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A second effect is that O 2 adsorbs much weaker on the even-numbered clusters. Accordingly, the unpaired electron in the odd-numbered clusters does not greatly affect CO adsorption. CO prefers to bind top or bridged to Au atoms with low coordination number on all of the Au n clusters and surfaces Figure S2. The Au atoms projected are those that will bond with CO. The canonical labels of the CO orbitals are indicated. Binding energies of atomic O also present an even—odd oscillation for the gold clusters.
Atomic O adsorbs stronger on the odd-numbered Au n planar clusters. The antibonding states around the Fermi level are completely occupied only in the even-numbered clusters, explaining why the odd-numbered clusters bind atomic O stronger.
The O atom adsorbs at the bridge site or in the threefold site of the clusters and surfaces except for the surface, where fourfold coordination is adopted. Next, CO oxidation was investigated on selected Au n clusters, i. As O 2 does not dissociate on Au clusters and surfaces, 28 , 37 an Eley—Rideal mechanism is not feasible. In the present work, we followed the well-accepted Langmuir—Hinshelwood mechanism 88 involving reaction between adsorbed CO and O 2.
The mechanism consists of five elementary reactions. As presented in Figures S4 and S5 , optimized CO, O 2 , and O adsorption configurations are considered as the initial states or final state to calculate the forward and backward reaction barriers. We neglected here possible lateral interactions. The presence of a support might change the structure of these Au clusters, which will influence the catalytic activity of CO oxidation. In addition, it is likely that active sites at the interface between Au clusters and the support will display different reactivities in CO oxidation.
Although the importance of support effects in CO oxidation is clear, this is beyond the scope of the present work. The elementary reaction barrier heights eV are indicated.
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It is found that stronger adsorption of CO and O 2 generally leads to a lower activation barrier for the formation of the OCOO intermediate, in line with previous findings. The reaction barrier for OCOO formation generally has an even—odd oscillation effect. The associated barriers vary from 0. CO oxidation is much easier on the odd-numbered clusters compared to the neighboring even-numbered ones, which especially relates to the stronger binding of O 2.
However, Au 4 shows deviant behavior in the sense that it is more reactive than Au 3 and Au 5 due to the highly exothermic formation of OCOO. The calculated reaction barriers are 1. For three-dimensional Au clusters and surfaces, OCOO intermediate formation is also facile with barriers between close to 0 and 0. Only on the Au 14 cluster, the barrier is substantially higher at 0. OCOO decomposition is highly exothermic on all considered models. The barrier for OCOO decomposition is lower when the intermediate binds stronger.
On planar clusters, OCOO dissociation barriers are in the 0. Compared to the even-numbered Au clusters, the neighboring odd-numbered ones exhibit a lower activation barrier for OCOO decomposition due to the activation of the O—O bond in the OCOO intermediate, an effect also observed for O 2 adsorption. The activation barrier is lower on the three-dimensional clusters and surfaces, ranging from 0.
It is associated with a higher exothermic reaction energy for these clusters. For the planar clusters, the reaction barriers for this reaction range from 0.
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Again, these barriers are higher than those encountered for the three-dimensional clusters and surface 0—0. For the three-dimensional clusters and surfaces, OCOO formation and decomposition barriers are comparable and lower than O removal. Only for the and surfaces, the O removal step is facile. On the basis of these kinetic data, we expect that the cluster size will considerably affect CO oxidation kinetics. We attempted to reduce the number of parameters by establishing linear scaling relations. In this way, we identified two types of linear scaling relationships, one for the planar clusters and one for the three-dimensional clusters and surfaces.
This is due to the different coordination numbers of the surface Au atoms on these two types of clusters, which results in different adsorption configurations of surface intermediates and, consequently, in different transition-state structures. The fitted linear equations are indicated. Accordingly, we omitted these three clusters in establishing the linear scaling relationships. It is found that on planar Au clusters all of the forward and backward barriers for the three involved elementary reaction steps scale linearly with these adsorption energies.
Therefore, reaction barriers relevant to CO oxidation can be approximated by the O 2 adsorption energy on planar Au n clusters. The negative slopes for the linear scaling relationship for the OCOO decomposition step are caused by the different O adsorption- and transition-state configurations among the various 3D Au structures. It also indicates that forward and backward barriers for OCOO decomposition increase with the exothermicity of this reaction step. The transition state for OCOO decomposition has an early character.
This trend shows that weaker adsorption of OCOO results in a higher barrier for its decomposition. Therefore, all of the reaction barriers involved in CO oxidation can be expressed by CO and O 2 adsorption energies as the reactivity descriptors for CO oxidation on three-dimensional clusters and surfaces.
It is clear that the scaling relationships between planar and three-dimensional Au clusters are different as a result of the different structures. The strong adsorption of O 2 on Au 9 results in low reaction barriers for the elementary reactions involved in CO oxidation. All of the odd-numbered Au clusters are more active than the even-numbered ones.
The most active one, the Au 4 cluster, is still significantly less active than the optimum Au 9 cluster. Identification of the catalytic activity of gaseous Au clusters remains a substantial challenge in gold catalysis. There are four regimes for the planar clusters distinguished by the dominant surface species. From the above discussion, we can deduce that reactant coverages and barriers, which mainly depend on CO and O 2 bond strength, determine the catalytic CO oxidation.
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Steady-state coverage of the intermediates a and degree of rate control b as a function of CO and O 2 adsorption energies on planar Au cluster. A positive DRC value for a particular elementary reaction step indicates that this step limits the reaction rate.
The dashed parts indicate the area in phase space where the activation barriers of the OCOO formation step are negative and thus unphysical. The morphology of very large Au nanoparticles can be approximated by Wulff construction.
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