt nanoparticle surface. The generalized coordination number CN of a surface site with m unique nearest neighbors is dened as: where CN j is the coordination number of nearest neighbor j and CN max is the number of nearest neighbors as if the site atoms would be in the bulk structure. The conventional coordination number of a surface site CN is dened as the total number of unique nearest neighbors of all atoms of the site. For example, for fcc metals, the CN max is 12 for ontop sites, 18 for bridge sites, 22 for fcc and hcp sites and 26 for four-fold hollow (trough) sites. A Pt atom is considered a nearest neighbor of another Pt atom if the distance between the two atoms is less that 3.4Å.

Calculating the adsorption energy and adsorption free energy
The adsorption energy of a single adsorbed oxygen atom on a Pt n nanoparticle is dened as: where E O 2 is the energy of an O 2 molecule. The adsorption energy (per oxygen atom) for N O oxygen atoms adsorbed on a nanoparticleĒ ads is dened as where E tot (Q) and E tot (Q ¼ 0) are the total energies of the oxygen covered nanoparticle and the bare nanoparticle, respectively, and N O is the number of adsorbed oxygen atoms. The oxygen coverage Q of the nanoparticle surface is dened in monolayers (ML) so that 1 ML is realized when the number of adsorbed oxygen atoms is equal to the number of surface Pt atoms. According to eqn (2) and (3), a lower (or more negative) adsorption energy means a stronger binding of the adsorbates to the nanoparticle whereas a higher (or more positive) adsorption energy means a weaker binding.
When metal surfaces are exposed to oxygen, various structures can be formed depending on the partial pressure of oxygen and on the temperature, such as surface adsorbed oxygen, surface oxide lms or bulk metal oxides. 21,54,55 Ab initio atomistic thermodynamics approach is applied to determine the effect of temperature (T) and pressure (p) on various surfaceadsorbate structures under realistic experimental conditions. 21,54,55 Using this approach, the most stable surface structure is determined at given temperature and oxygen partial pressure in the surrounding gas phase that enables the construction of a p-T phase diagram containing the stable regions of different phases. 21 In this approach, the Gibbs free energy of adsorption DG ads (Q, T, p) is dened in the equation: where G(Q, T, p) and G(Q ¼ 0, T, p) are the Gibbs free energies of the nanoparticle-oxygen complex at coverage Q and of the bare nanoparticle, respectively, and m O (T, p) is the chemical potential of gas-phase oxygen. The pressure dependence of the free energies G(Q, T, p) and G(Q ¼ 0, T, p) can be neglected because the nanoparticle-oxygen complex and nanoparticle are much less compressible than the gas phase. In addition, the temperature dependence can be neglected by assuming that the oxygen overlayer and the bare nanoparticle are equally affected by the temperature and these temperature dependent terms will cancel each other in the calculation. 21,55 Furthermore, the vibrational contributions to the free energies of the non-gas species usually nearly cancel in the total of the rst two terms on the right-hand side of eqn (4). 21 Therefore, the Gibbs free energies of the complex and of the bare nanoparticle can be approximated by the energies that can be readily computed using DFT. With these approximations, eqn (4) can be rewritten as The chemical potential of gas-phase oxygen m O (T, p) can be expressed as a function of temperature and pressure using the formula 21,54,55 where p 0 is the standard pressure (1 bar), p is the partial pressure of oxygen and k B is the Boltzmann constant.  Fig. 1) with sizes in the 1-2 nm range.

Adsorption of single oxygen atoms
First, we consider single oxygen atoms adsorbed on the nanoparticles at all possible adsorption sites. This information allows us to determine the most preferred sites in the limit of low coverage and is needed for the screening in Section 3.2 to select lowest-energy congurations for adsorption at higher coverage. The adsorption energies calculated using eqn (2) are summarized in Tables 1, 2, 3 and 4. Additionally, we have visualized the same data in Fig. 2. Because of the very complex behavior of the adsorption energy with variation of system size, facet/surface, site type and site location, we present the data also statistically in Fig. 2 and in Table 5. By computing the correlation coefficients (r 2 ), we test how good different linear regression models for the adsorption energy as a function of site coordination numbers t the available data. We choose a linear regression model assuming that the dependence of the adsorption energy on the coordination numbers is linear. This approach is well established for small adsorbate species, including atomic oxygen, on Pt nanoparticles. 52,53 A small r 2 means that the a linear model does not well t the data whereas a large r 2 implies (statistically) a good linear relationship.

Effects of the nanoparticle size and the adsorption site type
The variation of the adsorption energy with system size is shown in Fig. 2A. The ontop site adsorption energy is the highest compared to other sites that is also found for ontop adsorption on the extended (111) and (100) surfaces. On average, the adsorption energy increases with nanoparticle size and, with the exception of the Pt 116 nanoparticle, approaches the adsorption energy at ontop sites on the extended surfaces. The correlation coefficient for a linear regression model is only 0.12 (see Table 5). Adsorption of O atoms at corner ontop sites is stable for all nanoparticle sizes and the adsorption energy is increasing monotonously. In contrast, ontop adsorption on the (111) terrace is stable with increasing energy on the smaller Pt 38 and Pt 79 nanoparticles while unstable on the large Pt 116 and Pt 201 nanoparticles. The latter is very similar to the ontop terrace adsorption on the extended (111) surface with the same CN ¼ 9 and CN ¼ 7.5. Similarly to (111) terrace ontop adsorption, the adsorption energy at (100) terrace ontop site is increasing for Pt 116 and Pt 201 but is always lower than on the extended (100) surface. For all nanoparticles, the adsorption at bridge sites on the (111) terrace is unstable with no exception. During a structural relaxation starting with an oxygen atom at such bridge sites, the oxygen atom migrates to a nearby three-fold hollow site (fcc or hcp). The same behavior is found for the bridge adsorption on the extended (111) surface. In contrast, bridge site adsorption at any locations other than the (111) terrace is the most stable on Pt 79 , Pt 116 and Pt 201 . Bridge adsorption at edge sites is found particularly stable that agrees with the ndings in previous DFT studies of oxygen on truncated octahedron nanoparticles. 7,9,10,60 A similar site preference has been found for cuboctahedron nanoparticles. 11 Only on the smallest Pt 38 , the adsorption at three-fold hollow sites is the most stable that is again in agreement with previous DFT studies. 7,9 On average, the adsorption energy at bridge sites changes with nanoparticle size only slightly with no pronounced direction of change, that is described by the very low correlation coefficient of only 0.06. A similar behavior is found for the adsorption energy at four-fold hollow (trough) sites on the (100) facet. A linear regression analysis reveals a very slight increase of E ads with nanoparticle size with a correlation coefficient of 0.22. In contrast, at fcc and hcp sites, E ads strongly increases on average with nanoparticle size with correlation coefficients 0.72 and 0.60, respectively.
Adsorption energies on three-fold hollow sites (fcc and hcp) also exhibit large variations with the site locations. Adsorption on sites at corner locations is always more stable than at terrace and edge locations (see Tables 2, 3 and 4), while no regular preference between terrace and edge locations can be found. The energy differences are relatively small but, due to the large number of sites, the overall effect on the adsorption energy at high oxygen coverage can be very large. On the Pt 38 nanoparticle, the hcp adsorption mode is the most stable followed by the fcc adsorption mode. The three-fold hollow site adsorption becomes less stable than the bridge site adsorption on Pt 79 , Pt 116 and Pt 201 , and than the trough site adsorption on Pt 116 and Pt 201 . On average, the adsorption energy at fcc and hcp sites strictly increases with nanoparticle size. The E ads increase is weaker at fcc sites and stronger at hcp sites, as shown in Fig. 2A. This is in contrast to E ads variation at bridge, ontop and trough sites where only a slight change with almost no trend can be found. Considering the comparable number of hollow sites and bridge sites at edge locations, we expect that the bridge and trough sites will more likely contribute to the most stable congurations at high oxygen coverage than the three-fold hollow sites.
Adsorption at trough sites has a peculiarity that we briey discuss here. In the smaller Pt 38 and Pt 79 nanoparticles, where the single trough site is located in the middle of the 100 facet, the distance from the adsorbed oxygen atom to all four Pt atoms of the site is the same, 2.235Å and 2.239Å, respectively. In the larger Pt 116 and Pt 201 nanoparticles, the four trough sites are located at the corners of the 100 facet. On these two nanoparticles the distances from the adsorbed oxygen atom to the site atoms are different, e.g. Pt 116 the distances are 1.997Å to the corner atom, 2.970Å to the terrace atom, and 2.136Å to the edge atoms. Very similar, on the Pt 201 nanoparticle the distances are 2.017Å to the corner atom, 2.917Å to the terrace atom, and 2.144Å to the edge atoms. Therefore, the average adsorption bond lengths on Pt 116 and Pt 201 for trough sites are by about 0.1Å shorter than on the extended surface and on Pt 38 and Pt 79 , as it is shown in Fig. 2C.

Effect of the local environment
While, on average, the adsorption energy of single oxygen atoms increases with nanoparticle size, the variation for the same site type with nanoparticle size is more noticeable. In the previous subsection, it has been shown that adsorption energies on sites at different locations can strongly vary. This is because the number of nearest neighbors of the site atoms (CN), as well as the average coordination number of the nearest neighbors of the site atoms, i.e. the generalized coordination number CN, 52 depend on the specic location of the site of a given type. Therefore, in Fig. 2B, we consider here CN as a structural descriptor and investigate its relation to the computed adsorption energy. The same relationship has been studied for oxygen and other adsorbate species on Pt 201 nanoparticles and extended Pt surfaces. 52 Plotting the generalized coordination number against the adsorption energies yields a very good linear relation suggesting a decrease of binding energy of the oxygen adsorbate to the adsorption site, i.e. increase of adsorption energy, with the generalized coordination number for all different site types. A particularly high correlation coefficient 0.94 is obtained for the ontop site adsorption. The same correlation coefficient has been found for OH adsorption on different Pt nanoparticles. 52 Using the conventional coordination number CN results in signicantly lower correlation coefficient of 0.80 that is similar to the nding in ref. 52. In Table 5, the correlation coefficients found for the linear models with nanoparticle size, CN and CN as descriptors are summarized. While the correlation of E ads with nanoparticle size is very weak, it is much stronger with CN, particularly when the data is grouped according to site types. When all data is included in the linear t, the CN descriptor exhibits a poor correlation with correlation coefficient r 2 ¼ 0.06. A better correlation is obtained with CN for all sites except for the bridge sites where the correlation is of the same quality as with CN. When all data is included in the t, the correlation coefficient is 0.39, i.e. CN is a more reliable descriptor for oxygen adsorption than CN. The thus dened linear regression model predicts lower adsorption energy for lower CN. However, the uncertainty in E ads prediction by using CN alone is very large without using the site type as a second descriptor. As shown in Fig. 2B this uncertainty can be as large as 1 eV for CN in the range from 4 up to 7.5. In particular, adsorption energies at ontop sites are much higher than those at other site types with   Fig. 2C shows that the adsorption energy does not correlate with the average Pt-O bond length as it has been found previously for O adsorption on Pt 201 . 60 In contrast, the bond length correlates well with site type with very small variations owing to nanoparticle size effects and site locations. As shown in Fig. 2C, the average bond length can be used to determine ontop, bridge and hollow site types with high certainty.

Lowest-energy congurations with multiple oxygen adsorbates
In order to construct thermodynamic phase diagrams using eqn (5), it is important to nd the most stable congurations with multiple adsorbed O atoms that are characterized by the lowest total adsorption energies per atomĒ ads . Due to the extremely large number of possible congurations this is a nontrivial task. As a rst approximation, we consider congurations that include the maximum number of adsorbates of every site type.
For the maximum number of sites of a given type, see Tables 1,  2, 3  This is why there should be additional systematic screening of the congurations in order to reduce the number of candidate structures that would be feasible for DFT. Using the adsorption energies of single adsorbates from the previous section we construct an energy score: where s runs over all site types included in the particular conguration, N s is the number of sites of type s and E ads,s is the single oxygen adsorption energy at site s. To assess this screening criterion we have computed theĒ ads for all 31 generated congurations on Pt 38 , as well as four additional congurations with partially occupied sites of a given type and location, and plotted E score againstĒ ads for each conguration (see Fig. 3A). We nd that some of the congurations with lowest E score also have lowestĒ ads . Some congurations have much higher adsorption energies than suggested by the score and also three congurations with relatively high E score have very low adsorption energies. This can be explained with collective electronic effects and lateral repulsion between closely adsorbed oxygen atoms. The latter effect should decay with powers of the inverse distance between oxygen atoms. Indeed, the difference betweenĒ ads and E score is in a good correlation with the mean of the third power of the inverse distance h1/r 3 i, as seen in Fig. 3B. The quantity h1/r 3 i is dened as h1/r 3 i ¼ P i<j (1/r ij )/N pairs with N pairs the number of pairs of oxygen atoms (i, j). The good correlation suggests that the total adsorption energy is lower for larger distances between the adsorbed oxygen atoms. Thus, the quantity can be used as an additional criterion for selecting candidate congurations.
Thus, aer having performed calculations of all 35 congurations for Pt 38 , we calculated the adsorption energies of the rst 50, 20 and 11 congurations for Pt 79 , Pt 116 and Pt 201 , respectively, satisfying both criteria according to eqn (7) and (8). Additionally, for the larger nanoparticles, we added further adsorption congurations in that some site types are partially occupied and such that are not on the selection list but might be important considering their low adsorption energy of single O atoms. For example, the conguration on Pt 201 with all 24 bridge sites (#7 in Fig. 1, CN ¼ 9, CN ¼ 4.44) occupied by O atoms is only at positions 24 and 27 in the sorted criteria according to eqn (7) and (8), respectively. However, this is the second most stable adsorption mode for single O atoms on Pt 201 (see Table 4). Aer extending the list, we have computed the adsorption energy for 64, 35 and 36 congurations on Pt 79 , Pt 116 and Pt 201 , respectively. A full list of the considered congurations is provided in the ESI. † For every nanoparticle size, we have grouped the congurations with equal number of O atoms, i.e. according to the oxygen coverage in monolayers (ML). From every group we have Fig. 3 Relation between the score energy E score and the adsorption energyĒ ads (A) and betweenĒ ads À E score and h1/r 3 ij i (B) for the Pt 38 nanoparticle. (C) Change of the lowest adsorption energyĒ ads and the lowest energy score E score with oxygen coverage. The lowest coverage shown corresponds to single-oxygen adsorption for every nanoparticle. The symbols denote the data points and the lines are only added as a guide to the eye. selected the conguration with the lowest total adsorption energy. The relevant data is summarized in Table 6. Fig. 3C compares the adsorption energyĒ ads with the energy score E score for increasing oxygen coverage Q. Overall, the adsorption energyĒ ads increases with oxygen coverage. Particularly, the adsorption energy of all congurations with Q > 0.5 ML is higher than À1.3 eV per O atom. For single-atom adsorption, the adsorption energies vary between around À1.7 and À1.5 eV while at maximum coverage these vary from about À1.3 and À0.8 eV. A very similar increase of the adsorption energy with the coverage has been found in a DFT study of oxygen adsorption on cuboctahedral Pt 55 , Pt 147 , and Pt 309 nanoparticles 11 although the changes found here exhibit much stronger oscillations. In the same work, 11 a quantity that is equivalent to E score has been found to behave very similar on average, apart from the oscillations with increasing the coverage that are found here for O adsorption on truncated octahedral nanoparticles. Furthermore, the increasing difference between E score andĒ ads is in agreement with that found in ref. 11 and suggests that E score provides (statistically) good estimates of the adsorption energy for low and moderate oxygen coverage.
Furthermore, in Fig. 3C we compare the adsorption energy to the energy score E score that does not include effects such as electronic band effects due to bonding multiple oxygen atoms and the interactions between adsorbate atoms. At the lowest coverage, E score coincides withĒ ads . Then, in the low coverage range (Q < 0.5 ML), E score shows strong oscillations similar tō E ads and is relatively close toĒ ads . In the high coverage range (Q Table 6 Summary of the lowest-energy configurations with oxygen coverage Q < 1 ML including the nanoparticle size (N Pt ), number of adsorbed oxygen atoms (N O ), coverage (Q), the total number of considered configurations (N c ), adsorption energy per O atom (Ē ads in eV), the averaged Pt-Pt and Pt-O nearest-neighbor distances hr Pt-Pt i s (surface Pt atoms), hr Pt-Pt i (all Pt atoms) and hr Pt-O i, respectively, inÅ, the averaged Pt-Pt and Pt-O coordination numbers hCN Pt-Pt i and hCN Pt-O i, respectively, and the site occupation number N s and site index # according to Fig. 1 > 0.5 ML), E score is substantially lower thanĒ ads . The higher adsorption energy can be explained with the effects of the large number of adsorbed atoms that are close to each other at high coverage. The energy score E score does not include the latter effects and, therefore, does not change on average with the coverage, apart from the strong oscillations due to strongly different energies of the site types involved in the congurations. The increasing adsorption energy implies that congurations at high coverage will be stable only at sufficiently high oxygen chemical potential according to eqn (5). Aer having introduced two screening criteria for the initially generated adsorbate congurations, one can naturally ask how successful the suggested selection criteria are by comparing the obtained lowest energy congurations. On average, in the cases of Pt 79 and Pt 116 the distance criterion is more successful for selecting low-coverage congurations, while the energy score criterion is more successful for selecting highcoverage congurations (see Table 6, last two columns). In the case Pt 201 this also seems to be the case, though there are not many selected congurations in order to better support this nding. Overall, the distance criterion is more successful in selecting lowest-energy congurations on Pt 79 than on Pt 116 . Five out of eleven lowest-energy congurations on Pt 79 would have been missed if only the more simple energy score were used for screening. The Pt 79 structures at 0.13 ML and 0.27 ML coverage and Pt 201 structures at 0.39 ML and 0.72 ML coverage have been additionally considered due to their partial occupation, i.e. non-maximum possible N s .

Phase diagrams
As introduced above, the Pt nanocatalyst has applications in the context of the CO oxidation reaction, whereby the operation temperature can vary up to 800 K. An important question is whether the whole nanoparticles or their surfaces get oxidized to PtO 2 at high temperature, particularly at 600 K. 18 Furthermore, most of the studies of CO oxidation have been carried out either in ultra high vacuum (UHV) at pressure 10 À13 bar or at pressures around the standard pressure (1 bar). 23,61 Therefore, we vary both the pressure in a very large range enclosing the UHV pressures, as well as the standard pressure and consider different temperatures in the range from 100 K to 1800 K.
For every nanoparticle and oxygen coverage, we select the conguration with the lowest energy. Then using eqn (5) we compute the free energy as a function of the temperature and the O 2 partial pressure. In Fig. 4, we show the computed adsorption free energy at Q < 1 ML for the Pt 38 nanoparticle as a function of the pressure at T ¼ 600 K and as a function of the temperature at standard pressure (1 bar). Additionally, we have shown the free energy of the fully oxidized Pt 38 O 76 nanoparticle that was calculated using eqn (3) by replacing the total energy E tot (Q) of the nanoparticle-adsorbate complex with the total energy of the Pt 38 O 76 nanoparticle and setting N O ¼ 76.
Here, we explain the reason to consider PtO 2 nanoparticles as reference instead of the bulk PtO 2 phase. Comparing oxygen adsorption energies on extended surfaces to bulk PtO 2 energies is possible due to the innite reservoir of bulk Pt atoms below the surface. Beyond a critical oxygen chemical potential, an innitely large number of bulk Pt atoms would be oxidized to form bulk PtO 2 that would give rise to a vertical line in Fig. 4 (a detailed discussion can be found in ref. 62). In contrast, in the case of Pt nanoparticles, the reservoir of bulk Pt atoms in every nanoparticle is nite that is manifested by a non-vertical line in Fig. 4 for the fully oxidized phase. The number of surface atoms will increase proportionally with increasing the number of bulk atoms via the number of nanoparticles. Particularly, the Pt and PtO 2 nanoparticles are less stable than the corresponding bulk phases due to their large surface energy. Though this effect is known, we illustrate it in the ESI † based on the available data and show that all nanoparticles become more stable with increasing their size. On the other hand, under experimental conditions, no extended platinum oxide bulk phase but partially and fully oxidized Pt nanoparticles have been observed. 23,27,58 Consequently, we use the nanoparticle free energies and not those of the bulk phase in the thermodynamic stability analysis.  pressures p ( 10 À25 bar, the adsorbate-free Pt 38 nanoparticle is the most stable phase and at pressures p T 10 À4 bar the oxide nanoparticles become the most stable phase. Under UHV conditions, the phase with 0.5 ML coverage is found stable. Similarly, at standard pressure, for T ( 780 K and T T 1760 K, the Pt 38 O 76 nanoparticle and the bare Pt 38 nanoparticle, respectively, are the most stable phases. We note that other processes might take place in this high temperature range that are not considered in this study: (i) decomposition of PtO 2 to PtO and O 2 ; (ii) evaporation of the PtO 2 nanoparticles to PtO 2 gas. [63][64][65] However, temperatures beyond 800 K are too high compared to the typical operational temperature range of Pt nanocatalysts and we are aiming to explain and predict Pt nanoparticle stability against oxidation within the experimental temperature range relevant for catalytic applications. In addition, the region on the phase diagram including the PtO and gaseous PtO 2 phases would be only in a narrow range of pressures. 64 The computed p-T phase diagrams, shown in Fig. 5, include only the most stable phases. At standard pressure, the Pt 79 nanoparticle is fully oxidized for temperatures above 800 K. The critical pressure for full oxidation of Pt 79 at T ¼ 600 K is p $ 10 À4 bar. At standard pressure, the conguration at oxygen coverage of 0.9 ML is stable from $800 K up to $1150 K and under UHV conditions the same conguration is stable between 380 and 560 K. Between 560 and 770 K the conguration at coverage 0.4 ML is stable, followed by the conguration with one adsorbed oxygen atom at the (111)-(100) edge bridge site that is stable only up to 800 K aer that the bare Pt 79 nanoparticle becomes more stable.

Adsorption at low and moderate oxygen coverage
On Pt 116 the critical temperature of oxidation at standard pressure is $790 K which is very similar to the one found for Pt 38 and Pt 79 . Again, the maximum pressure at 600 K for a stable metallic Pt 116 oxygen-covered nanoparticle is $10 À4 bar. In UHV the critical temperature is 380 K. The congurations with coverage of 0.92 ML is stable up to $700 K. The conguration with 0.15 ML coverage is stable between 700 and 800 K followed by the single-adsorbate complex up to 870 K. Adsorption at edge bridge sites dominates in all most stable congurations on Pt 116 , in contrast to Pt 38 where only contributions of hcp adsorption modes, and to Pt 79 where hcp, fcc and trough adsorption modes occur in the phase diagram.
On Pt 201 , the critical temperature of total oxidation at standard pressure is $820 K that is higher than any of the smaller nanoparticles. The maximal pressure for a non-oxidized Pt 201 at 600 K is again $10 À4 bar as has been found for all smaller nanoparticles. Four of the seven lowest-energy congurations occur in the phase diagram. Under UHV conditions, the conguration at coverage of 0.98 ML becomes stable for T T 390 K. This conguration is stable for temperatures up to $512 K. At higher temperature, the conguration with coverage of 0.79 ML is formed and replaced only at $660 K by the conguration with Q ¼ 0.39 ML, followed by the complex with a single adsorbed oxygen atom (0.01 ML) occurring at 723 K that is stable up to 822 K. Notably, the two congurations at highest coverage of 0.79 and 0.98 ML combine (111)-(100) edge bridge and fcc adsorption modes while the conguration at moderate coverage of 0.39 ML combines corner fcc and trough adsorption modes.

Adsorption at high oxygen coverage
In the previous section, we have shown only data for coverage Q # 1 ML. Some of the selected congurations have oxygen coverage larger than 1 ML, i.e. the number of adsorbed oxygen atoms is larger than the number of surface atoms. The mean distance between the oxygen atoms is very small, however, some of these congurations are stabilized aer a signicant reorganization of the surface atoms and the adsorbed oxygen atoms during the structural relaxation. As we will show below, this reorganization does not only avoid the close initial distances between the adsorbed oxygen atoms but also leads to formation of an oxide layer on the surfaces of the nanoparticles.
In order to better quantify the degree of reorganization and oxidation of the nanoparticles with increasing the oxygen coverage, we investigated the lowest-energy structures, shown in Fig. S2 in the ESI, in more detail. † The full information about the reorganization towards nanoparticle oxidation is contained in the radial distribution function for the Pt atoms (Pt-Pt pair correlation function) and for the Pt and O atoms (Pt-O pair correlation function). In the following, we restrict the analysis to the averaged nearest-neighbor distance between Pt atoms hr Pt-Pt i and between Pt and O atoms hr Pt-O i, that is the most relevant quantity describing this effect. Additionally, we will use the averaged Pt-Pt and Pt-O coordination numbers hCN Pt-Pt i and hCN Pt-O i, respectively, that indicate the average number of Pt and O nearest neighbors, respectively, of a central Pt atom. The nearest-neighbor distance and coordination number correspond respectively to the position and the integral of the rst peak of the radial distribution function. These quantities are shown in Tables 6 and 7 for all lowest-energy adsorption congurations. For the sake of readability, we will omit the word "averaged" in the following.
First, we will consider the nearest-neighbor distances between surface Pt atoms hr Pt-Pt i s shown in Table 7. Their values vary from 2.92Å to 3.34Å for oxygen coverage from 1 up to 2 ML. For comparison, the nearest-neighbor distance in bulk fcc Pt, found in our DFT calculation, is 2.81Å while in b-PtO 2 , the two nearestneighbor Pt-Pt distances are 3.18Å and 3.59Å. The hr Pt-Pt i distance in the Pt 38 , Pt 79 , Pt 116 and Pt 201 nanoparticles has been found 2.68Å, 2.70Å, 2.72Å and 2.71Å, respectively.
For Pt 201 no congurations with Q > 1 ML have been selected using the two criteria according to eqn (7) and (8). The screening process for the Pt 116 nanoparticles yields several congurations with Q > 1 ML and seven of them are shown in Table 7 but none of these congurations contributes to the phase diagram. However, in the case of Pt 38 and Pt 79 , we have found lowest-energy congurations with Q > 1 ML occurring in the phase diagram shown in Fig. 6.
The lowest-energy congurations on Pt 38 with oxygen coverage 1.12 and 1.31 do not show substantial reorganization of the nanoparticle indicating an oxidation that is evidenced by hr Pt-Pt i s below 3Å. The conguration at Q ¼ 1.50 ML has the lowest absolute energy and appears prominently in the phase   diagram (see Fig. 6A). This conguration has moderate degree of surface reorganization that is characterized by hr Pt-Pt i sÅ . The congurations at coverage larger than 1.5 ML undergo a significant reorganization leading to oxidation of the corner platinum atoms. Characteristic for this reorganization are the high values of hr Pt-Pt i s that go beyond 3.25Å. The conguration at 1.03 ML on Pt 79 , with all fcc and trough sites occupied, exhibits a very weak reorganization of the surface Pt atoms, thus Pt 79 preserves its characteristic shape. This is supported by the short nearest-neighbor distance between the surface Pt atoms (2.99Å). The next lowest-energy conguration with 1.2 ML coverage, with 24 O atoms at (111)-(100) edge bridge sites and 48 O atoms at corner fcc sites is particularly stable and appears in the phase diagram (see Fig. 6B) although the initial average distance between the oxygen atoms is relatively short. The stabilization is due to a PtO 2 oxide monolayer with a cage shape formed during structural relaxation involving all 36 Pt atoms from the twelve edges and the (100) facet (see Fig. S2 in the ESI †). The remaining 43 Pt atoms stay in a metallic Pt nanoparticle core enclosed in the oxide cage. For larger amounts of oxygen (>1.2 ML), no further stable phases can be found except for the fully oxidized Pt 79 O 158 nanoparticle.
Overall, the degree of reorganization (oxidation) increases with oxygen coverage for all nanoparticles which is indicated by an increasing nearest-neighbor distance between the surface Pt atoms hr Pt-Pt i s in Tables 6 and 7 At coverage Q < 0.5 ML, the nearest-neighbor distance is smaller than 3Å in all considered congurations and nanoparticles. For Q > 1 ML, the nearestneighbor distance is larger than 3Å in many congurations and larger than 2.8Å in all congurations. The nearestneighbor distance as a function of oxygen coverage is depicted in Fig. S3 in the ESI. †

Discussion
In the following we will compare the results to experimental Xray photoelectron spectroscopy (XPS) 66 and X-ray absorption spectroscopy (XAS) measurements 58,67,68 on Pt nanoparticles.

Oxidation state
Svintsitskiy et al. 66 have studied platinum oxide nanoparticles of average size of 2.3 nm (this is the size of Pt 201 O 402 in this work) prepared by discharge sputtering of a Pt electrode in an oxygen atmosphere. Using XPS, they have found that the Pt(IV) oxide nanoparticles are stable at room temperature in UHV. Aer heating to 275 C (548 K) the oxide nanoparticles completely convert to Pt(0) nanoparticles going through Pt(II) oxide. This is in overall agreement with the computed phase diagrams in Fig. 5 and 6 except that the oxygen-free phase (bare Pt nanoparticles) sets on at signicantly higher temperature (800 K). The most likely reason for the overestimated transition temperature in our study is the PBE density functional used that is known to overestimate the adsorbate binding energy 69 thus making the phases at low oxygen coverage more stable.
From XAS (EXAFS) spectra, Boubnov et al. 58 have found O/Pt ratios between 0.32 and 0.90 for 1.2 nm and 2.1 nm Pt nanoparticles, depending on the oxidation state of the Pt nanoparticle. The highest O/Pt ratios of 0.66 and 0.90 aer NO and CO oxidation reactions, respectively, have been found for the smallest 1.2 nm nanoparticle. The O/Pt ratio of 0.66 found aer the NO oxidation reaction corresponds very closely (within 4%) to the phase with 0.90 ML coverage on the Pt 79 nanoparticle that is most stable for coverage below 1 ML. The O/Pt ratio of 0.90 found aer the CO oxidation reaction is very close (within 2%) to the one in the most stable phase at 1.20 ML coverage on the Pt 79 nanoparticle. On the 2.1 nm nanoparticles, Boubnov et al. 58 have found an O/Pt ratio of 0.32 aer the CO oxidation reaction that does not correspond to any stable phase on the Pt 201 nanoparticle (this corresponds to 0.52 ML oxygen on Pt 201 ). It is noted that the 2.1 nm nanoparticle is considerably larger than Pt 201 in this study that has a size of 1.7 nm.

Pt-Pt nearest-neighbor distances and coordination numbers
The Pt-Pt coordination numbers from EXAFS spectra 58 found for the 1.2 nm nanoparticles are between 2 and 6 in the oxidized state and 7 and 9 in reduced metallic state, in agreement with our results. The Pt-Pt coordination number found here is 8.5 for the bare Pt 79 nanoparticle and, with only few exceptions, for the phases for Q < 1 ML (see Table 6). With increasing the oxygen coverage above 1 ML, the Pt-Pt coordination number decreases indicating smaller number of metallic bonds. For coverage larger than 1.20, the Pt-Pt coordination number is below 8 (see Table 7). For the most stable phase at 1.2 ML we nd coordination number of 6.7. The coordination numbers between 2 and 6 found in ref. 58 must then correspond to more strongly oxidized nanoparticles than we have considered in this work. This is consistent with the Pt-Pt coordination number of 1.8 that we nd in the fully relaxed PtO 2 nanoparticle Pt 79 O 158 . This is somewhat smaller than the Pt-Pt coordination number (CN ¼ 2) in the bulk b-PtO 2 because in the bulk b-PtO 2 every Pt atom has two nearest neighbors, both along the x-axis, whereas in the PtO 2 nanoparticle some Pt atoms have only one nearest neighbor due the truncation. A similar decrease of the coordination numbers with the amount of adsorbed oxygen, starting with 8.9 for Q ¼ 0, is observed for the Pt 116 nanoparticle.
The Pt-Pt nearest-neighbor distances from EXAFS spectra 58 have been found between 2.67 and 2.74Å for 1.2 nm Pt nanoparticles depending on the oxidation state of the Pt nanoparticle. These small differences between the Pt-Pt nearest-neighbor distances in the reduced and oxidized phases are comparable to the experimental standard deviation error of 0.02Å. 58 In contrast, the Pt-Pt nearest-neighbor distance found in the Pt 79 nanoparticle increases with oxygen coverage from 2.75Å to 3.00Å. As discussed above, this is due to reorganization of the surface Pt atoms towards oxide formation that is supported by the found hr Pt-Pt i s ¼3.12Å in the phase at Q ¼ 1.2 ML corresponding to the Pt-Pt nearestneighbor distance within Pt-O-Pt bridges in b-PtO 2 . 67,68 For comparison, we have found a slightly larger hr Pt-Pt i s ¼ 3.14Å in the fully relaxed Pt 79 O 158 nanoparticle that is only slightly smaller from 3.18Å in the bulk b-PtO 2 .
In a study of electrochemical Pt oxidation in solution, Imai et al. 67 have reported a Pt-Pt nearest-neighbor distance of 2.75Å and coordination number of 9.5 for a 1.9 nm Pt nanoparticles. This is in agreement with the Pt-Pt nearest-neighbor distance of 2.77Å and Pt-Pt coordination number of 9.4 found here in the largest Pt 201 nanoparticle. The authors of ref. 67 have attributed the increased Pt-Pt nearest-neighbor distance of 3.1Å to the formation of PtO 2 oxides: a-PtO 2 for oxygen coverage up to 1.5 ML and the more stable b-PtO 2 at higher oxygen coverage.

Pt-O nearest-neighbor distances and coordination numbers
The Pt-O nearest-neighbor distance found varies from 1.93 up to 2.25Å. In the low-coverage congurations, the Pt-O nearestneighbor distance is determined by the type of adsorption modes included in the conguration and the number of adsorbate species pertinent to each mode. The different adsorption modes have very characteristic distances between the surface Pt atoms and the adsorbate oxygen atoms, as discussed in Section 3.1 and shown in Fig. 2C. In the congurations at high oxygen coverage, surface oxidation and reorganization of the surface Pt atoms occur and lead to Pt-O nearest-neighbor distances closer to those in the Pt oxides. A strong variation of Pt-O nearest-neighbor distance from 2.01 up to 2.19Å 58 and from 1.96 up to 1.99Å 68 has been found from EXAFS spectra. Imai et al. 67 have found a gradual transition from longer Pt-O bonds (2.2Å) due to adsorbed oxygen species into shorter Pt-O bonds in Pt oxides (2.0Å) based on XAFS measurements.
As expected, the Pt-O coordination number in the lowestenergy congurations is close to zero at low oxygen coverage ( Table 6). The Pt-O coordination number increases with the oxygen coverage, as seen in Tables 6 and 7 In the Pt 38 58 These are close to 2.06Å and 2.1, respectively, for the most stable conguration of Pt 79 at 0.90 ML oxygen coverage that has a very close O/Pt ratio. Similarly, for the nanoparticles of the same size aer CO oxidation the Pt-O nearest-neighbor distance and coordination number found are 2.11Å and 2.5, while the values determined for the 1.2 ML stable conguration on Pt 79 are 1.99Å and 2.4, respectively. Because the computed 0.90 ML and 1.2 ML phases also occur in the phase diagrams of Pt 79 (see Fig. 5 and 6), this agreement with the experimental EXAFS data is notable.
It is noted, that the effects of CO and NO used in the experiments 58 are not considered in this work. They may have inuence on the most stable adsorption phase both due to interaction and entropy contributions. In addition, the sizes of the nanoparticles 0.9, 1.9, 2.1 and 3.0 nm studied experimentally 58,67,68 are different from those of the model nanoparticle studied here except for the 1.2 nm nanoparticles 58 that correspond to Pt 79 . Moreover, under in situ experimental conditions the system may not be in thermodynamic equilibrium. Other factors not considered in our model are the silica, titania and alumina supports 58,68 and the metallic platinum support and solvent environment 67 that may also inuence the measured nanoparticle properties.

Conclusions
In this work, we have studied truncated octahedron platinum nanoparticles Pt 38 , Pt 79 , Pt 116 and Pt 201 exposed to oxygen using density functional theory. We have computed the adsorption energy for different amounts of adsorbed atomic oxygen on the nanoparticles considering all possible adsorption modes. In the case of single-atom adsorption, we have found that ontop adsorption is either unstable or has the highest adsorption energies compared to any other adsorption modes. Bridge adsorption at the (111) terrace sites is unstable without exceptions. The top-three most preferred adsorption sites are located at the edges and at the corners. Overall, we have found only weak correlation between adsorption energy and nanoparticle size as well as between the adsorption energy and coordination numbers (either generalized or the conventional). The latter correlation becomes more pronounced when the adsorption modes are considered separately. We nd that the generalized coordination number provides a better description (based on a linear t) for the adsorption energy than the conventional coordination number if every adsorption site type is taken separately.
Considering all stable single-atom adsorptions and neglecting ontop adsorptions, we have generated all possible adsorption congurations at maximum occupancy and used two different screening criteria to further reduce the number of congurations. The distance criterion is more successful for selecting congurations at low coverage, whereas the energy criterion works better for congurations at high coverage. Due to the variance of the criteria, there may be still some statistical uncertainty that can be further reduced by increasing the number of output structures. Molecular dynamics or Monte Carlo sampling methods can be considered to replace the screening, especially for larger nanoparticles where the generation of the input structures for screening may become infeasible due to their extremely huge number. At each oxygen coverage between 0 and 2 ML, we have selected the lowestenergy conguration and constructed thermodynamic p-T phase diagrams for the four systems.
Overall, with increasing the amount of oxygen, we have observed stronger reorganization of the surface layer evidenced by the increasing nearest-neighbor distance between the surface Pt atoms. This reorganization leads to the formation of oxide-like surface compounds on Pt 38 and Pt 79 for Q > 1 ML that are characterized by Pt-Pt and Pt-O nearest-neighbor distances and coordination numbers becoming closer to those in the corresponding PtO 2 nanoparticles. Overall, the computed phase diagrams and the structural data is in good qualitative agreement with XPS and XAS experimental measurements. For example, the nanoparticles are fully oxidized at room temperature both at standard pressure and highly oxidized in ultrahigh vacuum, that is in agreement with the experimental ndings. The computed structural data for Pt 79 , for which direct comparison has been possible, are in very good quantitative agreement with XAS structural characterization data. In particular, the degree of oxidation and structural data for the two most stable phases on Pt 79 correspond to these found in experiments with 1.2 nm nanoparticles.
This study has focused on the stability of the nanoparticlesoxygen system with regard to thermochemical conditions. In future, the presented approach can be readily extended to study stability of the system in various electrochemical conditions, i.e. for the construction of Pourbaix diagrams.

Author contributions
Conceptualization, K. F.; data curation, A. G. Y. and I. K.; formal analysis, A. G. Y. and I. K.; funding acquisition, I. K. and K. F.; investigation, A. G. Y. and I. K.; methodology, A. G. Y., I. K. and K. F.; project administration, I. K. and K. F.; resources, I. K. and K. F.; soware, A. G. Y. and I. K.; supervision, I. K. and K. F.; validation, I. K. and K. F.; visualization, A. G. Y. and I. K.; writing original dra, A. G. Y. and I. K.; writingreview & editing, A. G. Y., I. K. and K. F.

Conflicts of interest
There are no conicts to declare.