CoreâShell versus Other Structures in Binary Cu38ânMn Nanoclusters

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Core-Shell vs. Other Structures in Binary Cu M Nanocluster (M = Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au; n = 1, 2, and 6): Theoretical Insight into Determining Factors Nozomi Takagi, Kazuya Ishimura, Masafuyu Matsui, Ryoichi Fukuda, Masahiro Ehara, and Shigeyoshi Sakaki J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 26 Apr 2017 Downloaded from http://pubs.acs.org on April 28, 2017

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The Journal of Physical Chemistry

Core-shell vs. Other Structures in Binary Cu38-nMn Nanocluster (M = Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au; n = 1, 2, and 6): Theoretical Insight into Determining Factors

Nozomi Takagi,1 Kazuya Ishimura,2 Masafuyu Matsui,1 Ryoichi Fukuda,1,2 Masahiro Ehara,1,2 and Shigeyoshi Sakaki1,3*

1

Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, 1-30 Goryo-Ohara, Nishikyo-ku, Kyoto 615-8245, Japan

2

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

3

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

1 ACS Paragon Plus Environment

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ABSTRACT DFT calculations of binary transition metal nanoclusters Cu38-nMn (M = Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au; n = 1, 2, and 6) clearly show that a core-shell structure Cu32M6(core) with M in a core is stable for M = Ru, Rh, Os, and Ir but not stable for M = Pd, Ag, Pt, and Au. These results are consistent with the segregation energy evaluated for Cu37M. Electron population is more accumulated to the core M atoms in Cu38-nMn(core) (M = Ru, Rh, Os, and Ir) than to the core Cu atoms in Cu38. Such electron accumulation substantially occurs in M = Ru, Rh, Os, and Ir because their d orbitals are not fully occupied. A linear relationship is firstly found between the segregation energy and the increase in the d orbital population of the core atom, indicating that the electron accumulation to the Mn core is one of the important factors for the segregation energy and the stabilization of the core-shell structure; in other words, a core-shell structure with M atom(s) in a core is stable when the d orbitals of M are not fully occupied. In M = Pd, Pt, and Au, the fused-alloy structure is more stable than the core-shell and phase-separated ones. In M = Ag, the fused-alloy structure is as stable as the phase-separated one but the core-shell structure is less stable. In these metals, the d orbitals are either nearly or fully occupied and thereby the electron accumulation to the Mn core does not occur so much. In Cu32M6(core), the deformation energy of the Cu32 shell increases in the order Ru < Rh Cu37Ru(15) (+17.7 kcal/mol), where in the parenthesis is the potential energy difference from the most stable Cu37Ru(01) taking a doublet state. The segregation energy (Eseg) is defined here as a difference in energy between the most stable Cu37M(01) and the next stable one, either Cu37M(07) or Cu37M(15) in which M exists on the surface.11 In the case of Cu37Ru, it is 13.6 kcal/mol. The quartet state of Cu37Ru is calculated to be somewhat less stable than the doublet state. In the quartet state, the stability also decreases in the same order Cu37Ru(01) (+2.9


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kcal/mol) > Cu37Ru(07) (+16.8 kcal/mol) > Cu37Ru(15) (+19.3 kcal/mol) as that in the doublet state, where in the parenthesis is the relative energy to Cu37Ru(01) taking a doublet state. The relative energies of three isomers of Cu37M(01), Cu37M(07), and Cu37M(15) (M = Rh, Pd, Ag, Os, Ir, Pt, and Au) were investigated in a similar manner to those of Cu37Ru. We calculated several possible spin states and found that the energy difference between the lowest energy spin state and the next one is not large, as shown in Table 1; see Table S6 for the other unstable spin state. In Cu37Rh, Cu37Os, and Cu37Ir, the most stable structure has an M atom at the core position, the next one has it at the face, and the least one at the corner; in other words, the stability decreases in the order Cu37M(01) > Cu37M(07) > Cu37M(15) like in Cu37Ru. The segregation energy is the largest in Cu37Os and decreases in the order Cu37Os (18.7 kcal/mol) > Cu37Ir (9.5 kcal/mol) and Cu37Ru (13.6 kcal/mol) > Cu37Rh (4.1 kcal/mol). In other words, the segregation energy of group VIII metal is larger than that of group IX metal, and that of 5d metal is larger than that of 4d metal. In Cu37Pd and Cu37Pt, on the other hand, Cu37M(07) (M = Pd and Pt) is the most stable, whereas Cu37M(01) and Cu37M(15) are less stable. The segregation energy is negative but its absolute value is small (Table 1). In Cu37Ag and Cu37Au, Cu37M(15) (M = Ag and Au) is the most stable, Cu37M(07) is the next, and Cu37M(01) is the least stable. The segregation energy is negative and its absolute value is large (-20.5 and -15.3 kcal/mol for Ag and Au, respectively). These results suggest that Ru, Rh, Os, and Ir tend to take the inside position rather than the surface position, whereas Pd, Ag, Pt, and Au tend to take the surface position rather than the inside position. The sign of the segregation energy here agrees with that calculated for bulk metal.14 However, the sign differs from that calculated for the Cu54Pd and Cu54Pt particle,16 though the same sign was obtained for the other



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combinations. The absolute values of the segregation energies for the Cu-Pt and Cu-Pd combinations are small in all these calculations. These results suggest that the Cu-Pt and Cu-Pd combinations must be carefully considered.

2. Electronic Structures of Cu38 and Cu37M Nanoclusters (M = Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au) The charge distribution in the Cu38 cluster is one of the important properties, because it relates to the adsorption of small molecules such as CO, NO, and H2. Interestingly, the negative NBO charge is accumulated to the core Cu atoms (about -0.6 e), as shown in Figure 2; note that the NBO charge seems to overestimate the charge distribution but the trend is the same as that calculated by the Hirshfeld method (see Figure S1 and discussion in page S19 in the SI). Also, the Cu atoms at the face position of the surface are somewhat negatively charged (about -0.4 e), whereas the Cu atoms at the corner position are positively charged (about +0.2 e). Similar charge distribution is found in both of the triplet and singlet states; see Figure S2 in the SI. The spin distribution in the triplet state is, on the other hand, delocalized almost equivalently on all the Cu atoms; see Figure S2 in the SI. The decreasing order of the stability Cu37Ru(01) > Cu37Ru(07) > Cu37Ru(15) agrees with those of the coordination number and the negative charge of Ru in Cu37Ru, as shown in Table 2. In the most stable Cu37Ru(01) with the doublet state, the Ru(01) atomic charge (-2.13 e) is much more negative than the Cu(01) atomic charge (-0.60 e) in Cu38 (Table 2 and Figure 2). Instead, Cu(03) to Cu(18), which are either at the neighbor position to the Ru(01) or at the face position of the Cu(111) surface, become less negatively (or more positively) charged than in Cu38. The remaining Cu atoms have similar NBO charge to those in Cu38. These results indicate that the Cu atoms adjoining Ru(01) and those at the face position participate in the charge-transfer (CT) to Ru(01).54


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The Ru(01) atom has a somewhat smaller 5s orbital population (0.28 e) and much larger 5p and 4d orbital populations (1.29 e and 8.55 e, respectively) than those of a neutral Ru atom with a 4d75s1 configuration, as shown in Table 2. The Cu(01) in Cu38 has a somewhat smaller 4s orbital population (0.35 e) and much larger 4p and moderately smaller 3d orbital populations (1.39 e and 9.86 e, respectively) than those of a neutral Cu atom with a 3d104s1 configuration. A significant difference is observed in the d orbital population between the Ru(01) and Cu(01) atoms, though the s and p orbital populations are not different very much between them. Also, it is notable that the 4d orbital population of Ru in Cu37Ru decreases in the order Ru(01) (8.55 e) > Ru(07) (8.25 e) > Ru(15) (7.68 e). In Cu38, the Cu 3d orbital population is different little among Cu(01), Cu(07), and Cu(15) because the Cu atom has the 3d104s1 configuration in the ground state.55 These results strongly suggest that CT occurs from the neighboring Cu atoms to the 4d orbitals of Ru because the 4d orbitals of Ru are not fully occupied but such CT to the 3d orbital of Cu(01) from the neighboring Cu atoms does not occur in Cu38 because Cu has fully occupied 3d orbitals. Another important factor is the coordination number. Because the coordination number decreases in the order Ru(01) > Ru(07) > Ru(15) (Table 2), the CT from the Cu atoms to Ru becomes weaker in this order, as mentioned above. In other words, Ru(01) interacts with more Cu atoms than Ru(07) and Ru(15), which is favorable for the CT from Cu to Ru. Based on the above results, it is concluded that the atom which can receive electron population tends to take the core position with large coordination number. This is one factor for stabilizing Cu37Ru(01). In Cu37M (M = Rh, Os, and Ir), the d orbital population of M decreases in the order M(01) > M(07) > M(15) like that in Cu37Ru, as shown in Table 3. This decreasing order suggests that the electron accumulation to M is crucial for stabilizing the Cu37M(01) structure.



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On the other hand, the d orbital population is not different very much among three isomers of Cu37M (M = Pd, Ag, Pt, and Au), in which the Cu37M(01) structure is not stable. It is likely that in these clusters the electron accumulation to M is small and hardly contributes to stabilizing the Cu37M(01) structure; its reason will be discussed below. Ru, Rh, Os, and Ir have 4d75s1, 4d85s1, 5d66s2, and 5d76s2 electron configurations in the ground state, respectively. Ag and Au have an nd10(n+1)s1 electron configuration. Pd has a 4d10 electron configuration but Pt has a 5d96s1 electron configuration. Because the d shell is not completely full in M = Ru, Rh, Os, and Ir, the CT from Cu to Ru, Rh, Os, and Ir occurs largely in Cu37M(01). Indeed, the d orbital populations of Ru(01) and Rh(01) in Cu37M(01) increase very much by 1.55 e and 1.22 e relative to the 4d75s1 and 4d85s1 electron configurations of the neutral Ru and Rh atoms in the ground state, as shown in Tables 2 and 3. The similar increase in the d orbital population is observed in the 5d orbitals of Os and Ir. On the other hand, the electron population is not accumulated very much to Pd, Ag, Pt, and Au because the d shell is fully occupied in Pd, Ag, and Au and nearly occupied in Pt. Actually, the d orbital populations of Ag(01) and Au(01) slightly decrease in Cu37Ag(01) and Cu37Au(01)56 relative to the d10s1 electron configuration. Those of Pd(01) and Pt(01) increase by 0.65 e and 0.63 e relative to the d9s1 electron configuration57 to a much lesser extent than those of Rh(01) and Ir(01). We investigated if the electron accumulation to M relates to the LUMO energy and electron affinity of M; see Table S10. However, the increase in the d orbital population is not always parallel to the LUMO energy and electron affinity in these metals, suggesting that not only CT to the LUMO but also some other factor contributes to the electron accumulation to the M atom at the core. One plausible factor is the electrostatic potential at the core which is induced by nuclei. Such electrostatic potential is the most positive (attractive to electron) at the core of metal-cluster because the core position is


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surrounded by many nuclei. As a result, the electron accumulation occurs to the core moiety. Actually, the Cu atom at the core has negative NBO charge in Cu38. In the case of Cu37M(01) (M= Ru, Rh, Os, and Ir), such electron accumulation to M occurs larger than in the case of M = Cu because of their larger atomic number (i.e., larger nucleus charge) and the presence of vacancy in the d shell. In the case of M = Pd and Pt, the atomic number is large but the vacancy in the d shell is not enough. In the case of M = Ag and Au, there is no vacancy in the d shell. Therefore, the electron accumulation does not occur sufficiently in these metals; see page S16 in the SI for discussion of LUMO and electron affinity. All these results suggest that the presence of the unoccupied d orbital(s) is one of the important factors for stabilizing the structure having M atom at the core position.

3. Segregation Energy and Electron Distribution in Cu37M When Cu37M(01) is stable, the d orbital population of the M(01) atom in Cu37M(01) increases very much relative to the ground state electron configuration of M, as discussed above; see M = Ru, Rh, Os, and Ir in Tables 2 and 3. Stimulated by these results, we investigated the relation between the difference in the d orbital population from the ground state electron configuration and the segregation energy, as shown in Figure 3. Interestingly, a good linear relationship is found between them. This linear relationship clearly shows that M tends to take the core position when the d orbital of M has enough capacity to receive electron population. Such capacity is considered as one of the important factors in stabilizing the Cu37M(01) structure. Also, the CT from Au to Cu was experimentally reported,58 which is consistent with the computational result that the Au(15) is positively charged in the most stable Cu37Au(15) cluster (Table 3). Because the segregation energy of M2 is generally evaluated with a binary M1mM2 system (M1, M2 = TM element; m = large number), we wonder about its



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suitability for discussing the position of the second M2 atom in M1m-1M22. If useful, the segregation energy would be applied to discuss whether the core-shell structure is stable or not. We investigated here the stability of the Cu36Ru2 cluster. Cu36Ru2 has the thirty-one structural isomers. Some important structures are shown in Figure 1B and the relative energies are summarized in Figure 4; see Scheme S1 for all the optimized structures of Cu36Ru2. Apparently, a clear correlation is observed between the positions of two Ru atoms and the relative stability, as follows: The most stable isomer is Cu36Ru2(01,02) with a triplet state,59 where (01,02) represents the positions of two Ru atoms, as shown in Figure 1B. In this structure, both Ru atoms take the core position. The next stable isomer is Cu36Ru2(01,03), which has two Ru atoms in the core position, as shown in Figures 1B and 4. The structures which have one Ru atom at the core and another one at the face position are 15 - 20 kcal/mol above the most stable Cu36Ru2(01,02). The structures containing one Ru at the core position and another one at the corner position become more unstable by about 20 – 40 kcal/mol. The isomers containing one Ru atom at the face position and another one at either the face or the corner position become much more unstable than Cu36Ru2(01,02) by up to 60 kcal/mol. The isomers containing two Ru atoms at the corner positions become further unstable by up to 50 kcal/mol in the triplet state and up to 80 kcal/mol in the singlet state than Cu36Ru2(01,02). The most unstable isomer is Cu36Ru2(15,34) in which two Ru atoms take the corner position (Figure 1B); in other words, the stability of Cu36Ru2 decreases in the order, the structure having two Ru atoms at the core > at the face > at the corner. These relative stabilities are consistent with the segregation energy calculated with Cu37Ru, suggesting that the segregation energy is useful for discussing the structure of Cu36M2. The Ru(01) and Ru(02) atomic charges are negative in Cu36Ru2(01,02) but become much less negative as going to the face and the corner positions (Figure 4), which is


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essentially the same as the change in the Ru atomic charge in Cu37Ru. It is likely that the NBO charge evaluated with Cu37M is useful for discussing electron distribution in Cu36M2 and other similar nanoclusters.

4. Geometries of Cu32M6 Nanoclusters (M = Ru, Rh, Os, Ir, Pd, Ag, Pt, and Au); Core-shell Structure or not? Because the segregation energy suggests that a Cu-Ru nanocluster takes a core-shell structure with Ru in the core, we first investigate the Cu-Ru combination. Cu32Ru6 is the smallest model bearing an octahedral core structure in which six Cu atoms in the core position are replaced with six Ru atoms; this is represented as Cu32Ru6(core) hereafter. As shown in Figure 1C, the Ru6 core has a regular octahedral geometry. The triplet state is the most stable, while the septet and nonet states are above the triplet state only by 1.3 and 6.1 kcal/mol, respectively; the singlet and quintet states are much more unstable than the triplet state by 7.5 and 20.4 kcal/mol, respectively. Then, we calculated the isomers of Cu32Ru6 in which one Ru atom was moved from the core position to either the face or corner position, as shown in Figure 1C, which are named Cu32Ru5(core)Ru(face) and Cu32Ru5(core)Ru(corner), respectively. Despite of this tiny geometry change, Cu32Ru5(core)Ru(face) and Cu32Ru5(core)Ru(corner) are much more unstable than Cu32Ru6(core) by 16.4 and 34.8 kcal/mol, respectively, indicating that Cu32Ru6(core) is the most stable. This result is consistent with the fact that Ru atom wants to take the core position rather than the face and corner positions in Cu37Ru and Cu36Ru2 and the previous report by the first-principle calculation and the MD simulation in which Ru and Cu are not mixed with each other.60 As shown in Table 4, both of the 5p and 4d orbital populations of Ru(01) in Cu32Ru6(core) significantly increase by 1.23 e and 1.06 e, respectively, compared to the d7s1 electron configuration of neutral Ru atom, indicating that negative charge is more accumulated on the six Ru



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atoms at the core (about 1.5 e) in Cu32Ru6(core). Consistent with the electron accumulation on the Ru6 core, the negative charge on Cu(07) to Cu(14) in the face position becomes smaller in Cu32Ru6(core) than in Cu38, and the positive charge on Cu(15) to Cu(38) in the corner position becomes moderately larger (about 0.4 e) than in Cu38 (Figure 2). These results indicate that the Cu atoms at the face position mainly participate in the electron accumulation to the Ru atoms. It is noted here that the Ru atom is less negatively charged in Cu32Ru6(core) than in Cu37Ru(01). The less negative Ru atomic charge in Cu32Ru6(core) is reasonable because the Ru(01) atom interacts with smaller number of Cu atoms in Cu32Ru6(core) than in Cu37Ru(01). However, the total NBO charge of Ru6(core) in Cu32Ru6(core) (-8.51 e) is much larger than that of Cu5(core)Ru(01) in Cu37Ru(01) (-4.79 e), indicating that the electron accumulation to each Ru atom is smaller in Cu32Ru6(core) than in Cu37Ru(01) but that to Ru6(core) is larger than that to Cu5(core)Ru(01). Therefore, it is reasonably concluded that electron accumulation occurs more largely to the Ru6 core than to the Cu6 core, which contributes to the larger stabilization of the core-shell structure Cu32Ru6(core). In the case of M = Rh, Os, and Ir, Cu32M6(core) is more stable than Cu32M5(core)M(face) and Cu32M5(core)M(corner) like Cu32Ru6, as shown in Table 4. The energy difference between the most stable Cu32M6(core) and the least stable Cu32M5(core)M(corner) is much larger for M = group VIII than that for M = group IX and also much larger for M = 5d metals than that for M = 4d metals. These trends are the same as those observed in the segregation energy discussed above. In M = Pd, Ag, Pt, and Au, on the other hand, Cu32M5(core)M(corner) is the most stable, Cu32M5(core)M(face) is the next, and Cu32M6(core) is the least stable, as shown in Table 4. On the basis of these results, it is clearly concluded that the core-shell structure Cu32M6(core) is more stable than the others (fused-alloy and phase-separated)


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for M = group VIII and IX but less stable than the others for M = group X and XI, as summarized in Scheme 3. The energy difference between the most stable Cu32M5(core)M(corner) and the least stable Cu32M6(core) is larger for M = group XI than that for M = group X and also that for M = 5d metals is much larger than that for M = 4d metals. This trend is the same as that of the segregation energy shown in Figure 3; the segregation energy evaluated with Cu32M6 and the discussion are shown in Figure S4 and page S22 in the SI. At the end of this section, we wish to mention the relevance between the core-shell structure Cu32M6(core) (M = Ru, Rh, Os, and Ir) and catalytic reaction. Because the Cu32 surface is more positively charged in these clusters than that of Cu38, a gas molecule such as CO which has a donating orbital can interact more strongly with Cu32M6(core) than with Cu38. Their core-shell structures are useful for the reaction in which CT occurs from substrate to metal-particle. Such electronic structure of core-shell particles would be useful for catalytic activity.

5. Some Other Factors for Determining the Stability of Cu32M6 Though the stability of Cu32M6(core) is consistent with the segregation energy, it is important to investigate if some other factor influences the stability of the core-shell structure, because the energy difference between Cu32M6(core) and the others is not large in the Cu-Pd and Cu-Pt combinations (Table 4) and the segregation energies of Rh, Pd, and Pt are very small (Table 1). With consideration of previous work16 which discussed the stability of binary metal clusters in terms of the atomic size and the metal-metal cohesive energy, it is likely that the M-M and Cu-Cu distances in Cu38 and Cu32M6(core) significantly influence the relative stability of the core-shell structure besides the segregation energy. As shown in Table 5, the M-M distance of the M6 core in Cu32M6(core) significantly increases as going from the group VIII metal (Ru and Os)



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to the group X metal (Pd and Pt) and then moderately decreases as going to the group XI metal (Ag and Au). Also, the M-Cu distance, which corresponds to the interface distance between the M6 core and the Cu32 shell, is significantly large in M = Ag and Au. Consistent with the M-M distance in the core and the interface M-Cu distance, the Cu(face)-Cu(corner) and Cu(corner)-Cu(corner) distances in Cu32M6(core) are longer than in Cu38 and increase in the order M = Ru < Rh < Pd < Ag and M = Os < Ir < Pt < Au in Cu32M6(core), as shown in Table 5. These features suggest that the structure of the Cu32 shell is distorted in Cu32M6(core). The deformation energy of the Cu32 shell, which is defined as the energy difference between the Cu32 shell in Cu38 and that in Cu32M6(core), increases in the order Cu32Ru6 (19.9 kcal/mol) < Cu32Rh6 (23.9 kcal/mol) Cu-M for M = Os and Ir. In the Cu-Rh combination, the Rh-Rh bond energy (33.1 kcal/mol) is smaller than the Cu-Cu bond energy, but the Rh-Rh bond energy is considerably larger than the Cu-Rh one (30.8 kcal/mol), suggesting that Cu and Rh tend to be separated from each other. The large Rh-Rh bond energy is one of the important factors to stabilize the Cu32Rh6(core) structure despite of the small segregation energy of Rh; note that the stability of the Cu32Rh6(core) structure is larger than that expected by the segregation energy, because the segregation energy by Cu37M is defined independent on the Rh-Rh bond energy. In the Cu-Pd combination, the Pd-Pd bond energy (15.7 kcal/mol) is much smaller than the Cu-Pd (34.5 kcal/mol) and Cu-Cu bond energies, which suggests that Cu32Pd6(core) is not stable but other structures like the fused-alloy one become stable. In the Cu-Ag and Cu-Au combinations, the M-M and Cu-M bond energies (M = Ag or Au) are similar to the Cu-Cu bond energy; for instance, the Ag-Ag and Cu-Ag bond energies are 34.9 and 40.5 kcal/mol, respectively, and the Au-Au and Cu-Au ones are 43.5 and 52.4 kcal/mol. These bond energies lead to the conclusion that Cu32M6(core) is not stable but M and Cu atoms tend to mix with each other in the Cu-Ag and Cu-Au combinations. However, the structure of Cu32Pt6 cannot be explained by the Pt-Pt and Cu-Pt bond energies; the much larger Pt-Pt bond energy (59.7 kcal/mol) than the Cu-Pt one (52.5 kcal/mol) suggests that Cu32Pt6(core) is stable but Cu32Pt6(core) is calculated to be less stable than Cu32Pt5(core)Pt(face) and Cu32Pt5(core)Pt(corner). This discrepancy suggests that the bond energy of diatomic system is not always a good property for



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understanding and predicting the alloy structure but some other factors are crucial for destabilizing the Cu32Pt6(core) structure. Such important factor for destabilizing the Cu32Pt6(core) structure is the large deformation energy of the Cu32 shell, which was discussed above. Another important factor to be considered is cohesive energy of the M6 core. As shown in Table 6, the cohesive energies of Ru and Rh are larger than those of Pd and Ag,66 and also those of Os and Ir are larger than those of Pt and Au, indicating that the cohesive energy is important factor for discussing the stability of the core-shell structure. It is noted that because of the much smaller cohesive energies of Ag and Au than the others, these two metals never form the core-shell structure Cu32M6(core). Based on these results, it is concluded that the vacancy of the d shell, the deformation energy of the Cu32 shell, and the cohesive energy of the M6 core are useful for discussing and predicting the Cu32M6 structure.67-69 These factors would play important roles in determining the structure and stability of other combinations of two metal elements; for instance, the present results suggest that the Cu-Ni binary metal cluster has a core-shell structure with Ni atoms in the core because Ni has d8s2 electron configuration. Certainly, the theoretical study with the Gupta potential reported that such core-shell structure is stable.70 In discussing very large metal cluster/particle, however, the results of relatively small system here are not very useful and the factors discussed are not enough because some other factors such as size-mismatching effect and size-dependency of the cohesive energy etc. become more important.

6. Fused-alloy and Phase-separated Structures of Cu32M6 Nanoclusters In Cu-M (M = Pd, Ag, Pt, and Au) combinations, the Cu32M6(core) structure is not stable. Also, the segregation energy and the cohesive energy suggest that these M atoms tend to take the surface position. In such case, it is likely that either the fused-alloy or


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phase-separated structure is stable. Here, we investigated the stabilities of the fused-alloy and phase-separated structures in these combinations. Because numerous numbers of isomers are possible in the fused-alloy and phase-separated structures of Cu32M6, we constructed typical models of these two structures, as follows: In the fused-alloy structure, we placed six M atoms at the most distant position from each other so as to avoid the neighboring position. The number of M atoms in the core, face, and corner positions are represented hereafter as (l,m,n); for example, Cu32M6(2,2,2) represents that two M atoms are located in the core, face, and corner positions, respectively. Here, we investigated Cu32M6(2,2,2), Cu32M6(0,4,2), Cu32M6(0,2,4), Cu32M6(0,0,6), and Cu32M6(0,6,0). Only one isomer is possible in Cu32M6(2,2,2),

Cu32M6(0,4,2),

Cu32M6(0,2,4),

and

Cu32M6(0,0,6)

under

the

above-mentioned conditions, while five isomers are possible in Cu32M6(0,6,0), as shown in Scheme 4A. In constructing the phase-separated structure, the first M atom is placed at either the face position (07) or the corner one (15). The remaining five M atoms are placed on the surface at the neighboring position to the first M atom. This procedure leads to the formation of two phase-separated structures, as shown in Scheme 4B, which are named Cu32M6(PS-a) and Cu32M6(PS-b), respectively. The relative energies of thus-constructed fused-alloy and phase-separated structures are investigated in the binary Cu32M6 clusters (M = Pd, Ag, Pt, and Au) in which the core-shell structure is unstable. Certainly, the fused-alloy structures are significantly more stable than the core-shell structure in these binary metal clusters, as shown in Table 7. The energy difference between the core-shell and the most stable fused-alloy structures increases in the order Cu32Pd6 (~33 kcal/mol) < Cu32Pt6 (~52 kcal/mol) the face > the corner position, the stability decreases in the order Cu37M(01) > Cu37M(07) > Cu37M(15) for M = Ru, Rh, Os, and Ir. In Cu36Ru2, the relative stability decreases in the



Page 22 of 52

order, the structure having two Ru atoms at the core position > at the face position > at the corner position, and the Ru d orbital population becomes smaller in the same order like in Cu37Ru. These results suggest that the segregation energy is useful for discussing the structure of Cu36M2 and the electron accumulation to the core atom is crucial for increasing the segregation energy. The core-shell structure Cu32M6(core) is stable for M = Ru, Rh, Os, and Ir, as suggested by the segregation energy. In these combinations, the electron accumulation to the M6 core significantly occurs like in Cu37M. In M = Pd, Ag, Pt, and Au possessing a negative segregation energy, the Cu32M6(core) structure is not stable. In these metals, electron accumulation to the M6 core hardly occurs because of the fully or nearly occupied d orbitals of these metals, which is not favorable for the Cu32M6(core) structure. Another factor for stabilizing the core-shell structure is the deformation energy of the shell moiety, which is defined as the energy difference of the Cu32 shell between Cu38 and Cu32M6(core). This deformation energy increases in the order M = group VIII < IX Cu(07) (0.91 e) > Cu(15) (0.31 e) suggesting that the 4p orbitals act a role of acceptor orbital because of the 3d104s1 configuration of Cu in the ground state.

(56)

The moderate decrease in the d orbital population is induced by the exchange repulsion.

(57)

Here, the 4d95s1 electron configuration is taken as a reference in Pd, because many other atoms (Ru to Ag) have a 4dn5s1 electron configuration. Taking this configuration as a reference, we obtained better understanding, as will be discussed below. The orbital population of Pd in Cu37Pd is similar to that of Pt in Cu37Pt (Table 3), though Pd and Pt have the 4d10 and 5d96s1 electron configurations, respectively, in the ground state. Also, the 5s orbital population of Ru and Rh in Cu37M (M = Ru and Rh) are similar to that of Pd in Cu37Pd, though Ru and Rh have dns1 electron configuration in the ground state. Therefore, it is likely that the s orbital population is flexible and it is not useful as a


Page 33 of 52 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


criterion to understand the ground state electron configuration. (58)

Kuhn, M.; Sham, T. K. Charge redistribution and electronic behavior in a series of Au-Cu alloys. Phys. Rev. B 1994, 49, 1647-1661.

(59)

The singlet and quintet states are calculated to be 4.4 and 10.2 kcal/mol higher in energy than the triplet state, respectively. The triplet state is always more stable than the singlet state in the other structures except for Cu36Ru2(01,03) and Cu36Ru2(01,07); see Figure 4.

(60)

He, X.; Liang, S.-H.; Li, J. -H.; Liu, B. –X. Atomistic mechanism of interfacial reaction and asymmetric growth kinetics in an immiscible Cu−Ru system at equilibrium. Phys. Rev. B 2007, 75, 045431-045440.

(61)

Lahiri, D.; Bunker, B.; Mishra, B.; Zhang, Z.; Meisel, D.; Doudna, C. M.; Bertino, M. F.; Blum, F. D.; Tokuhiro, A. T.; Chattopadhyay, S.; Shibata, T.; Terry, J. Bimetallic Pt–Ag and Pd–Ag nanoparticles. J. Appl. Phys. 2005, 97, 094304-094311.

(62)

Rossi, G.; Rapallo, A.; Mottet, C.; Fortunelli, A.; Baletto, F.; Ferrando, R. Magic Polyicosahedral Core-Shell Clusters. Phys. Rev. Lett. 2004, 93, 105503-105506.

(63)

Ferrando, R.; Fortunelli, A.; Rossi, G. Quantum effects on the structure of pure and binary metallic nanoclusters. Phys. Rev. B 2005, 72, 085449-085457.

(64)

Guo, W.; Iwashita, T.; Egami, T. Universal local strain in solid-state amorphization: The atomic size effect in binary alloys. Acta Materialia 2014, 68, 229-237.

(65)

Panizon, E.; Ferrando, R. Strain-induced restructuring of the surface in core@shell nanoalloys. Nanoscale 2016, 8, 15911-15919.

(66)

The order of the cohesive energy is somewhat different from that of the bond energy of the diatomic system, especially for the Pd case; see Tables 6 and S3. This discrepancy arises from the electronic structure of the Pd atom. Because Pd



Page 34 of 52

has d10 electron configuration, there is no valence electron which contributes to bonding interaction in the diatomic system. In Pd6 and bulk, however, s-d hybridization would occur easily because the s orbital energy becomes lower by the increase in bonding overlap of s orbitals and the d orbital energy becomes higher by the increase in exchange repulsion with d orbitals in such systems. As a result, the bonding interaction becomes possible and the cohesive energy becomes larger in Pd6 and bulk metal than in the diatomic system. (67)

The surface energy is often employed in the discussion of binary transition metal nanoparticles.24,25,68,69 The difference in energy between Cu32M6(core) and Cu32M5(core)M(face or corner) for instance relates to the difference in the surface energy between the Cu32 and Cu31M shells and the energy difference between the M6 and M5Cu core. These energy differences mainly arise from the M-M, Cu-M, and Cu-Cu bond energies. Therefore, we did not mention the surface energy in the discussion. Because it is important to elucidate the relation between the surface energy and bond energy, we plan to investigate such relation in the next work.

(68)

Methfessel, M.; Hennig, D.; Scheffler, M. Trends of the surface relaxations, surface energies, and work functions of the 41 transition metals. Phys. Rev. B 1992, 46, 4816-4829.

(69)

Vitos, L.; Ruban, A. V.; Skiver, H. L.; Kollar, J. The surface energy of metals. Surface Sci. 1998, 411, 186-202.

(70)

Panizon, E.; Olmos-Asar, J. A.; Peressi, M.; Ferrando, R. Study of structures and thermodynamics of CuNi nanoalloys using a new DFT-fitted atomistic potential. Phys. Chem. Chem. Phys., 2015, 17, 28068-28075.

(71)

Molayem, M.; Grigoryan, V. G.; Springborg, M. Global Minimum Structures and Magic Clusters of CumAgn Nanoalloys. J. Phys. Chem C 2011, 115,


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22148-22162. (72)

The deformation energy of the Ag32 shell is -2.7 kcal/mol, as shown in Figure S6. This means that the deformation of the Ag32 shell moderately contributes to stabilization of the Ag32Cu6(core) structure. The similar result was observed in Au32Cu6(core); see Figure S6 in the SI for the detail.

(73)

Based on the results, it is likely to predict that the combination of Cu with Mo/W could have core-shell structure with Mo/W in the core, because Mo and W have enough vacancy in the d-shell. In the case of very early 4d and 5d metals such as Zr/Hf and Nb/Ta, the prediction is not easy because their d orbital at high energy is not favorable for electron accumulation to these metals. The additional studies of other combinations are in progress now.



Page 36 of 52

Table 1. Relative energies (in kcal/mol) of three isomers of Cu37Ma, b) and segregation energy of M (Eseg in kcal/mol).c) Cu37M(01)

Cu37M(07)

Cu37M(15)

Eseg

Cu37Ru

D; 0.0 [Q; +2.9]

D; +13.6 [Q; +16.8]

D; +17.7 [Q; +19.3]

13.6

Cu37Rh

T; 0.0 [S; +2.7]

T; +4.1

[S; +6.4]

S; +10.4 [T; +11.9]

4.1

Cu37Pd

Q; 0.0 [D; +3.5]

Q; -6.2

[D; -3.1]

D; -6.1

Cu37Ag

T; 0.0 [S; +1.2]

T; -13.0 [S; -12.0]

T; -20.5 [S; -18.2]

-20.5

Cu37Os

D; 0.0 [Q; +3.4]

D; +18.7 [Q; +24.4]

D; +31.8 [Q; +33.3]

18.7

Cu37Ir

S; 0.0 [T; +2.3]

T; +9.5

[S; +11.8]

T; +23.2 [S; +24.3]

9.5

Cu37Pt

D; 0.0 [Q; +2.0]

D; -1.0

[Q; -0.7]

D; +3.4 [Q; +5.1]

-1.0

Cu37Au

T; 0.0 [S; +1.4]

T; -9.4

[S; -8.6]

T; -15.3 [S; -11.7]

-15.3

a)

[Q; -6.0]

-6.1

The most stable spin state was employed. S, D, T, and Q represent singlet, doublet,

triplet, and quartet states, respectively. The next stable spin state is presented in the square bracket. b)

B3LYP* and PBE give similar results for the relative stabilities of the isomer and spin

state; see Table S7. c)

The segregation energy is defined as an energy difference between Cu37M(01) and the

most stable structure in Cu32M(07) and Cu37M(15), where a positive value represents that the structure having M at the core is more stable than that having M at the surface.


Page 37 of 52 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Coordination number (CN) of Ru, NBO charge (q in e), and s, p, and d orbital populations in Cu37M (M = Ru and Cu).a) Cu37Ru Ru(01)

Ru(07)

Ru(15)

12

9

6

-2.13

-1.28

-0.25

s

0.28 (-0.72)b)

0.35 (-0.65)b)

0.31 (-0.69)b)

p

1.29 (+1.29)b)

0.68 (+0.68)b)

0.26 (+0.26)b)

d

8.55 (+1.55)b)

8.25 (+1.25)b)

7.68 (+0.68)b)

CN of Ru q[Ru]

Cu38 Cu(01)

Cu(07)

Cu(15)

-0.60

-0.37

+0.28

s

0.35 (-0.65)b)

0.58 (-0.42)b)

0.51 (-0.49)b)

p

1.39 (+1.39)b)

0.91 (+0.91)b)

0.31 (+0.31)b)

d

9.86 (-0.14)b)

9.87 (-0.13)b)

9.90 (-0.10)b)

q[Cu]

a)

NBO charge and electron population are calculated in Cu37Ru with doublet state and

Cu38 with triplet state. b)

Difference in orbital population of M between Cu37M and the atomic ground state (Ru

(4d75s1) and Cu (3d104s1)).



Page 38 of 52

Table 3. NBO charge (q in e), s, p, and d orbital populations of M in Cu37Ma) (M = Rh, Pd, Ag, Os, Ir, Pt, and Au), and the difference in orbital population from the atomic ground state.b) Cu37M(01)a) Cu37M(07)a) Cu37M(15)a) Cu37Rh q[Rh] -1.79 -1.05 -0.53 b) b) s 0.29 (-0.71) 0.35 (-0.65) 0.23 (-0.77)b) p 1.27 (+1.27)b) 0.56 (+0.56)b) 0.22 (+0.22)b) d 9.22 (+1.22)b) 9.14 (+1.14)b) 9.08 (+1.08)b) Cu37Pd q[Pd] -1.28 -0.56 -0.11 s 0.33 (-0.67)b) 0.39 (-0.61)b) 0.26 (-0.74)b) p 1.30 (+1.30)b) 0.52 (+0.52)b) 0.19 (+0.19)b) b) b) d 9.65 (+0.65) 9.65 (+0.65) 9.66 (+0.66)b) Cu37Ag q[Ag] -0.74 -0.01 +0.36 s 0.43 (-0.57)b) 0.63 (-0.37)b) 0.61 (-0.39)b) p 1.42 (+1.42)b) 0.48 (+0.48)b) 0.10 (+0.10)b) d 9.89 (-0.11)b) 9.91 (-0.09)b) 9.93 (-0.07)b) Cu37Os q[Os] -2.15 -1.49 -0.51 b) b) s 0.40 (-0.60) 0.60 (-0.40) 0.61 (-0.39)b) p 1.41 (+1.41)b) 0.80 (+0.80)b) 0.37 (+0.37)b) b) b) d 8.34 (+1.34) 8.09 (+1.09) 7.53 (+0.53)b) Cu37Ir q[Ir] -1.99 -1.26 -0.76 s 0.52 (-0.48)b) 0.62 (-0.38)b) 0.54 (-0.46)b) p 1.43 (+1.43)b) 0.67 (+0.67)b) 0.33 (+0.33)b) b) b) d 9.04 (+1.04) 8.97 (+0.97) 8.90 (+0.90)b) Cu37Pt q[Pt] -1.71 -0.93 -0.47 b) b) s 0.63 (-0.37) 0.70 (-0.30) 0.61 (-0.39)b) b) b) p 1.44 (+1.44) 0.61 (+0.61) 0.27 (+0.27)b) d 9.63 (+0.63)b) 9.61 (+0.61)b) 9.59 (+0.59)b) Cu37Au q[Au] -1.14 -0.42 +0.03 b) b) s 0.78 (-0.22) 0.89 (-0.11) 0.98 (-0.02)b) p 1.48 (+1.48)b) 0.65 (+0.65)b) 0.11 (+0.11)b) b) b) d 9.87 (-0.13) 9.88 (-0.12) 9.88 (-0.12)b) a) The most stable spin state (Table 1) was employed. b) The difference from the ndm(n+1)s1 configuration which was taken as a reference state. Though Pd has 4d10 electron configuration as the ground state, 4d95s1 was taken here as a reference; see footnote 57.


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Table 4. Relative energies of several possible isomers (∆Erel in kcal/mol),a) NBO charge (q in e), s, p, and d orbital populations of M(01) in Cu32M6(core) (M = Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au) and the difference in orbital population from the atomic ground state.b) Cu32Ru6c)

Cu32Rh6d)

Cu32Pd6d)

Cu32Ag6c)

+16.4/+34.8a)

+19.5/+18.3a)

-6.1/-7.6a)

-16.9/-19.0a)

-1.56

-1.42

-1.22

-0.74

s

0.27 (-0.73)b)

0.29 (-0.71)b)

0.32 (-0.68)b)

0.41 (-0.59)b)

p

1.23 (+1.23)b)

1.23 (+1.23)b)

1.28 (+1.28)b)

1.44 (+1.44)b)

d

8.06 (+1.06)b)

8.90 (+0.90)b)

9.62 (+0.62)b)

9.90 (-0.10)b)

Cu32Os6d)

Cu32Ir6c)

Cu32Pt6d)

Cu32Au6c)

+33.0/+76.5a)

+29.4/+38.9a)

-5.5/-12.4a)

-23.7/-26.9a)

-1.40

-1.37

-1.39

-0.94

∆Erel q[M(01)]

∆Erel q[M(01)]

a)

s

0.31 (-0.69)

0.32 (-0.68)

0.38 (-0.62)

0.61 (-0.39)b)

p

1.37 (+1.37)b)

1.38 (+1.38)b)

1.41 (+1.41)b)

1.45 (+1.45)b)

d

7.72 (+0.72)b)

8.66 (+0.66)b)

9.60 (+0.60)b)

9.88 (-0.12)b)

Relative

b)

energies of

b)

Cu32M5(core)M(face) and

b)

Cu32M5(core)M(corner) to

Cu32M6(core) are presented before and after the slash, respectively. A positive value represents that the core-shell structure is more stable than Cu32M5(core)M(face) and Cu32M5(core)M(corner), and vice versa. b)

The difference from the ndm(n+1)s1 electron configuration which was taken as the

ground state. Though Pd has 4d10 electron configuration as the ground state, 4d95s1 was taken here as a reference; see footnote 57. c)

Triplet state.

d)

Singlet state.



Page 40 of 52

Table 5. Averaged M-M distance (in angstrom) in the M6 core, averaged Cu-Cu distance in the C32 shell, and deformation energy (Edef in kcal/mol) of the Cu32 shell in Cu32M6(core). M-M core-core

M-Cu

Cu-Cu

core-face core-corner face-corner corner-corner (i)b)

Cu38d)

Edefa)

(ii)c)

2.572

2.629

2.540

2.550

2.556 2.541

-

Cu32Ru6d) 2.684

2.701

2.562

2.616

2.581 2.646

19.9

e)

2.772

2.663

2.528

2.618

2.591 2.644

23.9

e)

2.880

2.677

2.537

2.631

2.684 2.578

40.3

Cu32Ag6d) 2.837

2.808

2.590

2.640

2.740 2.526

46.8

Cu32Os6e)

Cu32Rh6 Cu32Pd6

2.657

2.694

2.577

2.624

2.566 2.677

22.9

d)

2.738

2.686

2.543

2.617

2.592 2.639

22.3

e)

2.946

2.669

2.533

2.644

2.711 2.677

50.9

Cu32Au6d) 2.937

2.791

2.580

2.652

2.784 2.513

61.7

Cu32Ir6

Cu32Pt6

a)

Edef = E(Cu32-shell of Cu32M6(core)) – E(Cu32-shell of Cu38)

b)

The Cu-Cu distance between corner Cu atoms in the same Cu(100) surface such as

Cu(15)-Cu(17). c)

The Cu-Cu distance between corner Cu atoms in the different Cu(100) surfaces such

as Cu(17)-Cu(23). d)

Triplet state.

e)

Singlet state.


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Table 6. Cohesive energya) (in kcal/mol) calculated with the M6 core Cohesive energyb) c)

Cohesive energy

Cu

Ru

Rh

Pd

Ag

Os

Ir

Pt

Au

-31.5

-39.7

-32.4

-29.4

-21.3

-49.9

-50.8

-40.8

-25.5

(triplet)

(triplet)

(singlet)

(singlet)

(triplet)

(singlet)

(triplet)

(singlet)

(triplet)

-31.5

-50.0

-40.4

-30.5

-21.3

-58.6

-60.7

-42.3

-25.5

(triplet)

(17et)

(13et)

(triplet)

(triplet)

(15et)

(15et)

(triplet)

(triplet)

a)

Cohesive energy is defined as [E(M6) – 6E(M)]/6.

b)

M6 is calculated with the spin state which agrees with the total Cu32M6 system with the singlet Cu32 shell.

c)

M6 is calculated with the most stable spin state.

41

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Page 42 of 52

Table 7. Relative energies (in kcal/mol)a) of the fused-alloy and phase-separated structures of Cu32M6 (M = Pd, Pt, Ag, and Ru). fused-alloy (2,2,2)

(0,4,2)

(0,2,4)

PS-a

PS-b

c

d

e

-20.2

-33.1

-33.4

-33.1

-33.4

-33.1

+27.0

+24.9

-97.7

-109.6

-72.7

-72.9

-78.6

-77.2

-78.6

-108.1

-103.2

-26.5

-19.9

Cu32Ag6c)

-65.8

-86.6

Cu32Pt6b)

-29.0

-41.4

-31.7

-28.3

-51.6

-47.0

-47.0

-44.9

-46.6

+39.4

+35.3

c)

-85.9

-103.5

-110.8

-141.2

-96.2

-97.4

-106.2

-99.0

-105.1

-92.4

-97.6

c)

+80.0

+114.2

+146.8

+141.0

+102.0

+105.5

+113.7

+100.6

+113.8

+101.1

+105.5

Cu32Au6

a)

(0,6,0) b

-22.6

Cu32Ru6

(0,0,6) a

b)

Cu32Pd6

phase-separated

The core-shell structure Cu32M6(core) was taken as a reference. A negative value means that the core-shell structure is more unstable

than the others. b)

Singlet state.

c)

Triplet state.

42


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Scheme 1. Schematic representation of core-shell, phase-separated, and fused-alloy structures.



Page 44 of 52

Scheme 2. Numbering of Cu atoms in Cu38.


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Scheme 3. Schematic representation of the most stable structure of binary Cu32M6 cluster (M = Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au).



Page 46 of 52

Scheme 4. Schematic representation of fused-alloy and phase-separated structures of binary Cu32Pd6 cluster.


Page 47 of 52 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. Optimized structures of binary Cu37Ru, Cu36Ru2,a) and Cu32Ru6 clusters. Distances are in angstrom. a)

All the investigated isomers of Cu36Ru2 are shown in Scheme S1 in the SI.



Page 48 of 52

Figure 2. NBO atomic charges in Cu38 (triplet), Cu37Ru (doublet), and Cu32Ru6 (triplet) clusters.a) a)

Similar charge distribution is found in the singlet (Cu38 and Cu32Ru6) and quartet (Cu37Ru) states; see Figures S2 and S3 in the SI.

48


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Figure 3. Segregation energya) (Eseg) against the difference in d orbital populationb) of binary Cu37M clusters in Cu37M (M = Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au). a)

The segregation energy is defined as the energy difference between Cu37M(01) and

the most stable structure in Cu37M(07) and Cu37M(15). A positive value means that the structure having M atom in the core is more stable than that having M on the surface. b)

Difference in d orbital population of M between Cu37M(01) and the atomic ground

state (dns1 electron configuration).



Page 50 of 52

Figure 4. Relative energies (∆Erel) of Cu36Ru2 isomers to those of Cu36Ru2(01,02) in the triplet state and NBO atomic charge. The position of Ru is presented at the bottom in colors; blue (core), green (face), and yellow (corner).

50


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Figure 5. Optimized structures and relative energies of binary Ag32Cu6 clusters.



Page 52 of 52

Table of Contents


CoreâShell versus Other Structures in Binary Cu38ânMn Nanoclusters

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