Topics in Catalysis manuscript No.(will be inserted by the editor)

Catalytic activity of Pt nano-particles for H2 formation

Egill Skulason · Avan A. Faraj · Lilja

Kristinsdottir · Javed Hussain · Anna L.

Garden · Hannes Jonsson

Received: date / Accepted: date

Abstract Associative desorption of hydrogen at edges and facets on Pt nano-particleswas studied using density functional theory. The goal was to identify catalytically activesites on Pt nano-particles for the hydrogen evolution reaction. Since nano-particles usedin catalysis typically contain over a thousand atoms, calculations of whole particlesare too demanding and the adsorption sites were instead modeled by periodic facecentered cubic slabs representing an array of edges between two (111) micro-facets oredges between (111) and (100) micro-facets. The width of the facets in the periodicrepresentations was systematically increased to reach converged results for binding andactivation energy. For maximum hydrogen coverage, edges between (111) micro-facetswere found to be several orders of magnitude more active than edges between (100)and (111) micro-facets or flat terraces. Unlike the missing row Pt(110)-(2x1) surface,which has sometimes been used as a simple model for edges between (111) micro-facets,the converged edge model does not show the recently reported reentrant behavior indesorption mechanism [Gudmundsdottir et al., Phys. Rev. Lett. 108, 156101 (2012)].

Egill SkulasonScience Institute of the University of Iceland, VR-III, 107 Reykjavık, Iceland

Avan A. FarajScience Institute of the University of Iceland, VR-III, 107 Reykjavık, Iceland

Lilja KristinsdottirScience Institute of the University of Iceland, VR-III, 107 Reykjavık, Iceland

Javed HussainScience Institute of the University of Iceland, VR-III, 107 Reykjavık, Iceland

Anna L. GardenScience Institute of the University of Iceland, VR-III, 107 Reykjavık, Iceland

Hannes JonssonFaculty of Physical Sciences, VR-III, University of Iceland, 107 Reykjavık, IcelandDepartment of Applied Physics, Aalto University, Espoo, Finland

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Keywords nano-particles · hydrogen evolution · edges · density functional theory ·minimum energy paths

1 Introduction

Theoretical calculations based on density functional theory (DFT) and transition statetheory have led to a deeper understanding of catalytic activity and thus helped de-velop improved heterogeneous catalysts, a task that is vital for the design of processeswith higher energy and atom e�ciency in the chemical industry (1; 2). By provid-ing information about the factors controlling the reactivity, such as the energetics ofmolecule-surface interaction and the kinetics of elementary processes at solid surfaces,trends in the catalytic activity as the chemical composition of the catalyst is variedhave been established and predictions made for new and improved catalysts.

The interaction of hydrogen with the surface of platinum metal is of fundamen-tal importance to a wide range of technologies including various catalytic reactions,electrolysis and hydrogen fuel cells. The hydrogen-platinum system has, furthermore,become a model system where a great deal of e↵ort in surface science has been focused.The metal is typically dispersed as small particles embedded in a matrix. The activesites of such particles can be under-coordinated atoms at edges where crystal facetsmeet (3; 4), or at corners where edges meet. Under-coordinated atoms at steps have,in some cases, been shown to be the active sites on crystal surfaces (5; 6). Today anultra disperse platinum catalyst in PEM fuel cells contains particles with a diameteron the order of 3-100 nm (7; 8). The current focus is to make the particles smaller,thereby increasing the surface area and the density of under-coordinated sites. Ideal,low energy shapes of a nano-particle (NP) of an FCC metal can be icosahedral, deca-hedral, or cuboctahedral (9) with mainly (111) and (100) facets. Cuboctahedral NPshave atomic ordering characteristic of FCC crystals, decahedral NPs are twinned FCCcrystallites where five tetrahedral wedges share a common edge while icosahedral NPshave non-crystallographic ordering with local five-fold symmetry. When NPs becomelarge enough, the cuboctaheral structure becomes most stable and their propertiesapproach those of bulk FCC metal. The edges formed on the surface of such NPsare either between two (111) micro-facets or between a (111) and a (100) micro-facet(4). Particles of the same size but with di↵erent shape can have significantly di↵erentcatalytic activity (10).

A 3 nm particle contains on the order of a thousand atoms. DFT calculations of thecatalytic activity of a whole nano-particle of this size generally require a prohibitivelylarge computational e↵ort, although benchmark calculations of nano-particles withup to 1415 atoms have been conducted (11). An alternative approach is to construct aperiodic array of the sites under consideration, such as edges between micro-facets (12).The missing row reconstructed Pt(110)-(1x2) surface has been proposed as a model ofedges between (111) facets on nano-particles (13; 14; 15) but the width of the terraces inthis surface is very small, corresponding to just a single atom row. One of the questionsaddressed in the present study is how well the Pt(110)-(1x2) surface can represent edgeson nano-particles and how wide the terraces need to be in such a periodic slab modelto reach converged results for edges between large facets.

The hydrogen evolution reaction (HER) and hydrogen oxidation reaction (HOR)take place when water is electrolyzed or hydrogen is used in fuel cells. There, solvatedprotons in the electrolyte and electrons from the electrode form hydrogen molecules or

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the hydrogen molecules dissociate into protons and electrons, respectively. Simulationshave been used to model the interface between the electrolyte and the electrode withdensity functional theory (DFT) calculations (16; 17; 18; 19; 20; 21; 22). Reactionpath calculations for the transitions have shown that the Tafel reaction (2H⇤ *) H2)is much faster than the Heyrovsky reaction (H+ + e� + H⇤ *) H2) at U = 0 V vsSHE on all transition metal surfaces and the common facets, with and without defects(18). It has been seen that, for Pt(111), the activation energy for this process doesnot vary significantly with applied potentials from –2 to +2 V.(16) Furthermore, ithas been observed previously that the binding of H atoms to the Pt surface does notchange in the presence of an external field.(42) As a result, it is not necessary to includethe complicated electrochemical interface in calculations of the rate of HER and HORfor these conditions. It is su�cient to focus on the formation of H2 from adsorbedH-adatoms and dissociation of H2 to form H-adatoms.

Herein, we report calculations of the H-adatom binding energy and H2 desorptionactivation energy as a function of coverage, ranging from low to full coverage. We useperiodic models for the two most common types of edges present in FCC nano-particles,the edge formed between two (111) micro-facets and the edge formed between a (111)and a (100) micro-facet, and compare the catalytic activity to that of the flat crystalfacets.

2 Methodology

The DFT (23) calculations were carried out in combination with minimum energy path(MEP) calculations using the Vienna ab initio Simulation Package (VASP) (24) and theRPBE functional approximation (25). The valence electrons were represented with aplane-wave basis with an energy cuto↵ of 350 eV and Monkhorst-Pack k-point sampling.Convergence tests for the energy cuto↵ and k-point sampling were performed for thePt(110)-(1x2) system. It was found that increasing the k-point sampling from 4x4x1 to6x6x1 and the energy cuto↵ from 350 to 450 eV changed the total energy by less than0.01 eV. Ultra-soft pseudopotentials (26; 24) were used to represent the ionic cores.The MEPs for di↵usion and adsorption/desorption of hydrogen were calculated usingthe climbing image nudged elastic band (CI-NEB) method (27; 28; 29). The activationenergy was calculated as the energy of the highest maximum along the MEP minusthe initial state energy.

The slabs were separated from periodic images by at least 10 A of vacuum. Allconfigurations were optimized until atomic forces were less than 0.01 eV/A. The op-timal lattice constant for the crystal at zero temperature was found to be 4.011 A.The two uppermost layers in each slab configuration were allowed to relax and theremaining layers were kept frozen, with atomic distances consistent with this optimallattice constant.

The periodic slab models of the edges between micro-facets are shown in Fig. 1. Themissing row Pt(110)-(1x2) surface can be used as a model of an edge that is formedwhere two (111) facets meet. It resembles locally a B-type step on a (111) surface.The micro-facets in this model are only one atom row wide and it will henceforth bereferred to as the B1,1 model. Several models with wider micro-facets were generatedfor comparison. When the micro-facets include n atom rows the model is referred toas Bn,n. The adsorption energy and activation energy for associative desorption werecalculated for various widths of the micro-facets, with up to n=11 atom rows (models

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with up to 5 atom rows are shown in Fig. 1). In the direction along the edges, two orthree atom rows were included for the models with n < 5 but only one atom row forthe models with wider micro-facets. For B-type edges, a slab with 13 layers was usedfor the calculation of adsorption energy. For a few test systems, the number of layerswas increased to 15 and the calculated interaction energy was found to change by lessthan 0.02 eV. The activation energies of Bn,n were calculated for systems with n < 5.Due to the smaller facet size, fewer layers were required and it was found that 8 layerswere su�cient to obtain convergence within 0.02 eV.

An edge between a (111) and a (100) facet will be referred to as an A-type edgesince it locally resembles an A-type step on the (111) surface. An Am,n model has m

atoms rows in the (100) micro-facet and n atom rows in the (111) micro-facet. Theperiodically stepped (211) surface is thus an A0,1 model for the A-type edge, a verysmall one indeed. When four rows of atoms are removed from every other edge structurein that model, the width of the (100) micro-facet is increased by one row and the (111)micro-facet increased by two rows to yield the A1,3 model for the A-type edge, see Fig.1.

The potential energy surface (PES) for a H-adatom interacting with the surfacewas calculated by choosing a grid of (x,y)-coordinates and then minimizing the energywith respect to the z-coordinate of the H-atom as well as the top layer of Pt atoms.The (x,y) mesh size was smaller than 0.4 A.

The Pt(100) surface was modeled with four layers, the bottom two kept frozen,and a periodic (2

p2x2

p2)R45 model cell was used, except for the calculations of the

PES for an H-adatom where a (2x2) model cell was used with three layers in total, ofwhich only one was relaxed. The Pt(111) surface was in most cases modeled with arectangular simulation cell of (2x2) atoms in each layer, with three layers, two of whichwere kept fixed. For the MEP calculations, 6 layers were used, the bottom 3 of whichwere fixed.

3 Results

3.1 H adsorption at low coverage

A comparison of potential energy surfaces for an H-adatom on the B1,1 and A0,1 edgemodel surfaces is presented in Figure 2. The strongest binding occurs at bridge sitesat the edges, as has been previously reported from calculations on the Pt(110)-(1x2)surface (30; 31; 32; 33) and the Pt(211) surface (34; 35; 18). This low coordinatedbinding site is unusual for hydrogen on metal surfaces. In fact, the optimal binding sitefor hydrogen has sometimes been assumed to be the four-fold hollow site under steps(36) or trough sites on the Pt(110)-(1x2) surface (37).

The PES for the Pt(100) surface is also consistent with this preference for under-coordinated binding sites since the strongest binding is obtained at bridge sites whereasthe four-fold hollow site is only a shallow local minimum. Similar preference for bridgesites has been reported in calculations of an H-adatom on Ir(100) (38). The PES forthe H-adatom on the Pt(100) surface is shown in Fig. 2. The bridge sites are ⇠0.4eV lower in energy than the 4-fold hollow sites. This unusual adsorption site has beenargued to be due to relativistic e↵ects (38; 31; 39). A similar bridge site is also foundto be the lowest energy position on the missing row Pt(110)-(1x2) surface in Fig. 2a.In comparison with another Group 10 metal, calculations for the Pd(110)-(1x2) and

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Fig. 1 Side view of simulation cells (lighter colored atoms) for periodic slabs representing edgesbetween two (111) micro-facets, Bn,n, where n is the number of atom rows in the terrace, andedges between (100) and (111) micro-facets, Am,n where m is the number of atom rows in the(100) terrace.

Pd(211) surfaces give the threefold FCC site on the (111) micro-facet as the most stableadsorption site, rather than the bridge site on the edge (33; 40).

The PES for the Pt(111) surface is also shown in Fig. 2. In this case the on-top position is slightly lower in energy than the FCC 3-fold hollow site. The Pt(111)and Ir(111) surfaces are unique in this sense among 23 closed-packed transition metalsurfaces that have been studied recently (41).

In order to test the width of the micro-facet required to reach convergence towidely separated edges representative of large nano-particles, the micro-facet size wasincreased and the binding energy of the H-adatom calculated for positions along atransect from the ridge to the trough. Two di↵erent line scans were performed: (1)the initial position of the H-adatom is the lowest energy bridge position on the ridge,and (2) the initial position of the H-adatom is on-top of a Pt-atom in the ridge. Thecalculation was carried out for five di↵erent Bn,n model surfaces corresponding ton=1, 2, 3, 4 and 5 (see Fig. 3). The results show a remarkably small variation whenthe width of the micro-facet is increased. The largest di↵erence is observed for adatompositions at the ridge, the trough, and one of the saddle points, see Fig. 3. To obtainbetter convergence at those sites, calculations were carried out using models as largeas B11,11. Small oscillations of the energy at these positions occur as a function ofmicro-facet width but they eventually die out. The di↵erence in H-adatom bindingenergy between the smallest, B1,1, and largest, B11,11, edge model is less than 0.1 eV.

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Fig. 2 Left: On-top view of the atomic ordering in the surface layer, with a red square indi-cating the outline of the region covered in the corresponding contour graph of the potentialenergy surface (right). (a) B1,1 surface representing an edge between two (111) facets, (b)A0,1 surface representing an edge between a (100) facet and a (111) facet, (c) Pt(100) and(d) Pt(111) surfaces. Atomic positions are indicated by green circles and the key shows colorcoding of binding energy in eV with respect to H2 molecule and clean, relaxed surface.

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Fig. 3 Energy of an H-adatom along a transect in the surface plane from the ridge to thetrough for 5 di↵erent models for a B-edge ranging from B1,1 to B5,5. At each point the energy isminimized with respect to the position of the H-adatom in the direction normal to the surface.In (a), the initial position of the H-adatom is a bridge site at the ridge while in (b) it is anon-top site. The force on the atom along the line has been taken into account in the polynomialinterpolation (29). The insets show an on-top view of the surface marking the positions of theH-adatom within the surface plane.

3.2 Hydrogen adsorption at higher coverage

The adsorption energy is strongly dependent on the hydrogen coverage. By addingH-atoms to the surface one at a time, the energy per H-adatom was calculated and thedi↵erential adsorption energy evaluated as

�EH(n) = E[n)� (E(n� 1] +12EH2

) (1)

where n is the number of hydrogen atoms adsorbed on the surface and E(n) is thetotal energy of the surface with n adsorbed H atoms. The results are shown in Fig. 4.The hydrogen coverage, ✓H, is defined as the ratio of the number of H-adatoms to the

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Fig. 4 Di↵erential hydrogen adsorption energy as a function of coverage on B3,3, A1,3, Pt(111)and Pt(100) surfaces. The Pt(111) and Pt(100) values are taken from Ref. (18). On Pt(111),the FCC sites are filled up to ✓H = 1, above which the H atoms occupy the on-top sites. OnPt(100), the bridge sites are filled up to nearly ✓H = 2. The insets show the adsorption orderof H to the A- and B-type edges. On B-type edges, the bridge sites on the ridge are first filled,then the H atoms are placed in on-top sites on the micro-facets (F). After ✓H = 1, filling ofHCP sites is endothermic.

number of surface Pt-atoms, Nsurf , ✓H = n/Nsurf . The Pt-atoms in the trough are notcounted as surface atoms.

The results for the B1,1 system have been discussed in detail elsewhere (32; 33).In an agreement with the results of Zhang et al. (30; 31), the short bridge site on theridge (R) is the strongest adsorption site. This is true also of the larger micro-facetmodels B2,2, B3,3, and B4,4. As for low hydrogen coverage, the hydrogen adsorptionenergy converges quickly with the size of the micro-facet and there is little di↵erencein the di↵erential adsorption energy for all Bn,n edges. Accordingly, only data for B3,3

are presented in Fig. 4. After all of the R sites on the B-type edges have been filled,adsorption to either on-top, FCC or HCP sites on the facets was considered. The on-top site was found to yield the lowest overall energy, although the di↵erence betweenthe three sites was small. The preferred site is the F2 Pt atoms (see inset on Fig. 4).Interestingly, the F2 atoms are the first to be occupied after the R is filled, for allthe B-edge models with n > 1. The presence of the trough does not seem to matter,only the distance from the ridge. Addition of the second and subsequent H-atoms wasperformed from this on-top configuration and, accordingly, the configurations at highercoverage had all atoms in the on-top arrangement.

The di↵erential adsorption energy of H-adatoms on the A1,3 model of the A-edgeare also shown in Fig. 4. The order in which the sites are filled is shown in the insetof Fig. 4. As for the B-edge, the H-atoms first adsorb at ridge sites. After filling theridge, the additional H-atoms bind firstly to the (100) micro-facet and then to the(111) micro-facet. This is consistent with the fact that the (100) crystal surface bindsH-adatoms more strongly than the (111) crystal surface, as shown in Fig. 4. The A-

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edges and adjacent (100) micro-facet bind H-adatoms more strongly than B-edges, by⇠0.2 eV.

3.3 H2 desorption from edges and facets

In electrochemical production of H2 on Pt, a slightly negative potential versus SHE isapplied. Under such conditions, there is high coverage of hydrogen on the Pt surface(16; 42; 18). As the coverage increases, the binding energy of H-adatoms decreasesbecause of repulsive interaction between the H-adatoms. The maximum coverage of Hon the Pt surface is reached when the di↵erential adsorption free energy (consideringentropic e↵ects) is close to zero (18). The optimal coverage depends on the surfacestructure of the Pt electrode. The more open the surface is, the more hydrogen it canadsorb. This can be seen in Fig. 4 by comparing, for example, the Pt(111) and Pt(100)surfaces. Beyond ✓H = 1 hydrogen coverage, binding to the Pt(111) surface becomesendothermic as on-top sites become occupied after all the FCC sites have been filled.

The calculated MEPs for desorption of H2 molecules from various Pt surfaces at acoverage corresponding to an optimal coverage under typical HER conditions (18) (highhydrogen coverage) are shown in Fig. 5. It is worth noting that the reaction energies fordesorption are not related to the di↵erential adsorption energies presented in Fig. 4 as,in most cases, H2 desorption does not occur in the same order as adsorption. For theA- and B-edges, only desorption from the ridge is considered. The activation energyis much lower, by ⇠0.25-0.35 eV, for the B-edge than the other surfaces. This impliesthat the rate of the HER will be significantly higher at the B-edges than A-edges orflat terraces. Nano-particles with B-edges are, therefore, expected to be catalyticallymore active than particles with only A-edges. The reason for this is partly that thebinding energy of H-adatoms is lower at the B-edge than at the A-edge, as shown inFig. 4, but also that the shape of the MEP is also quite di↵erent. The large dip in thecurve for the B-edge being due to the formation of a Kubas complex (43) where theH2 molecule is partly formed but still chemically bound to a ridge Pt-atom (see insetof Fig. 5) (32; 33).

In Fig. 6, the calculated activation energy for H2 desorption from the B-edge, A-edge, Pt(111) and Pt(100) surfaces is shown as a function of hydrogen coverage and inFig. 7 as a function of reaction energy. The activation energy at the B-edge is lowestfor the relevant values of the coverage.

4 Discussion

The results of the calculations presented here indicate that the activation energy forH2 desorption is ⇠0.3 eV lower at a B-edge than at an A-edge at maximum hydrogencoverage (see Fig. 5). This di↵erence in activation energy would lead to a ⇠105-folddi↵erence in the rate of desorption at room temperature (assuming a similar prefactor).The calculations, therefore, indicate that the B-type edges are more catalytically activein forming H2 than A-edges. Hence, the catalytic activity of a nano-particle woulddepend strongly on its shape and the types of edges present.

It has recently been argued (44) that the missing row Pt(110)-(1x2) surface, whichis the B1,1 model of the B-edge, is not a good model for the edge of a nano-particle.However, there it was assumed that the active part of the surface are the trough sites.

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Fig. 5 Calculated minimum energy paths for H2 desorption from a B-edge, an A-edge, Pt(100)and Pt(111) at H coverage of ✓H = 1.0, 1.2, 1.25, 1.0 respectively, which is the optimal coveragefor each surface under typical HER conditions, corresponding to a high hydrogen coverage (seeFigure 4). The desorption paths for the A- and B-edges correspond to desorption from the ridgesites. This shows that a B-edge is by far the most active, with an activation energy 0.25-0.35eV lower than an A-edge and the flat terraces. Inset: Kubas complex formed on B-edge, R(H-H)=0.86 A, R(H2-Pt)=1.73 A.

Our results show that this is not the case. The results here also show that the edges ofthe Pt(110)-(1x2) surface have similar binding energy and desorption activation energyas the models with larger micro-facet micro-facets. Hence, this small model can be usedto model the adsorption and barriers on the edge with good accuracy, although modelswith larger micro-facets are more accurate, especially in the intermediate coverageregime, where a micro-facet size of n�3 is required.

In order to get faster convergence for the properties of the edge with respect to thewidth of the micro-facet, it is important not to populate the trough sites, since thatleads to strong, steric repulsion between the adatoms and a shift out of the optimalsites.

It was recently reported that DFT calculations of the H2 desorption from thePt(110)-(1x2) surface shows reentrant behavior in the desorption mechanism (32; 33).The three peaks observed in temperature programed desorption data could be associ-ated with desorption from just two types of sites, first ridge sites at low temperature,then micro-facet sites at intermediate temperature and then ridge sites again at hightemperature. The question then arises whether such reentrant behavior also occurswhen H2 is desorbed from Bn,n surfaces with n > 1. For the B-edges, desorption fromthe ridge is lower than desorption from a Pt(111), at all hydrogen coverages, see Fig.6. Thus the reentrant behavior is not expected to occur for the B-edges when themicro-facets become larger than one atom row. The situation is not as clear for the

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Fig. 6 Calculated activation energy of H2 desorption as a function of coverage for B-edge,A-edge, Pt(111) and Pt(100) surfaces. For the A- and B-edges desorption is from the ridgesites.

A-edges. At low coverages desorption is likely to occur from the ridge, as only the ridgeand strongly-binding (100) facet are populated. At intermediate coverages, the (111)facet becomes occupied, and it is likely that desorption will occur from these sites, asthe desorption from Pt(111) is much lower than both the A-edge ridge and Pt(100).Thus it seems possible that a reentrant mechanism could exist for the A-edges andthus nano-particles containing A-edges.

The current work represents only an initial investigation into the catalytic be-haviour of A- and B-type edges. Ongoing work is underway in explicitly calculatingthe desorption from the facets in the A- and B-type surfaces. In addition, adsorptionto edges is being considered in more detail, in allowing for phase transitions betweenon-top, FCC and HCP binding sites on the facets as the coverage is increased.

5 Summary

Results of theoretical calculations are presented of the catalytic activity of edges onPt surfaces in the formation of H2. Periodic models of edges have been used to obtainestimates for nano-particles that are typical for those used in, for example, fuel cells,but are too large to be simulated in their entirety. The results show that the activationenergy and thereby the rate of H2 formation is much higher at B-edges than at A-edges. As a result, the catalytic activity is strongly dependent on the shape of thenano-particle.

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Fig. 7 Calculated activation energy of desorption of H2 as a function of the reaction energyfor B-edge, A-edge, Pt(111) and Pt(100) surfaces. This is the same data as presented in Fig.6 shown in a di↵erent way. The same notation is used. For each type of binding site for theH-adatoms, the values tend to lie on a straight line, a manifestation of the Brønsted-Evans-Polayni (BEP) relation (1; 2). Here, data for each of the Bn,n (n = 1� 4) edges are includedto further illustrate the linear BEP relation.

Acknowledgements This work was funded in part by the Eimskip Fund of the Universityof Iceland, the Icelandic Research Fund and Nordic Energy Research by way of the NordicInitiative for Solar Fuel Development. HJ acknowledges support from the Academy of Finlandthrough the FiDiPro program. The calculations were in part carried out on the Nordic HighPerformance Computer (Gardar) located in Iceland.

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