Theoretical Investigation of Small Transition-Metal Clusters Supported

Article pubs.acs.org/JPCC

Theoretical Investigation of Small Transition-Metal Clusters Supported on the CeO2(111) Surface Maurício J. Piotrowski,*,† Polina Tereshchuk,*,‡ and Juarez L. F. Da Silva*,‡ †

Departamento de Física, Universidade Federal de Pelotas, Caixa Postal 354, 96010-900 Pelotas, Rio Grande do Sul, Brazil São Carlos Institute of Chemistry, University of São Paulo, PO Box 780, 13560-970 São Carlos, São Paulo, Brazil

‡

S Supporting Information *

ABSTRACT: We have performed a systematic investigation of 4-atom transition-metal (TM) clusters (TM = Cu, Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au) supported on the unreduced CeO2(111) surface using density functional theory calculations within the Perdew−Burke−Ernzerhof functional and on-site Coulomb interactions for the Ce f-states. We found two structure TM4 patterns on CeO2(111), namely, twodimensional (2D) arrays with zigzag orientation for Ru, Rh, Os, and Ir and tetrahedral three-dimensional (3D) configurations for Cu, Pd, Ag, Pt, and Au. Our analyses indicate that the occupation of the antibonding d-states and the hybridization of the TM d-states with O p-states play a crucial role in the magnitude of the TM−TM and TM−O interactions and determine the formation of the 2D and 3D configurations on CeO2(111). The interaction of TM4 with the CeO2(111) surface changes the nature of the occupied Ce f-states from itinerant (CeIV in the clean surface) to localized (CeIII) states; hence, it increases the atomic size of CeIII compared with CeIV by 4.4%, which plays a crucial role in building in a lateral tensile strain in the topmost Ce layer in the surface. Furthermore, we found an enhancement of the electron localization of the TM d-states upon the adsorption of TM4 on CeO2(111). We found that the number of Ce atoms in the CeIII oxidation state depends on the TM element and structure. For Ru, Rh, Os, and Ir on CeO2(111), all the Ce atoms in the topmost Ce layer change the oxidation state from IV to III (i.e., 100%), while for (Pd, Pt) and (Cu, Ag, Au) on CeO2(111), only 25% and 50% of Ce atoms, respectively, convert the oxidation state from IV to III.

I. INTRODUCTION Typical catalysts are composed of transition metals (TMs) such as Ru, Rh, Pd, and Pt supported on oxides (e.g., Al2O3, V2O5, CeO2, etc.), where the catalytic activity and selectivity of chemical reactions are dependent on the TM particles (chemical species, size, shape, etc.) and substrate properties (stability, surface orientation, oxygen vacancies, etc.), as well as on synergetic effects that might arise in the TM−oxide systems. Among a wide range of TMs and oxides combinations,1−8 TMs supported on cerium oxides (CeO2) have attracted great interest because of the wide use of cerium-oxides as support in catalysis,4−6,9−24 in particular, in three-way-catalysts,10 water− gas shift reaction,9,12,13,19,20,25 CO oxidation in ceria-based catalysts,8,21,24 growth of carbon nanotubes,22 methanol synthesis,11 etc. The figures of merit of cerium oxides have been attributed to the following key factors: (i) oxygen storage capacity,26,27 which is the ability of ceria to release or store oxygen; (ii) change in the oxidation state of the Ce atoms (e.g., from CeIV to CeIII or vice versa) under different environment conditions such as oxygen concentration;27−29 (iii) high thermodynamic stability (even for high concentration of oxygen vacancies);10,27,30 and (iv) synergetic effects that arise from the combination of CeO2 with different oxides. For example, it has © XXXX American Chemical Society

been suggested that the mixture of CeO 2 with ZrO 2 (CeyZr1−yO2) contributes to reduce the energy to create oxygen vacancies.27,30−32 Thus, there is a solid understanding of the figures of merit of CeO2; in contrast, our atomistic understanding of the interaction of TMs with cerium oxides is far from complete because of the small number of studies, and most of them focused on Pt and Au supported on CeO2(111).4−6,14−19,24 Bruix et al.18,19 studied the effects of Pt8 clusters supported on the reduced CeO2(111) surface employing spin-polarized density functional theory (DFT) calculations within a semilocal exchange-correlation functional with the addition of a Hubbard U parameter (i.e., DFT+U). They found indications of strong metal−support interactions; hence, large electronic perturbations were observed on the Pt cluster and ceria surface, that contributes to increase the ability of the metal to dissociate the O−H bonds of water molecules. Furthermore, they found that the formation of oxygen vacancies was facilitated by the spillover of oxygen from the substrate to the Pt particle, which affects the storage and release of oxygen atoms. Received: May 27, 2014 Revised: August 26, 2014

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dx.doi.org/10.1021/jp505216y | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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(VASP).42,43 The frozen core states are described relativistically, while the valence states are described by the scalar relativistic approximation (i.e., spin−orbit coupling is not taken into account for the valence states). All calculations were performed using the PAW projectors provided within VASP.44 To select the plane-wave cutoff energy, several calculations were performed as a function of the cutoff energy. From that, all total energy and geometry optimizations were performed using a cutoff energy of 400 eV, while for the equilibrium volume optimizations using stress tensor and atomic forces, we employed a cutoff energy of 800 eV, which is required because of the slow convergence of the stress tensor as a function of the number of plane-waves. To model the interaction of the TM4 clusters with the CeO2(111) surface, we employed the repeated slab geometry with a vacuum region of 15 Å and a (2 × 2) surface unit cell. The topmost interlayer relaxations in the clean unreduced CeO2(111) surface are in the range from 1.0−2.0%,45−47 which relates with the high stability of the CeO2(111) surface. We will consider the adsorption of TM4 only on the CeO2(111) surface, and no subsurface sites will be regarded. Thus, we accounted for a slab with six layers in our calculations. The topmost five layers were relaxed, while the bottom layer was frozen in the relaxed clean CeO2(111) surface positions. For the TM4 clusters and free-atom calculations in the gas phase, we employed a cubic (a = 14 Å) and orthorhombic (14 × 14.25 × 14.50 Å3) boxes, respectively, which can yield accurate results as the TM clusters contain only four atoms. For the Brillouin zone (BZ) integration, we employed a 6 × 6 × 1 k-mesh and a Gaussian smearing parameter, σ, of 0.10 eV for TM4/CeO2(111); however, for CeO2 in the bulk phase, we employed a 18 × 18 × 18 k-mesh with σ = 0.10 eV. For the cluster and free-atom calculations, in which there is no dispersion of the electronic states, we employed only a single k-point (Γ-point) with σ = 0.0010 eV. A small σ is required to avoid fractional occupation of the electronic states, which can affect the results for clusters and free-atoms calculations. For all calculations, the equilibrium geometry was obtained once the atomic forces on every atom were smaller than 0.025 eV/Å and employing a total energy convergence of 10−4 eV. The present set-up yields binding energies and geometric parameters with an accuracy of ±0.10 eV and ±0.05 Å, respectively. B. Atomic Structure Generation. To identify a reliable set of lowest-energy configurations for the TM4/CeO2(111) systems (TM = Cu, Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au), the following steps were performed: (i) Ab-initio molecular dynamics (MD) calculations using a cutoff energy of 300 eV (soft oxygen PAW potential) for about 20−30 ps (time step of 2 fs) were performed for TM4/CeO2(111) starting from TM4 clusters with tetrahedron or planar configurations supported on CeO2(111). For those calculations, an initial and final temperatures of 2000 and 0 K were employed, respectively, while only the TM atoms and the topmost O and Ce layers were allowed to relax along the MD calculations. (ii) A large number of atomic configurations were selected among the MD structures (about 100 models equally distributed along of the simulation) and analyzed, and a final set of about 15−20 configurations was selected for each system. (iii) All the selected configurations were optimized using the conjugated gradient algorithm as implemented in VASP. We found that different initial configurations can yield very similar local minimum structures. For those cases, the structures with great similarity were removed from our set and replaced by a new

The nucleation of small Aun (n = 1−11) clusters on ceria surface was investigated by Zhang et al.17 employing DFT calculations. In particular, they studied the nucleation patterns and found a reminiscent bulk Au feature (e.g., motifs of the face-centered cubic lattice) and indication of a novel hexagonal close-packed (hcp) structure. The mechanisms of Au adsorption on the reduced CeO2(111) surface were also investigated by Pan et al.33 by the combination of scanning tunneling microscopy and DFT calculations. They found that surface oxygen vacancies act as traps for Au adatoms while subsurfaces vacancies lead to the formation of Au pairs; consequently, Au atoms can be used as markers to understand the electron-localization phenomena of the Ce 4f-states. However, we would like to point out that surface oxygen vacancies are unstable. For example, oxygen vacancies are located in the subsurface oxygen layers and are not exposed directly to the vacuum region.29 Thus, the study of the TM−oxide interactions has become a central problem in the elucidation of the reaction mechanisms and catalytic properties of TM−oxide catalysts. There is great interest in understanding the chemical changes occurring along with the deposition, structural changes induced by the interaction of TMs with the oxides surface, changes in the density of states of the TMs particles near the Fermi level, and synergetic effects. Previous studies have provided an important advance in our understanding;4−6,9−21,23 however, they focused mainly on Pt and Au supported on ceria,4−6,14−19,24 and those conclusions cannot be easily transferred to other TM systems. Thus, a systematic investigation of the interaction of TM atoms with ceria is crucial for improving our atomistic understanding. Therefore, in this work, we report a systematic investigation of the interaction of TM4 clusters (TM = Cu, Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au) with the CeO2(111) surface employing firstprinciples DFT calculations with Hubbard U corrections. Here, we considered only the unreduced CeO2(111) surface, in which there are no oxygen vacancies.

II. THEORETICAL APPROACH AND COMPUTATIONAL DETAILS A. Total Energy Calculations. Our calculations are based on spin-polarized DFT within the generalized gradient approximation formulated by Perdew−Burke−Ernzerhof34 (PBE) to the exchange-correlation (XC) energy functional. To improve the description of the on-site Coulomb interactions in the Ce f-states, which is crucial for obtaining a correct description of cerium-based compounds,28,29,35−37 we employed the Hubbard correction proposed by Dudarev et al.,38 in which a Hubbard U term corresponding to the mean-field approximation of the on-site Coulomb interaction is added to the XC functional. This formulation is rotationally invariant; hence, only the difference between the Coulomb U and exchange J parameters is taken into account (i.e., Ueff = U − J). In this work, Ueff = 4.50 was added only for the Ce f-states, which was used in previous DFT+U calculations for ceriumbased compounds.28,29,35−37 Although the DFT+U results depend on the selection of the Ueff parameter,28,37 it is worth noting that the DFT+U framework using Ueff = 4.50 yields results similar to those of hybrid-DFT employing the Heyd− Scuseria−Ernzerhof39 (HSE) functional for the unreduced and reduced CeO2(111) surfaces.29 The DFT+U framework equations were solved employing the all-electron projected augmented wave (PAW) method,40,41 as implemented in the Vienna Ab Initio Simulation Package B



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subsurface O layer, the localized Ce f-states are located slightly below the Fermi level, and the CeIII ions are coupled by antiferromagnetic interactions (about 0.10 eV lower in energy than a ferromagnetic coupling among the CeIII ions). All those findings are consistent with previous results.3,45−47,54−57 B. Lowest-Energy TM4 Structures in Gas Phase. To obtain a better understanding of the TM4 clusters in the gas phase, a set of eight configurations was calculated, and the putative global minimum energy configurations are shown in 4 Figure 2 along with the binding energy per atom (Eb = (ETM tot −

trial configuration from our MD configuration set. (iv) The lowest-energy configurations identified for a particular TM4/ CeO2(111) system were used as an initial model for other TM4/CeO2(111) systems. (v) In the unreduced CeO2(111) surface, the Ce f-states are delocalized; however, the adsorption of TM atoms on CeO2(111) can induce the localization of the Ce f-states, in particular Ce atoms (i.e., a change in the oxidation state from CeIV to CeIII), which gives rise to strong local magnetic moments in the range 0.7−1.0 μB. Thus, several magnetic configurations were verified for all the systems. Therefore, although our configuration set is not large, it contains representative structural models which provide the possibility to build up a deep understanding for the interaction of TMs with the unreduced CeO2(111) surface.

III. RESULTS A. Bulk and Clean Surface. We obtained an equilibrium PBE+U lattice constant, a0, of 5.48 Å for CeO2 (i.e., a Ce−O bond length of 2.37 Å), which is overestimated by 1.3% compared with the experimental result (5.41 Å)48,49 and differs by 1.7% compared with results of hybrid-DFT calculations.28 From aPBE+U , we obtained an in-plane (xy-plane) distance 0 between the oxygen atoms that form a hexagonal array in the topmost CeO2(111) layer, of a0 = √2/2 = 3.88 Å (the same for the Ce and O atoms in the layers below). For the unreduced CeO2(111) surface, as mentioned above, there is no electron localization in the Ce f-states, which is supported by our density of states (DOS) analysis and local magnetic moments (Figure 1). Thus, the results indicate that all the Ce atoms are in the IV oxidation state, which is consistent with previous calculations.29,50−52

Figure 2. Lowest-energy PBE atomic structures for the TM4 clusters along with the binding energy (electronvolts per atom), total magnetic moment (μB), average TM−TM bond lengths (angstroms), and average effective coordination number (ECN). atom )/4), total magnetic moment (mT), average weighted 4ETM tot bond lengths (dav), and average effective coordination number atom 4 (ECN), see also Table 1. ETM and ETM are the total tot tot energies of the TM4 cluster and free TM atoms, respectively, while dav and ECN were calculated using the effective coordination concept.58−60 Most of the TM4 systems (Cu, Ru, Ag, Os, Ir, Pt, Au) adopt two-dimensional (2D) structures, namely, square (Ru, Os, Ir) and rhombus (Cu, Ag, Pt, Au), while only two systems (Rh and Pd) adopt the tetrahedron 3D structure, which are 30 meV/ atom (Rh) and 193 meV/atom (Pd) lower in energy than the best 2D configuration. There is no correlation with the occupation of the d-states; hence, the stability of the 3D structures cannot be explained by the occupation of the antibonding states. Previous hybrid-DFT61 (Rhn, n = 2−15) and DFT+U62 (Co13) calculations found that an enhancement of the Rh and Co d-states localization, which affects the d-states hybridization, increases the stability of compact structures instead of open structures. The 5d-states have a larger degree of delocalization than the 4d-states; hence, we would expect a larger preference for planar structures for the TM4 5d clusters, which is in fact obtained by our calculations. Furthermore, these results suggest that the localization of the 4d-states on the Rh4 and Pd4 clusters might be larger than that on Ru4 and Cu4. In contrast with the cluster structures, the trends in the binding energy, Eb, and bond lengths, dav, of the TM4 clusters can be explained by the occupation of the bonding and antibonding d-states, which was also verified by previous DFT calculations for TM13 clusters (3d, 4d, and 5d).63 For example, an increase in the occupation of the antibonding states, which are located at the upper part of the d-states, leads to decrease the magnitude of the binding energy from Ru4 to Ag4 and from Os4 to Au4; hence, it contributes to increasing the average bond lengths (e.g., from 2.23 Å for Ru4 to 2.72 Å for Ag4), which is expected to play a crucial role in the adsorbate structures on CeO2(111). The largest total magnetic moment was obtained

Figure 1. Local density of states for the unreduced and reduced CeO2(111) surface. The Fermi level is at zero energy, and the surface unit cells are indicated.

The interlayer relaxations are smaller than 3% (e.g., Δd12 = 1.3% and Δd23 = 2.5%), which relates to the great stability of CeO2, and those relaxations are substantially smaller than those in most oxide surfaces.2,53 Furthermore, to confirm previous results, we calculated also the reduced CeO2(111) surface with oxygen vacancies located in the topmost and subsurface O layers. We found that the oxygen vacancies are located in the C



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Table 1. Average Equilibrium Bond Lengths of the TM−TM, Binding Energy Per Atom (Eb 4), and the Total Magnetic Moment (mT) of the TM4 Clusters in the Gas Phase; Average Equilibrium Bond Lengths of the TM−TM, TM−O, CeIV−O, and CeIII−O Bonds in the TM4 Supported on CeO2(111); Adsorption Energy of TM4 on CeO2(111) with Respect to the TM4 a Clusters (Ecluster ) and to the TM Layer (Elayer ad ad ); and Total Magnetic Moment (mT) of the TM4/CeO2(111) Systems TM4 clusters in gas phase

a

TM4/CeO2(111)

TM

dTM−TM (Å) av

4 ETM (eV) b

mT (μB)

dTM−TM (Å) av

dTM−O (Å) av

Cu Ru Rh Pd Ag Os Ir Pt Au

2.35 2.23 2.47 2.61 2.72 2.26 2.31 2.51 2.68

−1.59 −3.09 −2.72 −1.62 −1.14 −4.07 −3.70 −2.72 −1.51

0.00 4.00 6.00 2.00 0.00 4.00 4.00 4.00 0.00

2.40 2.33 2.35 2.59 2.77 2.34 2.30 2.57 2.75

1.82 1.89 1.89 2.05 2.09 1.88 1.88 2.01 2.03

dCe av

4+

−O

3+

dCe av

(Å)

2.37 2.37 2.38 2.36 2.37 2.38 2.38 2.37 2.36

−O

(Å)

2.48 2.46 2.47 2.49 2.48 2.48 2.49 2.49 2.48

Ecluster (eV) ad

Elayer ad (eV)

mT (μB)

−1.28 −1.79 −1.29 −0.80 −0.64 −2.32 −2.01 −1.36 −0.66

−1.93 −2.68 −2.39 −1.00 −1.30 −3.28 −2.98 −1.62 −1.22

0.00 0.35 3.81 2.06 0.00 1.02 4.00 3.99 0.00

The CeIV and CeIII atoms in the TM4/CeO2(111) systems were identified using local magnetic moments and density of states analysis.

for Rh4 (6 μB), while the smallest value (mT = 0 μB) was obtained for the noble metal systems (Cu4, Ag4, and Au4) as the d-states are fully occupied. Our results are in good agreement with previous DFT calculations.61,64−68 C. Lowest-Energy TM4/CeO2(111) Configurations. The i relative total energies (ΔEtot = Econfig. − Elowest tot tot ) are shown in Figure 3 along with the most relevant TM4/CeO2(111)

array with a zigzag orientation, while the Cu4, Pd4, Ag4, Pt4, and Au4 clusters adopt a tetrahedron 3D configuration on CeO2(111). In the tetrahedron structure, the fourth atom is located on the hollow site formed by the three TM atoms. We would like to point out that the lowest-energy structure in the gas phase does not play a crucial role in the adsorbate structure. For example, only Rh4 and Pd4 form tetrahedron structures in the gas phase, while all the remaining systems form 2D structures; however, this trend is not reproduced for TM4/ CeO2(111). The 3D structures obtained for Cu4, Pd4, Ag4, Pt4, and Au4 on CeO2(111) are 0.42, 0.41, 0.51, 0.58, and 0.29 eV lower in energy than the lowest-energy 2D zigzag configuration, respectively. For Ru4, Rh4, Os4, and Ir4 on CeO2(111), the 2D zigzag lowest-energy configurations are 2.12, 1.08, 2.41, and 2.08 eV more stable than the 3D configurations, respectively. The relative energy between the best 2D−3D structures decreases (in most cases) from left to right in the periodic table. For example, 2.12, 1.08, −0.41, and −0.51 eV for Ru4, Rh4, Pd4, and Ag4 and 2.41, 2.08, −0.58, and −0.29 eV for Os4, Ir4, Pt4, and Au4 on CeO2(111), respectively. Thus, we can conclude that the contribution that favors the 3D configurations increases from left to right in the periodic table for the studied systems, which indicates that an increase in the occupation of the antibonding d-states plays a crucial role in the stability of the tetrahedron structures on CeO2(111). D. Adsorption Energies. To improve our understanding, we calculated the adsorption energy per atom of the TM4 clusters supported on CeO2(111), which can be calculated with respect to the TM4 clusters in the gas phase, Ecluster , and to the ad free-standing TM4 layers, Elayer ad . Thus

Figure 3. Relative total energies, ΔEtot, with respect to the lowestenergy configuration for each TM4/CeO2(111) system. Selected atomic configurations (top view) are indicated for all systems.

configurations. Although similar configurations were optimized, the ΔEtot results show a wide range of values. For example, the highest- and lowest-energy configurations for Pd4/CeO2(111) differ by about 1.40 eV, while it is 4.0 eV for several other systems (e.g., Ag4 and Os4 on CeO2(111)). Thus, the result indicates a strong preference of particular systems for configurations with specific features such as the formation of 2D or 3D TM4 motifs on CeO2(111), for which the TM−TM, TM−O, and O−O interactions are expected to play a crucial role. The lowest-energy TM4/CeO2(111) configurations are shown in Figure 4 for TM = Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au, while Cu4/CeO2(111) adopts the same pattern observed for Ag4 and Au4 on CeO2(111). Therefore, two patterns have emerged, namely, the systems Ru4, Rh4, Os4, and Ir4 adopt a 2D

cluster Ead =

TM4 /CeO2 CeO2 TM4 cluster Etot − Etot − Etot 4

and layer Ead =

TM4 /CeO2 CeO2 TM4 layer Etot − Etot − Etot 4

TM /CeO

CeO

TM cluster

TM layer

2 where Etot 4 , Etot 2, Etot 4 , and Etot 4 are the total energies of TM4/CeO2(111), CeO2(111), and TM4 clusters in the gas phase (lowest-energy configuration) and free-standing CeO2 TM4 layer, respectively. For Elayer and ad , the total energies Etot TM4 layer Etot are calculated using the same atomic positions (frozen) and unit cell as in the TM4/CeO2(111) system,

D



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Figure 4. Lowest-energy DFT+U atomic structures for the TM4/CeO2(111) systems employing a (2 × 2) surface unit cell. The adsorption energy (in electronvolts per atom), the total magnetic moment (in μB), and magnetic configurations (ferrimagnetic, FIM; ferromagnetic, FM; antiferromagnetic, AFM) are provided.

O binding energies. Furthermore, it can be seen that the TM− O interactions are stronger for 5d-states. E. Structural Parameters. Using local magnetic moment and local density of states (LDOS) calculations, we identified the location of the CeIV and CeIII ions in the TM4/CeO2(111) systems. For example, the CeIII ions have a local magnetic moment from 0.7−1.0 μB, while it is zero for the CeIV ions. The average TM−TM, TM−O, CeIV−O, and CeIII−O bond lengths are summarized in Table 1. In principle, we would expect an increase in the TM−TM bond lengths for all systems because of the binding of TM with the oxygen atoms in the topmost layer, which weakens the TM−TM binding; however, this is not the case. For example, we found that the TM−TM bond length for TM4/CeO2(111) can decrease or increase compared with TM4 in the gas phase; hence, there is no clear trend for that. The TM−TM bond length decreases for Rh4 (4.9%), Pd4 (0.8%), and Ir4 (0.4%) and increases for the remaining systems by similar magnitudes (e.g., 2.6% for Au4/CeO2(111)). The TM−O bond lengths range from 1.89 Å (Ru−O) to 2.09 Å (Ag−O), which is consistent with a strong binding for the early TM atoms with the O atoms, while the binding is weaker for noble metals with O atoms. Cu−O is 1.82 Å, which correlates with the strong adsorption energy compared with Ag4 on CeO2(111). From our analyses, we found that the CeIV−O and CeIII−O bond lengths are in the range of 2.36−2.38 Å and 2.46−2.49 Å, respectively; hence, the bond lengths increase by about 4.2− 4.6% because of the electron localization of the Ce f-states, in particular Ce atoms upon the adsorption of TM4 on

without the TM atoms and CeO2(111) substrate, respectively. The results are summarized in Table 1. , decreases in The magnitude of the adsorption energy, Ecluster ad absolute value with the increased occupation of the d-states (e.g., −2.32 eV/atom for Os4/CeO2(111) and −0.66 eV/atom 4 for Au4/CeO2(111)). Furthermore, we found that the ETM b / ratio yields values from 1.72 to 2.28 for the 4d and 5d Ecluster ad TM systems, while there is a clear deviation for Cu (1.24). Thus, these results indicate a strong dependence of the adsorption energy on the occupation of the antibonding TM dstates. It should be noted that the number of TM atoms interacting directly with the O atoms is different for the 2D (4 TM atoms) and 3D (3 TM atoms) TM4 structures, which is expected to affect the trends because of the differences in the TM−TM and TM−O interactions. Beyond that, geometric effects also play an important role, which will be discussed below. Although it is not obvious from the atomic structure models shown in Figure 4, the TM4 adsorbates affect quite strongly the CeO2(111) surface. Our calculations for the frozen CeO2(111) surface with the same atomic positions as in the TM4/ CeO2(111) system have higher total energies (e.g., from 0.21 to 1.43 eV per O atom in the surface). The largest differences are induced by the early TM atoms (e.g., Ru, Rh, Os, and Ir), which can be explained by the large magnitude of the TM−O interactions. Except minor differences, we obtained the same cluster . For Cu4 and Ag4 on CeO2(111), trends for Elayer ad as for Ead layer 4 the magnitude of Ead is smaller than for ETM b , which provides a good indication of the magnitude of the TM−TM and TM− E



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Figure 5. Local density of states for TM4/CeO2(111) at the lowest-energy configurations. The Fermi level is at zero energy. The unit cell representations of each lowest energy configuration are shown above the respective LDOS; the CeIII cations are indicated in green, while CeIV cations are yellow.

the CeIII and TM atoms, which can yield ferromagnetic (FM), antiferromagnetic (AFM), and ferrimagnetic (FIM) solutions. The lowest-energy magnetic solutions are FIM (for Ru4 and Os4), FM (for Rh4, Pd4, Ir4, and Pt4), and AFM (for Ag4 and Au4) on CeO2(111); however, a change in the magnetic solution using the same lowest-energy atomic structure would change the total energies by less than 200 meV because of the presence of local magnetic moments only on a few Ce and TM atoms and because of the small magnitude of the magnetic moments. Thus, the result indicates that temperature effects can play a crucial role in the ground-state structure at a given temperature. The number of Ce atoms in the CeIII oxidation state depends on the TM system. For Ru4, Rh4, Os4, and Ir4 on CeO2(111), all the Ce atoms in the topmost Ce layer change the oxidation state from IV to III. In contrast, only 25% of the Ce atoms change the oxidation state for Pd4 and Pt4 on CeO2(111); however, it increases to 50% for Ag4 and Au4. Thus, a compressive strain is built-in in the topmost CeO2 layer (O− Ce−O) because of the expansion of the atomic radius of the Ce atoms, which contributes to affect the stability of TM4/ CeO2(111). Because of the size of the unit cell and number of TM atoms, the preference for the location of the CeIII ions is unclear (i.e., near the TM atoms or far apart); however, we would expect that the CeIII ions would be located near the TM atoms to help in the release of the strain energy.

CeO2(111), which can be explained as follows. The localization of one electron in the Ce f-state extends the electron density of the Ce ion; hence, it increases the effective atomic radius compared with the CeIV ion (e.g., 0.97 Å for CeIV and 1.14 Å for CeIII).69 Thus, because of the increase of the atomic radius of the CeIII ions, a compressive strain is built-in within the topmost Ce layers, in particular for the case in which all the Ce atoms change the oxidation state from IV to III, which is expected to play an important role in the stability of the CeO2(111). F. Electron Localization of the Ce 4f-States. To obtain a better understanding of the electron localization of the Ce fstates, we calculated the LDOS, and the results are shown in Figure 5 along with the top view of the putative lowest-energy structures with the indication of the CeIII and CeIV ions. We found that the adsorption of TM4 on CeO2(111) changes the nature of the occupied Ce f-states from itinerant (CeIV) to localized (CeIII) states, which can be seen by the narrow shape of the Ce LDOS near the Fermi level (dominated by f-states) and by the local magnetic moment of nearly a unit of μB on the CeIII ions (green atoms in Figure 5), which is consistent with previous results.70,71 Furthermore, we found nonzero local magnetic moment on the TM atoms (e.g., Ru, Os, Pd, and Pt), which clearly indicates an enhancement of the electron localization in the TM d-states (Figure 5). Thus, several magnetic solutions can be obtained because of the magnetic interactions between the local moments located in F



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As expected from previous studies,70,71 we found that the adsorption of TM4 on CeO2(111) changes the nature of the occupied Ce f-states from itinerant (CeIV) to localized (CeIII) states, which can be seen by the narrow shape of the Ce LDOS near the Fermi level (dominated by f-states) and by the local magnetic moment of nearly a unit on the CeIII ions. Our analysis of the geometric parameters indicates clearly an increase in the size of CeIII compared with CeIV by 4.4%, which plays a crucial role in building in a lateral tensile strain in the topmost Ce layer in the surface (not directly exposed to the vacuum region). Furthermore, we found that local magnetic moment on the TM atoms (e.g., Ru, Os, Pd, and Pt) contributes for the total magnetic moments, which clearly indicates that the localization of the electronic states occurs not only for the Ce f-states but also for the d-states of the TM atoms. We found that the number of Ce atoms in the CeIII oxidation state depends on the TM element (structure). For Ru4, Rh4, Os4, and Ir4 on CeO2(111), all the Ce atoms in the topmost Ce layer change the oxidation state from IV to III (i.e., 100%). In contrast, only 25% of the Ce atoms change the oxidation state for Pd4 and Pt4 on CeO2(111); however, it increases to 50% for Ag4 and Au4. This behavior might be related to the type of atomic TM4 structures formed on CeO2(111), namely, 2D for Ru4, Rh4, Os4, and Ir4 and 3D for Pd4, Ag4, Pt4, and Au4, and connected with the magnitude of the binding of the respective TM with the O atoms. Because of the size of the unit cell, (2 × 2), the preference for the location of the CeIII ions is unclear (i.e., near the TM atoms or far apart); however, on the basis of the previous studies for O vacancies on CeO2(111), we would suggest that the location of the CeIII ions would be near the TM atoms. However, the release of compressive strain would play a crucial role in the exact location of the CeIII ions.

G. Hybridization Index. To improve our understanding of the interaction of TM4 with CeO2(111), we calculated the average hybridization index,62,72 hindex, using the LDOS from the TM d-states and the O p-states involved directly in the TM−O bonding. The hybridization index, as employed in the present work, is a qualitative analysis as it takes into account only the LDOS confined within the atomic spheres and not the projected DOS. For the 4d TM4 systems on CeO2(111), we obtained hindex = 1.58, 0.76, 0.21, and 0.38 for Ru4, Rh4, Pd4, and Ag4, respectively, while for the 5d TM4 systems on CeO2(111), we obtained hindex = 2.06, 2.49, 0.82, and 0.72 for Os4, Ir4, Pt4, and Au4, respectively. Thus, except for two cases, the hybridization index decreases by increasing the occupation of the d-states, which correlates with the magnitude of the adsorption energy. Therefore, the formation of 2D zigzag configurations for Ru4, Rh4, Os4, and Ir4 on CeO2(111) can be explained by the combination of two factors: (i) The strong hybridization between the TM d-states and O p-states, which is substantially smaller for Pd4 and Ag4 in relation to Ru4 and Rh4 (4d), and for Pt4 and Au4 in relation to Os4 and Ir4 (5d); hence, 3D configurations are preferable for Pd4, Ag4, Pt4, and Au4 on CeO2(111), with the formation of TM−TM bondings. (ii) All the Ce atoms in the topmost Ce layer change the oxidation state from CeIV to CeIII for Ru4, Rh4, Os4, and Ir4 on CeO2(111), while only one and two Ce atoms changed the oxidation states for Pd/Pt and Ag/Au, respectively. Thus, the changing in the Ce oxidation state and high hybridization index corroborate for the 2D (Ru4, Rh4, Os4, and Ir4) structures on CeO2 (111).

IV. CONCLUSIONS We have performed a systematic study for the adsorption of TM4 (TM = Cu, Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au) on the unreduced CeO2(111) surface using DFT calculations within the PBE+U functional. In the clean CeO2(111) surface, the distance between the O−O atoms in the topmost layer is 3.88 Å; hence, we would expect the same distance for a homogeneous distribution of four TM atoms on CeO2(111) using a (111)−(2 × 2) surface unit cell. However, this is not the case because of the attractive interactions among the TM atoms, which favors the nucleation of the four TM atoms on the CeO2(111) surface; hence, the formation of the 2D arrays with a zigzag orientation (Ru4, Rh4, Os4, and Ir4) and tetrahedron 3D (Cu4, Pd4, Ag4, Pt4, and Au4) structures. At first view, the TM atoms are located on the top of the oxygen atoms; however, the TM atoms are displaced in the xyplane from the oxygen top sites in the topmost layer by about 0.60−1.10 Å; the displacements are larger for the 2D and smaller for the 3D configurations. The obtained 2D and 3D structures are not directly related with their gas-phase atomic structures, which indicates an important role played by the strong magnitude of the TM−O interactions, in particular, because of the contribution of the hybridization among the TM d-states with the O p-states. We found that the stability of the 2D zigzag array decreases compared with the 3D configuration from left to right in the periodic table, except for slight deviations. Thus, on the basis of this trend, we can conclude that an increase in the occupation of the antibonding d-states plays a crucial role in the stability of the tetrahedron structures on CeO2(111) along with the hybridization of the TM d-states with the O p-states.

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ASSOCIATED CONTENT

S Supporting Information *

Figures for the local density of states and lowest-energy atomic structure for Cu4/CeO2(111) are provided. 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]. *E-mail: [email protected]. *E-mail: [email protected]. Phone: +55 52 3275 7542; +55 16 3373 6641. Fax: +55 16 3373 9952. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Authors thank the São Paulo Research Foundation (FAPESP), Rio Grande do Sul Research Foundation (FAPERGS), National Council for Scientific and Technological Development (CNPq), Coordination for Improvement of Higher Level Education (CAPES) for the financial support. Authors thank also the Research Computing Support Group (Rice University) for the computing time provided in the Blue Gene/P supercomputer, the Laboratory of Advanced Scientific Computing (University of São Paulo), and the Department of Information Technology - Campus São Carlos for the infrastructure provided to our computer cluster. G



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ABBREVIATIONS DFT, density functional theory; PBE, Perdew−Burke− Ernzerhof; BZ, Brillouin zone; VASP, Vienna Ab Initio Simulation Package

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Theoretical Investigation of Small Transition-Metal Clusters Supported

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