Nucleation of Rh n ( n = 1–5) Clusters on γ-Al 2 O 3 Surfaces: A Density Functional Theory Study

Nucleation of Rhn (n = 1−5) Clusters on γ-Al2O3 Surfaces: A DensityFunctional Theory StudyXue-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 nonhydratedγ-Al2O3(100), hydrated γ-Al2O3(100), and hydrated γ-Al2O3(110) surfaceshas been investigated using density functional theory methods. On thesesurfaces, Rh3 prefers a triangular geometry, while Rh4 and Rh5 adopt 3Dstructures. On the (100) surfaces, Rhn binds considerably more strongly onthe nonhydrated surface than on the hydrated surface. On the hydrated(110) surface, Rhn binds to surface hydroxyl groups, which is consistent withexperimental observations. Characterizing the structure of Rhn clusters makesit possible to identify the critical cluster size for nucleation on each surface.

1. INTRODUCTIONMany practical heterogeneous catalysts are prepared as smallmetal clusters supported on metal oxide supports. In this form,catalysts provide a large active surface area and limit the fractionof atoms of the active phase, often a precious metal, that areinaccessible to reactants. In addition to enhancing the catalyticactivity of the metal phase, the presence of metal clusters on asupport can alter the stability of the support. For example,Ravenelle et al. used a range of experimental techniques toshow that the presence of Ni or Pt particles significantly retardsthe transformation of γ-Al2O3 to a hydrated boehmite(AlOOH) phase in hot liquid water.1 Their results suggestedthat the metal particles affect the kinetics of this transformationby blocking specific surface hydroxyl groups that act as initialhydration sites.In this paper, we focus on the structure of small Rh clusters

on alumina surfaces. Nanosize rhodium clusters on aluminasupport have been examined in a number of previousexperimental and theoretical studies.2−5 Bowker et al. observeda “surface explosion” for the decomposition of acetate on anoxygen-precovered Rh-alumina catalyst and on single crystals ofRh.2 Argo et al. investigated the hydrogenation reactions ofethene, propene, and toluene on small clusters of rhodium(Rh6) and of iridium (Ir4 and Ir6) (as well as of largeraggregates of these metals) on oxide supports (γ-Al2O3, MgO,and La2O3).

3 The catalysts were characterized in the workingstate by extended X-ray absorption fine structure (EXAFS)spectroscopy, providing information about the cluster struc-tures and cluster−support interactions. The EXAFS dataindicate that the metal clusters, while remaining intact andmaintaining their bonding to the support during catalysis,underwent slight rearrangements to accommodate reactiveintermediates. Scanning tunneling microscopy (STM) experi-ments have been used to study the influence of OH groups onthe growth of rhodium on a well-ordered alumina film onNiAl(100).4,5 It was shown that at 300 K nucleation of Rh

clusters preferentially occurs on a hydrated surface relative to anonhydrated surface. Photoelectron spectroscopy of bothalumina and rhodium core levels pointed to a direct chemicalinteraction between metal atoms and surface hydroxyl groups.4

The structural complexity of nanosized metal clusters onmetal oxide supports makes it difficult to obtain completestructural and electronic information for these systems evenunder well-defined experimental conditions. Theoreticalapproaches based on first-principles calculations are useful tocomplement experimental results. A number of theoreticalstudies have examined the nucleation and growth of transitionmetals on alumina, including Pd on γ-Al2O3, Pt on γ-Al2O3, Cuon α-Al2O3, Au on α-Al2O3, and Ag on α-Al2O3.

6−11 To ourknowledge, however, however, little attention has been paid tonucleation and growth of Rh on γ-Al2O3. Motivated by thegenerality suggested by Ravenelle et al. for their observedstabilization of γ-Al2O3 by small metal clusters and the catalyticactivity of small Rh clusters on this support, we have used DFTcalculations to explore the structure and stability of small Rhclusters on γ-Al2O3.To understand the structure of small metal clusters on metal

oxide supports under experimentally relevant conditions, it isimportant to correctly describe the surfaces presented by thesupport. Digne et al. found that the surface coverage ofhydroxyls on γ-Al2O3 changes as a function of preparationtemperature. During pretreatment, supported γ-alumina Rhcatalysts are typically exposed to temperature in the range 400−700 K.2,12−14 We based our calculations on the surfacestructures defined by Digne et al.13 to study the nucleationand growth mode of Rh cluster on γ-Al2O3 that has beenpretreated at ∼600 K. Critically for our purposes, thesestructures include dehydrated and hydroxyl-covered surfaces.

Received: February 3, 2012Revised: April 11, 2012Published: April 25, 2012

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By comparing the properties of small Rh clusters on thesesurfaces, we are able to consider the surface stabilizationmechanism suggested by Ravenelle et al.1

2. METHODS AND MODELSAll calculations were performed with plane-wave densityfunctional theory (DFT)15 using the Vienna ab initio simulationpackage (VASP) with the Perdew−Wang generalized gradientapproximation of the exchange-correlation functional and theprojector augmented wave (PAW) method.16−21 Spin polar-ization was employed for all calculations, and the cutoff energyfor the plane wave basis set was fixed at 400 eV. Geometryoptimization was performed with a conjugate-gradient algo-rithm and considered to be converged when the forces on eachatom become 0.03 eV/Å or less. Reciprocal space was sampledonly at the Γ-point due to the large supercell. Numerical testswith a small number of clusters on the (100) surface indicatedthat using more k-points changed the calculated adsorptionenergies by less than 2%.We adopted models for alumina surfaces from ref 13.

According to this work, γ-Al2O3 shows two main surfaces at 600K, 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 alsoexamined the hydrated (100) surface, which has 8.8 OH/nm2.The hydrated (100) surface was predicted by Digne et al. to bestable for temperatures from 475 to 570 K.13 Illustrations ofthese three surfaces are shown in Figure 1. Although the twohydrated surfaces have similar net hydroxyl densities, thedistribution of the hydroxyl groups on the two surfaces is ratherdifferent. On the hydrated (100) surface, a distinct channel ofsurface Al and O atoms exists in which no hydroxyls are found.On the hydrated (110) surface, however, the hydroxyl groupsare distributed more uniformly. To avoid lateral interactionsbetween the periodic Rh clusters, we used a slab containing 2 ×2 unit cells in the plane of the surface and four layers normal tothe surface. With these choices, the computational supercellsfor 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

γ γ= ‐ − ‐ −E E E E(Rh / Al O ) ( Al O ) (Rh )n nads 2 3 2 3 (1)

where E(Rhn/γ-Al2O3), E(γ-Al2O3), and E(Rhn) are the totalenergies of the γ-Al2O3 with Rhn cluster, the bare γ-Al2O3substrate, and the energy minimized Rhn cluster in the gasphase. This energy can be decomposed into severalcomponents. The energy associated with deformation in thestructure of the Rh cluster between the gas phase and theadsorbed state was characterized using

= ′ −E E E(Rh ) (Rh )n ndef(Rhn) (2)

where E(Rhn′) is the energy of Rhn in the gas phase using thegeometry of the adsorbed cluster on γ-Al2O3. The surfacedeformation energy associated with adsorbing a cluster,Edef(surface), was calculated in a similar way:

γ γ= ‐ ′ − ‐E E E( Al O ) ( Al O )def(surface) 2 3 2 3 (3)

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

γ γ= ‐ ′ − ′ − ‐E E E E(Rh / Al O ) (Rh ) ( Al O )n nint 2 3 2 3 (4)

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

3. RESULTS AND DISCUSSION

3.1. Gas Phase Clusters. We first briefly describe thegeometries and energies of gas phase Rhn clusters, which areessential to understand the growth behavior of Rhn cluster on γ-Al2O3 surfaces. The geometries of Rhn (n = 2−5) and bulk fcc

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 thefirst 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 stickrepresentation.

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp301114n | J. Phys. Chem. C 2012, 116, 10623−1063110624


Rh were computed using the methods described above. Weconsidered 1D, 2D, and 3D structures for the gas phase Rhn,and only the energetically preferred geometries are summarizedin Table 1. Rh−Rh distances in the clusters are shorter than inthe bulk structure and increase with size, although the bulkvalue is far from being reached. The degree of bond contractionrelative to the bulk follows an approximately n−1/3 relation-ship.22 A similar bond contraction has been characterizedexperimentally for Pt clusters by EXAFS.23 Fulton et al. foundthat the Rh−Rh bond distance in organometallic Rh4−6 clustersis longer than the bulk value due to the role of ligandscoordinated to the cluster while small clusters without ligandsexhibit bond contraction.24 As expected, the cohesive energyincreases as the cluster size increases due to increased atomiccoordination. The difference between the cohesive energy of acluster and the bulk cohesive energy scales approximately asn−1/3. A similar n−1/3 dependence has been reported byAnkudinov et al. for small Pt clusters.22 Table 1 also includesthe results of other theoretical calculations dealing with gasphase Rh clusters. Our most stable structures and magneticmoments are consistent with other groups.25−28 The calculatedbond distance of the dimer is 2.22 Å, which is close to theexperimental value of 2.28 Å. Our calculated bond distances aregenerally slightly shorter than other theoretical results listed inTable 1.3.2. Adsorption of Rhn Clusters. 3.2.1. Adsorption on

the Nonhydrated and Hydrated γ-Al2O3(100) Surface. Wenow discuss the adsorption of Rh clusters on the nonhydratedand hydrated γ-Al2O3(100) surface. The adsorption of anisolated Rh atom was examined by placing a Rh atom on a large

number of well-defined adsorption sites that are available onthe surface. On the nonhydrated (100) surface, we consideredeight 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 thehydrated (100) surface, our calculations included 11 top sitesincluding each site labeled in Figure 1b, 12 bridge sites asdefined on the nonhydrated surface, and two hollow sites. Forthe hydrated (110) surface, Al (1), O(F), and O(J) are lessfavorable than the other labeled sites according to ref 6; thus,they are excluded from our present work. For Rhn clusters withn > 1, we used two methods to generate initial approximationsof adsorbed configurations. First, we added an additional Rhatom in various configurations to the most stable Rhn−1 cluster.Second, we put the Rhn (n > 1) cluster in its gas phasegeometry on the well-defined adsorption sites listed above. Themost energetically preferred structures obtained from energyminimization of this range of initial conditions on thenonhydrated surface are shown in Figure 2. The correspondingadsorption energies are listed in Table 2. The average Rh−Rhdistance for Rh atoms in contact with the support is slightlylarger than those for the free Rhn clusters, although the Rh−Rhdistances 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 atominserts approximately into the surface plane, with an adjacentoxygen atom moving upward to accommodate the Rh atom.

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

n geometry M (μB) d(Rh−Rh) (Å) CEa (eV/atom) BEb (eV)

2 D∞h 4(4c,d) 2.22(2.34,d 2.26,f 2.28g) −2.02 −4.043 D3h 3(3c,d) 2.39(2.45,d 2.42f) −2.63 −2.634 Td 0(0c,d) 2.45(2.50,d 2.49f) −3.11 −2.075 C4v 5(5c,e) 2.40/2.56(2.48/2.63g) −3.38 −2.11bulk fcc 0 2.72 −6.11 −1.02

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

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, andotherwise, the color scheme is identical to Figure 1.




Adsorbate-induced surface relaxation on γ-Al2O3(100) has beenobserved for other transition metals such as Pd.6 Comparisonof monomer and dimer species reveals that the Rh−Al bonddefined by the Rh in the plane of the surface enlarges to 2.39 Åin the dimer from 2.31 Å for the monomer. This is consistentwith the substantial increase in the surface deformation energyshown in Table 2, from 1.70 eV for the monomer to 2.58 eV forthe dimer.For Rh3 adsorption, the most stable structure is a triangular

Rh3 cluster on the surface with all Rh atoms bonded to thesurface. The most stable linear isomer is 0.17 eV higher inenergy than the triangular state. This energy difference can beattributed to the deformation of the surface and cluster. Asshown in Table 2, the deformation energies for the Rh3 clusterand the surface are, in the triangular case, 0.81 and 2.63 eV,respectively. The corresponding values are significantly largerfor 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 clusterare above the surface. This represents a transition from the highdeformation situation for n = 1−3 to a situation where thedeformation of the cluster is relatively small. The 2D squareplanar structure is less stable than the 3D structure. In the gasphase, the 3D tetrahedron structure is 0.18 eV lower than the2D square planar structure, while, for adsorption on the surface,the former is 0.43 eV lower than the latter. Similar results wereobserved for Rh5. For Rh4 and Rh5 clusters, the linear

configurations were also considered on the surface. Theadsorption energy Eads for linear Rh4 and Rh5 cluster is 1.06and 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 ahydroxyl coverage of 8.8 OH/nm2. The most favorablestructures are shown in Figure 3, and the correspondingadsorption energy is listed in Table 3.

As shown in Figure 3, a single Rh atom prefers to insert intothe surface, where it bonds to two surface O atoms, one surfaceAl, and one subsurface Al, yielding a strong surface deformationof 1.41 eV. When a dimer adsorbs, the original Rh atommonomer is extracted from the surface. The Rh−Rh bonddistance in the adsorbed dimer is 2.43 Å, compared to 2.22 Åfor the gas phase cluster. Adsorption of Rh3 forms a triangularcluster that is quite different from the result on thenonhydrated surface. On the hydrated surface, the trimerbinds to the surface just through one Rh atom. The lineartrimer binds to the surface through the two Rh atoms at theend of the cluster. Similar to the nonhydrated surface, Rh4 andRh5 favor 3D configurations on the hydrated surface. As for thenonhydrated surface, the average Rh−Rh distance for Rh atomsin contact with the hydrated support is slightly larger than thosefor the free Rhn clusters (although the Rh−Rh distances in theapex edges for Rh5 are shorter). Unlike the nonhydrated (100)

Table 2. The Adsorption Energy, Eads, Interaction Energy,Eint, Rhn Deformation Energy, Edef(Rhn), Surface DeformationEnergy, Edef(surface), and Average Rh−Rh Bond Distancesd(Rh−Rh) (Å) of Rhn Cluster on the Nonhydrated γ-Al2O3(100) Surface (All Energies Are in eV)

N Eads Eint Edef(Rhn) Edef(surface) d(Rh−Rh)

1 −3.39 −5.09 1.702 −2.70 −5.44 0.16 2.58 2.363-triangular −2.67 −6.11 0.81 2.63 2.523-linear −2.50 −7.61 1.14 3.97 2.474 −2.63 −4.55 0.22 1.71 2.56/2.44a

5 −3.07 −4.91 0.16 1.68 2.49/2.51a

aBase and apex edges, respectively.

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

Table 3. The Adsorption Energy Eads (eV), InteractionEnergy Eint (eV), Rhn Deformation Energy Edef(Rhn) (eV),Surface Deformation Energy Edef(surface) (eV), and AverageRh−Rh Bond Distances d(Rh−Rh) (Å) of Rhn Cluster onthe Hydrated (100) Surface

N Eads Eint Edef(Rhn) Edef(surface) d (Rh−Rh)


5 −2.34 −4.01 0.16 1.51 2.50/2.50a





surface, the average Rh−Rh distance for Rh atoms in the apexedges of Rh4 is slightly longer than those for the free Rh4clusters.Comparing Tables 2 and 3 shows that the adsorption energy

of Rhn clusters on the hydrated (100) surface is weaker thanthat on the nonhydrated (100) surface. For each cluster, thesurface OH groups have an unfavorable effect on theadsorption of Rhn clusters. It is noteworthy that the Rhnclusters prefer to adsorb at the terminal O or Al atoms of thehydrated surface instead on the surface hydroxyl layer. This isqualitatively consistent with the experiments by Ravenelle et al.,who found that the presence of Ni or Pt particles significantlyretards the transformation of γ-Al2O3 to a hydrated boehmite(AlOOH) phase in hot liquid water.1 It appears that this effectis likely to be general for a large range of metal clusters, whichcan stabilize the support by preferentially occupying thereactive sites that initiate conversion of the alumina surfaceinto boehmite.3.2.2. Adsorption on the Hydrated (110) Surface. We

performed similar calculations to those discussed above for Rhclusters on the hydrated γ-Al2O3(110) surface. The energeticparameters for these clusters are listed in Table 4, and the

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

Al2O3(110) surface are more uniformly distributed than thegroups on the (100) surface. This has important implicationsfor the adsorption on Rh clusters. As shown in Figure 4a, unlikethe nonhydrated and hydrated (100) surfaces, a Rh atom onthe hydrated (110) surface binds to the surface hydroxyl groupsdirectly, where it inserts in the first hydroxyl layer rather than inthe first oxide layer. The state with Rh binding to the surface(not the hydroxyl) is less stable by 0.48 eV. For the adsorbeddimer, both Rh atoms bind approximately in the surface plane,with one Rh atom binding to O in a hydroxyl and also a surfaceO and the other Rh binding to a surface Al. For the linearisomer of Rh3, the two bottom Rh atoms still insert in thesurface plane, while, for the trigonal trimer, all three atoms arein a plane above the first hydroxyl layer. The triangular clusteris more stable than the linear cluster by 0.06 eV. Theadsorption of a Rh4 cluster cleaves one of the Rh−Rh bonds inthe gas phase cluster. This enhances the cluster’s interactionwith the support at the cost of a large cluster deformationenergy. Rh5 adsorbs in a configuration quite similar to the gasphase cluster. Similar to the other surfaces, the average Rh−Rhdistance for Rh atoms in contact with the support is slightlylarger than those for the free Rhn clusters, while the Rh−Rhdistances 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 samefunctional in ref 30 showed that the strongest adsorption forRh on α-Al2O3 was −2.52 eV. This comparison reflects astronger metal/metal oxide interaction on the γ-Al2O3 surfacethan on α-Al2O3, in agreement with previous calculations andexperiments.31 It is well-known that the γ-Al2O3 is preferredover α-Al2O3 for catalytic purposes.

32

As shown in Table 5, Rh binds more strongly to the γ-Al2O3surface than Pd, in agreement with experimental results.Baumer et al. studied the growth of Rh and Pd on a thin,well-ordered alumina film at two different temperatures, 90 and300 K, although due to experimental limitations the character-ization of the deposits by STM was always performed at 300K.33 It was shown that the metal support interaction for Rh wasstronger than that for Pd, with a decrease of the overall mobility

Table 4. The Adsorption Energy Eads (eV), InteractionEnergy Eint (eV), Rhn Deformation Energy Edef(Rhn) (eV),Surface Deformation Energy Edef(surface) (eV), and AverageRh−Rh Bond Distances d(Rh−Rh) (Å) of Rhn Cluster onthe Hydrated (110) Surface

N Eads Eint Edef(Rhn) Edef(surface) d(Rh−Rh)


5 −3.21 −4.94 0.06 1.66 2.45/2.51a


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




of the more strongly adsorbed metal atoms on the surface. Forlarger clusters (n = 2−5), Rhn binds more strongly to the γ-Al2O3 surface than Pdn, except for Rh2 on the hydrated (110)surface. The adsorption of Rh2 on the hydrated (110) surfaceyields an adsorption energy of −1.83 eV, while the adsorptionenergy for Pd2 is −2.11 eV. Table 5 also includes the adsorptionenergy Eads of individual Ir, Co, Rh, Ni, Pd, Pt, Cu, Ag, and Auatoms on the Al-terminated α-Al2O3(0001) surface. All of thesemetal/metal-oxide interactions are weaker than Rh with γ-Al2O3 except Co and Ir. The interaction of Co and Ir with Al-terminated α-Al2O3(0001) is stronger than Rh adsorption onthe hydrated γ-Al2O3(100) and (110) surfaces but weaker thanthat on the nonhydrated γ-Al2O3(100) surface. Table 5 alsoshows that 4d metal (Rh, Pd, Ag) bonds to the surface weakestamong elements in the same column of the periodic table andthat, for elements in the same row, the adsorption energydecreases 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 thesupport, we define the nucleation energy for the processillustrated schematically in Figure 5. This energy is the energy

gained (or lost) in combining an adsorbed monomer with aRhn−1 cluster to form a Rhn cluster:

γ γ γ

γ

= ‐ + ‐ −

‐ − ‐−E E E E

E

(Rh / Al O ) ( Al O ) (Rh /

Al O ) (Rh / Al O )n nnuc 2 3 2 3 1

2 3 1 2 3 (5)

The calculated nucleation energies on each surface are shown inTable 6 and Figure 6. For each cluster size, we only consideredthe most energetically preferred structures. Figure 6 also showsthe equivalent quantity for gas phase Rhn (n = 1−5) clusters forcomparison.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,

and in weakening of previous Rh−Rh bond and Rh−supportinteraction. The competition of these two effects yields theoverall energy balance. As shown in Table 6, the nucleation of adimer on the (100) surfaces is thermodynamically unfavorable.For clusters with three or more Rh atoms, the nucleationbecomes favorable. That is, the critical cluster size for Rhcluster nucleation on the nonhydrated or hydrated (100)surfaces is 3.36,37

For the hydrated (110) surface, the growth profile for all theRh clusters we considered is exothermic. However, theexothermicity is still far lower than for gas phase clusters.Experiments that probed the influence of OH groups on thegrowth of rhodium over a well-ordered alumina film onNiAl(100) revealed that nucleation preferentially occurred onhydrated surfaces relative to nonhydrated surfaces.4,5 Ourcalculations cannot be directly compared to these experimentsbecause the supported films in the experiments are not identicalto the alumina surfaces described by our calculations.Nevertheless, our results also indicate the cluster nucleation ispreferred on hydrated surfaces relative to the nonhydratedalumina 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. Thenucleation of Pd and Rh shows different behavior. Thenucleation energy for Pdn clusters on the nonhydrated (100)surface is positive until n = 4. That is, the critical cluster size forPd on this surface is 4, while, for Rhn cluster, it is 3. Thecorresponding Enuc for Pdn on the nonhydrated (100) surface is0.22, 0.67, 0.16, and 0.74 eV higher than those for Rhn with nfrom 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) surfaceis 0.35, 0.81, 0.92, and 1.34 eV higher than those for Rhn with n

Table 5. The Adsorption Energy Eads (eV) of IndividualTransition Metal Atoms on Alumina

−EadsRh/γ-Al2O3 2.79−3.39e

Pd/γ-Al2O3a 1.72−2.04e

Co/α-Al2O3(0001)b 3.02f

Rh/α-Al2O3(0001)b 2.52f

Ir/α-Al2O3(0001)b 3.17f

Ni/α-Al2O3(0001)c 1.76f

Pd/α-Al2O3(0001)c 1.47f

Pt/α-Al2O3(0001)c 1.99f

Cu/α-Al2O3(0001)d 1.09f

Ag/α-Al2O3(0001)d 0.61f

Au/α-Al2O3(0001)d 0.81f

aReference 6, VASP code. bReference 9, VASP code. cReference 34,CASTEP code.35 dReference 30, VASP code. ePAW, GGA-PW91functional. fUltrasoft pseudopotential, GGA-PW91 functional.

Figure 5. Schematic illustration of the nucleation process consideredin the definition of Enuc.

Table 6. Nucleation Energy Enuc (eV) for Rhn Clusters on γ-Al2O3 Surfaces

N nonhydrated (100) hydrated (100) hydrated (110)

2 0.05 0.32 −0.293 −0.43 −1.61 −1.274 −1.12 −2.03 −2.195 −1.52 −1.37 −2.44

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





from 2 to 5, respectively. These results mean that thenucleation of Pdn clusters is considerably less favorable thanRhn clusters on the same γ-Al2O3 surface.3.4. Analysis of Electronic Properties. To provide insight

regarding the nature of chemical bonding between Rhn clustersand the Al2O3 substrate, we analyzed the charges on individualatoms. Atomic charges were computed with both Badercharge38 and density derived electrostatic and chemical(DDEC) charge analysis.39,40 Table 7 lists the net clustercharge for the lowest energy state of each cluster. The twocharge assignment methods give the same trend in that, on thenonhydrated and hydrated (100) surface, Rh accepts electronsfrom the surface, while the opposite is observed on thehydrated (110) surface. This result is similar to other transitionmetal adsorption on γ-Al2O3.

7,41 In ref 7, Hu et al. found Pd13or Pt13 clusters are negatively charged on the nonhydrated γ-Al2O3(100) surface, while those metal atoms interacting withhydroxyl become positively charged on the hydrated (110)surface. In ref 41, Valero et al. found that some of the Pdvalence electrons are transferred to the neighboring surfacealumnium and oxygen atoms for adsorption of a single Pd atomon the hydrated γ-Al2O3(110) surface. The different behavior ofcharge transfer on the (100) and (110) surfaces may be due tothe shift of the adsorption sites. On the nonhydrated andhydrated (100) surface, Rhn binds to the surface terminal Aland O, while, on the hydrated (110) surface, it binds to thesurface hydroxyl groups directly. This result is also consistentwith experiments.4 Libuda et al. proposed the Rhn cluster bindsto the surface hydroxyl group directly on the hydrated surfaceand the metal is positively charged.4 The quantitativedifferences between the Bader and DDEC charges in Table 7arise from the different approaches these two methods take topartitioning charge from the DFT-calculated electron densityamong atomic centers.We also examined the distribution of charge for adsorbed

monomers using electron density difference maps.39 Theelectron density difference (Δρ) was calculated using

ρ ρ γ ρ γ ρΔ = ‐ − ‐ −(Rh/ Al O ) ( Al O ) (Rh)2 3 2 3 fix

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

contacts. Our result is similar to Pd atom adsorption on γ-Al2O3surface.41 Valero et al. found some Pd d orbitals are depletedupon adsorption on the surface that is balanced by a significantincrease of the electron density along the Pd−Al bond. There isan approximately linear relationship between the averageabsolute change of Rh−Rh distance from the gas phase |Δd|(Rh−Rh) and Qbader for Rhn cluster adsorption on thenonhydrated and hydrated γ-Al2O3(100) surfaces, althoughthe 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 werecalculated to identify the spin distribution in the system.42 Thenet ASMs of Rhn clusters in each most stable Rhn/γ-Al2O3configuration are listed in Table 8. Our calculations also

Table 7. Average Absolute Change of Rh−Rh Distance from the Gas Phase |Δd| (Rh−Rh) (Å), Bader Charge QBader (e), andDDEC Charge QDDEC (e) for Rhn Clusters on γ-Al2O3 Surfaces (The Charges Are Shown for the Entire Cluster)

nonhydrated (100) hydrated (100) hydrated (110)

n |Δd| QBader QDDEC |Δd| QBader QDDEC |Δd| QBader QDDEC

1 −0.284 −0.092 −0.392 −0.067 0.528 0.3472 0.14 −0.711 −0.127 0.21 −0.316 −0.144 0.07 0.071 0.0573 0.13 −0.692 −0.088 0.06 −0.189 −0.293 0.06 0.203 0.0164 0.06 −0.505 −0.089 0.03 −0.185 −0.357 0.19 0.342 0.0485 0.07 −0.515 −0.184 0.08 −0.232 −0.418 0.05 0.486 0.032

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

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

n nonhydrated (100) hydrated (100) hydrated (110)

1 1 1 02 2 2 53 1 3 44 2 0 45 3 2 4




showed that the net ASM of γ-Al2O3 is 0. The net ASMs of Rhnclusters in each most stable configuration vary from 0 to 5,depending on which adsorbed cluster is considered. Comparingwith the gas phase cluster results listed in Table 1, we see thatin general, adsorption of a Rhn cluster changes its preferred spinstate. The only examples in which the gas phase and adsorbedclusters were found to have the same spin states were Rh3 andRh4 adsorption on the hydrated (100) surface.

4. SUMMARY

First principles DFT calculations based on periodic supercellmodels were employed to investigate the nucleation andstructure of Rhn (n = 1−5) clusters on nonhydrated γ-Al2O3(100), hydrated γ-Al2O3(100), and γ-Al2O3(110) surfaces.Our results show that individual Rh atoms adsorb strongly onthe γ-Al2O3 surface with adsorption energies in the range −3.39to −2.79 eV. Similar calculations in ref 30 showed that thestrongest adsorption for Rh on α-Al2O3 was −2.52 eV. Thissuggests a stronger metal/metal oxide interaction on the γ-Al2O3 surface than on α-Al2O3, in agreement with previouscalculation and experiments.31 It is well-known that the γ-Al2O3is preferred over α-Al2O3 for catalytic purposes.

32

When Rhn clusters interact with the alumina surface, theyprefer to adsorb at the terminal O or Al atoms of the hydrated(100) surface instead of on the surface hydroxyls that are alsopotential adsorption sites. This is qualitatively consistent withthe experiments by Ravenelle et al., who found that thetransformation of γ-Al2O3 to a hydrated boehmite (AlOOH)phase in hot liquid water is significantly retarded by thepresence of Ni or Pt particles.1 It appears that this effect is likelyto be general for a large range of metal clusters, allowing metalclusters to stabilize the support by preferentially occupying thereactive sites that initiate conversion of the alumina surface intoboehmite.Our calculations indicate that the nucleation of a dimer on

the (100) surfaces is thermodynamically unfavorable but thatnucleation becomes favorable for clusters with three or moreRh atoms. For the hydrated (110) surface, the growth profilefor all the Rh clusters we considered is exothermic. Theimplications of our calculations are in reasonable agreementwith experiments that probed the influence of OH groups onthe growth of rhodium over a well-ordered alumina film onNiAl(100), where nucleation preferentially occurred onhydrated surfaces relative to nonhydrated surfaces.4,5

Analysis of the charge distribution in adsorbed clustersshowed that a simple description of net charge transfer cannotapply to all of the surfaces we examined. The net charge of Rhncluster on the nonhydrated and hydrated (100) surface isnegative, while on the hydrated (110) surface it is positive.These different behaviors can be understood in terms of thedifferent 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 surfacehydroxyl groups. This result is also consistent with experiments,where Libuda et al. proposed the Rhn cluster binds to thesurface hydroxyl group directly on the hydrated surface and themetal is positively charged.4

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

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

■ REFERENCES(1) Ravenelle, R. M.; Copeland, J. R.; Kim, W.-G.; Crittenden, J. C.;Sievers, C. Structural changes of γ-Al2O3-supported catalysts in hotliquid water. ACS Catal. 2011, 1 (5), 552−561.(2) Bowker, M.; Cassidy, T. J. Decomposition of acetate groups onan 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 andrhodium: Hydrogenation of ethene, propene, and toluene. J. Phys.Chem. B 2006, 110 (4), 1775−1786.(4) Libuda, J.; Frank, M.; Sandell, A.; Andersson, S.; Bruhwiler, P. A.;Baumer, M.; Martensson, N.; Freund, H. J. Interaction of rhodiumwith hydroxylated alumina model substrates. Surf. Sci. 1997, 384 (1−3), 106−119.(5) Heemeier, M.; Frank, M.; Libuda, J.; Wolter, K.; Kuhlenbeck, H.;Baumer, M.; Freund, H. J. The influence of OH groups on the growthof 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 densityfunctional 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 particlestructure upon support hydroxylation: Ab initio insights into Pd13 andPt13/γ-Al2O3. J. Catal. 2010, 274 (1), 99−110.(8) Hernandez, N. C.; Sanz, J. F. First principles simulations of Cuand 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, Agand Au atoms deposited on the α-Al2O3 (0001) surface: a comparativedensity functional study. Surf. Sci. 2005, 575 (1−2), 189−196.(10) Sanz, J. F.; Hernandez, N. C. Mechanism of Cu deposition onthe 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 decarbonylatedtetrairidium clusters on γ-Al2O3: Structural characterization andcatalysis of toluene hydrogenation. J. Catal. 1998, 173 (1), 196−209.(13) Digne, M.; Sautet, P.; Raybaud, P.; Euzen, P.; Toulhoat, H. Useof DFT to achieve a rational understanding of acid-basic properties ofγ-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 practicalintroduction; 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 approximationfor exchange and correlation. Phys. Rev. B 1992, 46 (11), 6671−6687.(17) Perdew, J. P.; Wang, Y. Accurate and simple analyticrepresentation of the electron-gas correlation energy. Phys. Rev. B1992, 45 (23), 13244−13249.(18) Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquidmetals. Phys. Rev. B 1993, 47 (1), 558−561.(19) Kresse, G.; Furthmuller, J. Efficiency of ab-initio total energycalculations for metals and semiconductors using a plane-wave basisset. Comput. Mater. Sci. 1996, 6 (1), 15−50.



mailto:[email protected]

(20) Kresse, G.; Furthmuller, J. Efficient iterative schemes for abinitio total-energy calculations using a plane-wave basis set. Phys. Rev. B1996, 54 (16), 11169−11186.(21) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to theprojector 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 ofPt x-ray absorption near edge structure to the morphology of small Ptclusters. J. Chem. Phys. 2002, 116 (5), 1911−1919.(23) Frenkel, A. I.; Hills, C. W.; Nuzzo, R. G. A View from theInside: Complexity in the Atomic Scale Ordering of Supported MetalNanoparticles. 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? Anoperando EXAFS study of amine borane dehydrocoupling by Rh4−6clusters. 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 betweenmagnetism, 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. Magneticand electronic properties of rhodium clusters. Phys. Rev. A 1998, 58(3), 2196−2202.(28) Bae, Y.-C.; Osanai, H.; Kumar, V.; Kawazoe, Y. Nonicosahedralgrowth and magnetic behavior of rhodium clusters. Phys. Rev. B 2004,70 (19), 195413.(29) Gingerich, K. A.; Cocke, D. L., Thermodynamic confirmationfor the high stability of gaseous TiRh as predicted by the Brewer-Engelmetallic theory and the dissociation energy of diatomic rhodium. J.Chem. Soc., Chem. Commun. 1972, (9).(30) Hernandez, N. C.; Marquez, A.; Sanz, J. F.; Gomes, J. R. B.; Illas,F. Density functional theory study of Co, Rh, and Ir atoms depositedon 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. Microstructuralevolution of γ-alumina-supported Rh upon aging in air. J. Catal.1997, 170 (1), 62−74.(33) Baumer, M.; Frank, M.; Heemeier, M.; Kuhnemuth, R.;Stempel, S.; Freund, H. J. Nucleation and growth of transition metalson 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 ofthe 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 usingCASTEP. Z. Kristallogr. 2005, 220, 567−570.(36) Amar, J. G.; Family, F. Critical cluster size: Island morphologyand 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. Dimershearing as a novel mechanism for cluster diffusion and dissociation onmetal (100) surfaces. Phys. Rev. Lett. 1996, 76 (26), 4927−4930.(38) (a) Henkelman, G.; Arnaldsson, A.; Jonsson, H. A fast androbust 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 Badercharge allocation. J. Comput. Chem. 2007, 28 (5), 899−908. (c) Tang,W.; Sanville, E.; Henkelman, G. A grid-based Bader analysis algorithmwithout lattice bias. J. Phys.: Condens. Matter 2009, 21 (8), 084204.(39) Manz, T. A.; Sholl, D. S. Chemically meaningful atomic chargesthat reproduce the electrostatic potential in periodic and nonperiodicmaterials. J. Chem. Theory Comput. 2010, 6 (8), 2455−2468.

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



Documents

Nucleation of Rh n ( n = 1–5) Clusters on γ-Al 2 O 3 Surfaces: A Density Functional Theory Study