Identification of the Scaling Relations for Binary Noble-Metal

Article pubs.acs.org/JPCC

Identification of the Scaling Relations for Binary Noble-Metal Nanoparticles Qiang Fu,† Xinrui Cao,† and Yi Luo*,†,‡ †

Department of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, S-106 91 Stockholm, Sweden ‡ Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, Anhui, P. R. China S Supporting Information *

ABSTRACT: There exist a great many varieties of nanoparticles whose catalytic activities can be widely adjusted by changing their composition, shape, and size. Nørskov’s concepts to correlate the d-band center, adsorption energy, and activation energy offer an innovative approach to efficiently investigate the catalytic properties. Taking binary noble-metal polyhedral nanoparticles as representative systems, we found from first-principles simulations that the well-established scaling relations of the adsorption energies for extended surfaces can be seamlessly extended to the nanoscale. A systematic investigation of the correlation relations of the adsorption energies between the AHX groups and the corresponding A atoms in the binary noble-metal polyhedral nanoclusters of different compositions, shapes, and sizes clearly demonstrates the linear scaling relation. More remarkably, the scaling relation at the nanoscale can be effectively unified with the well-established scaling relations for extended surfaces. Such a description should be extremely helpful for the efficient screening of nanoparticles with superior catalytic properties.

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INTRODUCTION Transition-metal clusters at the nanoscale often exhibit excellent catalytic activities, which are usually attributed to the existence of low-coordinated atoms, large surface-to-volume ratios, and quantum size effects. Among these clusters, a great deal of effort has been directed toward noble-metal clusters, because of their fantastic catalytic properties toward a large number of chemical reactions.1−4 The catalytic properties of these clusters can be widely adjusted through changes in their compositions,5−10 shapes,11−18 and sizes.2,19−21 Remarkably, the synthesis of binary metal alloys adds a new dimension for tuning catalytic properties. The combination of different elements not only increases the type of candidate nanoparticles but, more importantly, provides catalytic performance superior to that of the constituent elements. 5−10 Tremendous experimental efforts have been made to control the growth and characterize the catalytic properties of noble-metal clusters, but it is very difficult, if not impossible, to exhaust all of the possibilities with such a trial-and-error approach. Thus, it would be highly desirable if the catalytic properties of noble-metal © 2013 American Chemical Society

nanoparticles could be efficiently predicted from theoretical modeling through a screening approach. The groundbreaking theoretical works for correlating the dband center, adsorption energy, and activation energy together offer an innovative and efficient way to screen new catalysts with novel properties.22−26 The scaling relation is one of the most important relations within the framework of correlation concepts.27 Among such relations, the adsorption energy of the group AHX is linearly correlated with the value of the corresponding atom A, and the slope is determined by the valence of the AHX group itself.27 This relation was first discovered for adsorption on transition-metal surfaces27 and was later extended to more complex systems,28,29 such as transition-metal carbide,28 nitride,29 oxide,29 and sulfide29 surfaces. It should be noted that the scaling relation also holds for the adsorption of more complicated molecules.30−32 Received: November 9, 2012 Revised: January 21, 2013 Published: January 30, 2013 2849

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Figure 1. (a−c) Schematic structures of the three types of binary noble-metal polyhedral clusters. (d,e) Adsorption energies of CH, CH2, and NH groups plotted against the adsorption energies of C and N atoms, respectively. The data from all three types of clusters are presented here.

Such scalability comes from identical variations in adsorption energy with respect to the valence configurations of both the surface and the adsorbates.33 According to the scaling relation, one can estimate the adsorption energies of complex molecules merely from the adsorption energy values of the simple atoms. This approach offers the possibility of efficiently evaluating a series of adsorption energies from only a limited number of calculations.22−26,34,35 For example, the potential energy diagrams of the methanation reaction and ammonia synthesis for 11 different transition-metal surfaces can be well constructed from the calculated results for only one surface.30 In addition, because various adsorption energies are highly correlated, the catalytic performance can be well described by a small number of independent quantities, which are usually called ”descriptors”.22−26 The descriptors play an essential role in determining the trends of the catalytic properties among a series of transition metals,22−26 for example, in the determination of the good activity and high selectivity of platinum toward HCN synthesis from NH3 and CH431 and in the prediction that Ni−Zn alloy is a better catalyst for the selective hydrogenation of acetylene.36 The usefulness of scaling relations has been well established for studies of catalytic properties; however, until now, their applicability has mainly been confined to extended surfaces, with very few exceptions.37 In this article, we present our studies examining the validity of scaling relations at the nanoscale. Nanoparticles can adopt a wide variety of structures; here, binary noble-metal polyhedral nanoclusters are selected as representative systems. Not only do polyhedral morphologies tend to be formed for noble-metal nanoparticles owing to the

minimization of the surface energies during growth in aqueous solutions,10,38−43 but also, because of the high ratios of lowcoordinated edge and corner atoms to well-coordinated atoms, polyhedral models can reflect the essential difference between nanoparticles and extended surfaces. We found that the scaling relation holds nicely at the nanoscale for noble bimetallic polyhedral particles of different compositions, shapes, and sizes. More importantly, the scaling relations of these nanoparticles can be well unified with the established scaling relations for extended surfaces. This implies that databases such as CatApp,34 which has been well developed for extended surface systems, can also be employed at the nanoscale. Such databases should be practically very useful for the rapid screening of nanoparticles with superior catalytic properties.

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COMPUTATIONAL DETAILS Our calculations were performed with spin-polarized density functional theory (DFT). Projector augmented wave (PAW) potentials44 were employed, and the energy cutoff was 400 eV for the plane-wave basis sets. The exchange correlations were described using the GGA-PW91 functional.45 A repeating cube supercell with a large lattice constant (25 Å) was employed. Only the gamma point was used for Brillouin zone sampling. All atoms were optimized until the forces were lower than 0.02 eV/Å. These calculations were carried out using the Vienna ab initio simulation package (VASP).46,47

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RESULTS AND DISCUSSION In Figure 1a−c, we show the nanoclusters used to establish the scaling relations. These clusters, containing 55 atoms, have a radius of about 1 nm. Two different shapes, namely, 2850

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Figure 2. Correlations between the adsorption energies of CH3, NH2, and OH groups at the top site and the adsorption energies of the corresponding C, N, and O atoms at the (a−c) hollow and (d−f) top sites. These relations come from the results for top-decorated icosahedral nanoclusters.

composition and shape. These results clearly demonstrate that a linear scaling relation holds well at the nanoscale. In fact, in comparison with the particles of a single element, the scaling relation for binary clusters is slightly complicated. The two elements might both appear on the surface of the clusters; thus, in the establishment of the relations, the adsorption site of the adsorbate might need to be specifically considered. This is the case for CH3, NH2, and OH groups. The most stable adsorption sites for the three groups are all atop sites, for which only one noble-metal element is directly involved in the bonding. In contrast, the corresponding C, N, and O atoms prefer to occupy the hollow sites, connecting to both of the elements. If the adsorption energies of AHX on the atop sites are plotted against those of the A atoms on the hollow sites, the data points in Figure 2a−c are scattered, and no clear trend can be identified. However, if the A atoms are also adsorbed on the atop sites, the linear scaling relations are restored, as shown in Figure 2d−f. These results thus indicate that, when constructing scaling relations for binary systems, the AHX groups and the corresponding A atoms should both

cuboctahedron and icosahedron, were employed to represent polyhedral nanoparticles. Figure 1a shows a cuboctahedral cluster with the top atoms decorated by another type of element. The cluster in Figure 1b has the same type of decoration, but with an icosahedral shape. In Figure 1c, the cluster also has an icosahedral shape, but it is of a core−shell configuration. Within these clusters, Ag, Cu, and Pd were selected as the core atoms, whereas Ag, Au, Cu, Pd, and Pt were used as the shell and decorating top atoms. From the results for the three types of nanoclusters, the dependence of the scaling relations on the composition and shape can be revealed. The scaling relations for the CH, CH2, and NH groups are presented in Figure 1d,e. In the optimized structures, the C and N atoms, as well as the CH and NH groups, are located at the hollow sites, whereas the CH2 groups occupy the bridge sites. Here, the AHX groups and the corresponding A atoms both connect the two elements of the clusters. One can see that the adsorption energies of the AHX groups all scale quite well with the corresponding values for the A atoms, even though the three clusters are quite different from each other in terms of 2851

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relative change of the adsorption energies for AHX (ΔEAHX) with respect to the change in the adsorption energies for atom A (ΔEA). For a particular AHX group, the value of the slope γ is determined by the valency of the group itself, regardless of the surface, and can be expressed as27 x −x γ = max xmax (1)

connect to the same kinds of elements in the correlation of their absorption energies. Such a consideration could also be applicable to the cases of extended surfaces with binary transition-metal alloys, such as the promising catalytic Pt-based binary alloy surfaces. Because the surface of binary core−shell clusters contains only one type of element, the performance of the scaling relations should not depend on the selection of the adsorption sites. Our calculations confirmed this prediction, as shown in Figure S3 of the Supporting Information. These results also indicate that site sensitivity might not be important in some extended alloy surface systems, in which the second element exists only in the subsurface layers.48−51 In addition to composition and shape, the size of noble-metal particles could also be a factor that affects the scaling relation. For smaller particles, we examined one type of cluster at the subnanoscale, namely, a binary core−shell icosahedral cluster composed of 13 atoms, and found that its scaling relation remains the same, as illustrated in Figure 3a. To understand the behavior of larger particles, the most straightforward approach is to directly compare the results we obtained for nanoclusters to those for extended surfaces. A linear scaling relation is determined by two parameters, namely, the slope γ and the intercept ζ. The slope γ reflects the

where xmax is the maximum number of the hydrogen atoms that can bond to atom A.27 We found that this expression can also be applied to the scaling relations of noble-metal nanoparticles. Therefore, the intercept ζ becomes a vital parameter that connects the scaling relations of different scales. We present the scaling relations for the nanoparticles and the extended surfaces all together in Figure 3b. The data for the extended surfaces were taken from ref 27. One can immediately notice that, for the adsorption of the CH group (red triangles and orange stars), the two sets of data points fall on almost the same line, that is, they obey the same scaling relation. The situation slightly changes for the adsorption of the CH2 group (blue triangles and green stars). Although the two sets of adsorption energies still follow the same trend (same slope), the intercepts seem to be different from each other. The difference in the intercepts of the scaling relation can be attributed to an inconsistent change in the adsorption energies of the AHX group and the A atom, because of the change in local adsorption configurations from one scale to the other. In the case of CH adsorption, both the CH group and the C atom locate at the hollow sites and connect with three noble-metal atoms, in the same manner as for adsorption on extended surfaces. The identical local configuration results in nearly the same intercept in the scaling relations. In the case of CH2 adsorption, the C atom still occupies the hollow site, but the CH2 group is located at the ridge (bridge site) on the nanoparticles. There is a significant difference in the local adsorption configurations of the CH2 group between the extended surfaces and the nanoparticles. On the extended close-packed surfaces, the bridge adsorption site is flat, whereas on the icosahedral nanoclusters, the corresponding bridge site (ridge) has curvature. This difference in the local adsorption configurations leads to the difference in intercepts. Similar phenomena have also been observed in the scaling relations27 and the Brønsted−Evans−Polanyi (BEP) relations23 for extended surfaces. It is worth noting that the difference in the intercepts of the scaling relations can actually be well estimated from some simple calculations. Because the scaling relation can be written as27 ΔE AHX = γ ΔE A + ζ

(2)

the difference in the intercept between nanoparticles and extended surfaces can then be expressed as Figure 3. (a) Comparison of the scaling relations for clusters between the nanoscale (triangles) and the subnanoscale (stars). (Inset) Schematic structure of the binary core−shell icosahedral subnanoscale cluster. (b) Comparison of the scaling relations between nanoclusters (red and blue triangles) and extended surfaces (orange and green stars). Red and orange denote the adsorption of CH groups, whereas blue and green refer to the adsorption of CH2 groups. The data for the extended surfaces are from the ref 27. (Inset) Unification of the scaling relations between nanoclusters and extended surfaces using the intercept difference estimated from the average values for Ag, Cu, and Pd.

AHX AHX A A Δζ = (ΔEnano − ΔEsurf ) − γ(ΔEnano − ΔEsurf )

(3)

Here, the slope γ can be calculated according to the valency of the adsorbate. Using this approach, the intercept difference between extended surfaces and nanoparticles can be determined. Using the adsorption energies on Ag, Cu, and Pd, the values of Δζ were estimated to be −0.10, 0.09, and 0.30 eV, respectively, for the CH group and 0.71, 1.00, and 0.58 eV, respectively, for the CH2 group. Thus, the difference in intercepts can be estimated using the average values, namely, 2852

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0.10 eV for the CH group and 0.76 eV for the CH2 group. The values agree very well with the results in Figure 3b. This means that, by taking into account the difference in the intercepts between extended surfaces and nanoparticles, a unified scaling relation can be obtained, as clearly demonstrated in the inset of Figure 3b. In this work, we employed polyhedral nanoparticles to investigate the performance of scaling relations at the nanoscale. For clusters with polyhedral shapes, the scaling relations hold well and can be unified with those for extended surfaces. In some cases, however, particles might not adopt regular polyhedral shapes or might lose polyhedral features as a result of strong interactions with adsorbates, which usually occurs in small nanoclusters. In these cases, there is no simple scaling relation of adsorption energies on particles of different compositions or shapes. Because the local adsorption configurations would be different from one cluster to another, every data point would have its particular intercept. As a result, the full set of data points would be scattered and would deviate from the simple linearity of the scaling relation. Although, in principle, the intercept difference can be estimated for every data point to unify the full set of adsorption values, as we did in Figure 3b, such an approach would not be easily implemented considering the diversity of structural changes in small nanoclusters. Further studies are still needed to search for an effective relation to correlate the intercept differences and changes in local adsorption configurations.

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CONCLUSIONS In summary, through the investigation of noble bimetallic polyhedral nanoparticles of different compositions, shapes, and sizes, we found that the scaling relation not only holds at the nanoscale but can also be unified with those obtained for extended surfaces. Our findings provide a useful basis for the efficient screening of nanoparticles with superior catalytic properties.

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ASSOCIATED CONTENT

S Supporting Information *

Optimized structures on the different adsorption sites and scaling relation for the core−shell icosahedral nanoclusters. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 0046-8-55378414. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine, the Swedish Research Council (VR), the Major State Basic Research Development Programs (2010CB923300), and the National Natural Science Foundation of China (20925311). The Swedish National Infrastructure for Computing (SNIC) is acknowledged for the use of supercomputer resources.

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