Article pubs.acs.org/JPCC
Oxidation at the Subnanometer Scale Adriana Trinchero, Simon Klacar, Lauro Oliver Paz-Borbón, Anders Hellman, and Henrik Grönbeck* Department of Applied Physics and Competence Centre for Catalysis, Chalmers University of Technology, SE-412 96 Göteborg, Sweden ABSTRACT: Metals are commonly oxidized under ambient conditions. Although bulk oxidation has received considerable attention, far less is known about oxidation at the subnanometer scale. This is unfortunate, as metal particles used in heterogeneous catalysis typically range from subnanometer to some nanometers. Here, density functional theory calculations are used to explore oxidation of gas-phase transition metal clusters in the range from the dimer to the dodecamer. Comparisons with the corresponding bulk systems uncover that the decomposition temperature of stoichiometrically oxidized clusters may be lower than for the bulk. Despite pronounced variations in ground state geometries, oxidized clusters closely mimic energetic trends across the periodic table valid for bulk systems.
■
INTRODUCTION Oxidation of metals is a daily phenomenon, and metals are generally oxidized under ambient conditions. The oxidation process is fast, and a fresh metal surface is covered by oxygen atoms in a few microseconds. Depending on the reaction conditions and the metal, a protective oxide film may develop that prevents further oxidation or alternatively the metal may be transformed into a bulk oxide.1 Detailed studies of surface structures during initial oxidation have in many cases revealed a complex pattern. Taking the example of Pd(111) oxidation, it has been shown that a p(2 × 2) structure (0.25 ML coverage) is initially formed and that a two-dimensional (2D) surface oxide with Pd5O4 stoichiometry2,3 is developed at higher coverage (0.67 ML). Further oxidation to the bulk (PdO) phase proceeds via PdO seeds that grow on the 2D oxide.4,5 The presence of phases during the initial oxidation that deviate from the structural motif of the bulk has been reported for several late transition metals such as Rh,6 Ag,7 and Pt.8 The oxidation of transition metal surfaces has received special attention because of the use of these metals in heterogeneous catalysis.9 Automotive catalysis is one example where oxide supported particles of palladium, platinum, and rhodium are used for oxidation reactions. In order to provide a large surface area, the metal particles are generally designed to be minute. The size distribution typically ranges from subnanometer to some 4−5 nm. Examples of catalysts with ultrasmall particles are zeolite supported Cu clusters for selective catalytic reduction of nitrogen oxides in oxygen excess10 or partial oxidation of methane to methanol.11 Although trends in oxidation have been explored for bulk surfaces, far less is known about oxidation at the subnanometer scale.12,13 This is unfortunate, as clusters in applications are generally oxidized either by the atmosphere or by the anchoring to a support. In the literature, mainly the initial oxidation has been considered by studies of molecular and dissociated O2 adsorption (e.g., see refs 14−17), whereas few attempts have been made to study oxidation to bulk stoichiometry.18,19 © XXXX American Chemical Society
Consequently, the understanding of fundamental properties such as formation energies and relevant structures is not as advanced as the understanding of bare metal clusters.20 The substantial efforts on bare clusters have revealed that small systems adopt structural motifs in clear variance with the common bulk packing. Gold clusters have shown to be a particularly surprising case with planar structures up to about Au12 21,22 (depending on charge state) and tubular motifs for clusters consisting of 20−30 atoms.23 The lack of systematic information on oxidized clusters13 has prompted us to explore trends in the oxidation of transition metal clusters. In particular, density functional theory (DFT) calculations have been used to study initial adsorption as well as stoichiometric conditions for even sized Cu, Ag, Au, Pd, and Pt clusters in the range from the dimer to the dodecamer. Pronounced size variations are predicted in both energetic and structural properties. Comparisons with the corresponding bulk systems reveal that the decomposition temperature of the oxidized system in some cases is lower for the clusters than for the bulk. Analysis of the bonding interestingly uncovers that trends across the periodic table for bulk systems also apply in the subnanometer regime. Given the large variations in ground state structures, these results exemplify the nearsighted character of the bonding.
■
COMPUTATIONAL METHOD The density functional theory (DFT) is used as implemented in the Dmol3 program with the gradient corrected exchange correlation (xc) functional proposed by Perdew, Burke, and Ernzerhof (PBE).24 The one-electron Kohn−Sham orbitals are Special Issue: Current Trends in Clusters and Nanoparticles Conference Received: August 17, 2014 Revised: September 21, 2014
A
dx.doi.org/10.1021/jp508302b | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
enthalpy and entropy for O2.36 Following ref 35, entropic differences between the bare and oxidized metal are omitted. The bulk systems and extended (111) surfaces are treated with periodic boundary conditions. Integration over the Brillouin zone is done by finite sampling using a large number of k-points that ensure converged results.
expanded using a local numerical basis set. The basis functions are atom-centered and stored on a radial grid.25,26 In particular, a so-called double numerical basis set with polarization functions (dnp) is used for all atoms. A real space cutoff of 5 Å is applied for all basis functions. Scalar relativistic pseudopotentials are used to describe the interactions between the valence electrons and the core for the metal atoms.27 The semicore is included in the valence, and the numbers of electrons treated variationally are Cu(19), Ag(19), Au(19), Pd(18), and Pt(18). The Kohn−Sham equations are solved self-consistently with an integration technique of weighted overlapping spheres located at each atomic center. The direct Coulomb potential is obtained by projection of the charge density onto angular dependent weighting functions also centered at each atom. The Poisson equation can in this way be solved by one-dimensional integration. Structural optimization of small clusters is challenging because of the vast number of possible isomers20 with similar total energies. For transition metal clusters with open d-shells, the situation is furthermore complicated by the possibility of closely lying spin multiplets. In the present work, a basin hopping (BH) Monte Carlo global optimization algorithm is used as implemented within the atomic simulation environment (ASE).28 The BH algorithm is a stochastic method in which the potential energy surface (PES) to be sampled is transformed into a collection of interpenetrating staircases.29,30 Starting from randomly generated cluster configurations, at least 500 BH steps were performed for each cluster size. Geometry optimization is performed using the BFGS method,31−33 and the structures are regarded optimized when convergence criteria of 0.002 eV/Å, 0.0002 eV, and 0.005 Å are met for the largest gradient, total energy, and largest change in coordinates, respectively. The stability of different spin states is investigated explicitly for low lying isomers. Vibrational analysis of the optimized structures is performed in order to validate that the isomers are true minima on the potential energy surface (PES). The harmonic frequencies are obtained by matrix diagonalization of the energy gradients, which are obtained through finite difference calculations. For the bare clusters, the binding energies are calculated per atom with respect to the spin-polarized spherical metal atom. Adsorption energies of O2 are calculated with respect to the bare cluster and O2 in the gas phase. As PBE is known to overbind O2,24 we have chosen to relate the total energy of O2 to the formation energy of H2O as described in ref 34. In order to estimate the thermal decomposition temperature of either the bulk oxides or the oxidized clusters (a cluster with n atoms of metal M and m oxygen atoms is denoted MnOm), the temperature is calculated for which the free energy difference between the oxide and the bare metal with O2 in the gas phase is zero:35 E M nOm − E M n − mμO(T , p) = 0
■
RESULTS AND DISCUSSION Bulk References. To put the results for the clusters in context, the corresponding bulk data are presented in Table 1. Table 1. Calculated (Experimental) Data for the Considered Bulk Phasesa a Cu Ag Au Pd Pt Cu2O Ag2O Au2O PdO PtO
⎛ pO ⎞⎞ 1⎛ ⎜⎜EO + μO′ + kBT ln⎜ 02 ⎟⎟⎟ 2 2⎝ 2 ⎝ p ⎠⎠
(3.61) (4.08) (4.06) (3.89) (3.92) a
4.32 (4.27) 4.88 (4.73) 4.83 a, c 3.13, 5.45 (3.03, 5.33) 3.17, 5.40 (3.05, 5.35)
Ec 3.39 2.50 2.90 3.50 5.05
(3.49) (2.80) (3.81) (3.94) (5.84) Ef
−1.35 (−1.63) −0.34 (−0.32) 0.31 Ef −1.01 (−0.89) −0.64 (−0.71)
structure fcc fcc fcc fcc fcc structure cubic cubic cubic structure tetragonal tetragonal
a
a and c are the lattice constants (Å). Ec and Ef are cohesive energy and energy of formation, respectively (eV). The bulk values are taken from refs 38 and 39.
All considered metals have an fcc lattice. Among the noble metals (Cu, Ag, and Au), Cu has the smallest lattice, whereas Ag and Au have similar lattice constants. The slight expansion with respect to the experimental values can be ascribed to the applied xc functional.37 Owing to net bonding in the d-shell, metals with open d-shells (d9s1) have a higher cohesive energies than the noble metal in the same row. The bulk values are in fair agreement with the experimental estimates except for the cohesive energies of Pt and Au, which also have been reported previously.37 The noble metal oxides are treated in a cubic cuprite structure, which is the experimental ground state for Cu2O and Ag2O. Because gold oxide does not have any stable bulk phase, the same structure was chosen for this element in order to facilitate comparisons. In the cuprite structure, metal atoms are linearly coordinated between oxygen atoms, thus having two neighbors. Oxygen atoms, on the other hand, have four neighbors. The comparison with experimental data is fair. We note that the copper oxide is far more stable than Ag2O and Au2O (which is endothermic). PdO has a tetragonal lattice in which both the metal and the oxygen atoms are coordinated to four neighbors. Platinum is known to form oxides with different stoichiometry, where PtO2 is the most common. However, to be able to perform clear comparisons, we explore here PtO, which adopts the same structure as PdO.39 In agreement with experiments, PdO is predicted to be more stable than PtO. Bare Clusters. The optimized structures for even-sized bare clusters in the range from the dimer to the dodecamer are shown in Figure 1. The structural evolution of small metal
(1)
Here, EMnOm and EMn are the total energies of the oxidized and bare metal cluster, respectively. μO is the oxygen chemical potential which is given by μO(T , p) =
3.64 4.19 4.20 3.97 4.00
(2)
EO2 is the total energy of oxygen, and μ′O2 accounts for translational, vibrational, and rotational contributions in B
dx.doi.org/10.1021/jp508302b | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
Figure 1. Ground state structures for Cun, Agn, Aun, Pdn, and Ptn. The net spin magnetic moments for Pd and Pt are given in Bohr magnetons The magnetic moments for the coinage metal clusters are zero.
clusters has been treated extensively in the literature, and predictions have, for example, appeared for Cu,40 Ag,15,41−46 Au,21,22,47 Pd,48,49 and Pt.50,51 The present results agree with previous reports using the same type of xc approximation. It has been recognized that the xc functional may alter the isomeric ordering.47,52 As the focus of the present work is on oxidized clusters, we only discuss the main trends. The relevant structures for Cu and Ag are similar in the present size range. Clusters up to the hexamer are planar, whereas three-dimensional isomers are relevant from the heptamer. This is related to the fact that the bonding in these types of clusters is determined by the delocalized selectrons and the filling of superatom shells.53 For the octamer, the dodecahedron and tetra-capped tetrahedron are close to energetically degenerate. The former is slightly preferred for Cu, whereas the latter is preferred for Ag. Beyond eight atoms, motifs that include 5-fold symmetry turn out to be competitive. The structures of bare gold clusters have been intensively studied over the past years. Interestingly, the low energy structures are two-dimensional in the studied size range and Au10 and Au12 are predicted to be flakes of a Au(111) lattice plane.21,22 In contrast to the noble metal clusters, Pd and Pt adopt three-dimensional structures already at the tetramer. The tetramer is a tetrahedron, and the hexamer is an octahedron. The octahedral motif is present also for the octamer (the ground state D2d structure can be viewed as a bicapped octahedron) and the decamer (two fused octahedra). Pd12 has Cs symmetry and a mixture of 5-fold and octahedral motifs. The structural evolution for Pt clusters is even more complex, as the hexamer turns out to be two-dimensional and the decamer could be viewed as two fused trigonal prisms with two caps. The compact structures for Pd and Pt are a consequence of net bonding in the open d-shell. Another effect of the open d-shell is the preference of higher spin states. Whereas the even numbered noble metal clusters all are spin singlets, the Pd and Pt clusters have higher magnetic moments. In agreement with previous reports,48 the spin magnetic moments are substantial for Pd12. Oxidized Clusters. The optimized structures for molecular and dissociative adsorption of O2 on the different clusters are
Figure 2. Structures of O2 adsorbed in molecular and dissociative configurations on the different elements. The net spin magnetic moment in Bohr magnetons are indicated. Atomic color code: Cu (brown), Ag (blue), Au (yellow), Pd (blue), Pt (white), O (red).
shown in Figure 2. The corresponding binding energies are reported in Figure 3. On copper clusters, molecular O2 is adsorbed in atop (Cu2), bridge (Cu4, Cu8, and Cu12), or hollow (Cu6 and Cu10) sites. The O−O bond distance is dependent on adsorption configuration and is calculated to be about 1.28, 1.37, and 1.51 Å for atop, bridge, and hollow, respectively. The calculated bond distance for O2 in the gas phase is 1.23 Å, whereas the bond distance for a negatively charged O2 (superoxo) is 1.35 Å. Thus, a superoxo species is formed when O2 is adsorbed in the bridge configuration. Although the structures with molecular adsorbed O2 are minima on the potential energy surface, O2 is preferably dissociated on copper clusters (Figure 3). Atomic oxygen adsorbs in bridge configurations on the small clusters, whereas hollow sites are preferred from the hexamer. We note that the charge transfer from metal to the oxygen atoms has large effects on the structure. One example is the hexamer which turns threedimensional in the presence of oxygen. For Ag clusters, molecular adsorption is preferred for the dimer and tetramer. Molecular oxygen adsorbs in atop or bridge configurations, with O−O bond distances of 1.25 and 1.31 Å, respectively. Adsorption in the atop site correlates with C
dx.doi.org/10.1021/jp508302b | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
high binding energies are not even present on open (321) bulk surface.54 However, despite the differences in absolute energies, the trends between the coinage metals (Cu > Ag > Au) clusters follow the trend for bulk surfaces. The d-states are filled for these metals, which means that the net bonding originates from s-contributions, which is similar (jellium like) for the three metals. The differences can instead be understood from the Pauli repulsion between the O 2p and metal d states which is largest for Au and smallest for Cu.55 The difference in filling of d-states explains the higher binding energies for Pd (Pt) as compared to Ag (Au). Even if the center of d-states with respect to the HOMO level is different for Pd and Pt clusters, the binding energies are similar for the larger sizes. For the dodecamers, the center of the d-states is 1.50 and 1.99 eV for Pd12 and Pt12, respectively. The corresponding binding energies of dissociated O2 are 2.89 and 3.18 eV. Turning to the stoichiometric oxidized clusters, the structures and the corresponding stabilities are shown in Figure 4. The stability is calculated with respect to the bare
Figure 3. Adsorption energies for molecular and dissociative O2 on different elements and cluster sizes. The dashed lines indicate the adsorption energy of two oxygen atoms on the corresponding bulk (111) surfaces. The adsorption energies are calculated at a coverage of 0.25 ML.
a lower binding energy. O atoms for the dissociated molecule preferably occupy hollow sites. This is a strong tendency, as already the tetramer turns three-dimensional. Dissociative adsorption is favored also for gold clusters. Interestingly, however, oxygen is found to break the Au−Au bonds and form clear O−Au−O units. This effect is most pronounced for Au2, Au6, and Au12. Molecular oxygen is adsorbed in atop or bridge configurations. The O−O bond length is in this case not very dependent on structure and is in all cases close to 1.26 Å. Dissociate adsorption is preferred also for palladium and platinum clusters. For Pd clusters, atomic O is adsorbed in bridge configurations for the smaller sizes, whereas hollow is preferred from the octamer. The situation is different for Pt where the bridge is preferred over the entire size range. In fact, platinum has the same O−Pt−O motif as for gold, although not as pronounced. Molecular oxygen is adsorbed in bridge configuration on all Pd clusters with an O−O bond length of ∼1.35 Å. The bridge configuration is also preferred for Pt clusters with a slightly enlarged molecular distance (1.39 Å). The corresponding binding energies of dissociated oxygen on the bulk (111) surfaces are indicated in Figure 3. The reported values are calculated with an adsorbate coverage of 0.25. The adsorption energies on the larger clusters are considerably higher than for the (111) surfaces. The effect is most pronounced on Ag where the adsorption energy on Ag12 is more than twice that on Ag(111). It is not surprising that the adsorption energies are higher on the clusters; however, the amount of enhanced binding is striking. For palladium, such
Figure 4. Ground state structures for (Cu2O)n, (Ag2O)n, (Au2O)n, (PdO)n, and (PtO)n. The enthalpy of formation is reported in eV.
cluster and O2 in the gas phase. The clusters are stoichiometric in the sense that the composition reflects the bulk stoichiometry. It is clear that the actual stoichiometry may depend on system size. However, to obtain trends among elements in the periodic table, we here restrict the search to the bulk stoichiometry. In general, adsorption of oxygen has pronounced effects on the structure. In fact, it is in most cases difficult to find any resemblance to the bare clusters or the structural motif in the bulk oxide. Interestingly, we find that the structures of (Cu2O)n and (Ag2O)n are very similar. It is only for the tetramer that molecular adsorption is favored over dissociated in the case of silver. A trend for the oxidized clusters is that the metal atoms are linearly coordinated between the adsorbed oxygen atoms. The bare clusters only contain surface atoms. However, we find that the stable (Cu2O)6 and (Ag2O)6 structures have core atoms that are coordinated to 11 metal neighbors. The D
dx.doi.org/10.1021/jp508302b | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
depending on oxygen chemical potential and temperature. This is actually what is observed for bulk surfaces.7,57 Another aspect that is neglected in the thermodynamic analysis is the possibility of removing metal oxide units. Such processes have been proposed for small metal particles in connection with sintering of supported platinum nanoparticles.58 To explore this possibility, we calculated the fragmentation of MnOm into the corresponding single units, M2O for the coinage metals, and MO for (PdO)m and (PtO)m. For the coinage metals, it is found that the (Cu2O)m clusters decompose preferably into Cu2O units, whereas the decomposition temperature along this channel is higher than reported in Figure 5 for silver and gold. Also for (PdO)2, and (PtO)2-(PtO)8 the MO channel is preferred. For the platinum clusters, this is consistent with the pronounced stability of the smallest sizes. The temperatures presented in Figure 5 are calculated with the assumption that the entropic differences between the bare and oxidized metal can be neglected.35 Whereas this may be a fair approximation for bulk systems where the degrees of freedom are large, the situation is different for finite systems, where, for example, the number of vibrational normal modes is different for the bare and oxidized clusters. The larger number of modes for the oxidized clusters will further enhance the stability with respect to the bare metal clusters. The same holds if configurational entropy would be taken into account. We have chosen not to include these effects in Figure 5, mainly because of the neglect of different oxidation states and decomposition patterns. It should be noted that although the decomposition temperatures are larger for the clusters than for the bulk, the systems are still undercoordinated and have a reduced stability in comparison with the bulk systems. The binding energies for the largest stoichiometric clusters are 72%, 67%, 75%, 72%, and 67% of oxidized bulk Cu, Ag, Au, Pd, and Pt, respectively. These values are slightly larger than for the bare clusters which can be understood from the larger number of atoms. In addition to the thermal stability, oxide systems are generally characterized with respect to the band gap and the charge separation. The clusters in the present study are small and are molecular in nature with, in several cases, distinct HOMO− LUMO separations. The same is true for the oxidized clusters. In fact, it is difficult to observe any trend with respect to the HOMO−LUMO gap between the bare and oxidized clusters in the present size regime. The charge separation in the clusters is analyzed by a Bader decomposition. With respect to cluster size, there is a slight trend that the charging of the atoms increases with cluster size. For example, the average metal valence charge for Cu2O is 10.53 electrons, whereas it is 10.49 e for Cu12O6. The corresponding value for bulk copper oxide is 10.41 e. Comparing the different elements, we find for the oxidized dodecamers that the valence charge is 10.49, 10.56, 10.64, 9.20, 9.21 electrons for Cu, Ag, Au, Pd and Pt, respectively. The corresponding bulk vales are 10.41 (Cu), 10.48 (Ag), 10.55 (Au), 9.01 (Pd), and 9.02 (Pt). The incomplete (with respect to the bulk) charge separation in the clusters is clearly a consequence of the reduced size and the loss of the stabilizing Madelung potential. However, the trends between the elements are the same for the clusters as for the bulk samples. In addition to the study of the size evolution of structural and electronic properties for each element, it is revealing to explore trends across the periodic table in the subnm regime. We have done this for the largest clusters (dodecamers), and the binding
structures of the oxidized gold clusters are clearly different from Cu and Ag. The preference of two-dimensional structures is to a large extent preserved and the ground states are planar with the exception of (Au2O)3 and (Au2O)6. Furthermore, the importance of a linearly coordinated Au atoms is clearly visible. All sizes have a rim with an O−Au−O motif. One may also note that the importance of linearly coordinated gold atoms has been observed for completely thiolated gold clusters which adopt ring and crown structures.56 The enthalpy of formation with respect to bare clusters and O2 in the gas-phase is reported in Figure 4. The calculated energies are generally larger than for the corresponding bulk sample; see Table 1. The higher energies have consequences with respect to the thermal stability. The decomposition temperatures as calculated by eq 1 are reported in Figure 5.
Figure 5. Decomposition temperatures of stochiometric clusters. The dashed lines indicate the corresponding (theoretical) bulk values.
This is the temperature when the entropy of oxygen in the gasphase stabilizes Gibbs energy of (Mn + (m/2)O2) with respect to (MnOm). For reference, the decomposition temperatures of the corresponding bulk systems are indicated by dashed lines. The decomposition temperature of gold oxide is zero, as this system does not exist at normal pressures. The decomposition temperature of PtO is calculated to be 665 K. The estimated decomposition temperatures presented in Figure 5 are constructed in order to investigate trends in stability of oxidized clusters. One restriction of the calculated temperatures is that only two states are taken into account, either an oxidized cluster or a metallic cluster. It is reasonable to assume that the experimental situation encompasses various phases where clusters change between different oxidation states E
dx.doi.org/10.1021/jp508302b | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
bulk metals. This suggests that trends in the periodic table largely are given by local bonding that is already developed for subnanometer sized clusters.
energy (per atom) and enthalpy of formation are reported in Figure 6. The results are compared to the corresponding bulk
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS Financial support from the Swedish Research Council and the Chalmers Areas of Advance Nano and Transport is acknowledged. The calculations have been performed at C3SE (Göteborg, Sweden) through a SNIC grant.
■
Figure 6. Top panel: Enthalpy of formation (Ef) for the bulk oxides and the stoichiometrically oxidized dodecamers. Lower panel: Bulk cohesive energy and binding energy (Ec) for the bare dodecamer clusters with respect to the gas-phase spherical atom (for bare clusters).
REFERENCES
(1) Cabrera, N.; Mott, N. F. Theory of the Oxidation of Metals. Rep. Prog. Phys. 1949, 12, 163−184. (2) Zheng, G.; Altman, E. The Oxidation of Pd(111). Surf. Sci. 2000, 462, 151−168. (3) Klikovits, J.; Napetschnig, E.; Schmid, M.; Seriani, N.; Dubay, O.; Kresse, G.; Varga, P. Surface Oxides on Pd(111): STM and Density Functional Calculations. Phys. Rev. B 2007, 76, 045405. (4) Kan, H. H.; Weaver, J. F. Mechanism of PdO Thin Film Formation during the Oxidation of Pd(111). Surf. Sci. 2008, 603, 2671−2682. (5) Gabasch, H.; Unterberger, W.; Hayek, K.; Klötzer, B.; Kleimenov, E.; Teschner, D.; Zafeiratos, S.; Hävecker, M.; Knop-Gericke, A.; Schlögl, R.; et al. In Situ XPS Study of Pd(111) Oxidation at Elevated Pressure, Part 2: Palladium Oxidation in the 10−1 mbar Range. Surf. Sci. 2006, 600, 2980−2989. (6) Klikovits, J.; Schmid, M.; Merte, L. R.; Varga, P.; Westerström, R.; Resta, A.; Andersen, J. N.; Gustafson, J.; Mikkelsen, A.; Lundgren, E.; Mittendorfer, F.; Kresse, G. Step-Orientation Dependent Oxidation: From 1D to 2D Oxides. Phys. Rev. Lett. 2008, 101, 266104. (7) Schnadt, J.; Knudsen, J.; Hu, X. L.; Michaelides, A.; Vang, R. T.; Reuter, K.; Li, Z.; Lægsgaard, E.; Scheffler, M.; Besenbacher, F. Experimetal and Theoretical Study of Oxygen Adsoption Structures on Ag(111). Phys. Rev. B 2009, 80, 075424. (8) Li, W.; Ö sterlund, L.; Vestergaard, E.; Vang, R.; Matthiesen, J.; Pedersen, T.; Laegsgaard, E.; Hammer, B.; Besenbacher, F. Oxidation of Pt(110). Phys. Rev. Lett. 2004, 93, 146104. (9) Bell, A. T. The Impact of Nanoscience on Heterogeneous Catalysis. Science 2003, 299, 1688−1691. (10) Gao, F.; Walter, E. D.; Washton, N. M.; Szanyi, J.; Peden, C. H. F. Synthesis and Evaluation of Cu-SAPO-34 Catalysts for Ammonia Selective Catalytic Reduction. 1. Aqueous Solution Ion Exchange. ACS Catal. 2013, 3, 2083−2093. (11) Chan, S. I.; Lu, Y.; Nagababu, P.; Maji, S.; Hung, M.-C.; Lee, M. M.; Hsu, I. J.; Minh, P. D.; Lai, J. C. H.; Ng, K. Y.; Ramalingan, S.; Yu, S. S. F.; Chan, M. K. Efficient Oxidation of Methane to Methanol by Dioxygen Mediated by Tricopper Clusters. Angew. Chem., Int. Ed. 2013, 52, 3731−3735. (12) Gates, B. C. Extending the Metal Cluster−Metal Surface Analogy. Angew. Chem., Int. Ed. 1993, 32, 228−229. (13) Goloboy, J. C.; Klemperer, W. G. Are Particulate Noble-Metal Catalysts Metals, Metal Oxides, or Something In-Between? Angew. Chem., Int. Ed. 2009, 48, 3562−3564. (14) Yoon, B.; Häkkinen, H.; Landman, U. Interaction of O2 with Gold Clusters; Molecular and Dissociative Adsoption. J. Phys. Chem. A 2003, 107, 4066−4071. (15) Klacar, S.; Hellman, A.; Panas, I.; Grönbeck, H. Oxidation of Small Sliver Clusters: A Density Functional Theory Study. J. Phys. Chem. C 2010, 114, 12610−12617.
values. For the bare clusters, the convergence of the binding energies is known to be slow, and the binding energy in the present size regime (where all atoms are surface atoms) is clearly reduced with respect to the cohesive energies of the bulk (Table 1). For the dodecamers, the binding energies are only 63%, 62%, 69%, 59%, and 68% of the bulk values for Cu, Ag, Au, Pd, and Pt, respectively. Interestingly, however, the same trends across the periodic table apply for the clusters and the bulk systems. Also for the stoichiometrically oxidized clusters, the heat of formation at the cluster-scale follows the corresponding bulk trend. That energetic trends at the bulkscale also are relevant for subnanometer sized clusters is to some extent remarkable given that the predicted structures are far from the local geometry in the bulk. The bare M12 clusters have not developed the fcc motif, and the oxidized clusters have structures that range from the fairly compact (Cu2O)6 and (Ag2O)6 to the open (Au2O)6 and (PtO)12. Our results suggest that trends in the periodic table are largely given by local bonding which is already developed for minute entities such as subnanometer sized clusters.
■
CONCLUSIONS Small metal clusters are used as atomically precise catalysts for many reactions of which NOx reduction and direct methanol synthesis only are two examples. As these reactions take place in an oxidizing environment, the clusters are most likely in an oxidized state. Understanding the molecular processes requires information on the structure and stability of the oxidized clusters. In the present work, we have presented a systematic study of oxidized even sized metal clusters of Cu, Ag, Au, Pd, and Pt clusters in the range from the dimer to the dodecamer. We find pronounced size variations in both energetic and structural properties. The structures have no resemblance to the corresponding bulk systems. For example, novel structures that divide the clusters in a metal part and O−M−O units are predicted for both Au and Pt clusters. However, despite sizable variations in ground state geometries, oxidized clusters closely mimic energetic trends across the periodic table valid for the F
dx.doi.org/10.1021/jp508302b | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
(16) Yuan, X.; Liu, L.; Wang, X.; Yang, M.; Jacksan, K.; Jellinek, J. Theoretical Investigation of Adsoption of Molecular Oxygen on Small Copper Clusters. J. Phys. Chem. A 2011, 115, 8705−8712. (17) Jennings, P. C.; Aleksandrov, H. A.; Neyman, K. M.; Johnston, R. L. A DFT Study of Oxygen Dissociation on Platinum Based Nanoparticles. Nanoscale 2014, 6, 1153−1165. (18) Xu, Y.; Shelton, W. A.; Schneider, W. F. Effect of Particle Size on the Oxidatibility of Platinum Clusters. J. Phys. Chem. A 2006, 110, 5839−5846. (19) Mittendorfer, F.; Seriani, N.; Dubay, O.; Kresse, G. Morphology of Mesoscopic Rh and Pd Nanoparticles under Oxidizing Conditions. Phys. Rev. B 2007, 76, 233413. (20) Ferrando, R.; Jellinek, J.; Johnston, R. L. Nanoalloys: From Theory to Applications of Alloy Clusters and Nanoparticles. Chem. Rev. 2008, 108, 845−910. (21) Weis, P.; Bierweiler, T.; Gilb, S.; Kappes, M. M. Structures of Small Silver Clusters Cations (Ag+n , n
