Optimum Particle Size for Gold-Catalyzed CO Oxidation.

The structure sensitivity of gold-catalyzed CO oxidation is presented by analyzing in detail the dependence of CO oxidation rate on particle size. Clusters with less than 14 gold atoms adopt a planar structure, whereas larger ones adopt a three-dimensional structure. The CO and O2 adsorption properties depend strongly on particle structure and size. All of the reaction barriers relevant to CO oxidation display linear scaling relationships with CO and O2 binding strengths as main reactivity descriptors. Planar and three-dimensional gold clusters exhibit different linear scaling relationship due to different surface topologies and different coordination numbers of the surface atoms. On the basis of these linear scaling relationships, first-principles microkinetics simulations were conducted to determine CO oxidation rates and possible rate-determining step of Au particles. Planar Au9 and three-dimensional Au79 clusters present the highest CO oxidation rates for planar and three-dimensional clusters, respectively. The planar Au9 cluster is much more active than the optimum Au79 cluster. A common feature of optimum CO oxidation performance is the intermediate binding strengths of CO and O2, resulting in intermediate coverages of CO, O2, and O. Both these optimum particles present lower performance than maximum Sabatier performance, indicating that there is sufficient room for improvement of gold catalysts for CO oxidation.

Introduction

Catalytic performance of dispersed metals is governed by the size of the (nano)particles and the local surface topology, as these determine the electronic structure of the surface atoms to which reactants bind.[1] Differences in the binding energies affect surface coverages and intrinsic barriers of the relevant elementary bond-breaking and bond-making steps. Understanding structure sensitivity in detail promises to accelerate design of better catalysts.[2] Much progress in this field has been possible through careful in situ characterization and kinetic testing of structurally well-defined model systems—often in the form of surface science models, but recently also increasingly by using nanoparticles—in combination with first-principles density functional theory (DFT) calculations of reaction mechanism.[3−14] In nanoparticle catalysis, the structure sensitivity manifests itself as a strong dependence of surface atom-based turnover frequency on particle size, predominantly because of the exposure of a significant fraction of corner, edge, and step-edge atoms at the surface of these particles.[4,14−20] When particles become clusters, well-developed facets disappear and quantum effects and local surface atom topology will start influencing catalytic reactivity.

A case in point of structure sensitivity is CO oxidation catalyzed by gold.[4,15−18] Gold catalysis has attracted widespread attention of the scientific community since the discovery that small supported Au nanoparticles exhibit unusual high activity in the CO oxidation reaction.[21−26] For instance, it has been demonstrated that Au nanoparticles with a size of 2–3 nm are optimum for CO oxidation in Au/TiO2 catalysts.[16] The role of the support in gold-catalyzed CO oxidation chemistry in such systems has recently been emphasized in recent years.[27−33] Moreover, Li et al. presented that single Au atom can be dynamically formed by CO adsorption on oxide-supported Au clusters influencing CO oxidation mechanism and activity.[34,35] Nørskov and co-workers mentioned that CO oxidation activity depends predominantly on the size of gold particles, regardless of the support.[36,37] However, it is still an open question why CO oxidation activity is very sensitive to the gold particle size. Accordingly, it is interesting to explore the influence of size of very small clusters/nanoparticles of gold on CO oxidation.

Because small gold clusters can be synthesized and confirmed nowadays,[38,39] it is desirable to study the intrinsic activity of CO oxidation on gaseous gold clusters. Interest in gold cluster catalysis for CO oxidation is growing.[26,30,40−48] For instance, Whetten et al. found that the gaseous Au6 anion is capable of oxidizing CO at a 2 orders of magnitude higher rate than supported gold catalysts.[40] Temperature-dependent radio frequency-ion trap mass spectrometry and first-principles simulations were conducted to investigate the reaction mechanism of CO oxidation by free Au2– ions in the presence of O2, and a metastable Au2CO3– was identified as an intermediate at low temperature.[41] It has also been demonstrated in experiments by the Wang group that the Au18– cage compound displays higher reactivity toward O2 among Au– clusters (n = 16–18).[43] Using computational chemistry, Nørskov’s group found that CO and O2 bind stronger to the low-coordinated Au atoms that appear on smaller particles.[36,37] Häkkinen and co-workers emphasized that strong binding of molecular oxygen to gold clusters smaller than 2 nm contributes to lowering the activation barrier of CO oxidation.[49] The work of Zeng also demonstrated that CO oxidation activity can be related to the adsorption energies of CO and O2.[10,50] Lee’s investigation indicates that a delicate balance between CO and O2 adsorption energies is required to maximize CO oxidation activity on Au nanoparticles.[51] A recent work used the concept of the orbital-wise coordination number as a reactivity descriptor for CO and O adsorption energies on extended gold surfaces and nanoparticles of varying size and shape.[52] It has also been mentioned that the greater structural flexibility of very small clusters may contribute to high catalytic activity.[53,54] To the best of our knowledge, the binding properties of CO and O2 as well as the relationships between their adsorption energies and reaction barriers relevant to CO oxidation have not been systematically investigated yet.

Herein, we report a combined first-principles density functional theory (DFT) and microkinetics study of CO oxidation on gold clusters/nanoparticles, revealing important insights into the structure dependence of the CO oxidation reaction. A search strategy based on a genetic algorithm (GA) is employed to determine the global minimum structures of small Au (n = 3–16 and 20) clusters. Larger particles of 38, 55, and 79 gold atoms as well as a Wulff particle are constructed by use of the Wulff theorem using computed surface energies. The well-accepted CO oxidation mechanism involving OCOO as a reaction intermediate is systematically studied on these models. We explore in detail the relationship between CO oxidation barriers and CO and O2 adsorption energies for gold particles. Planar and three-dimensional (3D) Au structures exhibit different scaling relationships due to their different topology and distinct coordination number of surface Au atoms. First-principles microkinetics simulations have been performed to compute reaction rates and determine possible rate-determining step for CO oxidation over these particles for the first time. Two types of volcano curves are identified for planar and three-dimensional gold structures. The odd-numbered planar clusters are significantly more active than the three-dimensional clusters. This work will provide valuable insight relevant to the design of more active gold catalysts for CO oxidation.

Methods

DFT Calculations

All spin-polarized density functional theory (DFT) calculations were conducted by using projector augmented wave (PAW)[55] potentials and the Perdew–Burke–Ernzerhof (PBE) functional[56] implemented in the Vienna ab initio simulation package[57,58] code. The global minimum structures of Au clusters were obtained by using a genetic algorithm (GA) code with structures optimized by first-principles DFT calculations. The clusters were placed in a large cubic supercell (at least 15 Å × 15 Å × 15 Å) for the structure optimizations. Brillouin zone sampling was restricted to the Γ point. All of the atoms in the clusters were allowed to relax. The energy cutoff of the plane wave basis set was 250 eV, and the convergence threshold for geometry optimizations was set to 1 × 10–4 eV for optimizing the structure of the clusters by the GA approach. Geometry optimization was deemed converged when the forces on each atom were below 0.05 eV Å–1.

The morphologies of Au38, Au55, and Au79 clusters were obtained by the Wulff construction based on the surface energies of the extended surfaces. To obtain accurate surface energies, we have adopted p(1 × 1) slab models with the atomic layers of at least 20 Å separated by a vacuum of at least 15 Å. All of the atoms in the slab are fully relaxed with the force convergence criteria of 0.02 eV Å–1. The density of k-points was kept at ∼0.04 Å–1 for the surface energies calculations. The surface energy (Esurface) was determined as Esurface = (Eslab – NEbulk)/2A, where Eslab and Ebulk are the total energies of the slab and one bulk Au atom, respectively, N is the number of Au atoms in the slab, and A is the surface area.

p(3 × 3) slab models were used for the calculation of CO oxidation mechanism on (111) and (100) surfaces, whereas p(2 × 3) and p(1 × 3) slab models were used for (211) and (221) surfaces, respectively. All of the four surfaces were simulated by using four equivalent (111) atomic layers (except for (100) surface with five layers) slabs. Neighboring slabs were separated by a vacuum of 15 Å to avoid self-interactions. All of the clusters were placed in a cubic supercell maintaining a vacuum gap of at least 10 Å between the neighboring images. Calculations of the clusters were performed in the Γ-point, whereas a 3 × 3 × 1 k-point mesh was used for all of the considered periodic surfaces, except for (211) surface with a 2 × 3 × 1 k-point mesh. The cutoff energy was set to 400 eV for calculations of the CO oxidation reaction mechanism for all of the Au clusters and surfaces. For the clusters, all of the atoms were allowed to relax. The top two equivalent (111) layers and adsorbates were relaxed for the periodic models. The improved force-reversed method[59] was used to determine the transition states (TSs) for CO oxidation, and a force tolerance of 0.02 eV Å–1 was used. The nature of some of the TSs was verified by the climbing-image nudged elastic band methods.[60,61] Vibrational mode analysis was done to verify the identified TSs.

Structure of Au Clusters

A standard genetic algorithm based on the principles of natural evolution was used. It includes four steps, involving generation of the initial population, optimization of the cluster structures, assigning the fitness, and generating new population by crossover, as introduced by Deaven and Ho,[62,63] as well as random mutations by moving of atoms.[64] Each structure in the population is optimized at the DFT–PAW–PBE level. The calculated energies are used to determine the fitness, and the structures with lower energy have higher possibilities to be maintained in the population.[65] Energies and bond distances are used to judge whether the two structures are the same to avoid multiple occurrences of one structure in the population. The cycle is terminated when no new structures are obtained for 80 cycles. Typically, several hundreds of structures have been optimized to obtain the global minimum structure of each Au cluster size.

Microkinetics Simulations

The calculated activation barriers were employed to compute the forward and backward rate constants for CO oxidation. For surface reactions, the rate constants for the forward and backward elementary reactions were determined by the Eyring equation[66]where k is the reaction rate constant in s–1; kb, T, h, and Ea are the Boltzmann constant, temperature, Planck’s constant, and the activation barrier, respectively; and QTS and Q refer to the partition functions of the transition and ground states, respectively. As an approximation, the prefactor is set to 1013 s–1 for all of the elementary surface reactions.

For nonactivated molecular adsorption, the rate of adsorption is determined by the rate of surface impingement of gas-phase molecules. The flux of incident molecules is given by the Hertz–Knudsen equation[67]Therefore, the molecular adsorption rate constant can be written aswith P the partial pressure of the adsorbate in the gas phase, A′ the surface area of the adsorption site, m the mass of the adsorbate, and S the sticking coefficient. The sticking coefficient used here is 1 for CO and O2 adsorptions.

For the desorption process, it is assumed that there are three rotational degrees of freedom and two translational degrees of freedom in the transition state. Accordingly, the rate of desorption is given bywhere σ and θ are the symmetry number and the characteristic temperature for rotation, respectively. Edes is the desorption energy.

The approach to microkinetics simulations has been presented in detail elsewhere.[13,68] Differential equations for all of the surface reaction intermediates were constructed using the rate constants and the set of elementary reaction steps. For each of the M components in the kinetic network, a single differential equation in the formis obtained. In this equation, k is the elementary reaction rate constant (see eq ), ν is the stoichiometric coefficient of component i in elementary reaction step k, and c is the concentration of component k on the catalytic surface.

The CO oxidation rate is calculated by the in-house developed MKMCXX program.[13,68,69] Steady-state coverages were calculated by integrating the ordinary differential equations (ODEs) in time until the changes in the surface coverages were very small. Because chemical systems typically give rise to stiff sets of ODEs, we have used the backward differentiation formula method for the time integration.[68] The rates of the individual elementary reaction steps can be obtained based on the calculated steady-state surface coverages. In our simulations, the gas phase contained a mixture of CO and O2 in 1:5 molar ratio at a total pressure of 40 Torr, which is the same as the experimental reaction conditions.[16]

The elementary reaction steps that contribute to the rate control over the overall reaction can be determined by the degree of rate control (DRC) concept introduced by Campbell et al.[70−72] For elementary step i, the degree of rate control XRC, can be defined aswhere k, K, and r are the rate constants, equilibrium constant for step i, and the reaction rate, respectively. Furthermore, the DRC coefficients have to obey the sum rule over all steps i in the mechanism in such a way that[71]

Results

Structure of Au Clusters and Nanoparticles

We employed a DFT-based genetic algorithm (GA) to determine the most stable structures of Au (n = 3–16 and 20) clusters (Figure ). A general observation is that even-numbered Au clusters exhibit higher symmetry than odd-numbered ones. Clusters with 13 atoms or less have a planar (two-dimensional) structure, whereas larger ones adopt a three-dimensional structure. The found Au20 cluster employs a Td symmetry that is in line with previous works,[38,39] indicating the stability of our GA approach. The identified structures agree with previous quantum-chemical calculations as well as experimental IR data used to resolve the structure of neutral gas-phase gold clusters.[38,73−77]

Figure 1

Most stable geometries and symmetries of Au clusters searched and obtained by genetic algorithm (Au3–Au20) and Wulff-constructed particles (Au38, Au55, Au79, and a real Wulff particle).

It is still challenging to experimentally determine the exact structure of larger clusters and nanoparticles.[78] As the first-principles GA approach is too expensive to predict the structure of nanoparticles, we used the Wulff theorem to obtain the structures of gold particles with 38, 55, and 79 atoms, using computed surface energies of extended surfaces. For this purpose, 10 common surface terminations were considered (Table S1). We also constructed a Wulff particle based on these calculated surface energies, which should reflect the structure of a sufficiently large nanoparticle as an approximation, in which edge and corner effects can be neglected.[79] These obtained three structures might not be the global minimum ones, but they can be served as models to investigate gold particle size effect theoretically. CO oxidations on the same structure of Au38 and Au79 clusters are studied theoretically before.[80,81] The surface of such nanoparticle is enclosed by (111), (100), (211), and (221) facets (Figure ).

The edge atoms of planar clusters have a coordination number between 1 and 4. The surface metal atoms in the three-dimensional clusters have coordination numbers between 3 and 9. For large (Wulff) nanoparticles, the lowest coordination number is 7 for corner atoms on (211) and (221) facets. These differences in coordination numbers might already suggest that planar Au clusters are more reactive than the three-dimensional ones. It is seen that the cohesive energy of the chosen 79-atom cluster is still appreciably lower than that of bulk Au. Similar to Pt clusters,[82] the calculated cohesive energy in planar and three-dimensional Au clusters is proportional to the number of atoms to the power of −1/3 (Figure S1). By extrapolating the cohesive energy to clusters of infinite size, the calculated cohesive energy is −3.44 eV, which is slightly lower than the experimental value of −3.81 eV per atom.[83] As well established, DFT-generalized gradient approximation underestimates the cohesive energy of bulk gold.[84] Next, we will investigate the adsorption of CO, O2, and O on these clusters as a proxy for their electronic structure. CO oxidation on the isomers of Au clusters with higher energies and support effect is out the scope of this work.

Adsorption of O2, CO, and O Adsorption

We computed the favorable adsorption geometries of CO, O2, and O on Au clusters and the four surfaces exposed in the Wulff particle. Consistent with previous findings,[85,86] CO and O2 prefer to adsorb at the apex site on small Au clusters (Figure S2). The trends in the resulting adsorption energies as a function of cluster size and surface are shown in Figure . Numerical values and configurations are collected in the Supporting Information (Figure S2 and Table S2). The adsorption energies of molecular oxygen on Au (n = 1–16) clusters present a strong even–odd oscillation, with the stronger binding occurring for odd-numbered clusters. The reason is that odd-numbered Au clusters have one unpaired 6s electron. To highlight these differences, a density of states (DOS) analysis was performed for O2 adsorption on Au7 and Au8 clusters (Figure a,b). In both cases, O2 binds to a corner Au atom with coordination number 2. Compared to Au8, the d-orbital of this Au atom is shifted to lower energies for Au7. Accordingly, the spin-down state of the 2π* orbital of adsorbed O2 is partially occupied for the Au7 cluster, which is not the case for the Au8 cluster. This difference results in more electron transfer from Au to the spin-down component of the 2π* orbital of O2 on the Au7 cluster. This enhanced back-donation is the reason for the stronger binding of O2 to Au7 with respect to Au8. Moreover, due to the lower position of the d-bands of Au7, the hybridization with the 5σ and 1π orbitals of O2 is slightly stronger.

Figure 2

Calculated adsorption energies (eV) of O2 (blue), CO (black), and atomic O (red) as a function of Au particle size. All of the adsorption energies are calculated with respect to the molecule or radical in the gas phase.

Figure 3

Spin-polarized density of state (DOS) and molecular orbitals of O2 adsorption on Au7 (a), Au8 (b), Au38 (c), and Au79 (d) clusters. The red and blue curves denote the DOS of Au atoms and O2, respectively. The Au atoms projected are those that bind with O2. The types of canonical labels of the CO orbitals are indicated.

Aside from the even–odd oscillation, there is a trend of increasing adsorption energy of O2 with increasing cluster size. Adsorption on the three-dimensional clusters is slightly weaker than on clusters with a planar geometry. In general, O2 prefers to bind to a single Au atom, except for clusters containing 5, 13, 38, and 79 atoms and on the (100), (211), and (221) surfaces, where O2 binds on two adjacent Au atoms. Binding to the extended surfaces is very weak, with a slight preference for the stepped (211) and (221) surfaces over the (100) and (111) terraces.

From Figure , it is apparent that O2 binds stronger on clusters containing 5 and 38 atoms than expected from the trend. We investigated this for the 38-atom cluster and found that O2 adsorption leads to a reconstruction of the surface atoms close to the adsorption site. The Au–Au distance to which oxygen binds increases from 2.78 to 3.36 Å, which results in stronger interactions between oxygen’s 5σ and 1π orbitals and the Au d-band (Figure c,d). Such an effect is also apparent for the Au5 cluster. Finally, it is worth noting that the strong size effect on the O2 adsorption energy observed for the odd-numbered clusters is nearly absent for the even-numbered clusters because the latter do not contain an unpaired electron. A second effect is that O2 adsorbs much weaker on the even-numbered clusters.

Compared to O2, the even–odd oscillations are hardly observed for CO adsorption on clusters containing between 1 and 16 atoms (Figure ). Again taking Au7 and Au8 clusters as an example, we illustrate how CO and O2 adsorptions differ. Figure clearly shows that the 2π* orbital of CO is too high in energy to hybridize with the d-band of Au. Accordingly, the unpaired electron in the odd-numbered clusters does not greatly affect CO adsorption. Relevant to CO oxidation is that CO adsorbs more strongly than O2 on all Au clusters. This is because of the stronger hybridization between CO 4σ and 5σ orbitals and the d-orbitals of the Au cluster, as can be appreciated by comparing Figures and 4. CO prefers to bind top or bridged to Au atoms with low coordination number on all of the Au clusters and surfaces (Figure S2). From Figure , it is observed that CO adsorbs strongly on Au (n = 2–4) clusters with adsorption energies in the range of −1.70 to −1.86 eV, in line with Nayak’s findings.[87] On larger clusters, CO adsorption strength decreases with increasing cluster size and CO adsorption energy varies from −1.25 to −0.74 eV. CO adsorbs much weaker on the four considered Au surfaces (ECO = −0.23 to −0.71 eV). As seen in Figure , CO always adsorbs stronger on the planar clusters compared to the three-dimensional Au structures, which is due to the lower coordination numbers of the edge atoms in the planar Au clusters.

Figure 4

Spin-polarized density of state (DOS) and molecular orbitals of CO adsorbed on Au7 and Au8 clusters. The red and blue lines denote the DOS of Au atoms and CO, respectively. 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 planar clusters. To understand this, we studied the DOS of O adsorbed on Au clusters with n = 4–7 clusters (Figure S3). 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 (100) surface, where fourfold coordination is adopted. The present DFT calculations show that O2, CO, and atomic O adsorptions depend strongly on cluster size and surface topology.

CO Oxidation

Next, CO oxidation was investigated on selected Au clusters, i.e., planar clusters with n = 3–13, three-dimensional ones with n = 14, 15, 20, 38, and 79, as well as the four extended surfaces exposed by the Wulff particle. As O2 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 O2. The mechanism consists of five elementary reactionswhere * represents surface vacancy. The OCOO adduct formed by reaction of adsorbed CO and O2 binds with the C and one of the O atoms to the surface. The potential energy diagrams for the gold models explored in this section are shown in Figure (numerical data in Table S3). As presented in Figures S4 and S5, optimized CO, O2, 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.

Figure 5

Potential energy diagrams for CO oxidation on (a) planar even-numbered Au4, Au6, Au8, Au10, and Au12 clusters; (b) planar odd-numbered Au3, Au5, Au7, Au9, Au11, and Au13 clusters; (c) three-dimensional Au (n = 14, 15, 20, 38, and 79) clusters; and (d) Au surfaces. The elementary reaction barrier heights (eV) are indicated.

It is found that stronger adsorption of CO and O2 generally leads to a lower activation barrier for the formation of the OCOO intermediate, in line with previous findings.[89−91] The formation of this intermediate involves a similar transition state on the considered clusters and surfaces (Figures S4 and S5). The reaction barrier for OCOO formation generally has an even–odd oscillation effect. The associated barriers vary from 0.10 to 0.37 eV for odd-numbered Au5–Au13 clusters and from 0.33 to 0.66 eV for even-numbered planar Au6–Au12 clusters. 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 O2. However, Au4 shows deviant behavior in the sense that it is more reactive than Au3 and Au5 due to the highly exothermic formation of OCOO. The calculated reaction barriers are 1.00, 0.02, and 0.37 eV for Au3, Au4, and Au5 clusters, respectively. For three-dimensional Au clusters and surfaces, OCOO intermediate formation is also facile with barriers between close to 0 and 0.25 eV. Only on the Au14 cluster, the barrier is substantially higher at 0.57 eV due to its high endothermic reaction energy.

OCOO decomposition is highly exothermic on all considered models. The barrier for OCOO decomposition is lower when the intermediate binds stronger. In the transition state, the CO2 fragment remains at the top site with the O atom moving to an adjacent top site on planar clusters or bridge sites on three-dimensional Au clusters/particles (Figures S4 and S5). On planar clusters, OCOO dissociation barriers are in the 0.34–0.71 eV range with an odd–even variation. 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 O2 adsorption. The activation barrier is lower on the three-dimensional clusters and surfaces, ranging from 0.09 to 0.48 eV. It is associated with a higher (exothermic) reaction energy for these clusters. The CO oxidation cycle is closed by the CO* + O* → CO2 + 2* reaction. For the planar clusters, the reaction barriers for this reaction range from 0.37 to 1.25 eV. Again, these barriers are higher than those encountered for the three-dimensional clusters and surface (0–0.45 eV, except for Au14, for which Eact = 0.79 eV).

The DFT calculations clearly show that CO oxidation is structure-sensitive on Au clusters and surfaces. For planar clusters, OCOO formation barriers are generally lower than barriers for OCOO decomposition and O removal except for Au3 and Au5 clusters, where OCOO decomposition is more feasible. For the three-dimensional clusters and surfaces, OCOO formation and decomposition barriers are comparable and lower than O removal. Only for the (100) and (111) 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.

Linear Scaling Relationships

Sabatier’s principle is one of the most powerful concepts in heterogeneous catalysis,[92] providing guidance in the selection of transition metals for specific catalytic reactions.[93,94] It manifests itself in the form of volcano-shaped dependency of reaction rate or activation barriers on adsorption strength of reactants, reaction intermediates, and products.[95,96] Its origins have been well studied for many reactions, and correlations have been formulated to describe reactivity, which strongly depends on activation barriers of elementary reaction steps, by more easily accessible parameters such as adsorption energies. The best-known example of such (linear) scaling relationships is the one between the activation energy and the enthalpy change of an elementary reaction, known as the Brønsted–Evans–Polanyi (BEP) relation.[97,98] The usefulness of this concept has been well established in computational studies, for instance, in predicting periodic activity trends.[1,99−103]

There are mainly eight kinetic parameters that determine the kinetics of the CO oxidation reaction: the adsorption energies of O2 and CO (EO and ECO), forward and backward reaction barriers for OCOO formation (E1f and E1b), CO2 formation through OCOO decomposition (E2f and E2b), and O removal (E3f and E3b). 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.

As shown in Figures and 7, planar and three-dimensional clusters exhibit different linear scaling relationships. 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. For instance, the OCOO intermediate adsorbs on planar structures at the edge site with one O binding single Au atom, whereas the O atom in OCOO generally prefers to bind two surface Au atoms on three-dimensional Au clusters. Moreover, a DOS and crystal orbital Hamilton population (COHP) analysis of OCOO adsorption clearly shows that the less occupied antibonding orbital between O and Au atoms around the Fermi level leads to stronger adsorption on planar compared to three-dimensional gold clusters (Figure ). As seen from Figures S4 and S5, the atomic O fragment moves to an adjacent top site on the planar clusters and to a bridge site on most three-dimensional clusters in the transition state for OCOO decomposition and CO + O → CO2 steps.

Figure 6

Linear scaling relations for CO oxidation on planar Au (n = 6–13) clusters. The blue and purple points are the forward and backward reaction barriers for OCOO formation, OCOO decomposition, and atomic O removal reactions as a function of ECO and EO on Au clusters, respectively. The fitted linear equations are indicated.

Figure 7

Linear scaling relations for CO oxidation on three-dimensional Au (n = 14, 15, 20, 38, and 79) clusters and surfaces. The green and purple points are the forward and backward reaction barriers for OCOO formation, OCOO decomposition, and the removal of atomic O reactions as a function of ΔE1 (EOCOO – ECO – EO), ΔE2 (ECO + EO – EOCOO), or EOCOO on three-dimensional Au clusters and surfaces, respectively. The fitted linear equations are indicated.

Figure 8

DOS and COHP analysis for OCOO adsorption on Au9, Au10, and Au79 clusters.

Extremely small planar Au clusters (n = 3–5) are different from the other planar Au ones for CO oxidation because of their significantly different local surface atom arrangement (Figure ). Accordingly, we omitted these three clusters in establishing the linear scaling relationships. We also excluded the Au6 cluster in considering scaling relationships of E2f and E2b versus ECO+O due to the large distortion of OCOO adsorption (Figure S4). The scaling relationship for CO oxidation on planar Au (n = 6–13) clusters is presented in Figure . CO and O2 adsorption energies are correlated to relevant CO oxidation barriers on Au clusters. 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, CO and O2 adsorption energies can serve as descriptors for CO oxidation on planar Au clusters. Stronger adsorption of CO and O2 lead to a lower reaction barrier for CO oxidation. It is worth noting that CO adsorption on planar Au (n = 6–13) is less structure-sensitive with adsorption energies varying from −1.02 to −1.22 eV. Therefore, reaction barriers relevant to CO oxidation can be approximated by the O2 adsorption energy on planar Au clusters.

For the three-dimensional Au clusters and surfaces, OCOO formation also follows the BEP relationship, i.e., the forward and backward reaction barriers (E1f and E1b) are proportional to the reaction enthalpy ΔE1 (ΔE1 = EOCOO – ECO – EO). A lower reaction energy for OCOO formation results in a lower forward and higher backward reaction barrier for OCOO formation reaction (Figure ). Similar to OCOO formation, the forward and backward reaction barriers (E2f and E2b) for OCOO decomposition display linear scaling relationships with the reaction energy ΔE2 (ΔE2 = ECO+ EO – EOCOO). 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. The removal of atomic O by the elementary reaction step CO + O → CO2 has a similar transition-state geometry to OCOO formation, involving the formation of a C–O bond. The forward and backward reaction barriers for atomic O removal scale linearly with ΔE1 and the adsorption energies of OCOO intermediate (EOCOO), respectively. In fact, ΔE2 scales linearly with ΔE1 and the adsorption of OCOO intermediate (EOCOO) is almost linearly related to CO adsorption (ECO) on three-dimensional Au clusters and surfaces, as shown in Figure S6.

Therefore, all of the reaction barriers involved in CO oxidation can be expressed by CO and O2 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.

Discussion

We use microkinetics simulations to compute catalytic CO oxidation rates for planar and three-dimensional Au structures using the in-house-developed MKMCXX code.[13,68,69] For this purpose, we use both the kinetic parameters of particular clusters and scaling relations derived from them for planar and three-dimensional clusters. Figure shows the dependencies of CO oxidation rate on CO and O2 adsorption energies for these cases.

Figure 9

CO consumption rate (log r, r in mol site–1 s–1 unit) as a function of CO and O2 adsorption energies for (a) planar and (b) three-dimensional Au structures. Microkinetics simulations were conducted at T = 350 K, p = 40 Torr, and a O2/CO ratio of 5.[16] The dashed part in (a) indicates the area in phase space where the activation barriers of the OCOO formation step are negative and thus unphysical.

The Au9 cluster has the highest predicted CO oxidation rate among the planar Au (n = 7–13) clusters. The strong adsorption of O2 on Au9 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. For the planar clusters, stronger O2 adsorption enhances CO oxidation (Figure a). CO oxidation rates show a maximum for CO and O2 adsorption energies of about −0.9 and −0.7 eV, respectively. The activities of the Au3, Au4, and Au5 clusters are 3 × 10–15, 3 × 103, and 3 × 10–1 mol site–1 s–1, respectively. The most active one, the Au4 cluster, is still significantly less active than the optimum Au9 cluster. Identification of the catalytic activity of gaseous Au clusters remains a substantial challenge in gold catalysis.

Figure a shows how surface coverage depends on the reactivity descriptors for planar Au clusters. A corresponding plot for the degree of control (DRC)[70−72] is also shown in Figure b. There are four regimes for the planar clusters distinguished by the dominant surface species. In regime I, CO adsorbs so strongly on gold (ECO < −0.9 eV) that the surface becomes poisoned with this reactant. As a consequence of the low coverage of O2, formation of OCOO is the rate-determining step (Figure b). However, when O2 adsorbs slightly stronger with the adsorption energy (−0.7 eV < EO < −0.3 eV), the O2 coverage will increase and OCOO dissociation will control the overall CO oxidation rate. In regime II, the surface is poisoned by O2, as now CO adsorbs only weakly and O2 strongly (ECO > −0.2 eV and EO < −0.8 eV). OCOO formation remains the rate-controlling step due to the low coverage of CO. In regime III, the surface coverages of CO and O2 are low on planar Au clusters when CO and O2 adsorb relatively weak (ECO > −0.8 eV and EO > −0.9 eV). OCOO formation still controls CO oxidation (Figure b). Regime IV is characterized by a high coverage of atomic O with intermediate CO and O2 adsorption energies (ECO > −0.9 eV and EO < −0.3 eV). CO2 formation through the CO + O → CO2 step is controlling the overall CO oxidation reaction rate, which is attributed to the low coverage of CO. From the above discussion, we can deduce that reactant coverages and barriers, which mainly depend on CO and O2 bond strength, determine the catalytic CO oxidation.

Figure 10

Steady-state coverage of the intermediates (a) and degree of rate control (b) as a function of CO and O2 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. Microkinetics simulations were conducted at T = 350 K, p = 40 Torr, and O2/CO = 5:1.[16]

The volcano-type dependency for CO oxidation on three-dimensional Au clusters and extended surfaces is shown in Figure b. Au79 exhibits the highest CO oxidation reaction rate (r = ∼103 mol site–1 s–1), followed by the Au (221) surface. The smaller Au14, Au15, and Au20 clusters have lower CO oxidation reaction rates (< 100 mol site–1 s–1). The morphology of very large Au nanoparticles can be approximated by Wulff construction. Given the rates on the periodic surfaces, we predict that the catalytic CO oxidation activity of large Au particles is dominated by that of the (221) facet with a CO oxidation rate of ∼102 mol site–1 s–1. It should be stressed that the Wulff particle presents much lower activity than the Au79 nanoparticle. These findings suggest that medium-sized Au clusters (1.3 nm/Au79) are optimal for CO oxidation for three-dimensional Au particles. The maximum CO oxidation rate is obtained for CO and O2 adsorption energies of about −0.8 and −0.4 eV on the three-dimensional clusters and surfaces, respectively. Our work indicates that, for three-dimensional Au nanoparticles, there exists an intermediate optimum size of gold for CO oxidation, which is in line with the seminal work of the Goodman group.[16]

The intermediate coverages and DRCs are different between planar and three-dimensional Au clusters due to significant variations in the binding properties. Four distinct regimes can also be distinguished for the three-dimensional cluster (Figure a). Similar to planar Au clusters, CO will poison three-dimensional Au clusters surface in regime I (ECO < −0.8 eV and EO > −0.8 eV), where OCOO formation is controlling the CO oxidation rate. Unlike the planar Au clusters, the OCOO decomposition reaction becomes the rate-determining step in regime II (ECO > −0.9 eV and EO < −0.9 eV). Moreover, CO oxidation rate is limited by OCOO formation or dissociation in regime III (ECO > −0.8 eV and EO < −0.8 eV). The removal of atomic O (CO + O → CO2) step is the rate-limiting step for CO oxidation when the three-dimensional Au cluster is fully covered by atomic O in regime IV.

Figure 11

Steady-state coverage of the intermediates (a) and degree of rate control (b) as a function of CO and O2 adsorption energies on three-dimensional Au clusters. A positive DRC value for a particular elementary reaction step indicates that this step limits the reaction rate. Microkinetics simulations were conducted at T = 350 K, p = 40 Torr, and O2/CO = 5:1, which is in line with experiment conditions for CO oxidation.[16]

Our work demonstrates the different catalytic behavior of small planar and larger three-dimensional gold clusters in CO oxidation. Due to the different coordination numbers of the surface atoms, binding properties of CO and O2 and reaction intermediates vary differently with cluster size for these two types of clusters. For each of the classes, linear scaling relations can be formulated that reliably predict the catalytic CO oxidation rate. Depending on the CO and O2 binding energies, different regimes can be distinguished on the basis of the most abundant reaction intermediate. The delicate balance between CO and O2 binding has a profound influence on CO oxidation activity. Optimum performance is obtained for intermediate bond strength of CO and O2 (i.e., respective optimum CO and O2 adsorption energies are ca. −0.9 and −0.7 eV for planar clusters and −0.8 and −0.4 eV for three-dimensional particles). Planar Au clusters generally require stronger O2 adsorption compared to the three-dimensional particles for optimum performance. The optimal planar Au cluster contains nine gold atoms and is predicted to have a higher CO oxidation rate than the optimum three-dimensional cluster comprising 79 atoms. The utility of the volcano approach is evident from our study: it demonstrates that there is room for improved CO oxidation performance of the most active planar and three-dimensional Au clusters by considering alloying or using a support to improve performance further.

Conclusions

DFT calculations have been performed to study CO oxidation on Au clusters and nanoparticles. Clusters with less than 14 gold atoms take on a planar shape, whereas larger ones adopt a three-dimensional shape. CO and O2 binding depends strongly on cluster size with strong even–odd oscillations noted for binding of oxygen atoms and molecules. All reaction barriers involved in CO oxidation display linear scaling relations with CO and O2 adsorption energies. These scaling relations are different for planar and three-dimensional Au clusters because of the different topologies of the surface and different coordination numbers of the surface atoms. On the basis of these scaling relationships and microkinetics simulations, it is found that planar Au9 and three-dimensional Au79 clusters are optimum for CO oxidation. Odd-numbered planar Au clusters have higher specific-mass activity than three-dimensional Au structures. Optimum CO oxidation rates occur for intermediate CO and O2 binding strengths and surface with moderate coverages CO, O2, and O. The planar structures are predicted to be substantially more active than the three-dimensional ones. The CO oxidation performance of the planar and three-dimensional clusters is below the Sabatier optimum, suggesting there is room to improve catalytic performance, for instance, by introducing alloying elements or particular metal–support interactions.