Oxidation and de-alloying of PtMn particle models: a computational investigation †

We present a computational study of the energetics and mechanisms of oxidation of Pt – Mn systems. We use slab models and simulate the oxidation process over the most stable (111) facet at a given Pt 2 Mn composition to make the problem computationally a ﬀ ordable, and combine Density-Functional Theory (DFT) with neural network potentials and metadynamics simulations to accelerate the mechanistic search. We ﬁ nd, ﬁ rst, that Mn has a strong tendency to alloy with Pt. This tendency is optimally realized when Pt and Mn are mixed in the bulk, but, at a composition in which the Mn content is high enough such as for Pt 2 Mn, Mn atoms will also be found in the surface outmost layer. These surface Mn atoms can dissociate O 2 and generate MnO x species, transforming the surface-alloyed Mn atoms into MnO x surface oxide structures supported on a metallic framework in which one or more vacancy sites are simultaneously created. The thus-formed vacancies promote the successive steps of the oxidation process: the vacancy sites can be ﬁ lled by surface oxygen atoms, which can then interact with Mn atoms in deeper layers, or subsurface Mn atoms can intercalate into interstitial sites. Both these steps facilitate the extraction of further bulk Mn atoms into MnO x oxide surface structures, and thus the progress of the oxidation process, with typical rate-determining energy barriers in the range 0.9 – 1.0 eV.


Introduction
The chemical state of catalyst nanoparticles (NPs) under reaction conditions, and in particular the chemical state of their catalytically active surfaces, is a topic of great interest and active current research due to its implications in the chemical activity and selectivity of the catalysts 1 as well as in a wealth of other phenomena, including corrosion, surface treatment, etc. [2][3][4] In heterogeneous catalysis, in particular, the presence and role of strongly interacting oxygen species, ubiquitous in all oxidation processes, in affecting structural and chemical dynamics at the NP surfaces has been long debated. Pure NPs [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] have been thus investigated, at both experimental and theoretical levels and in both surface-science model setups and under progressively more and more realistic (in situ) reaction conditions. The importance of surface oxidation in modulating the system work function, surface faceting and restructuring, and corrugation (insertion of oxygen atoms into subsurfaces) has been demonstrated and quantitatively discussed. Oxidation mechanisms of monometallic surfaces and particles have also been investigated for monometallic NPs of, e.g., Pt 20 and Pd, 19,20 suggesting a possible role of amorphization at high temperatures. Fewer studies have dealt with the more challenging topic of nanoalloy oxidation, [21][22][23][24][25][26][27] where the additional phenomenon of surface segregation induced by ligand adsorption offers a further complication. 28 Metal nanoalloys in fact undergo dynamic processes under reaction conditions, especially upon adsorption of strongly interacting species such as oxygen atoms. Less accumulated knowledge is however available on NP oxidation and oxidation-induced segregation of nanoalloys, due to the complexity of the phenomena involved and despite the critical role that rigorous information on these effects could have in understanding and eventually controlling surface structure, composition, and catalytic activity. To take an example, in the aqueous phase reforming (APR) reaction for hydrogen production, 29,30 Pt catalysts show a good catalytic performance, but the rate of hydrogen yield strongly depends on the amount of Pt loading. 31 Thus, in an effort to reduce the percent loading of the expensive Pt element, Pt-based bimetallic nanoalloy catalysts such as Pt-Mn have been proposed and demonstrated to be efficient catalysts and potentially superior in catalytic performance for hydrogen production compared to Pt catalysts. However, the Pt-Mn systems suffer from dealloying/oxidation of the electropositive element and leaching into the aqueous solution. 32 Oxidation-induced dealloying of the more electropositive element in a bimetallic system is thus an important concern, that a deeper understanding of its atomistic mechanisms could help avoid or at least minimize. Previous theoretical work has shed some light in this eld, especially considering the kinetics of atomic inter-diffusion in metal clusters and particles. Both rst-principles sampling of selected kinetic paths to atomic exchange and rearrangement and more systematic stochastic approaches using force-elds have been utilized, [33][34][35] pointing to a critical role of vacancy formation and surface diffusion/displacements in these phenomena. Despite this pioneering work, to the best of our knowledge no systematic investigation of the surface oxidation and mechanisms of multi-metallic systems has been conducted so far.
To make progress in this direction, here we investigate via computational simulations the energetics and atomistic mechanisms of the oxidation (and the resulting dynamics of chemical ordering, with special attention to Mn leaching) of Pt-Mn systems. To reduce the computational effort to manageable levels, we use slabs modeling the fcc (111) extended facets of alloy nanoparticles, and we limit our study to the Pt 2 Mn composition. We use Density-Functional Theory (DFT) as a rst-principles basis of energetics, and accelerate the sampling of the Potential Energy Surface (PES) and associated reactive mechanisms by mapping DFT onto Neural Network Potentials (NNPs). We do this in an incremental protocol which uses standard Molecular Dynamics (MD) and accelerated MD in the form of meta-Dynamics (m-Dyn) to generate candidate congurations whose DFT energy and forces are used as a database to interpolate the potential energy surface (PES) via the NNPs. We nd that oxidation of the Pt-Mn system goes through successive steps, in which surface Mn atoms dissociate O 2 and generate MnO x supported surface-oxide species (with x the degree of oxidation), simultaneously creating vacancy sites in the metallic framework. These vacancies favor the intercalation of oxygen or bulk Mn atoms into sub-surface interstitial sites, thus allowing the surface diffusion (segregation) of Mn atoms in deeper layers.

Computational approach
First-principles energetics was obtained via Density Functional Theory (DFT) calculations using the Quantum Espresso (QE) code. 36,37 Perdew-Burke-Ernzerhof (PBE) 38 functionals with GBRV's ultra-so pseudopotential 39 were used to calculate an exchange-correlation energy. A plane-wave cutoff of 200 Ry and a kinetic cutoff of 40 Ry were employed. The Grimme-D3 (ref. 40) scheme as implemented in the QE package was adopted to account for the van der Waals dispersion.
We create slab models of size (3 Â 3 Â 6) and we focus on the composition Pt 2 Mn which is of interest because it is around the composition investigated in several catalytic applications 32,41 and also because it seems that in the bulk phase diagram there is a competition between different chemical orderings: L1 2 , L1 0 and a layered phase in which 2 Pt (111) planes alternate with 1 Mn (111) plane. The lattice parameters were DFT-relaxed for a bulk structure built as a mixture of L1 2 and L1 0 chemical ordering as shown in Fig. S2 of the ESI. † Working with 6layer Pt 2 Mn (111) slabs, we used a 6 Â 6 Â 3 k-point to sample the Brillouin zone for the bulk structure. Aer relaxation of the bulk, a vacuum space of 15Å in the Zdirection was added to avoid the interaction between periodic images. In all m-Dyn and DFT simulations, we keep the atoms in the three bottom layers frozen, while allowing the rst three layers to fully relax. The convergence energy threshold for the self-consistent-eld (SCF) was set to 1 Â 10 À6 Ry and 3 Â 3 Â 1 kpoint grids were applied to sample the Brillouin zone.
In order to obtain transition states (TS) and energy barriers (E a ) for the PtMn oxidation, we performed two steps of transition state search. The nudged elastic band (NEB) method 42 was used in an initial TS calculation to nd an approximate minimum energy path and TS. Then, a NEB climbing-image (CI-NEB) 43 simulation was further performed to locate an accurate TS structure and energy. All NEB and CI-NEB calculations were performed using 6 intermediate images and the convergence on the force was set to 0.1 eVÅ À1 .
The E a was calculated as: where E TS and E IS refer to the total energy of the transition state and its preceding initial state, respectively. The Neural Network Potential (NNP) is a versatile tool which can be used in several technologies especially in materials science. 44,45 The generation of the NNPs, also named machine-learning potentials or machine-learning force-elds, was realized via the Behler-Parrinello method 44 as applied to a database of DFT congurations with associated energy and forces. In this study, we use the NNPs as the potentials to investigate reliably possible mechanisms for the oxidation of bimetallic Pt-Mn catalysts. We name the successive NNP generations as NNP1, NNP2, etc. in sequential order, also of increasing accuracy. We use the Behler-Parrinello formalism as implemented in n2p2. 46,47 For the architecture of the NNP, neural networks with 30 nodes in two hidden layers for each element were employed to t the Potential Energy Surface (PES), which is decomposed into the sum of atomic energies that depend on the local environments of atoms. In this work we apply a cutoff radius of 6Å to include all relevant interactions. All parameters of the NNP run are listed in Section S1 of the ESI. † The construction of the NNPs is heavily data-driven and relies on the accurate description of the atomic environment, which is realized via symmetry functions in the Behler-Parrinello method. Both the collection of DFT reference congurations and the choice of symmetry functions are essential for accurately reproducing the DFT PES. As described below, we extract DFT reference congurations from Molecular Dynamics (MD) or meta-Dynamics (m-Dyn) runs using an NNP. In particular, for the m-Dyn simulations that sample a vast reaction congurational space, the importance of collecting reference structures has been further leveraged. Here we used the active learning scheme underpinned by the CUR matrix decomposition method 48,49 that can incrementally and iteratively select new representative congurations from MD and m-Dyn simulations driven by each NNP/CV combination. The CUR decomposition method enables us to evaluate the importance of rows and columns that correspond to atoms and symmetry functions in our case. Therefore, the representative structures and the symmetry functions that best describe the atomic environment can be selected. The source codes for choosing symmetry functions are listed in Section S2 in the ESI. † In this work, the meta-Dynamics (m-Dyn) 50 method as implemented in PLUMED soware 51 is employed. m-Dyn is an efficient method for enhancing sampling in molecular dynamics simulation and determining the potential energy surface that provides the information of chemical reaction mechanisms. The details of the m-Dyn technique and its application in various catalytic elds were described by A. Barducci,M. Parrinello,et al. 52 In detail, the system can be dened as a function of a nite number of collective variables (CVs) S a (x), a ¼ 1,2,.d where d means the dimension of the CV space. The obtained potential energy surface and reaction mechanisms from the metadynamics run depend on the choice of the CVs. In this study, we use the coordination number (S ij ) between atom i and atom j as the CV. The expression to calculate the number of contacts between two sets of elements can be dened as P i˛A P i˛B S ij : According to this equation, S ij is equal to 1 if the contact between atom i and j is fully formed. If there is no interaction between i and j, the value of S ij is zero. The actual value of S ij is calculated as a switching function, whose equation is given by: We applied the well-tempered metadynamics 53 to generate the database for the construction of the NNPs and to explore oxidation mechanisms in Pt-Mn systems. The meta-Dynamics (m-Dyn)/NNP simulations were run using the following collective variables (CVs): CV-PtMn, CV-MnO, and CV-SurfMnO. CV-PtMn and CV-MnO refer to Pt-Mn coordination numbers and Mn-O coordination numbers, respectively. These two CVs were mainly used as global collective variables (global-CVs) to generate the training set for NNP constructions and start investigating the oxidation mechanism on various Pt 2 Mn slabs. In a successive stage, we use the coordination number of an individual surface Mn and 4O (CV-SurfMnO) as a local CV to further investigate other relevant oxidation mechanisms. The Gaussian width and height in the m-Dyn approach were 0.05Å and 0.1 eV, respectively. The Gaussian was added to the system every 500 steps of simulation time. The m-Dyn were run at two different temperatures: 300 K and 500 K (simulations at 500 K were used to accelerate the reactions of interest to within 100 ps for computational convenience).
The starting database of congurations for bare and oxidized systems was produced using the ACAT code. 54 We generate 200 structures for the bare system and 200 structures for the oxidized system via a stochastic generation. The details of the structure generation by this ACAT code can be found in ref. 54. The energy and forces of the training structures were evaluated via DFT single point calculations using the chosen DFT approach and the QE code. To investigate (oxidation) dynamics, we employed a variant of current protocols 55-58 engineered to incrementally explore the reactive space of the system. We used the starting database of congurations, energies, and forces to generate a rst NNP1 via the Behler-Parrinello method (see above). We then perform short runs of MD simulations in the canonical ensemble (NVT) using the NNP at a temperature T ¼ 300 K and for a typical time initially very short: t ¼ 1-5 ps, from which a set of single point congurations with associated energy and forces were extracted via the CUR decomposition approach to sample the neighborhood of the initial local minima. This procedure was repeated 5 times. The last NNP (NNP5) was then used to run m-Dyn simulations starting from a set of about 1000 structures with different chemical orderings and 4 oxygen atoms on the surface as initial points. In the m-Dyn runs, we used CV-PtMn and CV-MnO at temperature T ¼ 300 K and for a time initially in the range t ¼ 10-30 ps (in the successive m-Dyn runs, we progressively increased the simulation time up to 600 ps). DFT single-point calculations were then performed on congurations extracted from the m-Dyn runs via the CUR decomposition approach, and added to the DFT database to generate the next NNP version. The idea underlying this strategy is to sample congurations progressively further from the local minima and closer to the saddle points 55,58 as pictorially illustrated in a schematic way in Fig. S1 of the ESI. † In particular, in the initial NNP generations we extracted from the m-Dyn runs the rst "extrapolation warning" congurations, i.e., the rstly appeared m-Dyn congurations for which these structures were estimated to be outside the validity range of NNP prediction (implying that the NNPs are not able to predict the forces and energy errors of these warning structures accurately). Increasing the training set with the "extrapolation warning" structures has been reported as a convenient technique to extend the range of validity of NNP potentials since only missing structures will be further calculated at the DFT level and added to the training set. 46,59,60 As the NNP improved along the various generations, the number of "extrapolation warning" congurations decreased, so that we were able to progressively run the m-Dyn for longer times and include all of the fewer "warning" structures along the entire m-Dyn run in the DFT database. We repeated the above procedure iteratively several times, arriving at NNP12. We then switched to a local CV in the m-Dyn, i.e., CV-SurfMnO, ran m-Dyn simulations at 500 K for 100 ps, and extracted signicant congurations via the CUR decomposition approach to generate an NNP able to describe the reaction PES accurately. We repeated the above procedure iteratively a few times, generating a nal NNP19, with a nal database containing z12 000 structures. The energy and force root mean square errors (RMSEs) on the training set are less than 5 meV per atom and 0.18 eVÅ À1 , respectively. In general, we found that all NNPs starting from NNP12 produce m-Dyn runs with reasonably few warning structures. The low values of RSME imply that NNP19 is capable of describing the potential energy surface of the oxidation process accurately enough to provide paths and mechanisms to be nally double-checked with DFT/NEB. Indeed, the nal step of our protocol (whose results are reported in Fig. 2

Results and discussion
The logical stages of our study are as follows. In Section 3.1 we start from an analysis of the energetics of the bare systems, then we add oxygen adatoms and reassess the energetics, and nally we use global CVs to start exploring the oxidation process. In Section 3.2 we extend the previous results by employing local CVs to trigger further steps in the oxidation process and we analyze them in detail.

Energetics and rst oxidation steps
As anticipated in Section 2, the rst step of our study consisted of generating an initial database of slab congurations for bare Pt-Mn and oxidized Pt-Mn-O systems. On these congurations we calculated energy and forces using the chosen DFT approach and the QE code. We restricted ourselves to fcc (111) slab models and the composition with Pt : Mn ratio ¼ 2 : 1, however varying the distribution of the Mn atoms over the slab framework to explore a wide set of "homotops" (i.e., isomers sharing the same structural framework but differing in chemical ordering). To this purpose we used the ACAT code, 54 and generated stochastically around 200 bare-system congurations. In Fig. 1(a) we report the so-derived relative energies of the homotops with the lowest energies, i.e., the energy difference (E-E 0 ) between the total energy of each model and the total energy of the lowest-energy structure, coloring the data points differently according to the number of Mn atoms present in the top-most surface layer. Without going into a detailed analysis of the results, which would go beyond the scope of the present work, we mention that, around the chosen Pt 2 Mn composition, (i) ordered phases exist in the experimentally-derived bulk Pt-Mn phase diagram, and in particular the L1 0 phase at Pt : Mn ¼ 1 : 1 and the L1 2 phase at Pt : Mn ¼ 3 : 1, in addition to a layered phase in which 2 Pt (111) planes alternate with 1 Mn (111) plane, and (ii) our DFT energetics are consistent with these indications. In particular, we built a bulk structure at the chosen Pt 2 Mn composition as a hybrid mixture of L1 0 and L1 2 phases, as schematically illustrated in Fig. S2 of the ESI, † and we relaxed its lattice parameters, which were then used in the slab simulations aer freezing the unit cell in the directions parallel to the surface and the coordinates of the lower-most 3 layers. From both bulk and slab DFT simulations, we found that Mn has a strong tendency to alloy with Pt: congurations with aggregated Mn clusters were typically found at much higher energies than the ones in which Mn was well-distributed and intermixed with Pt. We also noticed a tendency of Mn to avoid outmost surface positions, but at the selected composition some minimal Mn surface segregation is needed to avoid Mn aggregation. Indeed in Fig. 1(a) the lowest-energy congurations of our slab models exhibit 1 Mn atom at the surface (the lowest-energy pure Pt surface model lies >0.7 eV higher than the global minimum homotop). For the convenience of the reader, the ten lowest-energy congurations in Fig. 1(a) are schematically depicted in Fig. S3 of the ESI. † The situation changes drastically when surface oxygen adatoms are added to the system. We again use the ACAT code to generate initial structures in which 4 O atoms are added randomly to hollow fcc sites of the low-energy models of Fig. 1(a), to produce 200 oxidized structures. The corresponding energetics are shown in Fig. 1(b), where it can be clearly observed that structures with surface Mn are now strongly favored. For the convenience of the reader, the ten lowest-energy congurations in Fig. 1(b) are also schematically depicted in Fig. S4 of the ESI. † Assuming that reduced (non-oxidized) Pt-Mn nanoparticles are produced by the experimental synthetic procedure as is typically the case, these well-alloyed, mostly few-surface-Mn congurations will therefore correspond to meta-stable states aer interaction with an oxidizing environment, and there will be a thermodynamic driving force to transform them into oxidation-induced Mn-surface-segregated and de-alloyed structures. To give an idea, we quote that the reaction energy of the process in which the 1-surface-Mn bare-system global minimum of Fig. 1(a) reacts with 2 O 2 molecules to give the lowest-energy 1-surface-Mn oxidized 4O-model of Fig. 1(b) amounts to À6.96 eV. This thermodynamic preference continues to hold when the free-energy of O 2 molecules is included: the oxidation process is energetically favorable under a wide set of thermodynamic conditions (oxygen dissociation on the surface can be energetically favorable even on the bare Pt surface). 15 Aer having claried the energetics of the initial and nal states of the oxidation process, we started exploring the reaction paths connecting the initial alloyed congurations to the nal oxidation products. To this end, we used metadynamics (m-Dyn) runs and two different collective variables to drive the system's dynamics: CV-PtMn and CV-MnO as dened in Section 2. These are global collective variables (CVs) in which we force the Pt-Mn or Mn-O coordination of all atoms in the system. We expect that these global variables are capable of sampling congurations away from the local minima and progressively closer to the reaction saddle points, as illustrated in Fig. S1 of the ESI. † A representative example of these initial m-Dyn simulations starting from the global minimum of the bare systems (only 1 Mn atom at the surface) to which 4 O atoms are added is provided in Fig. 2(a and b), whose results were obtained using NNP19 in an m-Dyn based on CV-MnO lasting 100 ps at a temperature of 500 K. In Fig. 2(a and b) we report for simplicity only the energy and the geometry of the local minimum states (aer DFT structure relaxation) as extracted from an analysis of the m-Dyn run, although the m-Dyn naturally provides also candidate saddle-point structures and energetics, because we intend to focus attention on the major results of these initial simulations. As apparent in Fig. 2(a), there exists a strong thermodynamic driving force in going from the Initial State (IS) to the rst (Int1) and second (Int2) intermediate states, with drops of more than 1 eV in the DFT energy. This drop in energy is associated with the extraction of the surface Mn atom from the metallic framework into a surface oxide conguration, as apparent in Fig. 2(b). In particular, Int1 corresponds to a MnO 2 surface oxide structure, which then transforms in Int2 into a MnO 3 oxide, that nally rearranges into a slightly more stable Final State (FS) structural isomer with a more modest energy drop of À0.25 eV. Notably, the extraction process leaves a vacancy site in the framework, to illustrate which we have tried to pictorially highlight the so-formed vacancy with a star symbol in the images of Fig. 2(b). As we will see later, the formation of a vacancy is a critical step to give way to successive steps in the oxidation process.
A second representative example of the initial m-Dyn simulations, now starting from a higher-energy state of the bare systems (2 Mn atoms are initially at the surface, to which 4 O atoms are added) is provided in Fig. 3(a and b), whose results were obtained using NNP19 in an m-Dyn based on CV-MnO lasting 100 ps at a temperature of 500 K. In Fig. 3(a and b) we report again for simplicity only the energy and the geometry of the local minimum states aer DFT structure relaxation. Once more, a strong thermodynamic force with steps of 0.65-1.13 eV in the DFT energy drives the system from the Initial State (IS) into the rst (Int1) intermediate state, corresponding to a MnO 2 surface oxide structure, and then to a MnO 3 surface oxide second (Int2) intermediate state, which then rearranges into Int3 and Int4 lower-energy intermediate isomers before extracting the second surface Mn atom into the over-layer in the Int5 and then the FS congurations. For the convenience of the reader, we have pictorially highlighted the vacancy site in the metallic framework with a star symbol in the images of Fig. 3(b). We underline that we are still considering 4 oxygen atoms on the surface: considering that we are now investigating structures with 2 Mn atoms on the top-most layer initially, this corresponds to a situation in which O is "under-stoichiometric", i.e., the system would thermodynamically favor the adsorption of a larger number of oxygen atoms, enough to create a MnO 3 surface oxide structure for both the surface Mn atoms. This is the reason why the drops in energy are generally smaller than in the previous case, and the vacancy sites are in some instances partially lled by the under-stoichiometric Mn 2 O 4 species (e.g., in the FS conguration). Despite this "lean-oxygen" situation, the thermodynamics of the process is still strongly exothermic (and also the NNP barriers suggest viable mechanisms, see below). We do not report examples of m-Dyn runs based on CV-PtMn, but we mention that the picture is qualitatively the same as that obtained using CV-MnO. We can conclude from these results that the global CVs thus far employed are useful to give a rst exploration of the reaction steps of the system. We can observe the diffusion of oxygen atoms on the surface toward the Mn species, and the extraction of Mn atoms from the top-most surface layer to form Mn y O x surface oxides. However, CV-PtMn and CV-MnO are global CVs that do not capture locality phenomena in the oxidation process. In the next subsection we then switched to a local CV, CV-SurfMnO, and used this local CV to trigger further, more localized oxidation mechanisms so as to achieve a qualitatively complete picture.

Later oxidation steps
As discussed in the previous section, the oxidation mechanisms obtained from m-Dyn runs using global-CVs mainly involve Mn and oxygen atoms on the surface: both 1 Mn-and 2 Mn-surface systems tend to form Mn x O y species and leave a vacancy site on the surface of the metallic framework as illustrated in Fig. 2 and  3. However, we observed that the later stages of the m-Dyn runs tended to produce high-energy congurations with dubious physical signicance. To investigate further possible oxidation mechanisms, we then used the local CV-SurfMnO (see Section 2 for the denition of CV-SurfMnO).
First, we ran m-Dyn starting from the global minimum of the bare systems (only 1 Mn atom at the surface, to which 4 O atoms are added) using the local CV-SurfMnO and NNP19 for a total of 100 ps simulation time at a temperature of 500 K. From this m-Dyn simulation we extracted the important structures, conrmed their stability via DFT relaxation, and calculated the DFT saddle points via NEB simulations. As an initial side observation, we note that when we switch from global CVs to a local CV, there is an obvious structure transformation as a function of the change of 1 Mn-O coordination numbers as depicted in Fig. S5. † In Fig. 4(a and b) we plot the DFT energy and geometry proles along the oxidation path in this 1 Mn-surface system. The reaction starts with a conguration in which the surface Mn atom is coordinated to only 1 oxygen adatom (a Mn-O species) as the Initial State (IS) and then forms MnO 2 and MnO 3 surface oxide species at the Int2 and Int3 states with downhill reaction energy changes of À0.83/ À1.00 eV at each step. As discussed in the previous subsection using m-Dyn runs using global-CVs and here conrmed by m-Dyn runs using a local-CV, the formation of the MnO 2 and MnO 3 surface oxides leaves a vacancy site in the metallic framework (the vacancy site in the metallic framework is pictorially highlighted with a star symbol in the pictures). The NEB and CI-NEB calculations allow us to locate the transition states and determine the kinetic barriers at each elementary step of the reaction. The results show that O migrations and surface Mn extraction to form MnO 2 at TS1 and MnO 3 at TS2 require a low kinetic barrier of 0.17 eV for MnO 2 creation and 0.43 eV for the MnO 3 formation (Fig. 4(a)). Aer a vacancy site is created at Int1-Int2, in Int3 a further step (not seen in the simulations of Section 3.1) brings a Mn atom from subsurface into an interstitial site between the topmost rst and second layers next to the vacancy, a position stabilized by the interaction with the Mn atom of the MnO 3 species. This process is nearly isoenergetic, and the barrier at TS3 is 0.45 eV. In the successive step (Int4), the MnO 3 species is pushed back away from the metal framework, and the subsurface Mn overcomes an energy barrier of 0.90 eV to occupy stably the empty vacancy site interacting with one of the surface oxygen atoms, with this latter interaction strongly stabilizing the system with an associated energy drop of 2.04 eV (the total energy drop is À3.82 eV). The reaction then continues with a nal step in which the O atom lis up the subsurface Mn and helps it to migrate into a Mn 2 O 4 surface oxide structure as a nal FS state. The energy barrier of this nal step at TS5 is 0.81 eV while the reaction energy of the entire process is À3.77 eV. Overall, the oxidation of the bimetallic PtMn system is therefore a strongly exothermic process. The rate-determining step corresponds to extracting the subsurface Mn from the vacancy site to the adlayer (thus re-creating a vacancy that can give rise to further processes) and has the highest energy barrier of 0.90 eV. Second, we ran m-Dyn starting from a conguration of the bare system with 2 Mn atoms and 4 added O atoms at the surface using the local CV-SurfMnO and NNP19 for a total of 100 ps simulation time at a temperature of 500 K. As before, from this m-Dyn simulation we extracted the important structures, conrmed their stability via DFT relaxation, and calculated the DFT saddle points via NEB simulations. In Fig. 5(a and b) we plot the DFT energy and geometry proles along the oxidation path. The reaction starts with a conguration in which the two surface Mn atoms are coordinated to 2 oxygen adatoms in Mn-O species as the Initial State (IS). The rst steps then correspond to progressively extracting both Mn atoms from the framework and forming MnO 2 and MnO 3 surface oxide species via Int2-Int3 intermediates to get the Int4 state, with a downhill reaction energy change of zÀ1.8 eV. It is interesting to note that three steps of formation of Mn x O y surface oxide species are thermodynamically favorable with very low kinetic barriers around 0.3/0.5 eV (see TS1-TS3). As discussed before, vacancy sites are so created in the metallic framework, and are pictorially highlighted with a star symbol in the pictures. The next oxidation steps are unique to this local-CV m-Dyn simulation: one of the oxygen atoms from the surface lls one of the vacancy sites thus coming to interact with a subsurface Mn atom, that is highlighted with an arrow in the Int5-Int6-Int7 congurations of Fig. 5(b). Naturally, this process even "worsens" the under-stoichiometric oxygen coordination of the surface Mn species, so that this raises the total energy by 0.26 eV. The reaction continues with the migration of the subsurface Mn into the interstitial layer in Int6. The O atom helps take the subsurface Mn to migrate into the interstitial layer, however the metal bonds of Mn-Pt and Mn-Mn in the second layer are elongated and constrained, so that this mechanism corresponds to the ratedetermining step and requires a barrier of around 1 eV at TS6. In Int7 the subsurface Mn atom is nally brought to the topmost surface layer, through an essentially isoenergetic process. In the conclusive two steps (Int8 and FS), the under-stoichiometric Mn 3 O 4 species migrate to ll the vacancy sites to reform Mn-O motifs and the Pt atom on the surface replaces the subsurface vacancy to stabilize the structure, corresponding to an overall energy drop of À1.14 eV. As in Section 3.1, we underline that, despite the "lean-oxygen" situation of this 2surface-Mn case (the system would thermodynamically favor the adsorption of a larger number of oxygen atoms, enough to create a MnO 3 surface oxide structure for all the surface Mn atoms), the thermodynamics of the process is exothermic and the barriers indicate viable mechanisms, with a rate-determining barrier of 1.00 eV.

Conclusions
The oxidation process of metallic surfaces is technologically important in a variety of elds, ranging from catalysis to corrosion, surface treatment, etc.  In heterogeneous catalytic processes in which oxygen species can appear, in particular, such as partial oxidation or hydrogen generation reactions, the importance of such oxygen species in determining static and dynamic structural properties such as surface faceting and restructuring, and corrugation, as well as electronic properties such as the system work function and the optical response, has long been researched. This has accumulated a wealth of information, especially at the fundamental model-system level, whereas the picture under realistic (in situ) reaction conditions is much less clear, due to the complexity of the phenomena involved and the difficulty in monitoring reaction intermediates and paths with atomistic precision. The situation is further complicated in the nanoalloy eld. In bimetallic nanosystems, oxidation plays a critical role in determining the surface composition and structure, and thus all connected quantities, including chemical, optical and electronic properties, especially when the two elements have very different oxygen propensity, or electronegativity. Metal nanoalloys can then undergo dynamic processes under reaction conditions, especially upon adsorption of strongly interacting species such as oxygen atoms, such as leaching and de-alloying. Due to the difficulty in correctly interpreting experiments in this complicated scenario so as to derive rigorous information, theory and simulations can play a crucial role in this topic, by clarifying thermodynamics and unveiling kinetics of oxygen adsorption on and restructuring of metal NPs and nanoalloys, including atomistic mechanisms of oxidation and the associated dynamics of chemical ordering.
Here we aim at shedding light on this topic by investigating via computational simulations one such case: the oxidation of Pt-Mn alloyed systems and the resulting surface migration and segregation into oxidized species of the electropositive Mn element. To reduce our study to a manageable computational effort, we use slabs modeling extended facets of Pt-Mn alloy nanoparticles at a xed Pt 2 Mn composition. We then combine DFT local geometry relaxations and singlepoint calculations of energy and forces with a recursive generation of machine learning force elds (Neural Network Potentials, NNPs) which are then used to explore increasingly larger basins of the Potential Energy Surface (PES) so as to feedback onto and enlarge the DFT database to generate increasingly more accurate NNPs. This protocol can be seen as the extension to reactive, dynamic processes (saddle points) of the procedures for deriving NNPs targeted to thermodynamic quantities (local minima), as in current active research. 58 The latestgeneration NNPs are so accurate that they can be used in MD or accelerated MD in the form of meta-Dynamics (m-Dyn) simulations to produce reaction paths that can then be validated by DFT/NEB saddle point searches, whose outcome is then fed back onto the DFT database and used for a nal NNP renement.
The picture resulting from the adopted computational protocol offers a comprehensive and apparently reasonable view of the oxidation and de-alloying process in Pt-Mn systems. The presence of Mn atoms in the topmost surface layer, which is thermodynamically favored at the Pt 2 Mn composition, provides the initial weak points for system dynamics. These atoms in fact not only easily dissociate incoming O 2 molecules and attract existing oxygen adatom species, but their strong interaction with these species drives the systems from surface-alloyed Mn toward MnO x surface oxide structures supported on the metallic framework (with x the degree of oxidation). This simultaneously leads to creating one or more vacancy sites in the metallic slab, which then favor atomistic exchange and rearrangement mechanisms, in which an exohedral surface oxygen can migrate into the framework lling up a vacancy site, or a subsurface Mn atom can diffuse to interstitial sites next to the vacancy. The congurations resulting from both these mechanisms are then prone to further evolution, in which the migrated or a surface oxygen picks up a subsurface or the interstitial Mn atom and draws it to the surface. The DFT estimate of the rate-determining barriers along such reaction paths ranges around 0.9-1.0 eV, thus suggesting a kinetics from a few tens of minutes to a few tens of hours at room temperature, in reasonable agreement with available experimental data. 30 Finally, we note that the present study offers several possibilities of development, among which we highlight two. First, now that an accurate NNP for the Pt-Mn-O system has been derived, this is available for tackling more complex phenomena occurring on realistic Pt-Mn NPs under a wide set of reaction conditions. Second, the database of structures and energetics derived for the Pt-Mn system could be used in a similar study to accelerate the derivation of NNPs for other ternary (bimetallic + oxygen) systems, thus possibly allowing one to derive general trends in the complex phenomenon of the oxidation of bimetallic NPs.

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