University of Birmingham A DFT study of oxygen dissociation on platinum based nanoparticles

Density functional theory calculations are performed on 38 and 79 metal atom truncated octahedron clusters to study oxygen dissociation as a model for the initial stage of the oxygen reduction reaction. Pure platinum and alloyed platinum – titanium core – shell systems are investigated. It is found that barrierless oxygen dissociation occurs on the (111) facet of the pure platinum clusters. A barrier of (cid:1) 0.3 eV is observed on the (100) facet. For the alloyed cluster, dissociation barriers are found on both facets, typically (cid:1) 0.6 eV. The di ﬀ erences between the two systems are attributed to the ability of oxygen to distort the (111) surface of the pure platinum clusters. We show that ﬂ exibility of the platinum shell is crucial in promotion of fast oxygen dissociation. However, the titanium core stabilises the platinum shell upon alloying, resulting in a less easily distortable surface. Therefore, whilst an alloyed platinum-titanium electrocatalyst has certain advantages over the pure platinum electrocatalyst, we suggest alloying with a more weakly interacting metal will be bene ﬁ cial for facilitating oxygen dissociation.


Introduction
The behaviour of oxygen (O) on platinum (Pt) surfaces has been studied extensively, [1][2][3][4][5][6][7][8] although much of the current work is focused on bulk systems, some studies have been performed on smaller cluster systems. [9][10][11][12] The interest in Pt-O systems is due in part to the relevance of Pt based catalysts in many industrial applications. A good example, is the extensive use of Pt to catalyse the oxygen reduction reaction (ORR) in fuel cells. [13][14][15][16] However, to develop and successfully market polymer electrolyte fuel cells (PEFCs), it is necessary to reduce the Pt catalyst loading of both anode and cathode electrodes, together with the associated cost, without compromising the performance.
The high intrinsic cost of Pt (£843.23 per ounce as of 10/07/13) forms a barrier to the widespread commercialisation of PEFCs. A ten-fold decrease in Pt loading in PEFC stacks is required to make PEFCs a commercially viable option. There are several ways to do this: lower the Pt loading by using a Pt alloy (either binary or ternary); 17,18 replace Pt with a non-precious electrocatalyst (inorganic or organic); 19,20 maximise the effective surface area of the Pt catalyst i.e. the surface contact between the electrode catalyst layers, the carbonaceous electronic conductor-gas diffusion layer, the polymer electrolyte membrane and the reactants (hydrogen and oxygen). 21,22 Another serious problem with PEFCs is that the hydrogen feed usually contains signicant amounts of carbon monoxide (CO), which poisons the Pt electrocatalyst. Alloying Pt to reduce loading and improve catalytic characteristics such as performance, durability and reactivity is a promising approach. We previously reported the results of theoretical calculations which suggested that alloying Pt with titanium (Ti), a much cheaper transition metal (£0.28 per ounce as of 10/07/13), to form Ti@Pt core-shell clusters (Ticore, Ptshell), results in weaker binding of hydroxyl (OH) and CO with reduced Pt loading. 23 Weaker binding of OH can lead to improvements in ORR kinetics, while weakening of CO binding lessens poisoning effects. Weaker adsorption was attributed to changes in the electronic structure attained through alloying; specically, changes in the d-band centre. 24 At the same time the catalyst has to facilitate the initial stage of ORR, namely O 2 dissociation.
In our present work, oxygen dissociation is studied on pure Pt clusters as well as core-shell Ti@Pt clusters. Dissociation on the (111) slab model is also included, as this can represent the process on (111) terraces of larger particles. Initially focusing on 38 atom clusters, barrier-free dissociation is observed for the Pt 38 cluster on the (111) facet. However, notable dissociation barriers are observed for the (100) facet as well as both (111) and (100) facets on the Pt 32 Ti 6 cluster. This behaviour is explained through an in depth study of cluster stability and is further investigated for 79 atom clusters.

Methodology
Calculations are performed using the Vienna Ab initio Simulation Package (VASP) 5.2. [25][26][27][28] The 5d 9 6s 1 of Pt, 3d 3 4s 1 of Ti and 2s 2 2p 4 of O are treated as valence electrons, while the ionic cores are represented by the projected augmented wave (PAW) method. 29,30 Electronic exchange and correlation are described using the generalised gradient approximation (GGA) using the Perdew Wang 91 (PW91) functional. 31,32 The Methfessel-Paxton smearing method is used with a width of 0.1 eV (extrapolated for computing nal energies to zero smearing) and an energy cutoff of 415 eV is employed. DFT-D calculations were also performed on a number of test cases, although the inclusion of van der Waals forces through the empirical treatment of Grimme results in little change and so was not considered in the following results.
The bulk systems were modelled by ve layers of repeated 3 Â 3 (111) slabs, allowing the top two layers of the Pt(111) slab to relax fully while xing the bottom 3 layers. A 5 Â 5 Â 1 k point mesh was used to sample the rst Brillouin zone. Approximately 10Å of vacuum was included between neighbouring systems. For the cluster systems, 38 and 79 atom clusters were considered, these are magic numbers leading to complete Truncated Octahedral (TO) structures. The clusters are placed in the centre of a large enough supercell to ensure sufficient separation ($10Å) between periodic images, the G point is used to sample the Brillouin zone. All atoms are relaxed according to the calculated atomic forces, with convergence criteria for total energies 1.0 Â 10 À4 eV and forces required to be less than 0.02 eVÅ À1 .
In order to assess the (atomic or molecular) oxygen adsorption strength to the Pt surface, the binding energy (E b ) is calculated, as dened in eqn (1).
E AB is the energy of the cluster with oxygen adsorbed, E A is the energy of the relaxed cluster 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 dened 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) for Pt nÀm Ti m (where n ¼ 38, 79 and m ¼ 0, 6,19) and eqn (4) for oxygen distortions.
Although specic 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. RMSD is calculated as dened in eqn (5).
N is the total number of atoms, M i is the position of a given atom (between 1 and N) for the relaxed bare cluster and M * i is the position of the same atom in the cluster following oxygen adsorption. Prior to applying this equation, a rotation and translation operator is used to align each cluster, thereby minimising the RMSD.
Dissociation pathways were investigated using the VASP Transition State Tools (VTST) implementation by the Henkelman Group, rst generating an approximate pathway using the Nudged Elastic Band (NEB) method, 33 with further renements achieved using the Dimer method. 34 Bader charge analysis 35 was performed using the Bader code 36 also from the Henkelman Group.

Slab model
Large metal nanoparticles are oen approximated in computational studies of catalysts by innite slab models of (111) surface. 37 Hence, we start our study investigating O 2 dissociation on slabs. There are four non-symmetry equivalent sites on the surface of the innite (111) slab, the atop, bridge, fcc and hcp sites. It is found that the bridge and fcc sites are energetically competitive, the E b for O 2 at the bridge site being À0.87 eV, while it is À0.86 eV for the fcc position. This is in good agreement with experimental and theoretical studies, which have found both sites favourable for O 2 chemisorption. [38][39][40][41][42] The hcp site is 0.1 eV higher in energy than the fcc site (at À0.76 eV), while migration occurs when locally minimising O 2 at the atop position, resulting in O 2 bonding to the more favourable fcc site.
For the Pt(111) system, the oxygen molecule is initially adsorbed on a three-fold fcc hollow site, before dissociating resulting in each O atom being bound to fcc hollow sites. The dissociation barrier on the Pt(111) slab is found to be 0.45 eV, in agreement with other calculations, which nd a barrier of between 0.4 and 0.6 eV, presented in the literature 1 , electron density is withdrawn from Pt  by O, with increased charge transfer as the system progresses  form the IS to the FS. There is greater Pt charge transfer when  comparing the TS to the FS, this is due to O 2 being bonded to one  3-fold fcc hollow site at the TS and two at the FS. We also considered PtTi (111) alloyed system, with a model (which has been studied before 47 ) where the second layer of the slab was set as Ti and the top three layers (Pt-Ti-Pt) were allowed to fully relax. During the geometry optimization, however it shows instability and surface and subsurface layers can no longer be identied as (111). In order to study a more realistic model of the PtTi(111) alloyed system, we considered Ti@Pt nanoparticles, with Ti cores, where the effect of edges, larger exibility, etc. can be taken into account. We studied two model clusters consisting of 38 and 79 metal atoms.  Table 1.
For the pure Pt 38 cluster, three-fold hollow positions 6 and 7 on the (111) facets, as well as the edge bridge position 5 between the (111) and (100) facets are the most stable for adsorption of atomic oxygen, À5.21, À5.12 and À5.12 eV, respectively. Interestingly, on Pt 32 Ti 6 , three-fold hollow positions are no longer locally stable and move to bridge sites (4 and 5). Position 5 is the most stable site, with an E b value of À4.78 eV, a decrease of 0.34 eV with respect to the same position on the pure Pt 38 cluster.
For O 2 adsorption, position 5, the edge-bridge site between (111) and (100) facets is most stable on both Pt 38  Step sites on Pt(111) surfaces have been reported to result in particularly stable oxygen bonding. 48,49 Furthermore, studies of Pt TO clusters has revealed favourable bonding at the edge-bridge sites. 50 Calculations on the Pt(100) surface have favoured bonding to bridge sites, in line with the results presented here. 51 As with the previous OH and CO adsorption studies, 23,24 weaker bonding for O 2 and O is calculated for the bimetallic Ti@Pt cluster when compared with the pure Pt cluster.
It is expected that oxygen dissociation will occur preferentially at sites with higher E b values, where oxygen is most likely to adsorb to the surface of the cluster. Due to the small size of the cluster, it would be relatively easy for molecular oxygen to dissociate and migrate to any of the other seven sites, or an equivalent site in a different location on the surface. It is therefore assumed that dissociation will also likely result in atomic oxygen being adsorbed on the most energetically favourable sites. The energetic ordering of adsorption for molecular oxygen was similar to that of atomic oxygen, making the proposed dissociation pathways relatively straightforward.
The most stable sites, the edge site 5, as well as hollow sites 6 and 7 are studied. For each pathway, O 2 dissociation proceeds from one site to an adjacent position at an equivalent site (e.g. O 2 bound to position 5 dissociates to atomic oxygen bound to separate 5 sites). Data for each dissociation pathway is presented in Table 2. In each case, distortion energies of the cluster and O 2 at each step of the dissociation pathway are presented.
3.2.2 Distortion and interaction energies. Representations of the minimised geometries for the IS, TS and FS can be found in Fig. S5-S10. † Studies of the IS show that the distortion energy values (DE(Pt nÀm Ti m )) associated with Pt 38 clusters are higher than those for the Pt 32 Ti 6 clusters. The distortion energies associated with both clusters are also found to be greater than those for the pure slab, in most cases. O 2 distortion energies (DE(O 2 )) show greater distortions of the O 2 molecule adsorbed on Pt 38 compared with Pt 32 Ti 6 for the IS structures. However, as  mentioned previously, larger in magnitude adsorption energies are observed for the Pt 38 clusters compared to the Pt 32 Ti 6 clusters. This suggests that the increased interaction energy of O 2 to the Pt surface of the pure cluster, overcomes the distortion energies to a greater extent than for the bimetallic clusters. Furthermore, the stronger Pt-O binding will likely aid in distorting both oxygen and the Pt 38 cluster to a greater degree than the Pt 32 Ti 6 cluster. DE(O 2 ) values calculated for the bulk system are found to be greater than those on the (100) facet of both clusters, however smaller than on the (111) facet. The greater distortions on the cluster (111) facets compared to those on the slab are likely due to the increased binding energies on the clusters.
Distortion energies in the TS structures show, in general, that there is a greater distortion energy associated with the Pt 32 Ti 6 clusters. The one exception is where distortion occurs on site 7 of the Pt 32 Ti 6 cluster, due to different types of TS structures. In this case, a "straight" dissociation pathway is located over the central atop position (site 1) of the Pt 32 Ti 6 cluster. For dissociation on site 6, however, a more curved pathway is preferred, avoiding the atop position and instead progressing over the hollow sites of the alloyed cluster. However, the fact that the distortion energies for the Pt 32 Ti 6 clusters are signicantly higher than for the Pt 38 clusters suggests that the presence of the Ti core in the alloyed cluster stabilises (makes more rigid) the Pt shell. Nevertheless, the alloyed cluster is still distorted by the adsorbate. In all cases, the cluster distortion energies are greater than that of the slab, suggesting that the slab is signicantly harder to distort than both clusters at the TS leading to little change in the slab structure. Similar to IS, data for the FS show the distortion energies associated with the Pt 38 clusters are higher than those for the alloyed Pt 32 Ti 6 clusters in all cases. Once again, there is generally greater distortion energies associated with the clusters than the slab. This was found to be the case also for positions 5 and 6.
For the pure Pt clusters, the IS and TS have similar distortion energies, the FS is found to have slightly greater distortion energies. This is consistent with atomic oxygen having a greater effect on the Pt surface than the single O 2 molecule. For the Pt 32 Ti 6 clusters, it is found that the TS generally has greater distortion energies than the IS or FS. The exception to this is dissociation occurring at position 7, where a relatively small distortion energy is found at the TS compared to a relatively high energy at the FS. In summary, this energetic ordering suggests that at sites 5 and 6 greater distortions occur at the TS, not the FS as with the pure Pt clusters.
RMSD of the metal atoms are also listed in Table 2, it is important to note that O 2 distortions are not accounted for. These indicate the geometric distortion of the metal particle due to adsorption of the O 2 molecule. Data on distortions to specic facets of the cluster are described later. For RMSD analysis, the geometry of the distorted cluster, with O 2 removed, is compared to the geometry of the relaxed gas phase cluster, with higher values suggesting greater distortion. For the Pt 38 clusters, there is a larger RMSD associated with O 2 adsorption Table 2 Values for cluster (DE(Pt nÀm Ti m )) and oxygen (DE(O 2 )) deformation energies, root mean squared displacements (RMSD) of the cluster, interaction energies (E int ), binding energies (E b ) and barriers for O 2 dissociation (DE s ). The ratios of distortion energy to RMSD (DE(Pt nÀm Ti m )/ RMSD) are also presented. Site numbering is introduced in Fig. 1. All energy values are given in eV, RMSD inÅ A high dissociation barrier (DE s ) is found for site 5, on the (100) facet of the Pt 32 Ti 6 cluster, 0.62 eV, this being approximately twice that of the pure Pt 38 cluster, 0.32 eV (Table 2). When considering the (111) facet of the Pt 32 Ti 6 cluster, the dissociation barriers for sites 7 and 5 are equal, 0.62 eV, while for site 6 the barrier, 0.34 eV, is about half that of the other two sites. The Pt 38 cluster is found to exhibit barrier-free dissociation on the (111) facet, this dramatically differs to the 0.45 eV barrier found on the Pt(111) slab. On the (100) facet of the Pt 38 cluster (site 5), comparable dissociation barriers are found to site 6 on the Pt 32 Ti 6 cluster.
3.2.3 Geometric analysis. Analysis of the system geometries can be found in Table 3. O-O bonds, in general, are shorter for the IS adsorption on the (100) facet. However, at the TS, generally shorter bond lengths are associated with the (111) facet. When studying the average Pt-O bond length, as the system moves from the IS to the TS, the average bond length gets smaller. The average Pt-Pt bond lengths are found to be 2.65, 2.70 and 2.70Å for bond types 1 to 3, respectively (Fig. 2) for the bare Pt 38 cluster, while for the bare Pt 32 Ti 6 cluster, the corresponding Pt-Pt bond lengths are slightly larger, 2.69, 2.71 and 2.74Å for sites 1 to 3, respectively.
Once oxygen is adsorbed on the (100) facet of the Pt 38 cluster, signicant elongation of bond type 2 by up to 0.54Å is observed, although there is less overall distortion of the cluster geometry. Following oxygen adsorption on the (100) facet, the average distortion of the Pt-Pt bonds calculated from the data in Table 3 is 0.43, 0.53 and 0.78Å for sites 5, 6 and 7 on the Pt 38 cluster, respectively. When O 2 is adsorbed on the (111) facet, there is a slight elongation of bond type 1 by up to 0.29Å, although not as much as for bond type 3 by up to 0.85Å, which is signicantly elongated. There is generally a slight contraction in the bond length of type 2 by up to 0.06Å. This suggests that the majority of the distortion that occurs when O 2 is adsorbed on the (111) facet of the Pt 38 cluster is due to changes in the bond length of type 3, bonding to the central (111) atom. For the Pt 32 Ti 6 cluster signicant elongation is observed of bond type 2 by up to 0.57Å, when O 2 is adsorbed on site 5 of the (100) facet. However, there is considerably less distortion of the other bond types when O 2 is adsorbed on the (111) facet, the maximum distortion observed being #0.37Å.
Pt-X centre values are only calculated for dissociations on the (111) facet. From the values presented in Table 4, there are few well-dened trends when comparing initial, transition and nal states. However, the point of these values is to demonstrate the differences between the Pt 38 and Pt 32 Ti 6 clusters. Pt-X centre was calculated by dening a plane through the cluster, parallel to the (111) facet on which oxygen is adsorbed and then measuring Pt distortions along the y-axis from that plane. The plane passes through the central atoms of the (111) surfaces surrounding the facet on which the O 2 is adsorbed, as shown in Fig. 3.
Following O 2 adsorption, Pt-X centre distances are presented in Table 4. This reveals small distortions, # 0.14 and # 0.08Å for the Pt 38 and Pt 32 Ti 6 clusters, respectively, measuring distances from the plane to the bottom of the cluster. More signicant changes are seen at the top of the cluster, #0.91 and #0.42Å for the Pt 38 an Pt 32 Ti 6 clusters, respectively. Furthermore, it is found that there is considerably stronger distortion of the Pt 38 cluster, with the atop central (111) atom being pulled out of the plane. The relationship between Pt-X centre and distortion barriers can be seen in Fig. S1 and S2 † for the IS and TS.

Bader charge analysis.
We previously studied charge transfer between Pt and Ti atoms within core-shell systems. 24 For reference, the electronegativities of Pt, Ti and O are 2.28, 1.54 and 3.44 on the Pauling scale, respectively. For the bare clusters, there is signicant electron donation from Ti to Pt, which likely results in the strong core-shell interactions that stabilise the Pt surface. The average charges for the Pt 32 Ti 6 cluster are found to be À0. 36 and +1.94 |e| for Pt and Ti, respectively. Following this, an analysis was performed of the effect of the adsorbate on the atomic charges, as shown in Table 5.
When O 2 is adsorbed on the surface of the pure Pt 38 cluster, the Pt atoms on which the oxygen is adsorbed have a positive charge +0.22 to +0.31 |e|. It is generally found on Pt 38 and Pt 32 Ti 6 clusters, that the Pt becomes more positively charged as the system moves from the initial to nal states, while the O atoms become more negatively charged at the same time. Furthermore, more positive Pt charge values are observed for O 2 adsorption on the (100) facet. This charge transfer is found to be comparable between the slab and cluster models. In the case of the Pt 32 Ti 6 cluster Pt has positive and negative charges depending on the state of the system, slightly positive (+0.04 |e|) when O 2 is adsorbed on the (100) facet and negative on the (111) facet (À0.22 to À0.23 |e|). At the same time, charges on the Ti atoms, which are remote from the adsorbates, do not change notably. They also do not change when the system progresses from IS to FS. Not surprisingly, the charges on the oxygen atoms get signicantly more negative as the system progresses from the initial to the nal states. This charge seems unaffected by the site at which oxygen is adsorbed, or whether it is the pure or alloyed cluster. Hence, one can conclude that O atoms have local effects on the withdrawal of electron density from the closest Pt atoms only. When O 2 is adsorbed on the (111) facet of the alloyed Pt 32 Ti 6 nanoparticle, Pt is found to have a negative charge at the initial state and a positive charge at the nal state, while on the (100) facet, the Pt atoms are positive for all states.
3.2.5 Conclusions. There are several conclusions that can be drawn from the 38 atom system. It is possible to see that there are signicant differences in the Pt 38 and Pt 32 Ti 6 systems, not only in adsorption energies but also in the way dissociation proceeds. Larger dissociation barriers are observed for the Pt 32 Ti 6 system. This is to be expected because oxygen is more weakly adsorbed onto the Pt surface of the alloyed cluster, hence the O-O bond is less activated and it therefore takes more energy to dissociate the O 2 molecule. Furthermore, for the Pt 38 cluster, a higher dissociation barrier is observed for the (100) facet whereas for Pt 32 Ti 6 there are similar barriers on the (111) and (100) facets. Once again, this coincides with the larger values of adsorption energies associated with the (111) facet for the Pt 38 system and the (100) facet for the Pt 32 Ti 6 system. Table 3 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. 2 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. The type of the bond is shown in brackets according to Fig. 2. All values are given inÅ Pt-X centre   IS  TS  FS  IS  TS  FS  IS  TS  FS  IS  TS [2] 2.65 [2] 2.69 [2] 3.27 3.26 2.95 3.43 [3] 3.44 [3] 2.93 [ [3] 3.55 [3] 2.98 [3] [3] 2.79 [3]  Finally, barrier-free dissociation is observed on the (111) facet of the Pt 38 cluster which appears to be due to signicant distortions of the facet. There are greater energetic costs associated with distorting the Pt 32 Ti 6 cluster, compared with Pt 38 cluster (Table 2). Although according to the cluster geometries there is greater distortion of the Pt 38 cluster. This suggests that the presence of the octahedral Ti core in the Pt 32 Ti 6 cluster stabilises the Pt shell and makes the structure more rigid, while Pt 38 nanoparticle is more exible and the surface Pt atoms become more easily distorted, hence more reactive. When compared to the Pt(111) bulk system, the barrier for O 2 dissociation is found to be 0.45 eV, however very little distortion of the (111) surface is observed. This supports the suggestion that it is the distortion of the (111) facet on the cluster that leads to barrier-free dissociation.

79 Atom clusters
3.3.1 Oxygen adsorption. Following the calculations on 38 atom clusters, studies progressed to larger 79 atom TO clusters, considering the pure Pt 79 and core-shell Pt 60 Ti 19 systems. On the surface of the 79 atom TO cluster there are 13 non-symmetry equivalent sites for a pure surface composition, depicted in Fig. 1. As with the 38 atom clusters, studies of these 13 sites are performed, looking at atomic and molecular oxygen. Binding energies are listed in Table 6.
For the pure Pt 79 cluster, the hollow site on the (111) facet is no longer as favourable as the edge-bridge sites on the (100) facet for O 2 and O adsorption. However, the site resulting in strongest bonding is the edge-bridge site of the (111) facet, labelled as site 7. For the Pt 60 Ti 19 cluster, in all cases, the edgebridge site on the (100) facet results in strongest bonding. This was also the case for Pt 32 Ti 6 .
In a similar fashion to the 38 atom system, O 2 dissociation has been investigated at various sites on the (111) and (100) facets of the 79 atom clusters (8, 9, 10 and 11 in Fig. 1). Due to the increased size of the (111) facet, it is no longer benecial to allow dissociation pathways from a certain site to an identical adjacent site, as this would span the entire facet. Following dissociation, any further barriers observed would be due to migration of the oxygen atoms over the surface, which is not the aim of this study. Therefore, for the 79 atom clusters, the pathways on the (111) facet terminate at the central site 12. As with the 38 atom clusters, dissociation on the edge-bridge site of the (100) facet proceeds from position 8 to two adjacent 8 sites.
The central positions on the (111) facet were also investigated, the hollow site 12 for the Pt 79 cluster and site 4 on Pt 60 Ti 19 . However, relatively small O 2 binding energies, particularly on the Pt 60 Ti 19 cluster, are associated with these sites. Hence, nding TS for O 2 dissociation proved difficult on these sites. The terrace site is unlikely to be active for oxygen dissociation due to the weaker Pt-O interactions associated with this position. On the 79 atom clusters, the central three-fold hollow site is surrounded by more favourable edge hollow and bridge sites. This means that it is far more likely that O 2 dissociation will occur at the edge sites of the facet, where stronger Pt-O bonding is observed. Furthermore, low-coordinated edge sites are able to distort to a greater extent (see below) than the central three-fold hollow site, hence facilitating lower barriers to O 2 dissociation.

Distortion and interaction energies.
Representations of the minimised geometries for the IS, TS and FS can be found in Fig. S11-S18. † Table 7 shows distortion energies, for the cluster and oxygen as well as interaction, binding energies and dissociation barriers. The IS studies reveal slightly greater energetic penalties (by an average of 0.11 eV) associated with distorting the Pt 79 cluster compared to the Pt 60 Ti 19 cluster. This same trend is observed for the FS, with greater distortion energies located for the Pt 79 cluster. These trends were also found for the smaller 38 atom clusters. However, the trends for the TS structures differ from those for the 38 atom clusters. For the 79 atom clusters, sites 8 and 11 result in greater distortion energies associated with the alloyed Pt 60 Ti 19 , whilst for sites 9 and 10, greater distortion energies are associated with Pt 79 .
As for Pt 38 , there are greater distortion energies associated with the FS compared to the IS or TS. This once again suggests that the strongly interacting atomic oxygen has a greater ability to distort the Pt 79 surface. For Pt 60 Ti 19 , there are greater distortion energies associated with the TS and FS compared to the IS. RMSD analysis demonstrates that for the Pt 79 cluster, there is generally least structural distortion when O 2 is adsorbed on position 9 on the (111) facet. Although, there is little difference between positions 8 on the (100) facet and 9 on the (111) facet. There is signicant distortion of Pt 79 when oxygen is adsorbed on sites 10 and 11. As with the 38 atom clusters, there is greater distortion of the pure Pt clusters, compared to the alloyed ones. For Pt 60 Ti 19 , there is generally little difference between the RMSD for the cases when O 2 is adsorbed on (111) and (100) facets, suggesting again that Ti@Pt structures are more rigid due to the strong interaction between Ti core and Pt shell.
When comparing the (111) and (100) facets, it is found that the Pt 79 cluster distortion energy associated with site 8 on the (100) facet is greater than that for site 9 on the (111) facet of the Pt 79 IS structure (Table 7). However, the distortion energies become equal at the TS but are 0.95 eV greater on site 9 for the FS structure. For sites 10 and 11 on the (111) facet, the distortion energy is greater than for site 8 in all cases. The DE(Pt 79 ) values for sites 9, 10 and 11 correlate with the differences between the dissociation barriers between sites. The smallest DE(Pt 79 ) value is for site 9 which also has the largest barrier, whilst site 10 has the largest DE(Pt 79 ) value and smallest barrier. There is less correlation between cluster distortion energies, surface sites and dissociation barriers for the Pt 60 Ti 19 system. DE(Pt nÀm Ti m )/RMSD has also been calculated for the 79 atom clusters. An average of 1.62, 4.05 and 0.64 eVÅ À1 more energy is required to distort the Pt 60 Ti 19 cluster, than the Pt 79 cluster at the IS, TS and FS, respectively. This further demonstrates the signicant energy barriers that need to be overcome in order to distort the Pt 60 Ti 19 cluster compared to the Pt 79 cluster.
Oxygen distortion values for the IS are greater for the Pt 79 system, compared to the Pt 60 Ti 19 system, in all cases. However, at the TS, signicantly greater distortion energies are associated with the Pt 60 Ti 19 clusters. This suggests that, initially, when oxygen is adsorbed on the surface of the Pt 79 cluster, due to the stronger Pt-O interactions, the O 2 molecule is distorted to a greater extent than on the alloyed system, where weaker bonding is observed. However, at the TS, on the more weakly bound Pt 60 Ti 19 system, greater distortion of the O 2 molecule is required, compared to the Pt 79 system. This greater distortion requires more energy and can rationalise larger dissociation barriers on Ti@Pt compared to the pure Pt nanoparticle. The same discussion is also valid for Pt 38 and Pt 32 Ti 6 nanoparticles. O 2 distortion energies correlate with the corresponding O-O distances. Furthermore, the smaller difference in the O-O distances between the IS and TS for the Pt 79 clusters compared to Pt 60 Ti 19 clusters show that TS are "earlier" on Pt 79 . Earlier TS are known to have lower barriers, which is found to be the case in this study.
Very similar dissociation barrier on the (100) facet are located for the 79 and 38 atom clusters (Tables 2 and 7). The dissociation barriers are about twice that for the alloyed clusters (0.62 and 0.66 eV for the Pt 32 Ti 6 and Pt 60 Ti 19 clusters, respectively) compared to the pure clusters (0.32 and 0.34 eV for the Pt 38 and Pt 79 clusters, respectively). However, for the dissociation barriers located on the (111) facet the relationship becomes a little more complicated. Table 7 Cluster (DE(Pt nÀm Ti m )) and oxygen (DE(O 2 )) deformation energies, root mean squared displacements (RMSD) of the cluster, interaction energies (E int ), binding energies (E b ) of O 2 and barrier of O 2 dissociation (DE s ). The ratios of distortion energy to RMSD (DE(Pt nÀm Ti m )/RMSD) are also presented. All energy values are given in eV, RMSD inÅ For the Pt 38 cluster, barrier-free dissociation was observed on sites 6 and 7 on the (111) facet. For the Pt 79 cluster, once again almost barrier-free dissociation is located on sites 10 and 11. However, a dissociation barrier of 0.21 eV is found for dissociation on site 9. When comparing binding energies at sites 9 and 11, there is a small difference of 0.12 eV. Probably this difference is not simply a matter of different Pt-O bonding strengths but is related more to differences in the sites. Sites 9 and 11 are hcp whilst site 10 is fcc. This suggests that the difference in dissociation barriers is probably due to the neighbouring surfaces to which the sites are adjacent. Whilst site 9 is neighbouring a (100) facet, sites 10 and 11 both neighbour (111) facets, implying that the adjacent (100) facet distorts less than an adjacent (111) facet and results in the small dissociation barrier for site 9 on the Pt 79 cluster (see Pt-X centre values in Table 8). Finally, dissociation barriers on the (111) facet of the Pt 60 Ti 19 clusters are similar to that of the (100) facet. Here again, correlation between barriers and Pt-X centre values is found since Pt-X centre values are also similar at both types of facets.

Geometric analysis.
Again, it appears that the more easily distorted shell on the Pt 79 cluster results in the observed barrier-free dissociation. Similar measurements to those performed for the 38 atom clusters, to quantify differences in distortions, are compiled in Table 8 (Fig. 2). For site 8 on the (100) facet, signicant distortion (by an average of 0.33Å) of bond type 2 is observed. However, for the initial and transition states this is unsurprising as O 2 is interacting with the one bond. Therefore, although there is signicant elongation of bond type 2, there is less overall distortion of the cluster. Bond types 3 and 4 are distorted (by an average of 0.42 and 0.56Å, respectively) to the greatest extent for O 2 adsorption on the (111) facet. The elongation of bonds surrounding the hollow sites at which oxygen is adsorbed on the (111) facet leads to greater overall distortions of the cluster.
The Pt-Pt bond lengths of the alloyed Pt 60 Ti 19 cluster are 2.68, 2.84, 2.73, 2.75 and 2.73Å for bond types 1 to 5, respectively. Once again, signicant elongation of bond type 2 is observed on the (100) facet when O 2 is adsorbed, 0.34Å, although as with the Pt 79 cluster, little overall distortion of the cluster is observed, #0.10Å. There is far less distortion of other bond types when studying dissociation on the (111) facet. This is expected as there appears to be far less distortion of the overall cluster geometries upon adsorbing O 2 .
Pt-X centre values for the bare pure Pt 79 cluster are 3.15 and 6.29Å for the top and bottom of the cluster, respectively. For the bare Pt 60 Ti 19 cluster, these values are found to be 3.02 and 6.05 A. Once again, there is considerable distortion of the Pt 79 cluster when O 2 is adsorbed on the (111) facet, with Pt-X centre distances elongated by up to 1.07Å (Table 9). There is less distortion of the IS (111) facet (Pt-X centre -0.06Å) associated with site 9, where a small dissociation barrier of 0.21 eV is observed. Less Table 8 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. 2 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. The type of the bond is shown in brackets according to Fig. 2 Pt-X centre   IS  TS  FS  IS  TS  FS  IS  TS  FS  IS  TS [2] 3.03 [2] 2.96 [2] ---Pt 60 Ti 19 [2] 3.22 [2] 3.04 [2] ---Pt 79 -9
3.3.4 Bader charge analysis. Charge analysis is performed, the results of which are given in Table 10. The charges for the bare Pt 60 Ti 19 cluster are À0.45 and +1.43 for Pt and Ti atoms, respectively. For the pure Pt 79 cluster, similar to the Pt 38 case, a positive charge is found on the Pt atoms interacting with the oxygen. These charges generally get more positive as the system progresses from the initial to nal state. Again, this coincides with the charge on the oxygen becoming more negative.
For the Pt 60 Ti 19 clusters, the charges on the Pt atoms bonded to oxygen generally get less negative as the system progresses from the initial to nal state. Only for the dissociation on the (100) facet are the Pt atoms positively charged for both the transition and nal states. In all cases, the Ti atoms remain positive, generally gaining greater positive charge than Ti atoms in the bare Pt 60 Ti 19 nanoparticle. This is consistent with electron donation from Ti to Pt which in turn donates to O, following the increase in electronegativity. The situation here differs from that on Pt 32 Ti 6 cluster, where the charge on the Ti atoms does not change appreciably when an O 2 molecule is adsorbed. This is likely due to the greater Ti : Pt ratio when comparing the 79 to the 38 atom clusters. The greater ratio of Ti : Pt in the Pt 60 Ti 19 clusters results in similarly negative charges on the Pt atoms, but smaller positive charges on the Ti atoms. This will mean that more charge can be drawn from the Ti core as the system progresses to the FS, which would not be possible for the Pt 32 Ti 6 clusters.
3.3.5 Conclusions. For most of the investigated features of the larger 79 atom clusters, it is possible to see similar trends to the 38 atom clusters. This implies that the present trends can be generalised also to somewhat larger nanoparticles, approaching the size of particles present in common experimental catalytic studies. For the pure Pt 79 clusters, essentially barrier-free dissociation barriers are observed on the (111) facet for sites 10 and 11. This coincides with signicant distortions of the (111) facet. However, for site 9, less distortion of the (111) facet is observed and a small dissociation barrier of 0.21 eV is found. This difference is attributed to stabilisation effects of the neighbouring (100) facet. As with the 38 atom cluster, a similar dissociation barrier of 0.34 eV is found at site 8, for the Pt 79 and site 5 for the Pt 38 models, on the less distorted (100) facet. Once again, dissociation barriers are observed for all sites on the Pt 60 Ti 19 cluster, which are attributed to a notably more structurally rigid outer Pt shell when the Ti core is present.

Nanoparticles vs. slab models
We found that the three-fold fcc site on the Pt(111) slab has similar binding energies to the central three-fold fcc site (position 12) on the Pt 79 cluster, À0.86 and À0.88 eV, respectively, though, as mentioned previously, position 12 on Pt 79 is not favourable for O 2 dissociation. It is therefore suggested that the central three-fold fcc site on Pt 79 is unlikely to facilitate oxygen dissociation, due to more favourable edge hollow and bridge sites. These sites are absent on the slab Pt(111) model (as no steps or defects are included in the model) it is therefore more likely that dissociation will occur at these three-fold fcc hollow sites, however with a notable barrier of 0.45 eV. The rigidity of the bulk slab leads to generally weaker Pt-O bonding compared to the majority of sites on the Pt clusters. However, Pt-O bonding is found to be generally stronger than on the clusters where alloying leads to changes in electronic effects that results in the weaker boding, as discussed earlier. Hence, the dissociation barrier on the slab model is found to lie in between the Pt clusters, with low dissociation barriers coupled with stronger Pt-O bonding, and the Ti@Pt clusters with higher dissociation barriers and weaker Pt-O bonding.

Surface exibility
From the discussion in subsections 3.2.3 and 3.3.3, we suggest that surface exibility has a profound effect on the potential of catalysts to activate O 2 dissociation. It is therefore of interest that Pt(111) surface lacks the ability to distort and therefore displays very different properties for oxygen dissociation when compared to pure Pt nanoparticles. We have further shown that surface exibility is not intrinsic property of nanoparticles. Core-shell interactions stabilise the Pt shell of Ti@Pt clusters reducing exibility. Calculating DE s /RMSD gives an idea of the dependence of the dissociation barrier on surface exibility. Values for this ratio are presented in Table 11 for the 38 and 79 atom clusters. The relationship between the RMSD at the TS and dissociation barrier DE s is plotted in Fig. S3, † while a plot of DE s /RMSD against E b is presented in Fig. S4. † Signicantly lower DE s /RMSD values are obtained for the 3-fold hollow sites on the Pt 38 (111) facet, where barrier free dissociation occurs. Higher values are found for all positions on Pt 32 Ti 6 as well as position 5 on Pt 38 . This shows a strong relationship between the dissociation barrier and cluster distortion. For Pt 79 , signicantly lower values are obtained for the 3-fold hollow sites 10 and 11, where barrier free dissociation occurs. DE s /RMSD for positions 8 and 9 on Pt 79 are higher than those for 10 and 11 on Pt 79 , but lower than all positions on Pt 60 Ti 19 . In general, values for Pt 79 are comparable with those for Pt 38 , one more indication that the O 2 dissociation barrier and cluster distortion are strongly related.
The DE s /RMSD for the Pt(111) surface is 9.00 eVÅ À1 . This is greater than for all positions on Pt 38 or Pt 32 Ti 6 . The DE s /RMSD values for the Pt(111) slab are greater than those for Pt 79 . This once again demonstrates the very important differences between the Pt clusters and slab. For the Pt 60 Ti 19 cluster, the majority of the DE s /RMSD values are greater than those for the slab (excluding position 11), due to the reduced oxygen adsorption energy, coupled with the lack of exibility of the Pt shell.

Conclusions
We found that when the adsorption strength of the O 2 molecule on the cluster surface increases, the dissociation barrier will subsequently decrease. Hence, dissociation barriers on the alloyed Ti@Pt clusters would be found to be greater than those for the pure Pt clusters that exhibit larger E b values. Further trends, outlined below, were discovered.
Pure Pt clusters are easily distorted when O 2 is adsorbed on the (111) facet. Furthermore, sites which are relatively easily distorted facilitate barrier-free dissociation of O 2 , a trend which is not only seen for the small 38 atom clusters but also the larger 79 atom clusters. As for the alloyed Ti@Pt clusters, in all cases signicant barriers are observed for all sites, which are greater than the barriers found for the pure Pt clusters.
The presence of the O 2 dissociation barriers for the Ti@Pt clusters is attributed to rigidity enhancement of the Pt shell by the Ti core. Signicant electron donation is observed from Ti to Pt suggesting strong interactions between the two, which coincides with signicantly less distortion of the Ti@Pt clusters, upon binding O 2 , when compared to the pure Pt clusters.
The presence of the barrierless dissociation on the (111) facet of the pure Pt cluster suggest that small Pt clusters would efficiently activate O 2 . However, the relatively strong adsorption strength of oxygen to the Pt surface, compared to the alloyed Ti@Pt cluster found in previous studies, means that it would be difficult to remove the resulting oxygen species from the pure Pt cluster surface. Therefore, whilst O 2 dissociation would require greater energetic input on the surface of the Ti@Pt clusters, the resulting species (following further transformations to e.g. H 2 O or H 2 O 2 ) would be easier to remove from the surface due to the weaker Pt-O interactions compared to the pure Pt cluster.
A very attractive development in the direction of optimal catalyst properties, resulting from ndings of the present study, would be substitution of Ti in the core of Pt-based bimetallic particles by another metal (M). The ideal M core would weaken adsorption of atomic oxygen compared to pure Pt, to allow for fast ORR kinetics in the later stages of the reaction (as Ti does), but form weaker Pt-M bonds than Pt-Ti, thus maintaining the kinetic exibility of the Pt shell which is advantageous for O 2 dissociation.