Theoretical Study of the Structures and Chemical Ordering of

Article pubs.acs.org/JPCC

Theoretical Study of the Structures and Chemical Ordering of Palladium−Gold Nanoalloys Supported on MgO(100) Ramli Ismail,†,‡ Riccardo Ferrando,§ and Roy L. Johnston*,† †

School of Chemistry, University of Birmingham, Edgbaston, B15 2TT Birmingham, United Kingdom Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany § Dipartimento di Fisica, Universita’ di Genova, 16146 Genova, Italy ‡

S Supporting Information *

ABSTRACT: Bimetallic nanoparticles composed of palladium and gold are particularly interesting from the viewpoint of their catalytic properties, for example, for selective hydrogenation and alcohol oxidation. More accurate catalytic modeling is achieved by the inclusion of the substrate (e.g., metal oxides). In this work, the structures and chemical ordering (atomic segregation) of Pd−Au clusters supported on MgO(100) were studied using a combined empirical potential−density functional theory approach. The focus is on 30- and 40-atom clusters, including variation in the bimetallic composition. Consistent with the available experimental findings, Pd atoms preferentially bind to the substrate oxygen sites. Good cluster-substrate epitaxy is observed, but there is a strong dependence on the size and composition of the clusters. findings for pure Au and Pd clusters on the MgO(100) surface,3,18 one aim of this work is to test atomistic modeling because it is the only way to study larger sizes (clusters with thousands of atoms) that are more easily observed in electron microscopy experiments. Moreover, atomistic modeling allows the simulation of cluster melting and growth for large sizes, something that it is not accessible to density functional theory (DFT). Supported Pd−Au nanoalloy clusters on MgO(100) are studied by determining the structural and chemical ordering of 30- and 40-atom clusters. Compositional variation is also taken into account by selecting three compositions that represents Pd-rich, medium, and Au-rich clusters. The article is organized as follows: section II deals with the computational methodology and the description of the model, section III reports the results and discussion for 30- and 40atom PdAu/MgO, and section IV presents the conclusions of this work.

I. INTRODUCTION Nanoclusters of the transition metals have been shown to adopt a variety of structures; e.g., face-centered cubic (fcc), polyicosahedral (pIh), and decahedral (Dh). This means that cluster structures and properties can be tailored for different applications.1,2 Supported clusters are of considerable interest as the combination of metal−metal and metal−substrate3,4 interactions give more ways of optimizing catalysts. The use of amorphous carbon, for example, produces a wide range of differently shaped gold and palladium particles, but magnesium oxide (MgO) typically stabilizes fcc-based motifs.5,6 In addition to being supports, oxide substrates are widely believed to act as active media in catalytic chemical reactions. Different supports have been reported to show optimum catalytic performance for Pd−Au, especially for the selective oxidation of styrene (Al2O37), toluene (carbon8), glycerol,9 and benzyl alcohol10 (TiO2). In the direct synthesis of hydrogen peroxide, similar results have been observed for carbon and SiO2 supports.11 Most modeling of bimetallic clusters12,13 focuses on free particles due to computational limitations. However, the inclusion of the support is of great importance in gaining a more accurate representation of the real heterogeneous catalytic system. Metal oxides such as MgO are interesting for their strong electrostatic interactions.14 Furthermore, MgO surfaces with minimal structural defects are relatively easy to prepare15 and act as a perfect background for electron microscopy.5 Computationally, it is possible for MgO to be modeled as a flexible slab.16,17 An extensive database of energetics, structures, and segregation has been developed12,13 for small Pd−Au clusters ( D3d > core. However, for the composition (32,6), only the average and new(a) potentials reproduce the DFT results (core > D3d > hex, while the other potentials obtain the D3d motif as the lowest energy configuration. Looking at the relative energies, these two potentials give a close result, but the magnitude is rather far from those given by the DFT calculations. However, as far as the homotop ranking is concerned, these potentials are in very good agreement with the DFT calculations. On the basis of these results, the new(a) potential has proven to be the most consistent in both tested regimes and selected for calculations of 30- and 40-atom Pd−Au clusters on MgO. Parameter values of this potential are listed in Table 2. Table 2. Parameters for the New Potential, with Pd−Au Heteronuclear Parameters Derived As the Arithmetic Mean of the Homonuclear Parameters parameters

Pd

Au

Pd−Au

A (eV) ξ (eV) p q

0.0501 1.1924 17.0000 2.0900

0.1289 1.5223 12.5000 3.5500

0.0895 1.3574 16.5500 2.2360

Further parametrization on the new(a) potential was carried out using eq 4 based on the method described in refs.12,34 This method has been shown to lead to better parameters in the Gupta potential. The heteronuclear Pd−Au Gupta potential parameters, P (A, ξ, p, or q) were derived as the weighted average of the corresponding pure metal Pd−Pd and Au−Au parameters. The weighting parameter was investigated in the range of 0 ≤ w ≤ 1, in steps Δ = 0.1; with other parameters being fixed at their arithmetic mean values (w = 0.5). 295

dx.doi.org/10.1021/jp3093435 | J. Phys. Chem. C 2013, 117, 293−301

The Journal of Physical Chemistry C PPd − Au = wPPd − Pd + (1 − w)PAu − Au

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minor role in the PBE calculations. However, selected clusters were also studied by allowing the substrate to relax together with the clusters, with differences in energy of less than 0.1 eV, and no changes of structural or ordering were observed (though there was an increase in time taken to reach convergence). Following convergence and accuracy tests, the following parameters were selected: kinetic energy cutoff = 40 Ry (544 eV); cell size = 30 Bohr (15.9 Å) for the tetragonal Bravaislattice; degauss = 0.004 (ordinary Gaussian spreading); convergence threshold = 1.00 × 10−6 to 1.00 × 10−8; mixing β < 0.3 for plain (Broyden) mixing mode. Comparison of the discrepancy of outcomes between the QE and NWChem codes is meaningful for validation. Our earlier work with the NWChem code mostly used the Perdew−Wang (PW91) exchange and correlation functional;40 but this functional is not available for Pd in QE. Hence, the PBE functional (available for both DFT codes) was selected to allow comparison of the two codes, as shown in Figure 4. Also shown

(4)

The A and ξ parameters make the largest contribution to structures and energies. Hence, parametrization of these components significantly affect the total energy; but, at the expense of crossover between the three studied motifs (core, hex, and D3d). On the basis of the parameters of the new potential (Table 2), the ratio between homonuclear Pd and Au for the A parameter is more than 2-fold (2.574), while the ratio for ξ is 1.277. These large differences indicate that, even with a change of just Δw = 0.1, there is a significant addition/ reduction of the attractive/repulsive intermetallic Pd−Au bonding. The p and q parameters, however, only determine the range of the repulsive and attractive interactions, respectively,20 so varying these parameters affect the energy but typically retain the homotop ranking. Weighting the p and/ or q parameters mostly (except for extreme weighting w → 0.0/ 1.0) gives results that agree with DFT for both cluster compositions. The best parametrization is identified for combined w(p,q) = 0.1 (values are listed in Table 2); which give the most accurate total energy (in addition to reproducing the DFT homotop ranking). This weighted potential is then used in the EP global optimization searches for 30- and 40atom Pd−Au clusters on MgO(100). The metal−oxide interaction potential is described in detail in refs 22 and 27. The parameters have been fitted to firstprinciples calculations, taking into account the metal−oxide.35 The metal−oxide features include no interdiffusion, small charge transfer (due to polarization effects and van der Waals interactions), and a very small contribution of covalent bonds. It does not explicitly include the metal-on-top effect,36 but the parameters are fitted to the ideal systems and DFT calculations. Also, because of their relatively small contribution (of the order of a few hundredths of an electronvolt) to the total energy, van der Waals interactions are not included. The M−MgO potential (in agreement with the DFT calculations to which it was fitted) gives stronger atomic Pd−O binding (1.42 eV) than Au−O (0.89 eV) and also reproduces the decrease in M− O bond strength upon increasing metal coordination number.22 Although these calculations have not taken into account the effect of alloying on the individual metal−substrate interactions, we believe this is justified because these effects are likely to be small31 and in the final stage, different supported cluster structures are compared at the DFT level, which includes these effects implicitly. B. Density Functional Theory Calculations. After generating a database from the EP searches, the lowest-energy and several low-lying higher energy local minimum clusters for each size and composition were then reoptimized at the DFT level using the Quantum ESPRESSO (QE)37 plane-wave selfconsistent field (PWscf) DFT code, with the Perdew−Burke− Ernzerhof (PBE) exchange-correlation (XC) functional38 and ultrasoft pseudopotentials. The MgO(100) substrate was modeled by a two-layer slab of 36 Mg and 36 O atoms (6 × 6 cell) in each layer, fixed in the lattice positions of the MgO rock-salt bulk structure (with an experimental MgO distance of 2.104 Å). The lattice spacing perpendicular to the (100) plane is 11.7 Å.39 Different slab sizes have been used3 to allow sufficient distance between periodic images, but in this work, the 6 × 6 cell is necessary for the particular studied sizes. The MgO substrate was fixed at the experimental distances of Mg and O atoms, as it has been shown3 that a nonrigid substrate plays a qualitatively very

Figure 4. Effect of different XC functionals on the DFT energies of (6,32) and (32,6) Pd−Au clusters (N = NWChem and P = plane wave QE).

in the figure are calculations with the other functionals (which are available for both Pd and Au): PBE, Perdew−Zunger (PZ81) local density approximation (LDA),41 and potentials that treat the semicore d states as valence orbitals (PBEd and PZ81d).37 All calculations gave similar homotop ranking (based on energy) for both compositions. For the composition (6,32), there is good agreement in the gaps: hex > D3d > core. The different codes (plane wave QE vs orbital based NWChem), however, exhibit a slight variation for composition (32,6) (core > D3d > hex); nevertheless, the energy ordering is consistent. In addition to this qualitative agreement, there are only small variations (i.e., almost quantitative agreement) for all possible combinations of functionals for the QE calculations; hence, comparisons with the previous calculations13,42 are valid. For performing tests on supported clusters, a model of 20atom Pd10Au10 on MgO(100) is used. The EP calculations show that the cluster with the fcc motif is the global minimum (GM). This motif with a PdAu(100)/MgO(100) interface is then reoptimized with QE, using the PBE and PZ81 (available for all involved elements: Pd, Au, Mg, and O) functionals, to see the effects of different functionals. The results show the PZ81 functional gives lower total energy (−0.146 eV/atom) 296


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than PBE. Nevertheless, structural observations suggest there is consistency between these functionals.

III. RESULTS AND DISCUSSION From the EP searches, several motifs are selected: Dh, icosahedral (anti-Mackay, Mackay, and low symmetry), fccbased, and close-packed (cp). In total, 9 and 11 motifs (for 30and 40-atom clusters, respectively) are chosen from the EP searches, after discarding very unfavorable (high energy) motifs. This is the database (first part of the combined empirical potential−density functional theory method) of initial configurations for the DFT reminimization (second part). Compared to free clusters, supported Pd−Au clusters on MgO exhibit more flattened structures, and a greater contact area with the substrate. This agrees with the compact structures of Pd clusters on MgO, starting at very small sizes,43,44 which reduces the interfacial energy.45,46 Au, however, has been shown to have a more complex combination of metal−substrate interactions with the additional effects of stickiness, directionality, and electronic shell closure, while 2D and cage structures should be encountered at sizes up to about 30 atoms.36,47,48 However, the inclusion of Pd in Au clusters is known to destabilize the 2D and cage structures,49 so only compact structures are considered here. Most of the selected motifs (GM and low-lying isomers) have unsymmetrical shapes. Upon rotation, different faces are in contact with the MgO surface. The EP searches, however, agree with DFT calculations, that Pd−Au clusters are most stable when there are the most Pd atoms (of the flat cluster surface) in contact with the substrate oxygen sites, as shown in Figure 5. In this example, all three clusters basically have the

Figure 6. Global minima of 30-atom Pd−Au clusters on MgO(100) for compositions (22,8), (15,15), and (8,22).

Figure 7. Global minima of 40-atom Pd−Au clusters on MgO(100) for compositions (30,10), (20,20), and (10,30).

Figure 5. Relative energies of decahedra of (15,15) Pd−Au clusters on MgO(100) as a function of different orientations and interfaces. (For MgO slabs, Mg and O atoms are denoted by blue and red colors, respectively, here and in subsequent figures.)

(40-atom), GM starts to adopt motifs that are close to the bulk (fcc), as can be seen for compositions (30,10) (fcc-hcp) and (20,20) (fcc). The other composition, (10,30), however, adopts the inc-Ih-Mackay motif with the complete core−shell ordering (with Au at the MgO interface), consistent with the DFT calculations for the free clusters.13,12,28,42 These structural observations show that, although there are effects of the cluster−substrate interaction, structural tuning is still possible by varying the composition, as is the case for free Pd−Au clusters.12,13,28 However, the tunability is likely to vanish for larger clusters, based on the observation of cluster progression from 30- to 40-atoms when bulk-like fcc structures start to prevail. The second rows (top view) of both Figures 6 and 7 exhibit core−shell chemical ordering, with Pd occupying core positions, leaving Au on the cluster surface. It seems that the ordering is similar to that of the free clusters;12 however, the third rows (bottom view) and fourth rows (first layer) of the figures show a difference. Surface Au is only maintained for the exposed sites (free surface of the cluster), while the cluster− substrate interface favors Pd−O over Au−O (i.e., there is Pd

same structural arrangement (Dh) of (15,15) Pd−Au clusters, but they have different cluster−substrate interfaces. As free clusters, the three are approximately of the same energy (with only a slight variation caused by small structural distortions); but on MgO, the greater the numbers of atoms in contact with the MgO substrate, the more stable the supported cluster. It is also seen, that, in comparison to free clusters, interaction with the MgO substrate is likely to flatten the Pd−Au clusters. However, there is a limit to the flattening process because homo- and heteroatomic metal−metal interactions retain the overall 3-dimensional shape of the clusters. The putative GM structures (at the DFT level) for the three different compositions of 30-atom [(8,22), (15,15), and (22,8)] and 40-atom [(10,30), (20,20), and (30,10)] Pd−Au clusters on a MgO(100) slab are shown in Figures 6 and 7, respectively. The 30-atom clusters show a strong competition between structural motifs in which putative GM evolve from incomplete Mackay-polyicosahedral (inc-Ih-Mackay) [composition (8,22)], to Dh [(15,15)] and fcc-TO [(22,8)]. For the larger clusters 297



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Table 3, indicating clear preference of the PdcoreAushell ordering over the reverse ordering (4−5 eV higher in energy).

segregation to the PdAu/MgO interface). This observation can be attributed to the stronger bonding of oxide to the transition metals of the Ni-group (Ni, Pd, and Pt) (approximately 1 eV) as compared to those of the Cu-group (Cu, Ag, and Au) (approximately 0.3 eV). Ni-group metals have the ability to form s−d hybrid orbitals due to the small s−d separation (0.51 eV for Pd, compared to 1.7 eV for Au). These hybrid orbitals can then interact with the p orbitals of oxygen to produce stronger covalent bonds. However, the d shell is filled for Cugroup elements, and interaction can only be formed by polarization and/or dispersion effects.50 For Au-rich compositions, however, Au occupies the interface (outer shell) to avoid the core positions, which would increase the strain and cause instability of the cluster.51 The other observation is the preference of the O site over Mg for the interactions between MgO and the cluster. This tendency has also been reported theoretically and experimentally for Cu, Ag, Ni, and Fe.45 The preference for adhesion of metal on oxygen sites (over surface Mg and hollow sites) for Pd and Au is supported by published findings from grazing incidence X-ray diffraction52 and electron microscopy.53 This behavior is associated with the metal-on-top stabilization,36 van der Waals interactions,54 and also charge transfer.55 In contrast, a few studies have suggested a preference for the Mg site.56,57 The fourth rows (first layer) of each figure show the cluster− substrate interactions (i.e., the bottom layer of the cluster and the top layer of the MgO slab) and indicate the occurrence of epitaxial matching. There is, however, a clear trend of a decrease in epitaxy, moving from Pd-rich, to medium and Aurich compositions; consistent with the addition of Au to the cluster−substrate interface. Good cube-on-cube epitaxy of Pd is driven by the strong preference for Pd to sit on top of the surface oxygen rather than other sites (Mg or hollow).4,17,43 In contrast, Au exhibits complicated binding character36,48 that leads to the stabilization of planar58,59 and cage structures.3,19 Hence, increasing the content of Au is thought to dilute the cube-on-cube epitaxy of Pd. It is important to understand epitaxial phenomena, which suggests enhancement of catalytic activity through a spillover mechanism60 in CO oxidation,61 NO dissociation,62 and the CO + NO reaction.63 In this work, better epitaxy of small Pdrich clusters compared to Au-rich is consistent with reported observations for pure Pd and Au clusters. There are stronger metal−support interactions for Pd (over Au) and better cubeon-cube epitaxy between Pd clusters and the MgO substrate.64 It should be noted that, at large sizes, pure Au clusters grow to large sizes with better epitaxy than pure Pd clusters because of the smaller bulk lattice mismatch between Au and MgO. For small clusters, lattice mismatch is less important, and the stronger interaction with the substrate is the main driving force.4,27 On the basis of the progression from 30- to 40-atom Pd-rich clusters, there is evidence for the decrease in epitaxy on increasing cluster size, due to size mismatch.4 However, compared to pure Pd clusters, 40-atom Pd−Au still shows good epitaxy, indicating release of the strain associated with size mismatch with the placement of some gold in clusters. It is also significant to note that all isomers selected from the EP searches (for the DFT reminimization) adopt PdcoreAushell ordering. Comparison of this ordering against reverse ordering (i.e., PdshellAucore, swapping atoms Pd ↔ Au), is possible for 1:1 composition clusters: (15,15) and (20,20), for 30- and 40atoms, respectively. The DFT relative energies are shown in

Table 3. Relative DFT Energies of Core−Shell and Inverse Core−Shell Configurations for (15,15) and (20,20) Pd−Au Clusters cluster

ΔE (PdcoreAushell) (eV)

ΔE (PdshellAucore) (eV)

(15,15) (20,20)

0.00 0.00

+4.375 +5.091

Relative to minima for each composition, the energetics of all selected motifs are summarized in Figures 8 and 9, for 30- and

Figure 8. Structural motif crossover of 30-atom Pd−Au clusters on MgO(100).

40-atom clusters, respectively. For both sizes, only a single Dh variant is considered, as the others are not energetically competitive. For the icosahedral motif, there are five variants that are in close-competition with the GM in the EP searches; incomplete anti-Mackay-polyicosahedral (inc-Ih-anti-Mackay),

Figure 9. Structural motif crossover of 40-atom Pd−Au clusters on MgO(100). 298



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inc-Ih-Mackay, low symmetry polyicosahedral (antiprism), and capped polyicosahedra with 6 interpenetrating Ih13 units (pIh6).65 For the inc-Ih-Mackay motif, two isomers are found that differ in their cluster−substrate interfaces; one has a regular pentagon in contact with MgO and the other has more atoms at the interface, the double-tetrahedral face (DT-face). The capped-pIh6 is not found for 30-atom clusters, but it may be a higher energy motif. Four fcc-based crystalline structures are observed at the EP level; fcc, fcc-hcp, fcc-TO, and square-fcc (although square-fcc is only competitive for size 30). The first variant (fcc) is a cluster with uneven shape; square-fcc has overhang atoms on each side of the square-shaped cluster; fcc-TO is the motif derived from the 38-atom TO, and fcc-hcp is a stacking fault structure. Although these structures look quite similar, the energetic profiles are distinct. The other group of motifs also have close-packing but have a truncated tetrahedron shape based on a 20-atom tetrahedral core (30-atom cluster, cp30) and a motif with an additional fcchcp layer (40-atom cluster, cp40). These two arrangements resemble the mixed decahedral-close-packed motifs commonly found for 34-atom bimetallic clusters, with either tetrahedral or double tetrahedral cores.29 Figure 8 shows that there is a complex crossover between the structural motifs of 30-atom clusters, that can be associated with small energy gaps.66 The inc-Ih-Mackay motif, which is the most stable structure for composition (22,8) is unfavorable for compositions (15,15) (+0.645 eV) and (8,22) (+0.241 eV). The Dh motif (putative GM for composition (15,15)) is disfavored by +0.100 and +0.047 eV for compositions (22,8) and (8,22), respectively. The other putative GM, fcc-TO (composition (8,22)), is disfavored by +0.572 and +1.047 eV, for compositions (15,15) and (22,8), respectively. The other studied motifs (fcc-hcp, antiprism, and cp) are energetically less stable for these three compositions, while DT, square-fcc, DTface, fcc, and inc-Ih-anti-Mackay motifs are very competitive but are not found as the GM for any composition. Structural crossovers for 40-atom Pd−Au clusters in Figure 9 are less complex compared to those for 30-atom clusters. The antiprism, cp, pIh6, and inc-Ih-anti-Mackay are high energy isomers, while Dh and DT-face are competitive non-GM structures. For this size, bulk-like (fcc) clusters are found for compositions (20,10) (fcc-hcp) and (20,20) (fcc). For the composition (30,10), these motifs do not emerge as the putative GM, but they are competitive; gaps of +0.522 and +0.330 eV (for fcc and fcc-hcp, respectively) compared to the putative GM. The putative GM for this composition is inc-IhMackay; however, it is disfavored for the other compositions (+1.628 and +0.642 eV for compositions (30,10) and (20,20), respectively). These results for 30- and 40-atom Pd−Au clusters on MgO show that there are small energy gaps between structural motifs and suggest that structural rearrangements of the clusters are possible upon interaction with the substrate. It is also interesting to note that the variation of structure is significantly affected by composition. Hence, change of composition in the preparation of clusters is also predicted to lead to the coexistence of several motifs, in agreement with experimental observations (for example, by Liu et al.67). Finally, it is significant to see how the potential used in this work agree with the DFT calculations, as shown in Table 4. Putative GM (based on the DFT calculations) for 30- (Dh) and 40-atom (fcc-hcp) clusters are not the best isomers at the EP

Table 4. Relative Energies of (15,15) and (20,20) Pd−Au Clusters at the DFT and EP Levels motif

ΔEDFT (eV)

ΔEEP (eV)

Dh (30) square-fcc (30) fcc-hcp (40) fcc (40)

0.00 0.13 0.00 0.39

0.14 0.00 0.03 0.00

level; however, both appear as the second lowest energy motifs for their respective sizes, with only small energy gaps to the EP minima. The accuracy of the EP calculations based on the new potential in this work suggests that model potentials will be of crucial importance for studying larger nanoparticles containing several hundreds or thousands of atoms, which are not accessible to DFT calculations but are of great interest with respect to experiments.67

IV. CONCLUSIONS The DFT calculations show that Pd−Au nanoalloys on the MgO support exhibit a preference for core−shell ordering, similar to those of the gas phase clusters. Because of the stronger metal−oxide interactions, Pd is preferred over Au to reside at the cluster−substrate interface. Very good epitaxy of Pd−MgO is shown for Pd-rich clusters, but it is reduced when the Au concentration is increased. The epitaxy is also reduced upon increasing the cluster size. The energy gap between structures are small, and there is a complex crossover for clusters in the region of 30−40 atoms. The coexistence of several structural motifs is highly possible, which supports many experimental observations. Analysis of the cluster structures also suggests that there is a structural transformation of the clusters, due to cluster−substrate interaction. This study shows that, as for the free clusters, the structures adopted by small Pd−Au clusters on MgO still depend on the composition. However, the effect is significantly reduced upon increasing cluster size. It should also be noted that 40-atom clusters already adopt fcc-based bulk-like motifs. This work gives good confidence in the new potential, which has been proved to be accurate in predicting the behavior of pure Pd and Au clusters on MgO substrates. For the bimetallic Pd−Au clusters, the parametrization method is adequate for reproducing DFT predictions. With this in mind, this potential could be employed in studying larger Pd−Au clusters supported on MgO. In the future, this work will also be extended to other binary nanoalloy systems and studied for the structures and segregation dynamics of supported nanoalloy catalysts under operational conditions, including the effect of temperature and competition between metal segregation at the cluster−support interface and adsorbate-induced segregation due to molecules in the reactant mixture.

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ASSOCIATED CONTENT

S Supporting Information *

Detailed comparison of the average and new potentials in regard to their reproduction of experimental/theoretical properties of Au and Pd. This material is available free of charge via the Internet at http://pubs.acs.org. 299



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS R.I. is grateful to the Universiti Pendidikan Sultan Idris and the Ministry of Higher Education (Malaysia) for the award of a Ph.D. scholarship. Some of the DFT calculations were performed at the CINECA supercomputing center (Bologna, Italy) under the HPC-EUROPA2 project (project number 228398), with the support of the European Community Research Infrastructure Action of FP7. Other calculations were performed on the University of Birmingham’s BlueBEAR high-performance computer (http://www.bear.bham.ac.uk). We acknowledge financial support from COST Action MP0903: “Nanoalloys as Advanced Materials: From Structure to Properties and Applications.” R.L.J. acknowledges financial support from EPRC grant EP/G070326/1.

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