Nucleation of Rhn (n = 1â5) Clusters on Î³-Al2O3 Surfaces: A Density

Article pubs.acs.org/JPCC

Nucleation of Rhn (n = 1−5) Clusters on γ-Al2O3 Surfaces: A Density Functional Theory Study Xue-Rong Shi and David S. Sholl* School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, United States ABSTRACT: The interaction of Rhn (n = 1−5) clusters with nonhydrated γ-Al2O3(100), hydrated γ-Al2O3(100), and hydrated γ-Al2O3(110) surfaces has been investigated using density functional theory methods. On these surfaces, Rh3 prefers a triangular geometry, while Rh4 and Rh5 adopt 3D structures. On the (100) surfaces, Rhn binds considerably more strongly on the nonhydrated surface than on the hydrated surface. On the hydrated (110) surface, Rhn binds to surface hydroxyl groups, which is consistent with experimental observations. Characterizing the structure of Rhn clusters makes it possible to identify the critical cluster size for nucleation on each surface.

1. INTRODUCTION Many practical heterogeneous catalysts are prepared as small metal clusters supported on metal oxide supports. In this form, catalysts provide a large active surface area and limit the fraction of atoms of the active phase, often a precious metal, that are inaccessible to reactants. In addition to enhancing the catalytic activity of the metal phase, the presence of metal clusters on a support can alter the stability of the support. For example, Ravenelle et al. used a range of experimental techniques to show that the presence of Ni or Pt particles significantly retards the transformation of γ-Al2O3 to a hydrated boehmite (AlOOH) phase in hot liquid water.1 Their results suggested that the metal particles affect the kinetics of this transformation by blocking specific surface hydroxyl groups that act as initial hydration sites. In this paper, we focus on the structure of small Rh clusters on alumina surfaces. Nanosize rhodium clusters on alumina support have been examined in a number of previous experimental and theoretical studies.2−5 Bowker et al. observed a “surface explosion” for the decomposition of acetate on an oxygen-precovered Rh-alumina catalyst and on single crystals of Rh.2 Argo et al. investigated the hydrogenation reactions of ethene, propene, and toluene on small clusters of rhodium (Rh6) and of iridium (Ir4 and Ir6) (as well as of larger aggregates of these metals) on oxide supports (γ-Al2O3, MgO, and La2O3).3 The catalysts were characterized in the working state by extended X-ray absorption fine structure (EXAFS) spectroscopy, providing information about the cluster structures and cluster−support interactions. The EXAFS data indicate that the metal clusters, while remaining intact and maintaining their bonding to the support during catalysis, underwent slight rearrangements to accommodate reactive intermediates. Scanning tunneling microscopy (STM) experiments have been used to study the influence of OH groups on the growth of rhodium on a well-ordered alumina film on NiAl(100).4,5 It was shown that at 300 K nucleation of Rh © 2012 American Chemical Society

clusters preferentially occurs on a hydrated surface relative to a nonhydrated surface. Photoelectron spectroscopy of both alumina and rhodium core levels pointed to a direct chemical interaction between metal atoms and surface hydroxyl groups.4 The structural complexity of nanosized metal clusters on metal oxide supports makes it difficult to obtain complete structural and electronic information for these systems even under well-defined experimental conditions. Theoretical approaches based on first-principles calculations are useful to complement experimental results. A number of theoretical studies have examined the nucleation and growth of transition metals on alumina, including Pd on γ-Al2O3, Pt on γ-Al2O3, Cu on α-Al2O3, Au on α-Al2O3, and Ag on α-Al2O3.6−11 To our knowledge, however, however, little attention has been paid to nucleation and growth of Rh on γ-Al2O3. Motivated by the generality suggested by Ravenelle et al. for their observed stabilization of γ-Al2O3 by small metal clusters and the catalytic activity of small Rh clusters on this support, we have used DFT calculations to explore the structure and stability of small Rh clusters on γ-Al2O3. To understand the structure of small metal clusters on metal oxide supports under experimentally relevant conditions, it is important to correctly describe the surfaces presented by the support. Digne et al. found that the surface coverage of hydroxyls on γ-Al2O3 changes as a function of preparation temperature. During pretreatment, supported γ-alumina Rh catalysts are typically exposed to temperature in the range 400− 700 K.2,12−14 We based our calculations on the surface structures defined by Digne et al.13 to study the nucleation and growth mode of Rh cluster on γ-Al2O3 that has been pretreated at ∼600 K. Critically for our purposes, these structures include dehydrated and hydroxyl-covered surfaces. Received: February 3, 2012 Revised: April 11, 2012 Published: April 25, 2012 10623

dx.doi.org/10.1021/jp301114n | J. Phys. Chem. C 2012, 116, 10623−10631

The Journal of Physical Chemistry C

Article

By comparing the properties of small Rh clusters on these surfaces, we are able to consider the surface stabilization mechanism suggested by Ravenelle et al.1

2. METHODS AND MODELS All calculations were performed with plane-wave density functional theory (DFT)15 using the Vienna ab initio simulation package (VASP) with the Perdew−Wang generalized gradient approximation of the exchange-correlation functional and the projector augmented wave (PAW) method.16−21 Spin polarization was employed for all calculations, and the cutoff energy for the plane wave basis set was fixed at 400 eV. Geometry optimization was performed with a conjugate-gradient algorithm and considered to be converged when the forces on each atom become 0.03 eV/Å or less. Reciprocal space was sampled only at the Γ-point due to the large supercell. Numerical tests with a small number of clusters on the (100) surface indicated that using more k-points changed the calculated adsorption energies by less than 2%. We adopted models for alumina surfaces from ref 13. According to this work, γ-Al2O3 shows two main surfaces at 600 K, the dehydrated (100) surface and the hydrated (110) surface. The latter surface has a hydroxyl coverage of 8.9 OH/ nm2. To further consider the effect of surface hydroxyls, we also examined the hydrated (100) surface, which has 8.8 OH/nm2. The hydrated (100) surface was predicted by Digne et al. to be stable for temperatures from 475 to 570 K.13 Illustrations of these three surfaces are shown in Figure 1. Although the two hydrated surfaces have similar net hydroxyl densities, the distribution of the hydroxyl groups on the two surfaces is rather different. On the hydrated (100) surface, a distinct channel of surface Al and O atoms exists in which no hydroxyls are found. On the hydrated (110) surface, however, the hydroxyl groups are distributed more uniformly. To avoid lateral interactions between the periodic Rh clusters, we used a slab containing 2 × 2 unit cells in the plane of the surface and four layers normal to the surface. With these choices, the computational supercells for the dehydrated (100), hydrated (100), and hydrated (110) surfaces contain 160, 184, and 248 atoms, respectively. The adsorption energy, Eads, of a Rh cluster was defined by Eads = E(Rh n/γ ‐Al 2O3) − E(γ ‐Al 2O3) − E(Rh n)

Figure 1. Top view of the γ-Al2O3 surfaces used in this work: (a) nonhydrated (100) surface, (b) hydrated (100) surface with 8.8 OH/ nm2, and (c) hydrated (110) surface with 8.9 OH/nm2. Atoms in the first layer are shown in a ball and stick form with white (H), red (O), and pink (Al) balls. The other layers are shown in a stick representation.

(1)

where E(Rhn/γ-Al2O3), E(γ-Al2O3), and E(Rhn) are the total energies of the γ-Al2O3 with Rhn cluster, the bare γ-Al2O3 substrate, and the energy minimized Rhn cluster in the gas phase. This energy can be decomposed into several components. The energy associated with deformation in the structure of the Rh cluster between the gas phase and the adsorbed state was characterized using Edef(Rhn) = E(Rh n′) − E(Rh n)

E int = E(Rh n/γ ‐Al 2O3′) − E(Rh n′) − E(γ ‐Al 2O3)

Here, unlike the definition of the adsorption energy, Eads, which uses the minimum energy structures for the gas phase Rhn cluster and the substrate, the interaction energy Eint uses energies for the separated clusters and substrate in the geometry associated with the fully relaxed adsorbed cluster. From eqs 1−4, it can be seen that Eads = Edef(Rhn) + Edef(surface) + Eint.

(2)

where E(Rhn′) is the energy of Rhn in the gas phase using the geometry of the adsorbed cluster on γ-Al2O3. The surface deformation energy associated with adsorbing a cluster, Edef(surface), was calculated in a similar way: Edef(surface) = E(γ ‐Al 2O3′) − E(γ ‐Al 2O3)

(4)

(3)

3. RESULTS AND DISCUSSION 3.1. Gas Phase Clusters. We first briefly describe the geometries and energies of gas phase Rhn clusters, which are essential to understand the growth behavior of Rhn cluster on γAl2O3 surfaces. The geometries of Rhn (n = 2−5) and bulk fcc

where E(γ-Al2O3′) is the energy of the γ-Al2O3 in the geometry associated with the adsorbed cluster but with the cluster removed. We also calculated the interaction energy, Eint, associated with the cluster/surface interaction, using 10624



Article

Table 1. Geometry, Magnetic Moment (M), and Energy of Gas Phase Rhn (n = 2−5) Clusters n 2 3 4 5 bulk a

geometry D∞h D3h Td C4v fcc

M (μB) c,d

4(4 ) 3(3c,d) 0(0c,d) 5(5c,e) 0

d(Rh−Rh) (Å) d

f

g

2.22(2.34, 2.26, 2.28 ) 2.39(2.45,d 2.42f) 2.45(2.50,d 2.49f) 2.40/2.56(2.48/2.63g) 2.72

CEa (eV/atom)

BEb (eV)

−2.02 −2.63 −3.11 −3.38 −6.11

−4.04 −2.63 −2.07 −2.11 −1.02

Cohesive energy = (E[Rhn] − nE[Rh])/n. bBond energy = nCE/m, where m is the number of Rh−Rh bonds in the cluster. cReference 27. Reference 26. eReference 28. fReference 25. gReference 29.

d

Figure 2. The energetically preferred Rhn (n = 1−5) adsorption structures on the nonhydrated γ-Al2O3(100) surface for (a) Rh, (b) Rh2, (c) triangular Rh3, (d) linear Rh3, (e) Rh4, and (f) Rh5. Each cluster is shown with a side view (left) and top view (right). The largest balls are Rh, and otherwise, the color scheme is identical to Figure 1.

number of well-defined adsorption sites that are available on the surface. On the nonhydrated (100) surface, we considered eight top sites, denoted O(A), O(C), O(D), O(F), Al(1), Al(2), Al(3), and Al(5) using the notation shown in Figure 1. Similarly, we examined 12 bridge sites (O(A)−O(B), O(A)− O(D), O(B)−O(C), O(E)−O(F), Al(3)−Al(4), Al(4)−Al(5), O(A)−Al(1), O(D)−Al(1), O(D)−Al(3), O(C)−Al(2), O(E)−Al(4), O(F)−Al(2)) and one hollow site. On the hydrated (100) surface, our calculations included 11 top sites including each site labeled in Figure 1b, 12 bridge sites as defined on the nonhydrated surface, and two hollow sites. For the hydrated (110) surface, Al (1), O(F), and O(J) are less favorable than the other labeled sites according to ref 6; thus, they are excluded from our present work. For Rhn clusters with n > 1, we used two methods to generate initial approximations of adsorbed configurations. First, we added an additional Rh atom in various configurations to the most stable Rhn−1 cluster. Second, we put the Rhn (n > 1) cluster in its gas phase geometry on the well-defined adsorption sites listed above. The most energetically preferred structures obtained from energy minimization of this range of initial conditions on the nonhydrated surface are shown in Figure 2. The corresponding adsorption energies are listed in Table 2. The average Rh−Rh distance for Rh atoms in contact with the support is slightly larger than those for the free Rhn clusters, although the Rh−Rh distances in the apex edges for Rh4 and Rh5 are shorter. As shown in Figure 2a, the adsorption of a Rh monomer induces a strong surface rearrangement in which the Rh atom inserts approximately into the surface plane, with an adjacent oxygen atom moving upward to accommodate the Rh atom.

Rh were computed using the methods described above. We considered 1D, 2D, and 3D structures for the gas phase Rhn, and only the energetically preferred geometries are summarized in Table 1. Rh−Rh distances in the clusters are shorter than in the bulk structure and increase with size, although the bulk value is far from being reached. The degree of bond contraction relative to the bulk follows an approximately n−1/3 relationship.22 A similar bond contraction has been characterized experimentally for Pt clusters by EXAFS.23 Fulton et al. found that the Rh−Rh bond distance in organometallic Rh4−6 clusters is longer than the bulk value due to the role of ligands coordinated to the cluster while small clusters without ligands exhibit bond contraction.24 As expected, the cohesive energy increases as the cluster size increases due to increased atomic coordination. The difference between the cohesive energy of a cluster and the bulk cohesive energy scales approximately as n−1/3. A similar n−1/3 dependence has been reported by Ankudinov et al. for small Pt clusters.22 Table 1 also includes the results of other theoretical calculations dealing with gas phase Rh clusters. Our most stable structures and magnetic moments are consistent with other groups.25−28 The calculated bond distance of the dimer is 2.22 Å, which is close to the experimental value of 2.28 Å. Our calculated bond distances are generally slightly shorter than other theoretical results listed in Table 1. 3.2. Adsorption of Rhn Clusters. 3.2.1. Adsorption on the Nonhydrated and Hydrated γ-Al2O3(100) Surface. We now discuss the adsorption of Rh clusters on the nonhydrated and hydrated γ-Al2O3(100) surface. The adsorption of an isolated Rh atom was examined by placing a Rh atom on a large 10625



Article

configurations were also considered on the surface. The adsorption energy Eads for linear Rh4 and Rh5 cluster is 1.06 and 2.38 eV higher than the most stable 3D structure, respectively; namely, they are less stable than the 3D structure. To consider the effect of surface hydroxyls, we studied Rhn cluster adsorption on hydrated γ-Al2O3(100), which has a hydroxyl coverage of 8.8 OH/nm2. The most favorable structures are shown in Figure 3, and the corresponding adsorption energy is listed in Table 3.

Table 2. The Adsorption Energy, Eads, Interaction Energy, Eint, Rhn Deformation Energy, Edef(Rhn), Surface Deformation Energy, Edef(surface), and Average Rh−Rh Bond Distances d̅(Rh−Rh) (Å) of Rhn Cluster on the Nonhydrated γAl2O3(100) Surface (All Energies Are in eV)

a

N

Eads

Eint

1 2 3-triangular 3-linear 4 5

−3.39 −2.70 −2.67 −2.50 −2.63 −3.07

−5.09 −5.44 −6.11 −7.61 −4.55 −4.91

Edef(Rhn)

Edef(surface)

d̅(Rh−Rh)

0.16 0.81 1.14 0.22 0.16

1.70 2.58 2.63 3.97 1.71 1.68

2.36 2.52 2.47 2.56/2.44a 2.49/2.51a

Table 3. The Adsorption Energy Eads (eV), Interaction Energy Eint (eV), Rhn Deformation Energy Edef(Rhn) (eV), Surface Deformation Energy Edef(surface) (eV), and Average Rh−Rh Bond Distances d̅(Rh−Rh) (Å) of Rhn Cluster on the Hydrated (100) Surface

Base and apex edges, respectively.

Adsorbate-induced surface relaxation on γ-Al2O3(100) has been observed for other transition metals such as Pd.6 Comparison of monomer and dimer species reveals that the Rh−Al bond defined by the Rh in the plane of the surface enlarges to 2.39 Å in the dimer from 2.31 Å for the monomer. This is consistent with the substantial increase in the surface deformation energy shown in Table 2, from 1.70 eV for the monomer to 2.58 eV for the dimer. For Rh3 adsorption, the most stable structure is a triangular Rh3 cluster on the surface with all Rh atoms bonded to the surface. The most stable linear isomer is 0.17 eV higher in energy than the triangular state. This energy difference can be attributed to the deformation of the surface and cluster. As shown in Table 2, the deformation energies for the Rh3 cluster and the surface are, in the triangular case, 0.81 and 2.63 eV, respectively. The corresponding values are significantly larger for the linear case, 1.14 and 3.97 eV, respectively. The most stable Rh4 cluster is a 3D structure. Unlike the smaller clusters discussed above, all the atoms of the Rh4 cluster are above the surface. This represents a transition from the high deformation situation for n = 1−3 to a situation where the deformation of the cluster is relatively small. The 2D square planar structure is less stable than the 3D structure. In the gas phase, the 3D tetrahedron structure is 0.18 eV lower than the 2D square planar structure, while, for adsorption on the surface, the former is 0.43 eV lower than the latter. Similar results were observed for Rh5. For Rh4 and Rh5 clusters, the linear

a

N

Eads

Eint


−2.91 −1.47 −2.14 −1.30 −2.55 −2.34

−4.32 −3.58 −3.22 −3.14 −4.09 −4.01

Edef(Rhn)

Edef(surface)

d̅(Rh−Rh)

0.32 0.09 0.77 0.04 0.16

1.41 1.79 0.99 1.07 1.50 1.51

2.43 2.45 2.24 2.48/2.47a 2.50/2.50a


As shown in Figure 3, a single Rh atom prefers to insert into the surface, where it bonds to two surface O atoms, one surface Al, and one subsurface Al, yielding a strong surface deformation of 1.41 eV. When a dimer adsorbs, the original Rh atom monomer is extracted from the surface. The Rh−Rh bond distance in the adsorbed dimer is 2.43 Å, compared to 2.22 Å for the gas phase cluster. Adsorption of Rh3 forms a triangular cluster that is quite different from the result on the nonhydrated surface. On the hydrated surface, the trimer binds to the surface just through one Rh atom. The linear trimer binds to the surface through the two Rh atoms at the end of the cluster. Similar to the nonhydrated surface, Rh4 and Rh5 favor 3D configurations on the hydrated surface. As for the nonhydrated surface, the average Rh−Rh distance for Rh atoms in contact with the hydrated support is slightly larger than those for the free Rhn clusters (although the Rh−Rh distances in the apex edges for Rh5 are shorter). Unlike the nonhydrated (100)

Figure 3. Similar to Figure 2 but for the hydrated γ-Al2O3(100) surface. 10626



Article

Al2O3(110) surface are more uniformly distributed than the groups on the (100) surface. This has important implications for the adsorption on Rh clusters. As shown in Figure 4a, unlike the nonhydrated and hydrated (100) surfaces, a Rh atom on the hydrated (110) surface binds to the surface hydroxyl groups directly, where it inserts in the first hydroxyl layer rather than in the first oxide layer. The state with Rh binding to the surface (not the hydroxyl) is less stable by 0.48 eV. For the adsorbed dimer, both Rh atoms bind approximately in the surface plane, with one Rh atom binding to O in a hydroxyl and also a surface O and the other Rh binding to a surface Al. For the linear isomer of Rh3, the two bottom Rh atoms still insert in the surface plane, while, for the trigonal trimer, all three atoms are in a plane above the first hydroxyl layer. The triangular cluster is more stable than the linear cluster by 0.06 eV. The adsorption of a Rh4 cluster cleaves one of the Rh−Rh bonds in the gas phase cluster. This enhances the cluster’s interaction with the support at the cost of a large cluster deformation energy. Rh5 adsorbs in a configuration quite similar to the gas phase cluster. Similar to the other surfaces, the average Rh−Rh distance for Rh atoms in contact with the support is slightly larger than those for the free Rhn clusters, while the Rh−Rh distances in the apex edges for Rh4 and Rh5 are shorter. Our results show that individual Rh atoms adsorb strongly on the γ-Al2O3 surface with adsorption energies in the range −3.39 to −2.79 eV. Similar calculations with the same functional in ref 30 showed that the strongest adsorption for Rh on α-Al2O3 was −2.52 eV. This comparison reflects a stronger metal/metal oxide interaction on the γ-Al2O3 surface than on α-Al2O3, in agreement with previous calculations and experiments.31 It is well-known that the γ-Al2O3 is preferred over α-Al2O3 for catalytic purposes.32 As shown in Table 5, Rh binds more strongly to the γ-Al2O3 surface than Pd, in agreement with experimental results. Bäumer et al. studied the growth of Rh and Pd on a thin, well-ordered alumina film at two different temperatures, 90 and 300 K, although due to experimental limitations the characterization of the deposits by STM was always performed at 300 K.33 It was shown that the metal support interaction for Rh was stronger than that for Pd, with a decrease of the overall mobility

surface, the average Rh−Rh distance for Rh atoms in the apex edges of Rh4 is slightly longer than those for the free Rh4 clusters. Comparing Tables 2 and 3 shows that the adsorption energy of Rhn clusters on the hydrated (100) surface is weaker than that on the nonhydrated (100) surface. For each cluster, the surface OH groups have an unfavorable effect on the adsorption of Rhn clusters. It is noteworthy that the Rhn clusters prefer to adsorb at the terminal O or Al atoms of the hydrated surface instead on the surface hydroxyl layer. This is qualitatively consistent with the experiments by Ravenelle et al., who found that the presence of Ni or Pt particles significantly retards the transformation of γ-Al2O3 to a hydrated boehmite (AlOOH) phase in hot liquid water.1 It appears that this effect is likely to be general for a large range of metal clusters, which can stabilize the support by preferentially occupying the reactive sites that initiate conversion of the alumina surface into boehmite. 3.2.2. Adsorption on the Hydrated (110) Surface. We performed similar calculations to those discussed above for Rh clusters on the hydrated γ-Al2O3(110) surface. The energetic parameters for these clusters are listed in Table 4, and the Table 4. The Adsorption Energy Eads (eV), Interaction Energy Eint (eV), Rhn Deformation Energy Edef(Rhn) (eV), Surface Deformation Energy Edef(surface) (eV), and Average Rh−Rh Bond Distances d̅(Rh−Rh) (Å) of Rhn Cluster on the Hydrated (110) Surface

a

N

Eads

Eint


−2.79 −1.83 −2.04 −1.98 −2.56 −3.21

−4.66 −3.58 −3.24 −4.99 −4.61 −4.94

Edef(Rhn)

Edef(surface)

d̅(Rh−Rh)

0.06 0.10 0.90 0.55 0.06

1.87 1.69 1.10 2.11 1.50 1.66

2.29 2.41 2.32 2.81/2.42a 2.45/2.51a


corresponding structures are shown in Figure 4. As noted in the discussion of Figure 1, the hydroxyl groups on the hydrated γ-

Figure 4. Similar to Figure 2 but for the hydrated γ-Al2O3(110) surface. 10627



Article

Table 6. Nucleation Energy Enuc (eV) for Rhn Clusters on γAl2O3 Surfaces

Table 5. The Adsorption Energy Eads (eV) of Individual Transition Metal Atoms on Alumina Rh/γ-Al2O3 Pd/γ-Al2O3a Co/α-Al2O3(0001)b Rh/α-Al2O3(0001)b Ir/α-Al2O3(0001)b Ni/α-Al2O3(0001)c Pd/α-Al2O3(0001)c Pt/α-Al2O3(0001)c Cu/α-Al2O3(0001)d Ag/α-Al2O3(0001)d Au/α-Al2O3(0001)d

−Eads

N

nonhydrated (100)

hydrated (100)

hydrated (110)

2.79−3.39e 1.72−2.04e 3.02f 2.52f 3.17f 1.76f 1.47f 1.99f 1.09f 0.61f 0.81f

2 3 4 5

0.05 −0.43 −1.12 −1.52

0.32 −1.61 −2.03 −1.37

−0.29 −1.27 −2.19 −2.44

a

Reference 6, VASP code. bReference 9, VASP code. cReference 34, CASTEP code.35 dReference 30, VASP code. ePAW, GGA-PW91 functional. fUltrasoft pseudopotential, GGA-PW91 functional.

of the more strongly adsorbed metal atoms on the surface. For larger clusters (n = 2−5), Rhn binds more strongly to the γAl2O3 surface than Pdn, except for Rh2 on the hydrated (110) surface. The adsorption of Rh2 on the hydrated (110) surface yields an adsorption energy of −1.83 eV, while the adsorption energy for Pd2 is −2.11 eV. Table 5 also includes the adsorption energy Eads of individual Ir, Co, Rh, Ni, Pd, Pt, Cu, Ag, and Au atoms on the Al-terminated α-Al2O3(0001) surface. All of these metal/metal-oxide interactions are weaker than Rh with γAl2O3 except Co and Ir. The interaction of Co and Ir with Alterminated α-Al2O3(0001) is stronger than Rh adsorption on the hydrated γ-Al2O3(100) and (110) surfaces but weaker than that on the nonhydrated γ-Al2O3(100) surface. Table 5 also shows that 4d metal (Rh, Pd, Ag) bonds to the surface weakest among elements in the same column of the periodic table and that, for elements in the same row, the adsorption energy decreases from the left to the right. 3.3. Nucleation of Rhn Clusters on γ-Al2O3. To better understand the nucleation or growth of Rhn clusters on the support, we define the nucleation energy for the process illustrated schematically in Figure 5. This energy is the energy

Figure 6. Nucleation energies Enuc of gas phase Rhn cluster, Rh on the nonhydrated and hydrated γ-Al2O3(100) surface, Rh on the hydrated γ-Al2O3(110) surface, and Pd on the nonhydrated γ-Al2O3(100) surface and the hydrated γ-Al2O3(110) surface. The data for Pdn cluster on γ-Al2O3 surfaces is from ref 6.

and in weakening of previous Rh−Rh bond and Rh−support interaction. The competition of these two effects yields the overall energy balance. As shown in Table 6, the nucleation of a dimer on the (100) surfaces is thermodynamically unfavorable. For clusters with three or more Rh atoms, the nucleation becomes favorable. That is, the critical cluster size for Rh cluster nucleation on the nonhydrated or hydrated (100) surfaces is 3.36,37 For the hydrated (110) surface, the growth profile for all the Rh clusters we considered is exothermic. However, the exothermicity is still far lower than for gas phase clusters. Experiments that probed the influence of OH groups on the growth of rhodium over a well-ordered alumina film on NiAl(100) revealed that nucleation preferentially occurred on hydrated surfaces relative to nonhydrated surfaces.4,5 Our calculations cannot be directly compared to these experiments because the supported films in the experiments are not identical to the alumina surfaces described by our calculations. Nevertheless, our results also indicate the cluster nucleation is preferred on hydrated surfaces relative to the nonhydrated alumina surface we examined. In Figure 6, we also include the nucleation energy of Pdn clusters on alumina, where the data is obtained from ref 6. The nucleation of Pd and Rh shows different behavior. The nucleation energy for Pdn clusters on the nonhydrated (100) surface is positive until n = 4. That is, the critical cluster size for Pd on this surface is 4, while, for Rhn cluster, it is 3. The corresponding Enuc for Pdn on the nonhydrated (100) surface is 0.22, 0.67, 0.16, and 0.74 eV higher than those for Rhn with n from 2 to 5, respectively. For nucleation on the hydrated (110) surface, the critical cluster size for Pd is 3, while for Rh it is 2. The corresponding Enuc for Pdn on the hydrated (110) surface is 0.35, 0.81, 0.92, and 1.34 eV higher than those for Rhn with n

Figure 5. Schematic illustration of the nucleation process considered in the definition of Enuc.

gained (or lost) in combining an adsorbed monomer with a Rhn−1 cluster to form a Rhn cluster: Enuc = E(Rh n/γ ‐Al 2O3) + E(γ ‐Al 2O3) − E(Rh n − 1/γ ‐Al 2O3) − E(Rh1/γ ‐Al 2O3)

(5)

The calculated nucleation energies on each surface are shown in Table 6 and Figure 6. For each cluster size, we only considered the most energetically preferred structures. Figure 6 also shows the equivalent quantity for gas phase Rhn (n = 1−5) clusters for comparison. The addition of a Rh atom to an existing Rhn cluster on the support results in new Rh−Rh bond formation and new Rh− support interactions, which are always energetically favorable, 10628



Article

Table 7. Average Absolute Change of Rh−Rh Distance from the Gas Phase |Δd| (Rh−Rh) (Å), Bader Charge QBader (e), and DDEC Charge QDDEC (e) for Rhn Clusters on γ-Al2O3 Surfaces (The Charges Are Shown for the Entire Cluster) nonhydrated (100) n 1 2 3 4 5

hydrated (100)

|Δd|

QBader

QDDEC

0.14 0.13 0.06 0.07

−0.284 −0.711 −0.692 −0.505 −0.515

−0.092 −0.127 −0.088 −0.089 −0.184

hydrated (110)

|Δd|

QBader

QDDEC

0.21 0.06 0.03 0.08

−0.392 −0.316 −0.189 −0.185 −0.232

−0.067 −0.144 −0.293 −0.357 −0.418

from 2 to 5, respectively. These results mean that the nucleation of Pdn clusters is considerably less favorable than Rhn clusters on the same γ-Al2O3 surface. 3.4. Analysis of Electronic Properties. To provide insight regarding the nature of chemical bonding between Rhn clusters and the Al2O3 substrate, we analyzed the charges on individual atoms. Atomic charges were computed with both Bader charge38 and density derived electrostatic and chemical (DDEC) charge analysis.39,40 Table 7 lists the net cluster charge for the lowest energy state of each cluster. The two charge assignment methods give the same trend in that, on the nonhydrated and hydrated (100) surface, Rh accepts electrons from the surface, while the opposite is observed on the hydrated (110) surface. This result is similar to other transition metal adsorption on γ-Al2O3.7,41 In ref 7, Hu et al. found Pd13 or Pt13 clusters are negatively charged on the nonhydrated γAl2O3(100) surface, while those metal atoms interacting with hydroxyl become positively charged on the hydrated (110) surface. In ref 41, Valero et al. found that some of the Pd valence electrons are transferred to the neighboring surface alumnium and oxygen atoms for adsorption of a single Pd atom on the hydrated γ-Al2O3(110) surface. The different behavior of charge transfer on the (100) and (110) surfaces may be due to the shift of the adsorption sites. On the nonhydrated and hydrated (100) surface, Rhn binds to the surface terminal Al and O, while, on the hydrated (110) surface, it binds to the surface hydroxyl groups directly. This result is also consistent with experiments.4 Libuda et al. proposed the Rhn cluster binds to the surface hydroxyl group directly on the hydrated surface and the metal is positively charged.4 The quantitative differences between the Bader and DDEC charges in Table 7 arise from the different approaches these two methods take to partitioning charge from the DFT-calculated electron density among atomic centers. We also examined the distribution of charge for adsorbed monomers using electron density difference maps.39 The electron density difference (Δρ) was calculated using

|Δd|

QBader

QDDEC

0.07 0.06 0.19 0.05

0.528 0.071 0.203 0.342 0.486

0.347 0.057 0.016 0.048 0.032

Figure 7. Electron density difference map for Rh atom adsorbed on the (a) nonhydrated γ-Al2O3(100) surface, (b) hydrated γ-Al2O3(100) surface, and (c) hydrated γ-Al2O3(110) surface: accumulation region in yellow and depletion regions in blue.

contacts. Our result is similar to Pd atom adsorption on γ-Al2O3 surface.41 Valero et al. found some Pd d orbitals are depleted upon adsorption on the surface that is balanced by a significant increase of the electron density along the Pd−Al bond. There is an approximately linear relationship between the average absolute change of Rh−Rh distance from the gas phase |Δd| (Rh−Rh) and Qbader for Rhn cluster adsorption on the nonhydrated and hydrated γ-Al2O3(100) surfaces, although the slope of this relationship is different for each surface. DDEC atomic spin moments (ASMs) of Rhn/γ-Al2O3 (n = 1−5) for the most stable configuration in each system were calculated to identify the spin distribution in the system.42 The net ASMs of Rhn clusters in each most stable Rhn/γ-Al2O3 configuration are listed in Table 8. Our calculations also

Δρ = ρ(Rh/γ ‐Al 2O3) − ρ(γ ‐Al 2O3)fix − ρ(Rh)

where ρ(Rh/γ-Al2O3) is the total electron density of the Rh/γAl2O3 system, ρ(Al2O3)fix is the electron density of the alumina substrate with the deformed geometry after adsorption, and ρ(Rh) is the electron density of an isolated Rh cluster in the same geometry as the adsorbed cluster. This analysis (Figure 7) reveals that some Rh orbitals are depleted upon adsorption on the surface. This depletion is balanced by an increase of the electron density of the Rh−Al bond on the nonhydrated and hydrated (100) surfaces. On the hydrated (110) surface, the electron density difference maps (Figure 7c) reveal that some Rh orbitals are depleted upon adsorption on the surface again; however, this depletion is balanced by an increase of the electron density of the Rh−H region due to the loss of Rh−Al

Table 8. DDEC Atomic Spin Moments (ASMs) of Rhn Clusters on γ-Al2O3 Surfaces in the Most Stable Configuration (n = 1−5)

10629

n

nonhydrated (100)

hydrated (100)

hydrated (110)

1 2 3 4 5

1 2 1 2 3

1 2 3 0 2

0 5 4 4 4



Article

showed that the net ASM of γ-Al2O3 is 0. The net ASMs of Rhn clusters in each most stable configuration vary from 0 to 5, depending on which adsorbed cluster is considered. Comparing with the gas phase cluster results listed in Table 1, we see that in general, adsorption of a Rhn cluster changes its preferred spin state. The only examples in which the gas phase and adsorbed clusters were found to have the same spin states were Rh3 and Rh4 adsorption on the hydrated (100) surface.

Notes

4. SUMMARY First principles DFT calculations based on periodic supercell models were employed to investigate the nucleation and structure of Rhn (n = 1−5) clusters on nonhydrated γAl2O3(100), hydrated γ-Al2O3(100), and γ-Al2O3(110) surfaces. Our results show that individual Rh atoms adsorb strongly on the γ-Al2O3 surface with adsorption energies in the range −3.39 to −2.79 eV. Similar calculations in ref 30 showed that the strongest adsorption for Rh on α-Al2O3 was −2.52 eV. This suggests a stronger metal/metal oxide interaction on the γAl2O3 surface than on α-Al2O3, in agreement with previous calculation and experiments.31 It is well-known that the γ-Al2O3 is preferred over α-Al2O3 for catalytic purposes.32 When Rhn clusters interact with the alumina surface, they prefer to adsorb at the terminal O or Al atoms of the hydrated (100) surface instead of on the surface hydroxyls that are also potential adsorption sites. This is qualitatively consistent with the experiments by Ravenelle et al., who found that the transformation of γ-Al2O3 to a hydrated boehmite (AlOOH) phase in hot liquid water is significantly retarded by the presence of Ni or Pt particles.1 It appears that this effect is likely to be general for a large range of metal clusters, allowing metal clusters to stabilize the support by preferentially occupying the reactive sites that initiate conversion of the alumina surface into boehmite. Our calculations indicate that the nucleation of a dimer on the (100) surfaces is thermodynamically unfavorable but that nucleation becomes favorable for clusters with three or more Rh atoms. For the hydrated (110) surface, the growth profile for all the Rh clusters we considered is exothermic. The implications of our calculations are in reasonable agreement with experiments that probed the influence of OH groups on the growth of rhodium over a well-ordered alumina film on NiAl(100), where nucleation preferentially occurred on hydrated surfaces relative to nonhydrated surfaces.4,5 Analysis of the charge distribution in adsorbed clusters showed that a simple description of net charge transfer cannot apply to all of the surfaces we examined. The net charge of Rhn cluster on the nonhydrated and hydrated (100) surface is negative, while on the hydrated (110) surface it is positive. These different behaviors can be understood in terms of the different adsorption sites favored on these surfaces; on the (100) surfaces, Rhn binds to the surface terminal Al and O, while, on the hydrated (110) surface, it binds to surface hydroxyl groups. This result is also consistent with experiments, where Libuda et al. proposed the Rhn cluster binds to the surface hydroxyl group directly on the hydrated surface and the metal is positively charged.4

(1) Ravenelle, R. M.; Copeland, J. R.; Kim, W.-G.; Crittenden, J. C.; Sievers, C. Structural changes of γ-Al2O3-supported catalysts in hot liquid water. ACS Catal. 2011, 1 (5), 552−561. (2) Bowker, M.; Cassidy, T. J. Decomposition of acetate groups on an alumina-supported rhodium catalyst. J. Catal. 1998, 174 (1), 65− 71. (3) Argo, A. M.; Odzak, J. F.; Goellner, J. F.; Lai, F. S.; Xiao, F. S.; Gates, B. C. Catalysis by oxide-supported clusters of iridium and rhodium: Hydrogenation of ethene, propene, and toluene. J. Phys. Chem. B 2006, 110 (4), 1775−1786. (4) Libuda, J.; Frank, M.; Sandell, A.; Andersson, S.; Brühwiler, P. A.; Bäumer, M.; Mårtensson, N.; Freund, H. J. Interaction of rhodium with hydroxylated alumina model substrates. Surf. Sci. 1997, 384 (1− 3), 106−119. (5) Heemeier, M.; Frank, M.; Libuda, J.; Wolter, K.; Kuhlenbeck, H.; Bäumer, M.; Freund, H. J. The influence of OH groups on the growth of rhodium on alumina: a model study. Catal. Lett. 2000, 68 (1), 19− 24. (6) Valero, M. C.; Raybaud, P.; Sautet, P. Nucleation of Pdn (n=1−5) clusters and wetting of Pd particles on γ-Al2O3 surfaces: A density functional theory study. Phys. Rev. B 2007, 75 (4), 045427. (7) Hu, C. H.; Chizallet, C.; Mager-Maury, C.; Corral-Valero, M.; Sautet, P.; Toulhoat, H.; Raybaud, P. Modulation of catalyst particle structure upon support hydroxylation: Ab initio insights into Pd13 and Pt13/γ-Al2O3. J. Catal. 2010, 274 (1), 99−110. (8) Hernandez, N. C.; Sanz, J. F. First principles simulations of Cu and Au deposition on α-Al2O3 surface. Appl. Surf. Sci. 2004, 238 (1− 4), 228−232. (9) Hernandez, N. C.; Graciani, J.; Marquez, A.; Sanz, J. F. Cu, Ag and Au atoms deposited on the α-Al2O3 (0001) surface: a comparative density functional study. Surf. Sci. 2005, 575 (1−2), 189−196. (10) Sanz, J. F.; Hernandez, N. C. Mechanism of Cu deposition on the α-Al2O3 (0001) surface. Phys. Rev. Lett. 2005, 94 (1), 016104. (11) Nigam, S.; Majumder, C. Growth pattern of Agn (n=1−8) clusters on the α-Al2O3(0001) surface: A first principles study. Langmuir 2010, 26 (24), 18776−18787. (12) Alexeev, O.; Panjabi, G.; Gates, B. C. Partially decarbonylated tetrairidium clusters on γ-Al2O3: Structural characterization and catalysis of toluene hydrogenation. J. Catal. 1998, 173 (1), 196−209. (13) Digne, M.; Sautet, P.; Raybaud, P.; Euzen, P.; Toulhoat, H. Use of DFT to achieve a rational understanding of acid-basic properties of γ-alumina surfaces. J. Catal. 2004, 226 (1), 54−68. (14) Digne, M.; Sautet, P.; Raybaud, P.; Euzen, P.; Toulhoat, H. Hydroxyl groups on γ-alumina surfaces: A DFT study. J. Catal. 2002, 211 (1), 1−5. (15) Sholl, D. S.; Steckel, J. A. Density functional theory: a practical introduction; John Wiley & Sons, Inc.: Hoboken, NJ, 2009. (16) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 1992, 46 (11), 6671−6687. (17) Perdew, J. P.; Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 1992, 45 (23), 13244−13249. (18) Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 1993, 47 (1), 558−561. (19) Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6 (1), 15−50.

■

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Department of Energy under Grant No. DE-FG02-09ER16078.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 10630

REFERENCES



Article

(20) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54 (16), 11169−11186. (21) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59 (3), 1758− 1775. (22) Ankudinov, A. L.; Rehr, J. J.; Low, J. J.; Bare, S. R. Sensitivity of Pt x-ray absorption near edge structure to the morphology of small Pt clusters. J. Chem. Phys. 2002, 116 (5), 1911−1919. (23) Frenkel, A. I.; Hills, C. W.; Nuzzo, R. G. A View from the Inside: Complexity in the Atomic Scale Ordering of Supported Metal Nanoparticles. J. Phys. Chem. B 2001, 105 (51), 12689−12703. (24) Fulton, J. L.; Linehan, J. C.; Autrey, T.; Balasubramanian, M.; Chen, Y.; Szymczak, N. K. When is a nanoparticle a cluster? An operando EXAFS study of amine borane dehydrocoupling by Rh4−6 clusters. J. Am. Chem. Soc. 2007, 129 (39), 11936−11949. (25) Nayak, S. K.; Weber, S. E.; Jena, P.; Wildberger, K.; Zeller, R.; Dederichs, P. H.; Stepanyuk, V. S.; Hergert, W. Relationship between magnetism, topology, and reactivity of Rh clusters. Phys. Rev. B 1997, 56 (14), 8849−8854. (26) Reddy, B. V.; Nayak, S. K.; Khanna, S. N.; Rao, B. K.; Jena, P. Electronic structure and magnetism of Rhn (n=2−13) clusters. Phys. Rev. B 1999, 59 (7), 5214−5222. (27) Chien, C.-H.; Blaisten-Barojas, E.; Pederson, M. R. Magnetic and electronic properties of rhodium clusters. Phys. Rev. A 1998, 58 (3), 2196−2202. (28) Bae, Y.-C.; Osanai, H.; Kumar, V.; Kawazoe, Y. Nonicosahedral growth and magnetic behavior of rhodium clusters. Phys. Rev. B 2004, 70 (19), 195413. (29) Gingerich, K. A.; Cocke, D. L., Thermodynamic confirmation for the high stability of gaseous TiRh as predicted by the Brewer-Engel metallic theory and the dissociation energy of diatomic rhodium. J. Chem. Soc., Chem. Commun. 1972, (9). (30) Hernández, N. C.; Márquez, A.; Sanz, J. F.; Gomes, J. R. B.; Illas, F. Density functional theory study of Co, Rh, and Ir atoms deposited on the α-Al2O3(0001) surface. J. Phys. Chem. B 2004, 108 (40), 15671−15678. (31) Ghosh, T. K.; Nair, N. N. Oxidative addition of water to Rhn (n = 1−4) clusters on alumina surfaces and spontaneous formation of H2. J. Phys. Chem. C 2011, 115 (31), 15403−15409. (32) Weng-Sieh, Z.; Gronsky, R.; Bell, A. T. Microstructural evolution of γ-alumina-supported Rh upon aging in air. J. Catal. 1997, 170 (1), 62−74. (33) Bäumer, M.; Frank, M.; Heemeier, M.; Kühnemuth, R.; Stempel, S.; Freund, H. J. Nucleation and growth of transition metals on a thin alumina film. Surf. Sci. 2000, 454−456 (0), 957−962. (34) Briquet, L. G. V.; Catlow, C. R. A.; French, S. A. Comparison of the Adsorption of Ni, Pd, and Pt on the (0001) Surface of α-Alumina. J. Phys. Chem. C 2008, 112 (48), 18948−18954. (35) Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert, M. I. J.; Refson, K.; Payne, M. C., First principles methods using CASTEP. Z. Kristallogr. 2005, 220, 567−570. (36) Amar, J. G.; Family, F. Critical cluster size: Island morphology and size distribution in submonolayer epitaxial growth. Phys. Rev. Lett. 1995, 74 (11), 2066−2069. (37) Shi, Z.-P.; Zhang, Z.; Swan, A. K.; Wendelken, J. F. Dimer shearing as a novel mechanism for cluster diffusion and dissociation on metal (100) surfaces. Phys. Rev. Lett. 1996, 76 (26), 4927−4930. (38) (a) Henkelman, G.; Arnaldsson, A.; Jonsson, H. A fast and robust algorithm for Bader decomposition of charge density. Comput. Mater. Sci. 2006, 36 (3), 354−360. (b) Sanville, E.; Kenny, S. D.; Smith, R.; Henkelman, G. Improved grid-based algorithm for Bader charge allocation. J. Comput. Chem. 2007, 28 (5), 899−908. (c) Tang, W.; Sanville, E.; Henkelman, G. A grid-based Bader analysis algorithm without lattice bias. J. Phys.: Condens. Matter 2009, 21 (8), 084204. (39) Manz, T. A.; Sholl, D. S. Chemically meaningful atomic charges that reproduce the electrostatic potential in periodic and nonperiodic materials. J. Chem. Theory Comput. 2010, 6 (8), 2455−2468.

(40) Manz, T. A.; Sholl, D. S. Improved Atoms-in-Molecule Charge Partitioning Functional for Simultaneously Reproducing the Electrostatic Potential and Chemical States in Periodic and Non-Periodic Materials. J. Chem. Theory Comput., submitted for publication. (41) Valero, M. C.; Raybaud, P.; Sautet, P. Influence of the hydroxylation of γ-Al2O3 surfaces on the stability and diffusion of single Pd atoms: A DFT study. J. Phys. Chem. B 2006, 110 (4), 1759− 1767. (42) Manz, T. A.; Sholl, D. S. Methods for Computing Accurate Atomic Spin Moments for Collinear and Noncollinear Magnetism in Periodic and Nonperiodic Materials. J. Chem. Theory Comput. 2011, 7 (12), 4146−4164.

10631


Nucleation of Rhn (n = 1â5) Clusters on Î³-Al2O3 Surfaces: A Density

Recommend Documents

Nucleation of Rhn (n = 1â5) Clusters on Î³-Al2O3 Surfaces: A Density