H2 Saturation on Palladium Clusters - The Journal of Physical

Article pubs.acs.org/JPCA

H2 Saturation on Palladium Clusters Adam W. Pelzer,*,†,‡,§ Julius Jellinek,*,‡ and Koblar A. Jackson*,§ †

Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, United States Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States § Department of Physics and Science of Advanced Materials Ph.D. Program, Central Michigan University, Mt. Pleasant, Michigan 48859, United States ‡

S Supporting Information *

ABSTRACT: The interaction of PdN clusters (N = 2, 3, 4, 7, and 13) with multiple H2 adsorbate molecules is investigated using density functional theory with the hybrid PBE0 functional. The optimal structure for each PdNH2(L) complex is determined systematically via a sequential addition of H2 units. The adsorption energy for each successive H2 addition is computed to determine the maximum number of molecules that can be stably added to a PdN at T = 0 K. The Gibbs free energy is then used to determine the saturation coverage at finite temperature. For N = 2, 3, and 4, a single H2 is found to dissociate, and up to two additional molecular H2 units per Pd atom can bind stably to the clusters at 0 K. At 300 K, one H2 unit dissociates, and only one additional H2 molecular unit per Pd atom is stably bound. For N = 7 and T = 0 K, two H2 units dissociate, and 11 additional H2 units bind molecularly. At 300 K, two units dissociate, and eight are bound molecularly. For N = 3, 4, and 7, we find that an additional H2 unit may dissociate if the underlying cluster structure rearranges. Eight H2 units dissociate on Pd13 at 0 K. At least one additional H2 binds molecularly at 0 K, but none bind at 300 K. This suggests that only dissociated H2 units will stably bind to larger Pd particles at room temperature. The influence of molecularly adsorbed H2 units on the migration of dissociated H atoms is investigated in a preliminary way. Both barrier heights and the relative stability of local minima of Pd4H2(L) are found to be affected by the degree of molecular H2 coverage. found to accurately reproduce available experimental data.14 We found that H2 dissociates with little or no energy barrier on PdN and that the dissociated H atoms can migrate across the surface of the Pd core with small energy barriers. In this paper, we present the results of new calculations that explore the interaction of multiple H2 adsorbate molecules on PdN. Such scenarios are clearly relevant for clusters serving as catalysts. We are interested in a number of questions: How many H2 molecules can stably bind to a PdN cluster? To what extent does the saturation coverage depend on temperature? What is the nature of the binding of multiple H2 molecules? For example, how many molecules undergo dissociative adsorption and how many molecular adsorption? How do the properties of the nanoparticle change from the pristine case to the case of saturation coverage? Previous investigations of reactions of Pd clusters with multiple H2 molecules have primarily focused on a limited number of H2 molecules reacting with few-atom clusters15,16 or full saturation of a single cluster packing.17 Zhou and co-

1. INTRODUCTION Nanoparticle-based catalysis is an active area of research.1−4 The use of nanoparticles as catalysts is interesting and important for several reasons. First, because most atoms in a nanoparticle, especially a smaller one, are at or very near to the particle surface where they can participate in chemical reactions, nanoparticle catalysts are expected to be very atom efficient. This is especially important for catalysts involving precious metals such as Pd, Pt, Rh, and so forth. In addition, at the small size limit, the reactivity of metal atom clusters can vary significantly with cluster size. Adding or removing even a few atoms can change the chemical properties of clusters dramatically.1,5,6 Related to this is the fact that metals that have no catalytic function at the bulk size limit can become catalytically active at the cluster size limit.7,8 This has motivated an active search for clusters of abundant metals that can replace precious metals in catalytic applications.9,10 Motivated by experiments that demonstrated the direct synthesis of H2O2 from H2 and O2 over Au, Pd, and AuPd nanoparticle catalysts,11−13 we recently investigated the interaction of a single H2 molecule with a PdN cluster as a function of cluster size using a computational approach based on first-principles density functional theory (DFT) that was © 2015 American Chemical Society

Received: December 18, 2014 Revised: March 18, 2015 Published: March 18, 2015 3594

DOI: 10.1021/jp512643a J. Phys. Chem. A 2015, 119, 3594−3603

Article

The Journal of Physical Chemistry A

Figure 1. Selected partially and fully saturated structures. The labeling, PdN(H)2D(H2)M, indicates the Pd cluster size (N), the number of H2 units dissociately adsorbed (D), and the number molecularly adsorbed (M). Properties of these complexes are given in Table 1. Geometries for all clusters and levels of saturation can be found in the Supporting Information.

dissociative) as a function of the cluster size N. We therefore set out to find the lowest-energy arrangement of PdN(H)2(L) complexes (where (L) is an integer indicating the total number of H2 molecules adsorbed either dissociatively or molecularly) for several cluster sizes (N = 2, 3, 4, 7, and 13) and including as many H2 molecules as possible. We define the type of adsorption by the H−H distance in the relaxed adsorption complex. Molecular adsorption results in a H−H separation between 0.8 and 0.85 Å, whereas in dissociative adsorption, the H atoms are separated by at least 1.9 Å. For each N, we began with the optimal Pd N (H) 2 configuration found in our recent study of H2 addition onto PdN.14 To that structure, we added a H2 molecule in an available (i.e., not occupied by a H atom or H2 molecule) atop-, edge-, or face-bonding site, starting the H2 at a distance of

workers performed GGA level calculations on a range of cluster sizes to determine the maximal number of dissociative adsoprtions possible for PdN clusters for N = 2−9.18 As will be discussed below, while we are able to reproduce their results, we find that the structures that they report correspond to local minima. The energetically more preferred cases for the same number of hydrogen atoms correspond to mixed dissociative and molecular adsorption. In the next section, we outline the computational methodology. In section 3, we present and discuss the results. Our summary remarks are given in section 4.

2. COMPUTATIONAL METHODOLOGY The primary purpose of this work is to determine the saturation coverage of Pd N clusters with H2 (molecular and/or 3595


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Figure 2. Pathways to the final dissociative adsorption (solid line) for PdN clusters, N = 3 (A), 4 (B), and 7 (C). The structures for minima and saddle points are shown. For comparison, pathways for molecular adsorption of the incident H2 are also shown for cases where molecular adsorption does not lie on the MEP leading to dissociative adsorption (dashed line).

used to evaluate the amount of charge transfer associated with each H2 addition. The nudged elastic band (NEB) method23 was utilized to obtain the minimum-energy paths between the equilibrium configurations of the cluster−hydrogen complex corresponding to minima of the potential energy surface and the corresponding transition-state structures and energies.

approximately 2 Å from the center of the atop, edge, or face. At this separation, the interaction between the H2 and the cluster is very weak. We then relaxed the new system to the closest minimum-energy geometry using a gradient-based relaxation algorithm. Note that essentially the same approach was used to find the optimal PdN(H)2 complexes reported in ref 14. This process was repeated systematically for multiple starting orientations of the H2 and for all atop, edge, and face sites. As discussed below, in some cases, the relaxation process led to dissociation of H2. In other cases, the H2 adsorbate remained intact, attaching to the cluster as a molecule. Comparing the energies of all of the resulting structures, we obtained the lowest-energy configuration for PdN(H)4. Repeating this procedure and adding the next H2 molecule to all of the vacant sites of the most stable configuration of PdN(H)4, we arrived at the most stable configuration of PdN(H)6 and so on. After the optimal structure was found for PdN(H)2(L), we computed its adsorption energy as Eads(L) = E(PdN (H)(2L − 2)) + E(H 2) − E(PdN H 2L)

3. RESULTS AND DISCUSSION A. Structures and Properties of PdNH2(L). A compendium of lowest-energy configurations of PdN(H)2(L) complexes for N = 2, 3, 4, 7, and 13 and different values of (L) is shown in Figure 1. The complexes are labeled PdN(H)2D(H2)M to indicate the size of Pd clusters and the number of H2 units added to them either dissociatively (D) or molecularly (M), where (L) = M + D. We did not consider any system with an odd number of H atoms as our motivation is to model the interaction of Pd clusters with a gas of H2 molecules. For each cluster size, we show the most stable form of the PdN(H)2 complex14 as well as the most stable conformations of all of the PdN(H)2D complexes that feature dissociative adsorption of all of the added H2 molecules for up to N = 7. For N = 13, only four of the eight dissociated Pd13(H)2D are shown. The figure also displays the most stable forms of complexes with additional H2 units adsorbed on the clusters molecularly. Coordinates for all PdN(H)2D(H2)M complexes are given in the Supporting Information. For N = 2, 3, 4, and 7, the largest complexes shown are the fully saturated structures (an attempt to add another H2 unit to them results in a negative binding energy at 0 K). For N = 13, the Pd13(H)16(H2) complex is the first that accommodates a molecularly adsorbed H2 in addition to eight H2 units that are adsorbed dissociatively The computational demands prevented us from investigating larger complexes. For N = 3, 4, and 7, we found two energetically competitive pathways to saturation. Both start with the same PdNH2D

(1)

where H2(L) denotes 2(L) hydrogens adsorbed on PdN molecularly and/or dissociatively. Eads(L) > 0 indicates that the PdN(H)2(L) complex is more stable than the free H2 molecule and PdN(H)2(L)−2 complex. All calculations were based on DFT using the hybrid PBE0 exchange−correlation functional19 as implemented in the NWChem software package.20 The Stuttgart 18 electron ccpVDZ-PP ((8s,7p,6d,1f) → [4s,4p,3d,1f]) basis set with a 28 electron effective core potential (ECP) was used for the Pd atoms.21 A strict SCF convergence criterion of 1 × 10−7H was used for the total energy, and the convergence criteria for geometry optimization were set to default values. Normal-mode analysis was carried out for all relaxed structures to ensure that they correspond to minima of the corresponding potential energy surface. The natural bond orbital (NBO) analysis22 was 3596


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Figure 3. Adsorption energy of each H2 (Eads), the sum of all charges on Pd atoms (Q(total)Pd), dissociated H atoms (Q(total)Hdiss), and molecularly adsorbed H2 molecules (Q(total)H2, and the average Pd−Pd bond length (⟨rPd−Pd⟩) for each cluster size versus the number of H2 molecules adsorbed (L) for the Pd2−Pd4 clusters. The label A indicates the case where the underlying PdN cluster maintains the same structure throughout, and B indicates the case where the PdN cluster distorts to accommodate an additional dissociative adsorption.

conformation, with D = 1 for N = 3 and 4 and D = 2 for N = 7. However, whereas along the first pathway the structure of the underlying PdN cluster framework remains intact, along the second pathway, it changes as H2 units are added to it. This change involves breaking of a Pd−Pd bond, which results in a larger number (by one) of H2 units that adsorb dissociatively. Consider as an example the case of N = 3. Pd3(H)2 is a triangular Pd3 with two H atoms attached to it on the opposite sides of the triangular face. Addition of the second H2 molecule leads to a molecular adsorption (conformation Pd3(H)2 (H2) in Figure 1) or to a second dissociative adsorption accompanied by opening of the Pd3 triangle to form a bent chain (conformation Pd3(H)4 in Figure 1). Addition of further H2 units leads to molecular adsorption on both the intact and the distorted Pd3 until saturation is reached at (L) = 7. The reader can follow the two pathways to saturation for the cases of N = 4 and 7 by examining Figure 1. Whereas for N = 7 as for N = 3 the two pathways lead to the same level of saturation (Pd7(H)4 (H2)11 versus Pd7(H)6 (H2)10), for N = 4, the resulting saturation levels (Pd4(H)2(H2)8 versus Pd4(H)4(H2)6) are different. In Figure 2, we show the minimum-energy pathways (MEPs) involved in the formation of Pd3(H)4 (panel A), Pd4(H)4 (panel B), and Pd7(H)6 (panel C), determined via NEB calculations connecting the separated PdNH2D + H2 starting points and the local minimum-energy structures for the PdN(H)2(D+1) structures. Dashed lines are used to show the formation of the Pd3(H)2(H2) and Pd7(H)4(H2) structures from the respective separated starting points. In the case of Pd4(H)2(H2), the minimum corresponding to molecular adsorption is on the MEP between separate reactants and the Pd4(H)4 complex; therefore, no additional dashed line is

needed. In the case of the Pd3 cluster, it is seen that a molecular adsorption onto Pd 3 (H) 2 forms the minimum-energy Pd3(H)2(H2) structure shown in Figure 1 with no energy barrier. The adsorption is strictly downhill in energy. However, a second structure can also form in which one of the dissociated H atoms moves to an edge site. The pathway from this structure to the Pd3(H)4 structure leads over an intermediate state in which the underlying triangular Pd3 structure opens into a bent chain structure. The highest-energy point along this path is only 0.04 eV above the separated limit. The relaxed Pd3(H)4 structure is approximately 0.1 eV lower in energy than Pd3(H)2(H2). In a similar way, a molecular adsorption of H2 onto Pd4(H)2 forms the Pd4(H)2(H2) structure, and this is connected via a few intermediate steps to Pd4(H)4 and a small overall energy barrier (0.03 eV) to the Pd4(H)4 structure in which both H2 units are dissociated, as seen in panel B of Figure 2. Structures Pd4(H)2(H2) and Pd4(H)4 are nearly degenerate. In ref 18, the authors found a Pd4(H)8 structure in which all four H2 molecules adsorb dissociatively. We found this metastable minimum as well, but this relaxed geometry placed two dissociated H atoms on an atop site. We found no cases where such a feature was energetically competitive. Further, a small disturbance of this geometry relaxed to our distorted cluster Pd4(H)4(H2)2. Within our PBE0 model, we found the undistorted Pd4(H)8 structure seen in ref 18 to be more than 1 eV higher in energy than the comparable undistorted cluster Pd4(H)2(H2)3 seen in Figure 1. Finally, the bottom panel in Figure 2 shows how a molecular adsorption onto Pd7(H)4 can lead over a larger energy barrier (0.34 eV) to Pd7(H)6. In this complex, the capped octahedral framework of the Pd7 cluster is altered into a more open 3597


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Figure 4. Same as Figure 3 but for the Pd7 and Pd13 complexes. Note that because the Pd13 cluster accepts a larger number of dissociatively adsorbed H2 molecules, the values are referenced to a different (right-hand side) scale than that for the Pd7 complexes.

Pd distance in the complex, ⟨rPd−Pd⟩. From right to left, we show the various clusters sizes (N). The data are also given in tabular form in Table 1. The trends in Eads(L) shown in the first column of Figure 3 clearly show the transition from dissociative to molecular adsorption in the PdN(H)2D(H2)M complexes because Eads(L) is generally much larger for dissociative than for molecular adsorption. This is clearly seen in the curves for the cases where the underlying PdN structure is preserved, where there is a clear drop in Eads(L) when the additions switch from dissociative to molecular. There is a slow decrease in Eads(L) as additional H2 units are added via molecular adsorption. The situation is slightly more complicated when the PdN structure distorts to accept an additional dissociative adsorption. In this case, Eads(L) for the last dissociative adsorption is much closer to that of the first molecular adsorption energy. This is because, as mentioned above, the larger value expected for Eads(L) for dissociation is partially offset by the energy cost of distorting the Pd framework. The steady drop in Eads(L) for sequential molecular additions is also seen for these complexes. It is interesting to track the charge transfer between the PdN framework and the adsorbed H2 units. In all cases, dissociative adsorption is accompanied by a transfer of electron charge from PdN to the H atoms, leaving the PdN core with a net positive charge. For the first dissociation, the transfer is 0.26, 0.25, 0.26, and 0.22 e for N = 2, 3, 4, and 13, respectively. The first dissociation on N = 7 transfers a larger amount of charge, 0.39 e. The second dissociation on Pd3(H)4 and Pd4(H)4 transfers an additional 0.16 and 0.28 e, respectively, giving an average transfer per dissociation of 0.21 and 0.27 e, respectively. On N = 7, the second dissociation transfers only an additional 0.05 e, so that the total net charge transferred per H2 unit is 0.22 e, more in line with the charge transfers seen for the other

framework consisting of a quasi-planar 6 atom unit, capped by a Pd atom over the central triangle. The Pd7(H)6 structure is 0.3 eV lower in total energy than Pd7(H)4(H2). In all three of the cases described above and shown in Figure 2, the energy cost of distorting the underlying PdN framework to reduce the number of Pd−Pd bonds is compensated for by making additional Pd−H bonds via the additional H 2 dissociation. The energy differences and barrier heights are such that one could expect to see all of the configurations under experimental conditions. The structures shown in Figure 1 have a number of common characteristics. Dissociated H atoms preferentially occupy three-fold face sites and two-fold edge sites. In no case do we find a dissociated atom attached to a one-fold atop site. By contrast, molecularly adsorbed H2 units only attach to atop sites. All atop sites are occupied by at least one H2 unit before a second molecular adsorption occurs at any site. Fully saturated PdN(H)2D(H2)M complexes feature at most two molecularly adsorbed H2 units attached to any surface Pd atom. Successive H2 additions tend to occur at sites that are well-separated from previous additions, although it is not the case that the most stable binding sites for the 2(H) (atoms or molecule) are the ones that place them maximally away from previous adsorbates. At saturation, 2N − 1 ≤ (M + D) ≤ 2N + 1 for N = 2−7. We were unable to determine the fully saturated Pd13(H)2D(H2)M complex due to the computational demands of calculations involving the larger clusters. In Figures 3 and 4, we show the evolution of physical and chemical properties of the PdN(H)2D(H2)M clusters as the maximum number of adsorbates, L, increases. From top to bottom in the figures, we show the H2 adsorption energy, Eads(L), the total net charge on the Pd atoms, QPd, the total net charge on the dissociated H atoms, Qdiss, the total net charge on the molecularly adsorbed H2 units, QH2, and the average Pd− 3598


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The Journal of Physical Chemistry A Table 1. Properties of Partial and Fully Saturated Structuresa N #H2

Eads (eV)

Pd2(H)2 Pd2(H)2(H2) Pd2(H)2(H2)2 Pd2(H)2(H2)3 Pd2(H)2(H2)4 sum Pd3(H)2 Pd3(H)2(H2) Pd3(H)2(H2)2 Pd3(H)2(H2)3 Pd3(H)2(H2)4 Pd3(H)2(H2)5 Pd3(H)2(H2)6 sum Pd3(H)2 Pd3(H)4 Pd3(H)4(H2) Pd3(H)4(H2)2 Pd3(H)4(H2)3 Pd3(H)4(H2)4 Pd3(H)4(H2)5 sum Pd4(H)2 Pd4(H)2(H2) Pd4(H)2(H2)2 Pd4(H)2(H2)3 Pd4(H)2(H2)4 Pd4(H)2(H2)5 Pd4(H)2(H2)6 Pd4(H)2(H2)7 Pd4(H)2(H2)8 sum Pd4(H)2 Pd4(H)4 Pd4(H)4(H2) Pd4(H)4(H2)2 Pd4(H)4(H2)3 Pd4(H)4(H2)4 Pd4(H)4(H2)5 Pd4(H)4(H2)6 sum

1.72 0.42 0.45 0.23 0.25 3.07 1.68 0.44 0.40 0.43 0.30 0.31 0.04 3.60 1.68 0.55 0.42 0.43 0.25 0.24 0.12 3.69 0.94 0.47 0.47 0.39 0.36 0.25 0.22 0.07 0.12 3.29 0.94 0.47 0.54 0.38 0.38 0.35 0.21 0.13 3.40

Mi → Mf

QPd (e)

QH (e)

3 1 1 1 1

→ → → → →

1 1 1 1 1

0.26 0.21 0.14 0.15 0.18

−0.26 −0.24 −0.22 −0.25 −0.30

3 1 1 1 1 1 1

→ → → → → → →

1 1 1 1 1 1 1

0.25 0.20 0.16 0.10 0.19 0.24 0.26

−0.25 −0.22 −0.22 −0.21 −0.21 −0.29 −0.30

3 1 1 1 1 1 1

→ → → → → → →

1 1 1 1 1 1 1

0.25 0.41 0.36 0.31 0.30 0.30 0.33

−0.25 −0.41 −0.40 −0.40 −0.43 −0.47 −0.53

3 1 1 1 1 1 1 1 1

→ → → → → → → → →

1 1 1 1 1 1 1 1 1

0.26 0.25 0.24 0.20 0.15 0.17 0.28 0.24 0.20

−0.26 −0.25 −0.27 −0.26 −0.26 −0.23 −0.26 −0.28 −0.27

3 1 1 1 1 1 1 1

→ → → → → → → →

1 1 1 1 1 1 1 1

0.26 0.54 0.44 0.42 0.38 0.34 0.42 0.43

−0.26 −0.54 −0.45 −0.48 −0.51 −0.52 −0.56 −0.58

⟨rPd−Pd⟩ Å

N #H2

Eads (eV)

0.03 0.08 0.11 0.12

2.70 2.71 2.72 2.75 2.79

0.02 0.06 0.11 0.02 0.05 0.04

2.68 2.69 2.74 2.76 2.76 2.80 2.84

0.05 0.09 0.14 0.17 0.20

2.68 2.73 2.74 2.75 2.77 2.79 2.83

0.03 0.06 0.11 0.06 −0.03 0.04 0.08

2.76 2.75 2.76 2.76 2.80 2.81 2.83 2.84 2.84

0.02 0.06 0.13 0.18 0.15 0.15

2.76 2.78 2.76 2.78 2.81 2.83 2.86 2.89

Pd7(H)2 Pd7(H)4 Pd7(H)4(H2) Pd7(H)4(H2)2 Pd7(H)4(H2)3 Pd7(H)4(H2)4 Pd7(H)4(H2)5 Pd7(H)4(H2)6 Pd7(H)4(H2)7 Pd7(H)4(H2)8 Pd7(H)4(H2)9 Pd7(H)4(H2)10 Pd7(H)4(H2)11 sum Pd7(H)2 Pd7(H)4 Pd7(H)6 Pd7(H)6(H2) Pd7(H)6(H2)2 Pd7(H)6(H2)3 Pd7(H)6(H2)4 Pd7(H)6(H2)5 Pd7(H)6(H2)6 Pd7(H)6(H2)7 Pd7(H)6(H2)8 Pd7(H)6(H2)9 Pd7(H)6(H2)10 sum Pd13(H)2 Pd13(H)4 Pd13(H)6 Pd13(H)8 Pd13(H)10 Pd13(H)12 Pd13(H)14 Pd13(H)16 Pd13(H)16(H2) sum

1.26 1.05 0.51 0.47 0.40 0.34 0.30 0.30 0.29 0.17 0.18 0.09 0.05 5.41 1.26 1.05 0.79 0.66 0.33 0.32 0.30 0.32 0.25 0.23 0.15 0.13 0.12 5.91 0.87 0.98 0.87 0.72 1.05 0.79 0.87 0.90 0.20 7.25

QH2 (e)

Mi → Mf

QPd (e)

QH (e)

3 3 1 1 1 1 1 1 1 1 1 1 1

→ → → → → → → → → → → → →

3 1 1 1 1 1 1 1 1 1 1 1 1

0.39 0.44 0.41 0.36 0.33 0.29 0.24 0.18 0.22 0.28 0.37 0.38 0.39

0.39 −0.44 −0.42 −0.41 −0.42 −0.39 −0.39 −0.38 −0.43 −0.46 −0.50 −0.51 −0.54

3 3 1 1 1 1 1 1 1 1 1 1 1

→ → → → → → → → → → → → →

3 1 1 1 1 1 1 1 1 1 1 1 1

0.39 0.44 0.71 0.72 0.68 0.61 0.58 0.53 0.50 0.46 0.49 0.53 0.61

−0.39 −0.44 −0.71 −0.74 −0.74 −0.72 −0.72 −0.70 −0.72 −0.70 −0.74 −0.77 −0.85

7 5 5 3 3 3 3 1 1

→ → → → → → → → →

5 5 3 3 3 3 1 1 1

0.22 0.45 0.79 1.03 1.36 1.68 1.98 2.17 2.08

−0.22 −0.45 −0.79 −1.03 −1.36 −1.68 −1.98 −2.17 −2.11

QH2 (e)

⟨rPd−Pd⟩ Å

0.02 0.05 0.08 0.11 0.15 0.20 0.21 0.18 0.13 0.14 0.15

2.72 2.78 2.77 2.77 2.79 2.79 2.80 2.81 2.82 2.83 2.85 2.86 2.88

0.03 0.07 0.11 0.14 0.18 0.22 0.23 0.24 0.24 0.24

2.72 2.78 2.81 2.81 2.82 2.81 2.82 2.83 2.85 2.86 2.87 2.88 2.90

0.03

2.73 2.75 2.77 2.78 2.79 2.79 2.81 2.81 2.82

The first column gives PdN(H)2D(H2)M, where N is the number of Pd atoms, D is the number of H2 units that adsorb dissociatively, and M is the number of H2 uints adsorbed molecularly. The second column gives the adsorption energy of the last dissociative or molecular adsorption on the cluster in eV. The third column gives the change in the spin multiplicity that occurs with the adsorption. The fourth through sixth columns give the total charge on the PdN cluster, dissociated H atoms, and molecularly adsorbed H atoms, respectively. The final column is the average Pd−Pd bond length in the cluster. a

Subsequent adsorptions transfer additional electron charge back to the PdN framework until all N atoms have a single molecular H2 unit attached. Thereafter, additional adsorptions result in electron charge again being transferred from the Pd N framework, leaving it more positively charged. Some of the charge is transferred to the dissociated H atoms, which become more negatively charged as the complexes near saturation. In Pd4(H)2(H2)M, the trend is slightly different as the charge on the dissociated H atoms remains approximately constant, and transfers due to additional molecular adsoprtions occur largely between the H2 units and the Pd4 tetrahedron. The trend in average Pd−Pd bond length is qualitatively similar for all cluster sizes. Dissociative adsorption invariably

dissociations. On Pd7(H)6, the third dissociation transfers an additional 0.37 e to the PdN. The average transfer per dissociation for Pd7(H)6 is therefore 0.24 e. For N = 13, each dissociation from D = 1 to 8 transfers an average of 0.27 e from the Pd framework to the dissociated H atoms. The charge transfer associated with the molecular adsorptions is also interesting. Molecular adsorption is weaker (Eads(L) is smaller), and thus the charge transfer with each adsorption is smaller. The molecularly attached H2 units generally lose electron charge in the adsorption process. The first adsorption transfers between 0.0 and 0.05 e from the H2 unit to PdN clusters for all PdN(H)2D(H2) complexes studied. This charge is largely transferred to the PdN framework. 3599


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Figure 5. Change in the Gibbs free energy for each adsorption versus temperature. Numerals indicate the number of H2 molecules adsorbed. For the Pd7 clusters, adsorptions 10, 11, 12, and 13 are indicated by circles, squares, diamonds, and ×’s, respectively. The label A indicates the case where the PdN maintains the same shape throughout, and B indicates the case where the PdN cluster distorts to accommodate an additional dissociative adsorption.

results in a clear increase in ⟨rPd−Pd⟩, although the magnitude of the expansion decreases with increasing N. By contrast, molecular adsorption initially causes little structural change, but as the atop sites become covered or nearly covered with one H2 unit, ⟨rPd−Pd⟩ gradually increases with subsequent molecular adsorptions B. Temperature Effects. In Figure 5, we explore the effect of temperature (T) on the saturation coverage of PdN clusters. To do this, we use the Gibbs free energy for the various complexes, as computed in NWChem. The calculation incorporates the appropriate contributions from the rotational and vibrational partition functions.24 The figure depicts the change in the Gibbs free energy (ΔG(L)) associated with the adsorption of the Lth (H)2 unit on the various clusters as a function of T. Numerals are used as symbols in Figure 5 to show ΔG(L) for each (L) as a function of temperature. The general trend in ΔG(L) values is qualitatively similar for all cluster sizes. The dissociative adsorptions have the most negative ΔG(L) values due to the corresponding large Eads(L) values. ΔG(L) remains negative for temperatures up to 500 K for all of the dissociative adsorptions. By contrast, ΔG(L) becomes positive for all molecular adsorptions studied at temperatures at or above 500 K. The implication of Figure 5 is that the number of H2 units that can be stably adsorbed on PdN varies with temperature. At 300 K, the results in Figure 5 predict that for N = 2, 3, 4, 7, and 13, the largest number of H2 units that can be adsorbed is 3, 4, 5, 8, and 8, respectively. Interestingly, this means that for the smaller clusters (N = 2, 3, and 4), the saturated structure at 300 K corresponds to one dissociated H2 plus one molecular H2 attached to each atop site. For N = 7 at 300 K, there are two dissociated H2 units, and all but one of the atop sites is covered

by a molecularly adsorbed unit. For N = 13, only the dissociated H2 units are stably bound at 300 K. This suggests that for still larger Pd nanoparticles, only dissociated H atoms would be stable at room temperature. Molecular H2 units would not bind or would readily escape from the surface. C. Effect of Saturation on H Atom Migration. It is of interest to consider the effect of H2 saturation on the migration of dissociated H atoms across a PdN surface. Such migration is expected to be important in catalytic processes because the ability of reactants to traverse the surface of a Pd nanoparticle will clearly influence reaction rates. Treating all possible pathways on the various cluster models is a formidable problem. Here, we treat the problem in a preliminary way by studying migration pathways on the Pd4 cluster. We chose this particular cluster because it is the smallest cluster that is still three-dimensional and yet its small size allows us to perform extensive calculations. NEB calculations were used to find the MEPs between different local minima for the dissociated hydrogens. All atoms, including the molecularly attached H2 units, are allowed to relax in the NEB calculations in order to find the MEPs. In Figure 6, we show the results for Pd4(H)2 clusters with increasing numbers of molecular H2 units attached to atop sites. To describe the H atom migration pathways, it is easiest to begin by considering the local minima on the Pd4(H)2 cluster. The minimum-energy structure for this system features the two dissociated H atoms bound to three-fold face sites (structure 1). The lowest-energy metastable geometry involves the two dissociated H atoms bound to two-fold edge sites, where the edges are on distinct faces (structure 11). A higher-energy structure involves the two dissociated H atoms bound to twofold edge sites on the same face (structure 7). In a fourth structure, one of the dissociated H atoms is bound to a face and 3600


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Figure 6. (Upper panel) NEB calculations for migration of dissociated H atoms on Pd4(H)2(H2)M clusters. The structures below indicate the placements of the dissociated H atoms on the Pd4 cluster for each minimum and transition state on the minimum-energy path. (A) Pathway for the Pd4(H)2 neutral case; (B) same for the Pd4(H)2+ cation. (C−F) Minimum-energy paths for the Pd4(H)2(H2), Pd4(H)2(H2)2, Pd4(H)2(H2)3, and Pd4(H)2(H2)4, respectively. The structures are drawn from the Pd4(H)2(H2)4 case due to the fact that many more stable points exist for the dissociated H atoms at this level of saturation. However, placement of the H atoms indicated by the numbers on the less saturated clusters is qualitatively the same as that shown for the Pd4(H)2(H2)4 case.

about 0.18 eV. Both of these values increase to 0.25 and 0.23 eV when two H2 units are present (panel D) and to 0.27 and 0.26 when three are present (panel E). When all four atop sites are covered by H2 units, the barrier jumps dramatically to about 0.46 eV, and the height of the metastable minimum climbs to 0.45 eV (panel F). The low-lying metastable minimum structure 11 lies about 0.02 eV above the ground-state structure 1 configuration when no additional molecular H2 units are attached to atop sites, and the barrier to the stable structure is about 0.09 eV. These values also change when H2 units are present on atop sites. For one attached H2, the heights of the minimum and the barrier are 0.06 and 0.07 eV, respectively; for two H2 units, these values change to 0.13 and 0.08 eV; for three, the values change to 0.17 and 0.06 eV; and for four, the values are 0.2 and 0.08 eV, respectively. These results show that the degree of H2 coverage

the other to an edge on a different face (structure 9). This is not a local minimum for the Pd4(H)2 system, but the energy surface is relatively flat in the vicinity of this structure. As discussed below, structure 9 becomes a local minimum when molecular H2 units are bound to the cluster. Panels A and B in Figure 6 show the MEPs for the cases of the Pd4(H)2 neutral and cation, respectively, while panels C−F show the MEPs for the neutral complexes with increasing molecular adsorption. In this case, the removal of an electron serves to both increase the overall mobility of the H atoms and switch the energetic ordering of the metastable minima. In the neutral case, the barrier for moving from structure 1 to the high-lying structure 7 state is about 0.30 eV. Roughly 0.27 eV of this barrier is the energy difference between the metastable minimum and the ground state. This barrier drops to about 0.22 eV when a molecular H2 is present on an atop site (panel C). The height of the metastable minimum also decreases to 3601


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Figure 7. Orbitals on the Pd4(H)2(H2)4 edge-face configuration. (A) Overlap of the H−Pd σ-bonding orbitals on the molecularly adsorbed H2 dimers (H3−H4, H7−H8, and H9−H10) with that of the dissociated hydrogen atom on the Pd1−Pd2−Pd4 face (H2). (B) Pd−H σ orbital for the H5−H6 dimer. (C) Bonding orbital for the edge-bound dissociated hydrogen atom H1. The charges on the H1 and H2 are 0.02 and −0.24 e, respectively. For the dimers, H3−H4, H7−H8, and H9−H10 have an average charge of 0.016 e and bond length of 0.83 Å compared to 0.003 e and 0.85 Å for H5−H6.

one molecular H2 per atop site, in addition to the one dissociated unit. For N = 3 and 4, a second dissociation may occur, accompanied by a significant change in the structure of the underlying PdN framework. In both cases, the alternate pathway involves overcoming a small energy barrier of less than 0.05 eV relative to the path leading to molecular adsorption. A similar alternative dissociative pathway was investigated for N = 7, and it was found to be separated by a barrier of 0.34 eV from the molecular adsorption pathway. It appears that dissociations leading to a change of the underlying PdN bonding framework become energetically unfeasible for larger Pd cores. Saturation for the N = 7 cluster involves 2 dissociated H2 units and 11 and 6 molecular H2 units at T = 0 and 300 K, respectively. For N = 13, computational demands limited our investigation. We find that eight H2 units dissociate, and at least one unit binds molecularly at T = 0 K. At T = 300 K, only the dissociated H atoms remain stably attached to the cluster. In general, dissociation of a H2 unit results in a transfer of electron charge from the PdN core to the dissociated H atoms, and the total amount of charge transferred per addition is roughly constant, independent of the number of dissociated H atoms. Attaching a molecular H2 unit generally results in a transfer of electron charge from the H2 units to the PdN core until all of the atop sites are covered. The charge transfer becomes more complicated as more H2 units are added beyond this coverage. The presence of molecular H2 units bound to atop sites is found to affect the migration of dissociated H atoms on Pd4. The effect is complex, with some migration barriers lowered and others raised at low coverage. When all of the atop sites are covered, in Pd4(H)2(H2)4, all barriers are increased, making the local minima more pronounced. The results reported here offer a detailed picture of the interactions that PdN particles would undergo in a H2-rich environment, such as would be the case if the particles were used in gas-phase catalysis involving H2 as a reactant. We leave for future study questions of how these interactions could be affected by attaching the PdN clusters to a substrate. It would also be interesting to further investigate the question of H atom migration on covered clusters, particularly for larger clusters.

can affect the energetics of the migration of dissociated H atoms on the cluster. It is interesting that the case where one H atom occupies an edge and the other a face (structure 9) becomes a metastable minimum as H2 units are added to atop sites. The depth of this local minimum and its energy relative to structure 1 depends on the number of attached molecular units. When all four atop sites are covered, structure 9 becomes slightly lower in energy than structure 1. The increase of barriers to H atom diffusion on Pd clusters with increased H2 coverage is consistent with STM results on Pd(111) slabs.24 We also note that a number of intermediate minima appear in the potential energy surface as saturation increases. This effect along with the previously discussed changes in the relative heights of metastable minima can be understood as the result of increased stability in cases where Kubas style Pd−H2 σ-bonding orbitals25,26 are collinear with the Pd−H bonds of the dissociated H atoms. This can be seen in Figure 7, where panel A shows the orbital that encompasses the face-bound H atom and three molecularly adsorbed H2 molecules, panel B shows the orbital for the lone molecularly adsorbed H2 where no overlap is formed, and panel C shows the orbital encompassing the edge-bound H atom. The stabilization brought about by the interaction in panel A explains why structures 3 and 9 in Figure 6 become the ground state for Pd4(H)2(H2)4; it leads to greatly increased charge transfer from the molecularly adsorbed H2 units to the dissociated atom (labeled “H2”). Edge-bound atoms such as the one labeled “H1” can make a maximum of two such interactions, explaining why configurations placing both H atoms on edges are higher in energy relative to face-bound configurations as saturation increases (structures 7 and 11 in Figure 6).

4. SUMMARY We have systematically studied the binding of multiple H2 units to PdN clusters for N = 2, 3, 4, 7, and 13, both at T = 0 K and for finite T. We determined both the number of H2 units that spontaneously dissociate on the cluster and the number of additional units that bind molecularly. For N = 2, 3, and 4, one H2 unit dissociates, and saturation coverage at T = 0 K corresponds to two molecular H2 units attached to each atop site on the PdN core. At T = 300 K, saturation corresponds to 3602


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Trimers for Hydrogen Peroxide Formation from H2 and O2. J. Phys. Chem. C 2007, 111, 7384−7395. (14) Pelzer, A. W.; Jellinek, J.; Jackson, K. A. H2 Reactions on Palladium Clusters. J. Phys. Chem. A 2013, 117, 10407−10415. (15) Moc, J.; Musaev, D. G.; Morokuma, K. Adsorption of Multiple H2 Molecules on Pd3 and Pd4 Clusters. A Density Functional Study. J. Phys. Chem. A 2000, 104, 11606−11614. (16) Wang, Y.; Cao, Z.; Zhang, Q. Density Functional Study of Multiple H2 Adsorption and Activation on a Pd6 Cluster. Chem. Phys. Lett. 2003, 376, 96−102. (17) Singh, A. K.; Ribas, M. A.; Yakobson, B. I. H-Spillover through the Catalyst Saturation: An Ab Initio Thermodynamics Study. ACS Nano 2009, 3, 1657−1662. (18) Zhou, C.; Yao, S.; Wu, J.; Forrey, R. C.; Chen, L.; Tachibana, A.; Cheng, H. Hydrogen Dissociative Chemisorption and Desorption on Saturated Subnano Palladium Clusters (Pdn, n = 2−9). Phys. Chem. Chem. Phys. 2008, 10, 5445−5451. (19) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110, 6158−6170. (20) Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Van Dam, H. J. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L.; et al. NWChem: A Comprehensive and Scalable Open-Source Solution for Large Scale Molecular Simulations. Comput. Phys. Commun. 2010, 181, 1477−1489. (21) Peterson, K. A.; Figgen, D.; Dolg, M.; Stoll, H. EnergyConsistent Relativistic Pseudopotentials and Correlation Consistent Basis Sets for the 4d Elements Y−Pd. J. Chem. Phys. 2007, 126, 124101/1−124101/12. (22) Weinhold, F.; Landis, C. R. Valency and Bonding: A Natural Bond Orbial Donor−Acceptor Perspective; University Press: Cambridge, U.K., 2005. (23) Henkelman, G.; Jonsson, H. Improved Tangent Estimate in the Nudged Elastic Band Method for Finding Minimum Energy Paths and Saddle Points. J. Chem. Phys. 2000, 113, 9978−9985. (24) Mitsui, T.; Rose, M. K.; Fomin, E.; Ogletree, D. F.; Salmeron, M. Hydrogen Adsorption and Diffusion on Pd(111). Surf. Sci. 2003, 540, 5−11. (25) Kubas, G. J. Molecular Hydrogen Complexes: Coordination of a σ Bond to Transition Metals. Acc. Chem. Res. 1988, 21, 120−128. (26) Kubas, G. J. Metal−Dihydrogen and -Bond Coordination: The Consummate Extension of the Dewar−Chatt−Duncanson Model for Metal−Olefin π Bonding. J. Organomet. Chem. 2001, 635, 37−68.

ASSOCIATED CONTENT

S Supporting Information *

The geometries of all partially and fully saturated clusters; the geometries of all points along the minimum-energy path for Figure 6F. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (A.W.P.). *E-mail: [email protected] (J.J.). *E-mail: [email protected] (K.A.J.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.W.P. and K.A.J. were supported by the U.S. Department of Energy under Award No. DE-SC0001330. J.J. was supported by the Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences, U.S. Department of Energy, under Contract No. DE-AC02-06CH11357. The calculations were performed using the facilities of the high performance computing center (HPCC) at Michigan State University, Laboratory Computing Resource Center (LCRC) at Argonne National Laboratory, and NERSC. K.A.J. gratefully acknowledges the hospitality of the School of Physics and Astronomy at the University of Minnesota and especially that of Prof. Ken Heller during his sabbatical stay.

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REFERENCES

(1) Knickelbein, M. B. Reactions of Transition Metal Clusters with Small Molecules. Annu. Rev. Phys. Chem. 1999, 50, 79−115. (2) Schlögl, R.; Abd Hamid, S. B. Nanocatalysis: Mature Science Revisited or Something Really New? Angew. Chem., Int. Ed. 2004, 43, 1628−1637. (3) Landman, U. Nanocatalysis; Springer: Berlin, Heidelberg, Germany, 2007. (4) Norskov, J. K.; Bligaard, T.; Rossmeisl, J.; Christensen, C. H. Towards the Computational Design of Solid Catalysts. Nat. Chem. 2009, 1, 37−46. (5) Jarrold, M. F. Nanosurface Chemistry on Size-Selected Silicon Clusters. Science 1991, 252, 1085−1092. (6) Johnston, R. L. Atomic and Molecular Clusters; CRC Press: Boca Raton, FL, 2002. (7) Haruta, M.; Daté, M. Advances in the Catalysis of Au Nanoparticles. Appl. Catal., A 2001, 222, 427−437. (8) Haruta, M. When Gold Is Not Noble: Catalysis by Nanoparticles. Chem. Rec. 2003, 3, 75−87. (9) Jagadeesh, R. V.; Surkus, A.-E.; Junge, H.; Pohl, M.-M.; Radnik, J.; Rabeah, J.; Huan, H.; Schünemann, V.; Brückner, A.; Beller, M. Nanoscale Fe2O3-Based Catalysts for Selective Hydrogenation of Nitroarenes to Anilines. Science 2013, 342, 1073−1076. (10) Friedfeld, M. R.; Shevlin, M.; Hoyt, J. M.; Krska, S. W.; Tudge, M. T.; Chirik, P. J. Cobalt Precursors for High-Throughput Discovery of Base Metal Asymmetric Alkene Hydrogenation Catalysts. Science 2013, 342, 1076−1080. (11) Landon, P.; Collier, P. J.; Carley, A. F.; Chadwick, D.; Papworth, A. J.; Burrows, A.; Kiely, C. J.; Hutchings, G. J. Direct Synthesis of Hydrogen Peroxide from H2 and O2 Using Pd and Au Catalysts. Phys. Chem. Chem. Phys. 2003, 5, 1917−1923. (12) Wells, D.; Delgass, W. N.; Thomson, K. T. Formation of Hydrogen Peroxide from H2 and O2 over a Neutral Gold Trimer: A DFT Study. J. Catal. 2004, 225, 69−77. (13) Joshi, A. M.; Delgass, W. N.; Thomson, K. T. Investigation of Gold−Silver, Gold−Copper, and Gold−Palladium Dimers and 3603


H2 Saturation on Palladium Clusters - The Journal of Physical

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