Letter pubs.acs.org/JPCL
Investigation of Catalytic Finite-Size-Effects of Platinum Metal Clusters Lin Li,† Ask H. Larsen,‡ Nichols A. Romero,§ Vitali A. Morozov,§ Christian Glinsvad,‡ Frank Abild-Pedersen,∥ Jeff Greeley,⊥ Karsten W. Jacobsen,‡ and Jens K. Nørskov*,†,∥ †
Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States Center for Atomic-scale Materials Design (CAMD), Department of Physics, Building 307, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark § Leadership Computing Facility, Argonne National Laboratory, Argonne, Illinois 60439, United States ∥ SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States ⊥ Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States ‡
ABSTRACT: In this paper, we use density functional theory (DFT) calculations on highly parallel computing resources to study size-dependent changes in the chemical and electronic properties of platinum (Pt) for a number of fixed freestanding clusters ranging from 13 to 1415 atoms, or 0.7−3.5 nm in diameter. We find that the surface catalytic properties of the clusters converge to the single crystal limit for clusters with as few as 147 atoms (1.6 nm). Recently published results for gold (Au) clusters showed analogous convergence with size. However, this convergence happened at larger sizes, because the Au d-states do not contribute to the density of states around the Fermi-level, and the observed level fluctuations were not significantly damped until the cluster reached ca. 560 atoms (2.7 nm) in size. SECTION: Surfaces, Interfaces, Porous Materials, and Catalysis
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sizes, the surface chemistry is affected by the morphology of the clusters, and clusters are known to reconstruct significantly, depending on the environment.8−10 As a first step to understanding these diverse effects, we address the much simpler intrinsic electronic finite-size effects. We analyze these results in detail for fixed platinum clusters, and we compare and contrast the results to previously published work on gold clusters with the same consistent and well-defined geometry. The platinum systems of interest are freestanding cuboctahedral clusters, ranging from 13 to 1415 atoms, shown in Figure 1. In order to make a direct comparison with the previously published results on Au clusters, the platinum clusters are constructed in a similar fashion.11 The cuboctahedron provides a convenient model for studying the correspondence between cluster surface properties and the properties of certain bulk surfaces. On each cluster, there is a “triangular face,” which locally resembles the close-packed (111) slab of platinum, and an “edge” that locally is analogous to the (211) slab. In this work, the chemical properties of the metal surface are characterized by the adsorption energies of CO and O. These adsorbates were chosen because their adsorption energies are used as activity descriptors for a wide range of reactions, such as CO oxidation and oxygen reduction.12−15 We will show how
eterogeneous catalysts play a crucial role in the global economy. They are used in practically every industrial process, from making fuels and polymers to performing pollution remediation.1 Many such catalysts consist of precious metals in the shape of particles ranging in size from micrometers down to the nanometer scale. The bulk part of these particles is completely inactive, since it is not exposed to the reactant. That means that large portions of the metal component are wasted. Additionally, as the size is reduced, the intrinsic catalytic properties of the material change due to a combination of localized coordination effects, changes in surface site distribution, surface relaxation, and quantum size effects. However, even the most careful experimental measurements have difficulty in deconvoluting these effects, and so in spite of the profound influence that these changes can have on the catalytic properties, they remain relatively poorly understood. In this study, we use DFT calculations to deconvolute the particle size effects mentioned above, and we concentrate on the intrinsic electronic finite-size effects of freestanding platinum clusters. The freestanding clusters are used as template systems, to better understand the correlation between cluster size and the electronic properties of the surface atoms. As mentioned above, however, in real catalysts, the chemical properties of the cluster surface atoms are affected by additional phenomena, such as adsorbate-induced perturbation, lattice strain, and support effects.2−7 Furthermore, for smaller cluster © 2012 American Chemical Society
Received: November 8, 2012 Accepted: December 22, 2012 Published: December 22, 2012 222
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Figure 1. All cuboctahedra platinum clusters studied, ranging from 13 to 1415 atoms. We have considered two adsorption sites for CO and O on every cluster. Oxygen fcc and CO top sites are placed as close to the center of the (111) like face as possible. Oxygen bridge edge and CO top edge sites are placed as close to the center of the edge as possible.
electronic effects vary with cluster size for these two local geometries. Through focusing on the changes in the electronic structures, we address the following questions: How does the calculated catalytic activity of the noble metal platinum vary with size? At what size do the quantum size effects become significant? Can one capture these variations using much more simple slab calculations, which only display certain specific surface geometries present on a nanoparticle? In order to single out how the electronic effects16 vary with cluster size, and exclude additional effects from geometric distortion, the clusters were calculated in fixed geometries. The adsorbates were placed on the cluster in the same local geometries as are preferred on the platinum (111) and (211) surface slabs. The adsorption energies were all calculated in the low coverage limit, with one single adsorbate per cluster, 1/16 ML coverage relative to the (111) surface on the close-packed slab, and 1/4 ML coverage relative to the step-edge atoms on the (211) surface slab. The total energies calculated in this study were obtained by density functional theory (DFT) calculations using the GPAW code.17,18 This code implements the projector augmented wave (PAW) 19 method using uniform real-space grids. The parallelization strategy in GPAW, along with access to a 40 960 node Blue Gene/P, permitted calculations on unit cells that contained up to 1415 platinum atoms. To describe the exchange and correlation energies, we chose the RPBE functional,20 which is a frequently used functional for describing the adsorption of small molecules on metal surfaces.21 A grid spacing of 0.14 Å was used for the convergence of adsorption energies. The Pt systems investigated were constructed using a lattice parameter of 3.999 Å, determined from RPBE. For the cluster calculations, a low Fermi-temperature of 0.01 eV was used. The clusters were enclosed in cells with 7 Å of vacuum to the nearest boundary. Periodic boundaries were not applied; therefore only the γ-point was sampled in the Brillouin zone. For the continuum slab model calculations, a 6-layer 4 × 4 surface computational cell was employed. The Brillouin zone was sampled with the Monkhorst−Pack scheme, using 4 × 4 × 1 k-points. The Fermi-temperature was set at 0.1 eV. Calculations of clusters 309 atoms and larger were carried out on the BlueGene/P supercomputer at Argonne National Laboratory. Figure 2 shows the different trends in the size dependence of adsorption energies on fixed platinum and gold clusters. The binding of CO and O in both cases becomes less negative (weaker binding) with increasing cluster size, and the platinum
Figure 2. Calculated adsorption energies of O and CO on the (111) plane and stepped facet on platinum and gold clusters. The left panel shows results for platinum where CO is adsorbed on top on the two facets and O is adsorbed 3-fold fcc and bridge on the (111) and stepped facets, respectively. The right panel shows similar results for adsorption sites identical to the ones on platinum for gold. The horizontal lines indicate the adsorption energies for O and CO on the (111) and (211) surface slabs. Experimentally obtained desorption energies for CO on Pt(111), Pt(211), and Au(211) are shown as dashed lines in the Figure.26−28
cluster appears to converge to the bulk limit faster than gold. For comparison and to show the reliability of our calculations, we have indicated experimental results for the CO adsorption, shown as dashed horizontal lines in the figure. The gold clusters showed clear finite-size effects on clusters smaller than 561 atoms (2.7 nm), especially for O adsorption.11 The 55 atom gold cluster shows a particularly weak binding of O and to a smaller extent CO. This can to a large extent be ascribed to electronic shell effects. The s-band hybridizes into electronic subshells consistent with jellium clusters.22,23 Fifty-eight selectrons correspond to a closed shell. As the 55 atom cluster is just below this size, it will easily accept electrons but not easily donate them. This decreases the binding of electronegative species such as O. By contrast, the 147 atom cluster is just above the shell closing at 138, and thus binds O more strongly. The adsorption energies on platinum clusters of 147 atoms (1.7 nm) and larger appeared to be identical to those values on the corresponding infinite surface. Due to s-shell filling, large 223
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Figure 3. Charge density difference (ρcluster+A − ρcluster − ρA) plots when (a) A is oxygen and (b) A is CO are adsorbed seen from above (upper panel) and the side (lower panel). The white and magenta color scale indicates areas where electrons are depleted and accumulated, respectively. The plotted contours are chosen to be (0.001e/A3).
appears to be more local on platinum clusters than similar results reported on gold. On gold clusters, the nearest and next nearest neighbors of the adsorption site appear to be affected by the screening cloud of the adsorbate.11 However, on platinum clusters, the next nearest neighbors are only slightly perturbed. One possible reason could be that the d-electrons in platinum provide better screening of the adsorbate, resulting in a more localized effect. Thus, the adsorbates on platinum mainly interact with the effects from the nearest neighbor atoms and much less from the corner and edge atoms. This will lead to the adsorption energies converging for smaller metal clusters than on gold. Figure 4 shows the transition from a molecular like to a metal like d-electron density of states (DOS) on the (111) surface of platinum clusters. In clusters smaller than 147 atoms, we observe an energy spectrum, which is clearly discrete, and above 147 atoms a more continuous band of states is formed. Thus, above 147 atoms, binding energies are expected to correlate with the position of the d-band to lowest order, and less with its intrinsic structure.24 In spite of this apparent correspondence between discreteness of the DOS and binding energies, however, it turns out that there is not a direct relationship between these two quantities for static clusters. In the following, we further describe this analysis for fixed Pt clusters, and we contrast the results to the very different behavior that has been described for fixed Au clusters.
oscillation in the adsorption energy with respect to size was observed on the gold clusters. However, for platinum clusters, the d-states are pinned to the Fermi level because of the fractional filling of d-states. This difference in the electronic structure accounts for the small oscillations observed in the CO and O adsorption energy on platinum clusters with size. From these results, we conclude that periodic surface calculations can be used to approximate adsorption energies in the fixedgeometry limit on platinum clusters above the critical size of 1.6 nm, and furthermore, finite-size effects disappear for smaller platinum clusters than on gold. In the following, we take a closer look at the O adsorption on the (111) surface, where the finite-size effects appear to be more pronounced. Figure 3 shows the charge density difference plot for O adsorption on the face-centered cubic (fcc)-like sites on the platinum cluster as well as on the (111) surface slab. The adsorbate-induced perturbation becomes more local as the cluster size increases. Indeed, the extent of charge perturbation on 147 atom platinum clusters and beyond appears to be very similar to the case on the (111) surface slab. This observation is consistent with the hypothesis that convergence in the adsorption energy coincides with convergence in the electron density response to the adsorption; the convergence in density response, in turn, implies that the response is no longer being perturbed by interaction with the corner and edge atoms of the larger clusters. In fact, the extent of charge density perturbation 224
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corner and edge atoms of the facet. This effect is local, and the critical size is based on the ability of the cluster to screen the adsorbate. In the case of gold clusters, this effect appears below 2.7 nm.11 On platinum, where the screening length is shorter, the bulk limit is reached around 1.6 nm. Finally, due to the selectron shell structure, quantum-size effects also play a role on small gold clusters. On those clusters, the spacing around the Fermi level can become large enough to significantly affect binding of adsorbates. In the case of platinum, the partially filled d-shell provides high density of states around the Fermi level, removing the gap around the Fermi level, and quantumsize effects were not observed. In conclusion, we have identified that the electronic finitesize effects in platinum clusters vanish beyond 1.6 nm, where the adsorption energies of CO and O match that of the extended surface. Just as in the case on gold, the convergence of the adsorption energy on platinum also coincides with the convergence of the charge density response to the adsorption. Platinum clusters appear to converge to the bulk limits more quickly than gold. This implies that the adsorbates have shorter screening lengths on platinum. Thus the local environment around the platinum adsorption site would become similar to that on the extend surface on smaller facets. In addition, due to the partially filled d-shell providing high density of states around the Fermi level, quantum-size effects were not observed in platinum clusters, in sharp contrast to the gold counterparts.
Figure 4. Projected d-density of states for surface (111) platinum atoms averaged over all platinum atoms in the (111)-like face on clusters.
The gaps in the electronic structures of the clusters could just as well be measured from the one-electron level spacing around the Fermi level. The gaps in the density of states would have significant impact on the adsorption energy if the level spacing were comparable to the adsorbate-cluster coupling matrix element. On gold clusters, the gaps in the density of states for 13 and 55 atom clusters are large enough to affect binding strength. The same is not true in the platinum case. For O adsorption, the coupling matrix element to the platinum clusters is around 4 eV.25 The level-spacings of the 13 and 55 atom clusters are found to be ca. 30 and 15 meV, respectively, and the ones for larger clusters are less than 10 meV. Since the level spacing is much less than the coupling matrix element, even for the smallest clusters the discreteness in the density of states is not expected to affect the binding significantly. In contrast, the coupling matrix element on gold clusters is around 3.4 eV, and the level spacings for the 13 and 55 atom clusters were found to be ca. 0.7 and 0.25 eV, respectively.11 Therefore, quantum-size effects were identified to play a role on those small gold clusters. In addition, it was recently shown that the adsorption energy of O on small platinum clusters depends strongly on the cluster geometry, and this dependence becomes less significant when the cluster size reaches above 110 atoms.22 Therefore, the finite-size effects experienced by the small platinum clusters are not due to quantum-size effects, but rather effects originating from the adsorption site geometry, and this effect disappears for clusters larger than 1.6 nm. In other words, on these small platinum clusters, the adsorbates would feel the effects from nearestneighbor corner and edge atoms of small facets, but not the effects of having discrete states or gaps around the Fermi level. To summarize, we comment on the three distinct finite-size effects that appeared on platinum and gold clusters. These effects account for the deviations in the surface behaviors from the bulk limit, absent of possible contributions from the support. First of all, a trivial effect of decreasing the cluster size is the increase in the exposed surface area of the metal. In addition, as the cluster size decreases, the corner and edge atoms accounts for a higher fraction of the cluster. Therefore, a difference in the surface properties of the catalyst would result from the increase in the fraction of undercoordinated sites on the surface. Second, for clusters below a certain size, the adsorbates start to feel the
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research used resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-06CH11357. L.L., F.A.P. and J.K.N. gratefully acknowledge support from the U.S. Department of Energy under Contract Number DE-AC0276SF00515. A DOE Early Career Award for J.G., together with use of the Center for Nanoscale Materials, was supported by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences, under Contract No. DE-AC0206CH11357.
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