ARTICLE pubs.acs.org/JPCC
The Electronic Structure of GoldPlatinum Nanoparticles: Collecting Clues for Why They Are Special Linn Leppert and Stephan K€ummel* Theoretical Physics IV, Physics Institute, University of Bayreuth, D-95440 Bayreuth, Germany ABSTRACT: We present a density functional study of the electronic and geometric structure of AuPt nanoparticles with up to 40 atoms. Our first-principles calculations consistently show a coreshell growth pattern, qualitatively confirming the findings of previous semiempirical calculations. The average bond lengths of small alloy clusters show a “Vegard’s law” type behavior independent of their specific geometry. We investigate the static electric dipole polarizability, the KohnSham density of states, and the spatial orbital structure as possible indicators for the special, catalysis-relevant electronic properties of AuPt particles. Our results show that small changes in the atomic structure may considerably influence the surface properties of nanoalloy particles.
1. INTRODUCTION Highly dispersed gold particles have proved their capacity as potent catalysts in a multitude of industrially important reactions.1 The origin of this remarkable catalytic activity is strongly dependent on support, size, and shape of the nanoparticles.25 A further refinement of the catalytic properties of nanoparticles can be achieved by alloying.6 For example, goldplatinum nanoparticles immobilized in spherical polyelectrolyte brushes (SPBs) show enhanced catalytic activity as compared to pure gold nanoparticles7 and have been found to be excellent catalysts of oxidation reactions.810 The structure of these particles has been intensely investigated experimentally,1115 with the conclusion that AuPt nanoparticles form alloys although Au and Pt are not miscible in the bulk. In contrast to the many experimental insights that have been gained, the theoretical understanding of nanoalloys is still limited. An explanation of their catalytic behavior in general, and especially an explanation for why alloy particles can show a dramatically different catalytic behavior from pure nanoparticles, is still lacking. To gain insight into the catalytic mechanism, an important prerequisite is to determine the atomic structure of the nanoparticles, which is intimately connected with their electronic structure. From a theoretical point of view, alloy nanoparticles are even harder to treat than their pure equivalents. The potential energy surface (PES), which can exhibit up to thousands of local minima for pure nanoparticles, is additionally complicated by the presence of a large number of so-called homotops,16,17 that is, clusters with the same number of atoms and the same composition of Au and Pt, which exhibit the same geometrical arrangement of these atoms, but differ in the way Au and Pt are distributed over the cluster. The challenge to find the global minimum of the PES,18 as well as the sizable electron number of heavy elements like Au and Pt, aggravate an ab initio treatment of these systems. r 2011 American Chemical Society
The vast computational effort that a first-principles description of these systems requires has led to an ample spectrum of insightful theoretical studies at lower levels of sophistication.1923 Considerably fewer first-principles studies exist.5,24 Based on density functional theory (DFT) calculations, the present work identifies a growth pattern for AuPt clusters by locating stable low energy structures for selected cluster sizes with many different compositions. Several different structures of comparable energy are found for each size, but throughout all the studied systems a coreshell pattern emerges as a unifying structural motif. We further investigate the density of states, the electronic polarization, and the spatial orbital structure as possible factors in determining catalytic properties. In the following sections 2 and 3, the theoretical foundations as well as computational details are briefly summarized. In section 4, geometrical and electronic properties of stable low-energy clusters are presented. Section 5 discusses the density of states, polarizability and orbital investigations, leading to the conclusions drawn in section 6.
2. THEORETICAL FRAMEWORK In our approach, we treat the valence electrons quantum mechanically using the density functional theory in the KohnSham framework. As discussed below, the PerdewBurkeErnzerhof Generalized Gradient Approximation (PBE GGA)25 and the Tao-Perdew-Staroverov-Scuseria (TPSS)26 Meta-GGA are used for taking into account exchange and correlation effects. The nuclei are treated as classical particles. The interaction between electrons and nuclei is described via ab initio energy-adjusted27 and TroullierMartins pseudopotentials,28 respectively. As Au Received: December 23, 2010 Revised: February 22, 2011 Published: March 18, 2011 6694
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and Pt are heavy elements with many core electrons and as the core electrons are physically and chemically inert, the pseudopotential approximation allows for considerable savings in computing time while still yielding accurate results. In addition, it provides for an elegant way of incorporating relativistic effects. Including the latter is crucial for heavy elements, as explicitly demonstrated, for example, in ref 5. Overall, the combination of density functional theory with semilocal exchange-correlation functionals and ab initio pseudopotentials allows for a relatively efficient first-principles investigation of metal clusters. We thus avoid the use of empirical interaction potentials and gain insights into microscopic, quantum mechanical details of the electronic structure.
3. DETAILS OF COMPUTATION, BASIS SETS, AND ACCURACY OF THE METHOD In our calculations, we predominantly used the TURBOMOLE program suite29 and the PBE GGA exchange correlation functional.25 The motivation of this choice is to avoid empirical parameters while at the same time limiting computational expense as much as possible. As an explicit density functional, the PBE GGA can be used in the regular KohnSham scheme, whereas orbital-dependent functionals such as Meta-GGAs or hybrid functionals require either construction of the Optimized Effective Potential or use of the Generalized KohnSham approach,30 which increases the computational load. Furthermore, interpreting the eigenvalues of the generalized KohnSham scheme requires special care,31 whereas we can resort to established theorems in the KohnSham case as discussed in section 5. Thus, the PBE functional is ideally suited for the purposes of this study. We note, though, that it has been reported that details in the energetic ordering of small Au clusters are best described with the TPSS meta-GGA,32 which we therefore used in some calculations for validation purposes. Table 5 in the Appendix gives an overview of different calculations for the Au dimer. Comparing the PBE and TPSS functionals for Au2, we find that binding energies differ by only 0.02 eV and bond lengths by only 0.01 Å, a result that lets using the PBE functional appear quite reasonable. Throughout this Article, the binding energy (per atom) of an AuPt nanoparticle with n Au atoms and m Pt atoms was defined so that positive values for this energy were gained; that is, a higher binding energy corresponds to a lower total energy and therefore to more stable clusters: EB ¼
Etotal ðn 3 EAu þ m 3 EPt Þ nþm
ð1Þ
In Table 1, we report the binding energies per atom for the three Au18Pt2 homotops shown in Figure 1. Again, PBE and TPSS yield quite similar results, leading to the same energetic ordering of the isomers and relative energy differences that are of comparable size. This confirms that for the level of accuracy relevant for our study the PBE functional is a good choice. We also carefully checked the influence of computational parameters such as basis sets, integration grids, etc. Coulomb interactions were treated within the resolution of the identity (RI) approximation.3335 This accelerates calculations considerably but leaves binding energies and bond lengths almost unchanged. The influence of the grid36 on which the quadrature of exchangecorrelation terms is carried out is also much smaller than that of basis set and functional (see Table 5 in the Appendix).
Table 1. Binding Energies per Atom Calculated with PBE and TPSS for Three Different Au18Pt2 Homotops cluster
PBE [eV]
TPSS [eV]
1
2.234
2.361
2 3
2.210 2.188
2.324 2.310
Figure 1. Au18Pt2 homotops used in the comparison of the PBE and TPSS functionals of Table 1.
The choice of basis set is crucial for the accuracy of binding energies, but has only minor influence on bond lengths (see again Table 5). We are only interested in relative stabilities, rather than in accurate absolute values for binding energies. For reasons of computing time, structure optimizations were therefore carried out with a split valence basis set with one polarization function (SVP).37 Where different structural isomers were to be compared, a triple-ζ basis set with two polarization functions was used.37 All structures were optimized using redundant internal coordinates38 and without any symmetry constraints. Scalar relativistic effects were taken into account by using small-core pseudopotentials with 19 valence electrons for Au and 18 valence electrons for Pt atoms.27 The bond length of the Au2 dimer was also compared to results calculated with a locally modified version39 of the real-space DFT-program PARSEC.42 PARSEC uses TroullierMartins-type pseudopotentials28 to account for scalar relativistic effects, considering 10 valence electrons of Au explicitly. Bond lengths of Au2 calculated with the larger triple- and quadruple-ζ basis sets are in very good agreement with the PARSEC result, providing a further consistency check for our methods.
4. STRUCTURE AND MIXING PATTERNS As already mentioned in the Introduction, our aim in the following cannot be to find all possible low energy structures of AuPt particles with tens of atoms, because the number of low energy configurations is overwhelmingly large. Furthermore, the typical catalysis experiments that motivate the interest in AuPt nanoalloys are conducted at finite temperatures. Therefore, it is to be expected that it is not decisive to find the one configuration that is the absolutely lowest in energy, but it is rather of much greater importance to understand the principles that govern the structure of AuPt particles and identify classes of low energy structures and the overall growth pattern, if there is one. This is our aim in the following. As electron scattering and transmission microscopy pictures show that many AuPt nanoparticles, especially those synthesized within SPBs, primarily show crystalline structures,7 we choose for our first investigation the Au20 cluster: Its structure is well established to be a tetrahedron40 and is thus part of the fcc bulk lattice. 6695
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Figure 2. There are three different possibilities to place a Pt atom within the Au20 tetrahedron: in the middle of one of the faces, at the edge, and at the corner of the tetrahedron.
Table 2. Binding Energies per Atom for Three Different Au19Pt1 Homotops cluster
binding energy [eV]
face
2.480
edge
2.475
corner
2.456
Starting from Au20, we replaced one Au atom by a Pt atom to introduce a small “perturbation” into the cluster. Figure 2 shows the three ways there are to do so. In each case, we reoptimized the cluster structure. The highest binding energy is found when the Pt atom is in the middle of one of the faces of the tetrahedron (Table 2), that is, when the Pt atom has the highest possible coordination number. We then replaced, one by one, further Au atoms by Pt atoms, in each case reoptimizing the structure and calculating the energy of the possible homotops. For all AuPt compositions, the energetically most favorable positions for newly added Pt atoms are again the ones where Pt has the highest possible coordination number. Figure 3 shows the lowest energy structures for all compositions AuxPty with x decreasing from 20 to 0 and y increasing from 0 to 20 that are obtained in this way. Because of the fact that only local relaxations were done, only the structures with x close to 20, that is, of clusters with only a small Pt content, can be hoped to also be global low energy structures. However, the main point is a different one: The series of structures suggests a relatively simple growth pattern for AuPt nanoparticles with increasing Pt content. As it is energetically favorable to replace an Au atom in such a way by a Pt atom that the Pt atom has the highest possible coordination number, a coreshell pattern with Au atoms as the shell and Pt atoms in the core emerges, as seen in Figure 3. We can go through the same procedure starting at the opposite end, that is, starting from Pt20 and adding Au atoms. For Pt20 we chose the structure that was found as the global minimum of Pt20 when modeling the interaction by a SuttonChen potential.43 As Pt atoms are replaced by Au atoms and the structures are locally optimized, we find as the structures with lowest energy for each composition the ones shown in Figure 4. Again, energetically favorable clusters feature Au atoms at “shell”-sites and Pt atoms in the core. We would like to stress that we tested the stability of the clusters Au20, Au15Pt5, Au10Pt10, Au5Pt15, and Pt20 both for the tetrahedral and for the amorphous isomers. For this purpose, we carried out several simulated annealing runs, where the clusters were heated to 600 K, followed by a slow annealing period. This procedure yields nearly unchanged structures for the tetrahedral Au20, Au15Pt5, and Au10Pt10, as well as for the amorphous Pt20,
Figure 3. Lowest energy structures for tetrahedral 20 atomic AuPt clusters. A coreshell growth pattern is observed.
Au5Pt15, and Au10Pt10 as compared to the starting geometries of these calculations. We note, though, that the resulting tetrahedral Au5Pt15 and Pt20 and the amorphous Au15Pt5 and Au20 deviate more distinctly from their original form. However, they still show characteristic features of their former tetrahedral and amorphous structure patterns, and, more importantly, the coreshell structure remains throughout the whole annealing process. This shows that the structures that we identified in our growth lines are indeed stable low energy structures and not artifacts. This reasoning is further corroborated by Figure 5 and Table 3 in which we compare several Au10Pt10 isomers with differing mixing patterns for a consistency check. Clearly, the coreshell pattern is energetically the most favorable for both the amorphous and the bulk-like tetrahedral structures. 6696
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Figure 5. Several structural isomers of Au10Pt10: (1) tetrahedral coreshell, (2) tetrahedral phase-separated, (3) tetrahedral random, (4) Gupta potential structure41 based on local reoptimization of the lowest energy structure from ref 19, (5) amorphous coreshell, and (6) amorphous random.
Table 3. Binding Energies per Atom for Several Different Au10Pt10 Isomers
Figure 4. Lowest energy structures for amorphous 20 atomic AuPt clusters. Again, a coreshell growth pattern is observed.
It is important to note that the geometries that we find by starting from Pt20 and optimizing locally are different from the ones that are found when starting from the tetrahedron. This shows that local optimization would not suffice if our aim were to find the global minimum. However, it also shows, and this is the important positive finding for our aim of identifying patterns instead of single structures, that the coreshell growth pattern is independent of a specific geometry and very clearly emerges in different geometrical growth lines.
cluster
binding energy [eV]
1
3.277
2
3.277
3 4
3.157 3.245
5
3.302
6
3.255
The coreshell pattern observed in our calculations is in line with previous theoretical studies based on empirical potentials,1923 but is in contrast to conclusions drawn from experiments,7,1115 which find homogenously mixed particles. One may speculate that the discrepancy is a consequence of the 20 atom systems being simply too small to develop a homogeneous mixture. In other words, one may suspect that the coreshell pattern that has been found so far will vanish as one goes to larger clusters. Alternatively, one may also argue that for 20 atom nanoparticles a differentiation between core and shell is disputable, and that therefore the conclusion about coreshell systematics is premature. Therefore, as further tests for the coreshell scheme, we calculated the binding energies of various AuPt nanoparticles with 40 atoms (Figure 6). Structures 13 in Figure 6 were obtained from the global minimum of Au40 when modeling the interaction with a SuttonChen potential,43 replacing 20 Au atoms by Pt atoms in each case and then locally optimizing the obtained clusters. Structures 46 are again local reoptimizations of Gupta potential structures from ref 19. For structure 5, the Pt and Au atoms were randomly distributed over the cluster, while in structure 6 two distinct phases were constructed before local reoptimization. These larger nanoparticles can more clearly be divided into core and shell regions. The results in Table 4 confirm again that AuPt nanoparticles prefer a coreshell pattern with a Pt core and a Au shell. Therefore, we conclude that the coreshell configuration is rather universal in AuPt nanoparticles. As the discrepancy to the experimental conclusions thus remains, we now take a closer look at the average bond length 6697
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Figure 6. Structural isomers of Au20Pt20 as obtained from DFT optimization. Structures are named after the geometry that served as the starting point of the DFT optimization; see main text. (1) SuttonChen random, (2) SuttonChen coreshell, (3) SuttonChen phaseseparated, (4) Gupta random, (5) Gupta coreshell, and (6) Gupta phase-separated.
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Figure 7. A Vegard’s type law can be seen for the nearest neighbor bond length both of tetrahedral and amorphous 20 atomic clusters.
Table 4. Binding Energies per Atom for Several Au20Pt20 Isomers with Varying Mixing Patterns cluster
binding energy [eV]
1
3.520
2
3.570
3 4
3.566 3.539
5
3.578
6
3.550
in the theoretically found structures. This is a close lying next step because the average bond length plays an important role in the experimental analysis: Typical experiments determine a lattice parameter from X-ray diffraction spectra and conclude that the investigated particles are homogeneous mixtures of Au and Pt when the thus determined lattice parameter changes linearly with varying Au or Pt content of the particles. In bulk samples, the linear dependence of the lattice parameter is termed Vegard’s law,44 and this law is usually interpreted as a hallmark signature for uniformly mixed particles. For finite clusters, it is not possible to define a lattice parameter as in bulk crystals, but one can define an averaged nearest neighbor bond length. One way of doing so is to determine the average distance of every atom in a cluster to its, for example, four nearest neighbors, and then taking the average over all atoms in the cluster. We have calculated the thus defined average bond length for a considerable number of AuPt nanoparticles. Figure 7 shows the average bond length as a function of the number of Au atoms in the cluster for the 20 atomic tetrahedral structures from Figure 3 in blue, and for the amorphous structures from Figure 4 in orange. In both cases, the average bond length increases linearly. To again ensure that we are not looking at an artifact or “special behavior” of 20 atom clusters, we calculated and show in Figure 8 the average bond length obtained for 40-atomic AuPt nanoparticles with varying Au content. The structures that were analyzed here are based on structure 5 in Figure 6, where the Au content was increased and decreased in steps of two atoms, always trying to stick to an overall coreshell pattern of the cluster. Eventually, all structures were again locally reoptimized. Also, for the 40-atom particles, we clearly see a linear trend in the average
Figure 8. A Vegard’s type law for selected 40 atomic clusters based on clusters from ref 19 as explained in the text.
bond length, and we checked that the linearity does not depend on the number of nearest neighbors taken into account in the averaging process. One may thus speak of a “Vegard’s law on the nano scale” that is observed for all systems that we studied. However, the linear relation is independent of whether the nanoparticles are amorphous or bulk-like, and it is observed both for coreshell and for randomly mixed nanoparticles. Therefore, it cannot be the only argument on which an analysis of mixing patterns is based. A more detailed analysis of the X-ray experiment interpretation is thus one task for future work. We would like to note, though, that there are other aspects that may influence the comparison between theoretically and experimentally obtained structures, such as a finite experimental temperature and the presence of solvents. However, in any case, the electronic structure of the AuPt nanoparticles must play an important role in their catalytic properties, and therefore we investigate it in the following section.
5. ANALYSIS OF THE ELECTRONIC STRUCTURE Our investigation is motivated by the remarkable catalytic properties of AuPt nanoparticles, which are exemplified by 6698
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Figure 9. The trace of the tensor of the static electric dipole polarizability per electron of the 20 atomic tetrahedral and amorphous clusters from Figures 3 and 4. It is nearly independent of the Au/Pt ratio.
experiments showing that the turnover rate of AuPt nanoparticles immobilized within SPBs is the highest at a Pt proportion of around 80%.7 To the best of our knowledge, there is so far no conclusive explanation for why nanoalloys in general are such suitable catalysts, and especially it is unclear why a specific percentage of 20% Au in AuPt nanoparticles is optimal. In the following, we investigate different electronic properties of AuPt clusters as a function of their composition and check whether special features are observed at certain composition ratios. If such features exist, they might provide a first clue to a better understanding of AuPt nanoparticles. The first electronic quantity that we report is the static 5. The polarizability specifies the electric dipole polarizability R linear response of the dipole moment μBto an external electrical field EB: T
μB ¼ R EB
ð2Þ
and more generally is a measure of how “flexible” the electronic density of a given system adapts to a perturbation. Electronic shell effects45 and structural properties of metal clusters are observable in the polarizability,46,47 and one may thus speculate that the special properties of AuPt nanoparticles may also be reflected in it. Figure 9 shows the trace of the polarizability tensor per electron for the tetrahedral clusters of Figure 3 and the amorphous ones of Figure 4. Neither of the two series shows any special features in the polarizability as a function of Au content. Thus, at least in these cases, the polarizability does not seem to be a relevant indicator for special properties. A quantity that typically is more directly related to a systems’ reactivity is its density of states (DOS), and in particular the DOS at the Fermi level. Early DFT literature denied the KohnSham eigenvalues any physical meaning, but in the past decades it has been shown that the highest occupied molecular KohnSham orbital (HOMO) is exactly equal to the negative of the lowest vertical ionization potential,48,49 and that the occupied KohnSham eigenvalues can yield approximate but rather accurate values for the vertical ionization potentials.50,51 Interpreting KohnSham eigenvalues has been used successfully in the investigation of metal clusters,52,53 and the physical significance of KohnSham
Figure 10. The KohnSham DOS for 40 atomic AuPt clusters. Top, Au40; middle, Au20Pt20; bottom, Pt40. With increasing Pt content, the density of states at the Fermi edge also increases.
eigenvalues can also be rationalized in terms of perturbation theory arguments.54 Analyzing the KohnSham DOS may therefore allow one to qualitatively gain insight into the “reactivity” of a system, and in our case may give a hint toward the role that alloying plays for the electronic structure of AuPt nanoparticles. Figure 10 shows the KohnSham DOS (normalized to the total number of electrons and broadened by a Gaussian function of 0.05 eV at full width half-maximum) for 40 atom clusters of 6699
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The Journal of Physical Chemistry C pure Au, half Au and half Pt, and pure Pt. The structures used here were obtained as described in section 4; that is, starting from structure 5 of Figure 6 Au atoms were replaced by Pt atoms (or vice versa) and the geometry was again optimized using DFT. Comparison of the upper, middle, and lower panel shows that the DOS close to the Fermi edge increases with increasing Pt content. To quantify this “optical impression”, we have evaluated
Figure 11. The KohnSham DOS of 40 atomic AuPt nanoparticles integrated around the Fermi level increases almost linearly with increasing Pt percentage.
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the DOS for a series of clusters with increasing Au content and integrated it from a threshold energy upward. The result is shown in Figure 11 for three different choices of the lower end of the integration threshold. One can clearly see that the DOS close to the Fermi level is monotonically increasing with increasing Pt content. There is no maximum at a certain Au/Pt ratio, and this observation is independent of which specific value of the integration threshold is chosen. This qualitative behavior of the DOS with increasing Pt content is observed independently of specific cluster geometries and is a rather universal feature. It can therefore be expected to also be seen in larger clusters. Thus, we conclude that it is unlikely that the DOS is directly related to the observation of an “optimum value” for the Au/Pt ratio in catalytic experiments. However, in addition to the rather direct possible influences of alloying that we just investigated, one may also think about more indirect effects, in particular those that are related to the cluster’s surface. Surface properties play an important role in catalysis, and one can imagine that particular mixing ratios of Au and Pt lead to special surface properties. For example, the presence of Pt may yield an important contribution to the reactivity via its DOS, whereas the presence of Au atoms may lead to a “softer” surface in which the atoms are more easily “rearrangeable” than in a pure Pt particle, allowing the surface, for example, to “adapt” to molecules that bind and unbind during a catalytic reaction. Such a mechanism, however, can only play a role when the rearrangement of a few surface atoms can have a noticeable influence on the electronic structure at the surface. That this is indeed possible is shown in
Figure 12. Plots of the highest occupied molecular orbital at þ0.04 a03/2 (red) and 0.04 a03/2 (blue) for two just slightly different Au10Pt10 cluster structures. Left: Coreshell Au10Pt10 cluster with tetrahedral geometry. There is no HOMO density to be seen at the top of the cluster. Right: The Pt atom at the bottom of the tetrahedron was moved to the top corner. This small structural rearrangement changes the HOMO distribution completely, so that HOMO density appears pronouncedly at the top of the cluster.
Figure 13. Plots of the highest occupied molecular orbital at þ0.04 a03/2 (red) and 0.04 a03/2 (blue) for two Au20Pt20 cluster structures. The HOMO density of a coreshell like Au20Pt20 cluster (structure 2 in Figure 6) is delocalized over the central Pt region. Right: Upon rearrangement of a few atoms (structure 3 in Figure 6), the HOMO is delocalized over the Pt “half” of the cluster. 6700
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The Journal of Physical Chemistry C Figures 12 and 13. Figure 12 shows the highest occupied KohnSham orbital (HOMO) of the Au10Pt10 homotops that are designated as structures 1 and 2 in Figure 5. The HOMO has physical relevance as it asymptotically dominates the density and its exponential decay is governed by the first ionization potential. Inspecting Figure 12 reveals that the only difference between the two structures is the rearrangement of a single Pt atom, in this case from the middle of the bottom face to the top corner. This seemingly small structural change leads to a complete disappearance of the HOMO from the bottom of the tetrahedron; that is, rearrangement of one atom changes the local electronic structure very noticeably. We stress that this feature is not special to the tetrahedral clusters. Similar effects are visible, for example, for the larger clusters presented in Figure 6. Rearranging a few atoms leads to a completely different distribution of the HOMO, as shown in Figure 13. Qualitatively similar effects can be expected at corrugations or steps and terraces of large surfaces. The combination of the high lying DOS contributed by Pt atoms and structural flexibility introduced by Au atoms may thus be a factor in determining the special catalytic properties of AuPt nanoparticles. These hints, here obtained from clusters with a few hundreds of valence electrons, will further be followed by future work focusing on larger clusters.
6. CONCLUSION In summary, we have performed first-principles calculations, which confirm that AuPt clusters prefer coreshell like structures with a Pt core and an Au shell. The average nearest neighbor bond length in the alloy clusters increases linearly with increasing Au content. This can be regarded as Vegard’s law on the nanoscale. The linear behavior is observed for different mixing patterns and therefore cannot be used to identify homogenously mixed nanoparticles. We further analyzed the electronic properties of the clusters with the aim of quantifying features that may make AuPt nanoparticles with certain mixing ratios electronically “special”, and which therefore may serve as first clues on the way to an understanding of their special catalytic properties. We showed that the static electric polarizability does not show any striking features with varying cluster composition. The density of states close to the Fermi level increases with increasing Pt content of the particles. In combination with the fact that small structural rearrangements can have a pronounced influence on the spatial extension of the electronic density, which we visualized by investigating the clusters’ HOMO, this can be a first hint at that a combination of structural and electronic properties may be important in determining the catalytic properties of AuPt nanoparticles. In future theoretical work, we will try to clarify this hypothesis by probing the surface structure of larger AuPt nanoparticles with the aim of quantifying its ability to rearrange under the influence of external perturbations, as well as clarify its electronic reaction to adsorbed molecules, solvents, and temperature effects, which may play a role as well. The growth pattern and electronic features that were identified in the present study provide a good starting point for such future work. ’ APPENDIX Table 5 gives an overview of the influence of the computational parameters that are discussed in section 3.
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Table 5. Binding Energies per Atom and Bond Lengths of Au2 with Different Parameters Used in the TURBOMOLE and the PARSEC (Last Line) Program Packages
basis
functional grid RI
binding energy [eV]
bond length [Å]
SVP
1.068
2.568
TZVP
1.120
2.531
TZVPP
1.137
2.522
QZVP
1.152
2.520
QZVPP PBE
1.160 1.068
2.516 2.568
TPSS
1.058
2.556
m3
1.068
2.568
m5
1.069
2.567
with
1.068
2.568
without
1.068
2.568
1.330
2.526
PARSEC
’ AUTHOR INFORMATION Corresponding Author
*Phone: þ49 921 55 3220. Fax: þ49 921 55 3223. E-mail:
[email protected].
’ ACKNOWLEDGMENT We are grateful to Roy L. Johnston for providing us with the coordinates from his AuPt cluster geometry optimizations and to Matthias Ballauff for discussions. We acknowledge financial support by the German Science Foundation via SFB 840. ’ REFERENCES (1) Haruta, M. Catal. Today 1997, 36, 153. (2) Zhou, X.; Xu, W.; Liu, G.; Panda, D.; Chen, P. J. Am. Chem. Soc. 2010, 132, 138. (3) Panigrahi, S.; Basu, S.; Praharaj, S.; Pande, S.; Jana, S.; Pal, A.; Ghosh, S. K.; Pal, T. J. Phys. Chem. C 2007, 111, 4596. (4) Zeng, J.; Zhang, Q.; Chen, J.; Xia, Y. Nano Lett. 2010, 10, 30. (5) H€akkinen, H.; Moseler, M.; Kostko, O.; Morgner, N.; Astruc Hoffmann, M.; Issendorff, B. v. Phys. Rev. Lett. 2004, 93, 093401–1. (6) Ferrando, R.; Jellinek, J.; Johnston, R. L. Chem. Rev. 2008, 108, 846. (7) Schrinner, M.; Proch, S.; Mei, Y.; Kempe, R.; Miyajima, N.; Ballauff, M. Adv. Mater. 2008, 20, 1928. (8) Lou, Y.; Maye, M. M.; Han, L.; Luo, J.; Zhong, C.-J. Chem. Commun. 2001, 2001, 473. (9) Stamenkovic, V. R.; Mun, B. S.; Arenz, M.; Mayrhofer, K. J. J.; Lucas, C. A.; Wang, G.; Ross, P. N.; Marcovic, N. M. Nat. Mater. 2007, 6, 241. (10) Mott, D.; Luo, J.; Njoki, P. N.; Lin, Y.; Wang, L.; Zhong, C.-J. Catal. Today 2007, 122, 378. (11) Mott, D.; Luo, J.; Smith, A.; Njoki, P. N.; Wang, L.; Zhong, C.-J. Nanoscale Res. Lett. 2007, 2, 12. (12) Njoki, P. N.; Luo, J.; Wang, L.; Maye, M. M.; Quaizar, H.; Zhong, C. J. Langmuir 1623, 21, 2005. (13) Luo, J.; Njoki, P. N.; Lin, Y.; Mott, D.; Wang, L.; Zhong, C. J. Langmuir 2006, 22, 2892. (14) Malis, O.; Radu, M.; Mott, D.; Wanjala, B.; Luo, J.; Zhong, C. J. Nanotechnology 2009, 20, 245708. (15) Luo, J.; Maye, M. M.; Petkov, V.; Kariuki, N. N.; Wang, L.; Njoki, P.; Mott, D.; Lin, Y.; Zhong, C. J. Chem. Mater. 2005, 17, 3086. (16) Jellinek, J.; Krissinel, E. B. In Theory of Atomic and Molecular Clusters; Jellinek, J., Ed.; Springer: Berlin, 1999; pp 277308. 6701
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dx.doi.org/10.1021/jp112224t |J. Phys. Chem. C 2011, 115, 6694–6702
