Al13@Pt42 core-shell cluster for oxygen reduction reaction.

To increase Pt utilization for oxygen reduction reaction (ORR) in fuel cells, reducing particle sizes of Pt is a valid way. However, poisoning or surface oxidation limits the smallest size of Pt particles at 2.6 nm with a low utility of 20%. Here, using density functional theory calculations, we develop a core-shell Al13@Pt42 cluster as a catalyst for ORR. Benefit from alloying with Al in this cluster, the covalent Pt-Al bonding effectively activates the Pt atoms at the edge sites, enabling its high utility up to 70%. Valuably, the adsorption energy of O is located at the optimal range with 0.0-0.4 eV weaker than Pt(111), while OH-poisoning does not observed. Moreover, ORR comes from O2 dissociation mechanism where the rate-limiting step is located at OH formation from O and H with a barrier of 0.59 eV, comparable with 0.50 eV of OH formation from O and H2O on Pt(111).

Proton exchange membrane fuel cells (PEMFCs) are promising candidates for mobile and transport applications due to their high energy density, zero emissions, relatively low operating temperature, and minimal corrosion problems1. Pt nanoparticles supported on carbon are commonly used as catalysts of the cathode for the oxygen reduction reaction (ORR)2. It is observed that the ORR activity highly depends on the size of nanoparticles, where Pt nanoparticles with diameters (D) of 2–5 nm are regarded as the best34. This is because the percentage of atoms on the active Pt(111) facets over the total number of atoms n, denoting as R(111), reaches the maximum256. If the particle takes an (111)-enclosed icosahedral shape as shown in Figure 1, in order to maximize R(111), the corresponding D (Dc) is 2.6 nm with n = 561, which brings out R(111) = 20%. Further reducing D could increase the surface/volume ratio, and the percentages of edge and vertex sites (Re and Rv) on the particle surfaces unfortunately increase where Re becomes predominant below Dc. Those Pt atoms at the low-coordinated sites are adverse for ORR due to the strong binding of O-containing intermediates478910. Thus, activating edge and vertex sites is the main challenge to miniaturize D.

Figure 1

Size-dependent percentage of atoms on (111), edge and vertex, expressed by R(111), Re and Rv.

Rshell denotes the percentage of atoms on the shell, and Rshell = R(111) + Re + Rv. Atoms in yellow, blue and orange denote Ptv, Pte and Pt(111)atoms. Inset is the structure of Pt561 where Re = R(111).

As adsorption energies of all intermediates of ORR are related to the O adsorption energy [Eads(O)] on (111) surfaces of transition metals, the activity is proposed to be a function of Eads(O)2111213. It has demonstrated that Eads(O) of a catalyst with the best activity for ORR should be 0.0–0.4 eV weaker than that of Pt(111)2913. Furthermore, a volcano activity curve based on the adsorption energy of OH [Eads(OH)] is present where Eads(OH) is 0.0–0.2 eV weaker than that of Pt(111), due to the scaling relationship between Eads(O) and Eads(OH)261214. Note that the coordination numbers of the vertex atoms and the edge atoms of nanoparticles differ from that of (111) surface of nine. Thus, the scaling relationship between Eads(O) and Eads(OH) may be changed and Eads(O) and Eads(OH) must be both inquired separately.

On the other hand, numerous experimental and theoretical studies have been carried out to study the kinetics of ORR mechanisms215161718. To our knowledge, there are mainly three mechanisms: O2 dissociation, OOH dissociation and H2O2 dissociation. Qi et al. have demonstrated that in the gas phase, instead of the high barrier (Ea) of OH formation from O and H with a value of 0.91 eV, OH is originated from OOH and H with Ea = 0.31 eV1516. However, this path is absent because H2O2 formation is forbidden in solution17. Recently, a new path is proposed: OH formation in solution comes from O and H2O, and ORR on Pt(111) is essentially carried out by O2 dissociation mechanism, namely O2 dissociation (Ea = 0.00 eV), OH formation (Ea = 0.50 eV) and H2O formation (Ea = 0.24 eV)18. It is doubted that whether ORR mechanism is changed due to the presence of the low-coordinated atoms at nano size. Thus, in order to fully understand the catalysis, the kinetics of ORR mechanisms needs to be further explored.

Alloying is a general technique to improve the ORR activity and stability of catalysts1314192021. Present works have been mainly concentrated on Pt-based alloys consisting of Pt and the late TM elements in the 3d series, typically Pt3Fe, Pt3Co and Pt3Ni. The alloys show better catalysis activity than Pt alone22. However, the severe degradation of catalysis and stability of these alloys during the voltage cycling in acids as a consequence of the continuous dissolution of TM atoms are present2223. This can be understood by their negligible heat of formation1324. Following the suggestion of Greeley et al., strong binding between Pt and other alloying elements is needed to improve the stability of any new alloy systems13. Since the formation energy of Pt3Al is much more negative than Pt-based alloys with late TM elements24, Pt3Al should be a good substitute of the above Pt-based alloys. It must be admitted that Pt-based alloys with early TM elements show good activity and stability, such as Pt3Sc and Pt3Y1322. However, these works are still located at the transition metals and the activity enhancement is resulted from the d-d interaction to modify the d band of Pt surface atoms1322. Thus, from the electronic aspect, the p-d interaction of Al-Pt systems would provide an attempt to look beyond the Pt-TM systems and explore novel catalysts.

Recent DFT calculations show that a core-shell structure plays an important role in increasing the stability of Pt-based nanoalloys, such as Co13@Pt42 and Rh13@Pt422526 where Pt shell benefits for the stability of the catalysts under the electrochemical environment2123272829. Thus, we here develop a new core-shell Al13@Pt42 cluster as ORR catalyst, whose surface is assembled with the twelve vertex atoms Ptv and the thirty edge atoms Pte. In addition, Al13 cluster with icosahedral symmetry have been shown to exhibit enhanced stability compared with other isomers3031. What is more, the ligand stabilized Al nanoparticles with the size range of 1.5 and 4 nm have been synthesized3233. It is noteworthy that although Al@Pt core-shell nanoparticles have not been synthesized to date, Al@Cu and Al@Co ones are fabricated via a displacement reaction3435. Although these particles had large particle sizes about 5 μm, the utilized experimental technique could also be applied to fabricate Al@Pt core-shell nanostructures as long as the size of Al nanoparticles is small, which has been be synthesized without difficulties3233. Note that although Al could be easily oxidized it has been easily avoided by an inert atmosphere33. At last, it is emphasized that our work offers only a theoretical prediction and we hope this new Al@Pt cluster will be picked up by experimentalists for empirical verification.

In light of our calculation by using Density Functional Theory (DFT), Al@Pt cluster possesses good stability due to the covalent bonding between Al13 core and Pt42 shell. Also, Eads(O) is located at the optimal range while Eads(OH) on Pte is 0.30 eV weaker than Pt(111). Furthermore, rate-limiting step (RDS) of the ORR reaction though O2 dissociation mechanism is located at OH formation from O and H (Ea = 0.59 eV). This barrier is comparable with 0.50 eV of Pt(111)18. Thus, alloying with Al effectively activates Pte atoms and lets the utility of Pt reach 70% (30 edge Pte atoms from the total 42 Pt atoms).

Results

Figure 2(a) shows a core-shell Al13@Pt42 cluster (n = 55) with an icosahedral structure where 13 Al atoms form an icosahedral core and all Pt atoms are located on the shell. All Pt atoms are all low-coordinated, which consist of 6-coordination vertex atoms (Ptv) and 8-coordination edge atoms (Pte). The Al13@Pt42 possesses a high symmetry and stability (the mean binding energy Eb = −4.8 eV/atom compared with −4.75 eV/atom of Pt55 according to our calculation). To understand physically the interaction between Al core and Pt shell of Al13@Pt42, partial density of states (PDOS) is shown in Figure 2(c). Compared with Pt55, the d band of Pt42 shell on Al13@Pt42 is moved away from the Fermi energy EF. That is, the d band center changes from −1.99 of Pt55 to −2.54 eV of Al13@Pt42. Furthermore, the d band of alloy cluster is clearly more discrete. The d band of Pt42 shell is concentrated in between 0 to −6.8 eV. For Al13 core, the p band has the same trend with the d band of Pt42 shell, which denotes the strong orbital hybridization. It is obvious that the d orbitals (at −1.7, −2.6, −3.4, −4.5, −5.5 and −6.3 eV) interact with the p orbitals (at −1.8, 2.6, −3.4, −4.9 and −6.3 eV) and weak p-d hybridization is present at −8.1 eV below EF. On the other hand, the main of s band is located below −6.8 eV. Compared with p-d hybridization, the s-d interaction is weak, appearing at −5.1, −6.4, −7.4 and −8.1 eV below EF. Therefore, the enhancement in stability is dominated by hybridization between Pt-5d band and Al-3p band. To confirm this interaction, the electron density difference Δρ calculated is presented in Figure 2(d). Obviously, electrons are accumulated between Pt and Al atoms, which are compatible with the observation of the corresponding PDOS and demonstrates the partial formation of the covalent Pt-Al bonds.

Figure 2

(a) The structure of icosahedral Al13@Pt42 cluster. Atoms in yellow denotes vertex Ptv, edge Pte atoms are in blue. Purple shows Al atoms. (b) The adsorption sites of high-symmetry on a triangular face. T1 and T2 top sites are located atop of Ptv and Pte, respectively; H1 and H2 show hcp and fcc hollow sites respectively. The former is surrounded by Ptv and Pte while the latter is surrounded by only Pte. (c) The partial density of states (PDOS). Top left is PDOS of Al13@Pt42. For clarity, the intensity of d-electrons is reduced to the one tenth. Top right is d-electron PDOS of Pt42 shell on Pt55 and Al13@Pt42. Bottom left and right are s- and p-electron PDOS of Al13 core in Al55 and Al13@Pt42. (d) The plot of electron density difference Δρ.The loss and enrichment of electrons are indicated in blue and red. Here, Al55 denotes 55-atomic Al cluster with icosahedral shape.

In order to further confirm the stability of Al13@Pt42, we consider the stability of Fe13@Pt42, Co13@Pt42 and Ni13@Pt42 for a comparison purpose as the three alloying elements have been well studied363738. Table 1 lists the core-shell interaction energy Ecs, which could interpret enhanced phenomenon132639, and the dissolution potential Udiss(M13@Pt42) of the Pt42 shell in M13@Pt42 icosahedral clusters (M = Al, Fe, Co, Ni). It is found that due to the alloying, Udiss(M13@Pt42) of clusters are enhanced compared with that of Pt55. That is, the stronger Ecs makes the higher dissolution resistance, which is similar to the relationship between the alloy formation energy and the ORR stability of the Pt3M bulk1339. The corresponding order is Al13@Pt42 > Fe13@Pt42 > Co13@Pt42 > Ni13@Pt42 > Pt55. Thus, we expect that the stability of Al13@Pt42 acted as ORR catalysts is well.

Table 1

The calculated core-shell interaction energies Ecs and the Pt42 shell dissolution potentials Udiss(M13@Pt42). The units are eV/atom and V, respectively

	Pt55	Al13@Pt42	Fe13@Pt42	Co13@Pt42	Ni13@Pt42
Ecs	−0.52	−0.84	−0.75	−0.62	−0.53
Udiss(M13@Pt42)	0.816	1.101	1.087	0.995	0.933

Eads(O) and Eads(OH) on Al13@Pt42 are firstly examined. For comparison purpose, these values on Pt55 and Pt(111) are also calculated. According to previous studies, we focused on the adsorption of O on hollow sites and OH on atop sites as the adsorption sites shown in Figure 2(b)1340. The corresponding Eads(O) and Eads(OH) values are listed in Table 2. The most favored Eads(O) and Eads(OH) values on Pt(111) are −4.51 on fcc site and −2.45 eV on atop site [the reported results are Eads(O) = −4.21 eV and Eads(OH) = −2.31 eV, respectively, being in accord with our data4142]. For O adsorption on Pt55, Eads(O) are −4.56 and −4.71 eV on H1 and H2 sites, respectively, which are stronger than that of Pt(111). Similarly, compared with Pt(111), OH adsorption are stronger with Eads(OH) of −3.13 eV on T1 site and −2.91 eV on T2 site. Therefore, Pt55 are both O and OH poisoned due to the enhanced adsorption ability of the low-coordinated Pt atoms43. On the other hand, for Al13@Pt42, Eads(O) are −4.15 and −4.25 eV on H1 and H2 sites, respectively, which are 0.36 and 0.26 eV weaker than that of Pt(111). Therein, the Eads(O) values are located at the optimal range for ORR213. For OH adsorption on T1 site, Eads(OH) is −2.81 eV and is 0.36 eV stronger compared with Pt(111). However, as OH on T2 site, Eads(OH) is 0.30 eV weaker than that of Pt(111) with a value of −2.15 eV. The scaling relationship between O and OH is broken on Al13@Pt421112. Although there is serious OH-poisoning at T1 site, OH-poisoning at T2 site is absent. Thus, OH adsorption on T2 site can easily be removed, and the recovery of T2 site for the next ORR cycle could take place. In light of viewpoint of OH-poisoning, it is likely that the only edge atoms (Pte) of Al13@Pt42 are effective for ORR.

Table 2

The calculated adsorption energy values of Eads(O) and Eads(OH) on Pt55, Al13@Pt42, and Pt(111) (The adsorption sites are described in caption of Figure 2b).The values in parentheses show differences between Eads(O) and Eads(OH) values on Al13@Pt42 and that on Pt(111)

	Eads(O)		Eads(OH)
	H1	H2	T1	T2
Pt55	−4.56(−0.05)	−4.71(−0.20)	−3.13(−0.68)	−2.91(−0.46)
Al13@Pt42	−4.15(0.36)	−4.25(0.26)	−2.81(−0.36)	−2.15(0.30)
Pt(111)	−4.51		−2.45

The above results are supported by the relationship between electronic structures and atomic ones of Al13@Pt42. It is known that surface atoms with larger coordination number have a lower d band center and weaker adsorption ability43. For Al13@Pt42, the effective coordination number (Neff) is proposed to show the effect of the Al alloying44. We carried out a simple linear regression analysis to correlate Eads(O) and Eads(OH) adsorbed on T1 and T2 sites with Neff of Pt atom, Neff = NPt + XNAl, where subscripts show the corresponding elements, X is the effect coefficient of one Al atom corresponding one Pt atom for Neff, which is obtained by fitting technique. By using this technique, X = 2.5 is obtained. That is, Neff values of Ptv and Pte on Al13@Pt42 are 7.5 and 11. The average Neff value of Pt42 shell consisting of Ptv and Pte is 10, being larger than 7.4 of Pt55 and 9 of Pt(111). The above atomic structural analysis corresponds to the fact that the d band center moves towards the lower-energy range from −1.99 eV of Pt55 to −2.54 eV of Al13@Pt42, which effectively illustrates that the presence of Al reduces the adsorption ability of the low-coordinated Pt atoms, as shown in Figure 2(c). On the other hand, the Mulliken charge analysis displayed in Figure 3(a) show that the electrons are transferred from the Al13 core to Pt42 shell, leading to the formation of negatively charged shell. Therein, the Q(Ptv) and Q(Pte) are −0.185 and −0.380e, respectively (Q defines as the number of the transferred electrons). After O adsorption on H2 site, Q(O) and Q(Pte) are −0.585 and −0.181e, respectively, which means the presence of electrostatic repulsion. However, a completely different situation is found on Pt(111). In Figure 3(b), Pt(111) is nearly electrically neutral with Q(Pt) = −0.006e. After O adsorption on fcc site, Q(O) and Q(Pt) are −0.548 and 0.149e, respectively. That is, the electrostatic attraction appears for O adsorption on Pt(111). It is plausible that the weaker Eads(O) of Al13@Pt42 is just due to this electrostatic repulsion between the electronegative O adatom and the Pt atoms4546. In order to demonstrate the effect of the negative charges on Eads(O), we artificially add electrons Qadd on Pt(111) and then calculate the corresponding Eads(O)47. In Figure 3(c), for O adsorption on Pt(111), the Q(Pt) sign is changed from positive to negative and Q(O) is more negative when Qadd is increased. Namely, the interaction between O and Pt(111) is changed from electrostatic attraction to electrostatic repulsion. As shown in Figure 3(d), Eads(O) is weakened as Qadd is increased. Furthermore, from the d-PDOS of the Pt(111) with different Qadd values shown in Figure 3(e), there is little change of the d band. Thus, the electrostatic repulsion indeed reduces the Eads(O). Since OH adsorption has a similar case of O adsorption, we do not show the corresponding results here. In summary, both electronic and atomic structures of Al13@Pt42 support its high poisoning resistance for ORR.

Figure 3

The Mulliken charges Q of Al13@Pt42 (a) and Pt (111) (b). (c) The Mulliken charges Q on Pt(111) with different Qadd. (d) The Eads(O) on Pt(111) with different Qadd. (e) The plot of d-electron PDOS of Pt(111) with different Qadd. For comparison, d-electron PDOS of Pt(111) without Qadd is shown in shaded. A negative value means electronic gain and a positive value means electronic loss.

In order to characterize ORR catalyzed on the Al13@Pt42, the distinct reaction paths are considered to determine transition states and activation energies or energy barrier (Ea) using nudged elastic band theory (NEB) for all elemental reaction steps involved in ORR in Figure S1 and the corresponding data are listed in Table 3. Firstly, the O2 dissociation mechanism, including O2 dissociation, OH formation, and H2O formation, is considered. The results are shown in Figure 4 and Table 3. For O2 dissociation, the Ea = 0.13 eV. Figure S2 illustrates the spin-polarized partial density of states (PDOS) projected onto the O-O bond where big change in PDOS is present. There is no spin polarization of the adsorbed O2 orbitals, and the 5σ, 1π and 2π* orbitals of O2 are broadened, which dominate the adsorption of O2. It is clear that the partial antibonding orbital 2π* of adsorbed O2 are filled compared with that in the gas phase. It is well known that partial population of the antibonding 2π* orbital of O2 is responsible for the catalytic activation of the adsorbed O2 and stretching of the O-O bond48. When O2 is adsorbed on Al13@Pt42 with Eads(O2) = −0.33 eV, the corresponding O-O bond is 1.398 Å (the O-O bond of the gas state is 1.225 Å), due to this charge transfer to the 2π* orbital of O2 (0.306 e). As results, the O2 on Al13@Pt42 is activated and then dissociated with such a small Ea value.

Table 3

The preferred activation energies (Ea) and reaction energies (Er) for elemental steps in ORR. All results are in unit of eV

	Al13@Pt42		Pt(111)
Reaction steps	Ea	Er	Ea	Er
O2 → 2O	0.13	−1.66	0.00	−2.18
O + H → OH	0.59	−0.59	0.97	−0.07
OH + H → H2O	0.31	−1.11	0.24	−0.56
H2O → H2O(gas)		0.41		0.58
O2 + H → OOH	0.81	−0.37	0.22	−0.19
OOH → O + OH	0.28	−0.91	0.00	−2.07
O + H2O → 2OH	0.57	0.57	0.50	0.49
O(H1) → O(H2)	0.44		0.62–0.66

aThe O diffusion energy barrier on Pt(111) are from references [15,16], the H2O desorption barrier is from reference [50]while other data on Pt(111) come from reference [18]

Figure 4

Optimized overall reaction path of O2 dissociation mechanism.

(a) The structures of initial, transition and final states, respectively. (b) Schematic energy profile.

In light of Table 3, Ea = 0.59 eV for OH formation from O and H, which is forbidden on Pt(111) because of the high Ea of 0.97 eV18. It has been demonstrated that the large component of this Ea comes from O diffusion from hollow site to a bridge site, which is consistent with our results15. On Al13@Pt42, O is easier to diffuse with 0.44 eV diffusion barrier due to the lower Eads(O) value compared with that of 0.62 or 0.66 eV on Pt(111)1516. That is the reason why Ea value of Al13@Pt42 is smaller than that of Pt(111) for OH formation from O and H. Thus, the path for OH formation becomes feasible on Al13@Pt42. For H2O formation, Ea = 0.31 eV, which is comparable with Pt(111)18. Similar with Pt(111), the disappearance of the OH diffusion makes Ea for H2O formation lower than that for OH formation16. The last step is removal of the adsorbed H2O and recovery the surface active site. Once H2O is formed, it needs to overcome 0.41 eV for desorption.

Discussion

Therein, as shown in Figure 4, the rate-limiting step (RDS) of O2 dissociation mechanism is located at OH formation from O and H with Ea = 0.59 eV. On the other hand, for OOH associative mechanism, RDS is located at OOH formation with Ea = 0.81 eV and Er = −0.37 eV. Since Ea value of RDS of O2 dissociation mechanism is lower than that of OOH associative mechanism, the former is more effective. In addition, we have excluded the two-electron reduction to H2O2 since H2O2 spontaneous dissociates into OH on Al13@Pt42, which is consistent with experimental results on Pt and other Pt alloys49. When we observe the corresponding data of Pt(111) in Table 3, RDS is located at OH formation from O and H2O with Ea = 0.50 eV1850. Ea value for OH formation on Al13@Pt42 is comparable with that on Pt(111). It is well known that when Ea < 0.75 eV, there is room temperature activity51. As results, Al13@Pt42 can effectively catalyze ORR at room temperature.

In summary, the core-shell Al13@Pt42 cluster is a good ORR candidate for the fuel cell application and possesses at least four superiorities listed below: (1) Excellent cluster stability due to the formation of the Al-Pt covalent bonds; (2) A better activity than Pt(111) due to the optimal O adsorption energy; (3) The maximal Pt atomic utilization of 70% due to the utility of the anti-poisoning edge Pt atoms with consideration of OH adsorption; (4) OH formation with Ea = 0.59 eV (being comparable with Pt(111) of 0.50 eV) as the RDS with O2 dissociation mechanism.

Methods

Most calculations are performed within the DFT framework as implemented in DMol3 code5253. The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional is employed to describe exchange and correlation effects54. The All Electron Relativistic (AER) core treat method is implemented for relativistic effects, which explicitly includes all electrons and introduces some relativistic effects into the core55. In this work, the double numerical atomic orbital augmented by a polarization p-function (DNP) is chosen as the basis set52. The orbital cutoff values are 4.5 Å and 4.8 Å for Pt55/Pt(111) and Al13@Pt42, respectively, which lead to the difference of the atomic energies is within 0.1 eV atom−1, compared with the cutoff value of 6.5 Å. Thus, the value satisfies the accuracy required. A smearing of 0.005 Ha (1 Ha = 27.21 eV) to the orbital occupation is applied to achieve accurate electronic convergence. The spin-unrestricted method is used for all calculations. The convergence tolerance of energy is 1.0 × 10−5 Ha, maximum force is 0.002 Ha/Å, and maximum displacement is 0.005 Å in Dmol3. Note that the DNP basis set is the most accurate for our studied systems in Dmol3 code when Pt element is included in any considered system and is comparable to the Gaussian 6–31(d) basis56 while DNP results have shown excellent consistency with experiments in literatures57.

It is known that the cell size effect for the calculations of 38 atomic clusters is negligible when the size is large than 25 Å58. In our case, we consider the calculations of 55 atomic clusters. Thus, we have tested cubic boxes with sizes of 25 Å and 30 Å. The results are shown in Table S1. It is found from Table S1 that the results with sizes of 25 Å and 30 Å are consistent each other within energy difference smaller than 0.001 Ha. Thus, the box size of 25 × 25 × 25 Å3 is chosen for our system.

A three-layer p(3 × 3) periodic slab is taken to simulate Pt(111) surface where the two bottom layers are fixed. To confirm the reliability of this Pt(111) model, the Eads(O) and Eads(OH) values on a four-layer slab with two fixed layers and a five-layer slab with three fixed layers are calculated and listed in Table S2. It is shown that compared with the three-layer slab, the Eads(O) and Eads(OH) values on the two cases have errors of 0.03, which do not change all results what we have obtained. Therefore, our Pt(111) model has reasonable accuracy. The k-points are Gamma point for clusters and (2 × 2 × 1) for Pt(111), respectively. The minimum energy paths (MEPs) for ORR are obtained by LST/QST tools in DMol3 code.

A conductor-like screening model (COSMO) is used to simulate a H2O solvent environment throughout the whole process in DMol3 code59 where the dielectric constant is set as 78.54 for H2O solvent. It is noteworthy that this environment is necessary to describe the solvation50. To confirm this consideration, the adsorption energy values of O2, O, H2O and OH in gas and solvent environments are calculated and shown in Table S3. As shown in the table, there are evident differences in the both cases. For O2, O and H2O adsorption under solvent environment, Eads are stronger while Eads(OH) is weaker, compared with gas environment.

It is well known that there is the convergence failure of magnetic systems in DMol3 code. To compare the stability among the different M13@Pt42 clusters, the core-shell interaction energy Ecs and the dissolution potentials of Pt42 shell Udiss(M13@Pt42) are calculated in CASTEP code with ultrasoft pseudopotentials60. The PBE is employed to describe exchange and correlation effects54. The use of a plane-wave kinetic energy cutoff of 400 eV is shown to give excellent convergence of total energies. The convergence tolerance of energy is 1.0 × 10−5 eV/atom, maximum force is 0.05 eV/Å, and maximum displacement is 0.005 Å in CASTEP. The 0.2 eV smearing is adopted for calculations.

To analyze the structural stability of alloy clusters with different numbers of Al atoms, the average binding energy of the cluster Eb is adopted, where Ecluster, EPt and EAl are the total energies of Pt55 or Al13@Pt42 clusters, Pt atom, and Al atom, respectively. NPt and NAl denote the numbers of Pt and Al atoms.

The core-shell interaction energy Ecs is calculated as following, where E(M13@Pt42), E(Pt42) and E(M13) are the total energies of M13@Pt42 clusters, Pt42 shell and M13 core, respectively.

Following the idea of Noh et al.26, we define the dissolution potential of M13@Pt42 cluster as the lowest potential at which the Pt-skin layer dissolves into acidic solution. Specifically, we considered the electrochemical reaction of M13@Pt42 cluster of eq. (3), where nshell is the number of Pt atoms in the M13@Pt42 (nshell = 42). The dissolution potential of the Pt42 shell is calculated by, where Udiss(M13@Pt42) and Udiss(Ptbulk) are the dissolution potentials of the outmost shell of M13@Pt42 clusters and that of a bulk Pt, respectively. E(Ptbulk) denotes the total energy of bulk Pt. Here, Udiss(Ptbulk) = 1.188 V.

The adsorption energies (Eads) of adsorbates on these clusters are calculated through, where Especies, Ecatalyst and Esys are the total energy of an isolated adsorbate species, the catalyst [Pt(111), Pt55 and Al13@Pt42] and the adsorption system, respectively. Eads < 0 corresponds to an exothermic adsorption process.