First-principles study of small Pd–Au alloy clusters on graphene

Abstract

We performed extensive density functional theory (DFT) calculations of palladium (Pd) and gold (Au) alloy clusters adsorbed on a graphene monolayer in order to clarify the geometries and charge transfer of Pd–Au bimetal alloy clusters on graphene. It is found that the Pd–Au cluster prefers to bind with graphene through Pd atoms, with strong p-d hybridization between graphene and Pd atoms. Although the gold atom has an unpaired electron, the magnetic moments are mainly contributed by palladium. Compared with Pd–Au bimetal, the bonds between Au atoms are stronger; therefore, the gold atoms form a gold cap covering the Pd cluster. Furthermore, Bader charge analysis demonstrates that Pd in alloy clusters tends to lose electrons, and the number of charge transfers increases with the introduction of the graphene monolayer. Gold atoms and graphene synergistically improve electron loss on the Pd atom, thus weakening the adsorption of anions, which is expected to prevent poisoning of Pd nanocatalysts and enhance the catalytic reactivity of alloy clusters. However, the Au–Au coupling could weaken their ability to gain electrons from Pd significantly. So, an important task for experimental research is to find a way to disperse gold atoms as far apart as possible to improve the catalytic properties of the Pd–Au alloy cluster.

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1. Introduction

Nanoclusters have attracted particular interest in the study of materials because of their properties, which are controllable by tuning their size, shape and composition.^1,2 Particularly, they exhibit tremendous potential applications in catalysis.³ The Pd cluster is a very efficient catalyst of hydrogen dissociation and acetylene hydrogenation.⁴ However, when monometallic Pd is used in groundwater treatment, components of groundwater, particularly sulfide⁵ and chloride,⁶ cause deactivation. To solve this problem, heterogeneous atoms are introduced into Pd clusters, forming bimetallic alloy clusters. Heck et al. reported Pd-decorated gold nanoparticles for trichloroethene (TCE) hydrodechlorination and found that the gold component could enhance both Pd catalytic activity and poisoning resistance for room-temperature, water-phase trichloroethene hydrodechlorination.⁷ Subsequently, Evangelisti et al. synthesized new Pd–Au bimetallic catalysts using Au and Pd vapours as reagents and found that the alloy cluster has higher catalytic activity and selectivity than the corresponding monometallic structure.⁸ Recently, compared with monometallic nanoclusters, bimetallic clusters have attracted more interest due to their rich mixture of physical and chemical behaviors.^9–18 By adding different types of metal adatoms, the nanoclusters' electronic, magnetic, optical and catalytic properties could be tuned, improving their widespread application prospects.

An appropriate substrate support for metallic clusters, for example graphene-based substrates, is also very important for catalysts.¹⁹ Graphene, which is a two-dimensional honeycomb carbon network, has attracted much scientific interest in the field of materials due to its linear energy dispersion at the Fermi level and zero-gap semiconductor character. Owing to its large surface area and good chemical stability, graphene is often applied as an ideal substrate for catalysts. Many kinds of metallic clusters, both homogeneous and heterogeneous, have been dispersed on the graphene surface, and very impressive catalytic properties in various reactions have been reported in previous works.^20–25

More recently, experimental results have been reported to demonstrate the high reactivity of the Pd–Au alloy cluster on graphene. In 2013, R. Y. Wang et al.¹⁰ investigated the catalytic properties of graphene supported Au–Pd bimetallic nanoparticles. They compared the catalytic performance of various Au–Pd catalysts in methanol oxidation reaction and found that Au–Pd supported on Al₂O₃/TiO₂ is inactive in methanol oxidation, and so is pure graphene. Monometallic Pd or Au supported on graphene shows very low activity, while bimetallic Au–Pd catalysts supported on graphene exhibit much higher activity. A methanol conversion of 90.2% and selectivity of 100% was attributed to the synergism of Au and Pd particles as well as the strong interaction between graphene and Au–Pd nanoparticles.

Theoretical studies on the interaction mechanism of all kinds of monometallic clusters supported by graphene, such as alkalis, alkali-earth, 3d-TM and noble metal atoms/clusters, can be found in the literature.^11,26–29 However, systematic studies on bimetallic alloy clusters supported by graphene have not yet been reported. Motivated by these experimental and theoretical works, and in order to improve the understanding on the microcosmic mechanism of the reaction, a systematical theoretical study on graphene-supported Pd–Au bimetallic alloy clusters is carried out under the density functional theory (DFT) framework. With more geometric and electronic combinations introduced, it will be of great interest to understand the formation mechanism of Pd–Au alloy clusters on graphene.

2. Details of computational method and verifications

Spin-unrestricted density functional theory (DFT) calculations are carried out using the plane-wave basis set and projector-augmented wave (PAW) pseudo-potentials,^30,31 which are implemented in the Vienna ab initio simulation package (VASP) code.^32,33 The generalized gradient approximation (GGA)-type functional, parameterized by Perdew, Burke and Ernzerhof (PBE),³⁴ is employed to treat the exchange and correlation energy. The self-consistent electronic iteration proceeds until the total energy is converged to 10⁻⁶ eV with spin-polarized calculation. Optimized structures are obtained after the geometric relaxations, with the maximum force tolerance of 0.01 eV Å⁻¹. In the relaxation of pure Pd_mAu_n clusters, the energies under different spin multiplicities are scanned carefully in order to determine the magnetic moments of the ground states. Also, a frequency calculation is performed after each geometric relaxation to make sure all the imaginary frequencies are eliminated so that a true minimum is reached.

We built a single-layer periodical (4 × 4) graphene consisting of 32 carbon atoms in the x–y plane, using the optimized C–C bond length of 1.425 Å. A vacuum of 20 Å and dipole corrections along the z direction are introduced to eliminate the periodic effect between slabs. Considering the high cost of noble metals, as well as our computational capacity, the size of the Pd–Au cluster is limited to be five atoms at most. After systematic tests, a Γ-centered Monkhorst–Pack 5 × 5 × 1 k-point mesh and an energy cut-off of 300 eV were used for the relaxations, which are increased to be 11 × 11 × 1 and 450 eV in the following calculations on electronic properties to make the result more reliable. Several trials with finer k-mesh and/or higher cut-off energies are also purposed, but only negligible energy error is observed. A Gaussian smearing of 0.01 eV is used to improve the convergence of iterations in the relaxations, while a tetrahedron method with Blöchl corrections is used in the accurate energy and DOS calculations to avoid the fractional occupancies in the band structures.

The averaged binding energy (BE) and adsorption energy (AE) of Pd_mAu_n/graphene are determined by the formula:

BE = (E_Gr + mE_Pd + nE_Au − E_PdmAun@Gr)/(m + n),

AE = E_Gr + E_PdmAun − E_PdmAun@Gr,

where Gr represents the perfect graphene, and E_PdmAun is the ground state energy of the isolated metal alloy cluster Pd_mAu_n. The energy value could be negative if the reaction is endothermic. Compared with binding energy, the adsorption energy is defined in a way that interactions between metal atoms are excluded, and therefore we can evaluate the binding between metal cluster and graphene independently.

The charge transfers are very important for us to understand the interaction between the metal clusters and graphene. The charge transfers and local magnetic moments on each atom are derived from the Bader analysis,³⁵ which is an intuitive scheme of dividing molecules into atoms purely based on electronic charge density in real space.

The Pd–Au alloy cluster, Pd/graphene and Au/graphene have been well characterized in the aspects of their geometry, electronic structure and catalysis properties, so it is good to test our settings by doing some verifications. The optimized bond length, spin multiplicity and binding energy of Pd and Au dimers are given in Table 1, which agree well with experiments. When Pd and Au atoms are placed onto graphene, their adsorption sites in the ground state are different. Pd prefers standing above the carbon–carbon bond, usually denoted as ‘bridge site.’ The distance between Pd and the graphene surface is 2.06 Å, and the bond between Pd and its nearest–nearest (NN) carbon is 2.18 Å, comparable with 2.04 Å and 2.16 Å in ref. 36. In contrast, the most stable site for Au is atop, i.e. directly above one of the carbon atoms. The gold atom drags the carbon atom, on which it stands, out of the graphene plane slightly, at a distance of 2.44 Å. Bader charge analysis further shows that Pd atom loses about 0.207e and is therefore positively charged, while in contrast gold is −0.086e and is negatively charged (comparable with −0.09e in ref. 37). Obviously, Pd has much stronger interaction with graphene than that of Au, indicating that Pd–Au alloy clusters will prefer to stand on graphene with Pd atoms connecting to carbon anchors than the opposite.

Table 1 The bond length (d), spin multiplicity (2S + 1) and binding energy (BE) of Pd₂, Au₂ and the alloy dimer Pd–Au, optimized compared with experimental results (BE^EXP)

Dimers	d (Å)	d^Exp (Å)	2S + 1	BE (eV)	BE^EXP (eV)
Pd2	2.483	2.57	3	1.288	1.13
Pd–Au	2.499		2	1.873
Au2	2.527	2.47	1	2.284	2.29

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The graphene-supported palladium dimer Pd₂ has a stable configuration parallel to the graphene plane, with both Pd atoms sitting on the bridge sites. The averaged Pd–C, Pd–Pd bond length and binding energy are 2.20 Å, 2.70 Å and 1.346 eV, comparable with results in ref. 36. In contrast, the gold dimer is perpendicular to the graphene surface, with one gold atom sitting on the top site. The Au–C, Au–Au bond length and binding energy are 2.33 Å, 2.52 Å and 1.362 eV, which agrees well with ref. 37.

3. Results and discussion

The initial configurations of graphene-supported metal clusters are usually prepared in two ways.³⁷ One is to drop the entire metal cluster with the given size gently onto the surface of graphene and watch the reconstruction during the landing, and the other is to observe the self-clustering (or to say self-assembly) between smaller clusters adsorbed previously on the graphene. Theoretically speaking, the first method helps us to better understand the geometric and electronic interactions between graphene and clusters that are already presented, and by the second method it is easier for us to obtain the reaction path showing the growth of clusters. Both ways are worked through in our simulations.

3.1. Single gold atom-doped Pd_mAu cluster on graphene

The relaxed bond length of the smallest Pd–Au alloy cluster (PdAu)₁ is found to be 2.499 Å, with the binding energy of 1.873 eV. As a result, the binding between Pd and Au atoms is weaker than between two gold atoms, but stronger than dual Pd atoms. The Pd atom has a close d-shell so that the binding is rather weak; in contrast, gold has one half-filled s orbital, making it easier to form a tightly bound dimer. The (PdAu)₁ cluster is the case in between. Although we cannot directly compare the bond length of Pd₂ and Au₂ because of their different number of shells, we expected that (PdAu)₁ would have a bond length in between as well. The results of the geometry and energy analyses can be found in Table 1.

Now we turn to the Pd–Au alloy cluster adsorbed on graphene. The (PdAu)₁ alloy cluster has its Pd–Au bond neither parallel nor perpendicular to the graphene surface according to the optimized configurations, as shown in Fig. 1. Besides, there is a metastable isomer with a Pd–Au bond perpendicular to graphene that is only 0.007 eV higher in total energy, indicating that the Au atom atop might have very high mobility. Actually, the interaction between metal atoms on the graphene is much stronger than that between Pd (as well as Au) and carbon atoms on the graphene.³⁶ Driven by the attractive interactions between them, palladium and gold atoms spontaneously move towards each other, even when the initial distance between them is up to 5 Å. As the binding between Pd and graphene becomes stronger, the energetic binding of Au–Pd/graphene, with Pd binding directly to graphene, has an energy that is 0.440 eV lower than the reverse (i.e. Pd–Au/graphene). This is easy to understand, as there are more electronic transfers from Pd to graphene than those of Au as mentioned above, resulting in a deeper energetic drop after the adsorption. The binding energy of Pd–Au/graphene is 1.270 eV, which is higher than the 1.073 eV of Pd/graphene, while the adsorption energy, in which the binding between Pd and Au is excluded, shows that the interaction between the Pd–Au cluster and graphene is as weak as 0.666 eV. Bader charge analysis shows that the gold atom could gain more than −0.300e electrons from the Pd atom, while the charge transfer between Pd and graphene is now only 0.03e. In comparison, graphene could gain −0.200e electrons from the Pd atom in the Pd/graphene. Meanwhile, the bond length between the Pd atom and the anchored carbon atoms in graphene increases from 2.18 Å to 2.21 Å after the inclusion of the gold atom. These indicate that the gold atom obviously weakens the interaction between the Pd atom and graphene by obtaining more electrons from Pd, thus pulling it away from the graphene surface.

Fig. 1 Geometrical structures of and Pd_mAu_n (m + n ≤ 5)-doped graphene. Brown balls represent carbon atoms, silver for Pd and golden ones for Au. Values are net charge distribution on each metal atom.

To understand the complex chemisorbed graphene, Bader analysis is usually employed to illustrate and quantify the local charge and spin distribution on each atom (see Table 2). Sometimes, the Fermi energies could also be employed to determine the charge transfer; these are also given in Table 2 for all the systems. Chan et al.³⁸ reported the differences in the definitions of charge transfers. They used the density of states (DOS) of the adatom–graphene system to determine the charge transfers by calculating the integral of DOS in the range of E_Fermi and E_Dirac, and assuming the rigid shift of the DOS of graphene. Even simpler, Sun et al. determined the charge transfer between the Pt–Au alloy cluster and graphene by comparing the Fermi level of both.³⁹ Here, the Fermi energy of free-standing graphene in our calculation is −2.949 eV, i.e., higher E_Fermi indicates that the electrons transfer from the metal cluster to graphene. The Fermi energy of Pd₁Au₁/graphene and Pd₂Au₁/graphene are −3.370 eV and −2.760 eV, where the charge transfer directions are consistent with Bader's analysis.

Table 2 The averaged net charge q̄ per Pd(Au) atom and total net charge on the graphene (Gr) substrate q from Bader charge analysis, the averaged binding energy per atom (BE), adsorption energy (AE), and total/local magnetic moments μ in alloy clusters Pd_mAu_n without and with graphene. Negative charge transfer values indicate that the atom gains electrons

PdmAun/Gr	q̄Au (e)	q̄Pd (e)	qGr (e)	BE (eV)	AE (eV)	μtotal (μB)	μPd (μB)	μAu (μB)
Pd1Au1	−0.207	+0.207		0.941		1.000	0.821	0.179
Pd2Au1	−0.157	+0.079		1.395		1.000	0.892	0.108
Pd3Au1	−0.128	+0.043		1.663		1.000	1.031	−0.031
Pd4Au1	−0.100	+0.025		1.773		1.000	1.030	−0.030
Pd1/Gr		+0.204	−0.204	1.074		0.000	0.000
Pd2/Gr		+0.154	−0.302	1.346		0.000	0.000
Pd3/Gr		+0.135	−0.405	1.514		0.000	0.000
Pd4/Gr		+0.069	−0.276	1.828		1.933	1.734
Pd1Au1/Gr	−0.300	+0.272	+0.028	1.270	0.657	0.523	0.272	0.180
Pd2Au1/Gr	−0.291	+0.241	−0.191	1.800	1.214	0.948	0.716	0.072
Pd3Au1/Gr	−0.280	+0.206	−0.338	1.942	1.118	0.553	0.428	0.025
Pd4Au1/Gr	−0.268	+0.175	−0.432	1.956	0.916	0.000	0.000	0.000
Pd1Au2	−0.057	+0.115		1.405		0.000	0.000	0.000
Pd1Au3	−0.078	+0.234		1.600		1.000	0.500	0.166
Pd1Au4	−0.045	+0.178		1.647		0.000	0.000	0.000
Pd2Au2	−0.077	+0.077		1.599		0.000	0.000	0.000
Pd2Au3	−0.084	+0.126		1.702		1.000	0.430	0.047
Pd3Au2	−0.193	+0.129		1.774		2.000	0.489	0.267
Pd1Au2/Gr	−0.070	+0.241	−0.101	1.681	0.829	0.523	0.272	0.180
Pd1Au3/Gr	−0.088	+0.240	+0.024	1.728	0.688	0.948	0.716	0.072
Pd1Au4/Gr	−0.052	+0.260	−0.052	1.785	0.690	0.553	0.428	0.025
Pd2Au2/Gr	−0.080	+0.208	−0.256	1.841	0.969	0.000	0.000	0.000
Pd2Au3/Gr	−0.053	+0.240	−0.321	1.983	1.407	0.000	0.000	0.000
Pd3Au2/Gr	−0.140	+0.197	−0.311	1.941	0.836	0.000	0.000	0.00

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Band structure in Fig. 2 shows the components of each band in PdAu@graphene. We can still see the Dirac point on graphene, while a gap of 0.086 eV appears at 0.5 eV above the Fermi level, indicating that the Pd–Au complex captures electrons, and the graphene layer is doped with holes (p-type doping). We can also see that the d orbital of Pd (represented by blue diamonds) has a much stronger hybridization with the d of Au (golden triangles) than with p_z of carbon (black circles). Meanwhile, the fairly localized d–d bond between Pd–Au dominates the bands of −0.3 to 0.7 eV. Both indicate that the interaction between Pd and graphene is weaker than that of Pd–Au and graphene. The s state of gold (red squares), however, is rather localized and occupies the valence band close to the Fermi level. Especially, the Pd₁Au₁/graphene system is spin-polarized, with a magnetic moment of 0.523 μ_B, which comes mainly from d bands of Pd. For the spin-down part, the s band of gold around Γ point, which was unoccupied in the gold atom, is now 4.8 meV below Fermi level, resulting in the whole system being metallic. As it is very close to Fermi level, it is possible to shift this band a little higher, by adding a low electronic field, to form a semi-metal material.

Fig. 2 Band structure and its orbital projected components of Pd₁Au₁/graphene. Black solid lines are energy bands, while bubbles are the orbital components of each band, in which the radius represents the percentage. Black circles stand for p_z of carbon, red squares stand for s of gold, golden triangles stand for d of gold, and blue diamond stands for d of Pd. Fermi energy level has been shifted to zero. Left panel is for spin-up, and right panel is for spin down.

On the other hand, comparing the gain of electrons on the gold atom with and without graphene, we can see that the quantity of charges transferred between Pd and Au atoms is higher when graphene acts as substrate. For example, the electron gained by gold in the free-standing Pd–Au alloy cluster is 0.207e, while on graphene it is 0.300e. It is clear that in the presence of graphene, the gold atom gains more electrons, while palladium loses more. One possible explanation comes from the hybridization between the Pd–Au alloy cluster and graphene near the Fermi level, where the highly localized d electrons hybridize with s of Au, as well as p_z of carbon, and delocalize significantly. From the band structure we can see that the band nearest to Fermi level has components of s, p_z and d, and it spreads in the energy range of −0.25 eV to 0.5 eV near K point. The delocalization of d enhances the departure of the outmost electrons in Pd.

The charge distribution is meaningful and could helus to step up their catalytic properties. When applied in production, many noble metal cluster catalysts suffer from poisoning. For example, CO gas could poison and inactivate Pt. Tang et al.¹⁹ studied the interaction between CO and the Pt₄ clusters, and indicated that the graphene-based substrate, which makes the Pt catalyst lose electrons, could weaken CO adsorption. Similarly, when used to purify bodies of water, Pd catalysts are usually poisoned by anions in the water, such as Cl⁻ and S²⁻. We expect that gold and graphene could weaken the interactions between Pd and the anions, therefore preventing catalyst poisoning.

We built a system by adding one chlorine (Cl) atom into Pd₂/graphene and Pd₁Au₁/graphene structures (see Fig. 4(a and b)). The table in Fig. 4 gives the adsorption energy of Cl (AE_Cl), as well as the net charge distributions. The value of AE_Cl is calculated by:

AE_Cl = E_PdmAun/Gr + E_Cl − E_Cl@PdmAun/Gr,

where Pd_mAu_n/Gr represents the Pd_mAu_n alloy cluster-decorated graphene monolayer. It is clear that the AE_Cl decreases when Au exists; in other words, Au indeed weakens the interaction between Pd and Cl. This could be easily understood by analysing the charge transfers. It can be found that the amount of charge transferring towards Cl in Pd₁Au₁/graphene is lower than that in Pd₂/graphene. We have known that Au (as well as graphene) has a higher ability to gain electrons than Pd, and it acts as electron acceptor when no Cl atom is included. After the Cl adsorption, both Au and Pd lose electrons; however, Au is able to hold more electrons than Pd, accordingly weakening the charge transfer between Pd and Cl.

Fig. 3 The projected DOS of Pd_1–4Au/graphene. Fermi levels are all shifted to zero.

Fig. 4 The geometry and adsorption energy of Cl atom, and the net charge distribution of (a) Cl@Pd₂/graphene and (b) Cl@Pd₁Au₁/graphene. Green balls represent Cl atoms. Charge values in the table are the net charge distributions, thus a value means loss of electrons, and vice versa.

Both experimental¹⁰ and our calculated results show that gold atoms and graphene synergistically improve the electron loss of the Pd atom, which could then weaken the adsorption of anions on Pd. This is expected to prevent the poisoning of Pd nanocatalysts and enhance the catalytic reactivity of alloy clusters. As a result, by varying the number and ratio of Pd–Au atoms, we can find which combination could make Pd lose more electrons.

One thing we have to clarify is that the “synergy” mentioned above is for the electron loss of Pd only, rather than that of graphene and Au atoms. According to the results in Table 2, in most cases, graphene acts as electron acceptor, while in some cases, such as when it is decorated by Pd₁Au₁ and Pd₁Au₃, it loses some electrons instead. One qualitative explanation could be given according to the order of their ability to gain electrons: Au > graphene > Pd. In Pd₁Au₁/graphene, as Au's ability to gain electrons is higher than that of either graphene or Pd, Au could gain electrons from Pd and graphene, making both positively charged. When the number of Pd atoms increases, e.g. Pd₂Au₁/graphene, there are enough electrons provided and saturating Au; thus some electron loss from Pd could move towards graphene.

Pd₂Au on graphene has a triangle configuration, with both Pd atoms bonding to graphene through bridge sites (see Fig. 1(b)). The bond length between two Pd atoms is 2.56 Å, which is shorter than that of Pd₂/graphene. The distance between Pd and Au atoms is 2.64 Å, which is longer than that of Pd₁Au₁/graphene. Thus, the introduction of Au atom enhanced the Pd–Pd bond; conversely, the Pd–Pd bond weakens interactions between Au and Pd. We can also see that electrons gained by the gold atom decrease from −0.300e in Pd₁Au₁/graphene to −0.291e. Meanwhile, the Pd–C bond length increases a little compared with Pd₂/graphene, from 2.20 Å to 2.25 Å, as we know that interaction between Pd and Au is stronger than that of Pd–carbon. The BE is 1.799 eV, which is higher than that of Pd₁Au₁/graphene. Fig. 3(b) shows that the DOS near Fermi level are mainly contributed by d of Pd. The s state of Au appears in the range of −1.5 eV to 0.75 eV, contributing almost nothing to the states around Fermi level. There is a localized peak standing 0.116 eV above Fermi level, which represents hybridization by d of Pd₂Au and p_z of carbon. It is interesting that the p_z component of this peak comes (differently from what we expected) not only from carbon atoms binding to the Pd atoms, but also those far away; therefore, it is not an electronically localized state in real space.

Pd₃Au also forms a somewhat deformed tetrahedron on graphene, with three Pd atoms connected with graphene through three bridge sites. BE increases to 1.942 eV compared with Pd₂Au/graphene. Similarly, Pd₄Au also has all its four Pd atoms connecting with graphene through four bridge sites (see Fig. 1(d)). The gold atom bonds with three Pd atoms, apart from the fourth Pd atom—as far as 3.73 Å. As the number of Pd atoms binding to gold does not change, BE is 1.956 eV, only a little higher than that of Pd₃Au. DOS results show the high hybridization between d of Pd and p_z of Pd near Fermi level, leading to the delocalization of Pd-d above Fermi level. Although the gold atom in Pd₄Au has an unpaired electron, making the total number of electrons in the cell odd, the magnetic moment of Pd₄Au₁/graphene is annihilated. It is different in homogeneous clusters. For example, it was reported by Srivastava et al.¹¹ that the total magnetic moments of Au_n@graphene (n < 6) corresponds to the parity of the total number of electrons in the super cell and could be explained by the electron pairing effect. This does not work on Pd–Au alloy clusters. We can see from the local magnetic moments shown in Table 2 that spin polarization mainly comes from Pd atoms, in both the case with and without graphene.

In Pd_m=1–4Au@graphene, the average binding energy increases with the size of the cluster, while the growth keeps slowing. The averaged binding energy when m = 3 and m = 4 are 1.942 eV and 1.956 eV respectively, which are quite close. Comparing the configurations in Fig. 1(c) and (d), we can see that the extra Pd atom in Pd₄Au@graphene stands a little far away from Au, with the distance of 3.73 Å. We guess that it is caused by the stronger Pd–Pd and Pd–Au interactions compared to the Pd/graphene one.

With the increased cluster size, the hybrid structures become more stable, indicating that the interaction between metal atoms is stronger than that between cluster and graphene, and implying the high mobility of Pd–Au clusters on top of graphene. It is clear that Pd atoms always lose electrons; however, with the increase in Pd atoms, electron loss from Pd decreases from 0.300e to 0.268e. The reason is that the increasing electronic localization caused by the binding between Pd atoms with increasing size surely weakens the Au–Pd binding strength; in other words, electrons become more localized in the Pd–Pd bond area, thus making it more difficult for others to pick up.

We can see from DOS that with the increase of Pd atoms from 1 to 4, the relative locations of Dirac cone to Fermi level do not change too much (open at 0.5 eV above Fermi level). New, localized d states from new Pd atoms appear below Fermi energy level, dominating the DOS near Fermi level and shifting Fermi energy from −3.374 eV to −2.514 eV. We have known that doping from graphene in PdAu@graphene is p-type. It seems that the ‘Dirac’ cones for Pd_2–4Au@graphene all shift above Fermi level; however, doping for graphene is instead actually n-type from Bader analysis. It is because the d of Pd, which was fulfilled by electrons, now dominates the ‘Dirac’ cone close to Fermi level. The complex hybridization between Pd, Au and graphene makes it difficult to identify the type of doping. Khomyakov et al. systematically studied the charge transfer between graphene and all kinds of metal atoms, including Pd and Au.²⁶ They indicated that when Pd adsorbs on graphene, the bands of graphene are strongly perturbed; particularly, the characteristic conical points of graphene at K are destroyed. The p_z states of graphene hybridize strongly with the d states of the metal, and the corresponding bands acquire a mixed graphene-metal character, which demonstrates that graphene is chemisorbed on the Pd cluster. In this case, they believe it is difficult to identify the Fermi-level shift (relative to the Dirac point of graphene), and therefore, the type and magnitude of doping by simply examining the band structure. In our system, we can see from the band structures that the interactions between Pd (note that graphene tends to bind with Pd instead of Au) and graphene are mainly covalent, in which Pd and Au could significantly alter the electronic structures of graphene.

3.2. Au–Au coupling and its effects

The configurations of the Pd–Au alloy cluster with more than one gold atom introduced are found in Fig. 1(e–j). Pd₁Au₂ forms a triangle on graphene, with Pd atom bonding with three carbon atoms, and the Pd–C distances are from 2.17 Å to 2.53 Å (see Fig. 1(e)). The Au–Au bond is 2.647 Å, which is longer than the gold dimer Au₂. Interestingly, both Pd–Au bonds also have a length of 2.64 Å, making the Pd₁Au₂ triangle almost equilateral. Pd₁Au₃ forms a planar quadrangle on graphene, with the Pd atom bonding to graphene through a bridge site (see Fig. 1(f)). The Pd–C bond is 2.24 Å, and the Pd–Au bond is 2.73 Å.

The ground state of Pd₃Au₂ has a bi-tetrahedral configuration, formed by a Pd₃ triangle with two gold atoms on each site. When it is adsorbed on graphene, two gold atoms bond with the three Pd atoms binding to graphene. The Au–Au bond length is 2.75 Å, longer than the Au dimer. The binding energy per metal atom is 1.941 eV, quite close to the 1.942 eV of Pd₃Au/graphene. Meanwhile, two gold atoms gain −0.13e and −0.14e respectively, compared with −0.28e of the gold atom in Pd₃Au/graphene; therefore it seems that two gold atoms share electrons gained from Pd.

Even when more Au atoms are introduced to our system, spin polarization still mainly comes from Pd atoms. The Pd–Au alloy clusters Pd₁Au₂ and Pd₁Au₄ both have non-magnetic ground states, while on graphene they are spin polarized. On the contrary, Pd₂Au₃ and Pd₄Au₁ both have unpaired electrons, but the magnetic moments annihilate on graphene. It is interesting that Pd-d in Pd₄Au₁/graphene also presents as delocalized around Fermi level, which hybrids with Au-d and C-p_z (see Fig. 3).

We can see in Fig. 1 that gold atoms prefer to stand together instead of mixing with Pd atoms. In experiments, Ferrer¹² et al. reported the internal structure of Au–Pd nanoparticles exhibiting three-layer core–shell morphology, which is composed of an evenly alloyed inner core, an Au-rich intermediate layer, and a Pd-rich outer shell. Gao et al. studied the Pd–Au bimetallic alloy cluster and reported that with increasing surface Au coverage, contiguous Pd ensembles disappear, and isolated Pd ensembles form.⁴⁰ In the energetic view, as is mentioned above, the Au–Au interaction strength is higher than Pd–Au and Pd–Pd, so that gold atoms in the Pd–Au alloy cluster prefer to assemble to form core–shell configuration. It is consistent with the experimental results. Meanwhile, Pd–C interaction is stronger than that of Au–C, resulting in the carbon atom in graphene preferring to connect with the cluster via Pd instead of Au. Consequently, the Pd–Au alloy cluster on graphene usually has such a configuration in which Pd atoms bond with graphene, and gold atoms tend to assemble, forming a ‘cap’ to cover Pd atoms.

When Au atoms bond to each other, they could share their electrons to form Au–Au covalent bonds, which are more stable than Pd–Au. This kind of “coupling” between Au atoms could obviously weaken their ability to gain electrons from outside, as well as the reaction activity of Pd. In the view of energy, the binding between gold atoms could affect the AE of clusters, defined by eqn (2). As Pd–Au alloy clusters prefer to bind with graphene through Pd atoms, AE here exhibits mainly the interaction between Pd atoms and graphene. For example, the AE of Pd–Au/graphene and PdAu₂/graphene are 0.657 eV and 0.829 eV respectively, where we can see that the coupling between gold atoms enhances the bond between Pd and graphene. In the view of the charge distribution (see Fig. 1(e)), we can see that two gold atoms in Pd₁Au₂/graphene bond with each other and gain only 0.07e electrons, and in Pd₁Au₃(i) we can find that the gold atom in the middle is almost neutral, although it bonds to Pd atoms. In (f) and (g) we can see some gold atoms even lose electrons and become positively charged. AE of PdAu₃/graphene (f) and PdAu₄/graphene (g) are 0.688 eV and 0.690 eV, respectively, which are quite close to each other. Meanwhile, the charge on the Pd atom is also similar (0.26e). Therefore, geometric and structural characteristics also play an important role in catalytic improvement. Zhang et al. reported⁹ the Pd–Au crown-jewel catalyst by replacing Pd atoms at active top sites with Au atoms, and their top Au atoms decorating the Pd nanocluster structure leads to significantly enhanced activities for aerobic glucose oxidation. In their paper, they mentioned that catalytic sites are located on the surface of the metal, especially at the tops (vertexes) with a high coordination vacancy. Finding a way to disperse gold atoms as far as possible is an important task for experimental research to improve the catalytic properties of the Pd–Au alloy cluster.

Fig. 5 shows the DOS of Pd_1–3Au₂. All have a semi-conductor character, with the energy gaps of 0.07 eV, 0.016 eV and 0.037 eV, respectively. Comparing their DOS we can see that there is an Au-s peak above Fermi level, which is the anti-bonding state of Au-s–s. We know that Pd has a filled d shell; thus now the s state of gold hybridizes with Pd-d, which indicates that Pd atoms lose electrons. Meanwhile, with the increase of Pd atoms, it is clear that the peak moves towards Fermi level. The height of Au-s remains the same when the number of Pd atoms increase, and the Pd-d component dominates the peak in Pd₃Au₂. The number of Pd-d peaks in the energy range of −2 to 0 eV increases significantly with the increase in Pd atoms. The peaks of Pd-d, as we can see, dominate the band structure closely below Fermi level, indicating that the most active sites are still around Pd atoms after the introduction of gold atoms. However, hybridizations between the d-band of Pd and Au are also clearly seen. Researchers believe that the d band character is more important for the catalytic properties of noble transition metals like Pd and Au. Some even consider that Pd could lose sp electrons but gain d electrons from Au to keep an atomic-like character.⁴⁰ Anyhow, gold atoms could at least affect the d electrons of Pd, which is also expected to weaken the binding between Pd and reactants, and then increase the poisoning resistance of alloy clusters.

Fig. 5 The projected DOS of Pd_mAu_n/graphene (n > 1). Fermi levels are all shifted to be zero.

4. Summary and prospect

By performing density functional calculations, in this paper we systematically studied the structure and electronic properties of the small Pd_mAu_n clusters absorbed on the graphene surface. As the Pd–C bond is much stronger than the Au–C, graphene prefers to bind with the cluster through Pd. Meanwhile, the Au–Au bond is stronger than Au–Pd and Pd–Pd, so that gold atoms tend to assemble, capping the Pd atoms. Although the gold atom has an unpaired electron, the magnetic moments are mainly contributed by palladium. The ability of Au to gain electrons is higher than graphene and Pd, while the Au–Au bond between gold atoms weakens this ability. The synergy between graphene and gold atoms to improve the electron loss of Pd could weaken the interaction between Pd and anions, which is expected to prevent anion poisoning of the Pd nanocatalyst. So it is important to separate gold atoms in the Pd–Au alloy cluster in order to improve the catalytic properties of Pd. We hope that our work can serve to encourage the important experimental and theoretical studies of alloy cluster adsorption on graphene in future.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant no. 11274143, 60471042, 61172028, and 11304121) and the Doctoral Foundation of University of Jinan (Grant no. XBS1433).

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