Assessment of Catalytic Activities of Gold Nanoclusters with Simple

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Research Article Cite This: ACS Catal. 2018, 8, 9702−9710

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Assessment of Catalytic Activities of Gold Nanoclusters with Simple Structure Descriptors Haoxiang Xu,† Daojian Cheng,*,† Yi Gao,*,‡ and Xiao Cheng Zeng*,†,§

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†

Beijing Advanced Innovation Center for Soft Matter Science and Engineering, State Key Laboratory of Organic−Inorganic Composites, Beijing Key Laboratory of Energy Environmental Catalysis, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China ‡ Division of Interfacial Water and Key Laboratory of Interfacial Physics and Technology, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, People’s Republic of China § Department of Chemistry and Department Biomolecular & Chemical Engineering, University of Nebraska, Lincoln, Nebraska 68588, United States S Supporting Information *

ABSTRACT: The de novo design of nanocatalysts with high activity is a challenging task, since prediction of catalytic activities of nanoclusters on the basis of simple descriptors is still a frontier of research. Herein, we present a simple model to build a geometry−adsorption−activity relationship for gold nanoclusters using CO oxidation as the benchmark probe. On the basis of extensive density functional theory calculations, the geometry indices (generalized local coordination number and curvature angle of the surface Au atoms) of numerous Au nanoclusters are found to be well correlated with the binding strength of CO and O2, as well as the activation barriers of CO oxidation by using the Brønsted−Evans−Polanyi (BEP) relationship and Sabatier analysis. In particular, this predictive model with simple structure descriptors can be extended to Au nanoparticles (NPs) with larger sizes and various shapes. Such a predictive model can provide a useful rule of thumb for experimentalists to quickly assess catalytic activity from only gathering the structural characteristics of Au NPs before performing more involved catalytic measurements. This model may also offer a cost-effective way for the rational design of nanocatalysts: for example, to assist experimentalists in making Au nanoclusters with the maximum number of active sites. KEYWORDS: Au nanoparticles, CO oxidation, geometry descriptor, density functional theory, activity prediction, catalyst design

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INTRODUCTION

are shown to be correlated with estimated catalytic activity via volcano plots.12−14 However, a Sabatier analysis alone cannot provide guidelines for finding optimal active sites on Au NPs, since a Sabatier analysis merely provides a correlation between adsorption energy and activation energy. In other words, even if the volcano-type activity plots can illustrate optimal energetic properties, it is still difficult to identify the specific geometry index of active sites that give rise to optimal adsorption energies of CO and O2. From a theoretical perspective, a simple and effective structure descriptor with solid physical−chemical foundations and reliable predictive capability is still absent for describing the geometry−adsorption relationship. Several theoretical models have provided atomic-level insight into how different geometric structures can affect the binding strength of adsorbates. The most successful example of such a descriptor is perhaps the d-band center, which is correlated with

Issues such as high costs with moderate efficiency still hinder the widespread implementation of nanocatalyst-based technologies, e.g., fuel cells, carbon-neutral processes, and electrolyzers. The low-temperature oxidation of CO and hydrocarbons catalyzed by gold nanoparticles (Au NPs), for example, has been widely investigated in fuel cells and other industrial processes.1−11 However, how to identify the most active sites for Au nanoparticles of different sizes and shapes is still not fully resolved, thus impeding the rational design of special gold nanocatalysts with the maximum number of active sites. Hence, it is timely to devise a simple structure−activity relationship that can benefit experimentalists to quickly assess the catalytic activity on a given catalytic center by using a simple and robust model before performing much more involved catalytic measurements. Recently, volcano-type activity plots derived on the basis of the Sabatier principle have been applied for the rational design of Au nanocatalysts for CO oxidation by analyzing trends of catalytic activity. The surface adsorption energies of CO and O2 © 2018 American Chemical Society

Received: June 22, 2018 Revised: September 6, 2018 Published: September 11, 2018 9702

DOI: 10.1021/acscatal.8b02423 ACS Catal. 2018, 8, 9702−9710

Research Article

ACS Catalysis

Figure 1. Optimized geometries of (a) an Au32 hollow cage supported on an MgO(100) surface and freestanding (b) Au16−, (c) Au17−, (d) Au18a−, (e) Au18b−, (f) Au27−, (g) Au28−, (h) Au30−, (i) Au32−, (j) Au33−, (k) Au35−, (l) Au38−, (m) Au44−, (n) Au46−, (o) Au47−, and (p) Au49− with numbered Au atoms. Au atoms marked with the numbers 1′ and 2′ have the same chemical environment as those marked with the numbers 1 and 2, respectively. The adsorption energies of CO and O2 as well as activation energies of CO oxidation on these Au clusters are used to build geometry−adsorption− reactivity relationships in Figures 2 and 5.

the adsorption energy of CO on a metal surface.15 Nevertheless, quantitative computation of the d-band center requires the use of computationally demanding density functional theory (DFT) calculations for every new case under investigation. The exact dband energy center for metal NPs cannot be easily measured experimentally. Moreover, the notion of d-band center may not work so well for the sub-nanometer catalysts.16−18 Another example is orbital roughness rules introduced by Metiu, which demonstrate that the shape of the LUMO (lowest unoccupied molecular orbital) of Au clusters regulates the adsorption sites and the adsorption energies of adsorbates.19 In addition, recently, a scaling relation between the generalized coordination numbers (CN) of the surface sites and adsorption energies of oxygen- and hydrogen-containing adsorbates have been identified for Pt nanoparticles.18,20 However, whether the notion of CN can serve as a simple and effective structure descriptor for other metals is still an open question. In addition, CN does not include information on the curvature angle of the surface sites of Au NPs, which has been previously shown to be another crucial parameter for correlating with site activity.21,22 Thus, a practical and effective structure descriptor that can quantify the local geometry differences among the corner, edge, and facet sites of Au NPs would be highly desirable, while its variation can be quantitatively linked to changes in adsorption energies and catalytic activities.

In this article, we show a systematic study of site-dependent adsorption energies and reaction barriers for CO oxidation on freestanding and supported Au nanoclusters, respectively. It is known that reducible metal oxides tend to transfer electrons to Au NPs.2,23−25 Thus, we use freestanding anionic Au nanoclusters as simple model systems to mimic Au nanoclusters supported on reduced metal oxides. In addition, to investigate the (nonreducible) support effect, an MgO-supported Au32 hollow cage26 was also taken into account. On the basis of a Loẅ din charge analysis on an Au32 hollow cage supported on MgO, the Au32 cage is negatively charged with one electron from the MgO slab. To indirectly account for the charge transfer effects on the adsorption strength and catalytic activity of supported nanoclusters, freestanding clusters in this study are charged with one electron. Importantly, we build a geometry− adsorption−activity relationship on the basis of the geometry indices (generalized coordination number and curvature angle of the surface Au atoms), BEP relationship, and Sabatier analysis. Such a relationship can quantify structure sensitivity: that is, a slight change in the surface structure may have a notable effect on the adsorption properties and catalytic activity. On the basis of the newly derived relationship, we predict adsorption energies and catalytic activities for larger-sized Au NPs (0.5−3.5 nm) with various shapes. A comparative computation indicates the reliability of the newly derived geometry−adsorption− 9703

DOI: 10.1021/acscatal.8b02423 ACS Catal. 2018, 8, 9702−9710

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Figure 2. (a) Adsorption energies of CO described by generalized coordination numbers (CN), (b) adsorption energies of O2 described by generalized coordination numbers (CN), (c) adsorption energies of CO described by relative curvature angle (CAr), and (d) adsorption energies of O2 described by relative curvature angle (CAr), for the sites to which the adsorbate is bound. The clusters considered include Au32 cage supported on MgO, freestanding Au16−∼Au18−, Au27−, Au28−, Au30−, Au32−, Au33−, Au35−, Au38−, Au44−, Au46−, Au47−, Au49− anionic clusters and extended surfaces. Leastsquares fits and related statistics are also given.

smearing procedure (with a smearing parameter of 0.002 Ry) was applied. The adsorption energies are defined as Eads = Eadsorbate+cluster − Ecluster − Eadsorbate, where Eadsorbate+cluster is the total energy of the composite cluster + absorbate system, Ecluster is the energy of the freestanding cluster, and Eadsorbate is the energy of an isolated molecule. The climbing-image nudged elastic band (CI-NEB) method30 was used to determine reaction paths for CO oxidation. Through vibrational frequency analyses, all transition states have been verified by ensuring that the transition state has only one significant imaginary vibrational frequency. All linear relationships were obtained by least-squares fits, and related statistics are also given.

activity relationship, which can be exploited to guide future catalytic experiments.

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COMPUTATIONAL DETAILS DFT calculations were performed using the PWSCF (planewave self-consistent field) code in the Quantum ESPRESSO package.27 All calculations were carried out using the spinpolarized Perdew−Burke−Ernzerhof (PBE) exchange-correlation functional28 with ultrasoft pseudopotentials.29 The regular MgO(100) surface was modeled with a two-layer slab. Each layer contains 36 Mg and 36 O atoms (6 × 6 cell), fixed during structural optimization at the equilibrium lattice positions (with the lattice parameter set to the experimental value of 4.208 Å). The periodically replicated surfaces are separated along the (100) direction by a vacuum region of 20 Å. All the atoms of the Au32 cage and reactant were allowed to relax. Because of the large supercells, a γ k-point sampling of the Brillouin zone was chosen. All calculations on cluster models were performed in a cubic supercell with appropriate side length to make sure that a large vacuum slab of 10 Å is inserted in three directions for cluster isolation to prevent interaction between neighboring image clusters. The Brillouin zone was sampled at the γ point. The kinetic energy cutoffs were fixed to be 40 and 400 Ry, respectively, for the wave function and electronic density. The convergence threshold for the iteration in self-consistent field (SCF) was set to be 10−6 Ry, and the geometry optimizations using the BFGS algorithm were stopped when the maximum force on the atoms was less than 10−3 Ry/bohr. A Gaussian

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RESULTS AND DISCUSSION Figure 1 shows the configurations for the supported Au32 hollow cage, anionic freestanding Au16−−Au18−, Au27−, Au28−, Au30−, Au32−, Au33−, Au35−, Au38−, Au44−, Au46−, Au47−, and Au49− clusters. The global-minimum atomic structures of these anionic clusters have been determined through a combination of anion photoelectron spectroscopy experiments and density functional theory calculations.31,32 Geometry−Adsorption Relationship. The adsorption energies of CO and O2 on a supported Au32 cage, freestanding anionic Au NPs, and an extended surface of gold (Figure S1) are given in Tables S1−S3. On the basis of previous work on Au NPs, several descriptors have been proposed to correlate with the adsorption ability of surface sites. For instance, coordination numbers have been used as an approximation to describe the electronic environment of an atom. For a gold crystal, the 9704

DOI: 10.1021/acscatal.8b02423 ACS Catal. 2018, 8, 9702−9710

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Figure 3. (a) Adsorption energies of CO described by generalized coordination numbers (CN), (b) adsorption energies of O2 described by generalized coordination numbers (CN), (c) adsorption energies of CO described by relative curvature angle (CAr), and (d) adsorption energies of O2 described by relative curvature angle (CAr), for the sites to which the adsorbate is bound. The clusters considered include Au16∼Au18, Au27, Au28, Au30, Au32, Au33, Au35, Au38, Au44, Au46, Au47, Au49 neutral clusters. Least-squares fits and related statistics are also given.

maximum coordination number is obtained in the bulk, where 12 nearest neighbors surround each atom. Atoms with coordination numbers less than 12 have tendencies toward the formation of bonds to compensate the reduced coordination. Therefore, trends in binding strength for adsorbates on extended transition-metal surfaces are well described by the traditional coordination number (cn) of the adsorption sites. In this work, the cutoff of bond length is defined to be 3.3 Å in order to count the coordination number. However, as seen in Figure S2a,b, wide spreads in the CO and O2 adsorption energies are observed at the same cn value. This spread indicates that cn loses its accuracy when nanoparticles are considered and cannot be an accurate structure descriptor for correlating with adsorption energy on Au NPs due to “finite-size effects”. Therefore more sophisticated structure descriptors are needed. We next choose the generalized coordination numbers (CNs) as descriptors:

Ead(O2 ) = 0.15 × CN − 0.93

∑ cn(j)nj /cn max j=1

CA r = CA/180°

To estimate the generalized coordination number (CN) of an atom i with ni nearest neighbors, the neighbors are weighted by their own usual coordination numbers. Therefore, every neighbor of atom i is accounted for with a weight of nj/cnmax (cnmax = 12 for an fcc crystal). For instance, site 1 of an Au32 cage supported on MgO has five nearest neighbors, one of which has cn = 5 and four have cn = 6. Thus, CN(1) = (1 × 5 + 4 × 6)/12 = 2.42. The detailed values of CN are given in Tables S1−S3. We find that Ead(CO) and Ead(O2) can be correlated with CN via eqs 1 and 2 for CN ⩾ 4. Ead(CO) = 0.14 × CN − 1.38

CN ⩾ 4

(2)

The linear relationships between CN and adsorption energies of CO and O2 are shown in Figure 2a,b, suggesting that a decrease in CN corresponds to an increase in binding strength, as intuitively expected. However, no linear correlation between CN and adsorption energy is found for CN < 4 (see Figure S2c,d), corresponding to corner and edge sites of nanoparticles. This result indicates that another structure descriptor is needed to quantify the geometry effect on adsorption energies for the corner and edge sites of Au NPs. As shown in Figure S3, we note that each Au atom on the surface of a cluster is surrounded by nearest-neighbor Au atoms to form a conelike structure. The curvature angle (CA) of the Au atom (red) is defined by the angle between one of the nearestneighbor sites (blue) and a midpoint on the opposing bond (connected by a green dashed line). We then take the average of all curvature angles stemming from different nearest-neighbor sites as the curvature angle (θ) of the Au atom (red) considered. We define the relative curvature angle as

ni

CN(i) =

CN ⩾ 4

As seen in Figure S4, CN has positive correlation with CAr for CAr < 0.7, which indicates that increasing the curvature angle will lead to increasing the coordination number proportionally. However, CN redistributes with disorder in a narrow region for CAr > 0.7, which suggests that CN cannot be used to reflect the structure change and, accordingly, cannot quantify the structure effect on adsorption and activity for CN < 4 and CAr > 0.7. This is a reason we chose the relative curvature angle as another geometric indicator. Figure 2c shows that CO adsorption energy is a monotonically increasing function of CAr of the Au atoms,

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DOI: 10.1021/acscatal.8b02423 ACS Catal. 2018, 8, 9702−9710

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Figure 4. (a) Adsorption energies of CO described by generalized coordination numbers (CN), (b) adsorption energies of O2 described by generalized coordination numbers (CN), (c) adsorption energies of CO described by relative curvature angle (CAr), and (d) adsorption energies of O2 described by relative curvature angle (CAr), for the sites to which the adsorbate is bound. The clusters considered include Au16+∼Au18+, Au27+, Au28+, Au30+, Au32+, Au33+, Au35+, Au38+, Au44+, Au46+, Au47+, Au49+ cation clusters. Least-squares fits and related statistics are also given.

and the data are fitted by linear regression. Ead(CO) can be correlated with CAr via eq 3: Ead(CO) = 1.55 × CA r − 1.92

CN < 4

oxidation to establish the adsorption−activity relationship. For the reaction mechanism of CO oxidation on Au NPs, the Eley− Rideal (E-R) and Langmuir−Hinshelwood (L-H) mechanisms have been widely accepted. Under the E-R mechanism, an O−O bond directly dissociates on the catalyst, creating two separated O atoms, followed by the attachment of a CO molecule to form CO2 and leaving an atomic O on the catalyst. The reaction barrier of O2 dissociation is the rate-limiting step under the E-R mechanism. For an Au32 cage, Au18a−, Au28−, Au33−, Au44−, and Au49− with an O2 molecule adsorbed, the computed activation barriers of O2 dissociation are all higher than 1 eV (see Table S5), indicating that the ER mechanism is unlikely to occur at room temperature.2 Under the LH mechanism, CO oxidation proceeds in four steps, including coadsorption of CO and O2, the formation of an OOCO intermediate, the dissociation of OOCO intermediate into CO2 and atomic O, and the removal of adsorbed atomic O by another CO. Previous studies have shown that coadsorption of CO and O2 on a gold cluster is the crucial initial step in the LH mechanism of CO oxidation. However, few systematic studies have focused on the correlation between the CO and O2 adsorption strength and activation energies on diverse surface sites. Here, since exhaustive computations of CO and O2 adsorption energies for all clusters are considered, we gain deeper insights into the structure−activity relationship for the CO oxidation on Au NPs. We also have tested different initial adsorption sites for O2 with CO preadsorbed on a nearestneighbor top site, including the top, bridge, and hollow sites for O2. As shown in Figure S5, the coadsorbed CO and O2 end up the top adsorption configuration of O2 on the neighbor top site of CO after geometric optimization on different sizes of Au clusters.

(3)

A linear relationship holds also between O2 adsorption energy and CAr (see Figure 2d): i.e., Ead(O2) can be correlated with CAr via eq 4: Ead(O2 ) = 0.90 × CA r − 0.99

CN < 4

(4)

A smaller curvature angle (CA) reflects stronger adsorption ability, consistent with previous results.21,22 The four linear relationships shown in Figure 2 indicate that both CN and CAr of surface sites are precise descriptors for the CO−Au and O2− Au interactions involved in both supported and freestanding Au NPs. Note that, because CN and CAr are arithmetical, their evaluation does not require highly demanding DFT calculations. We have also tested the applicability of these two structure descriptors (CN and CAr) on neutral and cationic Au clusters. A comparison between Table S2 and Table S4 suggests that an extra electron accumulation or depletion on an Au cluster has an effect on the adsorption energies of CO and O2. However, as shown in Figures 3 and 4, both structure descriptors (CN and CAr) can still be used to correlate with adsorption energies of CO and O2 of Au clusters with modified slope and intercept. Despite the effect of a charged cluster on adsorption properties, here we focus on identification of a structure−activity relationship with a simple descriptor. Indeed, both structure descriptors (CN and CAr) can quantify the structure effect on the adsorption and be applied to anionic, neutral, and cationic Au clusters altogether. Adsorption−Activity Relationship. With the obtained geometry−adsorption relationship of CO and O2 on Au NPs, we now turn to the investigation of the reaction mechanism of CO 9706

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Figure 5. (a) Calculated activation energy of all the elementary reactions as a function of the sum of the O2 and CO adsorption energies on anionic, neutral, and cationic Au nanoparticles (NPs). (b) Contour plot of Sabatier reaction rates for CO oxidation versus CO and O2 adsorption energy.

triangular Au3 sites, it can still assess the activity at most sites of Au nanoparticles. Thus, we explore the adsorption−activity relationship on the basis of only the conventional bimolecular LH mechanism below. Next, we performed a Sabatier analysis on the basis of a microkinetic model, which has been used to calculate the reaction rate of CO oxidation12,36,37 (see Part II in the Supporting Information), to identify the dominant factor affecting reaction rate and thereby the adsorption−activity relationships. According to the formula for computing the rate of CO2 formation (see Part II in the Supporting Information), there are six site-dependent parameters affecting the kinetics: Ead(CO), Ead(O2), Ecoad, EOOCO, ETS‑1, and ETS‑2. To find out the independent variables characterizing the reaction rate in the microkinetic model, we focus on estimating the four parameters relevant to the adsorption energy of O2 and CO. The coadsorption energies (Ecoad) of CO and O2 are found to be a monotonic function of the sum of Ead(CO) and Ead(O2) (see Figure S12a), and the data are fitted by using linear regression. The transition-state energies change linearly with the Ecoad values and relative energies of OOCO* (EOOCO), as shown for ETS‑1 and ETS‑2 in Figure S12b,d. Note that such Brønsted− Evans−Polanyi (BEP) relations that correlate adsorption energies and transition-state energies are quite generic for surface reactions.38,39 Furthermore, EOOCO scales with Ecoad (Figure S12c). The scaling relation shown in Figure S12 indicates that the activation energies are related to the adsorption energies of O2 and CO. In addition, we also calculate the activation energies on neutral and cationic Au clusters (Table S7). As shown in Figure 5a, the activation energies of all the elementary reactions can be estimated from the adsorption energies of O2 and CO on anionic, neutral, and cationic Au clusters. Therefore, the data are fitted by using linear regression. Ea can be correlated with Ead(CO) + Ead(O2) via eqs 5 and 6:

In Figures S6−S10, we display catalytic reaction pathways for the CO oxidation with various CO and O2 binding sites for anionic Au NPs in the size range of Au16−−Au49−. Detailed relative energies of all reaction states along the reaction pathway are displayed in Table S6. As the initial step, CO and O2 are coadsorbed on the gold clusters. Consistent with previous theoretical results,33,34 preadsorption of a CO molecule on an Au nanocluster can indeed enhance O2 adsorption, as determined by comparison between the coadsorption energies and sum of Ead(CO) and Ead(O2). In the subsequent step, CO and O2 move closer to one another, followed by overcoming the first activation energy barrier (Ea1) to reach Transition State 1 (TS1, shown in Figures S6−S10), forming the intermediate complex OOCO*. Upon the formation of the intermediate complex OOCO*, the unstable peroxide O−O bond needs to overcome another activation energy barrier (Ea2) to dissociate via crossing Transition State 2 (TS2, shown in Figures S6−S10), giving a free CO2 molecule and an adsorbed atomic O. Finally, to complete the full catalytic cycle, the adsorbed atomic O can interact with another CO molecule directly to form the second CO2 (Eley−Rideal mechanism). The computed activation energy barriers (Ea3) of this last step are given in Table S6. The reaction generally exhibits low activation barriers (or even barrierless), consistent with previous conclusion that the last step is not rate-limiting. The reaction barriers for the full reaction pathway under the LH mechanism are all around or lower than 0.5 eV (an upper limit for the barrier as reported previously2), suggesting that either the supported Au32 cage or the freestanding anionic Au nanocluster can catalyze the CO oxidation through an LH mechanism below room temperature. Note that the trimolecular Langmuir−Hinshelwood (LH) mechanism has recently been reported in a triangular Au3 active site of Au nanoparticles, where the extra coadsorbed CO can act as a promoter for the scission of an O−O bond and lead to the spontaneous formation of two CO2 molecules as products.35 To gain more information about the reaction mechanism, the trimolecular LH mechanism is also considered on some Au nanoparticles. As shown in Figure S11, the triangular Au3 active sites can promote the dissociation of an O−O bond. However, the rate-determining step of the trimolecular LH mechanism is the formation of OOCO, and the activation energies are comparable to or even slightly higher than those of OOCO formation under a conventional bimolecular LH mechanism. Although the conventional bimolecular LH mechanism may slightly overestimate the activation energies at the protruded

Ea(CO* + O2 * → OOCO*) = − 0.47 × (Ead(CO) + Ead(O2 )) − 0.26 (5)

Ea(OOCO* → CO2 * + O*) = − 0.67 × (Ead(CO) + Ead(O2 )) − 0.45 (6)

This means that the adsorption energies of reactants (Ead(CO) and Ead(O2)) can be regarded, to a first-order approximation, as 9707

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Figure 6. Comparison between the energies calculated with DFT (EDFT) and energies estimated using universal scaling relations (Eprediction): (a) CO adsorption energy, (b) O2 adsorption energy, and (c, d) activation energy of elementary steps from Au34−, Au42−, Au43−, Au45−, Au48−, Au50−, D5hAu55−, Oh-Au55−, Ih-Au55−, Au79−, D5h-Au147, Oh-Au147, Ih-Au147, Au201, and Ih-Au309. Estimates were calculated using the formulas shown in Figures 2 and 5. Mean absolute errors (MAEs) between calculated values and predicted values are also given. The diagonal (y = x) line is provided to mark the perfect agreement between EDFT and Eprediction.

energies on the basis of the structure descriptors (CN and CAr), the reliability of the adsorption−reactivity relationship should be confirmed. In Figures S14−S16, we display catalytic reaction pathways for the CO oxidation on the studied CO and O2 binding sites of anionic Au NPs in the size range of Au34−− Au79−. Detailed relative energies of all reaction states along reaction pathway are displayed in Table S9. Table S10 and Figure 6c,d show that the activation energies can be predicted quite accurately by the geometry−adsorption−reactivity relationship, in comparison with the DFT computation values for Au NPs shown in Figure S13. In general, the low mean absolute errors (MAEs) displayed in Figure 6, which are all below 0.2 eV (corresponds to the intrinsic accuracy of DFT at the GGA level40), corroborate the reliability and applicability of universal scaling relations and their dependence on geometry index counting rules and the Brønsted−Evans−Polanyi (BEP) relation. Consequently, eqs 1−6 above can be used to estimate, with reasonable accuracy, the adsorption properties and catalytic activity of Au nanoparticles. Finally, by using the newly established geometry−adsorption−reactivity relationships, we attempt to predict adsorption energy of CO and O2 (Tables S11−S13) on all catalytic sites of magic-number Au NPs with size up to 3.5 nm but different shapes (see Figure S17). We also predict reaction rates of CO oxidation on each site with CO adsorbed while O2 is adsorbed on its neighboring sites. The average reaction rates for the site on which CO is adsorbed stem from predicted reaction rates based on the adsorption of O2 at neighboring sites (Figure 7). As shown in Figure 7, Au NPs with decahedral and cuboctahedral symmetries possess more highly active sites in comparison to those with icosahedral symmetries and the same size. Catalytic sites with high activity for all Au clusters are typically the corner and edge sites. In addition, the ratio between catalytically active

the only independent variable characterizing reaction rate in the microkinetic model. To gain deeper insights into the correlation between adsorption and activity, we depict a contour plot of the Sabatier activity versus CO and O2 adsorption energy under typical experimental (temperature and partial pressure) conditions (T = 298 K, p(CO) = 0.01 bar, p(O2) = 0.21 bar), as shown in Figure 5b. The activity trend in Figure 5b is in good agreement with Norskov’s.12 The relative activities of different active sites on Au nanoclusters can be theoretically assessed by looking at the sum of the adsorption energy of CO and O2. In addition, according to the geometry−adsorption relationship established above, the reaction activity is structure dependent. In sum, we can predict relative catalytic activity on all sites of any Au NPs with various sizes and shapes, from the newly predicted geometry−adsorption−reactivity relationship. Validation and Application of Geometry−Adsorption−Reactivity Relationship. To further confirm the wide applicability of the newly derived geometry−adsorption− reactivity relationship, we applied the scaling relation to another set of Au nanoparticles (see Figure S13). As shown in Table S8 and plotted in Figure 6a,b, we found that the mean absolute errors (MAE) in adsorption energies of CO and O2, between our DFT computation results and predicted results, are quite small (0.04 eV for CO and 0.03 eV for O2). Thus, the scaling relation correlating adsorption energies of CO and O2 with CN and CAr established above is suitable for Au nanoclusters with diameters ranging from 0.5 to 1 nm, such as Au34−, Au42−, Au43−, Au45−, Au48−, Au50−, D5h-Au55−, Oh-Au55−, Ih-Au55−, and Au79− (high point-group symmetry: Ih, D5h, Oh). The adsorption energies predicted from the geometry−adsorption relationship for Au NPs with size up to 2 nm (e.g., D5h-Au147, Oh-Au147, Ih-Au147, Au201, Ih-Au309) are also quite close to those from DFT computations. Despite the successful prediction of adsorption 9708

DOI: 10.1021/acscatal.8b02423 ACS Catal. 2018, 8, 9702−9710

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geometry−adsorption−reactivity relationships pave the way for the rational design of Au NPs containing the optimal number active sites with specific geometry indices. These relationships, with some extensions, may also find applications beyond gold nanocatalysts and CO oxidation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscatal.8b02423. Additional tables and figures as detailed in the text and theoretical details (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail for D.C.: [email protected]. *E-mail for Y.G.: [email protected]. *E-mail for X.C.Z.: [email protected]. ORCID

Daojian Cheng: 0000-0001-7977-0750 Yi Gao: 0000-0001-6015-5694 Xiao Cheng Zeng: 0000-0003-4672-8585 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Lei Li, Dr. Wei Zhang, and Mr. Jian Jiang for valuable discussions. This work was supported by the National Natural Science Foundation of China (21576008, 91634116) and PetroChina Innovation Foundation (2016D-5007-0505). X.C.Z. acknowledges computational support from UNL Holland Computing Center.

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Figure 7. Schematics of predicted reaction rate of CO oxidation on all catalytic sites of nanoclusters with different magic numbers and different symmetries: (a) decahedral Au147 (D5h-Au147); (b) icosahedral Au147 (Ih-Au147); (c) cuboctahedral Au147 (Oh-Au147); (d) D5h-Au309; (e) Ih-Au309; (f) Oh-Au309; (g) D5h-Au561; (h) Ih-Au561; (i) Oh-Au561; (j) D5h-Au923; (k) Ih-Au923; (l) Oh-Au923.

REFERENCES

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sites (corner and edge) and catalytic spectator sites (facet) on the surface would decrease with an increase in Au cluster size. This is consistent with the conventional view regarding the active site distribution and size−activity relationship of Au nanocatalysts,6,11,12,22,35,36,41−44 further validating the underlying geometry−adsorption−reactivity relationship.

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CONCLUSION In conclusion, we have identified a reliable relationship between the geometry indices (generalized coordination number and curvature angle of the surface Au atoms) of Au NPs and the binding strengths of CO and O2. Notably, such a relationship could further predict catalytic activity of the Au NPs by using the BEP relationship and the Sabatier analysis. This simple and empirical geometry−adsorption−activity model can describe structure effects of the gold NPs on the adsorption strength, as well as the CO oxidation catalytic activity. In particular, this model can be easily applied to Au NPs with wider size range (0.5−3.5 nm) and shapes. Such reliable correlations could provide experimentalists with simple and yet precise estimation of the binding strength of the adsorbates on the surface of NPs, as well as the related catalytic activity, by only knowing the geometry characteristics of NPs. Overall, the newly derived 9709

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DOI: 10.1021/acscatal.8b02423 ACS Catal. 2018, 8, 9702−9710