Size Dependent Adsorption of Styrene on Pd Clusters: A DFT Study

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Size Dependent Adsorption of Styrene on Pd Clusters: A DFT Study Zhaoming Xia, Sai Zhang, Fuzhu Liu, Yuanyuan Ma, Yongquan Qu, and Chao Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b09477 • Publication Date (Web): 04 Jan 2019 Downloaded from http://pubs.acs.org on January 10, 2019

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The Journal of Physical Chemistry

Size Dependent Adsorption of Styrene on Pd Clusters: A DFT Study Zhaoming Xia, Sai Zhang, Fuzhu Liu, Yuanyuan Ma, Yongquan Qu* and Chao Wu*

Frontier Institute of Science and Technology and State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710054, China.

ABSTRACT: When the size of the reactant molecule is comparable to that of a nanometer catalyst (such as an aromatic compound and a nanometer or sub-nanometer metal catalyst), the adsorption configuration of the molecule on the catalyst becomes different from that on their larger counterparts. Consequently, distinct catalytic performance can be observed for catalysts of different size. Therefore, it is crucial to understand the adsorption behaviors of molecules on various metal nano catalysts. Here, the sizedependent adsorption of a representative system (i.e., styrene or ST on Pd clusters) was systematically explored using the density functional theory (DFT) calculations. For large

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Pd nanoparticles (size between 31 atoms to 73 atoms), the adsorption becomes weaker as the particle size increases. For the particles smaller than 31 atoms, the adsorption weakens rapidly with the decreasing size, which was also observed for Cu-supported Pd clusters. The peak of adsorption strength at middle-sized particles are caused by the combination of the geometric effect and the metal-molecule electron back-donation effect. Our results provide new insight of the relationship between the adsorption strength and particle size, which may benefit the design and optimization of nanocatalysts.

I. Introduction

Metal catalysts with different sizes possess natal differences in both their activity and selectivity for various reactions.1 In general, metal catalysts with smaller size exhibit larger surface to bulk ratio and higher atom efficiency. Thus they provide more surface sites for reactions and expose more corner and edge atoms with lower coordination numbers as well as higher activity.2 One of the most effective effort is to reduce the size of metal catalysts and subsequently expose more surface active sites to catalytic reaction. With


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the development of preparation techniques, the size of metal catalysts can be tuned from several nanometers to subnanometer, and even down to single atoms.3 However, the desired catalyst may not be the smallest ones, because the mechanism of a catalytic reaction might change along with the variation of its size. For example, the weakest CO adsorption is found on the Pd clusters of 30-50 atoms.4,5 For larger Pd clusters, the stronger CO adsorption has been explained by the increase of the average metal-metal bond length among the surface atoms and an increasing in the van der Waals attraction. While for smaller clusters, the stronger CO adsorption on Pd is attributed to the increased fractions of the low-coordinated corner and/or edge Pd atoms as well as the up-shifted d-band center. The size-dependent catalytic phenomena are generally observed1,2,6–12, but the change of the catalytic mechanism may remain unclear due to the lack of sufficient experimental evidences. For example, during the selective hydrogenation of 2-methyl-3-butyn-2-ol to 2-methyl-3-butene-2-ol, the catalytic performance in chemoselectivity and activity normalized to total surface atoms was independent of the size of Pd particles ranging from 6 nm to 13 nm.13 In another related study on semi-hydrogenation of alkynes to


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alkenes, the selectivity steeply declined with the increase of the fractions of edge Pd atoms.6 Moreover, detailed information about how conjugated molecules interact with the Pd particles and surfaces have been mapped out by using first-principles methods. For examples, previous DFT calculations already revealed that the vinyl groups tend to adsorb on Pd via a di-σ mode, where the two C atoms bond with two Pd atoms respectively (Pd-C-C-Pd),14 and the phenyl groups prefer to adsorb on the bridge site of Pd (111).15 Inspired by all the above literature, the complex size-dependent relation of the adsorption behaviors of conjugated organic molecules on different sized metal catalysts can finally be revealed at molecular level with the help of DFT calculations. Here we present a systematic computational study on the size dependency of the adsorption of styrene (ST) on Pd clusters, which are involved in many important industrial processes including epoxidation, dehydrogenation and hydrogenation. The DFT calculations were carried out to study the adsorption of ST on various Pd clusters (7 to 73 atoms). Three segments of trends were observed for the change of the ST adsorption energy along with


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the variation of the size of Pd particles, which were rationalized using geometric and electronic analyses, respectively. Finally, a full description of the relationship between the ST adsorption and Pt particle size was mapped out, which will help the design of more efficient nanocatalysts.

II. Methods

The DFT calculations presented in this paper employed the optB88-vdW functional16,17 implemented in the Vienna Ab-initio Simulation Package (VASP).18–20 This functional can account for van der Waals interactions and has shown consistently good agreement with the “averaged” experimental adsorption energies.21 A convergence criterion of 0.02 eVÅ−1 for the maximum final force was used for structural relaxations. Also convergence criteria of 10−5 electrons per unit volume for the charge density and 10−4 eV for the total energy of the system were utilized for all computations. The energy cut-off was set to 400 eV and the plane-wave basis set used the projector augmented wave (PAW) method.22,23 II.1 Pd lattice constant


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The lattice constant of bulk Pd was calculated by fitting the Birch–Murnaghan equation of state to DFT cohesive-energy curves.24–26 For sampling the Brillouin zone, we employed a 16×16×16 Monkhorst–Pack k-point mesh for the primitive cell.27

The

resultant lattice constant of Pd is 0.393 nm, in good agreement with the experimental data of 0.387 nm.28 II.2 Adsorption models

We chose the most stable surface Pd (111) facet to represent an extended surface. A 4×4 supercell was imposed to represent the periodic Pd (111) surface. The substrate was modeled by a slab with 3 atomic layers. The slab and its z-direction image were separated by 20 Å of vacuum, which ensures that the interaction between the adsorbed molecule and the periodic images of the slab is negligible. The adsorbate and the uppermost two metal layers were allowed to relax, while the bottom layers were fixed at their bulk positions. To sample the Brillouin zone of the supercell, we used a 3×3×1 Monkhorst– Pack k-point mesh.


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Figure 1 (a), (b) and (c) are three stable adsorption configurations. Before relaxation, the phenyl groups were on the bridge site which is the most stable site for benzene adsorption, and the vinyl groups replaced H atoms at different positions on benzene. During the relaxation, the position of phenyl groups slightly changed. (d). The adsorption sites on the top of the Pd31 cluster.

We explored the adsorption energy of a single ST by varying its orientation and position on top of the Pd (111) surface, then the structure was relaxed. The initial positions of ST were chosen by using a vinyl group to replace a hydrogen atom on the most stable configuration of benzene (Figure 1a-c).21,29 Figure 1a-c shows the configurations of ST adsorbed on the Pd (111) surface, which have the benzene ring parallel to the substrate. The adsorption energy, Ead, is defined as:

Ead = EAdSys - EPd - EST

(1)


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The subscripts AdSys, Pd, and ST denote the ST-Pd system, the Pd slab or cluster, and ST, respectively. The Pd clusters considered in this paper were shown in Figure 2. Small Pd clusters are usually synthesized on metal oxides, which strongly bind to the clusters to prevent their aggregation and distortion. So the positions of the bottom layer atoms in each cluster model were fixed to approximate the support effect. The clusters were placed in a box of 25×25×25 Å to minimize the interactions between neighboring cell images. In the case of large clusters (Pdn, n ≧ 73), adsorptions on both the edge and central sites were investigated. As big clusters are bulk-like, the initial adsorption configuration was chosen to be the same as that on the slab model. However, in the case of small clusters, especially when the surface atoms are less than seven, the Pd facet cannot bond with all of the C atoms in ST. The possible configurations for Pd16 and Pd31 were carefully investigated and will be discussed later. The initial configurations for Pd39 and Pd49 were chosen according to the most stable configuration of Pd31. The relaxed models were imported into DMol3 for orbital analysis.


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Figure 2. Pd clusters studied in the paper. 16-fcc is the Pd16 cluster with a fcc site on the first layer and 16-hcp is the cluster with a hcp site.

II.3 Bader charge analysis

We used the code developed by Henkelman, Trinkle and their co-workers to calculate the charge on each atom.30–32 The charge transfer was calculated by the Bader charge difference: δ = δM/ST - δad

(2)

δM/ST is the number of electrons in a clean metal cluster or ST, and δad is the number of electrons in the adsorption model. If δ is positive, this atom/group loses electrons in the adsorption process.


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III. Results & Discussion

III.1 Adsorption Configurations

Three adsorption configurations on Pd (111) were considered (Figure 1a-1c). The most stable ST adsorption configuration is slab-bridge-3 on the Pd (111) surface (Figure 1c) and the adsorption energy is -3.221 eV. Both the vinyl and phenyl groups are close to the “best site”, that is, the di-σ mode for alkene and the bridge site for benzene. The average coordination numbers (ACN) of the first layers of Pd73 are close to the bulk Pd value (ACN = 9). Thus, we assume that the most stable adsorption configuration is the same as that on the Pd (111) slab (slab-bridge3). In the case of Pd31, the sites on the surface was shown in Figure 2d. On-top site was omitted because the adsorption of aromatic ring on top site is weak as previously reported.29 Bridge1 is the edge of fcc 3-fold hollow site (the 2nd layer of fcc site is a hollow site) , bridge2 is the edge of hcp 3-fold hollow site (the 2nd layer of hcp site is an on-top site), and bridge3 is the border between the fcc and hcp hollow sites. However, there are only three sites (bridge1，bridge3 and hcp) produce appreciable difference in adsorption


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energy, thus they are discussed in the following parts. The name of each initial configuration is defined by the adsorption site of the center of aromatic ring and the direction of the molecule as shown in Scheme S1. The adsorption energies of the ST on the bridge1 and bridge2 are similar. The adsorption difference at the fcc and hcp sites is also negligible (-3.029 eV for hcp-(30o) and -3.022 eV for fcc-(30o)). Thus, bridge2 and fcc were not considered further in this paper. The isomerization of bridge3 (fcc-bridgehcp or hcp-bridge-fcc) and ST is not a critical factor to affect the adsorption energy, which was tested by rotating the Pd31 cluster to change the isomerization of bridge3, and the results are very close. Thus, the cis-trans isomerization of bridge3 was not considered. Fifteen adsorption configurations was relaxed for Pd31. Some of the relaxed configurations showed big difference from the initial ones. The aromatic ring tends to move to the bridge site and the vinyl group tends to bond with Pd in the di-σ mode. The center of aromatic ring leaves the supposed stable sites and moves to the edge. But we still use the name of initial configurations for convenience. The most stable adsorption configuration is hcp-(0o) (-3.029 eV). Its final relaxed configuration is similar to the bridge3-(0o) (-3.023 eV).


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For the Pd16 cluster, there are only 3 Pd atoms on the first layer. The fcc/hcp hollow sites and bridge sites of the first layer were considered. Ten configurations were relaxed (Scheme S2). For the Pd7 cluster, there are only one Pd atom on the first layer. Although the fcc site on the side of Pd7 may have stronger adsorption, the triangle shaped surface has already been studied in Pd16. Thus only the on-top site was considered. For Pd39 and larger clusters, two types of ST adsorption were considered: one is similar to the most stable configuration on the Pd (111) surface and the other one is similar to the most stable relaxed configuration on the Pd31 cluster. The adsorption of bridge1 is 0.5 eV stronger than that of bridge3, because ST can interact with most edge or corner Pd atoms, which are less coordinated and are easily to form new bonds. ST assumes a parallel adsorption configuration over most cluster and slab models (Figure 3, Scheme S3 and Table 1). For medium Pd nanoparticles (31 to 73 atoms), the adsorption is enhanced drastically with the decrease of size. And for small Pd nanoparticles (< 31 atoms), the adsorption again decreases rapidly with the decrease of size. The angle between the vinyl group and the aromatic ring of ST on slab (128.3o) is close to that of a free ST molecule (127.5o), while Pd clusters cause a large distortion of


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ST, evidenced by the much smaller angle (Table 1). The adsorption heights of ST over Pd7 and Pd16 are larger than those over other clusters, which indicates weaker adsorptions. The strong adsorption energy (more negative) of ST over the slab model corresponds to the smaller distortion of ST. It is worth noting that the adsorption height of ST over the Pd slab is much higher (by about 0.3 Å) than the values over medium sized clusters. It is a result of the definition of the adsorption height, as ST not only distorts in plane but the vinyl group is likely to tilt downward to maximize its interaction with the limited number of available surface Pd atoms (Scheme S1).


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Figure 3. The most stable adsorption configuration for each clusters and their adsorption energies.

Table 1. The adsorption energy and geometric parameters of ST over Pd clusters. # of

7

16-fcc

16-hcp

31

39

49

73

Slab

Ead(eV)a

-1.671

-2.039

-2.588

-3.029

-2.809

-2.757

-2.552

-3.221

LC=C(Å)b

1.40

1.39

1.4

1.45

1.45

1.45

1.43

1.45

Height(Å)c

2.02

1.87

1.75

1.40

1.44

1.44

1.42

1.74

Angle(o)d

126.5

124.1

123.6

122.3

123.1

121.8

122.8

128.3

atoms

Notes: a. The adsorption energy of ST over Pd clusters. b. The C-C bond length in the vinyl group. c. The adsorption height is the average distance between surface Pd atoms and carbon atoms in the z-direction. d. The angle is defined as the angle between the vinyl group and the aromatic ring (labeled in Scheme S3). III.2 Geometric effect

Adsorption configuration affects the adsorption energy, especially for small clusters. If the first layer of a cluster is close-packed hexagon shape, three types of Pd atoms can be identified according to their coordination number. The corner (c), edge (e), and (111) plane-like (p) Pd atoms have coordination numbers of 6, 7, and 9, respectively (Scheme S4). A ST molecule can be partitioned into the aromatic ring (a) and the vinyl group (v),


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whose bindings to the surface Pd atoms in theory have six distinct combinations and are labeled as ac, ae, ap, vc, ve and vp. The ST adsorption energy can be approximately expanded as a linear combination of the six types of bindings: 𝐸ad = 𝐸0 + ∑

i = a, v; 𝑏ij𝑁ij j = c, e, p

(3)

Ead is the ST adsorption energy. Nij is the number of each type of bindings and bij refers to the contribution of each binding. E0 is a constant. E0 can be regard as the interaction energy between ST and Pd surface, and the bijNij part is a correction term. The detailed method to calculate Nij is to count how many j-type-Pd are bonded with i-type group in ST. For example, there are only 3 corner Pd atoms on the first layer of Pd16 cluster (Scheme S2) that bond with the aromatic ring in Pd16-hcp-(30o)-r model. Thus Nac equals to 3. However, in Pd16-hcp-(0o)-r, the top 3 corner Pd atoms not only bond with the aromatic ring but also vinyl group. One of the three Pd atoms is bonded with one C atom in aromatic ring and two C atoms in vinyl group. Thus, Nvc = 2/3 ≈ 0.7, and Nac = 2 + 1/3 ≈ 2.3. This method was adapted to classify the chemical bonds in all the models.


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ST is fully bonded with the Pd surface in all of the models we considered (from Pd31 to Pd73). For the six types of bindings, we only chose four of them (𝑁𝑎𝑐,𝑁𝑎𝑒, 𝑁𝑎𝑝, 𝑎𝑛𝑑 𝑁𝑣𝑐) as linearly independent variables to run the linear regression. Because Nve shows a linear correlation coefficient of -0.86 with Nac, and Nvp shows a significant linear correlation of 0.93 with Nap. Also, the sample size of configurations that contains distinguished Nve and

Nvp are small. Thus, Nve and Nvp were removed from this fitting. Small clusters Pdn (n < 31) were excluded from the fitting set, as they are too small to have the three well-defined types of Pd atoms (detailed later). E0 and other parameters (bij) were all calculated by a Least Squares Multivariate Linear Regression mothed.33 The result is as follows: 𝐸ad = ―2.392 ― 0.114 × 𝑁ac ―0.09 × 𝑁ae ―0.04 × 𝑁ap ―0.126 × 𝑁vc

(4)

The correlation coefficient is 0.90. The adsorption energy and the number of bonding approximated linear relation. E0 = -2.392 eV implies that the attractive interaction between ST and the cluster is always strong. All the bij's are negative, meaning the attractive interaction prevails for all the binding types. The bindings between the aromatic ring/vinyl group to the corner Pd atoms (Nac, Nae and Nvc) contribute most of the adsorption energy. And the ternary contribution comes from the interactions between ST and the plane Pd


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(Nap). In other words, ST chooses to bind to the corner or edge Pd atoms first, through its aromatic ring or vinyl group. The adsorption energies of only a few special configurations like Pd31-fcc-(30o) and Pd31-bridge1-(60o) were poorly fitted because of the angle distortion of the vinyl group, a factor not included in the fitting. This may change the adsorption height and the bond length of C=C or C-Pd bonds, leading to a change of adsorption energy. Finally, the adsorption energy becomes stronger (more exothermic) as the number of bindings (Nij's) between ST and Pd clusters increases. Another important factor that leads to mistake in this regression is E0. It can be regarded as a constant number only in a small range of cluster size. Because the long-range force will change considerably will the increase of size. Also, the ACNs of the atoms on the top layer of Pd7 and Pd16 are even smaller than that of corner site Pd described in Figure 2d. Thus this regression cannot simply be extended to the extremely big Pd particle (Slab model) or extremely small clusters (Pdn with n < 31). However, we can still use the chemical bond-contributed part of equation (4) to analyze smaller Pd clusters. With the decrease of the Pd size, there are more corner sites or edge sites, which lead to stronger adsorption. However, ST cannot fully bond with small clusters (n < 31). Nij's decrease


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rapidly in small clusters. Thus its adsorption become weaker compared with larger clusters because of the reduction of C-Pd bonds. In line with our results, experiments and DFT simulations have shown that the sub-nanometer Pd clusters on CeO2 exhibited smaller adsorption constant compared with large nanoparticle.34 Notice that this is a rough model which ignores other less important parameters and is based on a limited number of computed configurations. The value of each parameter is meaningless, as the contribution of each atom changes along with the Pd-C distance. Every Pd-C bond is different in different adsorption configurations. However, if there are enough fully relaxed adsorption configurations, the averaged contribution of each factor can be obtained. Thus, some empirical rules may be derived. To sum up, first, the corner sites of clusters make the most contributions to the adsorption. Second, the adsorption becomes stronger with the increase of the chemical bond number between the adsorbate and the substrate. It is well-known that icosahedron and other-shaped clusters are often used to represent Pd nanoclusters35-37 and for clusters containing the same number of atoms but with different shapes, the adsorption properties are usually different. To have a concrete


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comparison, we calculated the adsorption of ST on a midsized icosahedron cluster Pd55 and a small "diamond-like" cluster Pd7. The Pd55 cluster model has a surface area (7 surface Pd atoms, Scheme S5) similar to our cluster model of Pd31 (7 surface Pd atoms, Figure 2). ST can lay flat and fully bond with both surfaces. However, due to their different shapes (i.e., the coordination number of surface Pd atoms), the adsorption of ST on Pd55 (Ead = -3.4 eV) is stronger than on Pd31 (Ead = -3.0 eV). Due to the same reason, for the irregular-shaped small cluster Pd7, the adsorption of ST on the icosahedron model (Scheme S6, CN=5, Ead = -1.2 eV) is weaker than on our model (Figure 2, CN=3, Ead = -1.7 eV).

However, limited by the computational resource, we could not finish calculating bigger icosahedron Pd clusters to make a complete comparison. It is probable that the variation range of the ST adsorption energy over icosahedron or other-shaped Pd clusters may be wider or narrower than that of our "chopped"-slab models. Nevertheless, because unsaturated surface atoms (i.e., corner and edge atoms) bind more strongly to adsorbates, the strongest adsorption between adsorbent and adsorbate must utilize as


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many corner and edge atoms as possible. This means that the exact number of atoms in the clusters near the dip of the cluster size-vs-adsorption energy plot (Figure 3) may be different according to different cluster models. Yet the overall trend should always remain.

III.3 Electronic effect

III.3.1 Electronic donation

The geometric model can quantitatively explain the adsorption energy difference for different configurations. However, it fails to predict the change of adsorption energy for the similar configurations on different clusters.

For example, the most stable

configurations of ST over Pd39 and Pd49 are the same (Nijs are the same), but they have different adsorption energies (-2.809 vs. -2.757 eV). Moreover, the adsorption of ST over Pd16-fcc and Pd16-hcp affords two nearly identical configurations but with distinct adsorption energies (-2.039 and -2.588 eV). This issue can be resolved by considering the variation of the electronic structure of different metal clusters. To our knowledge, there is no systemic and thorough mechanism research on ST adsorption. But the adsorption of some similar molecules were well studied. Zhao et al.


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studied the adsorption of toluene by in situ FT-IR spectra.38 There were red shifts of the C=C stretching vibration peak, whenever toluene was adsorbed on Brønsted acid or Lewis acid, which were caused by a decrease in the electric density of toluene. Thus, toluene was adsorbed on the metal cation sites by π complexation. Raybaud et al. studied the adsorption of olefins on Pt(111) and Pd(111) by the analysis of work function and PDOS.39 They found a strong mixing of both the molecular π and π* orbitals with the metal

d states. The work function of metal surface became more negative after the adsorption of ethylene, acetylene or benzene, and the changes of work function were related with the thermal stability of the adsorbates. Therefore, they thought that the adsorption was dominated by the electron donation from molecule to the surface rather than the metalmolecule electron back-donation effect.39 Belelli et al. also demonstrated that the electronic charge transfer from butane molecule was higher than the back-donation when butane was adsorbed on metal surface.40 Similar conclusion came from Nikolaev et al.41 They considered the electron rich alkenes as Lewis base which preferred to adsorb on electron acceptors (Lewis acid). Experiments on AuNi alloy catalysts also proved that partially positive-charged Au (as the electron acceptor) was more favorable than zero-


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charged Au for the adsorption of alkenes.41,42 However, Jiang et al. studied the adsorption of olefins on silver salt cluster supported on silica, and they found that the electrons were partially transferred from Ag to C2H4/C3H6 upon adsorption.43 The positively charged Ag decreased the adsorption strength. In our situation, if the adsorption is dominated by the electronic donation from ST, there should be a relationship between the adsorption energy and the charge transfer. We performed Bader charge analysis to calculate the charge of every atom before and after adsorption. Then, we obtain the charge transfer of each cluster as shown in Figure 4a. It shows that the electronic transfer from ST to Pd decreases with the decrease of cluster size (Pdn, n>7). And the direction of charge transfer reversed in the case of Pd7 cluster. This can be explained by the electron accepting ability of Pd clusters. The electron accepting ability can be evaluated by the concentration of holes in the metal’s d-orbitals. The electronic configuration is close to 4d105s0 in a single Pd atom. However, partial orbital hybridization occurs in bulk Pd to form Pd-Pd bonds. It leads to electronic filling in 5s- or 5p-orbitals and holes in delocalized d-orbitals. The more d-band holes, the more negative the d-band center will be. The Pd d-band centers are shown in Figure 4b. Large


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clusters have more negative d-band centers and the Pd (111) slab has the lowest d-band center. The small sized clusters with low average coordination numbers show fewer holes in the d-band and have a higher d-band center (Figure 4b). Since most of the Pd clusters have much lower d-band centers compared with the HOMO of ST, the π electrons in ST tends to move to the d-band holes in Pdn clusters (n>7), consistent with previous report. The d-band center of Pd7 is higher than the HOMO of ST. Therefore, Pd7 cluster will donate electrons to the π orbital of ST, similar with the situation of olefins adsorbed on Ag salt cluster.43 The relative position of metal d-band center and HOMO of ST validate the charge transfer perfectly. However, the size dependent adsorption energy has no obvious correlation with the charge transfer. Also, it cannot explain the difference of contribution of different sites.


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Figure 4. (a). Charge transfer from ST to Pd clusters calculated by Bader charge analysis. n is the number of atoms in a cluster. The negative value represents that the electrons in ST are transferred into Pd clusters. (b). Fermi level and d-band center of Pd clusters.

III.3.2 Back-donation effect

The charge transfers from ST to Pdn cluster (n>7) indicate that the electronic donation from ST is larger than the back-donation from Pd. However, the greater contribution to the charge transfer doesn’t imply the greater contribution to adsorption energy. The backdonation effect may be undervalued. A classical model that describes the back-donation effect is the Dewar-Chatt-Duncanson model.44,45 In this model, the π electrons from olefin is donated to the metal d orbital and some electrons from a different filled d-orbital donate into the empty π* antibonding orbital. Both of them benefit the adsorption. One possible reason for the decreasing trend of adsorption energy with the negative shifting of d-bandcenter is that the negative shifting of d-band center leads to more energy difference between metal d orbitals and the π* orbitals of ST, which weakens the back-donation (for Pdn clusters, n>16).


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Conrad et al. reported another mechanism that the back-donation from metal d orbitals to π* orbitals of ST would weaken the metallic bonds at the surface and the repulsive Pauli interactions led to a strong surface distortion.46 The moving of a Pd atom with high coordination number may cost more deformation energy than that of a low-coordinated Pd atom. Therefore, low-coordinated Pd clusters can be distorted with a small cost of energy, and lead to high adsorption energy. Additionally, the distortion of low-coordinated Pd clusters makes it more convenient to adjust the position and angle of d orbital so that it can be better overlapped with the π* orbital of ST. This can be observed in the orbital scheme. Figure 5 is the PDOS of ST adsorbed on Pd7 and Pd31. The first peak below Fermi level is the hybridization between metal d-level and the π* orbital on C8 of ST (the numeric identifier of C atoms is in the inset picture in Figure 5). Pd7 cluster showed a more negative hybridization (-4.93 eV) of back-donation than Pd31 cluster (-3.37 eV). Thus, low-coordinated Pd contributes more back-donation and lead to a more stable adsorption. This is consistent with the conclusion deduced by the mathematical model of equation (4) that Pd atoms in corner site contribute more to the adsorption.


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Figure 5. Top: the PDOS of ST adsorbed on Pd7. Bottom: the PDOS of ST adsorbed on Pd31. Red line is the p-orbital of C8. Blue line is the d orbital of the Pd atom bonded with C8. The two insets are the orbital schemes corresponding to the specified peaks in the PDOS figure.

IV.Conclusions


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In summary, the relationship between the adsorption energy of ST on Pd clusters and the particle size features an inversed “volcano curve”. Pd31 cluster exhibits the strongest ST adsorption energy. The adsorption energies don’t have a monotone relationship with the extent of charge transfer between the adsorbate and the cluster. For Pdn clusters (n>16), with the increasing size, their d-band centers downshift (become more negative) and the number of low-coordinated Pd atoms also decrease, which leads to a weakened metal-to-molecule electron back-donation. Thus, larger nanoparticles have weaker adsorption (n>16). However, when the surface of Pd cluster becomes too small (clusters between Pd7 and Pd16), the ST molecular cannot fully bond with the cluster. The adsorption strength decreases with the decreasing of the number of chemical bonds. In comparison, Pd slabs show the most stable adsorption, which may due to an increasing of van der Waals interaction, a decrease of distortion and it is a donation dominated mechanism (different from the back-donation dominated mechanism of Pd cluster). This will be discussed in details in our upcoming study. Supporting Information.


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The adsorption configurations of each clusters and their naming rules; The adsorption energy and some associated information AUTHOR INFORMATION

Corresponding Author * [email protected]; [email protected].

ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (No.21477096 and 21872109), State Key Laboratory for Mechanical Behavior of Materials (20182005) and the National 1000-Plan program. Y. Qu is also supported by the Cyrus Tang Foundation through Tang Scholar program. C.W. acknowledges support from the Fundamental Research Funds for the Central Universities and the World-Class Universities (Disciplines) and the Characteristic Development Guidance Funds for the Central Universities. The hardware and technical support of these calculations were supported by National Supercomputing Center in Tianjin and the Xi’an Jiaotong University High Performance Computing Center.


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TOC Graphic


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Size Dependent Adsorption of Styrene on Pd Clusters: A DFT Study

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