Article pubs.acs.org/JPCC
Cluster Size Effects in Ethylene Hydrogenation over Palladium Alvaro Posada-Borbón, Christopher J. Heard, and Henrik Grönbeck* Department of Physics and Competence Centre for Catalysis, Chalmers University of Technology, SE-412 96 Göteborg, Sweden ABSTRACT: Density functional theory calculations are used to investigate ethylene hydrogenation over palladium clusters in the range from Pd13 to Pd116. A comparison is made to single crystal surfaces, which exemplifies several novel aspects of clusters. We find that the adsorption energies are always higher for the clusters, even if the comparison is made to adsorption on stepped surfaces in the low-coverage regime. Clusters are found to accommodate higher adsorbate coverages than extended surfaces. The saturation coverage for Pd13 is unity, whereas it is 0.33 on Pd(111). The activation energies for hydrogenation of C2H4 to C2H5 over Pd38 are clearly different from Pd(111) and Pd(211), which stresses the limitation of extended surfaces as models for nanoparticles.
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hydrogen steers the site preference toward the π-configuration.12,14 In the present contribution, we use density functional theory (DFT) calculations to investigate ethylene adsorption and hydrogenation over Pd clusters in the form of truncated octahedra. We compare the results for clusters in the range from Pd13 to Pd116 with results for flat and stepped surfaces. The comparison enables the possibility to investigate effects of both finite size and under-coordination. Moreover, the study allows for conclusions regarding the ability to model ethylene hydrogenation on metal particles with stepped surfaces.
INTRODUCTION One main motivation to study clusters is their use in heterogeneous catalysis. Technical catalysts are generally designed by dispersion of subnanometer and nano-sized metal particles on oxide supports. To understand and eventually systematically improve catalytic performance, it is desired to unravel the intrinsic properties of the metal phase. Within the surface science paradigm, metal particles have generally been modeled by extended low-index surfaces.1,2 One such example is hydrogenation of ethylene, which is an important model reaction for the conversion of alkenes to saturated alkanes and selective upgrading of biofuels. Ethylene hydrogenation is often assumed to proceed via the Horiuti−Polanyi scheme3 in which ethylene is adsorbed on the surface and reacts in two sequential hydrogen addition steps with dissociatively chemisorbed H2. Ethylene adsorbs on metal surfaces in either the (di-)σ- or the π-mode. The molecule is adsorbed in a bridge configuration between two metal atoms in the σ mode, whereas the π-mode involves atop adsorption on one metal atom. The relative stability of the two modes and their role in the hydrogenation reaction has been discussed extensively in the literature, and it is established that the first hydrogenation step proceeds via the π-configuration.4−12 Because this step appears to determine the reaction rate for several transition metals13 it is important to understand the site preference with the aim to design systems where the π-mode is energetically preferred. Interestingly, it has been shown for palladium that the site preference may change as a function of particle size.14 Small particles were found to have ethylene adsorbed preferentially in the π-mode, whereas the σ-mode is preferred for extended surfaces.9 On the basis of X-ray photoelectron spectroscopy (XPS) measurements,15 it was suggested in ref 14 that smaller particles have a lower ability for charge transfer to ethylene, which would reduce the propensity for ethylene rehybridization to sp3, which is the state of carbon in the σ-mode. However, in addition to electronic effects, it is possible to modify the site preference by adsorbate−adsorbate interactions. It has, for example, been shown that preadsorbed © XXXX American Chemical Society
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COMPUTATIONAL METHODS Calculations are performed within DFT as implemented in the Vienna ab initio package.16−19 The Kohn−Sham orbitals are expanded in a plane-wave basis, truncated at an energy of 420 eV. The exchange-correlation energy is calculated within the generalized gradient approximation using the Perdew, Burke, Ernzerhof (PBE) formulation.20 Projected augmented wave potentials generated within PBE are used21,22 to describe the interaction between the valence electrons and the core. Hydrogen, carbon, and palladium are treated with one, four, and ten electrons in the valence, respectively. Integration over the Brillouin zone is approximated by finite sampling using the Monkhorst−Pack scheme.23 Methfessel and Paxton24 smearing of the Fermi discontinuity is applied with a smearing width of 0.05 eV. A threshold of 10−6 eV is used for the convergence of the electronic structure. Local geometry optimization is performed by the residual minimization scheme, direct inversion in the iterative subspace (RMM-DIIS) method, and the structures are considered to be optimized when all forces Special Issue: ISSPIC XVIII: International Symposium on Small Particles and Inorganic Clusters 2016 Received: November 30, 2016 Revised: February 13, 2017 Published: February 14, 2017 A
DOI: 10.1021/acs.jpcc.6b12072 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
distance is 2.795 Å for Pd in the bulk. We note that the distances in the radial and surface directions are different. For Pd38 the average nearest-neighbor distances in the radial direction is 2.756 Å, whereas the corresponding distance in the surface shell is 2.708 Å. The change in energetic and structural properties of Pd clusters as compared with the bulk is consistent with previous reports.28 The electronic configuration for the Pd atom in the gas phase is d10s0. For Pd in the bulk, a projected density of states analysis yields a d9.4s0.6 configuration. The change in configuration is related to the possibility to obtain net-bonding in both the sand d-channels. Despite the reduced coordination, the HOMO−LUMO separations are close to zero for all investigated clusters. To put the results for ethylene adsorption on palladium clusters in context, we have also performed calculations for extended Pd(100), Pd(111), Pd(211), and Pd(223) surfaces; see Figure 1. The considered surface cells are p(4 × 4) for Pd(100), p(2 × 1) for Pd(211), and p(2 × 1) for Pd(223). For Pd(111), ethylene adsorption was calculated in (√3× √3), p(2 × 2), p(3 × 3), p(4 × 4), and p(5 × 5). The stepped surfaces are chosen to model the (111)/(100) edge. Pd(211) and Pd(223) are different with respect to the width of the (111) terrace. Owing to stress release at the steps, the width of the terrace affects the nearest-neighbor distance, which is slightly strained as compared with the bulk values.29 Ethylene Adsorption. The ethylene adsorption energy is found to have an interesting cluster size dependence, and results for the σ- and π-configurations are reported in Table 1.
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