M = Ru, Rh, Os, and Ir

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Theoretical Insight into Core-shell Preference for Bimetallic PtM (M = Ru, Rh, Os, and Ir) Cluster and Its Electronic Structure Jing Lu, Kazuya Ishimura, and Shigeyoshi Sakaki J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 05 Apr 2018 Downloaded from http://pubs.acs.org on April 5, 2018

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The Journal of Physical Chemistry

Theoretical Insight into Core-Shell Preference for Bimetallic Pt-M (M = Ru, Rh, Os, and Ir) Cluster and Its Electronic Structure Jing Lu,1 Kazuya Ishimura,2 and Shigeyoshi Sakaki*1 1

Fukui Institute for Fundamental Chemistry (FIFC), Kyoto University, Takano-Nishihiraki-cho 34-4, Sakyou-ku, Kyoto 606-8103, Japan 2

Institute for Molecular Science (IMS), Okazaki 444-8585, Japan

ACS Paragon Plus Environment

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Abstract: PtmMn (M = Ru, Rh, Os, and Ir; m+n = 38 and 55) clusters are systematically investigated using DFT method. In octahedral 38-atom cluster, core-shell structure M6@Pt32 with M6 core and Pt32 shell is stable for Pt-Rh and Pt-Ir combinations but is not for Pt-Ru and Pt-Os combinations. In 55-atom cluster, icosahedral M13@Pt42 structure is stable for all Pt-M combinations, indicating that large cluster is more preferable to stabilizing the core-shell structure than small cluster. The difference in cohesive energy (Ecoh) between M13 and Pt13 and the distortion energy {Edis(M13)} of M13 are parallel to the segregation energy (Eseg), indicating that these are important factors for stabilizing M13@Pt42. One more crucially important factor is the interaction energy (Eint) between M13 core and Pt42 shell, because Eint is parallel to Eseg and its absolute value is much larger than those of Edis(M13) and Edis(Pt42). The Eint depends on energy gap between LUMO of M13 core and HOMO of Pt42 shell, indicating that LUMO energy of M13 and HOMO energy of Pt42 are good properties for understanding and predicting stability of core-shell structure. Pt atom is more positively charged in M13@Pt42 than in Pt55 and the HOMO energy of M13@Pt42 is higher than that of Pt55. The presence of these two contrary factors for O2 binding suggests that M13@Pt42 is not bad for O2 binding.


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INTRODUCTION Platinum-based clusters/particles play crucially important roles in many industrial applications. One of the representative roles is catalysis for oxygen reduction reaction (ORR) in proton exchange membrane fuel cell.1-4 A lot of efforts are being made to decrease platinum (Pt) content by increasing Pt dispersion and enhancing catalytic activity.5-7 One of typical approaches is to use core-shell structure consisting of Pt thin shell and nanoparticle core of less expensive and/or more abundant metal.8-10 In such bimetallic cluster/particle, physical and chemical properties of the Pt shell can be tuned by other metal at the core, leading to improvement in catalytic performance.11 Currently, bimetallic Pt-Ti,12-14 Pt-Fe,15,16 Pt-Co,17,18 Pt-Ni,19-23 Pt-Cu,24,25 Pt-Ru,26-30 and Pt-Pd5,31,32 clusters/particles with the core-shell structure have been reported as good candidate for ORR catalyst both experimentally and theoretically. For instance, octahedral Ti19@Pt60 cluster with Pt60 shell was reported to be highly efficient catalyst with lower Pt content for ORR, because O2 activation and OH formation were improved by the use of Ti19@Pt60 nanocluster compared to the octahedral Pt79 cluster,14 where expression of “Am@Bn” (A and B = metal elements) is used hereinafter to represent a core-shell structure consisting of Am core and Bn shell. The carbon-supported core-shell Pt-Ni nanoparticle (Ni@Pt/C) with a monolayer Pt shell was reported to exhibit higher ORR activity than pure Pt nanoparticle because of the less oxophilicity of the Pt shell of the core-shell nanoparticle.19 Also, core-shell Rum@Ptn nanoparticle was reported to be more active for CO oxidation than Mm@Ptn nanoparticle (M = Rh, Ir, Pd, or Au).29 These reports suggest that the bimetallic cluster/particle with Pt-shell is a promising candidate for inexpensive and good catalyst. To use such core-shell nanoparticle with Pt-shell as catalyst, the core-shell structure must be stable. In this regard, we need theoretical knowledge about the stability, electronic structure, and ORR reactivity of core-shell structure


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Mm@Ptn in comparison with those of Ptm+n cluster/particle. However, such knowledge has not been sufficiently presented yet as far as we know. Cohesive energy, atomic size, and segregation energy are often discussed as determining factors for taking a core-shell structure of bimetallic cluster/particle. Cohesive energy is defined as the difference between energy of free atom and averaged energy of atom in cluster, particle, or bulk.33 Metal element with larger cohesive energy tends to be bound with each other and take core position because binding energy of core is larger than that of surface due to larger coordination number of metal in core than in surface. Size of atom is also important; actually, small atom seems preferable to sterically confined core position because core undergoes compression in many cases. Segregation energy, which provides quantitative assessment of segregation behavior for bulk and particle, represents that an impurity atom takes an inside position or a surface position of bulk or particle.34,35 For bimetallic Am@Bn cluster/particle, segregation occurs by exchanging one A atom in the Am core with one B atom in the Bn shell. Such segregation energy differs from that of the system containing one impurity atom because cohesive energy is not important in the system with one impurity atom but important in Am@Bn. Thus, stability of Am@Bn depends on the balance of the segregation energy of impurity atom, cohesive energy, and atomic size as well as atomic number, shape, preparation method, and experimental conditions.2,34 In addition, charge transfer from shell to core is important for influencing segregation behavior.2,36 However, a systematic study about the stability of core-shell structure, determining factors, and their electronic structures has been limited so far. In this work, bimetallic Pt-M (M = Ru, Rh, Os, and Ir) clusters with 38 and 55 atoms are theoretically investigated using density functional theory (DFT), where Ru, Rh, Os, and Ir elements are selected as representative metals because some of them, for instance Pt-Ru combination, are expected as a good candidate for ORR catalyst.37 We selected rather small 38-


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and 55-atom clusters here because metal clusters with precise number of atoms have been investigated recently;38-41 such small metal cluster exhibits quantum confinement effect;42-44 see page S11 to S12 in the supporting information for the quantum confinement effect. Our purposes here are to perform comprehensive analysis of these bimetallic clusters, to elucidate determining factors for stability of core-shell structure such as size, shape, segregation energy, cohesive energy, distortion energies of Mn core and Ptm shell, and interaction energy between Mn core and Ptm shell, and to discuss electronic structure of these bimetallic core-shell clusters. Our goal is to give a guideline for understanding and predicting if the core-shell structure with Pt shell is stable and how much electronic structure and catalytic activity can be tuned by bimetallic core-shell structure.

COMPUTATIONAL DETAILS AND MODELS Spin-polarized DFT calculations were performed with the Vienna Ab-initio Simulation Package (VASP)45-47 using the PBE-D2 functional as implemented.48,49 Plane wave basis sets were employed with an energy cutoff of 400 eV. The Monkhorst-Pack grid method was used for 1×1×1 k-point sampling. The metal cluster was placed at the center of a 25×25×25 Å cubic box with periodic boundary condition, which was enough to neglect the interaction between a cluster and its periodic image. Convergence criteria for total energy and maximum force were set to 1.0 × 10-4 eV and 0.01 eV/Å (EDIFF = 0.0001 and EDIFFG = -0.01), respectively. To determine the lowest energy spin state, geometry optimization was performed at each possible spin state which was defined by difference between numbers of α and β electrons. Geometry and total energy were discussed on the basis of above-described DFT computations.


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HOMO and LUMO energies and NBO populations were evaluated by conventional DFT calculation with the B3LYP functional50 after comparing the orbital energy with those by B3PW9151,52 and PBE053,54 calculations, where SMASH program55 was employed. In these calculations, LANL2DZ56-58 basis sets with effective core potentials (ECPs) were used for all these metal atoms. NBO population analysis was made using Gaussian09 package,59 where the B3LYP functional was employed. Though highly symmetrical structure such as octahedral and icosahedral symmetries was reported not to be stable in the case of small transition metal clusters,60-63 octahedron and icosahedron shapes have been employed as model in theoretical investigation of segregation behavior and catalytic activity for ORR.64-65 In this context, the octahedron and icosahedron shapes were employed here as initial geometry for optimization of core-shell structure of Pt32M6 and Pt42M13, but geometry optimization was carried out without any symmetry constraint. Octahedral M38 cluster has eight (111) facets and six (100) facets, as shown in Scheme 1. Six atoms take core position, eight atoms take center position of the (111) facet, and twenty-four atoms take corner position of the (100) facet. M6@Pt32 (M = Ru, Rh, Os, and Ir) cluster consists of six M atoms in the core and thirty-two Pt atoms in the shell. Pt31Mcenter(M5Pt)core and Pt31Mcorner(M5Pt)core clusters were constructed by exchanging one M atom at the core with one Pt atom at the center or corner, respectively, as shown in Scheme 2A. Though there are many possible isomers, we calculated two representative structures for each of Pt31Mcenter(M5Pt)core and Pt31Mcorner(M5Pt)core; in Pt31Mcenter(M5Pt)core(I), the Mcenter is placed at the nearest center position to the Pt atom of the (M5Pt)core, and in the Pt31Mcenter(M5Pt)core(II), the Mcenter is placed at the most distant center position from the Pt atom of the core. Similarly, Pt31Mcorner(M5Pt)core(I) and Pt31Mcorner(M5Pt)core(II) are constructed by placing the Mcorner at the nearest and the most distant corner positions from the Pt atom of the core, respectively.


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Scheme 1 Scheme 2 In the case of 55-atom cluster, both of octahedral and icosahedral structures are possible because 55 is a magic number for these two structures. In both, there are three layers; one atom takes the center of the cluster (core-1), twelve and forty-two atoms form second (core-2) and third layers (shell), respectively. In the octahedral structure, the surface has three different positions such as edge, center, and corner. Twenty-four atoms take the edge position between the (100) and (111) facets. Six atoms take the center position of the (100) facet. Remaining twelve atoms take the corner position between the (100) and (111) facets. In the icosahedral structure, the surface has twenty equivalent triangular facets and every facet has two different positions, edge and vertex. Thirty atoms take the edge position and twelve atoms take the vertex position (Scheme 1). Taking Pt55 cluster as a parent, core-shell M13@Pt42 cluster (M = Ru, Rh, Os and Ir) was constructed by replacing thirteen Pt atoms in the core with thirteen M atoms. Then, Pt41Mshell(M12Pt)core cluster was constructed by exchanging one M atom in the core-1 position with one Pt atom in the shell position. In octahedral-like Pt41Mshell(M12Pt)core, three kinds of non-core-shell structure are constructed, as shown in Scheme 2B, because the Pt42 surface has three different sites, as mentioned above. In icosahedral-like Pt41Mshell(M12Pt)core structure, two kinds of non-core-shell structure are constructed (Scheme 2C), because the Pt42 surface has two different sites. Segregation energy Eseg is defined by eq. (1), where a positive Eseg value indicates that the core-shell structure is preferred to other one, according to the definition; Eseg = Et[Ptm-1Mshell(Mn-1Pt)core] – Et(Mn@Ptm)

(1)

where Et[Ptm-1Mshell(Mn-1Pt)core] and Et(Mn@Ptm) represent total energies of Ptm-1Mshell(Mn-1Pt)core and Mn@Ptm clusters in the lowest energy spin state, respectively.


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The cohesive energy (Ecoh) for pure Mn cluster is defined, as follow; Ecoh = Et(M) – Et(Mn)/n

(2)

where Et(M) and Et(Mn) are total energies of free M atom and Mn cluster, respectively. Distortion energy (Edis) and root-mean-square deviation of bond lengths (RMSD) of M13 cluster are calculated by eqs. (3) and (4), respectively; Edis(M13) = Et(M13dis)– Et(M13opt)

RMSD = ∑, −

(3)

(4)

where Et(M13dis) and Et(M13opt) are total energies of the M13 core in M13@Pt42 and optimized M13 cluster, respectively, is bond length between M atom at the core-1 and that at the core-2 of

M13@Pt42,

is that of optimized M13 cluster, and the subscript “i” represents the i-th M-M

bond. The Edis of Pt42 shell is defined by eq. (5); Edis(Pt42) = Et(Pt42 in M13@Pt42) – Et(Pt42 in Pt55)

(5)

Where Et(Pt42 in M13@Pt42) and Et(Pt42 in Pt55) are total energies of the Pt42 shells whose geometries are taken to be the same as those in M13@Pt42 and Pt55 clusters, respectively. Interaction energy (Eint) is defined as stabilization energy between distorted shell and distorted core; Eint = Et(M13@Pt42) – Et(M13dis) – Et(Pt42 in M13@Pt42)

(6)

where geometries of distorted M13 core and Pt42 shell were taken to be the same as those of the corresponding core and shell in optimized M13@Pt42.


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RESULTS AND DISCUSSIAN Geometries of Pt32M6 and Pt42M13 clusters and segregation energy Octahedral Pt38 cluster was optimized in singlet to nonet spin states. The most stable spin state was quintet, while the energy difference between two spin states (singlet to septet) was not large; details are shown in Table S1 in supporting information. Relative energy of the most stable non-core-shell structure Pt31Mshell(M5Pt)core to the core-shell structure M6@Pt32 is listed in Table 1, where the core-shell structure is taken as reference (energy zero); Tables S2 and S3 show the details of relative energies of these five Pt32M6 isomers. For M = Rh and Ir, the core-shell structure M6@Pt32 is the most stable and the stability decreases in the order of M6@Pt32 > Pt31Mcenter(M5Pt)core > Pt31Mcorner(M5Pt)core. However, Pt31Rucenter(Ru5Pt)core(II) in the quintet spin state and Pt31Oscenter(Os5Pt)core(II) in the triplet spin state are more stable than the core-shell structure. On the basis of above results, it is concluded that M element of group IX forms stable M6@Pt32 because it tends to take core position but M of group VIII does not because it tends to take surface position. In the case of 55-atom cluster, octahedral and icosahedral structures are possible, as mentioned above. For the octahedral Pt55 cluster, 13et spin state is the most stable but the next stable spin state (11et) is only 0.08 kcal/mol above the 13et state. Icosahedral Pt55 cluster has 15et spin state, where the energy difference from the next stable 13et spin state is very small, too. The other spin states are calculated at higher energy than these two spin states by more than 4 kcal/mol. As shown in Table 1, Ru13@Pt42, Os13@Pt42, and Ir13@Pt42 with core-shell structure are more stable than others in octahedral geometry, whereas only Rh13@Pt42 is less stable than Pt41Rhcorner(Rh12Pt)core; relative energies of other possible spin states are listed in Table S4.


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Notably, the energy difference between core-shell and non-core-shell structures is much larger in 55-atom clusters of Pt-Ru, Pt-Os, and Pt-Ir combinations than in those 38-atom clusters. These results indicate that the stability of the core-shell structure is enhanced by increasing cluster size, the reason of which will be discussed below. In the icosahedral structure, M13@Pt42 with core-shell structure is stable for all these 55-atom clusters; relative energies of other possible spin states are listed in Table S5. It is noted that icosahedral M13@Pt42 is much more stable than its octahedral isomer for all these combinations, as shown in the bracket of Table 1. Table 1 Eseg was calculated for M6@Pt32 and M13@Pt42, as shown in Figure 1, where Eseg is defined as the energy difference between the core-shell structure and the most stable non-core-shell structure; see eq. (1).34 Eseg of octahedral 55-atom cluster is larger than that of 38-atom one except for Pt-Rh combination, in which Eseg of Rh13@Pt42 is slightly smaller than that of Rh6@Pt32 but the difference is very small (0.10 eV). Eseg for the icosahedral structure is larger than that for the octahedral one, and in addition, Eseg is larger for the combination of Pt with 5d metal than that with 4d metal in the same group and larger for the combination of Pt with group VIII metal than that with group IX metal. On the basis of above results, it is concluded that the combination of Pt with Os (group VIII 5d metal) is the best for constructing the core-shell structure with Pt shell. Considering abundance of metal, Pt-Ru combination is one reasonable choice for preparing core-shell catalyst with Pt-shell. Figure 1 Hereinafter, we will discuss the stable icosahedral Pt42M13 cluster as a representative example for in-depth analysis of determining factors for stability of the core-shell structure.

Cohesive energies (Ecohs) of Ru, Rh, Os, Ir, and Pt


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It is likely that Ecoh is one determining factor for segregation of bimetallic core-shell cluster/particle, as mentioned above, because metal with large Ecoh tends to be bound with each other as many as possible to form a core moiety; remember that metal atom at core position interacts with each other as many as possible. We calculated firstly Ecoh values of pure Run and Ptn clusters by eq. (2) for M6, M13, M38, M55, M79, and M116. In all these clusters, Ecoh of Run is larger than that of Ptn, as shown in Figure 2(a), indicating that Ru tends to take a core position in the Pt-Ru combination. Also, Ecoh increases as cluster size increases from M6 to M116, and Ecoh values of Pt116 (5.82 eV) and Ru116 (6.52 eV) are close to experimental values of bulk metal (5.84 eV and 6.74 eV, respectively).33 However, the difference in Ecoh between octahedral and icosahedral Mn clusters (M = Pt or Ru; n = 13 or 55) is less than 0.10 eV. These results suggest that Ecoh is more sensitive to the size of cluster than the structure and Ecoh is responsible for the larger stability of Ru13@Pt42 than that of Ru6@Pt32. Figure 2 Ecoh values of group VIII and IX metals (4.86 eV, 4.28 eV, 5.41 eV, and 5.29 eV for icosahedral Ru13, Rh13, Os13, and Ir13, respectively) are larger than that of Pt13 (3.95 eV), suggesting that all these M elements tend to take a core position in Pt-M combination. Actually, icosahedral core-shell structure M13@Pt42 is more stable than non-core-shell structure for all these combinations. It is noted that 5d metals (Os and Ir) have larger Ecoh than 4d metals (Ru and Rh) and group VIII metals (Ru and Os) have larger Ecoh than group IX metals (Rh and Ir). These results are consistent with the larger Eseg of 5d metal than that of 4d metal and the larger Eseg of group VIII metal than that of group IX metal in icosahedral M13@Pt42. For understanding better the relationship between Eseg and Ecoh, the difference in cohesive energy (∆Ecoh) between M13 and Pt13 is plotted against Eseg in Figure 2b. A good correlation


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between Eseg and ∆Ecoh is found, leading to the conclusion that large ∆Ecoh between M and Pt is advantageous for taking the core-shell structure with Pt shell.

Distortion energies (Ediss) of icosahedral M13 core and Pt42 shell Distortion energy of the M13 core {Edis(M13)} is defined as an energy difference between distorted geometry of the M13 in M13@Pt42 and the optimized geometry of M13, as defined by eq. (3). The geometrical distortion is represented by RMSD; see eq. (4). As shown in Figure 3, we found a good linear relationship between them, as expected; i.e., Edis(M13) increases as RMSD increases. Edis(Os13) is the smallest, indicating that the Os13 core in Os13@Pt42 is the least distorted in these core-shell clusters examined here. The next is the Ir13 core and the largest is the Rh13 core. Also, Eseg increases as Edis(M13) decreases, as shown in Figure S1. Based on these results, it is concluded that the distortion of the M13 core is one of the determining factors for stability of the core-shell structure. Figure 3 Distortion energy of the Pt42 shell {Edis(Pt42)} in M13@Pt42 is calculated to be negative interestingly, as shown in Table 2; in other words, the Pt42 shell in M13@Pt42 is more stable than in Pt55. This result suggests that the Pt42 shell of Pt55 wants to shrink and a small M13 core is preferable to stabilizing the Pt42 shell. For icosahedral Ru13@Pt42, Rh13@Pt42, Os13@Pt42, Ir13@Pt42, and Pt55 clusters, the average bond length {R(Ptedge-Ptvertex)} between the edge and vertex Pt atoms in the Pt42 shell increases in the order of Ru ≈ Rh < Os < Pt ≈ Ir, and the average bond length {R(Ptedge-Ptedge)} between two edge positions increases in the order of Ru < Ir ≈ Ru ≈ Os < Pt, as shown in Table 2. RMSD for these distances decreases in the order of Ru > Rh > Os > Ir and Edis(Pt42) is almost parallel to the RMSD value, as shown in Figure S1. These bond lengths and RMSD values are consistent with


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the result that the Pt42 shell shrinks in M13@Pt42 compared to that of Pt55 and the small Pt42 shell is more stable than in Pt55. Based on these results, it is likely concluded that small core is advantageous for stabilizing the Pt42 shell. However, the Edis(Pt42) is not parallel to the Eseg. This means that some other factor(s) is crucially important for stabilizing the core-shell structure. Table 2

Interaction energy between M13 core and Pt42 shell As shown in Table 2, the interaction energy (Eint) between the M13 core and the Pt42 shell is significantly negative (attractive) and therefore significantly contributes to the stability of the core-shell structure. It should be noted that the absolute value of Eint is much larger than those of Edis(M13) and Edis(Pt42), indicating that the Eint is more important for enhancing the stability of the core-shell structure than the Edis(M13) and Edis(Pt42). Apparently, the Eint is the most negative for Os13@Pt42, indicating that the interaction between the Os13 core and the Pt42 shell is the strongest. Notably, the Eint of group VIII metal (Os and Ru) is more negative than that of group IX metal (Ir and Rh) and that of 5d metal (Os and Ir) is more negative than that of 4d metal (Ru and Rh) in the same group. These trends are the same as those of the Eseg. Actually, the Eint is parallel to the Eseg, as shown in Figure S2. On the basis of these results, it is concluded that the Eint is one of the crucially important factors for determining the stability of the core-shell structure. Because charge transfer (CT) occurs from the Pt42 shell to the M13 core, as will be discussed below, it is likely that the Eint depends on LUMO energy (εLUMO) of the M13 core and HOMO energy (εHOMO) of the Pt42 shell in M13@Pt42. Because the PBE functional tends to provide too small HOMO-LUMO energy gap, the B3LYP-calculated orbital energy is used for discussion here. The energy gap (∆εLU-HO) between εLUMO of the M13 core and εHOMO of the Pt42 shell decreases in the order of Rh13@Pt42 (2.70) > Ru13@Pt42 (2.38) > Ir13@Pt42 (2.08) >


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Os13@Pt42 (1.80), where in parenthesis is the ∆εLU-HO in eV unit. The ∆εLU-HO-1 increases in the order of Rh < Ru < Ir < Os, which is almost parallel to the decrease in the Eint,66 as shown in Figure 4a. Also, the Eseg is parallel to the ∆εLU-HO-1, as shown in Figure 4b. It is concluded that the ∆εLU-HO is one of the important factors for the Eint and Eseg and the ∆εLU-HO is useful to discussing the stability of the core-shell structure. Figure 4

Charge distribution, frontier orbital energy, and reactivity for O2 binding Charge distribution and orbital energy around HOMO and LUMO are important factors for reactivity and catalytic activity of binary metallic core-shell cluster/particle. As listed in Tables 3 and S9, the Pt atomic charge at the core-1 position in the Pt55 is -0.540 e, where B3LYP/LANL2DZ-calculated NBO charge is presented hereinafter. Ru, Rh, Os, and Ir atomic charges at the same position in M13@Pt42 are much more negative than the Pt atomic charge at the same position in Pt55. Similarly, the M atomic charge at the core-2 position of M13@Pt42 is more negative than the Pt atomic charge at the same position in Pt55. Consistent with these atomic charges at the core position, the Pt atomic charge at the vertex position of the Pt42 surface is more positive in M13@Pt42 than in Pt55. Also, the Pt atomic charge at the edge position is negative in Pt55 but positive in M13@Pt42. All these results lead to the conclusion that CT occurs from the Pt42 shell to the M13 core in M13@Pt42. Table 3 As discussed above, the CT interaction mainly depends on the ∆εLU-HO. The ∆εLU-HO is the smallest for Os13@Pt42 and the largest for Rh13@Pt42. The difference (∆qd) in the M d orbital population at the core-1 position between M13@Pt42 and M ground state is larger for the group VIII metal (Os and Ru) than for the group IX metal (Ir and Rh) and that for 5d metal is large than


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that for 4d metal in the same group. These trends are the same as that of the ∆εLU-HO-1, suggesting that CT occurs from the Pt42 shell to the M13 core to contribute to the interaction energy between them, as discussed above. For O2 binding with metal cluster/particle, it is likely that negatively charged surface is preferable because CT from metal cluster/particle to O2 is crucially important for stabilizing O2 binding species. This means that M13@Pt42 is not favorable for O2 binding, because the Pt shell becomes positively charged in M13@Pt42 by the CT from the Pt42 shell to the M13 core. On the other hand, the occupied orbital energy on the Pt42 surface is another important factor for O2 binding.67-68 As shown in Figure 5, DOSs calculated by VASP show that the HOMO band of M13@Pt42 mainly consists of the Pt42 shell expect for Rh13@Pt42 in which the HOMO band consists of both of the Pt42 shell and the Rh13 core.69 In Pt55, the HOMO band mainly consists of the Pt42 shell. These results mean that the HOMO band plays important roles for O2 binding. The B3LYP-calculated HOMO energy becomes lower in the order of Os13@Pt42 > Ir13@Pt42 > Ru13@Pt42 > Rh13@Pt42 ≈ Pt55, indicating that Os13@Pt42, Ir13@Pt42, and Ru13@Pt42 have higher energy HOMO than that of Pt55 and they are better than Pt55 for binding with O2 molecule from the viewpoint of orbital energy. Rh13@Pt42 has the lowest energy HOMO. Thus, Rh13@Pt42 is expected to be the least reactive for O2 binding. It is concluded that the CT from the Pt42 shell to the M13 core leads to the presence of positively charged Pt42 surface, which is not favorable for O2 binding, but the εHOMO of the M13@Pt42 is higher than that of the Pt55, which is preferable to O2 binding. This means that the M13@Pt42 is not bad for the electrode of fuel cell because these two factors compensate to each other. Figure 5 To check how much easily these core-shell cluster can bind O2 molecule, we calculated O2 binding energy Eb(O2) at the bridge site between one Pt atom at the vertex position and the other


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Pt at the edge position, because this adsorption was reported to be the most stable by previous works.70-71 Eb(O2) value for M13@Pt42 cluster is -0.95 eV, -1.26 eV, -0.94 eV, and -1.53 eV for M = Ru, Rh, Os, and Ir, respectively, as listed in Table S12. Though these values are less negative than that for Pt55 cluster (-1.70 eV), they are significantly negative, leading to the conclusion that M13@Pt42 cluster can be capable of binding O2 molecule.

CONCLUSIONS Stabilities and electronic properties of M6@Pt32 and M13@Pt42 core-shell structures with Pt thin-shell are systematically explored for Pt-M bimetallic clusters (M = Ru, Rh, Os, and Ir). For Pt32M6, M element in group IX (Rh and Ir) is more preferable than that in group VIII (Ru and Os) to stabilizing the core-shell structure. In 55-atom M13@Pt42 cluster, icosahedral symmetry is more stable than octahedral one. In the icosahedral symmetry, the core-shell M13@Pt42 structure (M = Ru, Rh, Os, and Ir) is more stable than others for all Pt-M combinations examined here. In the octahedral symmetry, the core-shell structure is not stable only for the Pt-Rh combination but stable for other combinations. It is reasonably concluded that the stability of the core-shell structure of the bimetallic Pt-M cluster increases as the size increases. Important factors for determining the stability of the core-shell structure are discussed in icosahedral M13@Pt42: (i) Large cohesive energy Ecoh and large difference in Ecoh (∆Ecoh) between M13 and Pt13 are advantageous to stabilizing the core-shell M13@Pt42 cluster. Actually, the ∆Ecoh is parallel to the segregation energy Eseg. (ii) The small distortion energy of the icosahedral M13 core from the equilibrium M13 structure is preferable to stabilizing M13@Pt42. Indeed, the Eseg increases as the Edis(M13) decreases. (iii) Small metal element is better for enhancing the stability of M13@Pt42, because the Pt42 shell wants to shrink in M13@Pt42 compared to that in Pt55; the


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negative distortion energy Edis(Pt42) of the Pt42 shell is its evidence, where Edis(Pt42) is defined as the energy difference of the Pt42 shell from that of Pt55. (iv) But, the Edis(Pt42) is not parallel to the Eseg. The interaction energy Eint between the Pt42 shell and the M13 core is crucially important for determining stability of the core-shell structure, because the absolute value of Eint is much larger than those of Edis(M13) and Edis(Pt42). Actually, Eint becomes more attractive in the order of Rh > Ru > Ir > Os as Eseg increases. And, (v) because Eint is important and CT occurs from the Pt42 shell to the M13 core, it is concluded that the low energy LUMO of the M13 core is preferable to stabilizing the M13@Pt42 structure. The energy gap (∆εLU-HO) between LUMO of the M13 core and HOMO of the Pt42 shell is a good property for understanding and predicting the stability of the core-shell structure. Actually, the Eint is parallel to the reverse of the ∆εLU-HO and a linear relationship is found between the ∆εLU-HO-1 and the Eseg. Because of the CT interaction from the Pt42 shell to the M13 core, the Pt42 surface is more positively charged in M13@Pt42 than in Pt55. Such positively charged Pt42 surface is not preferable to O2 binding. However, the HOMO of M13@Pt42, which largely consists of atomic orbitals of the Pt42 shell, is calculated at higher energy than that of Pt55. The high energy HOMO is favorable for O2 binding. These two factors are reverse to each other for O2 binding and therefore M13@Pt42 is not bad for the O2 binding.

ASSOCIATER CONTENT Supporting Information The relative energy for all these investigated Ptn, Pt32M6, and Pt42M13 isomers in the different spin states (Tables S1-S5); cohesive energies of the pure Ptn and Run (Table S6); discussion of the bond distance between M13@Pt42 and optimized isolated M13 cluster (Table S7); relative


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energy for icosahedral M13 clusters in different possible spin states (Table S8); Relationship between RMSD(Pt42) and Edis(Pt42) (Figure S1); Relationship between Eint and Eseg (Figure S2); NBO charge (q), s, p, and d orbital populations for M and Pt in icosahedral M13@Pt42 cluster (Table S9); B3LYP, B3PW91, and PBE calculated HOMO and LUMO energy of M13@Pt42 (Table S10); B3LYP/LANL2DZ calculated HOMO and LUMO energy of the M13 and the Pt42 in M13@Pt42 cluster (Table S11); HOMO feature for Rh13@Pt42 by PBE/LANL2DZ (Figure S3).

AUTHOR INFORMATION Corresponding Author [email protected] +81-75-711-7907 Note The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work is based in part on results obtained from a project commissioned by the New Energy and Industrial Technology Development Organization (NEDO). SS wish to thank “Elements Strategy for Catalysts and Batteries (ESICB)” in Kyoto University for support in part and JSPS for support by Grant-in-Aid for Scientific Research (15H03770). We wish to thank the computational center at the Institute of Molecular Science (IMS, Okazaki, Japan) for using its computer and the RIKEN Advanced Institute for Computational Science (RIKEN AICS, Kobe, Japan) for using K-computer.


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(66) According to the perturbation theory, the interaction energy between two molecular orbitals (MOs) is parallel to the reverse of the orbital energy difference between these two MOs. (67) Jóhannesson, G. H.; Bligaard, T.; Ruban, A. V.; Skriver, H. L.; Jacobsen, K. W.; Nørskov, J. K. Combined Electronic Structure and Evolutionary Search Approach to Materials Design. Phys. Rev. Lett. 2002, 88, 255506. (68) Froemming, N. S.; Henkelman, G. Optimizing Core-Shell Nanoparticle Catalysts with a Genetic Algorithm. J. Chem. Phys. 2009, 131, 234103. (69) In the HOMO calculated by the B3LYP/LANL2DZ, the contribution of the Rh13 core seems smaller than that of the Pt42 shell. This is reasonable because the CT is the weakest in Rh13@Pt42. The difference in HOMO feature between DOS by PBE-D2/plane-wave calculation and MO by B3LYP/LANL2DZ could be attributed to the difference in functional between PBE-D2 and B3LYP. In general, PBE functional provides more delocalized orbital pictures than B3LYP because of the difference in Hartree-Fock exchange. For the HOMO feature by PBE/LANL2DZ, the contribution of Rh13 core is large, see Figure S3 in SI. (70) Jennings, P. C.; Aleksandrov, H. A.; Neyman, K. M.; Johnston, R. L. A DFT Study of Oxygen Dissociation on Platinum Based Nanoparticles. Nanoscale 2014, 6, 1153-1165. (71) Tsai, H. C.; Hsieh, Y. C.; Yu, T. H.; Lee, Y. J.; Wu, Y. H.; Merinov, B. V.; Wu, P. W.; Chen, S. Y.; Adzic, R. R.; Goddard, W. A. DFT Study of Oxygen Reduction Reaction on Os/Pt Core-Shell Catalysts Validated by Electrochemical Experiment. ACS Catal. 2015, 5, 1568-1580.


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Table 1. Relative energies (in kcal/mol) of core-shell structure (Mn@Ptm) and the most stable non-core-shell structure (M = Ru, Rh, Os, and Ir).a Core-shell structure

The most stable non-core-shell structure 38-atom cluster (Oh) Ru6@Pt32 0.0 (Nonet) Pt31Rucenter(Ru5Pt)core(II) -3.6 (Quintet) Rh6@Pt32 0.0 (Quintet) Pt31Rhcenter(Rh5Pt)core(II) +1.1 (Triplet) Os6@Pt32 0.0 (Singlet) Pt31Oscenter(Os5Pt)core(II) -8.6 (Triplet) 0.0 (Quintet) +5.6 (Quintet) Ir6@Pt32 Pt31Ircenter(Ir5Pt)core(II) 55-atom cluster (Oh) +16.2 (Nonet) Ru13@Pt42 0.0 (11et) [+82.6]b Pt41Rucenter(Ru12Pt)core b corner core -1.2 (16et) Rh13@Pt42 0.0 (14et) [+29.2] Pt41Rh (Rh12Pt) b center core +31.7 (Singlet) Os13@Pt42 0.0 (Nonet) [+115.7] Pt41Os (Os12Pt) b center core +30.1 (Dectet) Ir13@Pt42 0.0 (Sextet) [+35.2] Pt41Ir (Ir12Pt) 55-atom cluster (Ih) +31.0 (Septet) Ru13@Pt42 0.0 (Septet) Pt41Ruvertex(Ru12Pt)core vertex core +6.9 (20et) Rh13@Pt42 0.0 (20et) Pt41Rh (Rh12Pt) vertex core +61.2 (Septet) Os13@Pt42 0.0 (Septet) (Os12Pt) Pt41Os edge core +41.5 (Quartet) Ir13@Pt42 0.0 (Dectet) Pt41Ir (Ir12Pt) a All these results are calculated at the DFT/PBE-D2 level with VASP program. The most stable spin state is presented in parenthesis. b In bracket is relative energy (in kcal/mol) to the icosahedral M13@Pt42 in the most stable spin state.


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Table 2. The distortion energies (Edis, in eV) and RMSD (in Å) of M13 core and Pt42 shell, selected bond lengths (in Å), and interaction energy (Eint, in eV) between M13 core and Pt42 shell in [email protected]

RMSD c R(Mcore-1-Mcore-2) RMSD Edis(Pt42) e R(Ptedge-Ptvertex) R(Ptedge-Ptedge) (M13) in M13@Pt42 (Pt42) 0.24 0.0225 2.450 (2.474) d -4.36 0.0393 2.644 (-0.033) f 2.755 (-0.048)f Ru 0.38 0.0454 2.489 (2.534) -3.24 0.0318 2.646 (-0.031) 2.770 (-0.033) Rh 0.00 0.0016 2.482 (2.481) -2.92 0.0262 2.654 (-0.023) 2.772 (-0.031) Os 0.01 0.0055 2.511 (2.516) -2.47 0.0206 2.680 (0.003) 2.768 (-0.035) Ir 1.11 0.0516 2.553 (2.605) 0.0 0.0 2.677 (0.0) 2.803 (0.0) Pt a All these calculations were performed at the DFT/PBE-D2 level with VASP program. b See eq. (3). Edis(M13) is evaluated here with the spin polarized value of M13 core in M13@Pt42. c See eq. (4). d In parenthesis is bond length of the optimized structure of M13. e See eq. (5). Edis(Pt42) is evaluated here with the spin polarized value of Pt42 shell in Pt55. f In parenthesis is difference in bond length of the Pt42 shell between M13@Pt42 and Pt55. g See eq. (6). M

Edis(M13) b

Eint g -54.19 -43.69 -76.02 -58.10 -46.60


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Table 3. NBO atomic charges (q), d orbital populations of M and Pt in icosahedral M13@Pt42 cluster. a M13@Pt42 Mcore1 Mcore2 Ptvertex Ptedge -0.540 -0.132 0.237 -0.024 M = Pt 9 1 5d: 8.17 [-0.83] 5d: 8.58 [-0.42] 5d: 8.41 [-0.59] 5d: 8.68 [-0.32] 5d 6s -3.685 -1.433 0.982 0.303 M = Ru 7 1 4d: 8.32 [+1.32] 4d: 8.03 [+1.03] 5d: 7.80 [-1.20] 5d: 8.38 [-0.62] 4d 5s -3.220 -1.774 1.190 0.341 M = Rh 8 1 4d: 9.13 [+1.13] 4d: 9.26 [+1.26] 5d: 7.54 [-1.46] 5d: 8.28 [-0.72] 4d 5s -2.274 -1.552 1.000 0.296 M = Os 6 2 5d: 8.45 [+2.45] 5d: 7.80 [+1.80] 5d: 7.67 [-1.33] 5d: 8.30 [-0.70] 5d 6s -1.425 -0.893 0.478 0.213 M = Ir 7 2 5d: 8.23 [+1.23] 5d: 8.29 [+1.29] 5d: 8.26 [-0.74] 5d: 8.45 [-0.55] 5d 6s a All these calculations were performed at the B3LYP level using SMASH and Gaussian09 programs. Difference in d orbital population (∆qd) from the atomic ground states is presented in parenthesis.

29 ACS Paragon Plus Environment


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Scheme 1. Model systems of 38 and 55-atom clusters with corresponding M6 and M13 cores, respectively. a

Octahedron: Oh; icosahedron: Ih.


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(A)

M6@Pt32

Pt31Mcenter(M5Pt)core(I) / (II) (B)

M13@Pt42

Pt31Mcorner(M5Pt)core(I) / (II)

55-atom cluster (Oh)

Pt41Medge(M12Pt)core Pt41Mcenter(M12Pt)core Pt41Mcorner(M12Pt)core (C)

M13@Pt42

38-atom cluster (Oh)

55-atom cluster (Ih)

Pt41Medge(M12Pt)core

Pt41Mvertex(M12Pt)core

Scheme 2. Schematic representations of Pt32M6 and Pt42M13 clusters.



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Figure 1. Segregation energy (Eseg, in eV) calculated for PtmMn (M = Ru, Rh, Os, and Ir; m+n = 38 and 55) clusters.


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Figure 2. (a) Relationship between cohesive energy (Ecoh) and size of cluster and (b) relationship between segregation energy (Eseg) and difference in cohesive energy (∆Ecoh) between M13 and Pt13.



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Figure 3. Relationship between distortion energy {Edis(M13)} a and root-mean-square deviation of bond lengths (RMSD) of M13 core. a The optimized geometry of M13 is taken as reference.


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Figure 4. (a) Relationship between interaction energy (Eint) between Pt42 shell and M13 core and the reverse of HOMO-LUMO energy gap (∆εLU-HO-1) and (b) relationship between Eseg and ∆εLU-HO-1. a a

The ∆εLU-HO is the energy difference between the LUMO of M13 core and HOMO of

Pt42 shell


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Ru13@Pt42

Rh13@Pt42

Os13@Pt42 α-HOMO

Ir13@Pt42

Pt55

-5.78

-6.15

-5.61 β-HOMO

-5.72

-6.00

-5.86

-5.87

-5.90

-5.66

-5.87

Figure 5. HOMO a and DOSs b of icosahedral M13@Pt42 (M = Ru, Rh, Ir and Os) and Pt55 clusters. a The B3LYP-calculated orbital energy (in eV unit). b These DOSs were calculated by PBE-D2/plane wave basis sets using VASP program.

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TOC


M = Ru, Rh, Os, and Ir

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