DFT studies of oxygen dissociation on the 116-atom platinum truncated octahedron particle

Density functional theory calculations are performed to investigate oxygen dissociation on 116-atom truncated octahedron platinum particles. This work builds on results presented previously [Jennings et al., Nanoscale, 2014, 6, 1153], where it was shown that shell flexibility played an important role in facilitating fast oxygen dissociation. In this study, through investigation of the larger particle size, it is shown that oxygen dissociation on the (111) facet of pure platinum species is still aided by shell flexibility at larger sizes. Only the hollow sites close to the edges of the (111) facet mediate oxygen dissociation; oxygen is bound too weakly at other hollow sites for dissociation to occur. Further studies are performed on the (100) facet, which is larger for the Pt116 particle than for either the Pt38 or Pt79 ones. Much higher dissociation barriers are found on the (100) facet compared to the (111) facet, where the bridge sites are favourable for oxygen dissociation.


Introduction
The interest in platinum (Pt) systems is due in part to the relevance of Pt based catalysts in many industrial applications, such as catalysing the oxygen reduction reaction (ORR) in hydrogen fuel cells. [1][2][3][4] For low temperature fuel cells, a common problem associated with the use of a Pt electrocatalyst is the strong Pt-O binding, which aids oxygen dissociation, but is responsible for reducing the rate of the ORR. [5][6][7] Modelling of the ORR is a very active area of research, with emphasis on computing the overall mechanism, [8][9][10][11][12] as well as chemisorption studies of specific intermediates within the reaction. [13][14][15] Oxygen chemisorption studies have been performed on a number of extended Pt surfaces, [16][17][18] although there is also significant interest in the study of both free [19][20][21] and supported particle systems. 22,23 Nanoparticle models can offer a greater number of symmetry inequivalent sites at which to bind oxygen and in the size regime where ''each atom counts'', 24 properties are often dominated by quantum effects. For these structures, the under-coordinated surface atoms of the particles provide a diverse range of electronic environments at which to bind O. 25 However, it should be noted that it is also possible to use particle models that are scalable with size. [26][27][28] In the work presented here, focus is placed on investigating O 2 dissociation on Pt particles. The behaviour of O 2 dissociation on Pt surfaces has been studied extensively. Whilst this has predominantly focused on bulk systems, [29][30][31][32][33][34][35][36] some studies have been performed on small particles. [37][38][39][40] In work published previously, we showed that when Pt is alloyed with titanium (Ti) to produce core-shell Ti@Pt moieties, changes in the electronic structure of the nanoparticle result in weaker Pt-O binding, through filling of the Pt d-band; 41,42 where similar trends have been found for a number of other Pt based alloy systems. [43][44][45] In later studies, it was found that whilst the strong core-shell interactions could result in a favourable reduction of Pt-O binding energies, these strong Pt-M interactions also inhibited oxygen dissociation. Shell flexibility plays an important role in facilitating fast oxygen dissociation, where on pure Pt particles the outermost shell can distort in such a way as to reduce the O 2 dissociation barrier from 0.4 eV on the (111) bulk slab, to o0.1 eV on the (111) facet of the particle. 46 The previous studies on oxygen dissociation were performed on 38-and 79-atom particles. 46 It is noted that other studies found significant variation in adsorption energies of O on small Pt particles, when nearby facets were modified; 47 although, this appears less pronounced for particle sizes 480 atoms. Therefore, size effects potentially play an important role in O binding as well as flexibility of the Pt shell for the small particle sizes investigated previously. In the work presented here, O 2 dissociation studies are performed on the larger truncated octahedron (TO) Pt 116 nanoparticles, which should be in the range that scales with size. It allows the investigation of, not only the size dependance of (111) facet flexibility, but also perform a more detailed study of the (100) facet. Although in the previous studies the (100) facet exhibited far higher dissociation barriers, the Pt 116 (100) facet is larger and allows for additional O 2 adsorption sites to be investigated.

Methodology
Calculations are performed using the Vienna Ab-initio Simulation Package (VASP) 5.2. [48][49][50][51] For all atom types, the valence electrons are treated explicitly, while the ionic cores are represented by the projected augmented wave (PAW) method. 52,53 Electronic exchange and correlation are described using the generalised gradient approximation (GGA) using the Perdew-Wang 91 (PW91) formula. 54,55 The Methfessel-Paxton smearing method is used with a width of 0.1 eV (extrapolated for computing final energies at zero smearing) and an energy cutoff of 415.0 eV has been employed. All particles are placed in the centre of large enough supercells to ensure sufficient separation of 10 Å between periodic images. The G point is used to sample the Brillouin Zone. Atoms are then relaxed according to the calculated atomic forces, with convergence criteria for energies and forces required to be better than 1.0 Â 10 À4 eV per atom and 0.02 eV Å À1 , respectively.
Dissociation pathways are investigated using the Transition State Tools implementation of the VASP code, by first generating an approximate pathway using the Nudged Elastic Band (NEB) method, 56 with further refinements achieved using the Dimer method. 57 Charges are calculated using the Bader method. 58,59 In order to assess the (atomic or molecular) oxygen adsorption strength to the Pt surface, the binding energy (E b ) is calculated, as defined in eqn (1).
E AB is the energy of the particle with oxygen adsorbed, E A is the energy of the relaxed particle and E B is the energy of the free oxygen atom or molecule, negative E b values imply favourable binding. The interaction energy (E int ) is defined in eqn (2).
The single point energies of species distorted upon adsorption are denoted by *, again negative values imply favourable interactions. Distortion energies can be calculated using eqn (3).
Although specific distortions, brought about by adsorption of oxygen, are discussed in detail, as a more general measure root mean squared displacements (RMSD) of atoms are calculated as defined in eqn (4).
N is the total number of atoms, m i is the position of a given atom for the relaxed bare Pt 116 and m i * is the position of the same atom in the particle following oxygen adsorption. Prior to applying this equation, rotation and translation operators are performed to align each particle, thereby minimising the RMSD. In this study, RMSD is calculated for Pt atoms to which O 2 is bound, as well as the nearest neighbour metal atoms.

Oxygen adsorption
In the previous studies, the Pt 79 TO model showed similar trends to the Pt 38 TO, although further site dependent trends were observed for the 79-atom particle that were not present on the limited (111) facet of the 38-atom particle. Therefore, in this study, one further particle size is considered for the pure Pt system. On the surface of the 116-atom TO model there are 15 symmetry inequivalent sites which are depicted in Fig. 1.
The results of atomic and molecular oxygen adsorption on Pt 116 are presented in Table 1.
Atomic oxygen is preferentially adsorbed at site 9, the edgebridge position between the (111) and (100) facets, with a binding energy of À5.02 eV. This is in agreement with the studies on the Pt 79 model. Whilst the atomic oxygen preferentially binds to the hcp hollow site (more stable by Z0.09 eV than the edge-bridge sites) on the 38-atom moiety, favourable binding is observed to the edge-bridge position between two (111) facets (strengthened by Z0.06 eV compared to hollow sites). This shows that there is competition between atomic oxygen adsorption on the edge-bridge and hollow sites on the 38-and 79-atom particles. However, on the 116-atom particle, the edge-bridge site between the (111) and (100) facets are found to be Z0.23 eV more stable when compared to the hollow positions. This indicates that, as the particle size increases, there is a move away from the hollow sites directed towards the edge-bridge sites. The exact edgebridge position also varies as seen when comparing Pt 79 , where the edge-bridge position between two (111) facets is favourable, to Pt 116 , where the edge-bridge site between the (111) and (100) facets is favourable. O 2 is preferentially adsorbed at position 8, the edge-bridge site between the two (111) facets. This is in agreement with results for Pt 79 , although it is found that the edge-bridge site between the (111) and (100) facets is most favourable for Pt 38 . O 2 at the edge-bridge site is found to be Z0.17 eV lower in energy than at hollow sites on Pt 38 , suggesting more site preference for O 2 binding when compared with atomic oxygen. This is also seen for the 79-and 116-atom species, where the preference for binding to edge-bridge sites over hollow sites is Z0.70 and Z0.80 eV, respectively. This also manifests size dependence, where the energy difference between the edgebridge and hollow sites increases as particle size increases. O 2 dissociation is investigated for sites on both the (111) and (100) facets. For Pt 116 , bridge sites 8, 9 and 10 have been investigated as well as hollow sites 11, 12 and 14. O 2 dissociation proceeds from an initial site and terminates at the central hollow position on the (111) facet (site 13). Any further migration of the atomic oxygen to other positions on the particle would lead to additional small barriers associated with moving between different sites but would have little importance. The central hollow site of the (111) facet was also investigated, although found to be unfavourable for O 2 dissociation, which is likely due to the small (in magnitude) O 2 binding energy of À0.68 eV.

Barriers for O 2 dissociation
Representations of the minimised geometries for the initial, transition and final states (IS, TS and FS, respectively) can be found in the ESI, † Fig. S1-S6. For comparative purposes, the minimised geometries for the initial, transition and final states of the extended Pt(111) surface can be found in the ESI, † Fig. S7. A greater range of facet sites were studied for Pt 116 , these included similar (111) hollow sites to those investigated previously (positions 11, 12, 13 and 14) but also a greater range of bridge sites (positions 5, 6, 7, 8, 9, and 10). As with Pt 79 , the (111) hollow site at the centre of the (111) facet, position 13, is found to exhibit weak Pt-O binding. This explains why the attempted O 2 dissociation studies were not successful, where the O 2 molecule favours migration away from the initial facet position, towards a more favourable one, instead of dissociating.
Relatively low binding energies are found for bridge positions 5, 6 and 7, À0.83 to À1.17 eV. Instead of O 2 dissociation barriers being located for these positions, small barriers, B0.1 eV are found for O 2 migration to a preferential site, e.g. an edge-hollow site. This suggests that, where possible, O 2 migrates to favourable binding sites prior to dissociation. Details for the positions at which dissociation barriers were located are given in Table 2.
For Pt 116 there are very low dissociation barriers for hollow positions 11, 12 and 14, at 0.08, 0.07 and 0.14 eV, respectively. Although the barrier at position 14 is slightly higher than those for 11 and 12, it is significantly lower than that of the bulk (B0.40 eV 46 ). Furthermore, it is comparable with that of position 9 on Pt 79 , which was found to be 0.21 eV. Whilst position 9 on Pt 79 is the hcp hollow site adjacent to a (100) facet, position 14 on Pt 116 is the fcc hollow site adjacent to another (111) facet site. There are few similarities between the two sites that could  lead to this slightly higher dissociation barrier aside from the fact that they are both adjacent to the ''short'' edge of the (111) facet. On Pt 79 , there are two hollow positions adjacent to (111) facets, and only one adjacent to the (100) facets. For Pt 116 there are two hollow sites adjacent to the (100) facets, but only one adjacent to the (111) facets. It is therefore likely that the facets on the ''short'' edge are slightly more difficult to distort, with the bridge bond between facets being more ridgid. However, as the central atoms of the (111) facet are more flexible, favourable distortions towards the centre of the facet are still possible, leading to these slightly higher dissociation barriers compared to other hollow positions on the (111) facet, but still lower than the Pt slab. Dissociation barriers for the Pt 38 and Pt 79 particles are presented in Table 3, along with those for the Pt 116 particles.  38 , none of the nanoparticle distortion energies are close to that of the slab (Z0.25 eV difference). For Pt 79 , site 9 is 0.04 eV lower in energy than the slab, however other sites are Z0.14 eV higher in energy. This shows a trend towards infinite surface like behaviour with increasing particle size. The greatest distortion energy on Pt 116 is found for position 12, 0.65 eV, although the distortion energies for the various sites are generally in line with those for the 38-and 79-atom particles of r0.50 eV. At the TS, position 8 once again has the lowest distortion energy associated with it. The particle distortion energy for site 8 is similar to that of the slab, 0.21 and 0.25 eV, respectively. However, all other sites have significantly higher distortion energies associated with them, 0.44-0.84 eV. The greatest distortion energies are found for positions 11 and 12 which are indicative of low O 2 dissociation barriers. The particle distortion energy for site 14 is similar to those of positions 9 and 10, although a significantly lower O 2 dissociation barrier is found for 14 compared to 9 and 10. The dissociation barrier for position 14 lies between the other low barrier (111) hollow sites and the high barrier bridge sites. There is a slight increase in the distortion energies when comparing the IS and TS structures, where the TS ones tend to have greater distortion energies. Furthermore, the distortion energies at the TS for Pt 116 tend to be greater than those for the Pt 38 and Pt 79 TS structures.

Distortion energies
At the FS, the Pt 116 distortion energies are all greater than for the Pt slab. Furthermore, positions 8 and 9 have comparable distortion energies, both B0.10 eV higher in energy than the slab model. The Pt 116 distortion energies for positions 8 and 9 are lower than other sites as adsorption on the bridge positions typically leads to less distortion. Position 10 has a larger distortion energy compared to the other bridge positions. In this case, O 2 dissociation occurs over the central atom of the (100) facet. This leads to similar distortions to the (111) facet, with the central atom being pulled out of the plane. However, for the (100) facet, this distortion does not lead to the very low dissociation barriers observed for the (111) facet. Instead, a high barrier of 0.69 eV is calculated. Position 14 has a higher distortion energy than the bridge sites, although this is lower than the distortion energy for the other hollow sites. As discussed previously, there is less distortion of the ''short'' facet edge, leading to a reduced distortion energy compared to positions 11 and 12.
RMSD is calculated for all particles, however only the atoms to which O 2 is bound as well as nearest neighbour Pt atoms are accounted for. There are generally greater displacement associated with the TS and FS. This is expected as the oxygen binds more strongly to the Pt surface as the system progresses from the IS to the FS. There are fewer trends when comparing the various sites being studied. Generally, there is a large RMSD associated with sites 11 and 12 (particularly at the TS), which exhibit larger distortion energies and lower O 2 dissociation barriers compared to other sites.
At the IS, the oxygen distortion energy shows that there is greater distortion of O 2 on the hollow sites, positions 11, 12 and 14. This means that at the positions for which there are very low dissociation barriers, there is greater distortion, away from the gas phase structure, of O 2 . Conversely at the TS, this trend inverts, where higher O 2 distortion barriers are found for the bridge sites, 8, 9 and 10. This shows that at the TS, there is less distortion of the O 2 on the hollow sites.

Interaction energies
E int gives an idea of the strength of the O 2 bond to the surface. From the IS studies it follows that there is little difference between the interaction energies for the various sites. This trend changes at the TS, where greater interaction energies are found for the bridge sites than for the hollow sites. Thus, at the bridge sites, where there is typically less distortion of Pt 116 and greater distortion of O 2 , there is a stronger Pt-O interaction. This is the opposite trend to that of the hollow sites, where there is greater distortion of Pt 116 and less of O 2 . Similar trends to this are found for the binding energy, although in this case the trends are not as obvious because E b includes the energetic contributions of distortions compared to the gas phase structures.

Geometric analysis
Calculated geometric parameters are listed in Table 4

Bader charge analysis
Results from the Bader charge analysis are given in Table 5. Charge density difference plots are shown in the ESI, † Fig. S8-S14.
Consistent with previous studies, 41,42,46,60 there is significant charge transfer from the Pt, which becomes positively charged, to the O, which becomes negatively charged. At the IS it is found that there is less charge transfer from Pt for site 8 compared to sites 9 and 10. Instead, the charge state of site 8 is comparable to the hollow sites, which are slightly less positively charged. When studying O 2 charge, it is found that there is a greater charge compared to the O associated with the hollow sites. For the hollow sites, charge transfer is investigated for the three Pt atoms directly bonded to O 2 , instead of the two atoms of the bridge sites. This means that, although there is typically less charge transfer from one Pt atom, as there are more Pt atoms interacting with O, the average charge on the O is greater.
The charge transfer at the TS is greater than that at the IS. As the O 2 dissociates, the interaction energy increases, coupled with a greater transfer of charge from the Pt to the O. At the TS, there is greater charge transfer at the bridge sites which is due to the coordination number of the O, where each O atom is bonded to a single Pt atom. For the hollow sites the charge transfer is spread over three Pt atoms, which results in the smaller transfer of charge. A similar trend is observed for the FS, where once again, greater charge transfer is found than at the IS or TS. Each O atom is now strongly bonded to the Pt surface and able to extract a greater charge than the molecular O 2 . At the FS, there is less difference in charge transfer between the bridge and hollow sites. This is because the transferred charge is spread over a greater number of atoms at each site. Table 4 Data for oxygen-oxygen distances (O-O), average platinum-oxygen bond lengths (Pt-O), average platinum-platinum bond lengths (Pt-Pt) for specific bonds defined in Fig. 1 and distances from the octahedral core to the central (111) atom in the y-direction (Pt-X centre ). Average Pt-Pt bond lengths are calculated for those atoms directly below the adsorbed O 2 molecule. Bond lengths are given in Å. The type of the bond according to Fig. 1

Conclusions
We have presented a comprehensive study of size effects on O 2 dissociation of Pt particles considering the Pt 116 particle and comparing with the previously obtained results for smaller Pt particles. Most of the trends observed in the previous studies on Pt 38 and Pt 79 species are also seen for the larger Pt 116 . It is seen that the small O 2 dissociation barriers, first calculated on Pt 38 , were not due to the small particle size. For the Pt 116 model much lower dissociation barriers are obtained on the (111) facet hollow sites at the edge between (111) and (100) facets, 0.07 eV, when compared to the Pt(111) slab, 0.45 eV. A slightly higher dissociation barrier, 0.14 eV, is found for the other hollow site located close to the edge between two neighbouring (111) facets, although this is significantly lower than for the Pt slab, or other bridge sites on the Pt 116 particle. For Pt 116 , other sites were also investigated: these included bridge sites on the (111) and (100) facets as well as the edge bridge sites between neighbouring (111) facets and between (111) and (100) facets. When studying the bridge sites on the (111) facet, it was found that the O 2 would, instead of dissociating, overcome low barriers to migrate to hollow sites. Both edge bridge sites exhibited similar characteristics. On the other hand, it was found that there was a higher dissociation barrier for the bridge site at (100) facets, when compared to the edge bridge sites. This demonstrates that O 2 dissociation will occur preferentially on (111) facets near the nanoparticle edges and the advantages of particles with greater numbers of (111) facet sites compared to (100) facet sites.