Tuning metal cluster catalytic activity with morphology and composition: a DFT study of O₂ dissociation at the global minimum of Pt_mPd_n (m + n = 5) clusters

Abstract

The Pt-based alloyed clusters are the important catalysts in the chemical industry. The global minimum structures of Pt_mPd_n (m + n = 5) clusters were searched for based on the CALYPSO algorithm, and the various properties of the lowest-energy Pt_mPd_n clusters have been studied. The results show that introducing the Pd element can modify the morphology and composition of the pure Pt₅ cluster, i.e., from a 2D planar to a 3D trigonal bipyramid structure, except for the Pt₄Pd₁ (square pyramid). According to the average cohesive energy, the Pt₄Pd₁ cluster possesses the highest stability among these Pt–Pd alloyed clusters. The O₂ molecule prefers to anchor on the clusters by the Yeager mode. The catalytic property for O₂ dissociation of the pure Pt₅ cluster can be further improved by introducing the Pd atoms. Moreover, the Pt₄Pd₁ cluster with the high Pt composition and the structure of square pyramid shows the highest catalytic activity. More importantly, the Brønsted–Evans–Polanyi relationship is found to be applicable to the current mini alloyed metal clusters. This study will help to understand the prediction of the global minimum structure of metal cluster by CALYPSO and shed light on the design of the less expensive and more effective alloyed cluster catalysts by controlling the morphology and composition in the fuel cells.

---

1. Introduction

Alloyed clusters,¹ as novel and important nano materials, are of great importance to the development of nanoscience for plasmonics, optics, catalysis, biochemistry and new energy resources.^2–4 They exhibit amazing physical and chemical properties that are significantly different from those of single metal clusters. For instance, Miyamura et al. have experimentally suggested that the Au–Pt alloyed cluster presents much higher activity and selectivity than the single metal Au or Pt cluster for aerobic oxidation of alcohols.⁵ Moreover, Geng et al. have shown that the metal clusters can be remarkably stabilized by alloying with another metal element.^6,7 Thus, alloying has been one of the most important way to improve various practical performances of metal clusters under ambient conditions.

Platinum clusters are always being investigated due to their applications in catalysis.^8,9 Given the easy poisoning and high cost of pure platinum,¹⁰ the Pt-based alloyed clusters have been widely suggested to replace the pure Pt clusters owing to the surprisingly improved activity and the reduction cost.^11–16 Recently, Wang and Johnson have investigated 132 Pt-based alloyed clusters using the GGA level of theory and found that having Au, Ag, Cu, and Pd as an impurity and Pt as the majority is thermodynamically and kinetically preferred in 55-atom binary alloyed clusters.¹⁷ Interestingly, Pd catalysts possess similar activity compared with Pt for O₂ dissociation¹⁸ and the Pt–Pd alloyed catalysts are reported to have the tolerance to methanol and surprisingly enhanced activity for ORR.^19–21 In addition, the charge transfer from a Pd to a Pt atom has been found in the Pt–Pd core–shell type alloyed clusters by means of UB3LYP/LANL2DZ,²² which plays a vital role in modifying the electronic state of the cluster surface and tuning the catalytic activity. Thus, the Pt–Pd alloyed clusters are the promising alternatives to exceed the scarce and expensive pure Pt clusters. However, it is essential to make clear the value of the mechanism for the composition and morphology. The lowest-energy Pt₅ cluster with the planar edge capped-square structure²³ has a relatively high energy barrier toward O₂ dissociation and few studies have focused on it. Thus, we hope the Pd atoms could be used as an alloying agent in Pt₅ cluster to markedly “turn on” the catalytic activity of Pt₅ by adjusting the morphology and chemical composition. The dissociation of O₂ on the catalyst of metal surfaces or clusters is a crucial reaction step in many chemical processes, from oxidation of CO, to more complex oxygen reduction reactions.^24–27 Thus, the dissociative adsorption of O₂, as a general mechanism for the activation of molecular oxygen by catalysts, will help to understand the catalytic performance of Pt_mPd_n (m + n = 5) clusters for the aerobic reaction in the fuel cells.

For the theoretical study, the prediction for the global minimum of cluster is a challenging task because it has to locate the global minimum of the potential energy surfaces, on which the number of local minimum increases exponentially with increasing cluster sizes.²⁸ Accordingly, we performed extensive searches on the global minimum of Pt_mPd_n (m + n = 5) clusters by applying the recently developed crystal structure analysis by particle swarm optimization (CALYPSO) algorithm with DFT calculations,^29–31 which only requires the known information of chemical compositions (the number of every element).³² The key element of the proposed method is the local PSO algorithm which enables a simultaneous search in different energy funnels of a potential energy surface. Indeed, the method can efficiently search the potential energy surface of a nonperiodic system and it enables the proposed global stable structures for the difficult systems (e.g., medium-sized Li₂₀, Li₄₀ and Li₅₈ clusters) to either match or improve the results of previous studies.²⁹ The current study here will help to understand the prediction of the global minimum structures of the metal clusters by CALYPSO and shed light on the design of the less expensive and more efficient alloyed cluster by controlling the morphology and composition of Pt_mPd_n (m + n = 5) clusters. More importantly, the Brønsted–Evans–Polanyi (BEP) relationship,^33–35 which provides a good framework for a systematic analysis of the catalytic activity for the small Pt_mPd_n (m + n = 5) clusters, is found to be applicable to the current mini alloying metal cluster.

2. Methods

The low-lying structures of Pt_mPd_n (m + n = 5) clusters are searched using CALYPSO cluster prediction^29–31 based on the particle swarm optimization (PSO) algorithm implemented in the CALYPSO code.^29–31,36 In order to provide good sampling structure sets for the local PSO evolution, point group symmetries are introduced into the generation of cluster structures. And the bond characterization matrix (BCM) technique allows a quantitative measure on the structural similarity and can be used to define desirable local search spaces. Moreover, the application of Metropolis criterion further improves the structural evolution towards low energy regimes of potential energy surfaces. The CALYPSO code has been well tested to predict the geometric structures of 0D clusters.^29,37 And the Pt₅ clusters has been also searched to perform the benchmark. The results show that the lowest-energy structure is planar edge capped-square, the second lowest-energy structure is found to be form trigonal bipyramid, and the higher-energy structure is W shaped plane, which are in excellent agreement with previous reports.²³

The further structural relaxations and spin polarization calculations are performed within dispersion-corrected density functional theory DFT (DFT-D) computations as implemented in DMol³ code³⁸ embedded in Materials Studio (Accelrys, SanDiego, CA), using a DFT semi-core pseudopotential (DSPPs)³⁹ with GGA-PBE functional⁴⁰ with long-range dispersion correction via Tkatchenko and Scheffler's scheme.⁴¹ During geometrical optimization, the basis set cut-off was chosen to be 4.5 Å. The convergence tolerances for the geometry optimization were set to 10⁻⁵ Ha (1 Ha = 27.21 eV) for the energy, 0.002 Ha Å⁻¹ for the force, and 0.005 Å for the displacement. The electronic SCF tolerance was set to 10⁻⁷ Ha. In order to achieve accurate electronic convergence, we apply a smearing of 0.005 Ha to the orbital occupation. The Pt_mPd_n clusters are placed in a cubic supercell 15 × 20 × 15 ų, which leads to negligible interactions between the system and their mirror images. The k-points are generated automatically using the Monkhorst–Pack method⁴² and only the Γ point are used for the structure relaxation. Frequency calculations reveal that the low-energy isomers are true minima by showing no imaginary frequencies. The complete linear synchronous transit (LST)/quadratic synchronous transit (QST) calculations⁴³ were performed to locate transition states (TS) in DMol³ code. It is found that the transition states have only one imaginary frequency. The accuracy of the present DFT methodology was assessed by benchmark calculations for Pd₂ and Pt₂ dimers. Upon spin polarization DFT-D calculation, the calculated bond (Pd–Pd) length (BL) of Pd dimer is 2.55 Å, which is in excellent agreement with theoretical value of 2.53 Å.²⁰ Similarly, the calculated Pt–Pt BL of 2.40 Å is in excellent agreement with 2.39 Å (ref. 20) and 2.33 Å (ref. 23) in theory, and the average cohesive energy of Pt dimer we calculated is 1.53 eV, which is also in excellent agreement with 1.57 eV in experiment.⁴⁴ In short, our PBE/DNP scheme is able to describe the structural information of the current Pt and Pd systems in a satisfactory manner.

The adsorption energy (E_ads) of an O₂ molecule is defined as:

E_ads = E(O₂) + E(Pt_mPd_n) − E(O₂/Pt_mPd_n) (1)

where E(O₂), E(Pt_mPd_n) and E(O₂/Pt_mPd_n) are the total energy of the free O₂ molecule, the corresponding support and the support with the adsorbate, respectively. All three types of energy were calculated using the same periodic box dimensions and the same calculated setting. With this definition, a positive value indicates an exothermic adsorption.

The activation barrier (E_a) and reaction energy (E_r) of O₂ dissociation on the clusters are defined as:

E_a = E(TS) − E(IS) (2)

E_r = E(IS) − E(FS) (3)

where E(IS), E(TS) and E(FS) are the total energy of initial state (IS), transition state (TS) and final state (FS) during the O₂ dissociation, respectively. Similarly, a positive value indicates an exothermic dissociation.

3. Result and discussion

3.1 The catalytic performance of global minimum for the pure Pt₅ clusters

Before studying the catalytic performance of global minimum for the pure Pt₅ cluster, its low-lying structures, has been predicted by CALYPSO and full relaxed by DMol³. The results are shown in Fig. 1a and the lowest-energy structure is planar edge capped-square, the second lowest-energy structure is found to be the trigonal bipyramid, and the higher-energy structure is W shaped plane, which are in excellent agreement with the previous reports.²³ In order to study the catalytic performance toward O₂ dissociation, the adsorption of O₂ molecule on the global minimum for the pure Pt₅ cluster has been explored with various initial structures to obtain the most stable adsorption configuration. Fig. 1b displays the most stable O₂ adsorption configuration and the charge difference density (CDD) between O₂ and Pt₅ cluster. The O–O BL of adsorbed O₂ is 1.377 Å and the calculated adsorption energy is 2.15 eV, which is larger than that of O₂ adsorbed on Pt₅ cluster with trigonal bipyramid (0.53 eV).^45,46 The Mulliken charge analysis shows that the adsorbed O₂ gets 0.35 electrons from the Pt₅ cluster, which is confirmed by charge accumulation regions in red of CDD. This results in the elongation of the O–O bond from the initial length of 1.225 Å in free O₂. Thus, the adsorbed O₂ is activated.

Fig. 1 (a) The low-lying configurations and corresponding geometric parameters of Pt₅ clusters. The relative energies (eV) are given in the red color. (b) The most stable O₂ adsorption with its charge difference density (the charge accumulation regions are rendered in red while the charge deplete regions are shown in blue) and (c) O₂ dissociation on the global minimum of pure Pt₅ cluster. Hereafter, the gray and red spheres represent Pt and O atoms, respectively. And the bond distances are in angstroms.

Fig. 1c displays the O₂ dissociation on the global minimum of pure Pt₅ cluster with the geometric structures of IS, TS and FS. It is found that the structural distortion of the pure Pt₅ cluster induced by O₂ dissociation is insignificant. The corresponding activation barrier and reaction energy are 0.66 eV and 0.85 eV, respectively. This activation barrier is larger than that on Pt₅ cluster with trigonal bipyramid (0.19 eV).⁴⁶ Thus, we hope the Pd atoms can be used as an alloying agent in Pt₅ cluster to markedly “turn on” the catalytic activity of Pt₅ for O₂ dissociation.

3.2 The global minimum structures for the Pt_mPd_n (m + n = 5) clusters

As mentioned above, the pure Pt₅ cluster may be not an ideal catalyst for O₂ dissociation. The Pd atoms are introduced to adjust the morphology, chemical composition and reactivity of Pt₅ cluster. In this section, we will mainly present the results of CALYPSO cluster prediction with some typical low-lying isomers for each composition of Pt_mPd_n (m + n = 5) clusters, as shown in Fig. 2 (hereafter, the result of Pt₅ cluster is also displayed to make the comparison). The global minimum of Pd_mPt_n (m + n = 5) clusters are shown in the top of Fig. 2. It is found that all these clusters have the highly symmetric structures. Note that by gas-phase methods, where clusters are produced in thermally excited conditions, the mixture of products is governed by the thermodynamics.⁴⁷ For cluster, in most cases, only one isomer—the global minimum—is formed as the product, which has been confirmed in experiment and theory studies for a series systems.^48–50 Thus, as the previous study,⁵¹ the global minimum of Pt–Pd clusters will be focused on in the following.

Fig. 2 The low-lying configurations and corresponding geometric parameters of Pt_mPd_n (m + n = 5) clusters. The relative energies (eV) are given in the red color and the global minimum of the clusters are shown in the top. Hereafter, the bice sphere represents Pd atom. And the bond distances are in angstroms.

From the geometric configuration, the global minimum of Pt₄Pd₁ possesses the 3D structure of square pyramid, where only Pd atom occupies the top site to support the cluster and the other four Pt atoms act as the substrate to form a square with the Pt–Pt bonds of 2.58 Å. Following by the increasing number of the Pd atoms, all the clusters (n = 2, 3, 4, 5) adopt the 3D structure of trigonal bipyramid and the lengths of Pt–Pt, Pt–Pd and Pd–Pd bonds in these four trigonal bipyramid are within 2.58 Å, 2.68–2.81 Å and 2.63–2.71 Å, respectively. Here, the global minimum of Pd₅ with trigonal bipyramid structure is in excellent agreement with previous report.⁵² These results indicate that the morphology and composition of Pt₅ cluster can be modified by the Pd element (from 2D planar to 3D structure) and the morphology is strongly correlated with the Pd composition (the clusters with high Pd composition possess the same configuration with the pure Pd₅ cluster).

Next we will further study the information from the geometric parameters of the global minimum of Pt_mPd_n (m + n = 5) clusters, whose corresponding average bond lengths (R_a, Å), average cohesive energies (E_C, eV), and mixing energies (E_M, eV) are shown in Table 1. It can be seen that the R_a of Pt_mPd_n (m + n = 5) clusters gradually becomes larger with Pd rich, which can be easily explained from that the atomic or ionic radius of Pd are slightly larger than that of Pt. Moreover, the calculated total magnetic moments (M, μ_B) have been shown in Table 1. Both the magnetic moments for global minimum of Pt₅ and Pd₅ clusters are 2.00 μ_B, which are in agreement with the previous works.^52–56 The magnetic moments of the alloyed Pt–Pd clusters are different from that of the pure clusters and the magnetic moments of Pt₄Pd₁ (3.14 μ_B), Pt₃Pd₂ (3.21 μ_B) and Pt₂Pd₃ (3.48 μ_B) clusters are much larger than that of pure clusters.

Table 1 The average bond lengths (R_a, Å), the average cohesive energies (E_C, eV), the total magnetic moments (M, μ_B) and the mixing energies (E_M, eV) for the global minimum of Pt_mPd_n (m + n = 5) clusters

	Pt5	Pt4Pd1	Pt3Pd2	Pt2Pd3	Pt1Pd4	Pd5
Ra (Å)	2.530	2.645	2.667	2.690	2.692	2.693
M (μB)	2.00	3.14	3.21	3.48	1.32	2.00
EC (eV)	2.66	2.44	2.26	2.07	1.87	1.66
EM (eV)	0	0.07	0.12	0.13	0.07	0

---

For the analysis of the cluster energetics, we have evaluated two different quantities: the average cohesive energy⁵⁷ and the mixing energy⁵⁸ for the various clusters. Thus, the cohesive energy is calculated as:

E_C(m, n) = [mE(Pt) + nE(Pd) − E(Pt_mPd_n)]/5 (4)

where m is the number of Pt atoms and n is the number of Pd atoms. E(Pt) and E(Pd) are the single atom energies of the Pt and Pd atoms, respectively. E(Pt_mPd_n) is the total energy of the global minimum for Pt_mPd_n clusters. From Table 1, it can be seen that the E_C decrease monotonically with the increasing composition of the Pd atom, resulting from the contribution of the 4d orbitals character of the Pd atoms. It is noticeable that the E_C of Pt₄Pd₁ cluster is the largest (2.44 eV) among the alloyed Pt–Pd clusters, indicating that the alloyed Pt–Pd clusters with the higher Pt composition possess the preferable stability.

In order to give a simple indicator for studying the clusters in experiment, the mixing energy is taken into consideration. It is defined as the following:

E_M(m, n) = mE(Pt₅)/5 + nE(Pd₅)/5 − E(Pt_mPd_n) (5)

where m is the number of Pt atoms and n is the number of Pt atoms, as defined above. E(Pt₅) and E(Pd₅) are the global minimum energies of pure Pt₅ and Pd₅ clusters, respectively. E(Pt_mPd_n) is the total energy of the global minimum for Pt_mPd_n clusters. In addition, 5 = m + n, it is the total number of atoms in the current clusters. The mixing energy provides a measure of how thermodynamically favorable is alloying at the given size and composition. With this definition, a positive value indicates an exothermic process when mixing Pt_m clusters and Pd_n clusters (m + n = 5) to produce the Pt_mPd_n alloyed clusters. It should be noted that the lowest mixing energy at some composition can be negative, suggesting that two species tend to dealloy or demix spontaneously. In the current study, it is found that the E_M of Pt₄Pd₁, Pt₃Pd₂, Pt₂Pd₃, and Pt₁Pd₄ alloyed clusters are all positive (Table 1), indicating an excellent miscibility between Pt and Pd atoms in the current clusters, which has been confirmed by the fact that the two metals form bulk alloys.⁵⁹

Summarily, the Pd element can modify the morphology and composition of the pure Pt₅ cluster and the geometric configuration are all trigonal bipyramid for the lowest-energy alloyed clusters, except for Pt₄Pd₁, which has the square pyramid configuration. From the cohesive energy, the stability of the Pt_mPd_n clusters are decreased with Pd rich, while the Pt₄Pd₁ is the most stable cluster among the Pt–Pd clusters. Moreover, the calculated E_M shows that the Pt and Pd atoms have a tendency to form the alloy in the small clusters.

3.3 The adsorption of O₂ on the global minimum of Pt_mPd_n (m + n = 5) clusters

Because the initial adsorption manner of a molecule on the catalyst greatly affects the subsequent reaction process and the adsorption of O₂ is a prerequisite for the dissociation of O₂ species on the catalyst, the adsorption of O₂ on these global minimum of Pt_mPd_n (m + n = 5) clusters are studied extensively. Also, the influence of the O₂ adsorption on the clusters is investigated when introducing Pd atom. Various possible adsorption configurations have been tested to obtain the most stable ones, as shown in Fig. 3. And the corresponding bond lengths of O–O (d_O–O, Å), adsorption energies (E_ads, eV) and Mulliken charge transfer (ΔQ, e) are summarized in Table 2. It is clear that the O₂ has the longest O–O bond when anchored on the Pt₄Pd₁ cluster.

Fig. 3 The most stable adsorption configurations of O₂ on the global minimum of Pt_mPd_n (m + n = 5) clusters and the corresponding charge difference density.

Table 2 The bond lengths of O–O (d_O–O, Å), the adsorption energies (E_ads, eV) of O₂ on the global minimum of Pt_mPd_n (m + n = 5) clusters, and the amount of charge transfer from Pt_mPd_n cluster to O₂ (ΔQ, e) according to the Mulliken charge analysis

	Pt5	Pt4Pd1	Pt3Pd2	Pt2Pd3	Pt1Pd4	Pd5
dO–O (Å)	1.377	1.401	1.398	1.375	1.366	1.347
Eads (eV)	2.15	2.26	2.01	1.89	1.80	1.65
ΔQ (e)	0.37	0.43	0.43	0.43	0.42	0.39

---

It is found that the O₂ molecule prefers to anchor on every cluster by the Yeager mode,⁶⁰ which illustrates that both two oxygen atoms bond with two different metal atoms respectively, forming an O–O bridge. Moreover, it is also noteworthy that the Yeager mode is the most activated type of O₂ bonding mode on the various Pt₆ clusters.⁶¹ In regard to the anchor site of the O atoms in the O₂ molecule, two Pt atoms, one Pd and one Pt atom, and two Pd atoms act as the anchor sites in the pure Pt₅ cluster, Pt₄Pd₁ and Pt₃Pd₂ cluster, Pt₂Pd₃ and Pt₁Pd₄ cluster, respectively. From this tendency of changed anchor sites, it can be found that the O atoms in the O₂ molecule are more preferable to anchor on the Pt site than the Pd site and the Pt atoms may serve as the mainly catalytic active center. The change of local electronic properties by introducing Pd atoms (the Pt serving as the electron accepter while the Pd act as the electron donor by the Mulliken charge analysis) may be respond to the conclusion above. Compared with the O₂ adsorption (2.15 eV) on the pure Pt₅ cluster, the E_ads of O₂ is decreased to 2.01 eV, 1.89 eV, 1.80 eV and 1.65 eV with Pd rich, except for that on Pt₄Pd₁ cluster (2.26 eV). This also suggests that O₂ prefers to anchor on the Pt site. Furthermore, all the O–O bonds of adsorbed O₂ are elongated compared with that of free O₂ molecule (1.225 Å) because the charge transfer from the Pt_mPd_n cluster to O₂ can weaken the O–O bond of the adsorbed O₂ molecule⁶² and facilitate the dissociation of the O₂. The charge transfer can be understood not only by the charge depletion/accumulation region (blue/red) in CDD but also by the Mulliken charge analysis, which shows that the adsorbed O₂ molecules get 0.39–0.47 electrons from the Pt_mPd_n clusters. And the magnetic moment of the whole system is fully quenched by the charge transfer after O₂ adsorption. From the ΔQ values, it is clear that more charge transfer from Pt–Pd cluster to O₂ than that from pure Pt₅ cluster, indicating the O₂ may prefer to be activated due to the modulation of the Pd atoms.

3.4 The stepwise dissociation of O₂ on the global minimum of Pt_mPd_n (m + n = 5) clusters

As mentioned above, the adsorbed O₂ molecules are believed to be activated because of the charge redistribution between the metal clusters and O₂ molecules. In the following, the dissociation steps of O₂ species on the various clusters are investigated carefully to evaluate the potential catalytic activity of small Pt_mPd_n clusters, which would help to understand whether the Pd atoms “turn on” the catalytic activity of Pt₅ or not. The geometric structures of IS, TS and FS for O₂ dissociation on the global minimum of Pt_mPd_n are shown in Fig. 4 and the corresponding activation barriers, the reaction energies, and the d-band centers of the pure Pt_mPd_n clusters are summarized in Table 3.

Fig. 4 The geometric structures of IS, TS and FS in the stepwise dissociation of O₂ on the global minimum of Pt_mPd_n (m + n = 5) clusters. The inserted numbers in the figures are the relative energies (eV).

Table 3 The activation barriers (E_a, eV), the reaction energies (E_r, eV) for the dissociation of O₂ species on the various Pt_mPd_n clusters, and the d-band centers (E_d-band, eV)

	Pt5	Pt4Pd1	Pt3Pd2	Pt2Pd3	Pt1Pd4	Pd5
Ea (eV)	0.66	0.23	0.42	0.50	0.60	1.60
Er (eV)	0.85	0.48	0.68	1.22	1.00	0.50
Ed-band (eV)	−2.19	−2.14	−1.90	−1.93	−1.71	−1.63

---

From the process of the O₂ dissociation in Fig. 4, the Pt atoms are found to be surrounded by the O₂ dissociation, further suggesting that the Pt atoms serve as the catalytic center. Formally, the Pd atoms are “spectators” for O₂ dissociation, whereas they act as the “modulator” for the charge transfer and stabilize the Pt atoms. It is found that there is a significant decrease of activation barriers for the O₂ dissociation on the Pt₄Pd₁ cluster (0.23 eV), compared with that on the Pt₅ cluster. Particularly, the O₂ dissociation on the Pt₄Pd₁ cluster via a two-step reaction with the E_a of 0.23 eV and 0.17 eV, respectively, where the first step (E_a, 0.23 eV; E_r, 0.48 eV) is the rate-limiting step. Following by the Pd rich, the activation barriers show gradual increase, which is 0.42 eV for the Pt₃Pd₂ cluster, 0.50 eV for the Pt₂Pd₃ cluster, 0.60 eV for the Pt₁Pd₄ cluster, and 1.60 eV for the Pd₅ cluster. From the calculated E_a of O₂ dissociation in the alloyed Pt–Pd clusters in Fig. 5, there is a positive correlation between the number of Pd atoms (n = 1, 2, 3, 4) and the E_a of O₂ dissociation. And the E_a has the order Pt₄Pd₁ < Pt₃Pd₂ < Pt₂Pd₃ < Pt₁Pd₄, i.e., the catalytic activity of the Pt–Pd clusters increases in the order Pt₁Pd₄ < Pt₂Pd₃ < Pt₃Pd₂ < Pt₄Pd₁, indicating the Pt–Pd clusters with lower Pd composition (higher Pt composition) show the higher catalytic activity. It is clear that the catalytic property of the small Pt₅ cluster can be further improved by introducing Pd element, whereas the Pd composition of the cluster should be appropriate, not too much. The present result indicates the key role of the composition in enhancing the catalytic activity of cluster. Furthermore, the morphology from the geometric structure is also correlated with the catalytic activity of the cluster, as reported by the theoretical⁶¹ and experimental^63,64 work. Indeed, the current study shows that Pt₄Pd₁ cluster with square pyramid has the higher catalytic activity toward the O₂ dissociation than the Pt₁Pd₄, Pt₂Pd₃ and Pt₃Pd₂ clusters with trigonal bipyramid.

Fig. 5 Variation of the E_a for O₂ dissociation on the Pt_mPd_n clusters (m + n = 5) with respect to the corresponding number of Pd atoms (n).

In order to investigate how the morphology and composition influence the O₂ activation, a thorough analysis of their electronic structure is mandatory. Firstly, we qualitatively analyze the frontier molecular orbitals. Fig. 6 shows the highest occupied states (HOS) for the global minimum of Pt₂Pd₃, Pt₃Pd₂ and Pt₄Pd₁ clusters, and their most stable O₂ adsorption configurations, correspondingly. Obviously, the ability of the HOS can be used as electron donors with chemically reactive electronic-deficient molecules/atoms. For the Pt₂Pd₃ and Pt₃Pd₂ clusters, their morphology are both trigonal bipyramid and their concentration level of corresponding HOS are difficult to distinguish, whereas clearly, their corresponding HOS for O₂ adsorption are different. From the O₂ adsorption site in the purple dash frame, it is noticeable that the Pt site has the higher HOS concentration than the Pd site, implying that Pt atom would be more capable to contribute electron than the Pd atom to the O₂ molecule on their corresponding site. This is verified by the Mulliken charge analysis, which shows a slightly larger amount of charge transfer from the Pt atom (0.16e) than the Pd atom (0.12e). This result of the HOS for the Pt₂Pd₃ and Pt₃Pd₂ explains how the composition of cluster influences the O₂ activation. For the Pt₃Pd₂ and Pt₄Pd₁ clusters, the later has a higher HOS concentration, while the former shows a more dispersive HOS. Moreover, the HOS of Pt₄Pd₁ with O₂ adsorption has the stronger hybridization between O₂ molecule and Pt₄Pd₁ than that for Pt₃Pd₂. Due to the higher HOS concentration and stronger hybridization, the Pt₄Pd₁ cluster with square pyramid possesses the higher catalytic activity than the Pt₃Pd₂ cluster with trigonal bipyramid. This comparative result explains how the morphology of cluster determines the O₂ activation. Thus, the morphology and composition of cluster improving the catalytic activity have been further investigated by the electronic structure analysis with the HOS.

Fig. 6 The highest occupied states (HOS) for the lowest-energy Pt₂Pd₃, Pt₃Pd₂ and Pt₄Pd₁ clusters (the isosurface value is ±0.03 a.u.) and most stable O₂ adsorption configurations (the isosurface value is ±0.01 a.u.), correspondingly.

For such reports, the important role of the transition metal (TM) d electrons for chemisorption and catalysis was early anticipated to establish relations between atomic structure and activity for TM catalysts. To gain a further insight into the electronic structure by the morphology and composition contributing to the catalytic activity toward the O₂ dissociation, measurement of the d-band centers may directly correlate the variations in the catalytic activity for the O₂ dissociation with the variations in the electronic structure of the Pt_mPd_n catalyst. Moreover, one generalized descriptor which is beyond the original d-band model, i.e., localized part of the d-band spectrum, is identified to analyze the catalytic activity of the catalysts.^65,66 In this work, we calculated the mean energy (center of gravity) of the localized d-band centers (E_d-band) of the Pt_mPd_n clusters without O₂ adsorption, as presented in Table 3. The E_d-band is calculated as:

where PDOS_d is the DOS projected onto the d orbitals of the pure Pd_mPt_n clusters and the E_F denotes the Fermi energy. Our results show that the E_d-band values of Pt₅, Pd₅, Pt₄Pd₁, Pt₃Pd₂, Pt₂Pd₃ and Pt₁Pd₄ are −2.19, −2.14, −1.93, −1.90, −1.71 and −1.63 eV, respectively. Obviously, as the rich of Pd atoms in the alloyed Pt–Pd clusters, the E_d-band is far close to the E_F, indicating that Pd atoms could up-shift the d-band center of the cluster. This is in good agreement with the earlier report which shows the d-band center of Cu is raised by the addition of Pd.⁶⁷ The raising of the d-band center can be understood in terms of charge redistribution (from Pd to Pt) in the Pt–Pd clusters. On the other hand, the d-band center of Pd can be lowered by the addition of Pt. In addition, it is found that the calculated E_d-band trend agrees quite well with the corresponding E_a of the O₂ dissociation on the alloyed clusters (Fig. 7a). It is noticeable that the lower E_d-band is, the lower is the E_a of O₂ dissociation for the small alloyed clusters (Pt₄Pd₁, Pt₃Pd₂, Pt₂Pd₃, and Pt₁Pd₄). Just as the previous study,^33,68 the d-band center moving away from the Fermi level can relatively lower the atomic O adsorption energy and weaken the O binding, which are beneficial for the O₂ dissociation and diffusion. This d-band center analysis result by the d-band center is in well agreement with the above result by the HOS analysis, which indicates the important role of morphology and composition of the cluster determining the catalytic activity toward the O₂ dissociation by the electronic structure analysis.

Fig. 7 Variation of the E_a for O₂ dissociation on the Pt_mPd_n clusters (m + n = 5) with respect to the corresponding (a) d-band centers of these clusters (E_d-band) and (b) E_r, respectively. The solid lines show the linear fitting of the data and are used to guide the eye.

3.5 The BEP relationship analysis for O₂ dissociation on the global minimum of Pt_mPd_n (m + n = 5) clusters

As we all know, the strong binding regime would limit the kinetics by the removal of products from the catalysts. Fortunately, the empirical BEP relationship^33–35 as a simplification work, provides a way to estimate the kinetic behavior of a chemical reaction from simple thermodynamic data. It relates the activation energy for a given reaction or elementary step with its corresponding reaction energy in a linear manner, and the bond breaking reactions of simple diatomic molecules are usually be focused on to study the BEP relationships. From Fig. 7b, it is found that there is a straight line (black, the intercept and slope are ∼0.50 and ∼−0.01 eV, respectively) through the energy points, where exceptions to this are that for the pure Pt₅ and Pd₅ clusters. The larger activation barriers (E_a) with smaller reaction energies (E_r) for O₂ dissociation on the pure Pt₅ and Pd₅ clusters may directly respond to the exceptions. The O atoms adsorption as well as the O atoms affinity and the difference of structural changes among the O₂ dissociation may be the underlying reasons. Importantly, from the straight line, the O₂ dissociation has the higher E_a (associating with an increase in E_r) on the small alloyed Pt–Pd clusters, although the E_a does not vary exactly corresponding to the change of their E_r. This trend between the E_a and E_r (black line) is in good agreement with the previous study about BEP relationship.^33,69,70 Summarily, the BEP relationship, which also provides a good framework for a systematic analysis of the catalytic activity for the small alloyed Pt_mPd_n clusters, is found to be applicable to the current mini alloyed metal cluster.

4. Conclusion

The pure Pt₅ cluster may be not an ideal catalyst for O₂ dissociation. The Pd atom is selected as an alloying agent in Pt₅ cluster to markedly “turn on” the catalytic activity of Pt₅ by adjusting the morphology and chemical composition. In this work, we have employed the PSO algorithm implemented in the CALYPSO code to predict the geometric structures of the small low-lying Pt_mPd_n (m + n = 5) clusters, and the first-principle DFT-D computations implemented in DMol³ code to study the O₂ dissociation on the lowest-energy Pt_mPd_n clusters, aiming at understanding the improved catalytic activity of Pt–Pd alloyed clusters. The calculated results show that:

(i) The Pd element can modify the morphology and composition of the pure Pt₅ cluster (from 2D planar to 3D structure). The morphology is strongly correlated with the Pd composition, i.e., the clusters with high Pd composition possess the same configuration of trigonal bipyramid with the pure Pd₅ cluster and only the Pt₄Pd₁ cluster with low Pd composition has the structure of square pyramid. From the average cohesive energy, we can see that the stability of the Pt_mPd_n clusters is decreased with Pd rich while the Pt₄Pd₁ is the most stable cluster among the Pt–Pd clusters. Moreover, the calculated E_M shows that the Pt and Pd atoms have a tendency to form the alloy in the current small clusters.

(ii) The O₂ molecule prefers to anchor on the clusters by the Yeager mode and the adsorption of O₂ molecule is gradually weakened by introducing Pd atoms into the pure Pt₅ cluster, except for the Pt₁Pd₄ cluster. And the charge transfer from the alloyed Pt–Pd clusters to the adsorbed O₂ is more than that from the pure Pt₅ cluster, which can weaken the O–O bond in the adsorbed O₂ molecule and facilitate the dissociation of the O₂.

(iii) The catalytic property of the pure Pt₅ cluster toward the O₂ dissociation can be further improved by introducing the Pd atoms, and the Pt₁Pd₄ with high Pt composition (low Pd composition) and square pyramid configuration shows the highest catalytic activity, which demonstrates both the particular morphology and composition of the cluster determine the catalytic activity toward the O₂ dissociation. Moreover, this structure–activity relationship has been investigated by the electronic structure analysis with the frontier molecular orbitals and d-band center.

(iv) More importantly, the BEP relationship, which also provides a good framework for a systematic analysis of the catalytic activity for the small alloyed Pt–Pd clusters, is found to be applicable to the current mini alloyed metal clusters.

In summary, we propose the study here will help to understand the prediction of the global minimum structure of metal cluster by CALYPSO and shed light on the design of the less expensive and more effective alloyed cluster catalysts by controlling the morphology and composition in the fuel cells.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51401078, 11474086 and U1504108); the Program for Science & Technology Innovation Talents in Universities of Henan Province (Grant No. 15HASTIT016); the Foundation for the key Young Teachers of Henan Province and Key Technology Research and Development Program of Henan Province (Grant No. 152102210083, 152102210286 and 142102210455); and the Science Foundation for the Excellent Youth Scholars of Henan Normal University (Grant No. 14YQ005). This work was also supported by The High Performance Computing Center of Henan Normal University.

References

1. H. Yasuda and H. Mori, Phys. Rev. Lett., 1992, 69, 3747.
2. R. Ferrando, J. Jellinek and R. L. Johnston, Chem. Rev., 2008, 108, 845.
3. F. Tao, M. E. Grass, Y. Zhang, D. R. Butcher, J. R. Renzas, Z. Liu, J. Y. Chung, B. S. Mun, M. Salmeron and G. A. Somorjai, Science, 2008, 322, 932.
4. L. Wu, Z. Liu, M. Xu, J. Zhang, X. Yang, Y. Huang, J. Lin, D. Sun, L. Xu and Y. Tang, Int. J. Hydrogen Energy, 2016, 41, 6805.
5. H. Miyamura, R. Matsubara and S. Kobayashi, Chem. Commun., 2008, 2031.
6. W. T. Geng and K. S. Kim, Phys. Rev. B: Condens. Matter Mater. Phys., 2003, 67, 233403.
7. P. L. Rodríguez-Kessler and A. R. Rodríguez-Domínguez, J. Phys. Chem. A, 2016, 120, 2401.
8. S. Vajda, M. J. Pellin, J. P. Greeley, C. L. Marshall, L. A. Curtiss, G. A. Ballentine, J. W. Elam, S. Catillon-Mucherie, P. C. Redfern, F. Mehmood and P. Zapol, Nat. Mater., 2009, 8, 213.
9. F. Vines, J. R. B. Gomes and F. Illas, Chem. Soc. Rev., 2014, 43, 4922.
10. F. Wang, D. Zhang and Y. Ding, J. Phys. Chem. C, 2010, 114, 14076.
11. P. C. Jennings, H. A. Aleksandrov, K. M. Neyman and R. L. Johnston, Nanoscale, 2014, 6, 1153.
12. P. B. Balbuena, D. Altomare, N. Vadlamani, S. Bingi, L. A. Agapito and J. M. Seminario, J. Phys. Chem. A, 2004, 108, 6378.
13. P. B. Balbuena, D. Altomare, L. Agapito and J. M. Seminario, J. Phys. Chem. B, 2003, 107, 13671.
14. F. Oemry, H. Nakanishi, H. Kasai, H. Maekawa, K. Osumi and K. Sato, J. Alloys Compd., 2014, 594, 93.
15. F. Zhao, C. Liu, P. Wang, S. Huang and H. Tian, J. Alloys Compd., 2013, 577, 669.
16. Y. Yang, P. Cheng and S. Huang, J. Alloys Compd., 2016, 688, 1172.
17. L.-L. Wang and D. D. Johnson, J. Am. Chem. Soc., 2009, 131, 14023.
18. X. Shen, W. Liu, X. Gao, Z. Lu, X. Wu and X. Gao, J. Am. Chem. Soc., 2015, 137, 15882.
19. J. Zhang, M. B. Vukmirovic, Y. Xu, M. Mavrikakis and R. R. Adzic, Angew. Chem., Int. Ed., 2005, 44, 2132.
20. H. Li, G. Sun, N. Li, S. Sun, D. Su and Q. Xin, J. Phys. Chem. C, 2007, 111, 5605.
21. D. Chen, F. Ye, H. Liu and J. Yang, Sci. Rep., 2016, 6, 24600.
22. M. Okumura, S. Sakane, Y. Kitagawa, T. Kawakami, N. Toshima and K. Yamaguchi, Res. Chem. Intermed., 2008, 34, 737.
23. K. Bhattacharyya and C. Majumder, Chem. Phys. Lett., 2007, 446, 374.
24. M. Shao, T. Yu, J. H. Odell, M. Jin and Y. Xia, Chem. Commun., 2011, 47, 6566.
25. C. Zhang and P. Hu, J. Am. Chem. Soc., 2001, 123, 1166.
26. H. Conrad, G. Ertl and J. Küppers, Surf. Sci., 1978, 76, 323.
27. K. W. Kolasinski, F. Cemic and E. Hasselbrink, Chem. Phys. Lett., 1994, 219, 113.
28. F. H. Stillinger, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 1999, 59, 48.
29. J. Lv, Y. Wang, L. Zhu and Y. Ma, J. Chem. Phys., 2012, 137, 084104.
30. Y. Wang, J. Lv, L. Zhu and Y. Ma, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 094116.
31. Y. Wang, J. Lv, L. Zhu and Y. Ma, Comput. Phys. Commun., 2012, 183, 2063.
32. H. Wang, Y. Wang, J. Lv, Q. Li, L. Zhang and Y. Ma, Comput. Mater. Sci., 2016, 112, 406.
33. Z. Duan and G. Wang, Phys. Chem. Chem. Phys., 2011, 13, 20178.
34. M. Evans and M. Polanyi, Trans. Faraday Soc., 1938, 34, 11.
35. F. Viñes, A. Vojvodic, F. Abild-Pedersen and F. Illas, J. Phys. Chem. C, 2013, 117, 4168.
36. Y. Wang, M. Miao, J. Lv, L. Zhu, K. Yin, H. Liu and Y. Ma, J. Chem. Phys., 2012, 137, 224108.
37. Y. Zhang and Z. Yang, Comput. Theor. Chem., 2015, 1071, 39.
38. B. Delley, J. Chem. Phys., 1990, 92, 508.
39. B. Delley, J. Chem. Phys., 2000, 113, 7756.
40. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865.
41. A. Tkatchenko and M. Scheffler, Phys. Rev. Lett., 2009, 102, 073005.
42. H. J. Monkhorst and J. D. Pack, Phys. Rev. B: Solid State, 1976, 13, 5188.
43. T. A. Halgren and W. N. Lipscomb, Chem. Phys. Lett., 1977, 49, 225.
44. A. Grushow and K. M. Ervin, J. Chem. Phys., 1997, 106, 9580.
45. T. Li and P. B. Balbuena, Chem. Phys. Lett., 2003, 367, 439.
46. T. Li and P. B. Balbuena, J. Phys. Chem. B, 2001, 105, 9943.
47. Z. Slanina, S.-L. Lee, F. Uhlík, L. Adamowicz and S. Nagase, Theor. Chem. Acc., 2006, 117, 315.
48. W. Huang, A. P. Sergeeva, H.-J. Zhai, B. B. Averkiev, L.-S. Wang and A. I. Boldyrev, Nat. Chem., 2010, 2, 202.
49. A. N. Alexandrova, H.-J. Zhai, L.-S. Wang and A. I. Boldyrev, Inorg. Chem., 2004, 43, 3552.
50. B. B. Averkiev, L.-M. Wang, W. Huang, L.-S. Wang and A. I. Boldyrev, Phys. Chem. Chem. Phys., 2009, 11, 9840.
51. P. L. Rodríguez-Kessler and A. R. Rodríguez-Domínguez, J. Phys. Chem. C, 2015, 119, 12378.
52. X. Xing, A. Hermann, X. Kuang, M. Ju, C. Lu, Y. Jin, X. Xia and G. Maroulis, Sci. Rep., 2016, 6, 19656.
53. V. Kumar and Y. Kawazoe, Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 66, 144413.
54. V. Kumar and Y. Kawazoe, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77, 205418.
55. T. Futschek, J. Hafner and M. Marsman, J. Phys.: Condens. Matter, 2006, 18, 9703.
56. T. Futschek, M. Marsman and J. Hafner, J. Phys.: Condens. Matter, 2005, 17, 5927.
57. C. M. Ramos-Castillo, J. U. Reveles, R. R. Zope and R. de Coss, J. Phys. Chem. C, 2015, 119, 8402.
58. G. Barcaro, L. Sementa and A. Fortunelli, Phys. Chem. Chem. Phys., 2014, 16, 24256.
59. H. Baker, ASM International, Introduction to alloy phase diagrams, Materials Park, OH, 1992.
60. E. Yeager, Electrochim. Acta, 1984, 29, 1527.
61. K. Joshi and S. Krishnamurty, New J. Chem., 2016, 40, 1336.
62. F. Shojaei, M. Mousavi, F. Nazari and F. Illas, Phys. Chem. Chem. Phys., 2015, 17, 3659.
63. L. Leppert, R. Q. Albuquerque, A. S. Foster and S. Kümmel, J. Phys. Chem. C, 2013, 117, 17268.
64. R. Esparza, J. A. Ascencio, G. Rosas, J. F. Sánchez Ramírez, U. Pal and R. Perez, J. Nanosci. Nanotechnol., 2005, 5, 641.
65. A. Vojvodic, A. Hellman, C. Ruberto and B. I. Lundqvist, Phys. Rev. Lett., 2009, 103, 146103.
66. A. Vojvodic, C. Ruberto and B. I. Lundqvist, J. Phys.: Condens. Matter, 2010, 22, 375504.
67. W. Tang, L. Zhang and G. Henkelman, J. Phys. Chem. Lett., 2011, 2, 1328.
68. Y. Zhang, P. Gao, L. Zhang and Z. Yang, J. Nanopart. Res., 2014, 16, 1.
69. T. Bligaard, J. K. Nørskov, S. Dahl, J. Matthiesen, C. H. Christensen and J. Sehested, J. Catal., 2004, 224, 206.
70. J. K. Nørskov, T. Bligaard, A. Logadottir, S. Bahn, L. B. Hansen, M. Bollinger, H. Bengaard, B. Hammer, Z. Sljivancanin, M. Mavrikakis, Y. Xu, S. Dahl and C. J. H. Jacobsen, J. Catal., 2002, 209, 275.

---