Communication pubs.acs.org/JACS
Extending the σ‑Hole Concept to Metals: An Electrostatic Interpretation of the Effects of Nanostructure in Gold and Platinum Catalysis Joakim Halldin Stenlid and Tore Brinck* Applied Physical Chemistry, School of Chemical Science and Engineering, KTH Royal Institute of Technology, Stockholm SE-10044, Sweden S Supporting Information *
be explained by the overlap of the singly occupied valence Au sorbitals when forming the bonding σ-orbitals. The molecular electrostatic potential V(r) is a wellestablished tool for analyzing chemical bonding and intermolecular interactions,12,13 and it is rigorously defined by
ABSTRACT: Crystalline surfaces of gold are chemically inert, whereas nanoparticles of gold are excellent catalysts for many reactions. The catalytic properties of nanostructured gold have been connected to increased binding affinities of reactant molecules for low-coordinated Au atoms. Here we show that the high reactivity at these sites is a consequence of the formation of σ-holes, i.e., maxima in the surface electrostatic potential (VS,max), due to the overlap of mainly the valence s-orbitals when forming the bonding σ-orbitals. The σ-holes are binding sites for Lewis bases, and binding energies correlate with the magnitudes of the VS,max. For symmetrical Au clusters, of varying sizes, the most positive VS,max values are found at the corners, edges, and surfaces (facets), decreasing in that order. This is in agreement with the experimentally and theoretically observed dependence of catalytic activity on local structure. The density of σ-holes can explain the increasing catalytic activity with decreasing particle size for other transition metal catalysts also, such as platinum.
V (r) =
A
ZA − |RA − r|
∫ ρ|r(′r′−) dr|r
where ZA is the charge on nucleus A, located at RA, and ρ(r) is the electron density. In contrast to many other charge distribution descriptors, such as atomic partial charges, V(r) is a physical observable that can be computed from an experimental or theoretical electron density distribution. When analyzing intermolecular interactions, it is common to compute and depict V(r) on the 0.001 au isodensity contour, which corresponds approximately to the van der Waals surface of a molecule.12−14 The V(r) value of an atom is spherically symmetric and everywhere positive, and it decreases monotonically toward zero when moving away from the nucleus. The formation of molecules leads to a redistribution of the electron density toward the more electronegative atoms and generation of areas of negative V(r). As an example, the surface V(r) [VS(r)] of ammonia has a strongly negative lone-pair region on nitrogen and positive hydrogens. The minimum (VS,min) and the maximum (VS,max) in VS(r) of these regions reflect the hydrogen bond basicity and acidity, respectively.12 The charge distribution of an atom in a molecule is also polarized, and VS(r) can simultaneously have negative and positive regions. Such polarization is particularly prominent for the heavier halogens (≥Cl). As shown by Brinck et al. in 1992,15 the negative potential (negative VS,min) on the side of the halogen, and the positive end (positive VS,max) of the atom at the extension of the bond, explain the tendencies of Lewis acids to interact with halogens in a side-on approach, and of Lewis bases to interact by an end-on approach, respectively (see Cl2 in Figure 1). The latter type of interaction is today referred to as halogen bonding and has become increasingly important in the design of supramolecular materials, catalysts, and drug molecules.16 Surface electrostatic potentials have become the standard tool to predict and analyze halogen bonding and are today routinely reported in the literature.
G
old has traditionally been considered the noblest of elements, an etiquette that is strongly connected to its chemical inertness. The discovery1 that nanoparticles of gold are efficient catalysts for carbon monoxide oxidation was groundbreaking and has paved the way for numerous applications of gold in catalysis.2,3 It is today established that the remarkable catalytic properties of nanostructured gold are linked to the stronger binding of reactant molecules to lowcoordinated Au atoms.4−7 The most catalytically active sites at Au nanoparticles are corners, edges, and surfaces (in decreasing order), and the binding strength generally decreases in that same order.5,6,8 Similarly, the binding energies and the catalytic activity of nanoporous gold catalysts are largely determined by the presence of kinks within surface steps on the inside of the pores.9 The strong correlation between catalytic activity and coordination number is not restricted to gold; similar relationships are also found for other transition metals, such as platinum.7,10,11 However, the physical origin of the correlation between binding strength and coordination number has remained elusive. In this work, we show that the higher activity at low-coordinated Au sites is connected to the presence of σ-holes, i.e., regions of depleted electron density, indicated by positive surface electrostatic potential, which can © 2017 American Chemical Society
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Received: June 9, 2017 Published: August 3, 2017 11012
DOI: 10.1021/jacs.7b05987 J. Am. Chem. Soc. 2017, 139, 11012−11015
Communication
Journal of the American Chemical Society
effects.23 In addition, for comparison, the VS(r) values of Cs Au13 were computed on the basis of electron densities obtained with an all-electron basis sets and the DKH24 and ZORA25 approximations to describe relativistic effects using the ORCA26 program. The VS(r) values thus obtained were found to be in good agreement with those obtained with the ECP but showed significant differences from all-electron nonrelativistic computations (see Table S2 in the Supporting Information (SI)). A more detailed description of the computational procedures is found in the SI. In forming the Au2 molecule, mainly the valence s-orbitals combine to a σ-orbital that is polarized toward the bond, and consequently VS(r) is negative over the center of the molecule and most positive (VS,max) over the end regions. The σ-hole at the end of each gold atom in Au2 is clearly seen from the VS(r) in Figure 1. The T-shaped geometry of the Au2 dimer is easily predicted by aligning the σ-hole of one Au2 unit with the negative potential region (the bond VS,min) of the other. Furthermore, in a similar manner as for the halogen molecules, Lewis bases preferentially interact with the σ-hole in the characteristic end-on approach. The charge distributions of larger Au clusters have a similar origin as for Au2; i.e., the valence s-overlap between atoms results in areas of positive potential (σ-holes) at the lowcoordinated sites of the atoms and negative potential in the bonding regions. Figure 1 shows the VS(r) of a low-energy Au13 cluster of Cs symmetry, and there are VS,max values at the sites on top of Au atoms. The magnitudes of the VS,max values vary and depend on the coordination number of the corresponding Au atom. More specifically, the VS,max positions indicate sites that are prone to bind Lewis bases, e.g., CO or H2O, and the binding energies correlate with VS,max. Figure 1 shows the linear relationships between the interaction energies of CO and H2O and VS,max for the Au13 cluster. It becomes further apparent that low-coordinated Au atoms are associated with areas of positive electrostatic potential when the icosahedral and cuboctahedral Au13, Au55, and Au137 clusters are analyzed in Figure 2. There are VS,max values on top of the Au atoms, and their magnitudes generally match the wellknown reactivity ordering at the different sites, i.e., decreasing binding affinity and catalytic activity in the order corners > edges > facets.5,6,8 Interestingly, the magnitudes of the VS,max values are relatively independent of cluster size; the corner VS,max values of the clusters in Figure 2 vary between 8.0 and 11.4 kcal/mol, with ico-Au55 having the most positive value and ico-Au137 the least positive value (Table 1). Furthermore, the periodic KS-DFT computations show that the large Au309 and Au561 clusters exhibit similar spatial variations in VS(r) as the smaller clusters (see SI for details), confirming the observation that particularly corners, but also edges, have an increased affinity to interact with Lewis bases that is largely independent of particle size. Even the largest clusters, Au561, which are sufficiently large to have surface (facet) adsorption energies similar to those of the crystalline surfaces of Au,8,27 have corner VS,max values similar in magnitude to those of the smaller clusters. These observations are in agreement with earlier experimental and theoretical studies of Au nanoparticles that showed that the increase in catalytic activity with decreasing size is mainly determined by the higher density of corners (and to some extent also edges) in the smaller nanoclusters.5,6 Our studies indicate that the strong dependence of the catalytic activity of gold on local structure is largely of electrostatic origin. The prototypical catalytic reaction of Au
Figure 1. Surface electrostatic potentials [VS(r)] on the 0.001 au isodensity surfaces of Cl2, Au2, and Au13 (left). Red, followed by yellow, indicates the most positive sites, i.e., the sites most prone to interact with Lewis bases. The plot to the right shows the correlations between computed interaction energies with CO and H2O and the maxima (VS,max) in VS(r) for Au13.
The positive VS,max at the end of the chlorine atom (Figure 1) is the result of a density depletion in this region, a σ-hole, due to the polarization of the σ-orbital toward the bond. In the case of fluorinated compounds, the VS,max at the end of the fluorine, which indicates a σ-hole, often has a negative value.17 Clark et al. originally argued that the presence of a σ-hole requires that the σ-orbital is formed from a singly occupied p-orbital on the halogen.18 Murray et al. extended the concept of σ-holes and σhole bonding to the group IV−VI elements.17 They found that a σ-hole can have a significant s-contribution and even suggested that hydrogen bonding should be considered a σhole interaction. The valence configuration (d10s1) of the noble metals Cu, Ag, and Au, e.g., [Xe5d106s1] for Au, is similar to that of hydrogen in that there is a singly occupied s-orbital. It is consequently of interest to determine whether σ-holes are formed at low-coordinated sites of noble metal clusters, and if the electrostatic potential at these sites can explain the experimentally observed correlation between catalytic activity and local structure. In order to investigate the existence of σ-holes on gold, a number of Au clusters were studied by Kohn−Sham density functional theory (KS-DFT). The geometrical structures of Au2 and an Au13 cluster of Cs symmetry were optimized at the PBE/ Def2-SV(P) level of theory. In addition, icosahedral and cuboctahedral Aun (n = 13−561) and Ptn (n = 13, 55) clusters were built with the interatomic distances matching those in the corresponding crystal structures. The VS(r) values of the smaller clusters (n ≤ 137) at the 0.001 au isodensity contour were evaluated from ρ(r) and V(r) obtained at the PBE/Def2SV(P) level using the Turbomole package19 and graphically depicted using the USF Chimera program.20 To analyze the variations in the VS(r) values of the larger Au clusters, periodic KS-DFT computations were performed using the VASP program21,22 with the PBE functional and the projected augmented wave (PAW) method. Binding energies, without correction for vibrational effects, for the interaction between the Au13 cluster and CO and H2O were computed at the PBE0D3/Def2-TVZPP//Def2-TVZP level. All computations using Gaussian basis sets described the inner electrons by an effective core potential (ECP) optimized to account for scalar relativistic 11013
DOI: 10.1021/jacs.7b05987 J. Am. Chem. Soc. 2017, 139, 11012−11015
Communication
Journal of the American Chemical Society
Pt55 clusters (Figure 3) show that the most positive VS,max values are located at corners and edges, and similarly to what is
Figure 3. VS(r) on the 0.001 au isodensity surfaces of cuboctahedral clusters of Pt13 and Pt55. The same color scheme for VS(r) as in Figures 1 and 2 is used. Similarly to the Au clusters, the most positive VS,max values are found at the corners, followed by edges, which corresponds to the ordering of catalytic activity.
observed for gold, the corners, followed by edges, are the most active sites. However, the Pt corner VS,max values are slightly larger in magnitude than the correponding values for the Au clusters (Table 1). Also for the Pt clusters, the formation of σholes at the low-coordinated atoms is a consequence of the polarization of the electron density toward the bonding regions, but this effect is harder to deduce because of the mix of s, p, and d orbital contributions. Clearly, surface electrostatic potentials can become a very useful tool for characterizing the catalytically active sites of nanostructured catalysts, including not only nanoparticles but also nanoporous materials and defect surfaces. In particular, we see the potential for characterizing structurally complex particles and surfaces using periodic DFT with plane-wave basis sets, since determining the spatial variations in VS(r) carries essentially no extra cost when performing such a DFT computation. In conclusion, we have shown that the intriguing effects of nanostructure on gold catalysis can be explained by the appearance of areas of positive electrostatic potential, i.e., σholes, at low-coordinated gold atoms due to the overlap of singly occupied s-orbitals. The σ-hole concept for catalytic activation is transferable to other transition metals, such as platinum, and the computation of surface electrostatic potentials has the potential to become an efficient tool in the characterization and design of nanostructured catalysts.
Figure 2. VS(r) values on the 0.001 au isodensity surfaces of icosahedral and cuboctahedral clusters of Au13, Au55, and Au137. The same color scheme for VS(r) as in Figure 1 is used. The most positive VS,max values are found at the corners, followed by edges and facets, which corresponds to the ordering of catalytic activity.
Table 1. Surface Electrostatic Potential Maxima (VS,max, kcal/ mol) of the Aun (n = 13, 55, 147) and Ptn (n = 13, 55) Nanoclustersa cluster
a
icosahedral
cuboctahedral
Au13
corner
site
9.2
8.1 (10.7)
Au55
corner edge facet (100)
11.4 4.5 −b
11.0 (12.8) 4.5 (4.6) 5.1 (−2.0)
Au147
corner edge facet (111) facet (100)
8.0 5.8 2.4 −b
9.6 6.1 3.1 1.8
Pt values in parentheses. bThere is no facet of this type.
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nanoclusters is the oxidation of CO to CO2, and it is not surprising that the electrostatic potential plays a key role in determining the adsorption affinity of the reactant and thereby the catalytic activity; CO is a Lewis base, and its negative lonepair regions are attracted to the Au sites with highest positive potential. Most catalytic reactions of gold follow the same mechanism, with the catalytic activity being determined by the strength of the binding of a Lewis base reactant. The similarity of the effects of nanostructure on Ag and Cu catalysis to the effects on Au catalysis can also be explained by the appearance of σ-holes at the low-coordinated atoms due mainly to s-orbital overlap.11,28 Platinum, which has the valence configuration (5d96s1), is another important metal catalyst that is known to exhibit increased catalytic activity with decreasing coordination number,7,11 and we find that the positional selectivity is connected to areas of positive electrostatic potential. The surface electrostatic potentials of the cuboctahedral Pt13 and
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b05987. VS(r) computed with VASP for Au clusters up to Au561; comparison of VS(r) for Au13 of Cs symmetry computed with ECP and with all-electron basis set (with and withour relativistic corrections); computational details; Cartesian coordinates and electronic energies for all Au clusters (PDF)
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AUTHOR INFORMATION
Corresponding Author
*
[email protected] ORCID
Joakim Halldin Stenlid: 0000-0003-3832-2331 Tore Brinck: 0000-0003-2673-075X 11014
DOI: 10.1021/jacs.7b05987 J. Am. Chem. Soc. 2017, 139, 11012−11015
Communication
Journal of the American Chemical Society Notes
(28) Gawande, M. B.; Goswami, A.; Felpin, F. X.; Asefa, T.; Huang, X.; Silva, R.; Zou, X.; Zboril, R.; Varma, R. S. Chem. Rev. 2016, 116, 3722−811.
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Funding from the Swedish Research Council (VR), the Swedish Nuclear Fuel and Waste Management Company (SKB), and the KTH CHE Excellence award is gratefully acknowledged. The calculations were performed using resources provided by the Swedish National Infrastructure for Computing (SNIC).
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DOI: 10.1021/jacs.7b05987 J. Am. Chem. Soc. 2017, 139, 11012−11015
