University of Birmingham DFT Global Optimization of Gas-Phase Subnanometer Ru–Pt Clusters

: The global optimization of subnanometer Ru − Pt binary nanoalloys in the size range 2 − 8 atoms is systematically investigated using the Birmingham Parallel Genetic Algorithm (BPGA). The e ﬀ ect of size and composition on the structures, stabilities and mixing properties of Ru − Pt nanoalloys are discussed. The results revealed that the maximum mixing tendency is achieved for 40 − 50% Ru compositions. Global minimum structures show that the Ru atoms prefer to occupy central and core positions and maximize coordination number and the number of strong Ru − Ru bonds.


■ INTRODUCTION
Subnanometer noble metal clusters are of great importance due to their extraordinary structural and electronic properties, which are intermediate between atomic and nanoparticular systems. 1 The interest in subnanometer clusters is growing, especially in the field of catalysis, owing to recent experimental results suggesting high selectivity and activity toward specific reactions, 2−4 as well as advances in experimental procedures that allow size selectivity of subnanometer clusters. 5 One example is platinum (Pt) for which Vajda et al. have shown up to 2 orders of magnitude higher catalytic activities than previous Pt catalysts for the selective oxidative dehydrogenation of propane. 4 Platinum is the key component in catalysts for low temperature methanol electro-oxidation, which is of great interest for direct methanol fuel cells. 6 However, pure platinum catalysts suffer from two main drawbacks: high cost and COpoisoning. 7 Addition of another metal has been investigated, either to reduce the usage of comparatively expensive platinum or to improve CO tolerance. To optimize the catalysts, various bimetallic alloys have been tested for their catalytic properties, including Pt−Ni, 8 Pt−Co, 9 and Pt−Ru. 10−12 Among all these electrode materials, Pt−Ru catalysts have showed promising catalytic activities toward fuel cell applications 13, 14 and higher CO tolerance. 15 Pt in the bulk exhibits face-centered cubic (fcc) packing, while bulk Ru is hexagonal close-packed (hcp). The binary Ru− Pt phase diagram 16 suggests a fcc-type structure when Pt is above 40%, a hcp-type structure when Pt is below 20% and a coexisting hcp(Ru-rich)-fcc(Pt-rich) phase region for intermediate compositions. This phase diagram refers to solids at a temperature above 1000°C, which is much higher than normal temperatures for Pt−Ru nanoalloy (NAs) synthesis and postsynthesis treatment. In addition, nanosize alloys sometimes show distinct structures from their bulk counterparts. 17,18 The atomic-scale structures of Pt−Ru nanoalloys, therefore, cannot be simply defined by their composition. Experimental conditions and synthetic methods also play important roles here. In the literature, composition-induced structural changes 19,20 were shown for Pt−Ru nanoalloys and mixed structures were obtained at low temperatures. Nevertheless, a high-temperature treatment after synthesis 21−23 showed Pt segregation to the surface, leading to "core-shell" particles and it has been shown that core−shell Ru@Pt nanoalloys have higher catalytic activity for CO oxidation than mixed Ru−Pt nanoparticles. 24 Since the catalytic activities of nanoalloys are closely related to their sizes and structures, it is important to rationalize the relationship between structures and catalytic properties as well as mixing patterns at the nanoscale. Theoretical studies here can give an insight into size and structural effects on catalyst stability and activity. Although in the literature there have been a number of experimental and theoretical studies of pure subnanometer Ru 25−33 and Pt 4,34−39 clusters, to our knowledge there has been no theoretical study of subnanometer Ru−Pt alloys.
In this study, low energy structures of subnanometer Ru−Pt alloys have been systematically studied by global optimization at the DFT level within the Birmingham Parallel Genetic Algorithm (BPGA).

■ METHODOLOGY
The BPGA-DFT 40,41 approach was applied to obtain low energy structures of (Ru,Pt) N alloy clusters in the size range N = 3−8, as well as pure Ru N and Pt N clusters. This method is an open-source genetic algorithm, improving on the Birmingham Cluster Genetic Algorithm (BCGA), a genetic algorithm for determining the lowest energy structures of nanoparticles and nanoalloys directly at the DFT level. 42 BPGA employs a pool methodology 43 to evaluate structures in parallel instead of based on generations. In each run, multiple BPGA instances are implemented, and in each instance, a set of processes are run in parallel and independently. Initially a number of random structures (10 in this study) are generated and geometrically relaxed (by local energy minimization at the DFT level) to form a population. Once the local minimization of the initial pool structures has been completed, the crossover and mutation operations of the genetic algorithm begin for each instance. In each instance, either a pair of clusters are taken from the pool according to "roulette-wheel" selection 42 for the crossover operation to generate an "offspring" structure or a single cluster is taken for mutation. Offspring structures are produced through weighted crossover according to the Deaven and Ho "cut and splice" method. 44 Mutated clusters are either obtained by displacing some of the atoms randomly or swapping different types of atoms in alloy clusters. The newly generated structures are then locally minimized to compare with existing structures in the pool and the pool is updated whenever a new cluster is found that is lower in energy.
All the DFT-level local minimizations mentioned above were performed with a plane wave basis set, as implemented in the Vienna ab initio Simulation Package (VASP), 45−48 including spin polarization. Spin states are optimized within VASP independently for each generated structure from BPGA during global optimization. The exchange-correlation energy was calculated using the generalized gradient approximation (GGA), with the Perdew−Burke−Ernzerhof (PBE) 49 exchange-correlation functional. The interaction between valence electrons and ionic cores was described by the projector augmented wave (PAW) method. 50,51 Methfessel-Paxton smearing, with a sigma value of 0.01 eV, was implemented to improve convergence of metallic systems. 52 For the comparison of the energetics of different composition nanoalloys, a mixing (or excess) energy term (Δ) was calculated, which is expressed as where the total energy (E tot ) of the nanoalloy A m B n is compared to the pure metal clusters of A and B of the same size (m + n). Hence, a negative value of Δ means an energy decrease upon mixing and therefore favorable mixing, whereas positive values indicate a demixing tendency. The stability of each cluster, relative to its neighbors, is indicated by the second difference in energy Δ 2 E, which is given by where A is Ru or Pt, E tot (A N ) corresponds to the total energy of the N-atom cluster, and E tot (A N+1 ) and E tot (A N−1 ) are the neighboring clusters when increased one atom more and decreased one atom less, respectively. The average binding energy per atom E b is given by where m and n are the numbers of A and B atoms; E tot (A 1 ), and E tot (B 1 ) are the electronic energies of a single Ru or Pt atom; and N is the total number of atoms (N = m + n).
■ RESULTS Ru Clusters. The lowest energy structures obtained from global optimization for pure Ru N clusters (3 ≤ N ≤ 12) are shown in Figure 1. Overall, the global minimum clusters and their corresponding spin multiplicities are in good agreement with structures suggested in previous theoretical works. 25−29 Ru 3 is an equilateral triangle (D 3h ) and Ru 4 is also planar, while the larger sizes adopt 3D structures. Ru 4 is a rectangle with bond lengths of 2.24 and 2.15 Å. Ru 5 is a square pyramid (C 4v ) and Ru 6 is a trigonal prism (D 3h ) again with high symmetries as for Ru 3 and Ru 4 (see Table 1).
The first low symmetry structure is Ru 7 with point group C s , which is in agreement with the cationic Ar-tagged species Ru 7 Ar + observed in gas phase experiments. 33 Ru 8 is found to be cubic (with full O h symmetry), while Ru 9 has an additional Ru atom capping a face of the cube (C 4v symmetry). These structures are in agreement with recent experiments on both cationic 33 and anionic 28 clusters, which indicate the occurrence of cubic structures for certain nuclearities. The lowest energy structure for Ru 10 is found to be pentagonal prism (D 5h ), as in previous theoretical studies. 25,27,29 However, a doubly capped cube has been shown to give a better fit to electron diffraction measurements for anionic Ru 10 − clusters. 28 The lowest energy structure for Ru 11 is found to be a cube with three atoms on the top face, missing one atom to complete the double cube, leading to the lowest (C 1 ) symmetry. Ru 12 is found to be a  , in which the configurations that fit the experimental results best have lower symmetry point groups than we have found for the neutral clusters. When we compared the effect of charge for Ru 8 (see Supporting Information, Figure 1), while Ru 8 − preserved the perfect cubic structure, Ru 8 + distorted into a squashed cube (with D 4h symmetry).
According to Table 1, the binding energies of the clusters increase with increasing cluster size, as expected, to converge on the bulk cohesive energy (calculated value = 6.78 eV). However, the higher binding energy calculated for Ru 8 than Ru 9 indicates the extra stability of the cubic structure of Ru 8 . This extra stability is also confirmed by fitting binding energies as a function of n 1/3 for small clusters (see Supporting Information, Figure 2). Although the cubic Ru 8 has the highest positive residual, indicating a "magic" size, larger cubic clusters Ru 11 and Ru 12 have negative residuals, indicating reduced relative stability.
Pt Clusters. Figure 2 shows the lowest energy structures of pure Pt N clusters (3 ≤ N ≤ 10). In addition to the equilateral triangular Pt 3 (D 3h ), the lowest isomer of Pt 6 is also planar (D 3h ), while Pt 4 has a slightly bent rhombus configuration and Pt 5 is an edge-bridged square with a slight bending out of the square plane. The global minimum configuration of Pt 7 is based on the planar structure of Pt 6 , with an outer triangle capped to generate a 3D structure (with C s symmetry).
For both Pt 8 and Pt 9 , global optimization leads to 3D structures, which are the same structures previously predicted 35 for Pt 8 + and Pt 9 + cations, though there are quasi-2D structures which are nearly degenerate with the 3D isomers. The 3D Pt 8 and Pt 9 structures are both based on the structure of Pt 6 mentioned above, with the planar structure of Pt 6 capped to form 3D triangular structures tending toward a tetrahedral structure. The 2D Pt 9 isomer is a 3 × 3 square lattice. 34−36 Pt 10 is found to be the tetrahedral (T d ) structure, corresponding to a small fragment of fcc packing.
Overall, our low energy structures and their corresponding spin multiplicities compare well with previous studies. 34 −36,38,39 For the high symmetry structures of Pt 3 , Pt 6 , and Pt 10 (see Table 2), all previous studies have shown the same lowest energy structures, while nonglobal optimization studies 34,36,38,39 did not considered some of the lowest energy structures for other sizes. However, most of lowest energy isomers presented here are in good agreement with a previous global optimization study. 35 Although it has been reported that all global minima up to Pt 9 are planar for neutral Pt clusters, here it is shown that 3D clusters become competitive after Pt 7 , that is, having almost the same binding energies as their planar counterparts. As for Ru clusters, binding energies of Pt clusters increase with increasing cluster size to converge on the bulk cohesive energy (calculated value = 5.58 eV) and the fit to n −1/3 reveals the extra stability of Pt 3 , Pt 6 , and Pt 10 clusters with positive residuals (see Supporting Information, Figure 3).
Ru−Pt Clusters. The global minima for all compositions of Ru m Pt n clusters for 3 ≤ m + n ≤ 8, are shown in Figure 3. For all sizes and compositions, due to the high cohesive energy of Ru (as shown in Table 3), the Ru atoms prefer to occupy corelike positions with higher coordination numbers. Moreover, when there is more than one Ru atom, Ru atoms tend to occupy adjacent positions, due to the stronger Ru−Ru bonds.
All the favored structures of Ru m Pt 1 are similar to the pure Ru clusters of the same size (Ru m+1 ), except for Ru 6 Pt 1 , in which the Pt atom caps one of the square faces of the trigonal prism structure of Ru 6 . Ru 1 Pt 3 , Ru 1 Pt 4 , and Ru 1 Pt 5 resemble the pure Pt clusters, while Ru 1 Pt 7 and Ru 1 Pt 6 both possess a Ru atom with high coordination number and differ significantly from the corresponding pure-Pt clusters. In Ru 1 Pt 2 , the triangle opens up and the Pt−Pt distance becomes 3.77 Å from the value of 2.46 Å in Pt 3 , while the Pt−Ru distances are 2.23 Å. In contrast, for Ru 2 Pt 1 , the Ru−Ru distance is smaller (2.12 Å) than Ru 3 (2.24 Å), while the Ru−Pt distances are 2.48 Å. For (Ru,Pt) 4 , the rhombus structure of Pt 4 is preserved until all but one Pt atom is replaced with Ru, at which point the structure converts to a distorted square structure similar to Ru 4 . Similarly, for (Ru,Pt) 5 and (Ru,Pt) 6 , pure Pt structures are preserved until more than 50% replacement of Ru, while an intermediate nonplanar trapezoidal structure is observed for Ru 3 Pt 2 before adopting the square pyramidal pure Pt structure. Ru 4 Pt 2 is an edge-bridged square pyramid, which has same coordination numbers (three and four) as Ru 3 Pt 2 .
For (Ru,Pt) 7 , the structure of Ru 1 Pt 6 has a Ru atom surrounded by six Pt atoms, so that the Ru atom obtain the maximum coordination number. In this structure, six Pt atoms around the Ru atoms form a chairlike configuration, in which the Ru atom sits ∼0.5 Å out of the vertical plane. In Ru 2 Pt 5 , the additional Ru atom moves toward to the center and binds to two extra Pt atoms while displacing the central Ru atom out of the plane. Ru 3 Pt 4 is two square pyramids sharing a triangular Ru 3 face, ensuring the three Ru atoms are bonded together and have high coordination numbers. The structures of Ru 4 Pt 3 and Ru 5 Pt 2 resemble the Ru 6 Pt 1 structure, corresponding to a trigonal prism with a square Ru 4 face capped by a Pt atom. For (Ru,Pt) 8 , when the composition is 50%, the structure is a  The Journal of Physical Chemistry C Article distorted cube, corresponding to two trigonal prisms sharing a square Ru 4 face. As the Ru percentage increases, the structure becomes more cubic. Apart from sizes n = 4 and 5, pure Ru n clusters have higher spin multiplicities than pure Pt n clusters (see Tables 1 and 2). Upon alloying (Table 4), as Ru replaces Pt, spin multiplicities increase in general for (RuPt) n clusters up to 40% Ru composition (see Supporting Information, Figure 4). For (Ru,Pt) 4 , (Ru,Pt) 5 , and (Ru,Pt) 6 , spin multiplicities on Ru doping of the Pt structure start to decrease when the Ru structure starts to dominate the alloy geometry. For (Ru,Pt) 7 , spin multiplicities do not follow the trend as all the alloy structures are significantly different than the pure Ru or pure Pt geometries. For (Ru,Pt) 8 , spin multiplicities become maximal as the cubic Ru structure dominates the alloy geometry, but decreases for pure Ru.
Energetic Analysis. The relative stabilities of the clusters can be studied by calculating the second difference in energy (Δ 2 E), which indicates the stability of an N atom cluster with respect to neighboring sizes. Figure 4 shows the plot of second difference in energy as a function of cluster size for pure Ru and pure Pt clusters, respectively. The significant positive peaks indicate the relatively stable clusters. Figure 4 reveals that Ru 8 and Pt 6 clusters are significantly more stable relative to their neighbors, suggesting they are "magic" sizes in the considered subnanometer regime. However, note that the energetic range for Ru clusters (approximately 5.0 eV) is larger than for Pt clusters (approximately 1.0 eV) and also the binding energy versus cluster size fit (see Supporting Information, Figure 3) reveals higher stability for tetrahedral Pt 10 than planar Pt 6 . For Ru clusters, the second difference energies also reveal an even−odd alternation, where even number of Ru clusters are more stable than the neighboring odd number clusters.
The effect of mixing Ru with Pt in small clusters is studied by calculating the mixing energy, Δ. Mixing energies as a function to the number of Ru atoms for all compositions of 3 ≤ m + n ≤ 8 for Ru m Pt n clusters are plotted in Figure 5. Negative values of mixing energy indicate a favorable mixing, whereas demixing is represented by positive values.
For (Ru,Pt) 3 , both alloy composition shows a mixing tendency. All compositions for (Ru,Pt) 4 clusters also favor mixing except for Ru 3 Pt 1 , in which the dopant Pt atom distorts the rectangular structure of Ru. For (Ru,Pt) 5 clusters, high Pt compositions show more negative mixing energies than high Ru compositions, and the mixing tendency is maximum for 40%  The Journal of Physical Chemistry C Article Ru. Similarly, the Ru 2 Pt 4 composition is found to have the maximum mixing tendency for (Ru,Pt) 6 clusters, which has a 33% Ru composition, while the second best was found for 50% composition, whereas for other compositions the mixing energies were found to be close to zero. For (Ru,Pt) 7 , the Ru 3 Pt 4 structure has the maximum mixing tendency, followed by the two neighboring compositions. Again, in (Ru,Pt) 8 , the 50% configuration favors mixing more than the other compositions. Pt-rich compositions for (Ru,Pt) 8 are found to have reduced mixing tendencies than the Ru-rich configurations because of the magic size of pure Ru 8 . The largest mixing energy is found for Ru 1 Pt 1 , and Ru 2 Pt 2 , followed by Ru 1 Pt 2 , Ru 2 Pt 3 , and Ru 3 Pt 4 . For (Ru,Pt) 6 clusters mixing tendency is lower than for (Ru,Pt) 5 and (Ru,Pt) 7 , in general, because of the magic size of pure Pt 6 , as in the Ru 8 case. Figure 5 also reveals that alloy clusters with even numbers of Ru atoms usually lie below the line connecting its neighbors. That is to say, clusters with even numbers of Ru atoms favor mixing more than the adjacent clusters, which have odd number of Ru atoms. This also fits with the even−odd stability order of pure Ru clusters (see Figure 4); however, the trend is not as clear as for the pure Ru clusters.
The binding energy per atom (E b ), which is related to the stability of nanoclusters, is shown in Figure 6. According to the figure, binding energy increases with increasing cluster size. The binding energy also increases with increasing Ru composition except for the Ru dimer, Ru 3 , and Ru 3 Pt 1 , which is in agreement with the higher cohesive energy of Ru than Pt. From the binding energy plot, it can be seen that values for 40−50% Ru compositions are slightly higher than the connecting lines, which indicates higher stabilities at these compositions. Mixing    The Journal of Physical Chemistry C Article energy and second difference in energy values for nanoalloy clusters also confirm this trend. In the second difference energy plot in Figure 7, there are positive peaks for 50% Ru compositions of (Ru,Pt) 4 and (Ru,Pt) 8 , while the peaks are at around 40% Ru composition for (Ru,Pt) 5 , (Ru,Pt) 6 , and (Ru,Pt) 7 .
HOMO−LUMO gaps are often used as an indicator for the structural stabilities of small clusters, with higher HOMO− LUMO gaps usually indicating higher stabilities. However, our calculations revealed that the HOMO−LUMO gaps are smallest for the "magic" sizes of Pt 6 and Ru 8 for pure metal clusters (see Supporting Information, Figure 5). For alloy clusters, higher HOMO−LUMO gaps correlate well with the suggested high stable compositions of (Ru,Pt) 4 , (Ru,Pt) 6 , and (Ru,Pt) 7 . However, smaller HOMO−LUMO gaps are found for (Ru,Pt) 5 and (Ru,Pt) 8 .
Although the trends discussed here only consider the lowest energy (global minimum) clusters, global optimization calculations also revealed several low-lying isomers of alloy clusters. For the higher stability compositions for each size (Ru 2 Pt 2 , Ru 2 Pt 3 , Ru 2 Pt 4 , Ru 3 Pt 4 , and Ru 4 Pt 4 ), no low-lying isomers were found within a binding energy range of 0.3 eV. Several low-lying isomers are found, however, for less stable alloy clusters. For example, for (Ru,Pt) 6 , low lying isomers found for Ru 3 Pt 3 and Ru 4 Pt 2 with 0.03 eV energy difference with corresponding global minima structures (see Supporting Information, Table 3). While Ru 3 Pt 3 isomer is a distorted structure of global minima Ru 3 Pt 3 , Ru 4 Pt 2 isomer is again an edge-capped square pyramid structure as in the global minimum Ru 4 Pt 2 , only with a different edge capped. Similarly for (Ru,Pt) 7 , low-lying isomers are found for Ru 4 Pt 3 and Ru 5 Pt 2 , which have the same geometric structure as the highly stable Ru 3 Pt 4 composition.
Bader charge analysis 54 shows that there is a 0.41 e − charge transfer from Ru to Pt in the RuPt dimer. For Ru m Pt 1 clusters, calculated Ru−Pt charge transfers are between 0.4 and 0.5 e − , while for Ru 1 Pt n clusters there is higher charge transfer (between 0.7 and 0.9 e − ). Charge transfer also increases as the composition get closer to 50% for alloy clusters (see Supporting Information, Figure 6). Ru−Pt charge transfer may play a role in strengthening Ru−Pt interactions and may also contribute to the stabilization of cluster isomers with Ru atoms occupying central positions, surrounded by Pt.

■ CONCLUSIONS
We have performed a computational study of Ru−Pt nanoalloys ranging from 3 to 8 atoms and compared them with pure Ru and Pt clusters in the same size range. The structural properties and energetics of bimetallic Ru−Pt nanoalloys have been studied within the framework of the BPGA-DFT approach that performs a global optimization search for the lowest energy configuration for each size and composition directly at the DFT level.
The calculations reveal that Ru atoms prefer central and adjacent positions due to stronger Ru−Ru bonds than Pt−Pt bonds, while the Pt atoms occupy peripheral positions. This, together with shorter Ru−Ru bond lengths, also predicts that "core-shell" Ru@Pt structures would become thermodynamically more stable as the cluster size increases. Energetic analysis shows that Ru compositions of 40−50% exhibit more favorable mixing than Ru-rich or Pt-rich compositions.
In future work, this study will be extended to larger bimetallic Ru−Pt nanoalloys, to investigate core−shell Ru−Pt structure formation.

* S Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b11329.
All the Cartesian coordinates and energy values for considered subnanometer clusters (PDF).