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Oxidation of Small Silver Clusters: A Density Functional Theory Study Simon Klacar,*,† Anders Hellman,† Itai Panas,‡ and Henrik Gro¨nbeck† Department of Applied Physics and Competence Centre for Catalysis and Department of EnVironmental Inorganic Chemistry, Chalmers UniVersity of Technology, SE-412 96 Go¨teborg, Sweden ReceiVed: March 25, 2010; ReVised Manuscript ReceiVed: June 7, 2010
The oxidation of small silver clusters (Agn, n e 9) was investigated through electronic structure calculations based on density functional theory. The adsorption energies of molecular and dissociated adsorption show a pronounced odd/even alternation, with lower energies calculated for even-sized clusters. Molecular adsorption is favored for n e 5, whereas dissociation is preferred for the larger sizes. Molecular oxygen is adsorbed in atop (Ag, Ag2, Ag6, Ag8) or bridge (Ag3, Ag4, Ag5, Ag7, Ag9) configurations, and atomic oxygen is preferably adsorbed in 3-fold hollow positions. Results for stoichiometric (Ag2nOn) clusters were compared to O2 adsorption on Ag(111), and ab initio thermodynamics was used to estimate the temperature for the oxide-to-metal phase transition. The barrier for O2 dissociation on Ag8 was calculated to be higher than the corresponding barrier on Ag(111), which indicates a slower oxidation process. Adsorption of NOx onto the oxidized clusters was found to proceed through a formal reduction of the clusters; that is, NOx is adsorbed as NOx+1 with x ) 1, 2. Introduction During the past two decades, significant efforts have been made to develop an understanding of materials at the nanoscale.1,2 These efforts combine physics, chemistry, and engineering and are motivated by novel phenomena and properties and the prospect of taking advantage of them in materials design. Atomic clusters represent the smallest nanoscale objects (typically smaller than 2 nm) and concern the nonscalable regime where properties can change from one cluster size to another. Notable examples are ionization potentials,3 electronic affinities,4 magnetic moments,5 and reactivity.6,7 Non-bulk-like features can, in many cases, be traced back to the electronic structure, with spatially confined electrons and, for the transition metals, an evolving d band. Delocalization of electrons in a confined region leads to the formation of a discrete energy spectrum, not unlike that of a particle in a box. The subsequent filling of the energy levels gives rise to a shell structure that dominates the properties of simple and noble metal clusters.8-10 One example is the ionization potentials, which, for monovalent elements, are measured to be relatively high for clusters with closed electronic shells, that is, 2, 8, 18, 20 ... atoms. In addition to variations that correlate with electronic shell closings, this type of cluster exhibits odd/even alternations with respect to the number of atoms in the cluster.4,11 The odd/even alternation originates from spin pairing in the electron energy levels. It should be noted that, although the noble metal clusters exhibit similar electronic properties, they differ in preferred structures. Anionic gold clusters are planar up to Au12,12,13 whereas silver and copper clusters turn three-dimensional at about the hexamer. The difference can be traced to a lowering of the electronic kinetic energy for planar as compared to three-dimensional structures for Au.13,14 As the fundamental understanding in cluster science increases, there is the possibility of applying this knowledge to areas where * To whom correspondence should be addressed. E-mail: klacar@ chalmers.se. † Department of Applied Physics and Competence Centre for Catalysis. ‡ Department of Environmental Inorganic Chemistry.
important processes occur at the nanoscale range, where heterogeneous catalysis is but one example. Heterogeneous catalysts are often realized as nanometer-sized particles dispersed on a high surface area oxide support. One interesting example is the Ag/Al2O3 catalyst, designed for selective catalytic reduction (SCR) of nitrogen oxides (NOx) under oxygen-rich conditions (lean combustion) with hydrocarbons or ammonia as reducing agents. This catalyst, which shows a high activity,15 is claimed to consist of small Agn clusters dispersed in the alumina matrix. Experimental characterization of the Ag/Al2O3 catalyst by UV-vis spectroscopy16 suggests that the active phase is silver clusters Agn, with n < 8. Interpretation of extended X-ray absorption fine structure (EXAFS) spectra17 supports this observation, as the average Ag-Ag coordination number is as small as ∼2.4. In ref 17, it was proposed that the active clusters are Ag trimers and tetramers. However, it should be realized that low coordination is also found for metal steps or other bulk defects. Thus, even if the Ag/Al2O3 catalyst shows promising catalytic properties, the actual active phase of the catalysts is still unclear. To understand and improve the performance of the Ag/Al2O3 catalyst, fundamental knowledge is required on the active phase and the NOx reduction process on these sites. Herein, we take one step in this direction by performing a theoretical first-principles investigation of Agn (n e 9) clusters in an oxidizing atmosphere. Results are presented for structural, electronic, kinetic, and thermodynamic properties and put into context through comparisons to extended surfaces. Structural and electronic properties of silver clusters in the gas phase have been investigated extensively in the past.18-20 Moreover, adsorption of oxygen,21-29 CO,21,25,27,30,31 NOx,32-34 H2,21 and ethylene21 onto silver clusters has been explored. These studies have elucidated how different cluster properties are affected by the electronic shell structure and demonstrated clear odd/even effects in, for example, adsorption energies and ionization potentials.
10.1021/jp102715r 2010 American Chemical Society Published on Web 07/06/2010
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Computational Method 35,36
Density functional theory was used with the gradientcorrected exchange correlation (xc) functional according to Perdew, Burke, and Ernzerhof (PBE).37 The Kohn-Sham, oneelectron orbitals were expanded in a local numerical basis set. The basis functions were centered on each atom and stored on a radial grid.38-40 Two atomic orbitals were used to describe each occupied valence state (double basis). For oxygen and nitrogen, this basis was augmented by polarization functions with d character. The bases used for oxygen, nitrogen, and silver were [1s2s2p(O), 2s2p(O2+), 3d(7+)], [1s2s2p(N), 2s2p(N2+), 3d(7+)], and [4s4p4d5s(Ag), 4d5s5p(Ag2+)], respectively. A real-space cutoff of 4.5 Å was used for the basis functions. For silver, a pseudopotential was used to describe the interaction between the valence electrons (4s24p64d105s1) and the core.41 The Kohn-Sham equations were solved self-consistently with an integration technique of weighted overlapping spheres located at each atomic center. The direct Coulomb potential was obtained by projection of the charge density onto angulardependent weighting functions also centered at each atom. Thereafter, the Poisson equation was solved by one-dimensional integration.38 Calculations of extended surfaces, Ag bulk, and Ag2O bulk oxide were performed with periodic boundary conditions. Integration over the Brillouin was approximated by finite sampling. For the bulk calculations, a (10, 10, 10) mesh was used, which corresponded to 500 unique k points. Ag(111) was cut from Ag in the bulk phase with an optimized lattice parameter. The Ag(111) surface model had a (4 × 4) surface cell with four layers (with the bottom two layers held fixed during geometry optimization). The surface slabs were separated by a 12-Å vacuum. The k-point sampling for the surface was done with a (6, 6, 1) mesh, which corresponded to 18 unique k points. A Fermi distribution smearing of 0.1 eV was applied in the bulk and slab calculations. Structural optimizations were performed until a convergence criterion of 0.002 eV/Å was met on the largest element of the gradients. Optimization of cluster structures with adsorbates was performed from several initial configurations. Using a Monte Carlo algorithm, a large set of random O and O2 adsorption configurations were generated. The structures were relaxed, and vibrational analysis of the optimized geometries was performed to ensure that the isomers represented true minima on the potential energy surface (PES). The applied procedure for vibrational frequency was based on a finite-difference calculation of energy gradients (i.e., force constants) for each atom. The harmonic frequencies were obtained by means of matrix diagonalization. The transition state of O2 dissociation was estimated by a linear synchronous transit and quadratic synchronous transit (LST/QST) method.42 LST was used first to bracket a maximum between the initial and final geometries. Energy minimization of the obtained maximum was performed to generate a first transition structure. A finer optimization of the structure was done with QST and finished by a conjugate gradient minimization. That the obtained transition states were true was verified by vibrational analysis. The adsorption energy for an adsorbate (X) was calculated according to
Eb(X) ) EAg + EX - EX/Ag
(1)
where EAg is the total energy of the bare silver cluster, EX is the total energy of the adsorbate in the gas phase, and EX/Ag is the total energy of the combined system (adsorbate and cluster). Ab initio thermodynamics has been used extensively to estimate the stability of surface structures as a function of temperature and partial pressures of gas-phase components,43 where one recent example is the composition of palladium nanoparticles in the presence of O2 and CO.44 The surface free energy γ(T,p) is calculated as
γ(T, p) ) [EO/Ag - EAg - NAgµAg - NOµO(T, p)]/A
(2) where the first and second terms are, respectively, the total energies of the considered O/Ag systems and Ag references, that is, bare clusters or clean Ag(111) surface. The difference in Ag atoms with respect to the corresponding reference system is given by NAg. µAg is the chemical potential for silver and represents the energy cost of transferring NAg atoms to/from the bulk reservoir. For this term, which is relevant only in the case of the reconstructed Ag(111) surface, the enthalpy of a Ag atom in silver bulk is used. The chemical potential for oxygen (µ0) is given by
µO(T, p) )
[
( )]
pO2 1 EO2 + µ′O2 + kBT ln 0 2 p
(3)
where EO2 is the total energy of the O2 molecule. µ′O2 is calculated with data from thermodynamic tables.45 In this way, contributions from translations, vibrations, and rotations are included for O2. The thermodynamic stability is often reported as free energy per unit surface area A (eq 2).43 This procedure is difficult to apply to small clusters for which a surface area cannot easily be defined. Instead, we chose to compare the temperatures for oxide decomposition, that is, the temperatures at which O2 desorbs from the different silver systems [γ(T, p) ) 0]. Results and Discussion Reference Systems. Several systems were investigated to check the performance of the computational approach and to serve as references. The stable phase of Ag in the bulk is facecentered cubic (fcc). The unit cell of Ag2O contains six atoms, where the oxygen atoms form a body-centered cubic (bcc) lattice. Each O atom is tetrahedrally coordinated by Ag atoms, and every silver atom is linearly coordinated between two oxygen atoms. The calculated lattice constants for Ag (4.19 Å) and Ag2O (4.88 Å) were found to be in agreement with corresponding experimental values of 4.08 and 4.73 Å, respectively. The slight expansion is a well-known effect of the applied approximation to the xc functional. The cohesive energy of Ag was calculated to be 2.5 eV, which is close to the measured value of 2.8 eV.46 The heat of formation (HfAg2O) for Ag2O (with respect to metallic silver and O2 in the gas phase) was calculated to be 0.26 eV. The corresponding experimental value is 0.32 eV.46 The spectroscopic constants for the three considered gas-phase adsorbates are presented in Table 1. The bond lengths and vibrational wavenumbers are in good agreement with experimental data. The bond lengths are typically overestimated by ∼1%. The largest deviation from experiments for the wavenumbers was obtained for the asymmetric stretch mode in NO2,
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TABLE 1: Calculated and Experimental Data for Selected Moleculesa Eb
Eexp b
d
dexp
ω
ωexp
O2 6.10 5.23 1.23 1.21 1574 1580 NO 7.23 6.51 1.16 1.15 1887 1904 NO2 5.72b 4.15b 1.21 1.19 739/1344/1653c 750/1318/1618c a Eb, binding energy (eV); d, bond length (Å); ω, vibrational wavenumber (cm-1). b Binding energy of O atom to NO. c Bending/symmetric stretching/asymmetric stretching modes. The calculated (experimental) O-N-O angle is 133° (134°).
which was overestimated by 2%. It is well-known that the present choice of xc functional overestimates the bond strength in O2.37 This was also found in the present work, where the dissociation energies were overestimated by 0.86 and 0.72 eV for O2 and NO, respectively. O adsorption on Ag(111) was investigated at two coverages: 1/16 and 1/4 ML. O adsorbs preferably in fcc positions. The energy difference between adsorption in hcp and fcc sites was calculated to be 0.1 eV at both coverages. There is only a slight effect of coverage on the calculated adsorption energy. The adsorption energy with respect to O2 in the gas phase is 0.41 eV at a coverage of 1/16 ML, whereas it is 0.39 eV at 1/4 ML. These values are in good agreement with previous reports at 1/4 ML.47,48 Surface X-ray diffraction, scanning tunneling microscopy, and core-level spectroscopy have been used to reveal the structure of the p(4 × 4) reconstruction of Ag(111) upon oxygen adsorption.49 The structure consists of a stoichiometric Ag12O6 top layer with two Ag6O3 subunits placed such that the six Ag atoms (in a planar, Ag6 clusterlike structure) assume fcc and hcp sites on the underlying metal substrate. This structure was modeled by the overlayer positioned over a three-layer Ag(111) slab. The spacing between the Ag6 units provide sites for two O atoms. The distance between the uppermost Ag layer in bulk registry and the two O atoms are distinctly different: 2.17 and 3.02 Å. This structure agrees with previous results,49 where the corresponding distances were reported to be 2.21 and 3.04 Å, respectively. The average binding energy of O is 0.48 eV with respect to an unreconstructed Ag(111) surface and O2 in the gas phase. Bare Clusters. The atomic structures of small Agn clusters have been studied extensively,20,33,50-52 and the stable structures for bare neutral and cationic systems have been established. In the present work, known low-energy isomers were structurally relaxed. The results for Ag2-Ag9 are shown in Figure 1. For the dimer, the bond distance, bond strength, and vibrational wavenumber were calculated to be 2.61 Å, 1.70 eV, and 175 cm-1, respectively. The corresponding experimental values are 2.53 Å, 1.66 eV, and 193 cm-1. Previous calculations based on DFT with the present xc functional in a plane-wave pseudopotential implementation gave a bond length of 2.63 Å and a bond strength of 1.70 eV.13 The trimer structure is an obtuse triangle (C2V) with a 74° angle and a short Ag-Ag distance of 2.68 Å. The Ag4-Ag6 clusters can be constructed by capping the trimer. The tetramer is a rhombus with D2h symmetry, the pentamer has C2V symmetry, and the hexamer has D3h symmetry. For the hexamer, the isomeric pentagonal pyramid is 0.25 eV above the ground state. This structure is the basis for growth into the heptamer, which has the pentagonal bipyramid as the lowest-energy structure. The octamer was found to be a tetra-capped tetrahedron (Td). This isomer is preferred by only 0.04 eV with respect to the dodecahedron (D2d). The pentagonal bipyramid with one
Figure 1. Ground-state isomers of bare Agn clusters, n ) 1-9. The symmetry groups and cohesive energies (eV) are indicated.
cap is 0.20 eV above the ground state. The pentagonal motif is relevant for the nonamer, which adopts a pentagonal bipyramid structure with two caps. In general, the growth of the clusters results in an elongation of the average Ag-Ag distance from 2.61 Å for the dimer to 2.89 Å for the nonamer. The corresponding bulk distance in the present computational approach is 2.97 Å. There is a general increase in binding energy per atom with increasing cluster size. The binding energies for Ag2-Ag9 were calculated to be 0.85, 0.84, 1.11, 1.21, 1.39, 1.39, 1.49, and 1.47 eV, respectively. The slight decreases in binding for Ag3 and Ag9 with respect to Ag2 and Ag8, respectively, can be attributed to the closed electronic shells for the dimer and octamer. The geometrical structures of Agn clusters can be understood from the bonds derived from the 5s electrons. These states are delocalized over the cluster and give rise to closed shells, namely, 1S, 1P, 1D, 2S ..., which correspond to 2, 8, 18, 20, ..., electrons. The three 5s electrons in the trimer fill the 1S state and partially one of the 1P states. This gives a Jahn-Teller distorted triangle with a doublet spin state (S ) 1/2). The cationic Ag3+ cluster is an equilateral triangle, as only the 1S state is filled in this case.53 The Ag4 has a filled 1Px state, which gives the D2h symmetry. A square geometry (D4h) is unstable with respect to Jahn-Teller distortions. If the two 1Px electrons are removed by ionization, only the 1S state is filled and the cluster adopts a tetrahedral structure.54 Silver clusters are planar up to the hexamer, which has the electronic configuration of 1S21Px21Py2. Beyond Ag6, out-of-plane orbitals are populated, which renders larger clusters three-dimensional. The first threedimensional structure is the heptamer, which forms a pentagonal bipyramidal. The ionized cationic heptamer, on the other hand, has the same electronic structure as the hexamer and takes a planar D6h structure. Within the studied size range, the dimer and hexamer have the highest ionization potentials (IPs). In addition to shell structure, the IP shows a pronounced odd/even alternation, which is a consequence of electron pairing in each electron level.11,55 The vertical ionization potentials (VIPs) were calculated to be 7.83, 5.96, 6.46, 6.12, 6.94, 5.83, 6.68, and 5.26 eV, respectively, for the dimer to the nonamer. This is in fair agreement with the corresponding measured electron impact56 values of 7.60, 6.20, 6.65, 6.35, 7.15, 6.40, 7.10, and 6.00 eV. The effect of structural relaxation upon ionization was calculated to be sizable. The adiabatic ionization potentials were calculated to be 7.77, 5.74, 6.45, 5.93, 6.84, 5.68, 6.57, and 5.19 eV, respectively. Molecular and Dissociative Adsorption. Here, the adsorption of atomic and molecular oxygen on Agn is explored. We repeatedly refer to oxidation or reduction of the silver clusters.
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Figure 2. Ground-state isomers of molecularly adsorbed O2. Two isomers are reported for Ag8 with relative energies in eV. Atomic color codes: Ag, blue; O, red. For O2/Ag4, the charge density difference is shown. Red (blue) corresponds to gain (depletion).
The process of oxidation involves charge transfer from the cluster to the adsorbate. A completely oxidized cluster corresponds to the stoichiometric composition Ag2O, where, formally, all 5s electrons have been transferred from the metal to the oxygen atoms. Molecular O2 adsorption [with the formation of superoxo (O2-) or peroxo (O22-) species] oxidizes the clusters to a lesser extent than does dissociative adsorption.57,58 By reduction of the clusters, we refer to the process of charge transfer to the cluster from the adsorbates. The stable structures for molecular adsorption are reported in Figure 2. O2 adsorbs at either atop or bridge sites. Atop adsorption is predicted for the dimer, hexamer, and octamer, which are even-numbered, whereas bridge adsorption is calculated for the trimer, tetramer, pentamer, heptamer, and nonamer. In general, atop adsorption has a small effect on the structures of the clusters. For example, only a slight elongation of the dimer Ag-Ag bond was calculated: 2.64 Å as compared to 2.61 Å. This could be compared to the Ag-Ag distance in Ag2+, which was calculated to be 2.78 Å. Similar conclusions are valid for the hexamer and octamer. Both sizes are close to their neutral shapes. On the hexamer, O2 is in the same plane as the metal cluster. The structural changes in the case of bridge adsorption are large for some clusters. For example, the trimer adopts a close-to-equilateral structure,59 which signals a cationic charge state. The largest conformational change was found for the heptamer, which assumes a planar D6h symmetry. Just as for the trimer, this corresponds to the cationic motif. Upon O2 adsorption, the structure of the nonamer deviates from that of the bicapped pentagonal bipyramid. However, the relaxed structure is connected to the bare geometry by a slight rotation of an atom pair. The structural analysis indicates that O2 oxidizes the clusters only when adsorbed in a bridge configuration. This is consistent with the calculated bond length of O2. When adsorbed in an atop position, the average bond length is 1.25 Å, which is close to the gas-phase value of 1.23 Å. On the other hand, for bridge adsorption, the O-O bond length is, on average, 1.35 Å, which indicates the formation of a superoxo state by charge transfer from the cluster to the molecular 2π* antibonding orbital. This is confirmed by the charge density difference analysis for Ag4 (Figure 2). The charge density difference, ∆F, was calculated as
∆F ) FO2/Ag4 - FAg4 - FO2
(4)
where FO2/Ag4, FAg4, and FO2 are charge densities for the O2/Ag4 system, the Ag reference, and the O reference, respectively. The
Figure 3. Ground-state isomers for dissociative O2 adsorption. Atomic color codes as in Figure 2.
odd clusters were calculated to be in doublet states, whereas the even clusters are triplets. For the dimer, hexamer and octamer, the spin is localized at the oxygen molecule. On Ag4, however, the spin density has weight on both O2 and the cluster. For this cluster, the singlet configuration (which is antiferromagnetic) is 0.08 eV higher in energy. In a recent study by Pereiro and co-workers,60 DFT calculations were reported for molecular O2 adsorption on Ag3-Ag8. The proposed low-energy structures for O2/Agn differ somewhat from those in Figure 2. The suggested trimer is a planar Ag triangle with O2 adsorbed atop. A 158.8° torsion of the planar Ag4 rhombus (D2h) is reported with molecular oxygen adsorbed in a bridge configuration. Structures for the pentamer and hexamer are similar to those in Figure 2; however, O2 is adsorbed in atop and bridge sites, respectively. The heptamer is reported with D5h symmetry with O2 atop. We considered these isomers, in addition to the proposed octamer structure,60 and, for the trimer, pentamer, heptamer, and octamer, found them to be well above the structures reported in Figure 2: 1.07 (Ag2), 0.48(Ag5), 0.44(Ag7), and 0.68 (Ag8) eV. The suggested structures for the tetramer and hexamer60 were not found to be true minima on the PES. Dissociative adsorption shows marked deformation of the clusters as compared to the bare neutral structures. The optimized structures are presented in Figure 3. The stable dimer is a linear Ag-O-Ag-O chain, with three Ag-O, O-Ag, Ag-O distances of 2.03, 1.94, and 1.92 Å, respectively. The trimer adopts a linear configuration with an elongated Ag-Ag distance of 3.05 Å. The two O atoms are adsorbed in bridge sites with Ag-O distances of 2.07 Å. With increasing cluster size, the O atoms preferentially adsorb in 3-fold positions. The favored geometry for the tetramer has one O atom in a 3-fold position and another adsorbed in bridge. However, a tetrahedral motif, with both O atoms in 3-fold configurations, is only 0.03 eV higher in energy. Addition of one Ag atom to the metastable tetramer gives the preferred pentamer structure. The hexamer is, along with the tetramer, the only cluster with a clear connection to the corresponding bare neutral cluster. The two O atoms are, in this case, adsorbed in 3-fold positions at opposite sides of the planar cluster. The situation with the two atoms adsorbed on the same side of the cluster is not a minimum on the potential energy surface. A structure with two O atoms adsorbed on an octahedral Ag6 cluster was found to be 0.13 eV above the ground state. However, the heptamer, octamer, and nonamer are based on structures of an octahedron by adding O and Ag atoms in 3-fold positions. We also considered structures with oxygen “subsurface”. In all cases, such structures were found to correspond to high-energy isomers. This could be
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Figure 4. Adsorption energies for molecular adsorption and dissociative adsorption. The energies are given per O atom with respect to gas-phase O2.
Figure 5. Relative thermal stability of stoichiometric clusters, Ag2O, in the bulk and surface oxide on Ag(111). The insets show the stable structures for AgnO0.5n.
attributed to the elongation of Ag-Ag bond lengths and loss of metallicity, as will be elaborated below. The adsorption energies for molecular adsorption (MA) and dissociated adsorption (DA) per O atom, with respect to O2 in the gas phase, are presented in Figure 4. In general, the adsorption energies show a large size dependence. There is a pronounced odd/even alternation of the adsorption energies where a higher energy is predicted for the odd-sized clusters. This result is consistent with the measured ionization potentials of silver clusters.56 In the case of DA, there is also a clear trend toward higher adsorption energies with increasing cluster size. On Ag2, DA is not stable with respect to gas-phase O2, whereas on Ag9, each O atom is bound by 0.82 eV. For MA, adsorption energies fluctuate between 0.10 and 0.61 eV. We note that the O2 adsorption energy on Ag(111) was calculated to be only 0.12 eV. One interesting result in Figure 4 is the transition from preferred MA to DA between Ag5 and Ag6. MA is energetically favored up to Ag5, whereas DA is preferred on the hexamer by 0.31 eV. The odd/even alternation vanishes for cluster sizes larger than the hexamer. This indicates that dissociative adsorption is a more complex process from an electron-counting point of view than is molecular adsorption. As addressed vide supra, the applied approximation to the exchange-correlation functional (PBE) overestimates the O2 binding energy by 0.43 eV per O atom. Furthermore, the calculated cohesive energy of bulk Ag is somewhat smaller than the corresponding experimental value. Because the results for O2 adsorption on Agn clusters suggest a low tendency for dissociation, it is important to investigate whether this result is a consequence of the overestimated bond strength in O2. To elaborate on this issue, we studied O2 adsorption on Ag4 with a hybrid functional (B3LYP) and Møller-Plesset perturbation theory calculations to the second order (MP2).61-63 The bond strength of O2 in the gas phase was calculated to be 5.39 and 5.46 eV within B3LYP and MP2, respectively. The corresponding O2 bond lengths were 1.21 Å (B3LYP) and 1.22 Å (MP2). The values are in good agreement with the experimental data in Table 1. On Ag4, MA is preferred over DA by 0.64 eV (0.44 eV) within B3LYP (MP2). Within both methods, O2/Ag4 was calculated to be a triplet. These results provide a consistency check of the PBE results (which favor MA over DA by 0.31 eV) and indicate that the stability of the MA configuration, in fact, might be underestimated within the present computational scheme. It is interesting to compare our results for Agn with a previous computational study on Aun in the same cluster size range.64
For Aun, the transition from MA to DA was predicted to occur already between Au3 and Au4 for both neutral and anionic clusters. Stoichiometric AgnO0.5n Clusters. In the bulk oxide, the stoichiometric relation between silver and oxygen is 2:1. Here, we investigate the corresponding case for small Agn clusters. In Figure 5, the stable structures for O/Ag2, 2O/Ag4, 3O/Ag6, and 4O/Ag8 are reported, and their thermodynamic stability are compared to the oxidized Ag(111) surface and the bulk oxide. Geometry optimization of the stoichiometric clusters was performed on the basis of most stable O2/Agn and 2O/Agn clusters. For Ag6O2 and Ag8O2, oxygen atoms were added until the stoichiometric ratio was reached. The dimer adopts a waterlike structure, with a Ag-O-Ag angle of 94° and a Ag-O bond length of 2.04 Å. The tetramer has the same structure as for MA; see Figure 2. The hexamer is a triangular antiprism with O in 3-fold positions. However, this isomer is energetically degenerate with a structure based on a distorted square pyramid with all O atoms in 3-fold configurations. On 4O/Ag8, three of the oxygen atoms are adsorbed in 3-fold hollow positions, whereas one occupies a bridge configuration. The oxygen adsorption energies (per O atom with O2 as the reference) for the stoichiometric clusters are -0.34, 0.24, 0.23, and 0.53 eV, respectively. The adsorption energy for O/Ag2 is endothermic, and the average oxygen bond for 3O/Ag6 is of similar strength as for 2O/Ag6 (see Figure 4). For 4O/Ag8, the average oxygen adsorption energy is reduced by 0.26 eV when O2 is adsorbed onto 2O/Ag8. The differential adsorption energy for 4O/Ag8 shows the same tendency: the two additional atoms are adsorbed by only 0.27 eV. The electronic ground state of 4O/Ag8 is a triplet, with an unpaired spin on the bridged O atom and the other delocalized over the metal cluster. For 4O/Ag8, MA atop of the second O2 onto 2O/ Ag8 was found as the first metastable isomer 0.42 eV above the ground state. This structure is a triplet with the spin density on the intact O2 molecule. That the spin on oxygen is not completely quenched upon adsorption suggests a modest ability of the second O2 to further oxidize the clusters. Thermodynamic Stability. Using ab initio thermodynamics, the stability of oxidized stoichiometric clusters was compared to the oxidized Ag(111) surface and Ag2O in the bulk phase (Figure 5). The transition temperature from bulk oxide to the oxidized surface was predicted to be at 295 K (green shaded area). The corresponding temperature for the transition to a clean Ag(111) was calculated to be at 463 K (gray shaded area). Both temperatures are lower than the experimental estimates of 350 and 598 K, respectively. We note that δγ/δT (eq 2) is small and gives a high sensitivity on the binding energies of oxygen:
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Figure 6. Barriers for O2 dissociation on the octamer and the Ag(111) surface where the insets represent the respective transition state structures. The energies are reported with respect to the stable structures for MA adsorption. Atomic color codes as in Figure 2.
100 K roughly corresponds to a difference of 0.1 eV in binding energy. Thus, addition of a zero-point correction to the chemical potential of O2 in the gas phase (0.10 eV) would shift the calculated results to the experimental transition temperatures. The results show that O/Ag2, O2/Ag4, and 3O/Ag6 are thermodynamically less stable than the bulk oxide and the oxidized surface. Their transition temperatures are all lower than 300 K. This indicates that these small clusters have a lower tendency for oxidation than the Ag(111) surface. The transition temperature of 4O/Ag8 was calculated to be 518 K, which is higher than that of the oxidized surface. However, as discussed above, one of the four O atoms is adsorbed in a bridge, and the system adopts a triplet state, which indicates only a partial oxidation. The thermodynamics of Agn oxidation is a balance between metal-to-oxygen charge transfer, the subsequent formation of ionic bonds, and the loss of intercluster interactions as given by the jellium states. For the Ag(111) surface, the metal bulk provides a sea of electrons, and the balance between metal-metal cohesion and the formation of anionic oxygen species is not as crucial.65 Moreover, the adsorbate stabilization owing to the buildup of an image charge is more pronounced for the extended surface. Barriers for O2 Dissociation. In the previous sections, we reported the thermodynamic stability of O2 in molecular and dissociated configurations on Agn. To investigate how facile the process of dissociation is, we address the barriers for O2 cleavage. This is done for the octamer and comparison is made to the Ag(111) surface. The results are presented in Figure 6. The initial configuration for O2/Ag8 is based on the first metastable (0.03 eV above the ground state) configuration: a pentagonal bipyramid with one cap where O2 is adsorbed in a bridge configuration with an O-O distance of 1.30 Å. The final configuration is the 2O in the stable configuration (both shown in Figure 3). Structural optimization of the initial and final states was performed with spin polarization. However, as the two structures are in different spin states (triplet and singlet), the activation barrier was evaluated without spin polarization. Hence, the calculated barrier represents a lower bound to the true barrier. The barrier was calculated to be 1.3 eV. In the initial configuration, the O-O bond length is 1.31 Å, whereas it is 2.10 Å at the transition state. On Ag(111), O2 is adsorbed as a doublet in a bridge configuration with an O-O bond length of 1.29 Å. The adsorption energy was calculated to be only 0.12 eV. Upon dissociation, O2 rotates 90°, whereby the two O atoms assume 3-fold configurations. The O-O distance at the transition state is 1.94 Å, and the barrier was calculated to be 1.00 eV. The
Figure 7. Total and projected densities of states for selected clusters. The projection (red) is done onto the oxygen states. Insets show the corresponding clusters and selected orbitals.
surface experiences only small distortions during the dissociation. Molecular adsorption and dissociation of O2 on Ag(111) has been addressed previously48 with a plane-wave pseudopotential implementation of the Kohn-Sham equations and the PW91 approximation to the exchange-correlation functional. In agreement with the present study, O2 was found to adsorb in a bridge configuration with an adsorption energy of 0.17 eV, and the barrier for dissociation was calculated to be 1.11 eV.48 The barrier for O2 dissociation is higher on Ag8 than on Ag(111). Moreover, the pathways for dissociation are different. The dissociation of O2 on Ag8 is associated with considerable structural deformations. O2 dissociation proceeds by charge transfer to antibonding 2π states. On the extended surface, there is a large reservoir of electrons in the valence band from which these electrons can be taken. For Ag8, on the other hand, the completely filled 1S21P6 jellium configuration renders the cluster somewhat resistant to charge depletion. Dissociation of O2 is connected to breaking of Ag-Ag (jellium) states and localization of electrons in Ag-O bonds. Because of the finite size, this balance between metal bonds and adsorbate-metal interaction is more crucial for the cluster than for the surface. Electronic Structure. To further clarify the oxidation process, the total density of states (DOS) and projected density of states (PDOS) were evaluated for Ag6, O/Ag6, 2O/ Ag6, O2/Ag6, and the stoichiometric 3O/Ag6 structure. The projection was done onto the oxygen states, and the results are collected in Figure 7. The DOS of Ag6 is an elucidative presentation of the jellium shell structure for a two-dimensional structure. The 1s state is found at the top of the d band at 1.41 eV below the HOMO level. The HOMO level66 is a degenerate 1P state well separated from the 1S state. The cluster has a large HOMO-LUMO separation of 2.2 eV. The LUMO is of 2S character, and the LUMO + 1 state is 1d. A single O atom is adsorbed on Ag6 in a 3-fold position with a binding energy of 0.14 eV with respect to O2 in the gas phase. A second isomer with O in bridge configuration is 0.56 eV higher in energy. The projected densities of states of both configurations are reported in Figure 7. In the case of O/Ag6, with O in the 3-fold configuration, only the HOMO level has clear 1p jellium character, whereas the HOMO - 1, HOMO 2, and HOMO - 3 are mainly of atomic oxygen 2p nature. Thus, close to two electrons from the 1p state are localized.
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Klacar et al. stable structures at 0.07 and 0.14 eV above ground state, respectively, show similar structural changes of the Ag dimer. NO adsorbed on O2/Ag4 yields a NO3 molecule with the same structural rearrangements as valid for the dimer. The Ag-Ag distance between the two oxygen-bound metal atoms decreases from 3.0 to 2.89 Å. In fact, 2.89 Å also corresponds to the bond length in the neutral Ag4 cluster. Upon NO2 adsorption, however, the metal cluster shows a significant deformation and adopts a tetrahedral structure with the formation of NO3 and one O atom in a 3-fold position. The ground-state structure of NO/3O/Ag6 shows that NO is preferably adsorbed as NO3. This further indicates the difficulty of cluster oxidation, as the corresponding metastable NO/3O/ Ag6 with NO2 instead is 0.41 eV higher in energy. Both structures are based on a C2V symmetry of the cluster, which is known to be relevant for the cation33 and the doubly ionized cluster.67 For the largest cluster, NO and NO2 adsorption leads to small deformation of the initial 4O/Ag8 motif, where no pronounced changes in bond lengths was calculated. This gives no clear indication as to changes in cluster oxidation. Conclusions
Figure 8. NO and NO2 adsorbed onto oxidized stoichiometric groundstate isomers. Isomers are reported with relative energies. The notation refers to the adsorbed molecules rather then the final structure.
The 1s jellium state is virtually unaffected by the O adsorption. Adsorption of O in the bridge configuration results in a lesspronounced hybridization with metal states. The 1s state is at the top of the d band, and one component of 1p is HOMO - 1. The other 1p component hybridizes with O(2p) and is located at HOMO - 2 and HOMO - 3. For 2O/Ag6 and the stoichiometric 3O/Ag6 cluster, there is an increased depletion of charge from the cluster, and no delocalized jelliumlike orbitals are found near the HOMO level. For 2O/Ag6, the 1s state is still intact, whereas for 3O/Ag6 cluster, no unperturbed jellium state can be found. For comparison, molecular adsorption (O2/Ag6) induces only small changes in the electronic structure of the cluster. The jellium states are close to undisturbed with 1s atop of the d band, and the HOMO level is the degenerate 1P state. Molecular oxygen states are found below the d band at energies typical for gas-phase O2. This exemplifies the weak interaction between O2 and the metal cluster upon molecular adsorption. NOx Adsorption. The adsorption of NOx on neutral Agn clusters has been studied in the past,32,33 and here, the issue of NOx adsorption on clusters with preadsorbed oxygen is addressed. In Figure 8, the structures are presented for NO and NO2 adsorption onto the stoichiometric O/Ag2, O2/Ag4, O3/Ag6, and O4/Ag8 clusters. All structures are related to the low-energy isomers of the stoichiometric clusters reported in Figure 5. In general, adsorption of NOx causes oxidation of nitrogen and reduction of the metal-oxide cluster; NO2 and NO3 are in all cases adsorbed at bridging conformations. The N-O distance in NO2 is 1.24 Å when adsorbed, and the O-N-O angle is 120°. This should be compared with the calculated gas-phase values of 1.21 Å and 133°, respectively. NO2 (NO) adsorption has pronounced effects on the Ag-Ag distances. For the dimer, the Ag-Ag distance is reduced from 2.98 Å in O/Ag2 to 2.69 Å in NO2/O/Ag2. The bond length in the bare neutral dimer is 2.61 Å. This suggests a reduction of the Ag dimer rather than oxidation upon NO2 adsorption. In NO2/O/Ag2, one jellium 1s state is occupied. Also, the meta-
We have presented a systematic DFT study of molecular and dissociated O2 adsorption on small gas-phase silver clusters in the range from one to nine Ag atoms. Electronic and structural properties of bare Agn clusters were determined by delocalized 5s electrons with the resulting shell structure and a pronounced odd/even alternation. O2 adsorption is sensitive to these features, and the molecular binding energy shows an odd/even variation with similar amplitude as the ionization potentials. Dissociative O2 adsorption is preferred for clusters larger than the pentamer. The thermodynamic stability of stoichiometric clusters (Ag2nOn) was compared to those of the bulk oxide (Ag2O) and the surface oxide of Ag(111). The calculations predict that, within the studied size range, only the stoichiometric Ag8O4 cluster has a higher temperature for oxide-to-metal transition than the oxidized bulk surface. A comparative study of O2 dissociation on Ag8 and Ag(111) reveals a higher barrier for the cluster. NO and NO2 adsorption onto the oxidized clusters results in a formal reduction of the clusters: NO is converted to a nitrite and NO2 to a nitrate. Our results demonstrate the balance between the formation of ionic bonds through metal-to-oxygen charge transfer and the loss of cluster cohesion as given by the delocalized Ag(5s) states. Despite the fact that the atoms in the studied clusters are severely undercoordinated, the oxide-to-metal transition temperature is lower than on the Ag(111) surface. Thus, oxidation of silver in the limit of small clusters is not as facile as on extended surface. This result is consistent with the study of NO and NO2 adsorption, which proceeds by an increase in the oxidation state of nitrogen instead of further cluster oxidation. Acknowledgment. Support from the Swedish Research Council is gratefully acknowledged. The Competence Centre for Catalysis is hosted by Chalmers University of Technology and financially supported by the Swedish Energy Agency and the member companies AB Volvo, Volvo Car Corporation, Scania CV AB, GM Powertrain Sweden AB, Haldor Topsoe A/S, and The Swedish Space Agency. The calculations were performed at C3SE (Go¨teborg, Sweden). References and Notes (1) Haberland, H. Clusters of Atoms and Molecules; Springer: New York, 1994.
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