Stability of oxidized states of ceria-supported PtOx particles under a wide range of gas-phase conditions

Nanostructured materials based on non-inert oxides CeO2 and PtyOx play a fundamental role in catalyst design. However, their characterization is often challenging due to their structural complexity and the tendency of the materials to change under reaction conditions. In this work, we combine calculations based on the density functional theory, a machine-learning assisted global optimization method (GOFEE) and ab initio thermodynamics to characterize stable oxidation states of ceria-supported PtyOx clusters in different environments. The collection of global minima for different stoichiometries resulting from the global optimisation effort is used to assess the effect of temperature, oxygen pressure, and support interactions on the phase diagrams, oxidation states, and structural properties of the PtyOx particles. We thus identify favoured structural motifs and O/Pt ratios, revealing that oxidized states of ceria-supported particles are more stable than reduced ones under a wide range of conditions. These results indicate that studies rationalizing activity of ceria-supported Pt clusters must consider such oxidized states, and that previous understanding of such materials obtained only with fully reduced Pt clusters may be incomplete.


INTRODUCTION
Nanostructured materials based on ceria (CeO2) and Pt have a wide range of applications in catalysis, such as in the three-way conversion in automobile exhausts, 1 in anode 2 or cathode 3 materials of fuel cells, or for mediating the water gas shift reaction, 4 among others. 5 CeO2 is typically used in such materials as a non-inert support for the more active Pt phase, leading to intricate metal-support interactions that affect the electronic structure and chemical properties of both the metal and the oxide. 4,[6][7][8] These electronic metal-support interactions further complicate the already challenging task of characterizing the properties of nanostructured catalytic materials, which are typically structurally complex. Their size, structure, and oxidation state not only depend on preparation conditions, but also often undergo significant transformations under reaction conditions, as revealed by in situ or operando spectroscopic techniques. [9][10][11] These structural and environmental complexities therefore hinder the straightforward computational modelling of working heterogeneous catalysts by means of first principlesbased approaches. 12,13 For systems based on Pt and ceria, Pt can be found in the form of nano-or subnanoparticles of varying size, 4,7,14,15 or as single atoms either anchored to the ceria surface 2, [16][17][18] or inserted in the ceria lattice. [19][20][21] Atomically dispersed Pt on ceria substrates has been studied extensively by means of combined experiment and computational approaches during the last decade because they allow to significantly increase specific activity for different reactions. 2,17,22 In such composites, Pt is often found in cationic form (i.e. Pt n+ species with n= 1, 2, or 4) either occupying Ce positions of the ceria lattice or deposited on undercoordinated sites of ceria substrates. The oxidation state of Pt atoms depends on their coordination environment and on the stoichiometry of ceria substrate, which can either accept or donate electrons by varying the occupation of the Ce4f states (reducing Ce 4+ cations to Ce 3+ and vice versa) and/or the amount of O in the ceria lattice.
Atomically dispersed Pt has often been distinguished from metallic nano-or subnano-Pt particles by the characteristic shifts of cationic Pt in X-Ray Photoemission Pt particles have considered non-oxidized states of Pt particles. [27][28][29][30] In addition, the majority of the aforementioned models (with notable exceptions) 25 were constructed by rather heuristic trial and error approaches, instead of using automated and unbiased global optimization or sampling approaches, which would ensure that the constructed models correspond to stable structures of the represented systems.
The use of sampling methods based on Monte Carlo approaches or of global optimization methods such as evolutionary algorithms have been available for years and applied quite successfully to determine the structure of supported metal or oxide clusters. 25,[31][32][33][34][35][36][37][38] Of particular interest to characterizing the oxidation states of supported metal clusters are approaches that combine global optimization of various stoichiometries with a subsequent thermodynamic analysis, 35,36 or those that directly sample structure and stoichiometries under given conditions using grand canonical approaches. 25,32 The resulting phase-diagrams allow to pinpoint which states are stable under which conditions, relying on well-defined and stable structural models.
In order to identify the stable structures and oxidation states of ceria-supported Pt particles, we therefore combine a novel global optimization method with ab initio thermodynamics. We focus on the characterization of prevailing structural motifs, the effects of conditions on the stability of different oxidation states, and the role of the ceria support. In particular, we use a machine-learning assisted algorithm for the exploration of the configurational space. 39 Once the most stable structures have been determined for the targeted stoichiometries, their Gibbs Free energy of formation is evaluated under varying conditions by means of ab Initio thermodynamics (AITD). 40,41 A consistent picture emerges for the formation and oxidation of both free-standing and ceria-supported PtOx particles, revealing support-effects on the structural and compositional properties of PtOx clusters, and the changes induced by exposure to different environmental conditions. Oxidized states of PtOx clusters are found to be prevalent under a wide range of reaction conditions.

METHODS AND COMPUTATIONAL DETAILS
We carry out a systematic global optimization study based on Density Functional Theory (DFT) calculations and the "global optimization with first-principles energy expression (GOFEE)" 39 method in order to elucidate the stability of PtOx oxidation states under different conditions, the effects of particle size and a CeO2(111) support, and the overall electronic structure of these systems.
We target PtyOx clusters with y = 3 or 6 and x = 0 -2y. Both free-standing and CeO2(111)-supported structures are evaluated. For the CeO2(111)-supported structures, only the supported particles are globally optimized, whereas the atoms of the CeO2 surface are kept in their bulk-terminated positions. The structural characterization of each targeted stoichiometry consists on obtaining the configuration with the lowest internal energy, i.e. the Global Minimum (GM). Once the GM has been characterized for all the considered stoichiometries of the system, AITD is used to evaluate the free energies of each system and to generate the corresponding phase diagrams. In this section, we describe the global optimization strategy using GOFEE, the DFT calculations, and the AITD approach used.

GOFEE method and global optimization strategy
The GOFEE method allows to reduce the number of energy and force evaluations carried out at the DFT level by training, on-the-fly, a surrogate machine-learning energy model. This model is used to carry out local relaxations of every evaluated candidate and to guide the exploration of conformational space, which supposes a considerable improvement in computational efficiency with respect to other algorithms. 31,38 The GOFEE code therefore relies o a selected number of single point calculations at the DFT level, circumventing the need for carrying out more demanding local relaxations at costly levels of theory.
For each considered stoichiometry, the method follows the subsequent algorithm (illustrated in Figure 1): 1. An initial population of structures is generated randomly and its energy evaluated at the selected level of theory (DFT in our case, see below for more details).
2. The surrogate model is trained with these evaluated structures and their energies, and the structure population updated.
3. New candidates are generated. 4. The new candidates are locally relaxed using the surrogate model. 5. The most promising candidate according to an acquisition function is evaluated explicitly by DFT and added to the population.
6. The surrogate model is retrained with the updated population. Subsequent cycles start on step 3.
The number of cycles is strongly related to the quality of the putative global minimum structure found, up to a certain point where the algorithm converges (not always to the real global minimum) . Convergence is reached sooner for smaller systems, and we therefore allow a different of cycles for structures of different size: -200 cycles for free-standing Pt3Oy stoichiometries.
-800 cycles for supported Pt6Oy stoichiometries. Our approach to optimize the structure of PtOx particles uses five different levels of theory (i.e. combinations of parameters, functional, corrections, and structural models).
The single-point calculations executed during each GOFEE run are carried out using lowlevel settings (see below for more details). All evaluated structures are subsequently filtered and relaxed at increasing levels of theory using low-level, mid-level and highlevel local relaxations. These levels are briefly summarized Figure 2 and described in more detail in the following sections.
Before each set of local relaxations at an increased level of theory, structures are filtered to avoid duplicates by using the bag-of-bonds method. 31 This sorts the interatomic distances of a particle by length, and compares this list of distances between particles.
Two particles are considered equal if max and dmax, as defined in 31

Density functional theory calculations
The electronic structure of the considered systems have been determined by means of periodic calculations based on DFT. To this end, the Vienna Ab Initio Package (VASP) 42

Ab Initio thermodynamics
Having obtained the putative GM for all of the considered stoichiometries, it is necessary to asses which of the compositions is most stable under different environmental conditions. Taking the formation energies using only the as-calculated absolute DFT energies is insufficient, since the stability of each oxidation state depends on how easy or hard it is to obtain O atoms from the gas-phase environment in contact with these particles. We therefore carry out an ab initio thermodynamics (AITD) analysis, which allows to obtain Gibbs free energies of formation as a function of macroscopic properties of the system from energies obtained by ab initio methods at 0 K.
We calculate the Gibbs free energies of each state within the canonical ensemble.
This assumes constant volume, temperature, and number of atoms of the system. We further assume the PtyOx particles to be in equilibrium with a gas-phase reservoir of O2 at a given T and pO2. This means that their composition is going to be influenced by the T and pO2. For any structure, the Gibbs free energy (G) is calculated as shown in equation 1: Where the internal energy (U) can be approximated as the total energy obtained in the DFT calculations of the system. F vib and F conf correspond to the vibrational and configurational contributions to the free energies, respectively. The Gibbs free energy of formation for the oxides is, thus, obtained by the difference of the Gibbs free energy of the oxide with the Gibbs free energy of the fully reduced cluster and the chemical potential of oxygen, related to temperature and pressure, as shown in equation 2.

∆ (
For the solid phase systems, the ∆F conf and ∆(pV) terms are not significant at the pressures and temperatures typical of operando catalytic processes. 40,52 The F conf and pV terms are similar for the different stoichiometries and cancel out when calculating relative (e.g. formation) free energies.
In turn, the vibrational contribution F vib of small and supported metal-oxide clusters were found to depend on the low frequency contributions of the metal atoms only. The difference between clusters with the same number of metal atoms is therefore small. The differences in zero-point energy contributions are more significant, but proportional to the number of O atoms and accountable in an approximate way (~ 0.1 eV per O atom in the particle). 36 The chemical potential of oxygen in the gas phase is evaluated in terms of the temperature and partial pressure of the molecular oxygen reservoir and the ZPE-corrected DFT energy of molecular oxygen. Hence, for any value of the temperature, the chemical potential can be expressed as shown in equation 3: With these approximations, the Gibbs free energy of formation for any PtyOx, particle in any given chemical potential of oxygen is obtained as: For the free-standing particles, the same approximations are used, substituting the DFT energy of the ceria supported reduced particle by that of the free-standing particle.
We use the same assumptions and approximations about the ∆F conf , ∆F vib , and ∆(pV) terms as for the ceria-supported particles, although these might not hold as well.
Nonetheless, a complete vibrational analysis of the free-standing particles falls out of the scope of the present work.
A useful analysis tool obtained from this treatment are the phase diagrams where the most stable phase at different chemical potentials corresponds to the state with lowest ΔGf.

Structure, growth, and oxidation of the PtyOx particles
We begin by describing the minimum energy structures found during the global minimum search for which the GOFEE method was employed. The considered PtyOx stoichiometries are y=3 or 6 and x=0 -2y for 20 different stoichiometries both freestanding and supported in a CeO2(111) surface, which amounts to 40 systems differing in composition.
For each system a large number of structures were evaluated with DFT (up to 1613 for a single run of the most complex system -ceria supported Pt6O12) in order to locate the GM. Each stoichiometry is run at least twice, and if the minimum energy structures of the runs don't coincide a third run of the algorithm is performed, which ensures that the obtained most stable structures are the best guess for each stoichiometry. After subsequent relaxations at increasing levels of theory, ~ 10 structures per stoichiometry are recalculated at the final HSE06 level.
The global minima obtained for the gas phase structures are depicted in Figure 3.
For the fully or highly reduced structures, triangular Pt3 motifs are prevalent and the structures are quite planar. As the particle becomes oxidized, it loses flatness in order to accommodate the new oxygen atoms while maintaining at least a mirror plane. This is prevalent for Pt6Ox stoichiometries in low oxidation states but it loses importance for higher oxidation states. In higher oxidation states the size of the particle forces it to  where an oxygen is located between the three platinum atoms. This is favorable because it forms three linear O-Pt-O motifs with the oxygen positions in the surface, which confers enough stability to the particle to compensate the differences between the Pt-Pt bond length and the distance between surface oxygen atoms.
The inequivalence in surface oxygen distance and Pt-Pt bond length are less notable with the Pt6Ox stoichiometries due to the increase in degrees of freedom, which allow the particle to adapt better to the surface. However, the tendency to form linear O-Pt-O bonds still proves to be significant since the observed minima include these motifs in all their structures, often bonding using O atoms from the ceria lattice to construct these linear motifs. For low and medium oxidation states, the particles form more compact structures (e.g., Pt6O9/CeO2(111)) where O atoms are shared between multiple platinum atoms.
However, as particles become more saturated with oxygen atoms, they tend to spread over the surface, increasing the average coordination of Pt atoms while avoiding oversaturating individual platinum atoms.
Therefore, the two main differences between the conformations adopted by the CeO2(111) supported particles and the free-standing particles are due to the topology of the CeO2 surface and to the possibility to form the aforementioned stable motifs with the O atoms of the ceria surface.

Phase diagrams of the PtyOx global minima
The variation for the free energy of the global minima found for each stoichiometry at different chemical potentials of the molecular oxygen reservoir is evaluated by means  The phase diagrams for the free-standing PtyOx and CeO2(111)-supported PtyOx systems is shown in Figure 5, indicating the more stable stoichiometry for each value of μO.
Common to all systems, higher values of μO (corresponding to oxidizing environments) increase the stability of stoichiometries with a higher oxidation state, a direct consequence of the thermodynamic equilibrium with a molecular oxygen reservoir from which it is easier to extract O from (i.e. with a higher chemical potential to react).
Notably, partially oxidized states are stable for a wide range of μO, including very reducing conditions of down to ΔμO ~ 3 eV.
For the free-standing structures and the ceria-supported Pt3Ox, the most stable structure at ΔμO=0 eV (T= 0K) is the structure with the Pt3O5 stoichiometry. For the free- These results indicate that the ceria surface contributes to stabilizing more oxidized states of the PtOx particles for some regions of the phase diagrams, but stabilizes more Odeficient states for others. A general stabilization of more O-deficient states would be expected due to the oxidizing behavior of the ceria surface, but our calculated phase diagrams demonstrate that intricate effects related to the kind of structures and structural motifs that each stoichiometry can form are more relevant than the oxidizing capacity of ceria.

Atomic charges of global minima
We now focus on the evolution of atomic charges in Pt atoms of the considered systems upon oxidation. The atomic charges (calculated by means of Bader's atoms in molecules approach) 53 of the Pt atoms of the most stable oxidation states of each system are shown on Figure 6. All considered stoichiometries follow similar trends in their charge distribution. As expected, as the system increases its oxidation states, so does the average charge. It is also notable that the effect of the oxygen atoms in the ceria surface on the charge of the platinum atoms is slightly lower than that of the oxygen atoms adsorbed in the platinum cluster. This is visible when comparing the ceria-supported Pt3O5 structure to the free-standing counterpart. Despite the contact to atoms from the ceria surface, the Pt atoms of the Pt3O5 particle appear to be more oxidized for the free-standing case. Thus, although the CeO2(111) surface has an oxidizing effect on the particles and allows to complete certain stable structural motifs, bonds formed with O atoms from the ceria lattice are weaker and less oxidizing than those with O atoms directly on the PtOx particles.

Conclusions
In this work, a systematic global optimization scheme has been employed in order to characterize free-standing and CeO2(111)-supported PtyOx structures, with y=3 and 6 and x=0-2y. The global optimization for each stoichiometry has been carried out with the GOFEE method, a novel approach which has proven to be fast and computationally efficient.
The morphological analysis of the obtained minima has revealed several structural motifs that are present in stable structures. Namely, the linear O-Pt-O, angled Pt-O-P (80-100º), square-planar PtO4 formations, and the quasi-molecular O pairs. The CeO2 (111) surface participates on the formation of such motifs, which leads to rather spread out structures for highly oxidized states.
The AITD analysis of the obtained global minima has revealed that oxidized particles are stable over a rather wide range of . Although the CeO2(111) surface has a slightly oxidizing effect, it generally does not stabilize states with lower oxidation states.
This is related to the fact that O atoms from the CeO2(111) have a much weaker oxidizing effect than O atoms directly on the PtOx clusters, as revealed by a detailed charge analysis.
In summary, the presented approach and resulting analysis constitutes a wellgrounded and computationally efficient strategy for constructing representative structural models of the free-standing and CeO2(111) supported PtOx clusters. This constitutes an improvement over non-machine-learning assisted global optimization algorithms or still prevalent human-guided approaches. It helps cement the combination of AITD with GO methods as a necessary step to characterize the structure and oxidation states of active sites preceding DFT-based mechanistic studies in catalysis.
The results of this work indicate that studies rationalizing activity of ceriasupported Pt clusters must consider oxidized states, and that previous understanding of such materials obtained only with fully reduced Pt clusters may be incomplete.
Forthcoming studies comparing the chemical and catalytic properties of the different oxidation states will therefore be of pivotal importance. We expect these findings to be relevant also for other metal clusters on both inert and non-inert oxide supports such as ZnO and TiO2.

Acknowledgements
Authors gratefully acknowledge support by the Spanish grants PGC2018-093863-B-C22 and MDM-2017-0767 as well as by the grants 2018BP00190 (for A.B.) and 2017SGR13 of the Generalitat de Catalunya. Computer resources have been provided by the Red Española de Supercomputación. This study was also supported the by European COST Action CA18234.