Potential Energy Surfaces for Oxygen Adsorption, Dissociation, and

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Potential Energy Surfaces for Oxygen Adsorption, Dissociation, and Diffusion at the Pt(321) Surface J. M. Bray† and W. F. Schneider*,†,‡ †

Department of Chemical and Biomolecular Engineering, 182 Fitzpatrick Hall, University of Notre Dame, Notre Dame, Indiana 46556, United States ‡ Department of Chemistry and Biochemistry, 251 Nieuwland Science Hall, University of Notre Dame, Notre Dame, Indiana 46556, United States ABSTRACT: We report a first-principles, periodic supercell analysis of oxygen adsorption, diffusion, and dissociation at the kinked Pt(321) surface. Binding energies and binding site preferences of isolated oxygen atoms and molecules have been determined, and we show that both atomic and molecular oxygen prefer binding in bridge sites involving coordinatively unsaturated kink Pt atoms. Binding energies of atomic and molecular oxygen in different sites correlate well with the average metallic Pt coordination number of Pt atoms forming each site, although differences exist between adsorbates in symmetrically similar sites due to the inherent chirality of the surface. Atomic O in the strongest binding bridge sites experiences relatively small energy barriers for diffusion to neighboring sites compared to O on Pt(111). However, due to the structure of the surface, O diffusion is only rapid between different sites around the kink Pt atom, whereas the effective long-range tracer diffusion, as determined from a simple course-grain model, is shown to be anisotropic and slower than on the Pt(111) surface. Four dissociation pathways for O2 at low coverage are also reported and found to be in agreement with experimental observations of facile dissociation, even at low temperature.

1. INTRODUCTION Oxidation catalysts play an important role in many processes of industrial and environmental relevance. Among transition metals commonly used in heterogeneous catalysis, platinum is uniquely suited for oxidation applications and is applied widely for treatment of automotive emissions. Platinum
oxygen interactions also play an important role in the reduction of oxygen in fuel cells. The adsorption and reactivity of oxygen at platinum surfaces has been and continues to be widely studied both experimentally and computationally. Computational and surface science studies in particular focus primarily on idealized, high-symmetry surfaces. Flat surfaces, including Pt(111) and (100), have been investigated in detail computationally,1
7 and stepped surfaces have received some treatment as well,8 but relatively little has been done to understand the unique aspects of oxygen on kinked platinum surfaces. Recent work by Fajin et al.9
14 has contributed some of the first computational studies of adsorption and reaction on (321) surfaces of gold and copper. Their results illustrate the complexity of adsorption on low-symmetry surfaces. Work from the Nørskov group has also introduced computational models of the kinked Au(532) surface in addition to Au clusters and stepped surfaces.15,16 For a number of different systems, trends have been identified linking the reactivity of sites with their metallic coordination, including Au systems where nanoparticles containing very low-coordination sites have been observed to behave very differently from extended Au surfaces.15
19 However, a comprehensive study of a kinked Pt surface is still lacking. r 2011 American Chemical Society

In contrast to the more noble gold, where only low coordination surface sites are reactive toward O2, the flat, high-symmetry platinum surfaces, such as Pt(111), are known to be active for O2 adsorption and dissociation.15,20 One might reasonably expect that lower-symmetry Pt surfaces would then be even more reactive, and may even bind oxygen so strongly as to render the surface catalytically inactive, in accordance with the simple Sabatier principle.21 A computational study of a kinked Pt surface would provide insight into the effect of metal surface structure on the adsorption and reactivity of oxygen. Studying the kink sites in particular on high index model surfaces is one approach to modeling similar coordinatively unsaturated sites on real catalyst particles. By identifying trends of adsorption and reactivity for different types of surface sites, a systematic understanding of structure effects can be developed, which will contribute to eventually bridging the materials gap. The Pt(321) surface is an ideal model surface for studying structure effects in catalytic oxidation. McClellan, McFeely, and Gland have reported experimental results for oxygen adsorption at the Pt(321) surface as well as for Pt(111) and other surfaces.22
24 They find that molecular oxygen dissociatively adsorbs on the Pt(321) surface at lower temperatures than on the (111) surface, and they also report higher saturation coverages of atomic O on Pt(321). Binding energies of atomic oxygen at low coverage are Received: April 1, 2011 Revised: May 16, 2011 Published: June 01, 2011 8177

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Langmuir difficult to compare due to the unknown contribution of rare defect sites to experimental measurements. However, at saturation coverages in an ultrahigh vacuum (UHV) O2 environment; approximately 3.8  1014 O/cm2 and 1  1015 O/cm2 for Pt(111) and Pt(321), respectively ;O binding energies are stronger on Pt(321) by between 30 and 40 kJ/mol O2 (∼0.15
0.2 eV/O).22,24,25 Oxidation of both CO and NO are frequently studied reactions due to their relative simplicity and relevance in many pollution control and energy applications. Gland et al. have studied CO oxidation on the Pt(321) surface and shown that during temperature-programmed reaction (TPR) experiments, CO2 formation begins at a lower temperature and persists until a higher temperature on Pt(321) than on Pt(111).26 This extended reactivity of Pt(321) was attributed to the existence of multiple distinct reaction pathways arising from the greater heterogeneity in CO and O binding sites on Pt(321).26,27 Surface structure sensitivity has been discussed for CO oxidation on other Pt facets as well, suggesting this reaction is sensitive to the surface structure.28,29 On the other hand, recent experimental results for catalytic NO oxidation on Pt(321) and Pt(111) show similar reaction rates to within a factor of 2.30 Recent theoretical and experimental work on the Pt(111) surface suggests that for NO oxidation, atomic O is the primary surface species.31 As the oxygen coverage increases to the range observed under reaction conditions, repulsive lateral interactions between adsorbates weaken the O binding energy. This in turn raises the barrier to dissociation according to a Brønsted
Evans
Polanyi (BEP) relationship, which links the binding energy of adsorbates with the activation energy of dissociation.21,32
34 As a result of the weakened O binding and higher dissociation barrier under NO oxidation conditions, O2 dissociation becomes rate limiting.35,36 For this reason, the behavior of oxygen alone on Pt(321), even in the absence of other adsorbates, may prove important in explaining the structure insensitivity of this reaction. In this paper we present a density functional theory (DFT) slab model of the Pt(321) surface. We characterize the wide variety of sites available for binding both atomic and molecular oxygen and explore the potential energy landscape surrounding these sites as a necessary prelude to studying adsorption at higher coverage. In particular, atomic and molecular oxygen adsorption, atomic oxygen tracer diffusion, and molecular oxygen dissociation are discussed and used to interpret experimental observations.

2. COMPUTATIONAL DETAILS DFT supercell calculations were performed in VASP using the PW91 implementation of the generalized gradient approximation (GGA).37 The effect of core electrons was described using the projector augmented wave (PAW) method.38 A plane wave basis set was used with a 400 eV energy cutoff, and spin polarization was found to have a negligible effect on energy differences for both atomic and molecular oxygen and was not used in calculations of the metal and metal
adsorbate systems. The lattice constant for platinum determined using these parameters was 3.986 Å, as reported elsewhere.39 The primitive 1  1 unit cell of the Pt(321) surface contains five unique types of surface Pt atoms, and one layer is defined by inclusion of each of these 5 Pt types (seen in Figure 1b). Pt(321) surface energies were determined for fully relaxed slabs of up to 12 layers (corresponding to slab thicknesses of up to 32 Å) according to eq 1, where γslab is the surface energy of the slab, Eslab is the DFT energy of the slab, NPt is the number of Pt atoms in the slab, Ebulk is the DFT energy per Pt atom of

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Figure 1. Representation of the Pt(321) surface (a) viewed from above along the [321] surface normal, showing the (111) terrace, a 1  1 unit cell, surface vectors, and the five types of surface atoms, numbered beginning at the kink; (b) viewed from the side showing the 2  2 4-layer supercell used for all calculations reported here; (c) viewed from above, showing possible hollow adsorption sites on (111) terrace of Pt(321); and (d) showing the decomposition into (111), (100), and (110) facets. Possible hollow adsorption sites on the (110) and (100) faces of the step are shown, as are the three bridge adsorption sites where atomic oxygen binds. the bulk metal, and A is the surface area of one side of the slab. γslab ¼

Eslab
NPt Ebulk 23A

ð1Þ

The final surface model consisted of a slab with four Pt layers (shown in Figure 1b) and 10 Å of vacuum between slabs. The coordinates of the bottom two layers were fixed in their bulk face-centered cubic (fcc) positions, and the upper two layers and all adsorbates were allowed to relax until forces fell below 0.03 eV/Å. An 8  6  1 Monkhorst
Pack k-point mesh was used for the 1  1 supercell, corresponding to approximately 40 k-points/Å
1, and it was scaled appropriately for larger supercells. Calculations at low oxygen coverage were performed using a 2  2 supercell containing 20 Pt atoms per layer. Defining coverage as the number of adsorbates per surface Pt atom, this corresponds to a coverage of 0.05 ML for one adsorbate. Calculations of the Pt(111) surface discussed here were performed on a four-layer 4  4 Pt slab (0.0625 ML for one adsorbate) with only the bottom layer of metal atoms fixed and using a 3  3  1 Monkhorst-Pack k-point mesh. The center of the d-band was determined from the first moment of the d symmetry projected density of states of each surface Pt atom. Transition states for diffusion and dissociation were determined using the climbing-image nudged elastic band (CINEB) method.40 Phonon spectra were calculated for all transition states to verify the existence of only one imaginary mode. In these calculations, spectra were calculated by fitting atomic forces due to differential displacements of 0.01 Å (0.02 Å for systems including the atop O mentioned later) to a harmonic model, where only adsorbates and adjacent metal atoms were displaced. The energy of an isolated O2 molecule was calculated with spinpolarization in its triplet ground state. The molecule was placed in an asymmetric 16  14.4  12.8 Å3 box, and the O
O bond was not 8178

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Table 1. Coordination Numbers of Each Type of Pt(321) Surface Atom Pt type

Pt
Pt coordination

1

6

2 3

8 9

4

10

5

11

oriented along any of the primary axes or diagonals to avoid artificial symmetry constraints.

3. RESULTS AND DISCUSSION 3.1. Surface Characterization. The (321) surface is composed of three-atom-wide (111) terraces separated by zig-zagged atomic steps. The five symmetry-distinct surface atoms are distinguished by their metal
metal coordination numbers. The most coordinatively unsaturated surface atom, referred to as the kink atom, has a coordination number of six and is labeled as atom 1 in Figure 1. For convenience, Pt atoms are then numbered sequentially moving across the terrace. These Pt types and their respective coordination numbers are summarized in Table 1. Surface energy is defined in eq 1 and was calculated for slabs ranging from 2 to 12 layers, corresponding to slab thicknesses between 5 and 32 Å, respectively. Surface energy fluctuated with the number of Pt layers, but beyond six layers fluctuations fell below 0.7 meV/Å2. From this analysis, we find a relaxed Pt(321) surface energy of 110.2 meV/Å2, approximately 20% greater than the 93.327 meV/Å2 for Pt(111) reported elsewhere.4 The surface relaxes most at the sites with lowest coordination. In particular, the step atoms are pulled down slightly toward the layer beneath and in toward atoms 3, 4, and 5. Pt
Pt bond lengths were reduced by as much as 0.170 Å from the bulk value of 2.819 Å. This relaxation has a surface energy benefit of approximately 10 meV/Å2, estimated from the four-layer slab. 3.2. Atomic Oxygen Adsorption. With five inequivalent surface atoms, a multitude of additional bridge and hollow sites arise beyond those normally seen on high-symmetry surfaces. It is well established for Pt(111) that atomic O prefers to bind in fcc sites for coverages below 0.5 ML.4,39 For this reason, hollow sites, labeled with letters a
i per the convention of Fajin et al.9 and shown in Figures 1c and 1d, were tested first for O adsorption on Pt(321). Of the nine hollow sites, f, g, and i were found to be unstable, and the other six were able to bind atomic O. Additionally, three bridge sites (shown in Figure 1d) and one atop site were also found to bind atomic O, for a total of 10 atomic O binding sites. Atop sites are denoted by the letter “a” and the number of the Pt surface atom to which they are bound. Bridge sites are indicated with the letter “b” followed by the label numbers of the two adjacent surface atoms (see Figure 1d). Due, however, to the lack of mirror symmetry at the surface, more than one unique bridge site will exist between any two surface atom types. To distinguish these sites, we adopt a convention wherein the order of surface atom numbers in the site label are listed from left to right and top to bottom based on the standard orientation shown in Figure 1d. This allows us to distinguish between a 2-1 bridge site and a 1-2 bridge site, for example. This labeling convention closely follows that used by Fajin et al. in their descriptions of other (321) surfaces.9 It is also important to note

that because the Pt(321) surface is chiral, as are all kinked surfaces of fcc metals,41 two (321) enantiomers exist with mirror symmetry to each other. The (321) surface used for this study corresponds to the S enantiomer as defined by Ahmadi et al.42 or the equivalent L enantiomer per the convention of Jenkins et al.41 While the chemistry of oxygen binding will be the same for either enantiomer, the site labeling convention used is clearly dependent on this chosen orientation. The chirality is manifested in a slight asymmetry of Pt
Pt bond lengths on the relaxed surface as well as the differences in adsorbate binding energies in similar but distinct binding sites discussed below. Oxygen adsorption induces a slight relaxation of the neighboring Pt atoms. In general, surface Pt atoms relax away from the adsorption site, resulting in a variety of changes in Pt
Pt bond length, depending on the particular adsorption site, but with the largest changes ranging from 3 to 10% of the original preadsorption bond length. Binding energies for both atomic and molecular oxygen, reported in Figures 2 and 4, are calculated according to eq 2, where σ represents any particular arrangement or configuration of oxygen in different adsorption sites, E(321) is the energy of the clean (321) surface, NO is the number of oxygen atoms adsorbed, and EO2 is the DFT energy of the isolated O2 molecule. According to this convention, negative binding energies are exothermic. ΔEads ðσÞ ¼ Eσ
Eð321Þ


NO EO 2 2

ð2Þ

The b21 bridge position is the strongest binding site for atomic oxygen, with a binding energy of
1.46 eV/O. This value is in excellent agreement with the low-coverage heat of adsorption of
290 kJ/mol O2 (
1.50 eV/O) reported by McClellan et al.22 An examination of the geometries of O in each adsorption site reveals that the strongest binding sites in some way involve the kink Pt. This observed ordering in site preference can partially be explained as an effect of each binding site’s Pt
Pt coordination, where sites with a lower average Pt
Pt coordination bind oxygen more strongly than those with higher average coordination. Similar arguments have been made for other adsorbate systems to explain binding energy trends.17,19 While this effect explains the general trend, it does not account for binding energy differences between sites of equal average Pt
Pt coordination, such as the b12 and b21 sites. In the case of the Pt(111) surface, all surface Pt have identical Pt
Pt coordination numbers, yet fcc sites are known to bind oxygen more strongly than hexagonal close-packed (hcp) sites by about 0.4 eV.4 This difference between fcc and hcp sites has been shown to extend to step sites as well, where, although the oxygen atoms are no longer 3-fold coordinated, they still exhibit an energetic benefit for the fcc-like site over the hcp-like site of approximately the same magnitude as that for the typical 3-fold hollow sites.8 We observe the same result for Pt(321), where fcc-like sites, having no atom directly below the adsorbate in the second Pt layer, bind oxygen more strongly than hcp-like sites, where there is an atom directly below the adsorbate in the second metal layer. Thus similar trends with Pt
Pt coordination exist for fcc-like and hcp-like sites, but they are offset from one another, as illustrated in Figure 3. Furthermore, the energetic difference between these types of sites is approximately constant, and the trend lines are thus approximately parallel. The offset ranges from 0.15 eV/O to 0.3 eV/O, somewhat less than the 0.4 eV/O seen for Pt(111), which emphasizes that ,while similar in general behaviors, other differences 8179

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Figure 2. Geometries of atomic O (red) bound in the 10 stable binding sites on Pt(321) (white). Site name (first letter indicates h-hollow, b-bridge, or a-atop), type, binding energy (eV/O), and average Pt
Pt coordination number are also listed for each site.

Figure 3. Correlation of atomic O binding energy and average Pt
Pt coordination of the binding site. *Atop sites a2, a3, and (111)atop are not stable for adsorption, but are included to illustrate the BE versus coordination trend.

exist between (321) and (111) facets that are not explained well by these simple arguments. Exceptions to the binding energy versus coordination trend in Figure 3 include the fcc-like “he” hollow site, which seems to follow the hcp-like trend rather than the fcc-like one. The distinction between the two site types may become less important for higher coordinated sites, or the correlation between binding energy and coordination number may become nonlinear at higher coordination numbers, as the observed linear behavior is simply an empirical observation with no particular theoretical basis. The b14 and hh sites, both of which lie on the step, do not clearly fit into either the fcc- or hcp-like categories; rather, they could be categorized better as (100) bridge and (110) 3-fold hollow sites, respectively. In spite of the difficulty in categorizing these two sites, they do obey the general trend with average Pt
Pt coordination, fitting in particularly well with the hcp-like grouping.

The most notable exception to this general binding energy correlation is the atop kink (a1) site. Atomic O adsorption at the atop site on Pt(111) is known to be unstable to the hollow sites. This inherent destabilization for atop binding clearly counteracts the binding enhancement seen for other adsorption sites at the undercoordinated kink site. The balance of these two effects allows the atop oxygen on the kink atom to remain metastable, but places it much higher in energy than the nearby bridge and 3-fold hollow sites. Atop binding was tested for the #2 and #3 Pt atoms as well. Oxygen is not stable in these sites, but by performing a constrained optimization allowing relaxation only in the direction normal to the surface, binding energies were obtained for oxygen in the a2 and a3 sites. It is interesting to observe that when these additional sites are considered, a very similar trend emerges for the atop binding sites as was seen for fcc-like and hcp-like sites. 3.3. Molecular Oxygen Adsorption. Molecular oxygen has been shown to preferentially bind on Pt(111) with the O
O bond parallel to the surface25 and primarily in bridge sites.43 O2 on the Pt(321) surface also binds at bridge sites, and of 15 possible surface bridge sites, nine were found to be local minima for O2 binding. Four additional bridge-hollow-atop (b-h-t) O2 binding sites were found to exist as well, and these sites are denoted differently in Figures 4
6, with the single number representing the atop site and the two-digit number representing the bridge site. This b-h-t type of O2 binding site and its relationship to bridge-bound molecular oxygen is discussed by Wang and Fisher for Pt(111).43 All O2 binding sites and their associated binding energies and geometries are summarized in Figure 4. The most stable binding site is again found at the step edge, but in the b12 bridge position as opposed to the b21 bridge site for atomic O. In general, O2 binds much more strongly to the (321) surface than to the (111), which may suggest qualitatively different adsorption behavior on the two Pt facets. The GGA-calculated O
O bond length of the gas phase O2 molecule is 1.236 Å. The lengthening of this bond upon adsorption to the surface is evidence of a chemisorbed rather than physisorbed state. We do not see one universal trend in O2 8180

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Figure 4. Images of O2 (red) adsorbed on Pt(321) (white). Site name, type, binding energy (eV/O2), and O
O bond length are also listed for each site.

Figure 5. O2 bond length versus O2 binding energy. O2 binding sites on Pt(321) are divided into three categories: step, terrace, and b-h-t sites.

Figure 6. Correlation between O2 binding energy and average Pt
Pt coordination number.

bond lengths for all binding sites; however, the geometry of the site seems to play an important role in determining bond lengths. O2 molecules bound in b-h-t sites uniformly have longer bond lengths, greater than 1.40 Å. Slightly shorter bond lengths are seen for O2 in terrace sites, and the shortest bond lengths are seen for sites along the step edge. Within each of these groups, however, we also see that the bond length is generally inversely proportional to the strength of binding, where the sites with a stronger (more negative) binding energy have the longest bond lengths. This effect is illustrated in Figure 5, where sites within the three categories appear to follow very well-defined trends,

with the exception of the b14 site, which should be categorized as a step site, but appears to fit better with the terrace sites. The relationship of bond length and binding energy is a result of electron transfer from the metal atoms to the partially occupied 2π* orbitals of the molecular oxygen. It has been proposed previously that, as the O2 binds more strongly to the metal, electron transfer to these antibonding orbitals increases, weakening the O
O bond and increasing its length.25 As was observed for the atomic O adsorption, we again find that the binding energy of the O2 molecules in different sites on Pt(321) correlates well with the average coordination of the 8181

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Langmuir surface metal atoms to which they are bound. This trend is shown in Figure 6. It is interesting to note how well O2 bound in a Pt(111) bridge site fits into this correlation. It is also apparent from Figure 6 that Pt(321) binds O2 much more strongly than Pt(111). The binding energy of O2 in the b12 site on Pt(321) is more than 0.8 eV more exothermic than that of bridge O2 on Pt(111). By comparison to Figure 3, it is clear that O2 binding is much more sensitive to surface structure than is atomic O. We return to this point in interpreting experimentally observed phenomena later in Section 3.6. 3.4. Electronic Structure Analysis. The correlation of both atomic and molecular oxygen binding energy with average Pt
Pt coordination shown in Figures 3 and 6 can also be described in the context of the d-band model of Hammer and Nørskov.28,44
46 It has been shown for many metal
adsorbate systems that binding energy correlates with the center of the d-band, which is calculated as the first moment of the d symmetry projected density of states of the surface metal atoms. Trends of this type appear both for adsorption across different metals and facets and for adsorbates in different inequivalent sites on the same metal facet.19,28 In general, when the d-band center of late transition metal surface atoms is raised relative to the Fermi level, stronger bonds can be formed with adsorbates. The metallic coordination number of a given surface metal atom will affect the width of its d-band, where higher coordination results in a widening and lower coordination results in a narrowing of the d-band. Within this model, the filling of the d-band is assumed to remain constant, thus narrowing of the d-band directly leads to an increase in the d-band center. Hence surface atoms with lower coordination have higher lying d states and are able to bind adsorbates more strongly than those with higher coordination.28,47,48 The plot of d-band center versus Pt
Pt coordination number shown in Figure 7a illustrates this relationship for the Pt(321) surface considered here. In Figure 7, all d-band centers have been referenced to the fermi energy. While the correlation between distance of the d-band center from the fermi level and Pt
Pt coordination is not exactly linear for the five surface atoms of the Pt(321) surface, it is clearly manifest that higher coordination of the surface atom results in a lower center of the d-band, as expected. From Figure 7a, we find that the d-band center of Pt(111) does not follow the Pt(321) trend, yet because they are the same metal, it does at least fall within the same range of (321) d-band centers. In particular, we note the difference between the # 3 Pt and the Pt(111) surface, both of which have the same coordination number, and conclude that while Pt
Pt coordination clearly influences the width and therefore the center of the d-band, it is not the sole factor contributing to the position of the d-band, particularly across different facets of a metal. Recent work by Bianchettin et al. examining the effect of coordination for Pt adatoms and addimers on the Pt(111) surface reports d-band centers for Pt coordination numbers ranging from 3 up to 12, showing that d-band center varies by as much as 1 eV over this range of coordination numbers.49 Their results agree well with those in Figure 7a, and they also see that Pt atoms with the same coordination may have different d-band centers when placed in different local environments, just as we observe in the case of the Pt(321) # 3 Pt and Pt(111). Bianchettin and co-workers point out that the correlation between d-band center and coordination number becomes more linear when an effective coordination number is defined that takes into account the effects of relaxation and Pt
Pt bond lengths.49,50 Understanding that there is a near-linear connection between Pt
Pt coordination and d-band center, we expect the binding

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Figure 7. (a) Correlation of Pt d-band center (εd
εF) and Pt
Pt coordination. Plots of (b) atomic O binding energy and (c) molecular O2 binding energy versus average Pt d-band center.

energy of both atomic and molecular oxygen, previously shown in Figures 3 and 6 to be linearly related to the Pt
Pt coordination, to correlate well with d-band center as well. We see from Figures 7b and 7c that this is indeed the case. In these figures, binding energy is plotted versus the arithmetic mean of the d-band centers of the adjacent surface atoms, just as was done for coordination numbers previously. Sites of lower Pt
Pt coordination and higher d-band center bind the adsorbates most strongly. In the context of simple classes of surface reactions, such as dissociation of small molecules, Hammer, Nørskov, and others have investigated the role of surface structure on reactivity. In particular, they break down the effect of structure into electronic and geometric contributions, which can be distinguished in BEP plots, where shifts along a trend line are electronic in nature while vertical shifts between two parallel trends are geometric in nature.21,47 Our results differ slightly in the sense that we have not reported a BEP relationship for a reaction. Instead, the plot in Figure 7b represents simple binding energies of atomic oxygen. Additionally, we have examined the variability of d-band center over only a very narrow range representing different types of sites 8182

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Figure 8. 2D colormap projection of the potential energy surface for O adsorption and diffusion on Pt(321). Left: fully corrugated model showing all binding sites (labeled as in Figure 2) and diffusion barriers. Right: simplified coarse-grained model containing only b21 site and seven diffusion barriers around the perimeter of the unit cell. Coarse-grain unit cell shown in black.

on a single Pt facet, whereas the trends examined by others generally involve multiple surface facets and metals. Yet in spite of these distinctions, we find a very similar story. Because different metal atoms on the Pt(321) surface have different individual d-band centers (Figure 7a), there is an electronic effect of local structure originating from the d-band centers of the particular surface atoms with which the adsorbates interact. However, the different geometries of the fcc, hcp, and atop sites allow the adsorbates to bond differently with the surface in each case. As pointed out by Sljivancanin et al., the simplified d-band model trends apply only where similar adsorbate
surface configurations are used,51 so we cannot expect the three types of binding sites to share a single trend line. Instead, we see a geometric effect clearly illustrated in Figure 7b where geometry differences in binding sites result in separate binding energy trends for fcc-like, hcp-like, and atop sites vertically shifted from one another. That the slopes of these three trend lines are similar is an indication that the electronic and geometric effects in this system are independent of one another. 3.5. Oxygen Tracer Diffusion. In modeling gas adsorption on a surface, one assumption affecting the availability and distribution of vacant adsorption sites is whether adsorbates may be treated as stationary or mobile on the surface. In order to gain insight into the mobility of adsorbed oxygen on the Pt(321) surface, we calculated diffusion pathways between each stable adsorption site. Nineteen pathways were identified between adjacent adsorption sites, and minimum energy diffusion pathways were calculated for each using the CINEB method. The binding energies of the 10 adsorption sites as well as the 19 diffusion transition states are represented by a Two-dimensional (2D) potential energy surface in Figure 8. The strongest binding sites are shown in red, intermediate sites in green, with the least stable positions shown in purple. The range of energies from the weakest to strongest bound sites in Figure 8 is approximately 1.6 eV. The barrier to oxygen leaving its most stable site (b21) is relatively low, only about 0.37 eV, or a little over half that of O diffusing from an fcc site on the Pt(111) surface.1,4 This single

low diffusion barrier does not automatically mean, however, that O diffusion on the Pt(321) will be faster than on the Pt(111) surface. Because of the hexagonal symmetry of the Pt(111) surface, an O atom leaving an fcc can go in three equivalent directions to identical hcp sites, and from there it can return to its original fcc site or diffuse into either of two other identical fcc sites. This type of random walk tracer diffusion, where only jumps to adjacent sites are permitted and successive jumps are assumed to be uncorrelated, is discussed in detail by Ala-Nissila et al.52 The diffusion coefficient for tracer diffusion, Dt, can be modeled by eq 3. Dt ¼

1 ΛÆl2 æ 23d

ð3Þ

where d is the dimensionality, Æl2æ is the mean square jump length, and Λ is the total jump rate as given by eq 4. Λ ¼ λ 3 ns

ð4Þ

Here, ns is a degeneracy of equivalent saddle points, and λ represents an individual jump rate, typically modeled by transition state theory as in eq 5. λ¼

Q   1
Ea ω Q IS exp 2π ωTS kB T

ð5Þ

For O on the (111) surface, dimensionality is 2, the mean square jump length is always the distance between fcc sites squared, or one Pt
Pt bond length squared, and the degeneracy of jumps is 3. Ea is the zero point corrected activation barrier found using the CINEB method, kB is the Boltzmann constant, T is temperature, and ωIS and ωTS are the vibrational modes of the adsorbate in the initial state and transition state, respectively, calculated within the harmonic approximation. Modes for oxygen were assumed to be sufficiently decoupled from the surface modes so that only the three modes involving O were included in the product. The diffusion coefficient for O on Pt(111) was calculated over a temperature range of 100
700 K (above which 8183

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Table 2. Comparison of O Tracer Diffusion Parameters for Pt(321) and Pt(111) surface (321) terrace

D0 (cm2/s)

Dt @ 300 K (cm2/s)

temperature range used for fit (K)

method

0.86

8.33  10
3

2.44  10
17


2

100
700

DFT

(321) step

0.78

1.17  10

7.65  10
16

100
700

DFT

(321) diagonal

1.34

1.84  10
2

5.18  10
25

100
700

DFT

(111)

0.59

4.74  10
3

5.75  10
13

100
700

DFT

(111)a

0.62

(111)b

0.55

∼ 10
3

∼ 5.8  10
13

(111)c

0.43

∼ 10
6.3

∼ 3  10
14

∼ 200

STM

3.91  10
16 8.46  10
17

2000
3000 2000
3000

MD MD/MC

d

(111) (111)e a

Ediffusion (eV)

0.76 0.79

DFT


3

2.29  10 1.58  10
3

DFT

Reference 4 (barrier reported without zero-point correction). b Reference 1. c Reference 53. d Reference 54. e Reference 55.

temperature oxygen is expected to desorb from the surface as O2) and then fit to an Arrhenius form shown in eq 6, with prefactor D0 and barrier Ediffusion.  
Ediffusion Dt ¼ D0 exp ð6Þ kB T Modeling O diffusion on the Pt(111) surface in this way, we find an effective O diffusion barrier of 0.589 eV. This agrees well with other theoretical studies1,4,53
55 summarized in Table 2, particularly with the results of Bogicevic et al.,1 which is expected since they also used a similar DFT approach with a GGA functional. Tracer diffusion on the Pt(321) surface is more complex due to the lower symmetry. An O atom leaving the b21 site can follow any of five inequivalent pathways. Assuming, according to Boltzmann statistics, that the pathway with the lowest activation barrier will occur most frequently, an O atom will almost always diffuse to the adjacent hb site, with an activation barrier for that pathway of 0.37 eV compared to the next lowest barrier of 0.72 eV to go to the b14 site. From the hb site, however, the smallest barrier to diffusion leads right back to the original b21 site. So although the O atom easily leaves the b21 site, its mean free path is expected to be very small before returning to its original position. Given enough energy to overcome the barrier between sites hb and ha of 0.64 eV (very similar to the Pt(111) barrier) then O can visit several additional sites, including ha, b12, and hh, but it is more or less confined to the sites immediately surrounding the kink Pt atom. In order to gain insight into the ability of O atoms to migrate greater distances on the surface, we therefore adopt a coarsegrain approach wherein a unit cell is defined around each b21 site. This unit cell, shown in black in Figure 8, essentially defines a dividing surface that an O atom must cross in order to diffuse from one b21 site to another. It is formed by following the ridge of highest energy diffusion barriers along all paths leading from one b21 site to any other b21 site. Each unit cell is then treated as a single “site”, with seven diffusion pathways connecting it to adjacent cells. Coarse graining in this way does not, however, remove the anisotropy of the surface. Thus, these seven pathways are placed into three categories: along the terrace, up and down steps, and diagonal. The isotropic model applied to the (111) surface can now be extended to the coarse-grained (321) surface in each of the three directions (shown in Figure 8) separately to obtain unique diffusion parameters for each direction. Total rates are determined in each direction by summing rates of the two or three

individual contributing pathways to calculate a total diffusion rate. This is done for a range of temperatures and fit to an Arrhenius form (eq 6) to obtain the parameters listed in Table 2. We conclude from these results that while diffusion within the Pt(321) unit cell occurs rapidly, O tracer diffusion over larger length scales (on the order of 10 Å or greater) on the Pt(321) surface will actually proceed more slowly than on the Pt(111) surface. Slow diffusion would lead to more localized adsorption, potentially with numerous distinct local surface environments developing on the surface, which could have implications in modeling adsorption or surface reactions. 3.6. Molecular O2 Dissociation. Adsorption experiments suggest that the barrier to O2 dissociation on Pt(321) is small based on the presence of atomic O on the surface even at 100 K, a temperature at which molecular O2 is known to be stable on the Pt(111) surface.22 To investigate this phenomenon, a variety of possible O2 dissociation pathways were tested on the Pt(321) surface using the CINEB method. The initial states, transition states, final states, and intermediate local minima are shown for all pathways in Figure 9 and are referred to throughout this section by the letters denoted in this figure. The lowest energy dissociation pathway (solid line ABCD), which begins from the b12 O2 binding site (image A), has a transition state energy of 0.466 eV relative to the initial state. The geometry of this transition state (image B) involves the dissociating O2 molecule bound to two adjacent kink Pt atoms. As discussed previously, due to their low Pt
Pt coordination, the kink sites have a strong stabilizing effect on chemisorbed O atoms, which would be considered an electronic effect. By being in simultaneous contact with two kink sites, this transition state structure receives an additional energetic benefit attributable to geometrical effects resulting from the close proximity of neighboring kink atoms on Pt(321). Thus the energetic advantage of this pathway is the result of a combination of electronic and geometrical effects. Other kinked surfaces with longer straight step segments between kinks could support similar reaction pathways, but the electronic and geometrical benefit of the (321) facet will be lessened due to the inability of adsorbates to interact with more than one kink atom at the same time, causing them to interact with step atoms instead. This transition state (image B) dissociates further to reach the fully dissociated final state structure shown in image C. This final state configuration is of particular interest because it incorporates an oxygen atom in the relatively high energy a1 atop site, and as is apparent from Figure 9, it is metastable to other adsorbate arrangements with O in more stable binding sites (e.g., images D and E). This pathway leading through transition state B to the 8184

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Figure 9. Minimum energy paths for four calculated O2 dissociation pathways beginning from the b12 (A) and b21 (F) sites. The lowest energy pathway is indicated by the solid line, while other pathways are drawn as dashed lines. Energies are relative to the clean Pt(321) surface and O2(g). Images of key geometries are shown with the O
O distance noted. The dotted line represents the hypothetical regime of tracer diffusion with the O atoms at infinite separation and a diffusion barrier of 0.78 eV (see Table 2).

interesting metastable dissociated state C is unavoidably reached for all pathways connecting the b12 O2 initial state (image A) to a final state with one of the O atoms in the adjacent b21 bridge site, such as those shown in images D and E. Pathway FGH is the mirror image of pathway ABC, following the same mechanism as the lower energy pathway, but with transition and final state energies shifted up in energy by between 0.15 and 0.2 eV. That these pathways are not energetically equivalent is again a result of the chirality of the surface. The calculations represented in Figure 9 by no means represent an exhaustive search of all possible O2 dissociation pathways on the clean Pt(321) surface; however, they do provide important insight into the experimental results of McClellan et al. already mentioned.22 The barrier along the ABC path relative to the energy of the molecular O2 initial state (image A) is about 0.05 eV less than the barrier for O2 dissociation on the clean Pt(111) surface. At temperatures around 100 K, this slight energetic advantage could account for 2
3 orders of magnitude difference in the reaction rate. However, the most important

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contribution to the increased dissociation rate on the (321) surface is most likely the relative O2 binding energy of the initial states. On Pt(321), O2 molecules bind in the b12 site more than 0.8 eV more strongly than does O2 on Pt(111). So while on Pt(111) O2 adsorption (ca.
0.7 eV) and dissociation (ca. 0.5 eV) processes have energy changes of similar magnitude, the Pt(321) O2 adsorption (ca.
1.6 eV) and dissociation (ca. 0.5 eV) processes are mismatched. With such highly exothermic molecular adsorption on Pt(321), dissipation of the energy released by adsorption will be more difficult, and the incoming molecules will more easily cross the barrier to dissociation, even at low temperature. The pathway FGH also benefits from this mismatch in the initial state adsorption energy and the dissociation barrier, so while based on energy barriers alone we would expect it to contribute much less to the overall dissociation rate than ABC, consideration of the overall energy profile suggests it (and similar pathways) could also contribute to the experimentally observed facile O2 dissociation. In the limit of low coverage, the dissociated O atoms will diffuse away from each other, as represented in Figure 9 by the pathways labeled “short-range diffusion”. This diffusion initially involves small barriers due to the repulsive interactions of the oxygens, but eventually they will reach great enough separation that they no longer interact, and they will then diffuse according to the model described in section 3.5. This diffusion regime is represented in Figure 9 by the dotted pathway labeled “tracer diffusion regime”. One expects that the fast dissociation of O2 described here will persist only as long as the key adsorption sites are available, but as coverage increases these sites will become poisoned and alternative, less favorable pathways, such as pathway FIJ or others not yet explored, will replace pathways ABC and FGH. Additional work is under way to understand the effects of increasing coverage on this system for molecular O2 binding, atomic O binding, and O2 dissociation as well.

4. CONCLUSIONS In this work we have used DFT to probe the effect of surface structure on the adsorption, dissociation, and diffusion of oxygen. We consider a Pt(321) surface, one that affords a large variety and high density of binding sites for atomic and molecular oxygen. At the low oxygen coverage studied here, the strongest binding sites are concentrated around the undercoordinated kink Pt atom, with oxygen binding most strongly in the b21 and b12 bridge sites for atomic and molecular oxygen, respectively. Binding energies of both atomic and molecular oxygen in different sites correlate well with both the Pt
Pt coordination numbers and d-band centers of the adsorbing surface atoms. O2 adsorption is even more sensitive to the surface structure than is atomic O, and absolute O2 binding energies at the most favorable sites are 0.85 eV greater on Pt(321) than on Pt(111). Nudged elastic band methods were applied to determine the energetics of several possible O2 dissociation pathways. The dissociation barriers obtained in this way were found to be slightly lower than for Pt(111) relative to an adsorbed molecular precursor state, but more than 0.8 eV lower relative to a gas phase O2 reference. From the limited low coverage O
Pt(321) experimental data available, the DFT model presented here is found to be in good agreement with experiment, specifically the atomic O heat of adsorption, the relative strength of O2 binding on Pt(321) and Pt(111), and the existence of a low-barrier O2 dissociation pathway allowing rapid dissociation of O2 even at low temperature. 8185

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Langmuir Tracer diffusion of O on the (321) surface was modeled using a coarse-graining approach. This model predicts that, at room temperature, oxygen diffuses more slowly on the (321) surface than the (111) surface by about 3 orders of magnitude. This may have important implications relating to the ability of adsorbates to migrate and reorder on the surface as they adsorb. Particularly in the context of O2 adsorption and dissociation at low temperatures, low surface mobility and the stochastic nature of gas impingement on the surface may contribute to the formation of small, isolated regions of locally lower or higher coverage. As with other metal surfaces, adsorbate coverage will likely have a large effect on the energetics and dynamics of reactions at the (321) surface, effects that are evidenced in observed TPD, vibrational spectroscopy, XPS, and presumably even in surface reactivity.22,30 The characterization of low coverage behavior developed here is the starting point for describing higher coverage behavior, the focus of current work.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]; phone: þ1-574-631-8754.

’ ACKNOWLEDGMENT We gratefully acknowledge funding from DOE BES Grant # DE-FG02-06ER15839 and the Arthur J. Schmitt Foundation as well as computing resources and technical support from the Notre Dame Center for Research Computing. We also appreciate the advice and collaboration of Dr. Andrew Smeltz and Prof. Fabio Ribeiro at Purdue University. ’ REFERENCES (1) Bogicevic, A.; Stromquist, J.; Lundqvist, B. I. Phys. Rev. B: Condens. Matter 1998, 57, 4289–92. (2) Lynch, M.; Hu, P. Surf. Sci. 2000, 458, 1–14. (3) Tang, H.; van der Ven, A.; Trout, B. L. Mol. Phys. 2004, 102, 273–9. (4) Getman, R. B.; Xu, Y.; Schneider, W. F. J. Phys. Chem. C 2008, 112, 9559–9572. (5) Ge, Q.; Hu, P.; King, D.; Lee, M.; White, J.; Payne, M. J. Chem. Phys. 1997, 106, 1210–1215. (6) Deskins, N.; Lauterbach, J.; Thomson, K. J. Chem. Phys. 2005, 122, 184709. (7) Liu, D.-J.; Evans, J. W. ChemPhysChem 2010, 11, 2174–2181. (8) Feibelman, P.; Esch, S.; Michely, T. Phys. Rev. Lett. 1996, 77, 2257–2260. (9) Fajin, J. L. C.; Cordeiro, M. N. D. S.; Gomes, J. R. B. J. Phys. Chem. C 2007, 111, 17311–17321. (10) Fajin, J. L. C.; Cordeiro, M. N. D. S.; Gomes, J. R. B. Surf. Sci. 2008, 602, 424–435. (11) Fajin, J. L. C.; Cordeiro, M. N. D. S.; Gomes, J. R. B. J. Phys. Chem. C 2008, 112, 17291–17302. (12) Fajin, J. L. C.; Cordeiro, M. N. D. S.; Gomes, J. R. B. J. Phys. Chem. C 2009, 113, 8864–8877. (13) Fajin, J. L. C.; Cordeiro, M. N. D. S.; Illas, F.; Gomes, J. R. B. J. Catal. 2009, 268, 131–141. (14) Fajin, J. L. C.; Cordeiro, M. N. D. S.; Comes, J. R. B. J. Mol. Struct. (THEOCHEM) 2010, 946, 51–56. (15) Janssens, T. V. W.; Clausen, B. S.; Hvolbaek, B.; Falsig, H.; Christensen, C. H.; Bligaard, T.; Nørskov, J. K. Top. Catal. 2007, 44, 15–26. (16) Jiang, T.; Mowbray, D. J.; Dobrin, S.; Falsig, H.; Hvolbaek, B.; Bligaard, T.; Nørskov, J. K. J. Phys. Chem. C 2009, 113, 10548–10553.

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